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diff --git a/Turbines_by_Compressors_And_Fans/11-Axial_Compressor_Stages.ipynb b/Turbines_by_Compressors_And_Fans/11-Axial_Compressor_Stages.ipynb new file mode 100644 index 0000000..6b43698 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/11-Axial_Compressor_Stages.ipynb @@ -0,0 +1,521 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: Axial Compressor Stages" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: Calculation_on_an_axial_compressor_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.1 Calculation on an axial compressor stage \n", +"\n", +"Rm=0.5; // Degree of reaction\n", +"funcprot(0);\n", +"T1=300; // in Kelvin\n", +"p1=1; // Initial Pressure in bar\n", +"gamma=1.4;\n", +"N=18e3; // rotor Speed in RPM\n", +"d=36/100; // Mean Blade ring diameter in m\n", +"h=6/100; // blade height at entry in m\n", +"cx=180; // Axial velocity in m/s\n", +"alpha_1=25; // air angle at rotor and stator exit\n", +"wdf=0.88; // work-done factor\n", +"m=70; // in kg/s\n", +"pr=2; // Pressure Ratio\n", +"n_st=0.85; // Stage Efficiency \n", +"n_m=0.967; // Mechanical Efficiency \n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"u=%pi*d*N/60;\n", +"n=(gamma-1)/gamma;\n", +"\n", +"// part(a) air angles at rotor and stator entry\n", +"cy1=cx*tand(alpha_1);\n", +"wy1=u-cy1;\n", +"beta1=atand(wy1/cx);\n", +"disp('degree',beta1,'air angles at rotor and stator entry are beta1=alpha2= ')\n", +"phi=cx/u;\n", +"\n", +"// part(b) mass flow rate of the air\n", +"ro1=(p1*1e5)/(R*T1);\n", +"A1=%pi*d*h;\n", +"m=ro1*cx*A1;\n", +"disp('kg/s',m,'(b) mass flow rate of the air is')\n", +"\n", +"// part(c) Determining power required to drive the compressor\n", +"beta2=alpha_1;\n", +"w=wdf*u*cx*(tand(beta1)-tand(beta2))\n", +"P=m*w/n_m;\n", +"disp ('kW' ,P/1000,'(c)Power required to drive the compressor is')\n", +"\n", +"// part(d) Loading coefficient\n", +"shi=w/(u^2);\n", +"disp (shi,'(d)Loading coefficient is')\n", +"\n", +"// part(e) pressure ratio developed by the stage\n", +"delTa=w/cp;\n", +"delTs=n_st*delTa;\n", +"pr=((1+(delTs/T1))^(1/n));\n", +"disp(pr,'(e)pressure ratio developed by the stage is')\n", +"\n", +"// part(f) Mach number at the rotor entry\n", +"w1=cx/(cosd(beta1));\n", +"Mw1=w1/sqrt(gamma*R*T1);\n", +"disp(Mw1,'(f)Mach number at the rotor entry is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: Calculation_on_an_axial_compressor_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.2 Calculation on an axial compressor stage \n", +"\n", +"T1=314; // in Kelvin\n", +"p1=768; // Initial Pressure in mm Hg\n", +"N=18e3; // rotor Speed in RPM\n", +"d=50/100; // Mean Blade ring diameter in m\n", +"u=100; // peripheral speed in m/s\n", +"h=6/100; // blade height at entry in m\n", +"beta1=51;\n", +"beta2=9;\n", +"alpha_1=7; // air angle at rotor and stator exit\n", +"wdf=0.95; // work-done factor\n", +"m=25; // in kg/s\n", +"n_st=0.88; // Stage Efficiency \n", +"n_m=0.92; // Mechanical Efficiency \n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"gamma=1.4;\n", +"n=(gamma-1)/gamma;\n", +"\n", +"// part(a) air angle at stator entry\n", +"cx=u/(tand(alpha_1)+tand(beta1));\n", +"disp(cx,'cx=')\n", +"alpha2=atand(tand(alpha_1)+tand(beta1)-tand(beta2))\n", +"disp('degree',alpha2,'air angle at stator entry is alpha2= ')\n", +"\n", +"// part(b) blade height at entry and hub-tip diameter ratio\n", +"ro1=(p1/750*1e5)/(R*T1);\n", +"h1=m/(ro1*cx*%pi*d);\n", +"disp('cm',h1*1e2,'(b)blade height at entry is')\n", +"dh=d-h1;\n", +"disp(dh,'dh=')\n", +"dt=d+h1;\n", +"disp(dt,'dt=')\n", +"disp(dh/dt,'and hub-tip diameter ratio is')\n", +"\n", +"// part(c) stage Loading coefficient\n", +"w=wdf*u*cx*(tand(beta1)-tand(beta2));\n", +"shi=w/(u^2);\n", +"disp (shi,'(d)Loading coefficient is')\n", +"\n", +"// part(d) stage pressure ratio\n", +"delTa=w/cp;\n", +"delTs=n_st*delTa;\n", +"pr=((1+(delTs/T1))^(1/n));\n", +"disp(pr,'(e)pressure ratio developed by the stage is')\n", +"\n", +"// part(e) Determining power required to drive the compressor\n", +"P=m*w/n_m;\n", +"disp ('kW' ,P/1000,'(e)Power required to drive the compressor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: Calculation_on_an_axial_compressor_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.3 Calculation on an axial compressor stage\n", +"\n", +"// part(c) Verification of stage efficiency of exa 11.1\n", +"beta1=54.82;\n", +"alpha_1=25;\n", +"beta2=alpha_1; \n", +"alpha_2=beta1;\n", +"phi=0.53; // Flow coefficient\n", +"YR=0.09; // loss coefficient for the blade rows\n", +"n_st=1-((phi*YR*(secd(beta1)^2))/(tand(beta1)-tand(beta2)))\n", +"disp('%',n_st*1e2,'stage efficiency n_st=')\n", +"// part(d) Determining efficiencies of the rotor and Diffuser blade rows\n", +"n_D=1-(YR/(1-((secd(alpha_1)^2)/(secd(alpha_2)^2))))\n", +"disp ('%',n_D*100,' Efficiency of the diffuser n_D=n_R=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.4: Calculation_on_hub_mean_and_tip_sections.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.4 Calculation on hub,mean and tip sections \n", +"\n", +"dm=50/100; // Mean Blade ring diameter in m\n", +"rm=dm/2;\n", +"dh=0.3098354; // from results of exa 11.2\n", +"dt=0.6901646;\n", +"um=100; // peripheral speed in m/s\n", +"beta_1m=51;\n", +"beta_2m=9;\n", +"alpha_1m=7; // air angle at rotor and stator exit\n", +"alpha_2m=50.177922;\n", +"omega=um/rm;\n", +"rh=dh/2;\n", +"rt=dt/2;\n", +"uh=omega*rh;\n", +"ut=omega*rt;\n", +"\n", +"// part(a) rotor blade air angles\n", +"cx=73.654965;\n", +"c_theta1m=cx*tand(alpha_1m);\n", +"C1=rm*c_theta1m;\n", +"c_theta1h=C1/rh;\n", +"c_theta1t=C1/rt;\n", +"c_theta2m=cx*tand(alpha_2m);\n", +"C2=rm*c_theta2m;\n", +"c_theta2h=C2/rh;\n", +"c_theta2t=C2/rt;\n", +"disp('(a) the rotor blade air angles are')\n", +"// for hub section\n", +"alpha1h=atand(C1/(rh*cx));\n", +"alpha2h=atand(C2/(rh*cx));\n", +"disp('for hub section')\n", +"disp('degree',alpha1h,'alpha1h=')\n", +"disp('degree',alpha2h,'alpha2h=')\n", +"beta1h=atand((uh/cx)-tand(alpha1h));\n", +"beta2h=atand((uh/cx)-tand(alpha2h));\n", +"disp('degree',beta1h,'beta1h=')\n", +"disp('degree',beta2h,'beta2h=')\n", +"\n", +"// for tip section\n", +"alpha1t=atand(C1/(rt*cx));\n", +"alpha2t=atand(C2/(rt*cx));\n", +"disp('for tip section')\n", +"disp('degree',alpha1t,'alpha1t= ')\n", +"disp('degree',alpha2t,'alpha2t= ')\n", +"beta1t=atand((ut/cx)-tand(alpha1t));\n", +"beta2t=atand((ut/cx)-tand(alpha2t));\n", +"disp('degree',beta1t,'beta1t= ')\n", +"disp('degree',beta2t,'beta2t= ')\n", +"\n", +"// part(b)Flow coefficients\n", +"disp('(b)Flow coefficients are')\n", +"phi_h=cx/uh;\n", +"disp(phi_h,'phi_h=')\n", +"phi_m=cx/um;\n", +"disp(phi_m,'phi_m=')\n", +"phi_t=cx/ut;\n", +"disp(phi_t,'phi_t=')\n", +"// part(c) degrees of reaction\n", +"disp('(c)Degrees of reaction are')\n", +"Rh=cx*(tand(beta1h)+tand(beta2h))*100/(2*uh);\n", +"disp('%',Rh,'Rh=')\n", +"Rm=cx*(tand(beta_1m)+tand(beta_2m))*100/(2*um);\n", +"disp('%',Rm,'Rm=')\n", +"Rt=cx*(tand(beta1t)+tand(beta2t))*100/(2*ut);\n", +"disp('%',Rt,'Rt=')\n", +"\n", +"// part(d) specific work\n", +"w=omega*(C2-C1);\n", +"disp('kJ/kg',w*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficients\n", +"disp('(e)the loading coefficients are')\n", +"shi_h=w/(uh^2);\n", +"disp(shi_h,'shi_h=')\n", +"shi_m=w/(um^2);\n", +"disp(shi_m,'shi_m=')\n", +"shi_t=w/(ut^2);\n", +"disp(shi_t,'shi_t=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5: Forced_Vortex_axial_compressor_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.5 Forced Vortex axial compressor stage \n", +"\n", +"dm=50/100; // Mean Blade ring diameter in m\n", +"rm=dm/2;\n", +"dh=0.3098354; // from results of exa 11.2\n", +"dt=0.6901646;\n", +"um=100; // peripheral speed in m/s\n", +"beta_1m=51;\n", +"beta_2m=9;\n", +"alpha_1m=7; // air angle at rotor and stator exit\n", +"alpha_2m=50.177922;\n", +"omega=um/rm;\n", +"rh=dh/2;\n", +"rt=dt/2;\n", +"uh=omega*rh;\n", +"ut=omega*rt;\n", +"// part(a) rotor blade air angles\n", +"cx=73.654965;\n", +"c_theta1m=cx*tand(alpha_1m);\n", +"C1=c_theta1m/rm;\n", +"c_theta1h=C1*rh;\n", +"c_theta1t=C1*rt;\n", +"K1=cx^2+(2*(C1^2)*(rm^2));\n", +"cx1h=sqrt(K1-(2*(C1^2)*(rh^2)));\n", +"cx1t=sqrt(K1-(2*(C1^2)*(rt^2)));\n", +"c_theta2m=cx*tand(alpha_2m);\n", +"C2=c_theta2m/rm;\n", +"c_theta2h=C2*rh;\n", +"c_theta2t=C2*rt;\n", +"K2=cx^2-(2*(C2-C1)*omega*(rm^2))+(2*(C2^2)*(rm^2));\n", +"cx2h=sqrt(K2+(2*(C2-C1)*omega*(rh^2))-(2*(C2^2)*(rh^2)));\n", +"cx2t=sqrt(K2+(2*(C2-C1)*omega*(rt^2))-(2*(C2^2)*(rt^2)));\n", +"disp('(a) the rotor blade air angles are')\n", +"// for hub section\n", +"alpha1h=atand(C1*rh/cx1h);\n", +"alpha2h=atand(C2*rh/cx2h);\n", +"disp('for hub section')\n", +"beta1h=atand((uh/cx1h)-tand(alpha1h));\n", +"beta2h=atand((uh/cx2h)-tand(alpha2h));\n", +"disp('degree',beta1h,'beta1h=')\n", +"disp('degree',beta2h,'beta2h=')\n", +"\n", +"// for tip section\n", +"alpha1t=atand(C1*rt/cx1t);\n", +"alpha2t=atand(C2*rt/cx2t);\n", +"disp('for tip section')\n", +"beta1t=atand((ut/cx1t)-tand(alpha1t));\n", +"beta2t=atand((ut/cx2t)-tand(alpha2t));\n", +"disp('degree',beta1t,'beta1t= ')\n", +"disp('degree',beta2t,'beta2t= ')\n", +"\n", +"// part(b) specific work\n", +"wh=omega*(C2-C1)*(rh^2);\n", +"wm=omega*(C2-C1)*(rm^2);\n", +"wt=omega*(C2-C1)*(rt^2);\n", +"disp('kJ/kg',wh*1e-3,'(b)specific work at hub is')\n", +"disp('kJ/kg',wm*1e-3,'specific work at mean section is')\n", +"disp('kJ/kg',wt*1e-3,'specific work at tip is')\n", +"// part(c) the loading coefficients\n", +"disp('(c)the loading coefficients are')\n", +"shi_h=wh/(uh^2);\n", +"disp(shi_h,'shi_h=')\n", +"shi_m=wm/(um^2);\n", +"disp(shi_m,'shi_m=')\n", +"shi_t=wt/(ut^2);\n", +"disp(shi_t,'shi_t=')\n", +"\n", +"// part(c) degrees of reaction\n", +"disp('(d)Degrees of reaction are')\n", +"Rh=((cx1h^2)*(secd(beta1h)^2)-(cx2h^2)*(secd(beta2h)^2))*100/(2*wh);\n", +"Rm=((cx^2)*(secd(beta_1m)^2)-(cx^2)*(secd(beta_2m)^2))*100/(2*wm);\n", +"Rt=((cx1t^2)*(secd(beta1t)^2)-(cx2t^2)*(secd(beta2t)^2))*100/(2*wt);\n", +"disp('%',Rh,'Rh=')\n", +"disp('%',Rm,'Rm=')\n", +"disp('%',Rt,'Rt=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.6: General_Swirl_Distribution_axial_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.6 General Swirl Distribution axial compressor \n", +"\n", +"Rm=0.5; // Degree of reaction\n", +"dm=36/100; // Mean Blade ring diameter in m\n", +"rm=dm/2;\n", +"N=18e3; // rotor Speed in RPM\n", +"h=6/100; // blade height at entry in m\n", +"dh=dm-h;\n", +"dt=dm+h;\n", +"cx=180; // Axial velocity in m/s\n", +"alpha_1m=25; // air angle at rotor and stator exit\n", +"alpha_2m=54.820124; \n", +"um=%pi*dm*N/60;\n", +"omega=um/rm;\n", +"rh=dh/2;\n", +"rt=dt/2;\n", +"uh=omega*rh;\n", +"ut=omega*rt;\n", +"\n", +"// part(a) rotor blade air angles\n", +"c_theta1m=cx*tand(alpha_1m);\n", +"c_theta2m=cx*tand(alpha_2m);\n", +"a=0.5*(c_theta1m+c_theta2m)\n", +"b=rm*(c_theta2m-c_theta1m)*0.5;\n", +"c_theta1h=a-(b/rh);\n", +"c_theta1t=a-(b/rt);\n", +"K1=cx^2+(2*(a^2)*((b/(a*rm))+log(rm)));\n", +"cx1h=sqrt(K1-(2*(a^2)*((b/(a*rh))+log(rh))));\n", +"cx1t=sqrt(K1-(2*(a^2)*((b/(a*rt))+log(rt))));\n", +"\n", +"c_theta2h=a+(b/rh);\n", +"c_theta2t=a+(b/rt);\n", +"K2=cx^2+(2*(a^2)*(log(rm)-(b/(a*rm))));\n", +"cx2h=sqrt(K2-(2*(a^2)*(log(rh)-(b/(a*rh)))));\n", +"cx2t=sqrt(K2-(2*(a^2)*(log(rt)-(b/(a*rt)))));\n", +"disp('(a) the rotor blade air angles are')\n", +"// for hub section\n", +"alpha1h=atand(c_theta1h/cx1h);\n", +"alpha2h=atand(c_theta2h/cx2h);\n", +"disp('for hub section')\n", +"beta1h=atand((uh/cx1h)-tand(alpha1h));\n", +"beta2h=atand((uh/cx2h)-tand(alpha2h));\n", +"disp('degree',beta1h,'beta1h=')\n", +"disp('degree',beta2h,'beta2h=')\n", +"\n", +"// for tip section\n", +"alpha1t=atand(c_theta1t/cx1t);\n", +"alpha2t=atand(c_theta2t/cx2t);\n", +"disp('for tip section')\n", +"beta1t=atand((ut/cx1t)-tand(alpha1t));\n", +"beta2t=atand((ut/cx2t)-tand(alpha2t));\n", +"disp('degree',beta1t,'beta1t= ')\n", +"disp('degree',beta2t,'beta2t= ')\n", +"\n", +"// part(b) specific work\n", +"w=2*omega*b;\n", +"disp('kJ/kg',w*1e-3,'(b)specific work is')\n", +"\n", +"// part(c) the loading coefficients\n", +"disp('(c)the loading coefficients are')\n", +"shi_h=w/(uh^2);\n", +"disp(shi_h,'shi_h=')\n", +"shi_m=w/(um^2);\n", +"disp(shi_m,'shi_m=')\n", +"shi_t=w/(ut^2);\n", +"disp(shi_t,'shi_t=')\n", +"\n", +"// part(c) degrees of reaction\n", +"disp('(d)Degrees of reaction are')\n", +"Rh=((cx1h^2)*(secd(beta1h)^2)-(cx2h^2)*(secd(beta2h)^2))*100/(2*w);\n", +"Rt=((cx1t^2)*(secd(beta1t)^2)-(cx2t^2)*(secd(beta2t)^2))*100/(2*w);\n", +"disp('%',Rh,'Rh=')\n", +"disp('%',Rm*100,'Rm=')\n", +"disp('%',Rt,'Rt=')\n", +"disp('Comment: book contains wrong calculation for Rt value')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.7: flow_and_loading_coefficients.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 11.7 flow and loading coefficients \n", +"u=339.29; // in m/s\n", +"cx=180; // Axial velocity in m/s\n", +"alpha_1m=25; // air angle at rotor and stator exit\n", +"phi(1)=0.2;\n", +"phi(2)=0.4;\n", +"phi(3)=cx/u;\n", +"phi(4)=0.6;\n", +"phi(5)=0.8;\n", +"n=5;\n", +"for i=1:n\n", +" shi(i)=1-phi(i)*(2*tand(alpha_1m));\n", +" disp(phi(i),'when flow coefficient phi=')\n", +" disp(shi(i),'then loading coefficient shi=')\n", +"end\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/12-Centrifugal_Compressor_Stage.ipynb b/Turbines_by_Compressors_And_Fans/12-Centrifugal_Compressor_Stage.ipynb new file mode 100644 index 0000000..2bbab87 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/12-Centrifugal_Compressor_Stage.ipynb @@ -0,0 +1,304 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 12: Centrifugal Compressor Stage" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.1: Calculation_on_a_centrifugal_compressor_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 12.1 Calculation on a centrifugal compressor stage \n", +"T01=335; // in Kelvin\n", +"funcprot(0);\n", +"p01=1.02; // Initial Pressure in bar\n", +"dh=0.10; // hub diameter in m\n", +"dt=0.25; // tip diameter in m\n", +"m=5; // in kg/s\n", +"gamma=1.4;\n", +"N=7.2e3; // rotor Speed in RPM\n", +"d1=0.5*(dt+dh); // Mean Blade ring diameter\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"R=287;\n", +"// I trial\n", +"ro1=(p01*1e5)/(R*T01);\n", +"cx0=m/(ro1*A);\n", +"T0=T01-((cx0^2)/(2*cp));\n", +"n=(gamma-1)/gamma;\n", +"p1=p01*((T0/T01)^(1/n));\n", +"ro=(p1*1e5)/(R*T0);\n", +"cx=m/(ro*A);\n", +"// II Trial\n", +"cx2=123;\n", +"T1=T01-((cx2^2)/(2*cp));\n", +"p2=p01*((T1/T01)^(1/n));\n", +"ro2=(p2*1e5)/(R*T1);\n", +"cx1=m/(ro2*A);\n", +"u1=%pi*d1*N/60;\n", +"beta1=atand(cx1/u1);\n", +"disp('degree',beta1,'air angle at inducer blade entry beta1=')\n", +"w1=cx1/(sind(beta1));\n", +"a1=sqrt(gamma*R*T1);\n", +"Mw1=w1/a1;\n", +"disp(Mw1,'the Relative Mach number at inducer blade entry Mw1=')\n", +"alpha1=atand(cx1/u1);\n", +"disp('degree',alpha1,'air angle at IGVs exit alpha1=')\n", +"c1=cx1/(sind(alpha1));\n", +"T1_new=T01-((c1^2)/(2*cp));\n", +"a1_new=sqrt(gamma*R*T1_new);\n", +"Mw1_new=cx1/a1_new;\n", +"disp(Mw1_new,'the new value of Relative Mach number Mw1_new=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.2: Calculation_on_a_centrifugal_air_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 12.2 Calculation on a centrifugal air compressor \n", +"T01=288; // in Kelvin\n", +"p01=1.02; // Initial Pressure in bar\n", +"dh=0.10; // hub diameter in m\n", +"dt=0.25; // tip diameter in m\n", +"m=5; // in kg/s\n", +"gamma=1.4;\n", +"n=(gamma-1)/gamma;\n", +"N=7.2e3; // rotor Speed in RPM\n", +"d2=0.45; // Impeller diameter in m\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"u2=%pi*d2*N/60;\n", +"pr0=((1+(u2^2/(cp*T01)))^(1/n));\n", +"disp(pr0,'pressure ratio developed pr0=')\n", +"w=u2^2;\n", +"disp('kW/(kg/s)',w*1e-3,'Power required to drive the compressor P=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.3: centrifugal_compressor_stage_17000_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 12.3 Calculation on a centrifugal compressor stage \n", +"\n", +"funcprot(0)\n", +"T01=306; // Entry Temperature in Kelvin\n", +"p01=1.05; // Entry Pressure in bar\n", +"dh=0.12; // hub diameter in m\n", +"dt=0.24; // tip diameter in m\n", +"m=8; // in kg/s\n", +"mu=0.92; // slip factor\n", +"n_st=0.77; // stage efficiency\n", +"gamma=1.4;\n", +"N=17e3; // rotor Speed in RPM\n", +"d_it=0.48; // Impeller tip diameter in m\n", +"d1=0.5*(dt+dh); // Mean Blade ring diameter\n", +"rm=d1/2;\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"R=287;\n", +"n=86; // number of iterations\n", +"ro01=(p01*1e5)/(R*T01);\n", +"cx(1)=m/(ro01*A);\n", +"for i=1:n\n", +" T1=T01-((cx(i)^2)/(2*cp));\n", +" p1=p01*((T1/T01)^(1/((gamma-1)/gamma)));\n", +"ro1=(p1*1e5)/(R*T1);\n", +"cx(i+1)=m/(ro1*A);\n", +"if cx(i+1)==cx(i) then\n", +" disp('m/s',cx(i+1),'cx=')\n", +" disp(T1,'T1')\n", +"disp(p1,'p1')\n", +"disp(ro1,'ro1')\n", +"end \n", +"end\n", +"cx1=cx(i+1);\n", +"u1m=%pi*d1*N/60;\n", +"omega=u1m/rm;\n", +"rh=dh/2;\n", +"rt=dt/2;\n", +"uh=omega*rh;\n", +"ut=omega*rt;\n", +"u2=d_it*u1m/d1;\n", +"beta1h=atand(cx1/uh);\n", +"beta1m=atand(cx1/u1m);\n", +"beta1t=atand(cx1/ut);\n", +"disp('(a) Without IGVs')\n", +"disp('degree',beta1h,'air angle at hub section beta1h=')\n", +"disp('degree',beta1m,'air angle at mean section beta1m=')\n", +"disp('degree',beta1t,'air angle at tip section beta1t=')\n", +"w1t=cx1/(sind(beta1t));\n", +"a1=sqrt(gamma*R*T1);\n", +"M1t=w1t/a1;\n", +"disp(M1t,'the maximum Mach number at inducer blade entry M1t=')\n", +"pr0=((1+(mu*n_st*(u2^2)/(cp*T01)))^(1/((gamma-1)/gamma)));\n", +"disp(pr0,'total pressure ratio developed is')\n", +"P=m*mu*(u2^2);\n", +"disp ('kW',P/1000,'Power required to drive the compressor without IGVs is')\n", +"\n", +"// part(b) with IGVs\n", +"alpha1h=beta1h;\n", +"alpha1m=beta1m;\n", +"alpha1t=beta1t;\n", +"disp('(b)With IGVs')\n", +"disp('degree',alpha1h,'air angle at hub section alpha1h=')\n", +"disp('degree',alpha1m,'air angle at mean section alpha1m=')\n", +"disp('degree',alpha1t,'air angle at tip section alpha1t=')\n", +"c1t=cx1/(sind(alpha1t));\n", +"T1t=T01-((c1t^2)/(2*cp));\n", +"a1t=sqrt(gamma*R*T1t);\n", +"Mw1t=cx1/a1t;\n", +"disp(Mw1t,'the maximum Mach number at inducer blade entry Mw1t=')\n", +"pr0_w=((1+(n_st*(mu*(u2^2)-(u1m^2))/(cp*T01)))^(1/((gamma-1)/gamma)));\n", +"disp(pr0_w,'total pressure ratio developed is')\n", +"P_w=m*(mu*(u2^2)-(u1m^2));\n", +"disp ('kW',P_w/1000,'Power required to drive the compressor is')\n", +"disp('Comment: here the solution is found out using programming, so this gives slightly small variation from tha answers given in hte book, but answers from the present solution are exact.')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.4: Radially_tipped_blade_impeller.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 12.4.b Radially tipped blade impeller\n", +"phi2=0.268; // Flow coefficient\n", +"T01=293; // in Kelvin\n", +"p01=1; // Initial Pressure in bar\n", +"dr=2.667; // diameter ratio(d2/d1)\n", +"gamma=1.4;\n", +"R=287;\n", +"N=8e3; // rotor Speed in RPM\n", +"d1=0.18; // Mean diameter at the impeller entry in m\n", +"u1=%pi*d1*N/60;\n", +"a1=sqrt(gamma*R*T01);\n", +"Mb1=u1/a1;\n", +"disp(Mb1,'the Mach number at inducer blade entry Mb1=')\n", +"M2=sqrt(((dr^2)*(Mb1^2)*(1+(phi2^2)))/(1+(0.5*(gamma-1)*(dr^2)*(Mb1^2)*(1-(phi2^2)))));\n", +"disp(M2,'the flow Mach number at impeller exit M2=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12.5: Radially_tipped_blade_impeller.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 12.5 Radially tipped blade impeller\n", +"// part(a) free vortex flow\n", +"r3=0.25; // volute base circle radius in m\n", +"c_theta3=177.5; // tangential velocity component of air in m/s\n", +"K=r3*c_theta3;\n", +"b=0.12; // width in m\n", +"Q=5.4; // discharge in m3/s\n", +"n=8;\n", +"disp('part(a)')\n", +"theta(1)=%pi/4;\n", +"theta(2)=%pi/2;\n", +"theta(3)=3*%pi/4;\n", +"theta(4)=%pi;\n", +"theta(5)=5*%pi/4;\n", +"theta(6)=3*%pi/2;\n", +"theta(7)=7*%pi/4;\n", +"theta(8)=2*%pi;\n", +"disp('the volute radii at eight angular positions are given below:')\n", +"for i=1:n\n", +" r4(i)=r3*exp(theta(i)*Q/(2*%pi*K*b))\n", +" disp('radian',theta(i),'at theta=')\n", +" disp('cm',r4(i)*100,'r4=')\n", +"end\n", +"L=r4(8)-r3;\n", +"disp(L/(2*r3),'(a)throat-to-diameter ratio (L/d3)=')\n", +"\n", +"// part(b) constant mean velocity of 145 m/s\n", +"cm=145; // constant mean velocity in m/s\n", +"disp('part(b)')\n", +"for i=1:n\n", +" r4b(i)=r3+(Q/(cm*b)*(theta(i)/(2*%pi)));\n", +" disp('radian',theta(i),'at theta=')\n", +" disp('cm',r4b(i)*100,'r4=')\n", +"end\n", +"L_b=r4b(8)-r3;\n", +"disp(L_b/(2*r3),'(b)throat-to-diameter ratio (L/d3)=')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/13-Radial_Turbine_Stages.ipynb b/Turbines_by_Compressors_And_Fans/13-Radial_Turbine_Stages.ipynb new file mode 100644 index 0000000..6aaabb5 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/13-Radial_Turbine_Stages.ipynb @@ -0,0 +1,222 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 13: Radial Turbine Stages" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.1: ninety_degree_IFR_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 13.1 ninety degree IFR turbine\n", +"t=650; // in degree C\n", +"T01=t+273; // in Kelvin\n", +"p3=1; // Exit Pressure in bar\n", +"gamma=1.4;\n", +"sigma=0.66; // blade-to-isentropic speed ratio\n", +"N=16e3; // rotor Speed in RPM\n", +"b2=5/100; // blade height at entry in m\n", +"alpha_2=20; // air angle at nozzle exit\n", +"d_r=0.45; // rotor diameter ratio(d3/d2)\n", +"p01_3=3.5; // total-to-static Pressure Ratio(p01/p3) \n", +"n_N=0.95; // Nozzle Efficiency \n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"n=(gamma-1)/gamma;\n", +"\n", +"// part(a) the rotor diameter\n", +"c_0=sqrt(2*cp*T01*(1-(p01_3^(-n))))\n", +"u_2=sigma*c_0;\n", +"d2=60*u_2/(%pi*N);\n", +"disp('cm',d2*1e2,'(a)the rotor diameter is')\n", +"\n", +"// part(b) air angle at rotor blade exit\n", +"d3=d2*d_r;\n", +"c_r2=u_2*tand(alpha_2);\n", +"u3=%pi*d3*N/60;\n", +"beta3=atand(c_r2/u3);\n", +"disp('degree',beta3,'(b) air angle at rotor blade exit beta3=')\n", +"\n", +"// part(c) mass flow rate\n", +"T03=T01-((u_2^2)/cp);\n", +"T3=T03-((c_r2^2)/(2*cp));\n", +"T2=T3+((0.5*(u_2^2))/cp);\n", +"c2=u_2/(cosd(alpha_2));\n", +"p01_2=(1-(((0.5*(c2^2))/(cp*n_N))/T01))^(-1/n);\n", +"p01=p3*p01_3;\n", +"p2=p01/p01_2;\n", +"ro2=(p2*1e5)/(R*T2);\n", +"m=ro2*c_r2*%pi*d2*b2;\n", +"disp('kg/s',m,'(c) mass flow rate is')\n", +"\n", +"// part(d) hub and tip diameters at the rotor exit\n", +"ro3=(p3*1e5)/(R*T3);\n", +"b3=m/(ro3*c_r2*%pi*d3);\n", +"dh=d3-b3;\n", +"disp('cm',dh*1e2,'(d)hub diameter at the rotor exit is')\n", +"dt=d3+b3;\n", +"disp('cm',dt*1e2,'(d)tip diameter at the rotor exit is')\n", +"\n", +"// part(e) Determining the power developed\n", +"P=m*(u_2^2);\n", +"disp ('kW',P/1000,'(e)Power developed is')\n", +"\n", +"// part(f) the total-to-static Efficiency of the stage\n", +"n_ts=(u_2^2)/(cp*T01*(1-((p3/p01)^n)));\n", +"disp('%',n_ts*1e2,'(f)the total-to-static Efficiency of the stage is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.2: Mach_Number_and_loss_coefficient.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 13.2 Mach Number and loss coefficient\n", +"t=650; // in degree C\n", +"T01=t+273; // in Kelvin\n", +"p3=1; // Exit Pressure in bar\n", +"gamma=1.4;\n", +"sigma=0.66; // blade-to-isentropic speed ratio\n", +"N=16e3; // rotor Speed in RPM\n", +"b2=5/100; // blade height at entry in m\n", +"alpha_2=20; // air angle at nozzle exit\n", +"d_r=0.45; // rotor diameter ratio(d3/d2)\n", +"p01_3=3.5; // total-to-static Pressure Ratio(p01/p3) \n", +"n_N=0.95; // Nozzle Efficiency \n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"n=(gamma-1)/gamma;\n", +"c_0=sqrt(2*cp*T01*(1-(p01_3^(-n))))\n", +"u_2=sigma*c_0;\n", +"Mb0=u_2/sqrt(gamma*R*T01);\n", +"\n", +"// part(a) Mach number at nozzle exit\n", +"M2=Mb0/(cosd(alpha_2)*sqrt(1-(0.5*(gamma-1)*(Mb0^2)*(secd(alpha_2)^2))));\n", +"disp(M2,'(a)the flow Mach number at nozzle exit M2=')\n", +"\n", +"// part(b)rotor exit Relative Mach number\n", +"d2=60*u_2/(%pi*N);\n", +"d3=d2*d_r;\n", +"c_r2=u_2*tand(alpha_2);\n", +"u3=%pi*d3*N/60;\n", +"beta3=atand(c_r2/u3);\n", +"w3=u3/(cosd(beta3));\n", +"T03=T01-((u_2^2)/cp);\n", +"T3=T03-((c_r2^2)/(2*cp));\n", +"a3=sqrt(gamma*R*T3);\n", +"M3_rel=w3/a3;\n", +"disp(M3_rel,'(b)the Relative Mach number at rotor exit is')\n", +"\n", +"// part(c) Nozzle enthalpy loss coefficient\n", +"T2=T3+((0.5*(u_2^2))/cp);\n", +"c2=u_2/(cosd(alpha_2));\n", +"T2s=T01-((0.5*(c2^2))/(cp*n_N));\n", +"c2=u_2/(cosd(alpha_2));\n", +"zeeta_N=cp*(T2-T2s)/(0.5*(c2^2));\n", +"disp(zeeta_N,'(c)the Nozzle enthalpy loss coefficient is')\n", +"\n", +"// part(d)rotor enthalpy loss coefficient\n", +"\n", +"p01_2=(1-(((0.5*(c2^2))/(cp*n_N))/T01))^(-1/n);\n", +"p01=p3*p01_3;\n", +"p2=p01/p01_2;\n", +"T3s=T2/((p2/p3)^n);\n", +"zeeta_R=cp*(T3-T3s)/(0.5*(w3^2));\n", +"disp(zeeta_R,'(d)the rotor enthalpy loss coefficient is')\n", +"disp('comment: Nozzle enthalpy loss coefficient value is not correctly calculated in the textbook. the above value is correct.')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.3: IFR_turbine_with_Cantilever_Blades.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 13.3 IFR turbine with Cantilever Blades\n", +"phi=0.4; // flow coefficient\n", +"funcprot(0);\n", +"P=100; // Power developed in kW\n", +"n_tt=0.9; // total-to-total Efficiency\n", +"N=12e3; // rotor Speed in RPM\n", +"m=1; // in kg/s\n", +"T01=400; // in Kelvin\n", +"gamma=1.4;\n", +"d_r=0.8; // rotor diameter ratio(d3/d2)\n", +"u2=sqrt(P*1000/(2*m));\n", +"d2=60*u2/(%pi*N);\n", +"disp('cm',d2*1e2,'the rotor diameter at entry is')\n", +"d3=d2*d_r;\n", +"disp('cm',d3*1e2,'the rotor diameter at exit is')\n", +"beta2=atand(phi);\n", +"disp('degree',beta2,'air angle at rotor entry is beta2=')\n", +"d3=d2*d_r;\n", +"u3=%pi*d3*N/60;\n", +"c_r2=u2*phi;\n", +"beta3=atand(c_r2/u3);\n", +"disp('degree',beta3,'air angle at rotor exit is beta3=')\n", +"cp=1005;\n", +"n=(gamma-1)/gamma;\n", +"alpha_2=atand(c_r2/(2*u2));\n", +"disp('degree',alpha_2,'air angle at nozzle exit is alpha_2=')\n", +"p01_03=(1-((2*(u2^2))/(n_tt*cp*T01)))^(-1/n);\n", +"disp(p01_03,'stagnation pressure ratio across the stage is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/14-Axial_Fans_and_Propellers.ipynb b/Turbines_by_Compressors_And_Fans/14-Axial_Fans_and_Propellers.ipynb new file mode 100644 index 0000000..5ecfcba --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/14-Axial_Fans_and_Propellers.ipynb @@ -0,0 +1,299 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 14: Axial Fans and Propellers" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.1: Axial_fan_stage_960_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.1 Axial fan stage 960 rpm\n", +"beta3=10; // rotor blade air angle at exit in degree\n", +"dh=0.3; // hub diameter in m\n", +"dt=0.6; // tip diameter in m\n", +"N=960; // rotor Speed in RPM\n", +"P=1; // Power required in kW\n", +"phi=0.245; // flow coefficient\n", +"T1=316; // in Kelvin\n", +"p1=1.02; //Initial Pressure in bar\n", +"R=287;\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"d=0.5*(dt+dh);\n", +"u=%pi*d*N/60;\n", +"cx=phi*u;\n", +"Q=cx*A;\n", +"ro=(p1*1e5)/(R*T1);\n", +"delp0_st=ro*(u^2)*(1-(phi*(tand(beta3))));\n", +"disp('mm W.G.',delp0_st/9.81,'stage pressure rise is')\n", +"IP=Q*delp0_st/1000; // ideal power required to drive the fan in kW\n", +"n_o=IP/P;\n", +"disp('%',n_o*1e2,'the overall Efficiency of the fan is') \n", +"beta2=atand(u/cx);\n", +"disp('degree',beta2,'the blade air angle at the entry beta2=')\n", +"delp_st=0.5*ro*(u^2)*(1-(phi^2*(tand(beta3)^2)));\n", +"DOR=delp_st/delp0_st;\n", +"disp('%',DOR*1e2,'the degree of reaction is') \n", +"omega=2*%pi*N/60;\n", +"gH=delp0_st/ro;\n", +"NS=omega*sqrt(Q)/(gH^(3/4));\n", +"disp(NS,'the dimensionless specific speed is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.2: Downstream_guide_vanes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.2 Downstream guide vanes\n", +"\n", +"beta3=10; // rotor blade air angle at exit in degree\n", +"dh=0.3; // hub diameter in m\n", +"dt=0.6; // tip diameter in m\n", +"N=960; // rotor Speed in RPM\n", +"phi=0.245; // flow coefficient\n", +"d=0.5*(dt+dh);\n", +"u=%pi*d*N/60;\n", +"cx=phi*u;\n", +"cy3=u-(cx*tand(beta3));\n", +"alpha3=atand(cy3/cx);\n", +"disp('the rotor blade air angles, overall efficiency, flow rate, power required and degree of reaction are the same as calculated in Ex14_1')\n", +"disp('degree',alpha3,'the guide vane air angle at the entry alpha3=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.3: upstream_guide_vanes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.3 upstream guide vanes\n", +"beta2=86; // rotor blade air angle at inlet in degree\n", +"dh=0.3; // hub diameter in m\n", +"dt=0.6; // tip diameter in m\n", +"N=960; // rotor Speed in RPM\n", +"phi=0.245; // flow coefficient\n", +"T1=316; // in Kelvin\n", +"p1=1.02; //Initial Pressure in bar\n", +"R=287;\n", +"n_o=0.647; // overall Efficiency of the drive\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"d=0.5*(dt+dh);\n", +"u=%pi*d*N/60;\n", +"cx=phi*u;\n", +"Q=cx*A;\n", +"ro=(p1*1e5)/(R*T1);\n", +"\n", +"// part(i) static pressure rise in the rotor and stage\n", +"delh0_st=(u^2)*((phi*(tand(beta2)))-1);\n", +"delp0_st=ro*delh0_st;\n", +"disp('mm W.G.',delp0_st/9.81,'(i)static pressure rise in the stage is')\n", +"beta3=atand(u/cx);\n", +"w2=cx/(cosd(beta2));\n", +"w3=cx/(cosd(beta3));\n", +"delp_r=0.5*ro*((w2^2)-(w3^2));\n", +"disp('mm W.G.',delp_r/9.81,'and the static pressure rise in the rotor is')\n", +"\n", +"// part(ii) the stage pressure coefficient and degree of reaction\n", +"shi=2*((phi*(tand(beta2)))-1);\n", +"disp(shi,'(ii)stage pressure coefficient is')\n", +"DOR=0.5*((phi*(tand(beta2)))+1);\n", +"disp('%',DOR*1e2,'and the degree of reaction is') \n", +"\n", +"// part(iii) the blade air angle at the rotor exit and the air angle at the UGV exit\n", +"disp('degree',beta3,'(iii)the blade air angle at the rotor exit beta3=')\n", +"cy2=(cx*tand(beta2))-u;\n", +"alpha2=atand(cy2/cx);\n", +"disp('degree',alpha2,'and the air angle at the UGV exit alpha2=')\n", +"\n", +"// part(iv) Power required to drive the fan\n", +"m=ro*Q;\n", +"P=m*delh0_st/n_o;\n", +"disp('kW',P/1000,'(iv)Power required to drive the fan is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.4: rotor_and_upstream_guide_blades.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.4 rotor and upstream guide blades\n", +"beta2=30; // rotor blade air angle at inlet in degree\n", +"beta3=10; // rotor blade air angle at exit in degree\n", +"dh=0.3; // hub diameter in m\n", +"dt=0.6; // tip diameter in m\n", +"N=960; // rotor Speed in RPM\n", +"phi=0.245; // flow coefficient\n", +"T1=316; // in Kelvin\n", +"p1=1.02; //Initial Pressure in bar\n", +"R=287;\n", +"n_d=0.88; // Efficiency of the drive\n", +"n_f=0.8; // Efficiency of the fan\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"d=0.5*(dt+dh);\n", +"u=%pi*d*N/60;\n", +"cx=phi*u;\n", +"Q=cx*A;\n", +"ro=(p1*1e5)/(R*T1);\n", +"delh0_st=(u^2)*phi*(tand(beta2)-tand(beta3));\n", +"n_o=n_f*n_d;\n", +"delp0_st=n_f*ro*delh0_st;\n", +"disp('mm W.G.',delp0_st/9.81,'static pressure rise in the stage is')\n", +"shi=2*phi*(tand(beta2)-tand(beta3));\n", +"disp(shi,'stage pressure coefficient is')\n", +"m=ro*Q;\n", +"P=m*delh0_st/n_d;\n", +"disp('kW',P/1000,'Power required to drive the fan is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.5: DGVs_and_upstream_guide_vanes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.5 DGVs and upstream guide vanes\n", +"beta2=86; // rotor blade air angle at inlet in degree\n", +"beta3=10; // rotor blade air angle at exit in degree\n", +"dh=0.3; // hub diameter in m\n", +"dt=0.6; // tip diameter in m\n", +"N=960; // rotor Speed in RPM\n", +"phi=0.245; // flow coefficient\n", +"T1=316; // in Kelvin\n", +"p1=1.02; //Initial Pressure in bar\n", +"R=287;\n", +"n_d=0.8; // Efficiency of the drive\n", +"n_f=0.85; // Efficiency of the fan\n", +"A=%pi*((dt^2)-(dh^2))/4;\n", +"d=0.5*(dt+dh);\n", +"u=%pi*d*N/60;\n", +"cx=phi*u;\n", +"Q=cx*A;\n", +"ro=(p1*1e5)/(R*T1);\n", +"delh0_st=2*(u^2)*((phi*(tand(beta2)))-1);\n", +"delp0_st=n_f*ro*delh0_st;\n", +"disp('mm W.G.',delp0_st/9.81,'static pressure rise in the stage is')\n", +"shi=4*((phi*(tand(beta2)))-1);\n", +"disp(shi,'stage pressure coefficient is')\n", +"m=ro*Q;\n", +"P=m*delh0_st/n_d;\n", +"disp('kW',P/1000,'Power of the electric motor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14.6: open_propeller_fan.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 14.6 open propeller fan\n", +"c_u=5; // upstream velocity in m/s\n", +"c_s=25; // downstream velocity in m/s\n", +"t=37; // in degree C\n", +"T=t+273; // in Kelvin\n", +"d=0.5;\n", +"p=1.02; // Initial Pressure in bar\n", +"R=287;\n", +"n_o=0.4; // overall Efficiency of the fan\n", +"A=%pi*(d^2)/4;\n", +"c=0.5*(c_u+c_s);\n", +"Q=c*A;\n", +"ro=(p*1e5)/(R*T);\n", +"m=ro*c*A;\n", +"disp('kg/s',m,'(a) flow rate through the fan is')\n", +"delh_0=0.5*((c_s^2)-(c_u^2));\n", +"delp_0=ro*delh_0;\n", +"disp('mm W.G.',delp_0/9.81,'(b)static pressure rise in the stage is')\n", +"P=m*delh_0/n_o;\n", +"disp('kW',P/1000,'(c)Power required to drive the fan is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/15-Centrifugal_Fans_and_Blowers.ipynb b/Turbines_by_Compressors_And_Fans/15-Centrifugal_Fans_and_Blowers.ipynb new file mode 100644 index 0000000..34d7ca8 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/15-Centrifugal_Fans_and_Blowers.ipynb @@ -0,0 +1,138 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 15: Centrifugal Fans and Blowers" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 15.1: Centrifugal_fan_stage_1450_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 15.1 Centrifugal fan stage 1450 rpm\n", +"\n", +"d1=0.18; // inner diameter of the impeller in m\n", +"d2=0.2; // outer diameter of the impeller in m\n", +"N=1450; // rotor Speed in RPM\n", +"c1=21; // Absolute velocity at entry in m/s\n", +"w1=20; // relative velocity at entry in m/s\n", +"c2=25; // Absolute velocity at exit in m/s\n", +"w2=17; // relative velocity at exit in m/s\n", +"m=0.5; // flow rate in kg/s\n", +"n_m=0.78; // overall Efficiency of the motor\n", +"ro=1.25; // density of air in kg/m3\n", +"\n", +"u1=%pi*d1*N/60;\n", +"u2=%pi*d2*N/60;\n", +"delp_r=0.5*ro*((w1^2)-(w2^2))+(0.5*ro*((u2^2)-(u1^2)));\n", +"delp0_st=0.5*ro*(((w1^2)-(w2^2))+((u2^2)-(u1^2))+((c2^2)-(c1^2)));\n", +"disp('mm W.G.',delp0_st/9.81,'(a)stage pressure rise is')\n", +"DOR=delp_r/delp0_st;\n", +"disp(DOR,'(b)the degree of reaction is') \n", +"w_st=delp0_st/ro;\n", +"P=m*w_st/n_m;\n", +"disp('W',P,'(c)the motor Power required to drive the fan is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 15.2: Centrifugal_blower_3000_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 15.2 Centrifugal blower 3000 rpm\n", +"\n", +"beta2=90; // rotor blade air angle at inlet in degree\n", +"N=3e3; // rotor Speed in RPM\n", +"T1=310; // in Kelvin\n", +"p1=0.98; //Initial Pressure in bar\n", +"R=287;\n", +"n_d=0.88; // Efficiency of the drive\n", +"n_f=0.82; // Efficiency of the fan\n", +"Q=200/60; // discharge in m3/s\n", +"h=1000; // mm column of water\n", +"delp0=h*9.81;\n", +"Pi=Q*delp0/1000; // ideal power\n", +"P=Pi/(n_d*n_f);\n", +"disp('kW',P,'(a)Power required by the electric motor is')\n", +"\n", +"// part(b) impeller diameter\n", +"ro=(p1*1e5)/(R*T1);\n", +"u2=sqrt(delp0/(ro*n_f));\n", +"d2=u2*60/(%pi*N);\n", +"disp('cm',d2*1e2,'(b)the impeller diameter is')\n", +"\n", +"// part(c) inner diameter of the blade ring\n", +"c_r2=0.2*u2;\n", +"c_i=0.4*u2;\n", +"d1=sqrt(Q*4/(%pi*c_i));\n", +"disp('cm',d1*1e2,'(c)the inner diameter of the blade ring is')\n", +"\n", +"// part(d) air angle at the entry\n", +"u1=u2*d1/d2;\n", +"beta1=atand(c_r2/u1);\n", +"disp('degree',beta1,'(d)the air angle at the entry beta1=')\n", +"\n", +"// part(e) impeller widths at entry and exit\n", +"b1=Q/(c_r2*%pi*d1);\n", +"disp('cm',b1*1e2,'(e)the impeller width at entry is')\n", +"b2=b1*d1/d2;\n", +"disp('cm',b2*1e2,'and the impeller width at exit is')\n", +"\n", +"// part(f) number of impeller blades\n", +"z=8.5*sind(beta2)/(1-(d1/d2));\n", +"disp(z,'(f)the number of impeller blades is')\n", +"\n", +"// part(g) the specific speed\n", +"gH=u2^2;\n", +"omega=2*%pi*N/60;\n", +"NS=omega*sqrt(Q)/(gH^(3/4));\n", +"disp(NS,'(g)the dimensionless specific speed is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/16-Wind_Turbines.ipynb b/Turbines_by_Compressors_And_Fans/16-Wind_Turbines.ipynb new file mode 100644 index 0000000..c821f23 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/16-Wind_Turbines.ipynb @@ -0,0 +1,74 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 16: Wind Turbines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 16.1: Wind_turbine_output_100_kW.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 16.1 Wind turbine output 100 kW\n", +"\n", +"c_u=48*5/18; // wind upstream velocity in m/s\n", +"n=0.95; // overall Efficiency of the drive\n", +"P=100; // aerogenerator power output in kW\n", +"n_m=0.9; // mechanical Efficiency of the drive\n", +"n_a=0.7; // aerodynamic Efficiency\n", +"ro=1.125; // density of air in kg/m3\n", +"cp_max=0.593; // power coefficient for the windmill(Pi/Pu)\n", +"\n", +"// part(a) propeller diameter of the windmill\n", +"A=2*P*1e3/(ro*(c_u^3)*n*n_m*n_a*cp_max);\n", +"d=sqrt(4*A/%pi);\n", +"disp('m',d,'(a)the propeller diameter of the windmill is')\n", +"\n", +"// part(b)\n", +"disp('(b)corresponding to maximum power')\n", +"c=2*c_u/3;\n", +"disp('m/s',c,'the wind velocity through the propeller disc is')\n", +"delp1_a=5*ro*(c^2)/8;\n", +"disp('mm W.G.',delp1_a/9.81,'the gauge pressure just before the disc is')\n", +"delp2_a=-3*ro*(c^2)/8;\n", +"disp('mm W.G.',delp2_a/9.81,'the gauge pressure just after the disc is')\n", +"Fx=(delp1_a-delp2_a)*A;\n", +"disp('kN',Fx*1e-3,'and the axial thrust is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/18-Miscellaneous_Solved_Problems_in_Turbomachines.ipynb b/Turbines_by_Compressors_And_Fans/18-Miscellaneous_Solved_Problems_in_Turbomachines.ipynb new file mode 100644 index 0000000..292751f --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/18-Miscellaneous_Solved_Problems_in_Turbomachines.ipynb @@ -0,0 +1,2781 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 18: Miscellaneous Solved Problems in Turbomachines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.10: Calculation_on_combined_cycle_power_plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.10 Calculation on combined cycle power plant\n", +"\n", +"P_gt=25.845; // Power Output of gas turbine plant in MW\n", +"P_st=21; // Power Output of steam turbine plant in MW\n", +"m_gt=115; // mass flow rate of the exhaust gas in kg/s\n", +"n_T=0.86; // Turbine Efficiency\n", +"gamma_g=1.33;\n", +"R=0.287;\n", +"cp=(gamma_g/(gamma_g-1))*R; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"T3=1341; // Maximum Temperature in gas turbine in degree K from Ex18.9\n", +"p1=84; // steam Pressure at the entry of steam turbine in bar\n", +"// from steam tables\n", +"t_6s=298.4; // saturation temperature at 84 bar in degree C\n", +"t_5s=t_6s;\n", +"h_6s=1336.1; // from steam table liquid vapour enthalpy at 84 bar\n", +"t6=535; // steam temperature at the entry of steam turbine in degree C\n", +"T6=t6+273; // in Kelvin\n", +"h_4s=3460; // from mollier diagram at t=535 degree C\n", +"h_7=2050;\n", +"p_c=0.07; // Condenser pressure in bar\n", +"r=8.8502464; //optimum pressure ratio from Ex18.9\n", +"T4=875.92974; //from Ex 18.9\n", +"t4=T4-273; // in degree C\n", +"h_7s=163.4; // Specific Enthalpy of water in kJ/kg\n", +"m_st=P_st*1e3/((h_4s-h_7)*n_T); // mass flow rate of the steam in kg/s\n", +"\n", +"// part(a)Exhaust gas temperature at stack\n", +"t_7=t4-((m_st*(h_4s-h_7s))/(m_gt*cp)); // energy balance for the economiser entry(7') to the superheater exit(4')\n", +"disp('degree celsius',t_7,'(a)Exhaust gas temperature at stack is')\n", +"\n", +"// part(b)mass of steam per kg of gas\n", +"disp('kg',m_st/m_gt,'(b)mass of steam per kg of gas is')\n", +"\n", +"// part(c) Pinch Point(PP)\n", +"t_6=t_7+((m_st*(h_6s-h_7s))/(m_gt*cp)); // energy balance for the economiser\n", +"PP=t_6-t_6s;\n", +"disp('degree celsius',PP,'(c)Pinch Point(PP) is')\n", +"\n", +"// part(d)thermal efficiency of steam turbine plant\n", +"delh4s_7ss=(h_4s-h_7)*n_T;\n", +"n_st=delh4s_7ss/(h_4s-h_7s);\n", +"disp('%',n_st*100,'(d)thermal Efficiency of steam turbine plant is')\n", +"\n", +"// part(e) thermal efficiency of the combined cycle plant\n", +"n_B=0.978; // Assuming Combustion chamber Efficiency\n", +"Qs=102.72554; // heat supplied in the combustion chamber from Ex 18.9\n", +"Qss=Qs/n_B; // power supplied to the combined cycle\n", +"n_gst=(P_gt+P_st)/Qss;\n", +"disp ('%' ,n_gst*100,'(e)thermal Efficiency of combined gas and steam power plant is')\n", +"\n", +"// part(f)the dryness fraction of steam at the turbine exhaust\n", +"x=0.875; // from Mollier diagram at p=0.07 bar\n", +"disp(x,'(f)the dryness fraction of steam at the turbine exhaust is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.11: Calculation_on_combined_cycle_power_plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.11 Calculation on combined cycle power plant\n", +"\n", +"P_gt=25.845; // Power Output of gas turbine plant in MW\n", +"P_st=21; // Power Output of steam turbine plant in MW\n", +"m_gt=115; // mass flow rate of the exhaust gas in kg/s\n", +"n_T=0.86; // Turbine Efficiency\n", +"gamma_g=1.33;\n", +"R=0.287;\n", +"cp=(gamma_g/(gamma_g-1))*R; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"T3=1341; // Maximum Temperature in gas turbine in degree K from Ex18.9\n", +"p1=84; // steam Pressure at the entry of steam turbine in bar\n", +"// from steam tables\n", +"t_6s=298.4; // saturation temperature at 84 bar in degree C\n", +"h_6s=1336.1; // from steam table liquid vapour enthalpy at 84 bar\n", +"pp(1)=20; // pinch point in degree C\n", +"pp(2)=28.2;\n", +"pp(3)=35;\n", +"\n", +"for i=1:3\n", +" printf('\nfor PP=%d degree C\n',pp(i))\n", +"t_6=t_6s+pp(i);\n", +"h_4s=3460; // from mollier diagram at t=535 degree C\n", +"h_7=2050;\n", +"p_c=0.07; // Condenser pressure in bar\n", +"T4=875.92974; //from Ex 18.9\n", +"t4=T4-273; // in degree C\n", +"h_7s=163.4; // Specific Enthalpy of water in kJ/kg\n", +"\n", +"// part(a)steam flow per kg of gas\n", +"m_st_gt=cp*(t4-t_6)/(h_4s-h_6s); // steam flow per kg of gas\n", +"disp('kg',m_st_gt,'(a)steam flow per kg of gas is')\n", +"\n", +"// part(b)Exhaust gas temperature at stack\n", +"t_7=t_6-((m_st_gt*(h_6s-h_7s))/(cp)); // energy balance for the economiser entry(7') to the superheater exit(4')\n", +"disp('degree celsius',t_7,'(b)Exhaust gas temperature at stack is')\n", +"\n", +"// part(c)steam turbine plant output\n", +"h_7ss=2247;\n", +"P_st=m_st_gt*m_gt*(h_4s-h_7ss);\n", +"disp('MW',P_st/1e3,'(c)Power output of the steam turbine plant is')\n", +"\n", +"// part(d)thermal efficiency of steam turbine plant\n", +"delh4s_7ss=(h_4s-h_7)*n_T;\n", +"n_st=delh4s_7ss/(h_4s-h_7s);\n", +"disp('%',n_st*100,'(d)thermal Efficiency of steam turbine plant is')\n", +"\n", +"// part(e) thermal efficiency of the combined cycle plant\n", +"n_B=0.978; // Assuming Combustion chamber Efficiency\n", +"Qs=102.72554; // heat supplied in the combustion chamber from Ex 18.9\n", +"Qss=Qs/n_B; // power supplied to the combined cycle\n", +"n_gst=(P_gt+(P_st*1e-3))/Qss;\n", +"disp('%',n_gst*100,'(e)thermal Efficiency of combined gas and steam power plant is')\n", +"end\n", +"\n", +"disp('Comment: Error in Textbook, Answers vary due to Round-off Errors')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.12: turbo_prop_Gas_Turbine_Engine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.12 turbo prop Gas Turbine Engine\n", +"\n", +"Ti=268.65; // in Kelvin\n", +"n_C=0.8; // Compressor Efficiency\n", +"c1=85; // entry velocity in m/s\n", +"m=50; // mass flow rate of air in kg/s\n", +"R=287;\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"u=500/3.6; // speed of a turbo prop aircraft in m/s\n", +"delT=225; // temperature rise through the compressor(T02-T01) in K\n", +"pi=.701; // Initial Pressure in bar\n", +"n_D=0.88; // inlet diffuser efficiency\n", +"a_i=sqrt(gamma*R*Ti);\n", +"Mi=u/a_i;\n", +"Toi_i=1/0.965; // (Toi/Ti)from isentropic flow gas tables at Mi and gamma values\n", +"T01=Ti*Toi_i;\n", +"T1=T01-(0.5*(c1^2)/(cp*1e3));\n", +"\n", +"//part(a)\n", +"T1s_i=1+n_D*((T1/Ti)-1); // (T1s/Ti)isentropic temperature ratio through the diffuser\n", +"p1_i=T1s_i^(gamma/(gamma-1)); // (p1s/pi)isentropic pressure ratio\n", +"p1=p1_i*pi;\n", +"delp_D=p1-pi;\n", +"disp('bar',delp_D,'(a)isentropic pressure rise through the diffuser is')\n", +"\n", +"// part(b) compressor pressure ratio\n", +"T02s=T01+(delT*n_C);\n", +"r_oc=(T02s/T01)^(gamma/(gamma-1)); //compressor pressure ratio(p02/p01)\n", +"disp(r_oc,'(b)compressor pressure ratio is')\n", +"\n", +"// part(c)\n", +"P=m*cp*delT;\n", +"disp('MW',P*1e-3,'(c)power required to drive the compressor is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.13: Turbojet_Gas_Turbine_Engine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.13 Turbojet Gas Turbine Engine\n", +"\n", +"T1=223.15; // in Kelvin\n", +"n_C=0.75; // Compressor Efficiency\n", +"c1=85; // entry velocity in m/s\n", +"m=50; // mass flow rate of air in kg/s\n", +"R=287;\n", +"n_B=0.98; // Combustion chamber Efficiency\n", +"Qf=43*1e3; // Calorific Value of fuel in kJ/kg;\n", +"T03=1220; // Turbine inlet stagnation temp in Kelvin\n", +"n_T=0.8; // Turbine Efficiency\n", +"gamma=1.4; // Specific Heat Ratio\n", +"n_m=0.98; // Mechanical efficiency\n", +"sigma=0.5; // flight to jet speed ratio(u/ce)\n", +"n_N=0.98; // exhaust nozzle efficiency\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"u=886/3.6; // flight speed of a turbo prop aircraft in m/s\n", +"delT=200; // temperature rise through the compressor(T02-T01) in K\n", +"pi=.701; // Initial Pressure in bar\n", +"n_D=0.88; // inlet diffuser efficiency\n", +"a1=sqrt(gamma*R*T1);\n", +"M1=u/a1; // Mach number at the compressor inlet\n", +"T1_01=0.881; // (T1/T01)from isentropic flow gas tables at M1 and gamma values\n", +"T01=T1/T1_01;\n", +"T1=T01-(0.5*(c1^2)/(cp*1e3));\n", +"\n", +"// part(a) compressor pressure ratio\n", +"T02s=T01+(delT*n_C);\n", +"r_oc=(T02s/T01)^(gamma/(gamma-1)); //compressor pressure ratio(p02/p01)\n", +"disp(r_oc,'(a)compressor pressure ratio is')\n", +"\n", +"// part(b)\n", +"T02=T01+delT;\n", +"f=((cp*T03)-(cp*T02))/((Qf*n_B)-(cp*T03)); // f=(ma/mf);energy balance in the combustion chamber \n", +"disp(1/f,'(b)Air-Fuel Ratio is')\n", +"\n", +"// part(c) turbine pressure ratio\n", +"// turbine power input P_T=n_m*(ma+mf)*cp*(T03-T01)\n", +"// power input to the compressor P_C=ma*cp*(T02-T01)\n", +"T04s=T03-(delT/(n_m*n_T*(1+f))); // from energy balance P_T=P_C\n", +"r_ot=(T03/T04s)^(gamma/(gamma-1)); //turbine pressure ratio(p03/p04)\n", +"disp(r_ot,'(c)turbine pressure ratio is')\n", +"\n", +"// part(d)exhaust nozzle pressure ratio\n", +"ce=u/sigma; // jet velocity at the exit of the exhaust nozzle\n", +"T04=T03-(delT/(n_m*(1+f)));\n", +"Te=T04-(0.5*(ce^2)/(cp*1e3));\n", +"Tes=T04-((T04-Te)/n_N);\n", +"r_N=(T04/Tes)^(gamma/(gamma-1)); //exhaust nozzle pressure ratio(p04/pe)\n", +"disp(r_N,'(d)exhaust nozzle pressure ratio is')\n", +"ae=sqrt(gamma*R*Te);\n", +"Me=ce/ae; // Mach number\n", +"disp(Me,'and the Mach Number is')\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.15: Impulse_Steam_Turbine_3000_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab code Exa 18.15 Impulse Steam Turbine 3000 rpm\n", +"\n", +"P=500; // Power Output in kW\n", +"u=100; // peripheral speed of the rotor blades in m/s\n", +"cy2=200; // whirl component of the absolute velocity at entry of the rotor\n", +"cy3=0; // whirl component of the absolute velocity at exit of the rotor\n", +"alpha2=65; // nozzle angle at exit\n", +"n_st=0.69; // isentropic stage efficiency\n", +"p2=8; // steam pressure at the exit of the first stage in bar\n", +"t2=200; // steam temperature at the exit of the first stage in degree C\n", +"N=3e3; // rotor Speed in RPM\n", +"\n", +"//part(a)Mean diameter of the stage\n", +"d=u*60/(%pi*N);\n", +"disp('m',d,'(a)Mean diameter of the stage is')\n", +"\n", +"// part(b)mass flow rate of the steam\n", +"w_st=2*(u^2)*1e-3; // specific work\n", +"m=P/w_st;\n", +"disp('kg/s',m,'(b)mass flow rate of the steam is')\n", +"\n", +"// part(c)isentropic enthalpy drop\n", +"delh_s=w_st/n_st;\n", +"disp('kJ/kg',delh_s,'(c)isentropic enthalpy drop is')\n", +"\n", +"// part(d)rotor blade angles\n", +"cx=cy2/(tand(alpha2));\n", +"beta3=atand(u/cx);\n", +"disp('degree',beta3,'(d)the rotor blade angles are beta2=beta3=')\n", +"\n", +"// part(e)blade height at the nozzle exit\n", +"v_s2=0.2608; // from steam tables at p2=8bar and t2=200 degree C\n", +"Q=m*v_s2;\n", +"h=Q/(cx*%pi*d);\n", +"disp('m',h,'(e)blade height at the nozzle exit is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.16: large_Centrifugal_pump_1000_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.16 large Centrifugal pump 1000rpm\n", +"\n", +"N=1e3; // rotor Speed in RPM\n", +"H=45; // height in m\n", +"ro=1e3;\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"n_o=0.75; // overall Efficiency of the drive\n", +"dr=2; // diameter ratio(d2/d1)\n", +"phi=0.35; // flow coefficient(cr2/u2)\n", +"Q=2.5; // discharge in m3/s\n", +"\n", +"//part(a)Power required to drive the pump\n", +"P=(ro*Q*g*H)/(n_o);\n", +"disp('kW',P*1e-3,'(a)Power required to drive the pump is')\n", +"\n", +"// part(b) impeller diameters at entry and exit\n", +"u2=sqrt(g*H);\n", +"w_p=u2^2;\n", +"d2=u2*60/(%pi*N);\n", +"disp('cm',d2*1e2,'(b)the impeller diameter at exit is')\n", +"d1=d2/2;\n", +"disp('cm',d1*1e2,'and the impeller diameter at entry is')\n", +"\n", +"//part(c) impeller width\n", +"c_r2=phi*u2;\n", +"b=Q/(c_r2*%pi*d2);\n", +"disp('cm',b*1e2,'(c)the impeller width is')\n", +"\n", +"// part(d)impeller blade angle at the entry\n", +"c_r1=Q/(b*%pi*d1);\n", +"u1=u2/dr;\n", +"beta1=atand(c_r1/u1);\n", +"disp('degree',beta1,'(d)the impeller blade angle at the entry beta1=')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.17: three_stage_steam_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.17 three stage steam turbine\n", +"\n", +"t1=250; // Initial Temperature in degree C\n", +"n_T=0.75; // overall Efficiency of the turbine\n", +"p1=10; //Initial Pressure in bar\n", +"n_m=0.98; // Mechanical Efficiency\n", +"m=5;\n", +"N=1e3; // rotor Speed in RPM\n", +"H=45; // height in m\n", +"ro=1e3;\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"Q=2.5; // discharge in m3/s\n", +"\n", +"P=(ro*Q*g*H)/(n_T);\n", +"delh_T=P/(m*n_m*1e3);\n", +"delh_st=delh_T/3;\n", +"delh1_4ss=delh_T/n_T;\n", +"\n", +"//part(a)steam conditions\n", +"h1=2940; // from Mollier diagram\n", +"disp('(a)steam conditions at the turbine exit are:')\n", +"h_4ss=h1-delh1_4ss;\n", +"p4=1.2; // in bar\n", +"disp('bar',p4,'pressure:')\n", +"h4=2640;\n", +"x4=0.98;\n", +"t4=104.8; // in degree C\n", +"disp('degree C',t4,'temperature:')\n", +"disp(x4,'the dryness fraction is:')\n", +"\n", +"// part(b)stage Efficiencies\n", +"h2=h1-delh_st;\n", +"p2=5;\n", +"h3=h2-delh_st;\n", +"p3=2.5;\n", +"h4=h3-delh_st;\n", +"h2s=2795;\n", +"h3s=2705;\n", +"h4s=2605;\n", +"n_st1=delh_st/(h1-h2s);\n", +"n_st2=delh_st/(h2-h3s);\n", +"n_st3=delh_st/(h3-h4s);\n", +"disp ('%',n_st1*100,'(b)Efficiency of the first stage is')\n", +"disp ('%',n_st2*100,'Efficiency of the second stage is')\n", +"disp ('%',n_st3*100,'Efficiency of the third stage is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.18: Ljungstrom_turbine_3600_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.18 Ljungstrom turbine 3600 rpm\n", +"\n", +"d1=0.92; // inner diameter of the impeller in m\n", +"d2=1; // outer diameter of the impeller in m\n", +"N=3.6e3; // rotor Speed in RPM\n", +"aplha_1=20; // blade exit angle in degree\n", +"p2=0.1; //exit Pressure of steam in bar\n", +"x2=0.88; // dryness fraction at exit\n", +"n_st=0.83; // stage Efficiency\n", +"u1=%pi*d1*N/60;\n", +"u2=%pi*d2*N/60;\n", +"\n", +"//part(a)power developed\n", +"sigma=cosd(aplha_1)/2;\n", +"w_st=u1^2+u2^2;\n", +"disp('kW/(kg/s)',w_st*1e-3,'(a)power developed per unit flow rate is')\n", +"\n", +"//part(b) isentropic enthalpy drop\n", +"delh_s=w_st/n_st;\n", +"disp('kJ/kg',delh_s*1e-3,'(b)isentropic enthalpy drop is')\n", +"\n", +"// part(c)steam conditions at entry\n", +"disp('(c)steam conditions at entry are:')\n", +"p1=0.18; // in bar\n", +"disp('bar',p1,'pressure:')\n", +"x1=0.9;\n", +"disp(x1,'the dryness fraction is:')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.19: blower_type_wind_tunnel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.19 blower type wind tunnel \n", +"\n", +"T01=310; // in Kelvin\n", +"p01=1.013; // Initial Pressure in bar\n", +"n_n=0.96; // nozzle efficiency\n", +"n_c=0.78; // compressor efficiency\n", +"Ma(1)=0.5;\n", +"Ma(2)=0.9;\n", +"pi(1)=0.837; // from isentropic flow gas tables\n", +"pi(2)=0.575;\n", +"gamma=1.4; // Specific Heat Ratio\n", +"R=287;\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"\n", +"for i=1:2\n", +"printf('when Ma=%f',Ma(i))\n", +"//part(a)\n", +"Ms=((n_n/(Ma(i)^2))-(((gamma-1)/2)*(1-n_n)))^(-1/2);\n", +"disp(Ms,'(a)Mach number for isentropic flow is')\n", +"\n", +"// part(b)\n", +"p0e=1;\n", +"p_r0(i)=p0e/pi(i);\n", +"disp(p_r0(i),'(b)pressure ratio of the compressor is')\n", +"\n", +"// part(c)\n", +"delT0e_0i=((p_r0(i)^((gamma-1)/gamma))-1)/n_c;\n", +"T0e=T01+(T01*delT0e_0i);\n", +"delT0e_t=n_n*(1-(p_r0(i)^((1-gamma)/gamma)))*T0e;\n", +"T_t=T0e-delT0e_t;\n", +"disp('K',T_t,'(c)the test section temperature is')\n", +"a_t=sqrt(gamma*R*T_t);\n", +"c_t=Ma(i)*a_t;\n", +"disp('m/s',c_t,'and the test section velocity is')\n", +"\n", +"// part(d)\n", +"ro_t=p01*1e5/(R*T_t);\n", +"A_t=0.17*0.15;\n", +"m=ro_t*A_t*c_t;\n", +"disp('kg/s',m,'(d)mass flow rate is')\n", +"\n", +"// part(e)\n", +"P(1)=m*cp*(T0e-T01);\n", +"P(2)=m*cp*(T_t-T01);\n", +"disp('kW',P(i),'(e)power required for the compressor is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.1: Gas_Turbine_nozzle_row.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.1 Gas Turbine nozzle row \n", +"\n", +"T1=600; // Entry Temperature of the gas in Kelvin\n", +"p1=10; // Inlet Pressure in bar\n", +"gamma_g=1.3;\n", +"delT=32; // Temperature drop of the gas(T1-T2) in K\n", +"cp_g=1.23*1e3; // Specific Heat of gas at Constant Pressure in kJ/(kgK)\n", +"pr1_2=1.3; // pressure ratio(p1/p2)\n", +"T2s=T1/(pr1_2^((gamma_g-1)/gamma_g));\n", +"delTs=T1-T2s;\n", +"\n", +"// part(a) nozzle efficiency\n", +"n_N=delT/delTs;\n", +"disp('%',n_N*100,'(a) nozzle efficiency is')\n", +"\n", +"// part(b)\n", +"disp('(b)(i)for ideal flow:')\n", +"p2=p1/pr1_2;\n", +"h_01=cp_g*T1;\n", +"h2s=cp_g*T2s;\n", +"c_2s=sqrt((h_01-h2s)/0.5);\n", +"disp('m/s',c_2s,'the nozzle exit velocity is')\n", +"R_g=cp_g*((gamma_g-1)/gamma_g);\n", +"M_2s=c_2s/(sqrt(gamma_g*R_g*T2s));\n", +"disp(M_2s,'and the Mach number is')\n", +"disp('(b)(ii)for actual flow:')\n", +"T2=T1-delT;\n", +"a2=sqrt(gamma_g*R_g*T2);\n", +"c_2=sqrt((cp_g*delT)/0.5);\n", +"disp('m/s',c_2,'the nozzle exit velocity is')\n", +"M2=c_2/a2;\n", +"disp(M2,'and the Mach number is')\n", +"\n", +"// part(c) stagnation pressure loss across the nozzle\n", +"p01=p1;\n", +"p02=p2/0.79; // from isentropic gas tables p2/p02=0.79 at gamma=1.3 and M2=0.613\n", +"delp0=p01-p02;\n", +"disp('bar',delp0,'(c)the stagnation pressure loss across the nozzle is')\n", +"\n", +"// part(d) nozzle efficiency based on stagnation pressure loss\n", +"delp=p1-p2;\n", +"n_N_a=1-(delp0/delp);\n", +"disp('%',n_N_a*100,'(d)the nozzle efficiency based on stagnation pressure loss is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.20: Calculation_on_an_axial_turbine_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.20 Calculation on an axial turbine cascade\n", +"\n", +"beta1=35; // blade angle at entry\n", +"beta2=55; // blade angle at exit\n", +"i(1)=5; // incidence\n", +"i(2)=10;\n", +"i(3)=15;\n", +"i(4)=20;\n", +"delta=2.5; // deviation\n", +"alpha2=beta2-delta; // air angle at exit\n", +"a_r=2.5; // aspect ratio(h/l)\n", +"\n", +"n=4;\n", +"for m=1:n\n", +"//part(a)\n", +"printf('\nfor incidence=%d\n',i(m))\n", +"alpha1=beta1+i(m); // air angle at entry\n", +"ep=alpha1+alpha2; // deflection angle\n", +"disp('degree',ep,'(a)flow deflection is')\n", +"p_c=0.505; //(s/l)\n", +"\n", +"//part(b) loss coefficient from Hawthorne relations\n", +"\n", +"z_p=0.025*(1+((ep/90)^2)); // Hawthorne's relation\n", +"disp (z_p,'(b)the profile loss coefficient from Hawthorne relation is')\n", +"z=(1+(3.2/a_r))*z_p; // the total cascade loss coefficient\n", +"disp (z,'and the total loss coefficient is')\n", +"Y=z; \n", +"\n", +"// part(c)drag and lift coefficients\n", +"alpham=atand((0.5*(tand(alpha2)-tand(alpha1))));\n", +"C_D=p_c*Y*((cosd(alpham)^3)/(cosd(alpha2)^2));\n", +"disp (C_D,'(c)the drag coefficient is')\n", +"\n", +"C_L=(2*p_c*(tand(alpha1)+tand(alpha2))*cosd(alpham))+(C_D*tand(alpham));\n", +"disp (C_L,'and the Lift coefficient is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.21: low_reaction_turbine_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.21 low reaction turbine stage\n", +"\n", +"Beta2=35; // rotor blade air angle in degree\n", +"alpha1=0; // fixed blade air angle in degree\n", +"alpha2=65;\n", +"beta3=52.5;\n", +"I(1)=0; // incidence angle\n", +"I(2)=5;\n", +"I(3)=10;\n", +"I(4)=15;\n", +"I(5)=20;\n", +"a_r=2.5; // aspect ratio(h/l)\n", +"\n", +"for i=1:5\n", +"disp('degree',I(i),'when incidence=')\n", +"beta2(i)=Beta2+I(i); // beta2 varies with incidence\n", +"\n", +"//part(a)\n", +"phi=cosd(alpha2)*cosd(beta2(i))/(sind(alpha2-beta2(i)));\n", +"ep=alpha1+alpha2; // deflection angle\n", +"disp(phi,'(a)flow coefficient is')\n", +"p_c=0.505; //pitch-chord ratio(s/l)\n", +"\n", +"//part(b)blade to gas speed ratio\n", +"sigma=sind(alpha2-beta2(i))/(cosd(beta2(i)));\n", +"disp(sigma,'(b)blade to gas speed ratio is')\n", +"z_N=2.28*0.025*(1+((ep/90)^2)); // Hawthorne's relation\n", +"\n", +"// part(c)degree of reaction\n", +"R=0.5*phi*(tand(beta3)-tand(beta2(i)));\n", +"disp('%',R*1e2,'(c)the degree of reaction is')\n", +"\n", +"// part(d)total-to-total efficiency\n", +"e_R=beta2(i)+beta3; // Rotor deflection angle\n", +"zeeta_p_R=0.025*(1+((e_R/90)^2)); // profile loss coefficient for rotor\n", +"zeeta_R=(1+(3.2/a_r))*zeeta_p_R; // total loss coefficient for rotor\n", +"a=(zeeta_R*(secd(beta3)^2))+(z_N*(secd(alpha2)^2));\n", +"b=phi*(tand(alpha2)+tand(beta3))-1;\n", +"n_tt=inv(1+(0.5*(phi^2)*(a/b)));\n", +"disp('%',n_tt*1e2,'(d)total-to-total efficiency is')\n", +"\n", +"end\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.22: Isentropic_or_Stage_Terminal_Velocity_for_Turbines.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.22 Isentropic or Stage Terminal Velocity for Turbines \n", +"\n", +"T01=1273; // in Kelvin\n", +"funcprot(0);\n", +"p01=5; // Initial Pressure in bar\n", +"p02=3.5; // exit gas Pressure in bar\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"gamma=1.4; // Specific Heat Ratio\n", +"m=28; // mass flow rate of the gas in kg/s\n", +"n_tt=0.84; // stage efficiency\n", +"shi=1.7; // stage loading coefficient\n", +"pr_0=p01/p02;\n", +"delh01_03ss=cp*T01*(1-(pr_0^((1-gamma)/gamma)));\n", +"\n", +"//part(a)stage terminal velocity\n", +"c0=sqrt(2*delh01_03ss*1e3);\n", +"disp('m/s',c0,'(a)stage terminal velocity is')\n", +"\n", +"// part(b)isentropic blade to gas speed ratio\n", +"sigma_s=sqrt(0.5*n_tt/shi);\n", +"disp(sigma_s,'(b)the isentropic blade to gas speed ratio is')\n", +"\n", +"//part(c) peripheral speed of the rotor\n", +"u=sigma_s*c0;\n", +"disp('m/s',u,'(c)peripheral speed of the rotor is')\n", +"\n", +"//part(d) the power developed\n", +"P=m*n_tt*delh01_03ss;\n", +"disp('MW',P*1e-3,'(d) the power developed is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.23: axial_compressor_stage_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.23 axial compressor stage efficiency \n", +"\n", +"R=0.5; // Degree of reaction\n", +"n_R=0.849; // efficiency of rotor blade row\n", +"n_D=0.849; // efficiency of diffuser blade row\n", +"n_st=R*n_R+(1-R)*n_D;\n", +"disp('%',n_st*1e2,'the value of stage efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.24: Calculation_on_an_axial_compressor_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.24 Calculation on an axial compressor cascade \n", +"\n", +"beta1=51;\n", +"beta2=9;\n", +"alpha_1=7; // air angle at rotor and stator exit\n", +"u=100; // test section velocity of air in m/s\n", +"cx=u/(tand(alpha_1)+tand(beta1));\n", +"w1=cx/cosd(beta1);\n", +"alpha2=atand(tand(alpha_1)+tand(beta1)-tand(beta2))\n", +"c2=cx/cosd(alpha2);\n", +"Y_D=0.0367; // loss coefficient for diffuser blade row\n", +"Y_R=0.0393; // loss coefficient for rotor blade row\n", +"z_R=Y_R*((w1/u)^2);\n", +"z_D=Y_D*((c2/u)^2);\n", +"phi=cx/u;\n", +"n_st=1-(0.5*phi*(z_D*(secd(alpha2)^2)+z_R*(secd(beta1)^2))/(tand(beta1)-tand(beta2)));\n", +"disp('%',n_st*1e2,'the value of stage efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.25: Calculation_on_two_stage_axial_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.25 Calculation on two stage axial compressor \n", +"\n", +"T01=310; // in Kelvin\n", +"funcprot(0);\n", +"gamma=1.4;\n", +"p01=1.02; // Initial Pressure in bar\n", +"pr_o=2;\n", +"pr_o1=1.5;\n", +"N=7.2e3; // rotor Speed in RPM\n", +"d=65/100; // Mean Blade ring diameter in m\n", +"h=10/100; // blade height at entry in m\n", +"n_p=0.9; // polytropic efficiency\n", +"wdf=0.87; // work-done factor\n", +"m=25; // in kg/s \n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"R=287;\n", +"T01(1)=T01;\n", +"// part(a) stage pressure ratio\n", +"pr_o2=pr_o/pr_o1;\n", +"disp(pr_o2,'(a)pressure ratio developed by the 2nd stage is')\n", +"\n", +"//part(b) stage efficiency\n", +"n=(gamma-1)/gamma;\n", +"n_st1=((pr_o1^n)-1)/((pr_o1^(n/n_p))-1);\n", +"disp('%',n_st1*1e2,'(b)stage efficiency for the stage 1 is')\n", +"n_st2=((pr_o2^n)-1)/((pr_o2^(n/n_p))-1);\n", +"disp('%',n_st2*1e2,'and stage efficiency for the stage 2 is')\n", +"// part(c)power required to drive the compressor\n", +"T02=T01*(pr_o1^((gamma-1)/gamma));\n", +"P1=m*cp*(T02-T01)/n_st1;\n", +"disp('kW',P1,'(c) power required for the 1st stage is')\n", +"T02s=T01+(T01*(pr_o1^((gamma-1)/gamma)-1)/n_st1);\n", +"P2=m*cp*T02s*(pr_o2^((gamma-1)/gamma)-1)/n_st2;\n", +"disp('kW',P2,'and power required for the 2nd stage is')\n", +"\n", +"\n", +"\n", +"// part(d) air angles of the rotors and stators\n", +"A1=%pi*d*h;\n", +"ro_01=(p01*1e5)/(R*T01);\n", +"cx=m/(ro_01*A1);\n", +" T1=T01-((cx^2)/(2*cp*1e3));\n", +" p1=p01*((T1/T01)^(1/((gamma-1)/gamma)));\n", +"ro1=(p1*1e5)/(R*T1);\n", +"cx_new=m/(ro1*A1);\n", +"c1=cx_new;\n", +"disp('for first stage')\n", +"u=%pi*d*N/60;\n", +"beta1=atand(u/c1);\n", +"disp('degree',beta1,'beta1=')\n", +"wst1=cp*(T02-T01)*1e3/n_st1;\n", +"cy2=wst1/(wdf*u);\n", +"alpha2=atand(cy2/cx_new);\n", +"disp('degree',alpha2,'alpha2=')\n", +"beta2=atand((u/cx_new)-tand(alpha2));\n", +"disp('degree',beta2,'beta2=')\n", +"R=cx_new*(tand(beta1)+tand(beta2))*100/(2*u);\n", +"disp('%',R,'degree of reaction for the first stage is')\n", +"\n", +"T01_II=T02s;\n", +"disp('for second stage')\n", +"T02_II=T01_II*(pr_o2^((gamma-1)/gamma));\n", +"wst2=cp*1e3*(T02_II-T01_II)/n_st2;\n", +"alpha1s=beta2;\n", +"cy1s=cx_new*tand(alpha1s);\n", +"cy2s=(cy1s)+(wst2/(wdf*u));\n", +"alpha2s=atand(cy2s/cx_new);\n", +"disp('degree',alpha2s,'alpha2s=')\n", +"beta1s=atand((u-cy1s)/cx_new);\n", +"disp('degree',beta1s,'beta1s=')\n", +"beta2s=atand((u-cy2s)/cx_new);\n", +"disp('degree',beta2s,'beta2s=')\n", +"R_II=cx_new*(tand(beta1s)+tand(beta2s))*100/(2*u);\n", +"disp('%',R_II,'Degree of Reaction for the second stage is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.26: Calculation_on_an_axial_compressor_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.24 Calculation on an axial compressor cascade \n", +"\n", +"R=0.5906; // Degree of reaction\n", +"beta1=66;\n", +"beta2=22;\n", +"alpha2=61;\n", +"p_R=0.865; // pitch-chord ratio(s/l) for rotor\n", +"p_S=0.963; // pitch-chord ratio(s/l) for stator\n", +"alpha_3=beta2; // air angle at rotor and stator exit\n", +"u=100; // test section velocity of air in m/s\n", +"Y_D=0.077; // profile loss coefficient for stator blade row\n", +"Y_R=0.08; // loss coefficient for rotor blade row\n", +"beta_m=atand(0.5*(tand(beta1)+tand(beta2)));\n", +"C_D_R=p_R*Y_R*(cosd(beta_m)^3)/(cosd(beta1)^2);\n", +"C_L_R=(2*p_R*(tand(beta1)-tand(beta2))*cosd(beta_m))-(C_D_R*tand(beta_m));\n", +"n_R=1-(2*C_D_R/(C_L_R*sind(2*beta_m)));\n", +"disp('%',n_R*1e2,'the value of rotor cascade efficiency is')\n", +"\n", +"alpham=atand(0.5*(tand(alpha2)+tand(alpha_3)));\n", +"C_D_S=p_S*Y_D*(cosd(alpham)^3)/(cosd(alpha2)^2);\n", +"C_L_S=(2*p_S*(tand(alpha2)-tand(alpha_3))*cosd(alpham))-(C_D_S*tand(alpham));\n", +"n_D=1-(2*C_D_S/(C_L_S*sind(2*alpham)));\n", +"disp('%',n_D*1e2,'the value of diffuser cascade efficiency is')\n", +"\n", +"n_st=R*n_R+(1-R)*n_D;\n", +"disp('%',n_st*1e2,'the value of stage efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.27: Isentropic_Flow_Centrifugal_Air_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.27 Isentropic Flow-centrifugal Air compressor \n", +"\n", +"T01=335; // in Kelvin\n", +"p01=1.02; // Initial Pressure in bar\n", +"beta1=61.4; // air angle at the inlet of axial inducer blades\n", +"gamma=1.4;\n", +"d1=0.175; // Mean Blade ring diameter at entry\n", +"d2=0.5; // impeller diameter at exit\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"A1=0.0412; // Area of cross section at the impeller inlet\n", +"R=287;\n", +"\n", +"N(1)=5700; // rotor Speed in RPM\n", +"N(2)=6200;\n", +"N(3)=6700;\n", +"N(4)=7200;\n", +"for i=1:4\n", +"printf('\n for N=%d rpm\n\n',N(i))\n", +"u1=%pi*d1*N(i)/60;\n", +"u2=%pi*d2*N(i)/60;\n", +"c1=u1*tand(beta1);\n", +"T1=T01-((c1^2)/(2*cp));\n", +"p1=p01*((T1/T01)^(gamma/(gamma-1)));\n", +"ro1=(p1*1e5)/(R*T1);\n", +"pr0=((1+(u2^2/(cp*T01)))^(gamma/(gamma-1)));\n", +"disp(pr0,'(a)pressure ratio is')\n", +"m=ro1*A1*c1;\n", +"disp('kg/s',m,'(b)mass flow rate of air is')\n", +"T02=T01*(pr0^((gamma-1)/gamma));\n", +"P=m*cp*(T02-T01);\n", +"disp('kW',P*1e-3,'(c)Power required to drive the compressor P=')\n", +"end\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.28: centrifugal_Air_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.28 centrifugal Air compressor \n", +"T01=335; // in Kelvin\n", +"p01=1.02; // Initial Pressure in bar\n", +"beta1=61.4; // air angle at the inlet of axial inducer blades\n", +"gamma=1.4;\n", +"N=7200; // rotor Speed in RPM\n", +"d1=0.175; // Mean Blade ring diameter at entry\n", +"d2=0.5; // impeller diameter at exit\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"A1=0.0412; // Area of cross section at the impeller inlet\n", +"R=287;\n", +"b2=A1/(%pi*d2);\n", +"disp('cm',b2*1e2,'(a)width of the impeller at exit is')\n", +"u2=%pi*d2*N/60; \n", +"//for N=7200 rpm\n", +"p1=0.9444579; // from Ex18.27 \n", +"pr=1.4206988; //pressure ratio \n", +"m=5.0061078; //mass flow rate of air in kg/s \n", +"T02=370.35381;\n", +"ro2=1.1; //trial and error\n", +"cr2(1)=m/(A1*ro2);\n", +"n=2;\n", +"for i=1:n\n", +" c2(i)=sqrt(cr2(i)^2+(u2^2));\n", +" T2=T02-((c2(i)^2)/(2*cp));\n", +" p02=pr*p01;\n", +" p2=p02*((T2/T02)^(1/((gamma-1)/gamma)));\n", +"ro2=(p2*1e5)/(R*T2);\n", +"cr2(i+1)=m/(ro2*A1);\n", +"end\n", +"cr=cr2(3);\n", +"disp(p2/p1,'(b)the static pressure ratio is')\n", +"\n", +"//part(c)\n", +"alpha2=atand(cr/u2);\n", +"disp('degree',alpha2,'(c)the direction alpha2 of the absolute velocity vector(c2) or the diffuser angle at entry is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.29: Centrifugal_compressor_with_vaned_diffuser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.29 Centrifugal compressor with vaned diffuser \n", +"T01=310; // in Kelvin\n", +"p01=1.103; // Initial Pressure in bar\n", +"dh=0.10; // hub diameter in m\n", +"d2=0.55; // impeller diameter in m\n", +"c1=100; // Velocity of air at the entry of inducer\n", +"c3=c1; // Velocity of air at diffuser exit\n", +"shi=1.035; // power input factor\n", +"mu=0.9; // slip factor\n", +"m=7.5; // in kg/s\n", +"gamma=1.4;\n", +"N=15e3; // rotor Speed in RPM\n", +"disp('(a)for radially tipped blades')\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"n_tt=0.81; // total to total efficiency\n", +"T1=T01-((c1^2)/(2*cp));\n", +"p1=p01*((T1/T01)^(gamma/(gamma-1)));\n", +"ro1=(p1*1e5)/(R*T1);\n", +"A1=m/(ro1*c1);\n", +"dt=sqrt((A1*4/(%pi))+(dh^2));\n", +"disp('cm',dt*1e2,'(i)tip diameter of the inducer at entry is')\n", +"d1=0.5*(dt+dh); // Mean Blade ring diameter\n", +"u1=%pi*d1*N/60;\n", +"w1=sqrt((u1^2)+(c1^2));\n", +"a1=sqrt(gamma*R*T1);\n", +"M1_rel=w1/a1;\n", +"disp(M1_rel,'(ii)the Relative Mach number at inducer blade entry Mw1=')\n", +"u2=%pi*d2*N/60;\n", +"w_st=shi*mu*(u2^2);\n", +"T02=T01+(w_st/cp);\n", +"T02s=T01+(n_tt*(T02-T01));\n", +"pr_0=(T02s/T01)^(gamma/(gamma-1));\n", +"disp(pr_0,'(iii)stagnation pressure ratio developed is')\n", +"P=m*cp*(T02-T01);\n", +"disp('kW',P*1e-3,'(iv)the power required is')\n", +"disp('(b)for vaned diffuser')\n", +"c_theta2=mu*u2; // velocity of whirl(swirl component) at the impeller exit\n", +"// vaneless space between the impeller exit and the vaned diffuser entry=0.1*impeller radius\n", +"//r2s=r2*1.1;\n", +"// width of the casing after the impeller exit=1.4*impeller passage width\n", +"c_theta2s=c_theta2/(1.1*1.4);\n", +"cr2=c1;\n", +"cr2s=cr2/(1.1*1.4);\n", +"c2s=sqrt((cr2s^2)+(c_theta2s^2));\n", +"alpha2s=atand(cr2s/c_theta2s);\n", +"disp('degree',alpha2s,'(i)the direction of flow at the diffuser entry is alpha2s=')\n", +"T2s=T02-((c2s^2)/(2*cp));\n", +"a2s=sqrt(gamma*R*T2s);\n", +"M2s=c2s/a2s;\n", +"disp(M2s,'(ii)the Mach number at the diffuser entry is')\n", +"Ar=c2s/c3;\n", +"d3_2s=1.16; // d3/d2s from last trial given in the book\n", +"alpha3=acosd(cosd(alpha2s)/d3_2s);\n", +"Ar_v=d3_2s*sind(alpha3)/(sind(alpha2s));\n", +"disp(Ar_v,'(iii)Area ratio of the vaned diffuser is')\n", +"T03=T02;\n", +"T3=T03-((c3^2)/(2*cp));\n", +"pr3_1=(((T3*T01)/(T1*T03))^(gamma/(gamma-1)))*pr_0;\n", +"disp(pr3_1,'(iv)the static pressure ratio of the compressor is')\n", +"disp('comment: Calculations in the book are wrong in the beginning itself for p1. so the values slightly differs here only for part(a)')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.2: Steam_Turbine_nozzle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.2 Steam Turbine nozzle \n", +"\n", +"t1=550; // Entry Temperature in Kelvin\n", +"p1=170; // Inlet Pressure in bar\n", +"p2=120.7; // Exit Pressure in bar\n", +"d=1; // Mean Blade ring diameter in m\n", +"alpha_2=70; // nozzle angle in degree\n", +"gamma_g=1.3; // for superheated steam\n", +"R=0.5*1e3; // in J/kgK\n", +"m=280; // in kg/s\n", +"\n", +"// part(a) exit velocity c2 of steam\n", +"h1=3440; // from superheated steam tables at p1 and t1\n", +"h2=3350; // at p2\n", +"t2=503; // at p2 in degree C\n", +"v_s2=0.0268; // Specific Volume at p2 in m3/kg\n", +"c_2=sqrt((h1-h2)*1e3/0.5);\n", +"disp('m/s',c_2,'(a)the nozzle exit velocity is')\n", +"\n", +"// part(b)\n", +"T2=t2+273;\n", +"a2=sqrt(gamma_g*R*T2);\n", +"M2=c_2/a2;\n", +"disp(M2,'(b)and the exit Mach number is')\n", +"\n", +"// part(c)\n", +"cx=c_2*cosd(alpha_2);\n", +"h=m*v_s2/(%pi*cx*d);\n", +"disp('cm',h*1e2,'(c)nozzle blade height at exit is')\n", +"\n", +"T2s=0.87*(t1+273); // T2s/T1=0.87 from gas tables\n", +"p2s=0.546*p1; // p2s/p1=0.546 from gas tables\n", +"vs_s=0.031; // from steam tables\n", +"a_s=sqrt(gamma_g*R*T2s);\n", +"disp('m/s',a_s,'the corresponding nozzle exit velocity is')\n", +"cx_s=a_s*cosd(alpha_2);\n", +"m_max=cx_s*%pi*d*h/(vs_s);\n", +"disp('kg/s',m_max,'the maximum possible mass flow rate is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.30: Inward_Flow_Radial_Gas_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.30 Inward Flow Radial Gas turbine\n", +"\n", +"T1=873; // the gas entry temperature at nozzle in Kelvin\n", +"p1=4; // the gas entry pressure at nozzle in bar\n", +"n_T=0.85; // isentropic efficiency\n", +"d2=0.4; // rotor blade ring diameter at entry in m\n", +"d3=0.2; // rotor blade ring diameter at exit in m\n", +"pr_t=4; // static Pressure Ratio across the turbine(p3/p1)\n", +"pr_n=2; // static Pressure Ratio across the nozzles(p3/p1) \n", +"phi=0.3; // flow coefficient at impeller entry\n", +"gamma=1.4;\n", +"N=18e3; // rotor Speed in RPM\n", +"m=5; // mass flow rate of gas in kg/s\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"u2=%pi*d2*N/60;\n", +"u3=%pi*d3*N/60;\n", +"cr2=phi*u2;\n", +"// part(a)\n", +"T3ss=T1/(pr_t^((gamma-1)/gamma));\n", +"T3=T1-n_T*(T1-T3ss);\n", +"T2s=T1/(pr_n^((gamma-1)/gamma));\n", +"T2=T2s+(0.5*(T3-T3ss)); // half of the losses(T3-T3ss) occur in the nozzles\n", +"p2=p1/pr_n;\n", +"rho2=(p2*1e5)/(R*T2);\n", +"b2=m/(rho2*cr2*%pi*d2);\n", +"disp('cm',b2*1e2,'(a)axial width of the impeller blade passage at entry is')\n", +"alpha2=atand(cr2/u2);\n", +"disp('degree',alpha2,'(b)nozzle exit air angle is')\n", +"cx3=cr2;\n", +"beta3=atand(cx3/u3);\n", +"disp('degree',beta3,'(c)impeller exit air angle is')\n", +"c_theta3=0;\n", +"c_theta2=u2;\n", +"P=m*(u2*c_theta2-u3*c_theta3);\n", +"disp('kW',P*1e-3,'(d)power developed is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.31: Cantilever_Type_IFR_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.31 Cantilever Type IFR turbine\n", +"\n", +"P=150; // Power developed in kW\n", +"T01=960; // the gas entry temperature at nozzle in Kelvin\n", +"p01=3; // the gas entry pressure at nozzle in bar\n", +"beta2=45; // air angle at rotor blade entry (from radial direction)\n", +"beta3=65; // air angle at rotor blade exit (from radial direction)\n", +"d2=0.2; // rotor blade ring diameter at entry in m\n", +"d3=0.15; // rotor blade ring diameter at exit in m\n", +"gamma=1.4;\n", +"N=36e3; // rotor Speed in RPM\n", +"alpha_2=15; // air angle at nozzle exit(from tangential direction)\n", +"pr0=2.29; // total-to-static Pressure Ratio(p01/p3) \n", +"n_N=0.94; // Nozzle Efficiency \n", +"cp=1100; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=cp*((gamma-1)/gamma);\n", +"u2=%pi*d2*N/60;\n", +"u3=%pi*d3*N/60;\n", +"\n", +"// part(a) mass flow rate of the gas\n", +"cr2_theta2=tand(alpha_2); // cr2_theta2=cr2/c_theta2\n", +"c_theta2=u2/(1-cr2_theta2); // c_theta2=cr2*tan(alpha2)+u2\n", +"cr2=c_theta2*cr2_theta2;\n", +"cr3=cr2;\n", +"c_theta3=(cr3*tand(beta3))-u3;\n", +"w_st=(u2*c_theta2)+(u3*c_theta3);\n", +"m=P/(w_st*1e-3);\n", +"disp('kg/s',m,'(a)mass flow rate of the gas is')\n", +"\n", +"// part(b)rotor blade axial length at entry\n", +"c2=cr2/sind(alpha_2);\n", +"T2s=T01-((0.5*(c2^2))/(cp*n_N));\n", +"T2=T01-((T01-T2s)*n_N);\n", +"p_rn=(T2s/T01)^(gamma/(gamma-1));\n", +"p2=p01*p_rn;\n", +"rho2=(p2*1e5)/(R*T2);\n", +"b2=m/(rho2*cr2*%pi*d2);\n", +"disp('cm',b2*1e2,'(b)rotor blade axial length at entry is')\n", +"\n", +"// part(c)total-to-total turbine efficiency\n", +"T03ss=T01*(pr0^((1-gamma)/gamma));\n", +"n_T=P/(m*cp*1e-3*(T01-T03ss));\n", +"disp('%',n_T*1e2,'(c)total-to-total turbine efficiency is')\n", +"\n", +"//part(d)rotor blade length at exit\n", +"p03=p01/pr0;\n", +"T03=T01-(P/(m*cp*1e-3));\n", +"c3=sqrt((cr3^2)+(c_theta3^2));\n", +"T3=T03-((cr3^2)/(2*cp));\n", +"p3=p03*((T3/T03)^(gamma/(gamma-1)));\n", +"ro3=(p3*1e5)/(R*T3);\n", +"b3=m/(ro3*cr3*%pi*d3);\n", +"disp('cm',b3*1e2,'(d)rotor blade length at exit is')\n", +"\n", +"// part(e) degree of reaction\n", +"DOR=(T2-T3)/(T01-T03);\n", +"disp('%',DOR*1e2,'(e)degree of reaction is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.32: IFR_turbine_stage_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.32 IFR turbine stage efficiency\n", +"\n", +"// part(b)\n", +"R=0.48;\n", +"sigma_s=0.6;\n", +"n_n=0.92;\n", +"alpha_2=15; // air angle at nozzle exit(from tangential direction)\n", +"n_st=2*sigma_s*sqrt(n_n*(1-R))*cosd(alpha_2);\n", +"disp('%',n_st*100,'stage efficiency of the radial turbine is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.33: Vertical_Axis_Crossflow_Wind_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.33 Vertical Axis Crossflow Wind turbine\n", +"\n", +"c1=24/3.6; // wind speed in m/s\n", +"c2=30/3.6; // rotor speed in m/s\n", +"m1=25; // mass flow rate of air at wind side in kg/s\n", +"m2=31.25; // rotor air mass flow rate in kg/s\n", +"d1=3; // rotor outer diameter in m\n", +"d2=2; // rotor inner diameter in m\n", +"gamma=1.4;\n", +"alpha=37; // air angle at rotor entry(from tangential direction)\n", +"c(1)=c1;\n", +"c(2)=c2;\n", +"m(1)=m1;\n", +"m(2)=m2;\n", +"\n", +"for i=1:2\n", +"c_theta1=c(i)*cosd(alpha);\n", +"u1=c_theta1/2;\n", +"u2=u1*d2/d1;\n", +"disp('kmph',c(i)*3.6,'for speed=')\n", +"\n", +"// part(a)optimum rotor speed\n", +"N=60*u1/(%pi*d1);\n", +"disp('rpm',N,'(a)optimum rotor speed is')\n", +"\n", +"// part(b)blade to wind speed ratio\n", +"sigma=u1/c(i);\n", +"disp(sigma,'blade to wind speed ratio is')\n", +"\n", +"// part(c)hydraulic powers and efficiencies\n", +"Ph=m(i)*((2*(u1^2))+(u2^2));\n", +"disp('Watts',Ph,'(c)hydraulic power is')\n", +"n_h=((2*(u1^2))+(u2^2))/(0.5*(c(i)^2));\n", +"disp('%',n_h*1e2,'and hydraulic efficiency is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.34: Counter_Rotating_fan.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.34 Counter Rotating fan\n", +"\n", +"n=0.809; // combined efficiency of the fans\n", +"phi=0.245; // flow coefficient\n", +"A=0.212; // data from Ex14.1\n", +"d=0.45; // data from Ex14.1\n", +"u=22.62; // data from Ex14.1\n", +"cx=phi*u;\n", +"Q=1.175; // in m3/s\n", +"delp0_I=550.755; // data from Ex14.1\n", +"delp0_II=delp0_I;\n", +"delp0=delp0_I+delp0_II;\n", +"disp('mm W.G.',delp0/9.81,'(a)the overall pressure rise obtained is')\n", +"IP=Q*delp0; // power required for isentropic flow in Watts\n", +"P=IP/n;\n", +"disp('kW',P*1e-3,'(b)the Power required is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.35: Sirocco_Radial_fan_1440_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.35 Sirocco Radial fan 1440 rpm\n", +"\n", +"d2=0.4; // outer diameter of the impeller in m\n", +"d1=0.36; // inner diameter of the impeller in m\n", +"b=0.5; // axial length of the impeller in m\n", +"rho=1.25; // density of air in kg/m3\n", +"N=1440; // rotor Speed in RPM\n", +"P=50; // Power required in kW\n", +"\n", +"u1=%pi*d1*N/60;\n", +"u2=%pi*d2*N/60;\n", +" \n", +"beta1=atand(d2/d1);\n", +"disp('degree',beta1,'(a)the blade air angle at the impeller entry beta1=')\n", +"beta2=90-beta1;\n", +"disp('degree',beta2,'and the blade air angle at the impeller exit beta2=')\n", +"delp0=2*rho*(u2^2);\n", +"disp('mm W.G.',delp0/9.81,'(b)the stagnation pressure rise across the fan is') \n", +"cr1=u1*tand(beta1);\n", +"m=rho*cr1*%pi*d1*b;\n", +"disp('kg/s',m,'(c)mass flow rate of the air through the fan is')\n", +"c_theta1=0; // for zero inlet swirl\n", +"w_st=2*(u2^2);\n", +"IP=m*w_st/1000; // ideal power required to drive the fan in kW\n", +"n=IP/P;\n", +"disp('%',n*1e2,'(d)the Efficiency of the fan is') " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.37: Calculation_for_the_specific_speed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.37 Calculation for the specific speed\n", +"\n", +"//part(1)specific speed of Axial flow gas turbine\n", +"P1=0.5e3; // Gas Turbine Power Output in kW\n", +"N1=60; // Speed in RPS\n", +"omega1=%pi*2*N1;\n", +"ro1=2;\n", +"delh_1=30; // change of enthalpy in kJ\n", +"NS_1=omega1*sqrt(P1*10e2/ro1)*((delh_1*1e3)^(-5/4));\n", +"disp(NS_1,'1.the specific speed of Axial flow gas turbine is')\n", +"\n", +"//part(2)specific speed of IFR gas turbine\n", +"P2=0.75e3; // Gas Turbine Power Output in kW\n", +"N2=300; // Speed in RPS\n", +"omega2=%pi*2*N2;\n", +"ro2=1;\n", +"delh_2=250; // change of enthalpy in kJ\n", +"NS_2=omega2*sqrt(P2*10e2/ro2)*((delh_2*1e3)^(-5/4));\n", +"disp(NS_2,'2.the specific speed of IFR gas turbine is') \n", +"\n", +"// part(3)the specific speed of an axial compressor\n", +"N_c=120; // Speed in RPS\n", +"omega_c=%pi*2*N_c;\n", +"Q_c=25; // flow rate in m3/s\n", +"delh_3=40; // change of enthalpy in kJ\n", +"NS_c=omega_c*sqrt(Q_c)*((delh_3*1e3)^(-3/4));\n", +"disp(NS_c,'3.the specific speed of an axial compressor is')\n", +"\n", +"// part(4)the specific speed of a centrifugal compressor\n", +"Q=5; // flow rate in m3/s\n", +"delh_4=35; // change of enthalpy in kJ\n", +"NS_4=omega_c*sqrt(Q)*((delh_4*1e3)^(-3/4));\n", +"disp(NS_4,'4.the specific speed of a centrifugal compressor is')\n", +"\n", +"// part(5)the specific speed of an axial fan\n", +"N5=22; // Speed in RPS\n", +"omega_5=2*%pi*N5;\n", +"Q_5=3.5; // flow rate in m3/s\n", +"rho=1.25; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"H1=55/rho; // head in m\n", +"NS_5=omega_5*sqrt(Q_5)*((g*H1)^(-3/4));\n", +"disp(NS_5,'5.the dimensionless specific speed of an axial fan is')\n", +"\n", +"// part(6)the specific speed of a Radial fan\n", +"N6=20; // Speed in RPS\n", +"omega_6=2*%pi*N6;\n", +"Q_6=1.4; // flow rate in m3/s\n", +"\n", +"H2=52/rho; // head in m\n", +"NS_6=omega_6*sqrt(Q_6)*((g*H2)^(-3/4));\n", +"disp(NS_6,'6.the dimensionless specific speed of a Radial fan is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.38: Kaplan_turbine_70_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.38 Kaplan turbine 70 rpm\n", +"\n", +"//part(a)flow rate and specific speed \n", +"P=8e3; // Gas Power Output in kW\n", +"N=70; // Speed in RPM\n", +"H=10; // net head in m\n", +"n_m=0.85; // efficiency\n", +"omega=%pi*2*N/60;\n", +"NS=omega*sqrt(P*10e2)*(H^(-5/4))/549.016;\n", +"disp(NS,'(a)the specific speed of turbine is')\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"Q=P*1e3/(n_m*rho*g*H);\n", +"disp('m3/s',Q,'and the flow rate is')\n", +"\n", +"// part(b) determining the speed, flow rate and power for the model\n", +"Dp_m=12; // Dp_m=Dp/Dm\n", +"Np=N; // Speed for prototype\n", +"Hm=3; // head of the model\n", +"Hp=H; // head for prototype\n", +"Nm=Np*Dp_m*sqrt(Hm/Hp);\n", +"disp('rpm',Nm,'(b)speed for the model is')\n", +"Dm_p=1/Dp_m;\n", +"Qp=Q;\n", +"Qm=(Dm_p^2)*sqrt(Hm/Hp)*Qp;\n", +"disp('m3/s',Qm,'the flow rate for model is')\n", +"Pm=n_m*rho*g*Qm*Hm;\n", +"disp('kW',Pm*1e-3,'the power for the model is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.39: Calculation_for_Pelton_Wheel_prototype.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.39 Calculation for the Pelton Wheel\n", +"\n", +"Nm=102; // Speed for the model in RPM\n", +"Hm=30; // net head for the model in m\n", +"n_m=1; // Assuming efficiency\n", +"Qm=0.345; // discharge in m3/s\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"omega_m=%pi*2*Nm/60;\n", +"Pm=n_m*rho*g*Qm*Hm;\n", +"NS=omega_m*sqrt(Pm)*(Hm^(-5/4))/549.016;\n", +"disp(NS,'the specific speed of turbine is')\n", +"\n", +"// determining the speed, flow rate and power for the prototype\n", +"Hp=1500; // head for prototype\n", +"Pp=((Hp/Hm)^(3/2))*Pm;\n", +"disp('MW',Pp*1e-6,'the power for the prototype is')\n", +"omega_p=NS*549.016*(Hp^(5/4))/(sqrt(Pp));\n", +"Np=omega_p*60/(2*%pi);\n", +"disp('rpm',Np,'speed for the prototype is')\n", +"Qp=sqrt(Hp/Hm)*Qm;\n", +"disp('m3/s',Qp,'the flow rate for prototype is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.3: Irreversible_flow_in_nozzles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.3 Irreversible flow in nozzles\n", +"pr=0.843; // pr=p/p0\n", +"n_n=0.95; // nozzle efficiency\n", +"gamma=1.4;\n", +"Ms=0.5; // from gas tables for gammma and pr value\n", +"Ma=sqrt((2/(gamma-1))*(n_n/(1-n_n+(2/((gamma-1)*(Ms^2))))));\n", +"disp(Ma,'actual value of the Mach number is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.40: Francis_turbine_910_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.40 Calculation for the Francis turbine\n", +"\n", +"// part(a) determining the speed, specific speed and power for the model\n", +"Qm=0.148; // discharge in m3/s\n", +"N=910; // Speed in RPM\n", +"Hm=25; // net head in m\n", +"n=0.9; // efficiency\n", +"omega=%pi*2*N/60;\n", +"NS=omega*sqrt(Qm)*(Hm^(-3/4))*0.1804;\n", +"disp(NS,'(a)the specific speed of turbine is')\n", +"Nu=N/(sqrt(Hm));\n", +"disp('rpm',Nu,'unit speed for the model is')\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"Pm=rho*g*Qm*Hm;\n", +"disp('kW',Pm*1e-3,'the power for the model is')\n", +"\n", +"// part(b)determining the speed, flow rate and power for the prototype\n", +"Hp=250; // head for prototype\n", +"Dp_m=6; // Dp_m=Dp/Dm\n", +"Qp=sqrt(Hp/Hm)*Qm*(Dp_m^2);\n", +"disp('m3/s',Qp,'(b)the flow rate for prototype is')\n", +"Pp=rho*g*Qp*Hp*n;\n", +"disp('MW',Pp*1e-6,'the power for the prototype is')\n", +"omega_p=NS*(Hp^(3/4))/(0.1804*sqrt(Qp));\n", +"Np=omega_p*60/(2*%pi);\n", +"disp('rpm',Np,'speed for the prototype is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.41: Calculation_for_the_Pelton_Wheel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.41 Calculation for the Pelton Wheel\n", +"NS=0.1; //specific speed\n", +"H1=1000; // net head for the model in m\n", +"Q1=1; // discharge in m3/s\n", +"omega1=NS*(H1^(3/4))/(sqrt(Q1)*0.1804);\n", +"N1=omega1*60/(2*%pi);\n", +"disp('rpm',N1,'speed of the rotation is')\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"P1=rho*g*Q1*H1;\n", +"\n", +"// determining the speed, flow rate and power for the prototype\n", +"H2=100; // head for prototype\n", +"N2=N1*sqrt(H2/H1);\n", +"disp('rpm',N2,'speed for the prototype is')\n", +"Q2=sqrt(H2/H1)*Q1;\n", +"disp('m3/s',Q2,'the discharge for the prototype is')\n", +"P2=((H2/H1)^(3/2))*P1;\n", +"disp('MW',P2*1e-6,'the power for the prototype is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.42: Calculation_for_Tidal_Power_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.42 Calculation for Tidal Power Plant\n", +"\n", +"T=50e6; // capacity of basin in cubic meters of sea water\n", +"N=60; // Speed for the model in RPM\n", +"NS=3; //specific speed\n", +"H=9.8; // net head for the model in m\n", +"n_o=0.78; // Assuming efficiency\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"n(1)=5; // number of turbines\n", +"n(2)=10;\n", +"omega=%pi*2*N/60;\n", +"\n", +"P=(NS^2)*(H^(5/2))*(549.016^2)/(omega^2);\n", +"disp('MW',P*1e-6,'(a)the power for the turbines is')\n", +"Q=P/(n_o*rho*g*H); // discharge in m3/s\n", +"disp('m3/s',Q,'(b)the discharge rate for the turbines is')\n", +"disp('(c)')\n", +"for i=1:2\n", +" disp(n(i),'when number of turbines are:')\n", +" t=T/(n(i)*Q*3600);\n", +"disp('hours',t,'duration of operation is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.43: Francis_turbine_250_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.43 Francis turbine 250 rpm\n", +"\n", +"NS=0.4; //specific speed\n", +"N=250; // Speed in RPM\n", +"H=75; // net head in m\n", +"beta3=25; // exit angle of the runner blades\n", +"n_o=0.81; // overall efficiency\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"rho=1000; // density in kg/m3\n", +"// part(a)\n", +"u2=0.6*sqrt(2*g*H);\n", +"cr2=0.21*sqrt(2*g*H);\n", +"omega=%pi*2*N/60;\n", +"Q=(NS^2)*(H^(3/2))/((0.1804^2)*(omega^2));\n", +"disp('m3/s',Q,'(a)the discharge rate for the turbine is')\n", +"// part(b)\n", +"d2=u2*60/(%pi*N);\n", +"disp('m',d2,'(b)outer diameter of the runner blade ring is')\n", +"cr3=cr2;\n", +"cx3=cr3;\n", +"//Euler work,w_ET=u2*c_theta2\n", +"c_theta2=((g*H)-(0.5*(cx3^2)))/u2;\n", +"u3=cx3/(tand(beta3));\n", +"d3=u3*60/(%pi*N);\n", +"disp('m',d3,'and inner diameter of the runner blade ring is')\n", +"// part(c)\n", +"alpha2=atand(cr2/c_theta2);\n", +"disp('degree',alpha2,'(c)the inlet guide vane exit angle is')\n", +"beta2=atand(cr2/(c_theta2-u2));\n", +"disp('degree',beta2,'and inlet angle of the runner blades is beta2= ')\n", +"// part(d)\n", +"n_h=(u2*c_theta2)/(g*H);\n", +"disp('%',n_h*1e2,'(d)the hydraulic efficiency is')\n", +"// part(e)\n", +"P=n_o*rho*g*Q*H;\n", +"disp('MW',P*1e-6,'(e)the output power is')\n", +"disp('comment: the calculation for c_theta2 is done wrongly in the book. hence the values of alpha2,beta2, n_h differs from the book.')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.44: Pelton_Wheel_360_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.44 Pelton Wheel 360 rpm\n", +"\n", +"d=2; // mean diameter in m\n", +"N=360; // Speed in RPM\n", +"theta=150; //deflection angle of water jet in degree\n", +"H=140; // net head for the model in m\n", +"q=45000; // discharge in litres/min\n", +"Q=q*1e-3/60; // in m3/s\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"// part(a)\n", +"u=%pi*d*N/60;\n", +"c2=sqrt(2*g*H);\n", +"sigma=u/c2;\n", +"disp(sigma,'(a)blade to jet speed ratio is')\n", +"// part(b)\n", +"w2=c2-u;\n", +"w3=w2;\n", +"beta2=0;\n", +"beta3=180-theta;\n", +"cy2=c2;\n", +"cy3=u-(w3*cosd(beta3));\n", +"w_T=u*(cy2-cy3);\n", +"m=rho*Q;\n", +"P_T=m*w_T;\n", +"disp('kW',P_T*1e-3,'(b)the power developed is')\n", +"// part(c)\n", +"n=w_T/(0.5*(c2^2));\n", +"disp('%',n*1e2,'(c)the efficiency is')\n", +"// part(d)\n", +"n_max=0.5*(1+cosd(beta3));\n", +"disp('%',n_max*1e2,'(d)the Maximum efficiency is')\n", +"P_max=m*g*H*n_max;\n", +"disp('kW',P_max*1e-3,'and the Maximum power developed is')\n", +"// part(e)\n", +"sigma_opt=0.5; // for Maximum efficiency\n", +"u_opt=sigma_opt*c2;\n", +"N_opt=u_opt*60/(d*%pi);\n", +"disp('rpm',N_opt,'(e)speed of the rotation corresponding to Maximum efficiency is')\n", +"// part(f)\n", +"omega=%pi*2*N/60;\n", +"NS=omega*sqrt(P_T)*(H^(-5/4))/549.016;\n", +"disp(NS,'(f)the specific speed of turbine is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.45: Kaplan_turbine_120_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.45 Kaplan turbine 120 rpm\n", +"\n", +"N=120; // Speed in RPM\n", +"H=25; // net head in m\n", +"Q=120; // discharge in m3/s\n", +"dt=5; // runner diameter in m\n", +"dh_t=0.4; // hub-tip ratio of the runner\n", +"beta2=150; //inlet angle of the runner blades in degree\n", +"n_o=0.8; // overall efficiency\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"// part(a)\n", +"P=n_o*rho*g*Q*H;\n", +"disp('MW',P*1e-6,'(a)the output power is')\n", +"// part(b)\n", +"omega=%pi*2*N/60;\n", +"NS=omega*sqrt(P)*(H^(-5/4))/549.016;\n", +"disp(NS,'(b)the specific speed of turbine is')\n", +"// part(c)\n", +"dh=dh_t*dt;\n", +"d=0.5*(dt+dh); // mean diameter of the impeller blade in m\n", +"u=%pi*d*N/60;\n", +"cx=Q*4/(%pi*(dt^2-dh^2));\n", +"cy2=u-(cx*tand(90-(180-beta2)));\n", +"alpha2=atand(cx/cy2);\n", +"disp('degree',alpha2,'(c)the inlet guide vane exit angle is')\n", +"// part(d)\n", +"beta3=atand(cx/u);\n", +"disp('degree',beta3,'(d)the exit angle of the runner blades is beta3= ')\n", +"// part(e)\n", +"n_h=(u*cy2)/(g*H);\n", +"disp('%',n_h*1e2,'(e)the hydraulic efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.46: Fourneyron_Turbine_360_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.46 Fourneyron Turbine 360 rpm\n", +"\n", +"d2=3; // outer diameter of the impeller in m\n", +"d1=1.5; // inner diameter of the impeller in m\n", +"H=50; // net head in m\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"N=360; // rotor Speed in RPM\n", +"n_o=0.785; // overall efficiency\n", +"P=4; // Power Output in MW\n", +"u1=%pi*d1*N/60;\n", +"u2=%pi*d2*N/60;\n", +"// part(a)\n", +"Q=P*1e6/(n_o*rho*g*H);\n", +"disp('m3/s',Q,'(a)the discharge is')\n", +"c2=9; // velocity of water at exit in m/s\n", +"// part(b)\n", +"w_ET=(g*H)-(0.5*(c2^2));\n", +"n_h=w_ET/(g*H);\n", +"disp('%',n_h*1e2,'(b)the hydraulic efficiency is')\n", +"// part(c)\n", +"cr2=c2;\n", +"b=Q/(cr2*%pi*d2); // axial length of the impeller in m\n", +"disp('cm',b*1e2,'(c)the runner passage width is')\n", +"// part(d)\n", +"beta2=atand(cr2/u2);\n", +"disp('degree',beta2,'(d) the blade air angle at the impeller exit beta2=')\n", +"c_theta1=w_ET/u1;\n", +"cr1=Q/(b*%pi*d1);\n", +"beta1=atand(cr1/(u1-c_theta1));\n", +"disp('degree',beta1,'and the blade air angle at the impeller entry beta1=')\n", +"// part(e)\n", +"alpha1=atand(cr1/c_theta1);\n", +"disp('degree',alpha1,'(e)the guide vane exit angle is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.47: Crossflow_Radial_Hydro_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.47 Crossflow Radial Hydro turbine\n", +"\n", +"N=50; // Speed in RPM\n", +"H=25; // net head in m\n", +"Q=150; // discharge in m3/s\n", +"P=20; // Power Output in MW\n", +"d1=3.5; // runner diameter in m\n", +"dr=1.3; // diameter ratio of the runner\n", +"rho=1000; // density in kg/m3\n", +"g=9.81; // gravitational acceleration in m/s2\n", +"u1=%pi*d1*N/60;\n", +"u2=u1/dr;\n", +"c_theta1=2*u1;\n", +"c_theta2=u2;\n", +"w_st1=(u1*c_theta1)-(u2*c_theta2);\n", +"u3=u2;\n", +"c_theta3=u2;\n", +"c_theta4=0;\n", +"w_st2=(u3*c_theta3)-(u1*c_theta4);\n", +"w_st=w_st1+w_st2;\n", +"// part(a)\n", +"n_h=w_st/(g*H);\n", +"disp('%',n_h*1e2,'(a)the hydraulic efficiency is')\n", +"Ph=rho*Q*w_st;\n", +"disp('MW',Ph*1e-6,'and the hydraulic power is')\n", +"n_o=P*1e6/(rho*Q*g*H);\n", +"disp('%',n_o*1e2,'and the overall efficiency is')\n", +"// part(b)\n", +"omega=%pi*2*N/60;\n", +"NS=omega*sqrt(P*1e6)*(H^(-5/4))/549.016;\n", +"disp(NS,'(b)the specific speed of turbine is')\n", +"// part(c)\n", +"disp('(c)Adopting the flow model of the crossflow wind turbine')\n", +"P_h=rho*Q*((2*(u1^2))+(u2^2));\n", +"disp('MW',P_h*1e-6,'the hydraulic power is')\n", +"nh=((2*(u1^2))+(u2^2))/(g*H);\n", +"disp('%',nh*1e2,'and hydraulic efficiency is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.48: Calculation_on_a_Draft_Tube.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.48 Calculation on a Draft Tube \n", +"\n", +"pa=1.013; // atmospheric pressure in bar\n", +"p3=0.4*pa; // turbine exit pressure in bar\n", +"rho=1e3; // density in kg/m3\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"n_D=0.82; // Efficiency of the Draft Tube\n", +"delHi=3.1058869; // from Ex 18.5\n", +"// part(b)\n", +"Hd=delHi;\n", +"Hs=((pa-p3)*1e5/(rho*g))-(n_D*Hd); // Hs=Z3-Z4\n", +"disp('m',Hs,'(b)the suction head(height of the turbine exit above the tail race) is')\n", +"disp('comment: the calculation for Hs is done wrongly in the book. hence the value of Hs differs from the book.')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.49: Centrifugal_pump_890_kW.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.49 Centrifugal pump 890 kW\n", +"\n", +"H=50; // head developed in m\n", +"P=890; // Power required in kW\n", +"NS=0.75; //specific speed\n", +"rho=1e3;\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"n_h=0.91; // hydraulic efficiency\n", +"f=0.925; // blockage factor for the flow\n", +"Q=1.5; // discharge in m3/s of water\n", +"u2=0.8*sqrt(2*g*H);\n", +"cr2=0.3*sqrt(2*g*H);\n", +"dr=0.5; // diameter ratio(d1/d2)\n", +"// part(a)\n", +"omega=NS*(H^(3/4))/(0.1804*sqrt(Q));\n", +"N=omega*60/(2*%pi);\n", +"disp('rpm',N,'(a)the speed of rotation is')\n", +"// part(b) impeller diameter\n", +"d2=u2*60/(%pi*N);\n", +"disp('m',d2,'(b)the impeller diameter is')\n", +"//part(c)\n", +"c_theta2=g*H/(u2*n_h);\n", +"beta2=atand(cr2/(u2-c_theta2));\n", +"disp('degree',beta2,'(c)the blade air angle at the impeller exit beta2=')\n", +"u1=u2*dr;\n", +"cr1=cr2;\n", +"beta1=atand(cr1/u1);\n", +"disp('degree',beta1,'and the blade air angle at the impeller entry beta1=')\n", +"//part(d)\n", +"b2=Q/(cr2*%pi*d2*f);\n", +"disp('m',b2,'(d)the impeller width at exit is')\n", +"//part(e)overall Efficiency\n", +"n_o=rho*Q*H*g/(P*1e3);\n", +"disp('%',n_o*1e2,'(e)overall efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.4: Calculation_on_a_Diffuser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.4 Calculation on a Diffuser \n", +"\n", +"pe=35; // Initial Pressure in mm W.G.\n", +"pa=1.0135; // ambient pressure in bar\n", +"c1=100; // entry velocity in m/s\n", +"C_pa=0.602; // actual pressure recovery coefficient\n", +"ro=1.25; // density in kg/m3\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"Ar=1.85; // Area Ratio of Diffuser\n", +"\n", +"// part(a)\n", +"C_ps=1-(1/(Ar^2));\n", +"disp(C_ps,'(a)ideal value of the pressure recovery coefficient is')\n", +"\n", +"// part(b)\n", +"n_D=C_pa/C_ps;\n", +"disp ('%',n_D*1e2,'(b)Efficiency of the diffuser is')\n", +"\n", +"// part(c)\n", +"p1=pa+(pe*g*1e-5);\n", +"p01=p1+(0.5*ro*(c1^2)*1e-5);\n", +"delp_0=(C_ps-C_pa)*(0.5*ro*(c1^2)*1e-5);\n", +"disp('mm W.G.',delp_0*1e5/g,'(c)the stagnation pressure loss across the diffuser is')\n", +"\n", +"// part(d)\n", +"p02=p01-delp_0;\n", +"c2=c1/Ar;\n", +"p2=p02-(0.5*ro*(c2^2)*1e-5);\n", +"disp('mm W.G.',(p2-pa)*1e5/g,'(d)the gauge pressure at the diffuser exit is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.50: Centrifugal_pump_1500_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.50 Centrifugal pump 1500 rpm\n", +"\n", +"N=1500; // rotor Speed in RPM\n", +"H=5.2; // head in m\n", +"b=2/100; // width in m\n", +"d1=2.5/100; // entry diameter of the blade ring in m\n", +"d2=0.1; // exit diameter of the blade ring in m\n", +"rho=1e3;\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"n_o=0.75; // overall Efficiency of the drive\n", +"u2=%pi*d2*N/60;\n", +"u1=u2*d1/d2;\n", +"// part(a)impeller blade angle at the entry\n", +"c_r2=0.4*u2;\n", +"c_r1=c_r2*d2/d1;\n", +"beta1=atand(c_r1/u1);\n", +"disp('degree',beta1,'(a)the impeller blade angle at the entry beta1=')\n", +"//part(b) discharge\n", +"Q=c_r1*%pi*d1*b;\n", +"disp('litres/sec',Q*1e3,'(b)the discharge is')\n", +"//part(c)Power required\n", +"P=(rho*Q*g*H)/(n_o);\n", +"disp('kW',P*1e-3,'(a)Power required to drive the pump is')\n", +"// part(d)\n", +"omega=%pi*2*N/60;\n", +"NS=(H^(-3/4))*0.1804*(omega)*sqrt(Q);\n", +"disp(NS,'(d)the specific speed is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.51: Axial_pump_360_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.51 Axial pump 360 rpm\n", +"\n", +"N=360; // rotor Speed in RPM\n", +"dh=0.30; // hub diameter of the impeller in m\n", +"beta2=48; // exit angle of the runner blades(from the tangential direction)\n", +"cx=5; // axial velocity of water through the impeller in m/s\n", +"n_h=0.87; // hydraulic efficiency\n", +"n_o=0.83; // overall Efficiency \n", +"Q=2.5; // discharge in m3/s\n", +"rho=1e3;\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"//part(a)\n", +"dt=sqrt((4*Q/(cx*%pi))+(dh^2));\n", +"disp('m',dt,'(a)the impeller tip diameter is')\n", +"// part(b)impeller blade angle at the entry\n", +"d=0.5*(dt+dh); // mean diameter of the impeller blade in m\n", +"u=%pi*d*N/60;\n", +"beta1=atand(cx/u);\n", +"disp('degree',beta1,'(b)the impeller blade angle at the entry beta1=')\n", +"// part(c)\n", +"cy2=u-(cx/tand(beta2));\n", +"H=n_h*u*cy2/g;\n", +"disp('m',H,'(c)the head developed is')\n", +"//part(d)Power required\n", +"P=(rho*Q*g*H)/(n_o);\n", +"disp('kW',P*1e-3,'(d)Power required to drive the pump is')\n", +"// part(e)\n", +"omega=%pi*2*N/60;\n", +"NS=(H^(-3/4))*0.1804*(omega)*sqrt(Q);\n", +"disp(NS,'(e)the specific speed is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.52: NPSH_for_Centrifugal_pump.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.52 NPSH for Centrifugal pump\n", +"\n", +"H=30; // head developed in m\n", +"ds=0.15; // suction pipe diameter in m\n", +"f=0.005; //Coefficient of friction for the suction pipe\n", +"pa=1.013; // atmospheric pressure in bar\n", +"As=%pi/4*(ds^2); // Cross-sectional Area of the suction pipe in m2\n", +"rho=1e3; // density of water in kg/m3\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"t=30; // temperature of water in degree C\n", +"pv=0.0424; // vapour pressure of water at t value\n", +"Hv=pv*1e5/(rho*g);\n", +"Z(1)=0; // altitude in m\n", +"Z(2)=2500;\n", +"p(1)=pa; // at altitude Z=0\n", +"p(2)=0.747; // at Z=2500m\n", +"Q(1)=0.065; // discharge in m3/s of water\n", +"Q(2)=0.1;\n", +"Q(3)=0.15;\n", +"Hs(1)=3; // vertical length of the suction pipe in m\n", +"Hs(2)=5;\n", +"for i=1:3\n", +" disp('m3/s',Q(i),'when Q=')\n", +" cs=Q(i)/As;\n", +" for k=1:2\n", +" disp('m',Hs(k),'and Hs=')\n", +" delHf=4*f*(Hs(k)/ds)*(cs^2/(2*g));\n", +" for j=1:2\n", +" disp('m',Z(j),'and Z=')\n", +" Ha=p(j)*1e5/(rho*g);\n", +" H1=Ha-(Hs(k)+(cs^2/(2*g))+delHf);\n", +" NPSH=H1-Hv;\n", +"disp(NPSH,'NPSH=')\n", +"sigma=NPSH/H;\n", +"disp(sigma,'Cavitation Coefficient sigma=')\n", +"end\n", +"end\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.53: NPSH_and_Thoma_Cavitation_Coefficient.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.53 NPSH and Thoma Cavitation Coefficient\n", +"\n", +"H=60; // head developed in m\n", +"c1=8; // exit velocity in m/s\n", +"pa=1.0133; // ambient pressure in bar\n", +"rho=1e3;\n", +"n_d=0.8; // Efficiency of the Draft Tube\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"ta=30; // ambient temperature of water in degree C\n", +"pv=0.0424; // vapour pressure of water at t value\n", +"Hv=pv*1e5/(rho*g);\n", +"//Q=c1*A1=c2*A2\n", +"Ar(1)=1.2; // draft tube area ratio(A2/A1=c1/c2)\n", +"Ar(2)=1.4;\n", +"Ar(3)=1.6;\n", +"Hs=2.5; // vertical length of the draft tube between the turbine exit and the tail race in m\n", +"Ha=pa*1e5/(rho*g);\n", +"for i=1:3\n", +" Hsd=(c1^2)*(1-(1/(Ar(i)^2)))/(2*g); // ideal head gained by the draft tube\n", +" Hd=n_d*Hsd; //Actual head gained by the draft tube\n", +" disp(Ar(i),'for Area Ratio Ar=')\n", +" disp('m',Hd,'(a)Actual head gained by the draft tube is')\n", +" H1=Ha-(Hs+Hd);\n", +" NPSH=H1-Hv;\n", +"disp(NPSH,'(b)NPSH=')\n", +"sigma=NPSH/H;\n", +"disp(sigma,'and Cavitation parameter(Thoma Number) sigma=')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.54: Maximum_Height_of_Hydro_Turbines.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.54 Maximum Height of Hydro Turbines\n", +"\n", +"H=52; // head developed in m\n", +"c1=6.5; // exit velocity in m/s\n", +"pa=1.0133; // ambient pressure in bar\n", +"rho=1e3;\n", +"n_d=0.75; // Efficiency of the Draft Tube\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"ta=20; // ambient temperature of water in degree C\n", +"sigma_cr=0.1;\n", +"pv=0.023; // vapour pressure of water at t value(from tables)\n", +"Hv=pv*1e5/(rho*g);\n", +"//Q=c1*A1=c2*A2\n", +"Ar=1.5; // draft tube area ratio(A2/A1=c1/c2)\n", +"Z(1)=0; // altitude in m\n", +"Z(2)=2500;\n", +"Z(3)=3000;\n", +"Z(4)=4000;\n", +"p(1)=pa; // at altitude Z=0\n", +"p(2)=0.747; // at Z=2500m\n", +"p(3)=0.701; // at altitude Z=3000m\n", +"p(4)=0.657; // at Z=4000m\n", +" Hsd=(c1^2)*(1-(1/(Ar^2)))/(2*g); // ideal head gained by the draft tube\n", +" Hd=n_d*Hsd; //Actual head gained by the draft tube\n", +"Ha=pa*1e5/(rho*g);\n", +"for i=1:4\n", +" disp('m',Z(i),'For Z=')\n", +" Ha=p(i)*1e5/(rho*g);\n", +" H1=Ha-(Hsd+Hd);\n", +" Hs=Ha-((sigma_cr*H)+Hd+Hv); // vertical length of the draft tube between the turbine exit and the tail race in m\n", +" disp('m',Hs,'the maximum height of the turbine exit above the tail race is')\n", +" NPSH=sigma_cr*H;\n", +"disp(NPSH,'NPSH=')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.55: Propeller_Thrust_and_Power.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.55 Propeller Thrust and Power\n", +"\n", +"c_u=5; // upstream velocity in m/s\n", +"c_s=10; // downstream velocity in m/s\n", +"rho=1e3; // density of water in kg/m3\n", +"c=0.5*(c_u+c_s); // velocity of water through the propeller in m/s\n", +"d(1)=0.5; // propeller diameter in m\n", +"d(2)=1;\n", +"d(3)=1.5;\n", +"delh_0=0.5*((c_s^2)-(c_u^2));\n", +"delp_0=rho*delh_0;\n", +"disp('bar',delp_0*1e-5,'(b)stagnation pressure rise across the propeller is')\n", +"for i=1:3\n", +" disp('cm',d(i)*1e2,'for propeller diameter=')\n", +"A=%pi*(d(i)^2)/4;\n", +"Q=c*A;\n", +"m=rho*Q;\n", +"disp('m3/s',Q,'(a) flow rate through the propeller is')\n", +"Fx=A*delp_0;\n", +"disp('kN',Fx*1e-3,'(c) thrust exerted by the propeller on the boat is')\n", +"P=m*delh_0;\n", +"disp('kW',P/1000,'(d)the ideal Power required to drive the propeller is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.5: Calculation_on_a_Draft_Tube.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.5 Calculation on a Draft Tube \n", +"\n", +"c2=6.25; // exit velocity in m/s\n", +"ro=1e3; // density in kg/m3\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"AR=1.6; // Area Ratio of Diffuser\n", +"Q=100; // discharge in m3/s\n", +"n_D=0.82; // Efficiency of the Draft Tube\n", +"\n", +"// part(a)\n", +"c1=c2*AR;\n", +"A1=Q/c1;\n", +"disp('m2',A1,'(a)area of cross-section at entry is')\n", +"A2=A1*AR;\n", +"disp('m2',A2,'and the area of cross-section at exit is')\n", +"\n", +"// part(b)\n", +"delHi=((c1^2)-(c2^2))/(2*g);\n", +"delH_a=delHi*n_D;\n", +"disp('m',delH_a,'(b)actual head gained by the Draft Tube is')\n", +"\n", +"// part(c)\n", +"m=ro*Q;\n", +"delP_a=m*g*delH_a;\n", +"disp('MW',delP_a*1e-6,'(c)the additional power generated is')\n", +"\n", +"// part(d)\n", +"Loss=delHi-delH_a;\n", +"disp('m',Loss,'(d)the loss of head due to losses in the draft tube is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.6: Calculations_on_a_Gas_Turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.6 Calculations on a Gas Turbine \n", +"\n", +"m=472; // flow rate of hot gases in kg/s\n", +"T01=1335; // Turbine inlet temp in Kelvin\n", +"p01=10; // Turbine Inlet Pressure in bar\n", +"c2=150; // exit velocity in m/s\n", +"pr0=10; // Turbine pressure ratio\n", +"gamma_g=1.67;\n", +"T2=560; // Temperature of gases at exit in Kelvin\n", +"cp_g=1.157; // Specific Heat of gas at Constant Pressure in kJ/(kgK)\n", +"\n", +"// part(a) Determining total to total efficiency\n", +"T02=T2+(0.5*(c2^2)/(cp_g*1e3));\n", +"T02s=T01/(pr0^((gamma_g-1)/gamma_g));\n", +"n_tt=(T01-T02)/(T01-T02s);\n", +"disp('%',n_tt*100,'(a)total to total efficiency is')\n", +"\n", +"\n", +"// part(b) Determining total to static efficiency\n", +"T2s=T02s-(0.5*(c2^2)/(cp_g*1e3));\n", +"n_ts=(T01-T02)/(T01-T2s);\n", +"disp('%',n_ts*100,'(b)total to static efficiency is')\n", +"\n", +"// part(c) Determining the polytropic efficiency\n", +"n_p=((gamma_g)/(gamma_g-1))*((log(T01/T02))/(log(pr0)));\n", +"disp('%',n_p*100,'(c)polytropic efficiency is')\n", +"\n", +"// part(d) Determining power developed by the turbine\n", +"P=m*cp_g*(T01-T02);\n", +"disp('MW',P/1e3,'(d)Power developed by the turbine is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.7: RHF_of_a_three_stage_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.7 RHF of a three stage turbine\n", +"\n", +"p1=1.0; // Initial Pressure in bar\n", +"gamma=1.4;\n", +"T1=1500; // Initial Temperature in K\n", +"s=3; // number of stages\n", +"opr=11; // Overall Pressure Ratio\n", +"pr=opr^(1/s); // equal Pressure Ratio in each stage\n", +"n_T=0.88; // Overall Efficiency \n", +"delTa=T1*(1-opr^(-((gamma-1)/gamma)))*n_T;\n", +"T2=T1-delTa;\n", +"n_p=(log(T1/T2))/(((gamma-1)/gamma)*(log(opr))); // polytropic or small stage efficiency\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"n_st=(1-pr^(n_p*(-((gamma-1)/gamma))))/(1-pr^(-((gamma-1)/gamma))); // stage efficiency\n", +"T(1)=T1;\n", +"for i=1:3\n", +" delT(i)=T(i)*(1-pr^(n_p*(-((gamma-1)/gamma))));\n", +" delw_s(i)=delT(i)*cp/n_st;\n", +" T(i+1)=T(i)-delT(i);\n", +"end\n", +"w_a=cp*delTa;\n", +"w_s=w_a/n_T;\n", +"RHF=(delw_s(1)+delw_s(2)+delw_s(3))/w_s;\n", +"disp(RHF,'the reheat factor is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.8: Calculation_on_an_air_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.8 Calculation on an air compressor\n", +"\n", +"funcprot(0)\n", +"p1=1.0; // Initial Pressure in bar\n", +"T1=305; // Initial Temperature in degree K\n", +"k=16; // number of stages\n", +"m=400; // mass flow rate through the compressor in kg/s\n", +"p_rc=10; // overall Pressure Ratio\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"n_p=0.88; // polytropic efficiency\n", +"\n", +"// part(a) Determining stage Pressure Ratio\n", +"pr=p_rc^(1/k);\n", +"disp(pr,'(a)stage Pressure Ratio is')\n", +"\n", +"// part(b) Determining the stage efficiency\n", +"T2s=T1*(pr^((gamma-1)/gamma));\n", +"T2=T1*(pr^((gamma-1)/(gamma*n_p)));\n", +"n_st=(T2s-T1)/(T2-T1);\n", +"disp('%',n_st*100,'(b)stage Efficiency of the compressor is')\n", +"\n", +"// part(c) Determining power required for the first stage\n", +"P1=m*cp*(T2-T1);\n", +"disp ('MW',P1/1e3,'(c)Power required for the first stage is')\n", +"\n", +"// part(d)Overall Compressor Efficiency\n", +"T17=T1*exp(((gamma-1)/(gamma*n_p))*(log(p_rc))); // k+1=17;\n", +"T17s=T1*(p_rc^((gamma-1)/gamma));\n", +"n_C=(T17s-T1)/(T17-T1);\n", +"disp ('%',n_C*100,'(d)Overall Compressor Efficiency is')\n", +"\n", +"// part(e) Determining power required to drive the compressor\n", +"P=m*cp*(T17-T1);\n", +"disp ('MW',P/1e3,'(e)Power required to drive the compressor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.9: Constant_Pressure_Gas_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 18.9 Constant Pressure Gas Turbine Plant\n", +"\n", +"T1=298; // Minimum Temperature in Kelvin\n", +"beeta=4.5; // Maximum to Minimum Temperature ratio(T_max/T_min)\n", +"m=115; // mass flow rate through the turbine and compressor in kg/s\n", +"n_C=0.79; // Compressor Efficiency\n", +"n_T=0.83; // Turbine Efficiency\n", +"gamma_g=1.33;\n", +"R=0.287;\n", +"cp=(gamma_g/(gamma_g-1))*R; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"alpha=beeta*n_C*n_T;\n", +"t_opt=sqrt(alpha); // For maximum power output, the temperature ratios in the turbine and compressor\n", +"\n", +"// part(a) Determining optimum pressure ratio of the plant\n", +"r=t_opt^(gamma_g/(gamma_g-1));\n", +"disp(r,'(a)optimum pressure ratio of the plant is')\n", +"\n", +"// part(b)Carnot's efficiency\n", +"n_Carnot=1-(1/beeta);\n", +"disp('%',n_Carnot*100,'(b)Carnot efficiency of the plant is')\n", +"\n", +"// part(c) Determining Joule's cycle efficiency\n", +"n_Joule=1-(1/t_opt);\n", +"disp('%',n_Joule*100,'(c)efficiency of the Joule cycle is')\n", +"\n", +"// part(d) Determining thermal efficiency of the plant for maximum power output\n", +"n_th=(t_opt-1)^2/((beeta-1)*n_C-(t_opt-1));\n", +"disp('%',n_th*100,'(d)thermal efficiency of the plant for maximum power output is')\n", +"\n", +"// part(e) Determining power output\n", +"wp_max=cp*T1*((t_opt-1)^2)/n_C; // maximum work output\n", +"P_max=m*wp_max;\n", +"disp ('MW',P_max/1e3,'(e)Power output is')\n", +"\n", +"// part(f) Determining power generated by the turbine required to drive the compressor\n", +"T3=beeta*T1; // Maximum Temperature in degree K\n", +"T4s=T3*(r^(-((gamma_g-1)/gamma_g)));\n", +"T4=T3-((T3-T4s)*n_T);\n", +"P_T=m*cp*(T3-T4);\n", +"disp ('MW',P_T/1e3,'(f)Power generated by the turbine is')\n", +"\n", +"// part(g) Determining power absorbed by the compressor\n", +"T2s=T1*(r^((gamma_g-1)/gamma_g));\n", +"T2=T1+((T2s-T1)/n_C);\n", +"P_C=m*cp*(T2-T1);\n", +"disp ('MW',P_C/1e3,'(g)Power absorbed by the compressor is')\n", +"\n", +"//part(h)heat supplied in the combustion chamber\n", +"Qs=m*cp*(T3-T2);\n", +"disp('MW',Qs/1e3,'(h)heat supplied in the combustion chamber is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/2-Thermodynamics.ipynb b/Turbines_by_Compressors_And_Fans/2-Thermodynamics.ipynb new file mode 100644 index 0000000..2b77e9e --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/2-Thermodynamics.ipynb @@ -0,0 +1,322 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: Thermodynamics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: Calculation_on_a_Diffuser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 2.1 Calculation on a Diffuser \n", +"\n", +"p1=800; // Initial Pressure in kPa\n", +"T1=540; // Initial Temperature in K\n", +"p2=580; // Final Pressure in kPa\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=0.287; // Universal Gas Constant in kJ/kgK\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"sg=13.6; // Specific Gravity of mercury\n", +"n=0.95; // Efficiency in %\n", +"AR=4; // Area Ratio of Diffuser\n", +"delp=(367)*(1e-3)*(g)*(sg); // Total Pressure Loss Across the Diffuser in kPa\n", +"pr=p1/p2; // Pressure Ratio\n", +"T2s=T1/(pr^((gamma-1)/gamma));\n", +"T2=T1-(n*(T1-T2s));\n", +"c2=sqrt(2*cp*(T1-T2));\n", +"ro2=p2/(R*T2);\n", +"c3=c2/AR;\n", +"m=0.5*1e-3*ro2*((c2^2)-(c3^2));\n", +"n_D=1-(delp/m);\n", +"disp ('%',n_D*1e2,' Efficiency of the diffuser is')\n", +"p3=(p2+n_D*m)*1e-2;\n", +"disp('m/s',c2,'the velocity of air at diffuser entry is')\n", +"disp('m/s',c3,'the velocity of air at diffuser exit is')\n", +"disp('bar',p3,'static pressure at the diffuser exit is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: Determining_the_infinitesimal_stage_efficiencies.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Exa 2.2 Determining the infinitesimal stage efficiencies\n", +"p1=1.02; // Initial Pressure in bar\n", +"T1=300; // Initial Temperature in K\n", +"\n", +"// part(a)\n", +"T2=315; // Final Temperature in K\n", +"gamma=1.4; // Specific Heat Ratio\n", +"g=9.81; // Gravitational acceleration in m/s^2\n", +"sg=1; // Specific Gravity of air\n", +"delp=(1500)*(0.001)*(g)*(sg); // Total Pressure Loss Across the Diffuser in kPa\n", +"p2=p1+(0.01*delp);\n", +"pr=p2/p1; // Pressure Ratio\n", +"T2s=T1*(pr^((gamma-1)/gamma));\n", +"n_c=(T2s-T1)/(T2-T1); // Efficiency in %\n", +"n_p=((gamma-1)/gamma)*((log(p2/p1))/(log(T2/T1)));\n", +"disp ('%',n_c*100,'(a)Efficiency of the compressor is')\n", +"disp ('%',n_p*100,'and infinitesimal stage Efficiency or polytropic efficiency of the compressor is')\n", +"\n", +"// part(b) Determining the infinitesimal stage efficiency\n", +"\n", +"p2_b=2.5; // Final pressure in bar\n", +"n_b=0.75; // Efficiency\n", +"pr_b=p2_b/p1; // Pressure Ratio\n", +"T2s_b=T1*(pr_b^((gamma-1)/gamma));\n", +"T2_b=T1+((T2s_b-T1)/n_b);\n", +"n_p_b=((gamma-1)/gamma)*((log(p2_b/p1))/(log(T2_b/T1)));\n", +"disp ('%' ,n_p_b*100,'(b)infinitesimal stage Efficiency or polytropic efficiency of the compressor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: Calculations_on_air_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 2.3 Calculation on a compressor\n", +"p1=1.0; // Initial Pressure in bar\n", +"t1=40; // Initial Temperature in degree C\n", +"T1=t1+273; // in Kelvin\n", +"s=8; // number of stages\n", +"m=50; // mass flow rate through the compressor in kg/s\n", +"pr=1.35; // equal Pressure Ratio in each stage\n", +"opr=pr^s; // Overall Pressure Ratio\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"n=0.82; // Overall Efficiency\n", +"\n", +"// part(a) Determining state of air at the compressor exit\n", +"p9=opr*p1;\n", +"delTc=T1*(opr^((gamma-1)/gamma)-1)/n;\n", +"T9=T1+delTc;\n", +"disp('bar',p9,'(a)Exit Pressure is')\n", +"disp('K',T9,'and Exit Temperature is')\n", +"\n", +"// part(b) Determining the polytropic or small stage efficiency\n", +"n_p=((gamma-1)/gamma)*((log(p9/p1))/(log(T9/T1)));\n", +"disp('%',n_p*100,'(b)small stage Efficiency or polytropic efficiency of the compressor is')\n", +"\n", +"// part(c) Determining efficiency of each stage\n", +"n_st=(pr^((gamma-1)/gamma)-1)/(pr^(((gamma-1)/gamma)/n_p)-1);\n", +"disp ('%',n_st*100,'(c)Efficiency of each stage is')\n", +"\n", +"// part(d) Determining power required to drive the compressor\n", +"n_d=0.9; // Overall efficiency of the drive\n", +"P=m*cp*delTc/n_d;\n", +"disp ('MW' ,P/1e3,'(d)Power required to drive the compressor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: compressor_with_same_temperature_rise.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Exa 2.4 compressor with same temperature rise\n", +"\n", +"p1=1.0; // Initial Pressure in bar\n", +"t1=40; // Initial Temperature in degree C\n", +"T1=t1+273; // in Kelvin\n", +"s=8; // number of stages\n", +"pr=1.35;\n", +"opr=pr^s; // Overall Pressure Ratio\n", +"n=0.82; // Overall Efficiency \n", +"p9=opr*p1;\n", +"gamma=1.4;\n", +"delTc=(T1*(opr^((gamma-1)/gamma)-1)/n);\n", +"delTi=delTc/s;\n", +"T9=T1+delTc;\n", +"n_p=((gamma-1)/gamma)*((log(p9/p1))/(log(T9/T1))); // small stage Efficiency or polytropic efficiency\n", +"m=8;\n", +"T(1)=T1;\n", +"for i=1:m\n", +" T(i+1)=T(i)+delTi;\n", +" pr(i)=(1+(delTi/T(i)))^(n_p/((gamma-1)/gamma));\n", +" n_st(i)=(pr(i)^((gamma-1)/gamma)-1)/(pr(i)^(((gamma-1)/gamma)/n_p)-1);\n", +"disp(T(i),'T is');\n", +"disp(pr(i),'pressure ratio is')\n", +"disp(n_st(i),'efficiency is' )\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: Calculations_on_three_stage_gas_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 2.5 Calculation on three stage gas turbine\n", +"\n", +"p1=1.0; // Initial Pressure in bar\n", +"gamma=1.4;\n", +"T1=1500; // Initial Temperature in K\n", +"s=3; // number of stages\n", +"opr=11; // Overall Pressure Ratio\n", +"\n", +"// part(a)Determining pressure ratio of each stage\n", +"pr=opr^(1/s); // equal Pressure Ratio in each stage\n", +"disp (pr,'(a)Pressure ratio of each stage is')\n", +"\n", +"// part(b)Determining the polytropic or small stage efficiency\n", +"n_o=0.88; // Overall Efficiency \n", +"delT=T1*(1-opr^(-((gamma-1)/gamma)))*n_o;\n", +"T2=T1-delT;\n", +"n_p=(log(T1/T2))/(((gamma-1)/gamma)*(log(opr)));\n", +"disp ('%',n_p*100,'(b)small stage Efficiency or polytropic efficiency of the turbine is')\n", +"\n", +"// part(c) Determining mass flow rate\n", +"P=30000; // Power output of the Turbine in kW\n", +"n_d=0.91; // Overall efficiency of the drive\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"m=P/(cp*delT*n_d);\n", +"disp ('kg/s',m,'(c)mass flow rate is')\n", +"\n", +"// part(d) Determining efficiency of each stage\n", +"n_st=(1-pr^(n_p*(-((gamma-1)/gamma))))/(1-pr^(-((gamma-1)/gamma)));\n", +"disp ('%',n_st*100,'(d)Efficiency of each stage is')\n", +"d=3;\n", +"T(1)=T1;\n", +"for i=1:d\n", +" delT(i)=T(i)*(1-pr^(n_p*(-((gamma-1)/gamma))));\n", +" T(i+1)=T(i)-delT(i);\n", +" P(i)=m*cp*delT(i);\n", +"printf('\n P(%d)=%f MW',i,P(i)*1e-3)\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: Calculations_on_a_Gas_Turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 2.6 calculation on a gas turbine\n", +"\n", +"funcprot(0);\n", +"p1=5; // Inlet Pressure in bar\n", +"p2=1.2; // Exit Pressure in bar\n", +"T1=500; // Initial Temperature in K\n", +"gamma=1.4;\n", +"m=20; // mass flow rate of the gas in kg/s\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"n_T=0.9; // Overall Efficiency \n", +"pr=p1/p2; // Pressure Ratio\n", +"// part(a)\n", +"T2s=T1/(pr^((gamma-1)/gamma));\n", +"T2=T1-(n_T*(T1-T2s));\n", +"n_p=(log(T1/T2))/(log(T1/T2s));\n", +"disp('%',n_p*100,'(a)small stage Efficiency or polytropic efficiency of the expansion is')\n", +"P=m*cp*(T1-T2);\n", +"disp('kW',P,'and Power developed is')\n", +"\n", +"// part(b)\n", +"AR=2.5; // Area Ratio of Diffuser\n", +"R=0.287; // Universal Gas Constant in kJ/kgK\n", +"p3=1.2; // Exit Pressure for diffuser in bar\n", +"c2=75; // Velocity of gas at turbine exit in m/s\n", +"c3=c2/AR;\n", +"n_d=0.7; // Efficiency of the diffuser\n", +"ro2=p2/(R*T2);\n", +"delp=n_d*(0.5*0.001*ro2*((c2^2)-(c3^2))); // delp=p3-p2d\n", +"disp('mm W.G.',delp*100000/9.81,'(b)static pressure across the diffuser is')\n", +"p2d=p3-delp;\n", +"prd=p1/p2d;\n", +"T2sd=T1/(prd^((gamma-1)/gamma));\n", +"T2d=T1-(n_T*(T1-T2sd));\n", +"Pd=m*cp*(T1-T2d);\n", +"disp('kW',Pd-P,'and Increase in the power output of the turbine is')\n", +"\n", +"disp('Comment: Error in Textbook, Answers vary due to Round-off Errors')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/3-Gas_Turbine_Plants.ipynb b/Turbines_by_Compressors_And_Fans/3-Gas_Turbine_Plants.ipynb new file mode 100644 index 0000000..e2b3f4b --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/3-Gas_Turbine_Plants.ipynb @@ -0,0 +1,285 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: Gas Turbine Plants" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: Constant_Pressure_Gas_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 3.1 Constant Pressure Gas Turbine Plant\n", +"\n", +"t1=50; // Minimum Temperature in degree C\n", +"T1=t1+273; // in Kelvin\n", +"t3=950; // Maximum Temperature in degree C\n", +"T3=t3+273; // in Kelvin\n", +"n_c=0.82; // Compressor Efficiency\n", +"n_t=0.87; // Turbine Efficiency\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"beeta=T3/T1;\n", +"alpha=beeta*n_c*n_t;\n", +"T_opt=sqrt(alpha); // For maximum power output, the temperature ratios in the turbine and compressor\n", +"\n", +"// part(a) Determining pressure ratio of the turbine and compressor\n", +"pr=T_opt^(gamma/(gamma-1));\n", +"disp(pr,'(a)Pressure Ratio is')\n", +"\n", +"// part(b) Determining maximum power output per unit flow rate\n", +"wp_max=cp*T1*((T_opt-1)^2)/n_c;\n", +"disp('kW/(kg/s)',wp_max,'(b)maximum power output per unit flow rate is')\n", +"\n", +"// part(c) Determining thermal efficiency of the plant for maximum power output\n", +"n_th=(T_opt-1)^2/((beeta-1)*n_c-(T_opt-1));\n", +"disp('%',n_th*100,'(c)thermal efficiency of the plant for maximum power output is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: Gas_Turbine_Plant_with_an_exhaust_HE.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 3.2 Gas Turbine Plant with an exhaust HE\n", +"T1=300; // Minimum cycle Temperature in Kelvin\n", +"funcprot(0);\n", +"pr=10; // pressure ratio of the turbine and compressor\n", +"T3=1500; // Maximum cycle Temperature in Kelvin\n", +"m=10; // mass flow rate through the turbine and compressor in kg/s\n", +"e(1)=0.8; // thermal ratio of the heat exchanger\n", +"e(2)=1;\n", +"n_c=0.82; // Compressor Efficiency\n", +"n_t=0.85; // Turbine Efficiency\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"beeta=T3/T1;\n", +"T2s=T1*(pr^((gamma-1)/gamma));\n", +"T2=T1+((T2s-T1)/n_c);\n", +"T4s=T3*(pr^(-((gamma-1)/gamma)));\n", +"T4=T3-((T3-T4s)*n_t);\n", +"\n", +"for i=1:2\n", +"T5=T2+e(i)*(T4-T2);\n", +"T6=T4-(T5-T2);\n", +"Q_s=cp*(T3-T5);\n", +"Q_r=cp*(T6-T1);\n", +"// part(a) Determining power developed\n", +"w_p=Q_s-Q_r;\n", +"P=m*w_p;\n", +"printf('for effectiveness=%f, \n (a)the power developed is %f kW',e(i),P)\n", +"\n", +"// part(b) Determining thermal efficiency of the plant\n", +"n_th=1-(Q_r/Q_s);\n", +"disp ('%',n_th*100,'(b)thermal efficiency of the plant is') \n", +"end\n", +"\n", +"// part(c) Determining efficiencies of the ideal Joules cycle\n", +"n_Joule=1-(pr^((gamma-1)/gamma)/beeta);\n", +"disp('%',n_Joule*100,'(c)efficiency of the ideal Joules cycle with perfect heat exchange is')\n", +"n_Carnot=1-(T1/T3);\n", +"disp('%',n_Carnot*100,'and the Carnot cycle efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: ideal_reheat_cycle_Gas_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 3.3 ideal reheat cycle gas turbine\n", +"T1=300; // Minimum cycle Temperature in Kelvin\n", +"r=25; // pressure ratio of the turbine and compressor\n", +"gamma=1.4;\n", +"T3=1500; // Maximum cycle Temperature in Kelvin\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"beeta=T3/T1;\n", +"n=(gamma-1)/gamma;\n", +"t=(r^n);\n", +"d=1/sqrt(t);\n", +"// part(a) Determining mass flow rate through the turbine and compressor\n", +"c=2*beeta*[1-d];\n", +"wp_max=cp*T1*(c+1-t);\n", +"m=1000/wp_max;\n", +"disp ('kg/s',m,'(a)mass flow rate through the turbine and compressor is')\n", +"\n", +"// part(b) Determining thermal efficiency of the plant\n", +"n_th=(c+1-t)/(2*beeta-t-(beeta/sqrt(t)));\n", +"disp ('%',n_th*100,'(b)thermal efficiency of the plant is') " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: Calculations_on_Gas_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 3.4 Calculations on Gas Turbine Plant for an ideal reheat cycle with optimum reheat pressure and perfect exhaust heat exchange\n", +"T1=300; // Minimum cycle Temperature in Kelvin\n", +"r=25; // pressure ratio of the turbine and compressor\n", +"T3=1500; // Maximum cycle Temperature in Kelvin\n", +"gamma=1.4; // Specific Heat Ratio\n", +"cp=1.005; // Specific Heat at Constant Pressure in kJ/(kgK)\n", +"beeta=T3/T1;\n", +"n=(gamma-1)/gamma;\n", +"t=(r^n);\n", +"d=1/sqrt(t);\n", +"// part(a) Determining mass flow rate through the turbine and compressor\n", +"c=2*beeta*[1-d];\n", +"wp_max=cp*T1*(c+1-t);\n", +"m=1000/wp_max;\n", +"disp ('kg/s' ,m,' mass flow rate through the turbine and compressor is')\n", +"\n", +"\n", +"// part(b) Determining thermal efficiency of the plant\n", +"c=sqrt(t)*(sqrt(t)+1)/(2*beeta);\n", +"n_th=1-c;\n", +"disp ('%',n_th*100,' thermal efficiency of the plant is') " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: Calculations_on_Gas_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 3.5 Calculations on Gas Turbine Plant \n", +"\n", +"P=10e4; // Power Output in kW\n", +"T1=310; // Minimum cycle Temperature in Kelvin\n", +"p1=1.013; // Compressor Inlet Pressure in bar\n", +"pr_c=8; // Compressor pressure ratio\n", +"gamma=1.4;\n", +"gamma_g=1.33;\n", +"R=0.287; \n", +"p2=pr_c*p1; // Compressor Exit Pressure in bar\n", +"T3=1350; // Maximum cycle Temperature(Turbine inlet temp) in Kelvin\n", +"n_c=0.85; // Compressor Efficiency\n", +"p3=0.98*p2; // turbine inlet pressure\n", +"p4=1.02; // turbine exit pressure in bar\n", +"CV=40*10e2; // Calorific Value of fuel in kJ/kg;\n", +"n_B=0.98; // Combustion Efficiency\n", +"n_m=0.97; // Mechanical efficiency\n", +"n_t=0.9; // Turbine Efficiency\n", +"n_G=0.98; // Generator Efficiency\n", +"cp_a=1.005; // Specific Heat of air at Constant Pressure in kJ/(kgK)\n", +"\n", +"// Air Compressor\n", +"T2s=T1*(pr_c^((gamma-1)/gamma));\n", +"T2=T1+((T2s-T1)/n_c);\n", +"w_c=cp_a*(T2-T1);\n", +"\n", +"// Gas Turbine\n", +"n_g=(gamma_g-1)/gamma_g;\n", +"cp_g=1.157; // Specific Heat of gas at Constant Pressure in kJ/(kgK)\n", +"pr_t=p3/p4;\n", +"T4s=T3/(pr_t^((gamma_g-1)/gamma_g));\n", +"T4=T3-(n_t*(T3-T4s));\n", +"w_t=cp_g*(T3-T4);\n", +"w_net=w_t-w_c;\n", +"w_g=n_m*n_G*w_net;\n", +"\n", +"// part(a) Determining Gas Flow Rate\n", +"m_g=P/w_g;\n", +"disp ('kg/s',m_g,'(a)Gas flow rate is')\n", +"\n", +"// part(b) Determining Fuel-Air Ratio\n", +"F_A=((cp_g*T3)-(cp_a*T2))/((CV*n_B)-(cp_g*T3));\n", +"disp(F_A,'(b)Fuel-Air Ratio is')\n", +"\n", +"// part(c) Air flow rate\n", +"m_a=m_g/(1+F_A);\n", +"disp('kg/s',m_a,'(c)Air flow rate is')\n", +"\n", +"// part(d) Determining thermal efficiency of the plant\n", +"m_f=m_g-m_a;\n", +"n_th=m_g*w_net/(m_f*CV);\n", +"disp ('%',n_th*100,'(d)thermal efficiency of the plant is')\n", +"\n", +"// part(e) Determining Overall efficiency of the plant\n", +"n_o=n_m*n_G*n_th;\n", +"disp ('%',n_o*100,'(e)overall efficiency of the plant is')\n", +"\n", +"// part(f) Determining ideal Joule cycle efficiency\n", +"n_Joule=1-(1/(pr_c^((gamma-1)/gamma)));\n", +"disp ('%',n_Joule*100,'(f)efficiency of the ideal Joule cycle is')\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/4-Steam_Turbine_Plants.ipynb b/Turbines_by_Compressors_And_Fans/4-Steam_Turbine_Plants.ipynb new file mode 100644 index 0000000..7f710c2 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/4-Steam_Turbine_Plants.ipynb @@ -0,0 +1,255 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: Steam Turbine Plants" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Calculations_on_Steam_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 4.1 Calculations on Steam Turbine Plant \n", +"\n", +"p1=25; // Turbine Inlet Pressure in bar\n", +"p2=0.065; // Condenser Pressure in bar\n", +"n_B=0.82; // Boiler efficiency\n", +"delp=p1-p2;\n", +"v_w=0.001; // Specific Volume at condenser Pressure in m3/kg\n", +"\n", +"h1=160.6; // from steam tables at p1=0.065 bar\n", +"h2=h1+(delp*100*v_w);\n", +"\n", +"//part(a) Determining exact and approximate Rankine efficiency of the plant\n", +"h3=2800; // from steam table vapour enthalpy at 25 bar\n", +"h4=1930; // from steam table\n", +"n_rankine_ex=(h3-h4-(h2-h1))/(h3-h1-(h2-h1));\n", +"disp ('%',n_rankine_ex*100,'(a)(i) Exact Rankine efficiency is')\n", +"\n", +"n_rankine_app=(h3-h4)/(h3-h1);\n", +"disp ('%',n_rankine_app*100,' (a)(ii)Approximate Rankine efficiency is')\n", +"\n", +"//part(b) Determining thermal and relative efficiencies of the plant\n", +"n_t=0.78; // Turbine Efficiency\n", +"CV=26.3*10e2; // Calorific Value of fuel in kJ/kg;\n", +"n_th=(n_t*(h3-h4))/(h3-h1);\n", +"disp('%',n_th*100,'(b)(i)thermal efficiency of the plant is')\n", +"n_rel=n_th/n_rankine_app;\n", +"disp('%',n_rel*100,'(ii)relative efficiency of the plant is')\n", +"\n", +"//part(c) Determining Overall efficiency of the plant\n", +"n_o=n_th*n_B;\n", +"disp('%',n_o*100,'(c)overall efficiency of the plant is')\n", +"\n", +"//part(d) Turbine and Overall heat rates\n", +"hr_t=3600/n_th; \n", +"disp('kJ/kWh',hr_t,'(d)(i)Turbine Heat Rate is')\n", +"hr_o=3600/n_o; \n", +"disp('kJ/kWh',hr_o,'(d)(ii)overall Heat Rate is')\n", +"\n", +"//part(e) Steam Consumption per kWh\n", +"m_s=3600/(n_t*(h3-h4));\n", +"disp('kg/kWh' ,m_s,'(e)Steam Consumption is')\n", +"\n", +"//part(f) Fuel Consumption per kWh\n", +"m_f=3600/(CV*n_o);\n", +"disp('kg/kWh' ,m_f,'(f)Fuel Consumption is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Steam_Turbine_Plant_for_different_reheat_cycles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// scilab Code Exa 4.2 Steam Turbine Plant for different reheat cycles\n", +"\n", +"p1=160; // Turbine Inlet Pressure in bar\n", +"T1=500; // Turbine Entry Temperature in Degree Celsius\n", +"p2=0.06; // Condenser Pressure in bar\n", +"\n", +"// from steam tables at p1=0.06 bar, \n", +"h1=147; // Specific Enthalpy of water in kJ/kg\n", +"h2=2567; // Specific Enthalpy of steam in kJ/kg\n", +"\n", +"h3=3295; // from steam table\n", +"h4=1947; // from steam table\n", +"q_n=h3-h1;\n", +"n_N=(h3-h4)/(q_n);\n", +"x=(h4-h1)/(h2-h1);\n", +"disp('%',n_N*100,'for non reheat cycle plant efficiency is')\n", +"disp ('kJ/kWh',3600/n_N,'Turbine Heat Rate is')\n", +"disp(x,'final dryness fraction is')\n", +"// for reheat cycle\n", +"\n", +"p(1)=70;\n", +"h5(1)=3412; // in kJ/kg\n", +"h7(1)=3065; // in kJ/kg\n", +"h6(1)=2094; // in kJ/kg\n", +"p(2)=50;\n", +"h5(2)=3433; // in kJ/kg\n", +"h7(2)=2981; // in kJ/kg\n", +"h6(2)=2144; // in kJ/kg\n", +"p(3)=25;\n", +"h5(3)=3475; // in kJ/kg\n", +"h7(3)=2826; // in kJ/kg\n", +"h6(3)=2249; // in kJ/kg\n", +"for i=1:3\n", +" q_r(i)=h5(i)-h7(i);\n", +"a(i)=(h6(i)-h4)/(q_r(i));\n", +"n_r(i)=1-a(i); // exact Rankine efficiency\n", +"b(i)=q_r(i)*n_r(i)/n_N;\n", +"n_th(i)=(q_n+b(i))*n_N/(q_n+q_r(i));\n", +"hr_t(i)=3600/n_th(i);\n", +"x(i)=(h6(i)-h1)/(h2-h1);\n", +"disp('bar',p(i),'for reheat pressure' )\n", +"disp('kJ',q_r(i),'q_R=')\n", +"disp('kJ',h6(i)-h4,'H6-H4= ')\n", +"disp('%',n_r(i)*100,'Rankine efficiency of the plant is')\n", +"disp('%',n_th(i)*100,'thermal efficiency of the plant is')\n", +"disp('kJ/kWh',hr_t(i),'Heat Rate is')\n", +"disp(x(i),'final dryness fraction is')\n", +" \n", +"end\n", +"\n", +"disp('Comment: Error in Textbook, Answers vary due to Round-off Errors')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Calculations_on_Steam_Turbine_Plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 4.3 Calculations on Steam Turbine Plant \n", +"\n", +"p1=82.75; // Turbine Inlet Pressure in bar\n", +"T1=510; // Turbine Entry Temperature in Degree Celsius\n", +"pc=0.042; // Condenser Pressure in bar\n", +"H=3420;\n", +"n_e=0.85;\n", +"gamma=1.4;\n", +"n_st1=0.85;\n", +"\n", +"p2=22.75;\n", +"// for regenerative cycle\n", +"hs(1)=121.4; // from steam tables and mollier chart\n", +"p(6)=p2; // pressure at bleed point 1\n", +"Hs(6)=3080; // Enthalpy of steam at bleed point 1\n", +"h1s=931;\n", +"hs(6)=h1s; // Enthalpy of water at bleed point 1\n", +"H_22=H-(n_st1*(H-h1s));\n", +"\n", +"p(5)=10.65; // pressure at bleed point 2\n", +"Hs(5)=2950; // Enthalpy of steam at bleed point 2\n", +"hs(5)=772; // Enthalpy of water at bleed point 2\n", +"\n", +"p(4)=4.35; // pressure at bleed point 3\n", +"Hs(4)=2730; // Enthalpy of steam at bleed point 3\n", +"hs(4)=612; // Enthalpy of water at bleed point 3\n", +"\n", +"p(3)=1.25; // pressure at bleed point 4\n", +"Hs(3)=2590; // Enthalpy of steam at bleed point 4\n", +"hs(3)=444; // Enthalpy of water at bleed point 4\n", +"\n", +"p(2)=0.6; // pressure at bleed point 5\n", +"Hs(2)=2510; // Enthalpy of steam at bleed point 5\n", +"hs(2)=360; // Enthalpy of water at bleed point 5\n", +"\n", +"m=1;\n", +"h_c=121.4;\n", +"x=0.875;\n", +"disp(x,'(a)the final state at point C is')\n", +"for i=2:6\n", +"alpha(i)=(Hs(i)-hs(i-1))/(Hs(i)-hs(i));\n", +"m=m*alpha(i); \n", +"end\n", +"disp('kg',m,'(b)The mass of steam raised per kg of steam reaching the condenser is')\n", +"// part(c) thermal efficiency with feed heating\n", +"H_c=2250;\n", +"h_n=hs(6);\n", +"n_th=1-((H_c-h_c)/(m*(H-h_n)));\n", +"hr_t=3600/n_th;\n", +"//(c) the improvement in thermal efficiency and heat rate\n", +"c=H-H_c;\n", +"d=H-h_c;\n", +"n_R=(H-H_c)/(H-h_c);\n", +"hr_R=3600/n_R;\n", +"deln_th=(n_th-n_R)/n_R;\n", +"disp ('%',deln_th*100,'(c)therefore, the improvement in efficiency is')\n", +"delhr_t=(hr_R-hr_t)/hr_R;\n", +"disp ('%',delhr_t*100,' and, the improvement in heat rate is')\n", +"\n", +"// part(d) decrease of steam flow to the condenser per kWh due to feed heating\n", +"q_s=m*(H-h_n);\n", +"q_r=H_c-h_c;\n", +"w_t=q_s-q_r;\n", +"wt_m=w_t/m;\n", +"sf_r=3600/wt_m;\n", +"s_c=sf_r/m;\n", +"// without feed heating\n", +"wt_f=H-H_c;\n", +"m_wf=3600/wt_f;\n", +"sr_c=(m_wf-s_c)/m_wf;\n", +"disp ('%',sr_c*100,'(d)the decrease in steam reaching the condenser is')\n", +"disp('comment: the calculation for the improvement in efficiency is wrong in the book.')\n", +" " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/5-Combined_Cycle_Plants.ipynb b/Turbines_by_Compressors_And_Fans/5-Combined_Cycle_Plants.ipynb new file mode 100644 index 0000000..6a09987 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/5-Combined_Cycle_Plants.ipynb @@ -0,0 +1,139 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Combined Cycle Plants" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Calculation_on_combined_cycle_power_plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 5.1. Calculation on combined cycle power plant\n", +"\n", +"P_gt=1e5; // Power Output in kW\n", +"m_g=400; // mass flow rate of the exhaust gas in kg/s\n", +"cp_g=1.157; // Specific Heat of gas at Constant Pressure in kJ/(kgK)\n", +"x=0.9; // dryness fraction of steam at the turbine exit\n", +"\n", +"// part(a) Determining capacity of the boiler in kg of steam per hour \n", +"p1=90; // steam Pressure at the entry of steam turbine in bar\n", +"// from steam tables\n", +"t_6s=303.3; // saturation temperature at 90 bar in degree C\n", +"t_5s=t_6s;\n", +"h_fg=1380.8; // from steam table liquid vapour enthalpy at 90 bar\n", +"pp=20; // pinch point in degree C\n", +"t_6=t_6s+pp;\n", +"h_5s=2744.6;\n", +"h_6s=1363.8;\n", +"\n", +"t4=592.6; // Exhaust gas temperature at gas turbine end in degree C\n", +"T4=t4+273; // in Kelvin\n", +"p_c=0.1; // Condenser pressure in bar\n", +"t7=176; // Exhaust gas temperature at stack in degree C\n", +"T7=t7+273; // in Kelvin\n", +"h_7s=191.8; // Specific Enthalpy of water in kJ/kg\n", +"\n", +"m_st=(m_g*cp_g*(t_6-t7))/(h_6s-h_7s);\n", +"disp ('tonnes/hr' ,m_st*3.6,'(a)capacity of the boiler in kg of steam per hour is')\n", +"\n", +"// part(b) temperature of steam at turbine entry\n", +"t_5=t_6+((m_st*(h_5s-h_6s))/(m_g*cp_g)); // energy balance for the evaporator\n", +"\n", +"h_4s=h_5s+(m_g*cp_g*(t4-t_5)/m_st);\n", +"t_4s=540; // in degree C from steam table at p=90 bar\n", +"disp('degree celsius',t_4s,'(b)temperature of steam at turbine entry is')\n", +"\n", +"// part(c)steam turbine plant output and thermal efficiency \n", +"h_5=2350;\n", +"h_6=2150;\n", +"w_st_s=h_4s-h_5;\n", +"w_st_g=w_st_s*(m_st/m_g);\n", +"P_st=m_st*w_st_s;\n", +"disp('MW',P_st/10e02,'(c)Power output of the steam turbine plant is')\n", +"q_st=h_4s-h_7s;\n", +"n_st=w_st_s/q_st;\n", +"disp ('%' ,n_st*100,'thermal Efficiency of staem turbine plant is')\n", +"\n", +"// part(d) thermal efficiency of the combined cycle plant\n", +"n_gt=0.2666; // Gas turbine plant Efficiency\n", +"w_gt=P_gt/m_g;\n", +"q_gt=w_gt/n_gt;\n", +"n_c=(w_gt+w_st_g)/q_gt;\n", +"disp ('%' ,n_c*100,'(d)thermal Efficiency of combined cycle plant is')\n", +"disp('Comment: Error in Textbook, Answers vary due to Round-off Errors')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: combined_gas_and_steam_cycle_power_plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 5.2 combined gas and steam cycle power plant\n", +"P_gt=10e03; // Power Output in kW\n", +"n_st=0.32; // Steam turbine power plant Efficiency\n", +"\n", +"// part(a)steam turbine plant output \n", +"n_gt=0.2; // Gas turbine plant Efficiency\n", +"q_gt=P_gt/n_gt;\n", +"q_st=(1-n_gt)*q_gt;\n", +"P_st=n_st*q_st;\n", +"disp('MW',P_st/10e02,'(a)Power output of the steam turbine plant is')\n", +"\n", +"// part(b) thermal efficiency of the combined cycle plant\n", +"n_c=n_gt+n_st-(n_gt*n_st);\n", +"disp ('%' ,n_c*100,'(b)thermal Efficiency of combined cycle plant is')\n", +"\n", +"// part(c) the heat rate of the combined cycle plant\n", +"hr_c=3600/n_c; \n", +"disp ('kJ/kWh',hr_c,' (c)Heat Rate of the combined cycle plant is')\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/6-Fluid_dynamics.ipynb b/Turbines_by_Compressors_And_Fans/6-Fluid_dynamics.ipynb new file mode 100644 index 0000000..561a4cb --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/6-Fluid_dynamics.ipynb @@ -0,0 +1,136 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Fluid dynamics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: inward_flow_radial_turbine_32000rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 6.1 inward flow radial turbine 32000rpm\n", +"P=150; // Power Output in kW\n", +"N=32e3; // Speed in RPM\n", +"d1=20/100; // outer diameter of the impeller in m\n", +"d2=8/100; // inner diameter of the impeller in m\n", +"V1=387; // Absolute Velocity of gas at entry in m/s\n", +"V2=193; // Absolute Velocity of gas at exit in m/s\n", +"\n", +"// part(a) determining mass flow rate\n", +"u1=%pi*d1*N/60;\n", +"u2=d2*u1/d1;\n", +"w_at=u1^2/10e2;\n", +"m=P/w_at;\n", +"disp ('kg/s' ,m,'(a)mass flow rate is')\n", +"\n", +"// part (b) determining the percentage energy transfer due to the change of radius\n", +"n=((u1^2-u2^2)/2e3)/w_at; \n", +"disp ('%',n*100,'(b)percentage energy transfer due to the change of radius is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: radially_tipped_Centrifugal_blower_3000rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 6.2 radially tipped Centrifugal blower 3000rpm\n", +"P=150; // Power Output in kW\n", +"N=3e3; // Speed in RPM\n", +"d2=40/100; // outer diameter of the impeller in m\n", +"d1=25/100; // inner diameter of the impeller in m\n", +"b=8/100; // impeller width at entry in m\n", +"n_st=0.7; // stage efficiency\n", +"V1=22.67; // Absolute Velocity at entry in m/s\n", +"ro=1.25; // density of air in kg/m3\n", +"\n", +"// part(a) determining the pressure developed\n", +"u2=%pi*d2*N/60;\n", +"u1=d1*u2/d2;\n", +"w_ac=u2^2;\n", +"delh_s=n_st*w_ac;\n", +"delp=ro*delh_s;\n", +"disp ('mm W.G.' ,delp/9.81,'(a)the pressure developed is')\n", +"\n", +"// part (b) determining the power required\n", +"A1=%pi*d1*b;\n", +"m=ro*V1*A1;\n", +"P=m*w_ac/10e2;\n", +"disp('kW',P,'(b)Power required is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Calculation_on_an_axial_flow_fan.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 6.3 Calculation on an axial flow fan\n", +"N=1.47e3; // Speed in RPM\n", +"d=30/100; // Mean diameter of the impeller in m\n", +"ro=1.25; // density of air in kg/m3\n", +"\n", +"// part(b) determining the pressure rise across the fan\n", +"u=%pi*d*N/60;\n", +"w_c=u^2/3;\n", +"delp=ro*w_c;\n", +"disp ('mm W.G.' ,delp/9.81,'(b)the pressure rise across the fan is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/7-Dimensional_Analysis_and_Performance_Parameters.ipynb b/Turbines_by_Compressors_And_Fans/7-Dimensional_Analysis_and_Performance_Parameters.ipynb new file mode 100644 index 0000000..af0e519 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/7-Dimensional_Analysis_and_Performance_Parameters.ipynb @@ -0,0 +1,229 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: Dimensional Analysis and Performance Parameters" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1: Calculation_for_the_specific_speed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 7.1 Calculation for the specific speed\n", +"funcprot(0)\n", +"//part(a)specific speed of gas turbine\n", +"P=2e3; // Gas Turbine Power Output in kW\n", +"N=16e3; // Speed in RPM\n", +"T1=1e3; // Entry Temperature in Kelvin\n", +"p1=50; // Entry Pressure in bar\n", +"p2=25; // Exit Pressure in bar\n", +"cp=1.15e3; // Specific Heat at Constant Pressure in J/(kgK)\n", +"gamma_g=1.3;\n", +"omega=%pi*2*N/60;\n", +"ro=p1*1e5/(((gamma_g-1)/gamma_g)*cp*T1);\n", +"pr=p2/p1; // pressure ratio\n", +"T2s=T1*(pr^((gamma_g-1)/gamma_g));\n", +"delh_s=cp*(T1-T2s);\n", +"NS=omega*sqrt(P*10e2/ro)*delh_s^(-5/4)\n", +"disp(NS,'(a)the specific speed of gas turbine is')\n", +"\n", +"// part(b)the specific speed of a centrifugal compressor\n", +"pr_b=2; // Compressor pressure ratio\n", +"N_b=24e3; // Speed in RPM\n", +"m=1.5; // in kg/s\n", +"cp_a=1.005e3; // Specific Heat of air at Constant Pressure in kJ/(kgK)\n", +"R=0.287;\n", +"gamma=1.4;\n", +"T1_b=300; // Entry Temperature in Kelvin\n", +"p1_b=1; // Entry Pressure in bar\n", +"ro_b=p1_b*1e2/(R*T1_b);\n", +"omega_b=%pi*2*N_b/60;\n", +"Q=m/ro_b;\n", +"T2=T1_b*(pr_b^((gamma-1)/gamma));\n", +"delh_s_b=cp_a*(T2-T1_b);\n", +"NS_b=omega_b*sqrt(Q)*delh_s_b^(-3/4);\n", +"disp(NS_b,'(b)the specific speed of a centrifugal compressor is')\n", +"\n", +"// part(c)the specific speed of an axial compressor\n", +"pr_c=1.4; // Compressor pressure ratio\n", +"N_c=6e3; // Speed in RPM\n", +"m_c=15; // in kg/s\n", +"omega_c=%pi*2*N_c/60;\n", +"Q_c=m_c/ro_b;\n", +"T2_c=T1_b*(pr_c^((gamma-1)/gamma));\n", +"delh_s_c=cp_a*(T2_c-T1_b);\n", +"NS_c=omega_c*sqrt(Q_c)*delh_s_c^(-3/4)\n", +"disp(NS_c,'(c)the specific speed of an axial compressor is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2: Calculating_the_discharge_and_specific_speed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"\n", +"// scilab Code Exa 7.2 Calculating the discharge of a geometrically similar blower and specific speed of the fan\n", +"pr=2; // Compressor pressure ratio\n", +"N1=1.47e3; // fan Speed in RPM\n", +"N2=0.36e3; // blower Speed in RPM\n", +"Q1=2; // discharge in m3/s\n", +"h=10e-3; // in m W.G.\n", +"ro_w=10e2;\n", +"ro_a=1.25; // density of air in kg/m3\n", +"omega1=%pi*2*N1/60;\n", +"g=9.81; // in m/s2\n", +"p=ro_w*g*h\n", +"H=p/(ro_a*g);\n", +"delh_s=g*H;\n", +"NS=omega1*sqrt(Q1)*delh_s^(-3/4)\n", +"disp(NS,'the specific speed is')\n", +"// for the same specific speed of two geometrically similar fans\n", +"a=N1/N2;\n", +"Q2=a^2*Q1;\n", +"disp('m3/s',Q2,' and the discharge of a geometrically similar blower is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3: Calculation_on_a_small_compressor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 7.3 Calculation on a small compressor\n", +"pr=1.6; // Compressor pressure ratio\n", +"N1=54e3; // Speed in RPM\n", +"n_c=0.85; // efficiency\n", +"m_a=1.5778; // in kg/s\n", +"cp_a=1.009; // Specific Heat of air at Constant Pressure in kJ/(kgK)\n", +"gamma=1.4;\n", +"// part (a) determining the power required to drive the compressor\n", +"T01=300; // Entry Temperature in Kelvin\n", +"p01=1.008; // Entry Pressure in bar\n", +"n=(gamma-1)/gamma;\n", +"T2s=T01*(pr^n);\n", +"delh_s=cp_a*(T2s-T01)/n_c;\n", +"P=m_a*delh_s;\n", +"disp('kW',P,'(a)Power required to drive the compressor is')\n", +"\n", +"// part (b) determining the speed, mass flow rate, pressure ratio and power required of a geometrically similar compressor\n", +"// geometrically similar compressor of 3 times the size of small compressor is constructed \n", +"N2=N1/3;\n", +"disp('rpm',N2,'(b)(i)speed of a geometrically similar compressor is')\n", +"m2=9*m_a;\n", +"disp('kg/s',m2,'(b)(ii)mass flow rate of a geometrically similar compressor is')\n", +"disp(pr,'(b)(iii)pressure ratio of a geometrically similar compressor is')\n", +"P2=9*P;\n", +"disp('kW',P2,'(b)(iv)Power required is')\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4: Calculation_on_design_of_a_single_stage_gas_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 7.4 Calculation on a single stage gas turbine\n", +"\n", +"gamma_g=1.33;\n", +"gamma=1.4\n", +"R_g=284.1;\n", +"R=287;\n", +"P=1e3; // Power Output in kW\n", +"N1=3e3; // Speed in RPM\n", +"n_t=0.87; // efficiency\n", +"cp_g=1.145; // Specific Heat of gas at Constant Pressure in kJ/(kgK)\n", +"cp_a=1.0045; // Specific Heat of air at Constant Pressure in kJ/(kgK)\n", +"\n", +"// part (a)mass flow rate of the gas through the turbine\n", +"T01=1000; // Entry Temperature in Kelvin\n", +"p01=2.5; // Entry Pressure in bar\n", +"T01a=500; // Entry Temperature of air in Kelvin\n", +"p01a=2; // Entry Pressure of air in bar\n", +"p02=1; // Exit Pressure in bar\n", +"pr0=p01/p02;\n", +"T02=T01*(pr0^(-((gamma_g-1)/gamma_g)));\n", +"delh_s1=cp_g*(T01-T02)*n_t;\n", +"m_g=P/delh_s1;\n", +"disp('kg/s',m_g,'(a)mass flow rate of the gas through the turbine is')\n", +"\n", +"// part (b)speed, mass flow rate, pressure ratio and power required \n", +"N2=sqrt(1/2)*5*N1;\n", +"disp('rpm',N2,'(b)(i)speed of a geometrically similar compressor is')\n", +"a=0.2; // a=D2/D1;\n", +"m2=(a^2)*sqrt(R_g/R)*sqrt(T01/T01a)*(p01a/p01)*m_g;\n", +"disp('kg/s',m2,'(b)(ii)mass flow rate of a geometrically similar turbine is')\n", +"delh_s2=0.5*delh_s1;\n", +"P2=m2*delh_s2;\n", +"disp('kW',P2,'(b)(iii)Power developed is')\n", +"pr=(1-(delh_s2/(cp_a*T01a*n_t)))^(-1/((gamma-1)/gamma));\n", +"disp(pr,'(b)(iv)pressure ratio of a geometrically similar turbine is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/8-Flow_Through_Cascades.ipynb b/Turbines_by_Compressors_And_Fans/8-Flow_Through_Cascades.ipynb new file mode 100644 index 0000000..ec3e817 --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/8-Flow_Through_Cascades.ipynb @@ -0,0 +1,291 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: Flow Through Cascades" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Calculation_on_a_compressor_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 8.1 Calculation on a compressor cascade\n", +"\n", +"V1=75; // Absolute Velocity of air at entry in m/s\n", +"alpha1=48; // air angle at entry\n", +"alpha2=25; // air angle at exit\n", +"p=1.1; // pitch-chord ratio\n", +"delps=11; // stagnation pressure loss in mm W.G.\n", +"ro=1.25; // density of air in kg/m3\n", +"g=9.81;\n", +"a=0.5*(tand(alpha1)+tand(alpha2)); \n", +"alpham=atand(a);\n", +"b=0.5*ro*(V1^2);\n", +"Y=delps*g/b;\n", +"disp (Y,'the loss coefficient is')\n", +"c=(cosd(alpham)^3)/(cosd(alpha1)^2);\n", +"C_D=p*Y*c;\n", +"disp (C_D,'the drag coefficient is')\n", +"d=2*p*(tand(alpha1)-tand(alpha2))*cosd(alpham);\n", +"e=C_D*tand(alpham);\n", +"C_L=d-e;\n", +"disp (C_L,'the Lift coefficient is')\n", +"f=(cosd(alpha1)^2)/(cosd(alpha2)^2);\n", +"C_ps=1-f;\n", +"disp (C_ps,'the Ideal pressure recovery coefficient is')\n", +"C_pa=C_ps-Y;\n", +"disp (C_pa,'the Actual pressure recovery coefficient is')\n", +"n_D=C_pa/C_ps;\n", +"disp (n_D,'the Diffuser efficiency is')\n", +"n_dmax=1-(2*C_D/C_L);\n", +"disp (n_dmax,'the Maximum Diffuser efficiency is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Calculation_on_a_turbine_blade_row_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 8.2 Calculation on a turbine blade row cascade\n", +"\n", +"beta1=35; // blade angle at entry\n", +"beta2=55; // blade angle at exit\n", +"i=5; // incidence\n", +"delta=2.5; // deviation\n", +"alpha1=beta1+i; // air angle at entry\n", +"alpha2=beta2-delta; // air angle at exit\n", +"t_c=0.3; // maximum thickness-chord ratio(t/l)\n", +"a_r=2.5; // aspect ratio\n", +"\n", +"//part(a)optimum pitch-chord ratio from Zweifels relation\n", +"C_z=0.8; // from Zweifel's relation \n", +"p_c=C_z/(2*(cosd(alpha2)^2)*(tand(alpha1)+tand(alpha2)));\n", +"disp (p_c,'(a)the optimum pitch-chord ratio from Zweifels relation is')\n", +"\n", +"//part(b) loss coefficient from Soderbergs and Hawthorne relations\n", +"ep=alpha1+alpha2; // deflection angle\n", +"Zeeta=0.075;\n", +"b=(1+Zeeta)*(0.975+(0.075/a_r))\n", +"zeeta=b-1;\n", +"disp (zeeta,'(b)(i)the loss coefficient from Soderbergs relation is')\n", +"z_p=0.025*(1+((ep/90)^2)); // Hawthorne's relation\n", +"disp (z_p,'(b)(ii)the loss coefficient from Hawthorne relation is')\n", +"z=(1+(3.2/a_r))*z_p; // the total cascade loss coefficient\n", +"Y=0.5*(z+zeeta); \n", +"\n", +"// part(c)drag coefficient\n", +"alpham=atand(0.5*(tand(alpha2)-tand(alpha1)));\n", +"C_D=p_c*Y*(cosd(alpham)^3)/(cosd(alpha2)^2);\n", +"disp (C_D,'(c)the drag coefficient is')\n", +"\n", +"// part(d)Lift coefficient\n", +"C_L=(2*p_c*(tand(alpha1)+tand(alpha2))*cosd(alpham))+(C_D*tand(alpham));\n", +"disp (C_L,'(d)the Lift coefficient is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Calculation_on_a_compressor_cascade.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 8.3 Calculation on a compressor cascade\n", +"theta=25; // Camber angle\n", +"gamma_a=30; // stagger angle\n", +"i=5; // incidence\n", +"t_c=0.031; // momentum thickness-chord ratio(t/l)\n", +"p_c=1; // pitch-chord ratio\n", +"\n", +"//part(a)cascade blade angles\n", +"beta1=((2*gamma_a)+theta)*0.5; // blade angle at entry\n", +"beta2=((2*gamma_a)-theta)*0.5; // blade angle at exit\n", +"disp ('(a)therefore, the blade angles are')\n", +"disp ('degree',beta1,'beta1=')\n", +"disp ('degree',beta2,'beta2=')\n", +"\n", +"//part(b) the nominal air angles\n", +"alpha1=beta1+i; // air angle at entry\n", +"alpha2=atand(tand(alpha1)-(1.55/(1+(1.5*p_c)))); // air angle at exit\n", +"disp ('(b)therefore, the air angles are')\n", +"disp ('degree',alpha1,'alpha1=')\n", +"disp ('degree',alpha2,'alpha2=')\n", +"\n", +"//part(c) stagnation pressure loss coefficient\n", +"Y=2*t_c*p_c*(cosd(alpha1)^2)/(cosd(alpha2)^3);\n", +"disp (Y,'(c)the stagnation pressure loss coefficient is')\n", +"\n", +"// part(d)drag coefficient\n", +"alpham=atand(0.5*(tand(alpha1)+tand(alpha2)));\n", +"C_D=p_c*Y*(cosd(alpham)^3)/(cosd(alpha1)^2);\n", +"disp (C_D,'(d)the drag coefficient is')\n", +"\n", +"// part(e)Lift coefficient\n", +"C_L=(2*p_c*(tand(alpha1)-tand(alpha2))*cosd(alpham))-(C_D*tand(alpham));\n", +"disp (C_L,'(e)the Lift coefficient is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Calculation_on_a_blower_type_annular_cascade_tunnel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 8.4 blower type annular cascade tunnel\n", +"\n", +"t=35;\n", +"T=t+273; // test Temperature in Kelvin\n", +"p=1.02; // test Pressure in bar\n", +"dm=50/100; // mean diameter of the impeller blade in m\n", +"b=15/100; // blade length in m\n", +"n_o=0.6; // stage efficiency\n", +"R=287;\n", +"c=100; // Maximum Velocity upstream of the cascade in m/s\n", +"ro=p*10e4/(R*T); // density of air in kg/m3\n", +"\n", +"// part(a) determining the total pressure developed by the blower\n", +"d_h=0.5*ro*(c^2);\n", +"loss=0.1*d_h;\n", +"delp=d_h+loss;\n", +"disp ('mm W.G.' ,delp/9.81,'(a)the pressure developed is')\n", +"\n", +"// part (b) determining the discharge\n", +"A=%pi*dm*b; // the annulus cross-sectional area \n", +"Q=c*A;\n", +"disp ('m3/min' ,Q*60,'(b)the discharge is')\n", +"\n", +"// part (c) determining the power required to drive the blower\n", +"P=Q*delp/(n_o*10e2);\n", +"disp('kW',P,'(c)Power required to drive the blower is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Calculation_on_a_compressor_type_radial_cascade_tunnel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 8.5 compressor type radial cascade tunnel\n", +"\n", +"M=0.7; // Mach Number\n", +"pr=0.721; // pr=pt/p0 From isentropic gas tables\n", +"t_opt=0.911; // t_opt=Tt/T0\n", +"pa=1.013; // Atmospheric Pressure in bar\n", +"Ta=306; // in K\n", +"n_c=0.65; // efficiency\n", +"R=288;\n", +"gamma=1.4;\n", +"alpha=30;\n", +"dm=45/100; // mean diameter of the impeller blade in m\n", +"b=10/100; // blade width in m\n", +"cp_a=1.008; // Specific Heat of air at Constant Pressure in kJ/(kgK)\n", +"\n", +"// part(a) pressure ratio of the compressor\n", +"pr_c=1/pr;\n", +"disp(pr_c,'(a)pressure ratio of the compressor is')\n", +"\n", +"// part(b) stagnation pressure in the settling chamber\n", +"p02=pa*pr_c;\n", +"disp('bar',p02,'(b)stagnation pressure in the settling chamber is')\n", +"\n", +"// part(c)test section conditions(static pressure, temperature and velocity)\n", +"n=(gamma-1)/gamma;\n", +"T02s=Ta*(pr_c^((gamma-1)/gamma));\n", +"T02=Ta+((T02s-Ta)/n_c);\n", +"T_t=t_opt*T02;\n", +"p_t=pr*p02;\n", +"c_t=M*sqrt(gamma*R*T_t);\n", +"disp('(c)test section conditions are given by: ')\n", +"disp('bar',p_t,'static pressure of air in the test section is')\n", +"disp('K',T_t,'static temperature of air in the test section is')\n", +"disp('m/s',c_t,'velocity of air in the test section is')\n", +"\n", +"// part(d) determining mass flow rate\n", +"c_r=c_t*sind(alpha);\n", +"ro_t=p_t*1e5/(R*T_t); // density of air in kg/m3\n", +"A_t=%pi*dm*b;\n", +"m=ro_t*A_t*c_r;\n", +"disp('kg/s',m,'(d) mass flow rate of compressor is')\n", +"\n", +"// part (e) determining the power required to drive the air compressor\n", +"delh_s=cp_a*(T02-Ta);\n", +"P=m*delh_s;\n", +"disp('kW',P,'(e)Power required to drive the air compressor is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Turbines_by_Compressors_And_Fans/9-Axial_Turbine_Stages.ipynb b/Turbines_by_Compressors_And_Fans/9-Axial_Turbine_Stages.ipynb new file mode 100644 index 0000000..dd5485c --- /dev/null +++ b/Turbines_by_Compressors_And_Fans/9-Axial_Turbine_Stages.ipynb @@ -0,0 +1,503 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Axial Turbine Stages" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: Calculation_on_multi_stage_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 9.1 Calculation on multi stage turbine\n", +"\n", +"d=1; // mean diameter of the impeller blade in m\n", +"T1=500; // Initial Temperature in degree C\n", +"t1=T1+273; // in Kelvin\n", +"p1=100; // Initial Pressure in bar\n", +"N=3e3; // Speed in RPM\n", +"m=100; // in kg/s\n", +"alpha2=70; // exit angle of the first stage nozzle blades\n", +"\n", +"// part(a) single stage impulse \n", +"nsti=0.78;\n", +"u=%pi*d*N/60;\n", +"sigma=0.5*(sind(alpha2)); // maximum utilization factor\n", +"c2=u/sigma;\n", +"cx=c2*(cosd(alpha2));\n", +"beta2=atand(0.5*(tand(alpha2))); // beta2=beta3\n", +"wst=2*(u^2)*1e-3;\n", +"P=m*wst;\n", +"disp('(a)for single stage impulse')\n", +"disp('degree',beta2,'blade angles are beta2=beta3= ')\n", +"disp('MW',P*1e-3,'Power developed is')\n", +"\n", +"sv=0.04; // specific volume of steam after expansion in m3/kg\n", +"h=(m*sv)/(cx*%pi*d); // h2=h3=h\n", +"disp('cm',h*1e2,'blade height is')\n", +"delhs=wst/nsti;\n", +"disp('final state of the steam is')\n", +"p=81.5; // from enthalpy-entropy diagram\n", +"T=470;\n", +"disp('bar',p,'p=')\n", +"disp('degree C',T,'T=')\n", +"\n", +"// part(b) Two-stage Curtis wheel \n", +"nstc=0.65;\n", +"u=%pi*d*N/60;\n", +"sigma2=0.25*(sind(alpha2));\n", +"c2_2=u/sigma2;\n", +"cx2=c2_2*(cosd(alpha2));\n", +"beta2_2=atand((3*u)/cx2); // beta2=beta3\n", +"alpha3=atand((2*u)/(c2_2*cosd(alpha2))); // alpha2'=alpha3\n", +"beta2_s=atand((u)/cx2); // beta2'=beta3'\n", +"wI=6*(u^2)*1e-3;\n", +"wII=2*(u^2)*1e-3;\n", +"wst2=wI+wII;\n", +"P2=m*wst2;\n", +"disp('(b)for Two-stage Curtis wheel')\n", +"disp('degree',alpha3,'air angles are alpha2s=alpha3= ')\n", +"disp('degree',beta2_2,'for first stage blade angles are beta2=beta3= ')\n", +"disp('degree',beta2_s,'for second stage blade angles are beta2s=beta3s= ')\n", +"\n", +"disp('MW',P2*1e-3,'Power developed is')\n", +"\n", +"delhs2=wst2/nstc;\n", +"// from enthalpy-entropy diagram for the expansion\n", +"disp('final state of the steam is')\n", +"p2=27;\n", +"T2=365;\n", +"v2=0.105; // specific volume of steam after expansion in m3/kg\n", +"disp('bar',p2,'p=')\n", +"disp('degree C',T2,'T=')\n", +"disp('m3/kg',v2,'v=')\n", +"h2=(m*v2)/(cx2*%pi*d);\n", +"disp('cm',h2*1e2,'blade height is')\n", +"\n", +"// part(c) Two-stage Reateau wheel \n", +"nst1=0.78;\n", +"wI3=2*(u^2)*1e-3;\n", +"wII3=2*(u^2)*1e-3;\n", +"wst3=wI3+wII3;\n", +"P3=m*wst3;\n", +"disp('(c)for Two-stage Reateau wheel')\n", +"disp('degree',beta2,'blade angles are beta2=beta3= ')\n", +"disp('MW',P3*1e-3,'Power developed is')\n", +"delhs3=wst3/nst1;\n", +"disp('final state of the steam is')\n", +"p3=65; // from enthalpy-entropy diagram\n", +"T3=445;\n", +"v3=0.05; // specific volume of steam after expansion in m3/kg\n", +"disp('bar',p3,'p=')\n", +"disp('degree C',T3,'T=')\n", +"disp('m3/kg',v3,'v=')\n", +"h3=(m*v3)/(cx*%pi*d);\n", +"disp('cm',h3*1e2,'blade height for the second stage is')\n", +"\n", +"// part(d) single stage 50% reaction \n", +"nstr=0.85;\n", +"sigma4=sind(alpha2); // maximum utilization factor\n", +"c2_4=u/sigma4; // c2_4=w_3\n", +"cx4=c2_4*(cosd(alpha2)); // alpha2=beta3;\n", +"beta2_4=0; // beta2=alpha3\n", +"wst4=(u^2)*1e-3;\n", +"P4=m*wst4;\n", +"disp('(d)for single stage 50% reaction')\n", +"disp('degree',beta2_4,'blade angles are beta2=alpha3= ')\n", +"disp('degree',alpha2,'and beta3=alpha2= ')\n", +"disp('MW',P4*1e-3,'Power developed is')\n", +"delhs4=wst4/nstr;\n", +"// from enthalpy-entropy diagram \n", +"disp('final state of the steam is')\n", +"p4=90;\n", +"T4=485;\n", +"v4=0.035;\n", +"disp('bar',p4,'p=')\n", +"disp('degree C',T4,'T=')\n", +"disp('m3/kg',v4,'v=')\n", +"h4=(m*v4)/(cx4*%pi*d);\n", +"disp('cm',h4*1e2,'the rotor blade height at exit is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: Calculation_on_an_axial_turbine_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 9.2 Calculation on an axial turbine stage \n", +"\n", +"dh=0.450; // hub diameter in m\n", +"dt=0.750; // tip diameter in m\n", +"d=0.5*(dt+dh); // mean diameter of the impeller blade in m\n", +"r=d/2;\n", +"T1=500; // Initial Temperature in degree C\n", +"t1=T1+273; // in Kelvin\n", +"p1=100; // Initial Pressure in bar\n", +"N=6e3; // rotor Speed in RPM\n", +"m=100; // in kg/s\n", +"alpha2m=75; // air angle at nozzle exit\n", +"beta2m=45; // air angle at rotor entry\n", +"beta3m=76; // air angle at rotor exit\n", +"u=%pi*d*N/60;\n", +"uh=%pi*dh*N/60;\n", +"ut=%pi*dt*N/60;\n", +"// for mean section\n", +"c2m=(cosd(beta2m)/sind(alpha2m-beta2m))*u;\n", +"cx2m=c2m*cosd(alpha2m);\n", +"ct2m=c2m*sind(alpha2m);\n", +"ct3m=(cx2m*tand(beta3m))-u;\n", +"C2=r*ct2m;\n", +"C3=r*ct3m;\n", +"\n", +"// part(a) the relative and absolute air angles \n", +"disp('for mean section')\n", +"disp('(a) the relative and absolute air angles are')\n", +"disp('degree',beta2m,'air angle at rotor entry is beta2m= ')\n", +"disp('degree',beta3m,'air angle at rotor exit is beta3m= ')\n", +"disp('degree',alpha2m,'air angle at nozzle exit is alpha2m= ')\n", +"// part(b) degree of reaction\n", +"cx=cx2m;\n", +"R=cx*(tand(beta3m)-tand(beta2m))*100/(2*u);\n", +"disp('%',R,'(b)degree of reaction is')\n", +"// part(c) blade-to-gas speed ratio\n", +"sigma=u/c2m;\n", +"disp(sigma,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"omega=2*%pi*N/60;\n", +"w=omega*(C2+C3);\n", +"disp('kJ/kg',w*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"z=w/(u^2);\n", +"disp(z,'(e)the loading coefficient is')\n", +"\n", +"// for hub section\n", +"rh=dh/2;\n", +"alpha2h=atand(C2/(rh*cx));\n", +"disp('for hub section')\n", +"disp('(a) the relative and absolute air angles are')\n", +"disp('degree',alpha2h,'air angle at nozzle exit is alpha2h= ')\n", +"beta2h=atand(tand(alpha2h)-(uh/cx));\n", +"disp('degree',beta2h,'air angle at rotor entry is beta2h= ')\n", +"beta3h=atand((C3/(rh*cx))+(uh/cx));\n", +"disp('degree',beta3h,'air angle at rotor exit is beta3h= ')\n", +"// part(b) degree of reaction\n", +"Rh=cx*(tand(beta3h)-tand(beta2h))*100/(2*uh);\n", +"disp('%',Rh,'(b)degree of reaction is')\n", +"// part(c) blade-to-gas speed ratio\n", +"c2h=cx/(cosd(alpha2h));\n", +"sigmah=uh/c2h;\n", +"disp(sigmah,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"wh=uh*cx*(tand(beta3h)+tand(beta2h));\n", +"disp('kJ/kg',wh*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"zh=wh/(uh^2);\n", +"disp(zh,'(e)the loading coefficient is')\n", +"\n", +"// for tip section\n", +"rt=dt/2;\n", +"alpha2t=atand(C2/(rt*cx));\n", +"disp('for tip section')\n", +"disp('(a) the relative and absolute air angles are')\n", +"disp('degree',alpha2t,'air angle at nozzle exit is alpha2t= ')\n", +"beta2t=atand(tand(alpha2t)-(ut/cx));\n", +"disp('degree',beta2t,'air angle at rotor entry is beta2t= ')\n", +"beta3t=atand((C3/(rt*cx))+(ut/cx));\n", +"disp('degree',beta3t,'air angle at rotor exit is beta3t= ')\n", +"// part(b) degree of reaction\n", +"Rt=cx*(tand(beta3t)-tand(beta2t))*100/(2*ut);\n", +"disp('%',Rt,'(b)degree of reaction is')\n", +"// part(c) blade-to-gas speed ratio\n", +"c2t=cx/(cosd(alpha2t));\n", +"sigmat=ut/c2t;\n", +"disp(sigmat,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"wt=ut*cx*(tand(beta3t)+tand(beta2t));\n", +"disp('kJ/kg',wt*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"zt=wt/(ut^2);\n", +"disp(zt,'(e)the loading coefficient is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: Calculation_on_an_axial_turbine_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 9.3 Calculation on an axial turbine stage \n", +"\n", +"dh=0.450; // hub diameter in m\n", +"dt=0.750; // tip diameter in m\n", +"d=0.5*(dt+dh); // mean diameter of the impeller blade in m\n", +"r=d/2;\n", +"R_m=0.5; // degree of reaction for mean section\n", +"T1=500; // Initial Temperature in degree C\n", +"t1=T1+273; // in Kelvin\n", +"p1=100; // Initial Pressure in bar\n", +"N=6e3; // rotor Speed in RPM\n", +"m=100; // in kg/s\n", +"alpha2m=75; // air angle at nozzle exit\n", +"beta_2m=0; // air angle at rotor entry\n", +"beta_3m=75; // air angle at rotor exit\n", +"// assuming radial equillibrium and free vortex flow in the stage, axial velocity is constant throughout\n", +"u_m=%pi*d*N/60;\n", +"uh=%pi*dh*N/60;\n", +"ut=%pi*dt*N/60;\n", +"// for mean section\n", +"c_xm=u_m*cotd(alpha2m);\n", +"c_2m=(1/sind(alpha2m))*u_m;\n", +"c_t2m=u_m;\n", +"\n", +"disp('for mean section')\n", +"// part(c) blade-to-gas speed ratio\n", +"sigma_m=u_m/c_2m;\n", +"disp(sigma_m,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"w_m=u_m*c_t2m;\n", +"disp('kJ/kg',w_m*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"shi_m=w_m/(u_m^2);\n", +"disp(shi_m,'(e)the loading coefficient is')\n", +"\n", +"// for hub section\n", +"rh=dh/2;\n", +"n=(sind(alpha2m)^2);\n", +"c_x2h=c_xm*((r/rh)^n);\n", +"c_t2h=c_t2m*((r/rh)^n);\n", +"c_2h=c_2m*((r/rh)^n);\n", +"disp('for hub section')\n", +"disp('(a) the relative air angles are')\n", +"beta2h=atand((c_t2h-uh)/c_x2h);\n", +"disp('degree',beta2h,'air angle at rotor entry is beta2h= ')\n", +"beta3h=atand(uh/c_x2h);\n", +"disp('degree',beta3h,'air angle at rotor exit is beta3h= ')\n", +"// part(b) degree of reaction\n", +"Rh=c_x2h*(tand(beta3h)-tand(beta2h))*100/(2*uh);\n", +"disp('%',Rh,'(b)degree of reaction is')\n", +"// part(c) blade-to-gas speed ratio\n", +"sigmah=uh/c_2h;\n", +"disp(sigmah,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"wh=uh*c_t2h;\n", +"disp('kJ/kg',wh*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"shi_h=wh/(uh^2);\n", +"disp(shi_h,'(e)the loading coefficient is')\n", +"\n", +"// for tip section\n", +"rt=dt/2;\n", +"c_x2t=c_xm*((r/rt)^n);\n", +"c_t2t=c_t2m*((r/rt)^n);\n", +"c_2t=c_2m*((r/rt)^n);\n", +"disp('for tip section')\n", +"disp('(a) the relative air angles are')\n", +"beta2t=atand((c_t2t-ut)/c_x2t);\n", +"disp('degree',beta2t,'air angle at rotor entry is beta2t= ')\n", +"beta3t=atand(ut/c_x2t);\n", +"disp('degree',beta3t,'air angle at rotor exit is beta3t= ')\n", +"// part(b) degree of reaction\n", +"Rt=c_x2t*(tand(beta3t)-tand(beta2t))*100/(2*ut);\n", +"disp('%',Rt,'(b)degree of reaction is')\n", +"// part(c) blade-to-gas speed ratio\n", +"sigmat=ut/c_2t;\n", +"disp(sigmat,'(c)blade-to-gas speed ratio is')\n", +"// part(d) specific work\n", +"wt=ut*c_t2t;\n", +"disp('kJ/kg',wt*1e-3,'(d)specific work is')\n", +"// part(e) the loading coefficient\n", +"shi_t=wt/(ut^2);\n", +"disp(shi_t,'(e)the loading coefficient is')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: axial_turbine_stage_3000_rpm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 9.4 axial turbine stage 3000 rpm \n", +"\n", +"d=1; // mean diameter of the impeller blade in m\n", +"r=d/2;\n", +"N=3e3; // rotor Speed in RPM\n", +"a_r(1)=1; // aspect ratio\n", +"a_r(2)=2;\n", +"a_r(3)=3;\n", +"alpha2=70; // air angle at nozzle exit\n", +"alpha3=0;\n", +"beta_2=54; // air angle at rotor entry\n", +"sigma=0.5*(sind(alpha2)); // blade to gas speed ratio\n", +"u=%pi*d*N/60;\n", +"c2=u/sigma;\n", +"cx=c2*(cosd(alpha2));\n", +"beta_3=beta_2; // air angle at rotor exit\n", +"phi=cx/u;\n", +"e_R=beta_2+beta_3; // Rotor deflection angle\n", +"zeeta_p_N=0.025*(1+((alpha2/90)^2)); // profile loss coefficient for nozzle\n", +"zeeta_p_R=0.025*(1+((e_R/90)^2)); // profile loss coefficient for rotor\n", +"for i=1:3\n", +"disp(a_r(i),'when Aspect ratio=')\n", +"zeeta_N=(1+(3.2/a_r(i)))*zeeta_p_N; // total loss coefficient for nozzle\n", +"zeeta_R=(1+(3.2/a_r(i)))*zeeta_p_R; // total loss coefficient for rotor\n", +"a=(zeeta_R*(secd(beta_3)^2))+(zeeta_N*(secd(alpha2)^2));\n", +"b=phi*(tand(alpha2)+tand(beta_3))-1;\n", +"c=(zeeta_R*(secd(beta_3)^2))+(zeeta_N*(secd(alpha2)^2))+(secd(alpha3)^2);\n", +"n_tt=inv(1+(0.5*(phi^2)*(a/b)));\n", +"disp('%',n_tt*1e2,'total-to-total efficiency is')\n", +"n_ts=inv(1+(0.5*(phi^2)*(c/b)));\n", +"disp('%',n_ts*1e2,'total-to-static efficiency is')\n", +"end" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: Calculation_on_a_gas_turbine_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// scilab Code Exa 9.5 Calculation on a gas turbine stage \n", +"\n", +"Rm=0.5; // Degree of reaction\n", +"funcprot(0);\n", +"T1=1500; // in Kelvin\n", +"p1=10; // Initial Pressure in bar\n", +"N=12e3; // rotor Speed in RPM\n", +"m=70; // in kg/s\n", +"pr=2; // Pressure Ratio\n", +"n_st=0.87; // Stage Efficiency \n", +"alpha_2=60; // Fixed Blade exit angle \n", +"cp=1005; // Specific Heat at Constant Pressure in J/(kgK)\n", +"R=287;\n", +"gamma=1.4;\n", +"n=(gamma-1)/gamma;\n", +"T3ss=T1/(pr^n);\n", +"delh1_3=cp*(T1-T3ss)*n_st;\n", +"delh1_2=0.5*delh1_3;\n", +"c2=sqrt(2*delh1_2);\n", +"sigma_opt=sind(alpha_2);\n", +"u=sigma_opt*c2;\n", +"// part(a) Flow coefficient\n", +"cx=c2*cosd(alpha_2);\n", +"phi=cx/u;\n", +"disp(phi,'(a)Flow coefficient is')\n", +"\n", +"// part(b) mean diameter of the stage\n", +"d=u*60/(%pi*N);\n", +"disp('m',d,'(b)mean diameter of the stage is')\n", +"\n", +"// part(c) power developed\n", +"P=m*delh1_3;\n", +"disp('MW',P*1e-6,'(c)power developed is')\n", +"\n", +"// part(d) pressure ratio across the fixed and rotor blade rings\n", +"delh1_3ss=delh1_3/n_st;\n", +"delT1_3=delh1_3/cp;\n", +"delT1_3ss=delh1_3ss/cp;\n", +"stage_loss=delT1_3ss-delT1_3;\n", +"delT1_2=delh1_2/cp;\n", +"delT1_2s=delT1_2+(0.5*stage_loss)\n", +"pr_stator=((1-(delT1_2s/T1))^(-1/n));\n", +"disp(pr_stator,'(d)pressure ratio across the fixed blade rings is')\n", +"pr_rotor=pr/pr_stator;\n", +"disp(pr_rotor,'and pressure ratio across the rotor blade rings is')\n", +"\n", +"// part(e) hub-tip ratio of the rotor \n", +"p2=p1/pr_stator;\n", +"T2=T1-delT1_2;\n", +"ro2=(p2*1e5)/(R*T2);\n", +"l2=m/(ro2*cx*%pi*d);\n", +"p3=p2/pr_rotor;\n", +"T3=T1-delT1_3;\n", +"ro3=p3*1e5/(R*T3);\n", +"l3=m/(ro3*cx*%pi*d);\n", +"l=0.5*(l2+l3);\n", +"rm=d/2;\n", +"rh=rm-(l/2);\n", +"rt=rm+(l/2);\n", +"disp(rh/rt,'(e)hub-tip ratio of the rotor is')\n", +"\n", +"// part(f) degree of reaction at the hub and tip\n", +"Rh=1-((1-Rm)*(rm^2/rh^2));\n", +"Rt=1-((1-Rh)*(rh^2/rt^2));\n", +"disp('%',Rh*1e2,'(f)degree of reaction at the hub is')\n", +"disp('%',Rt*1e2,'(f)degree of reaction at the tip is')" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |