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diff --git a/Gas_Turbines_by_V_Ganesan/11-Impulse_and_Reaction_Turbines.ipynb b/Gas_Turbines_by_V_Ganesan/11-Impulse_and_Reaction_Turbines.ipynb new file mode 100644 index 0000000..7861731 --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/11-Impulse_and_Reaction_Turbines.ipynb @@ -0,0 +1,262 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: Impulse and Reaction Turbines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: Estimation_of_maximum_number_of_stages_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p02=6; // Inlet pressure in bar\n", +"T02=900; // Inlet temperature in kelvin\n", +"p0fs=1; // Outlet pressure in bar\n", +"eff_isenT=0.85; // insentropic efficiency of turbine\n", +"alpha_2=75; // Nozzle outlet angle in degree\n", +"u=250; // Mean blade velocity in m/s\n", +"Cp=1.15*10^3; // Specific heat in J/ kg K\n", +"r=1.333; // Specific heat ratio\n", +"\n", +"T0fs=T02/(p02/p0fs)^((r-1)/r); // Isentropic temperature at the exit of the final stage\n", +"Del_Toverall=eff_isenT*(T02-T0fs); // Actual overall temperature drop\n", +"c2=2*u/sind (alpha_2); // absolute velocity\n", +"c3= c2*cosd (alpha_2);// absolute velocity\n", +"c1=c3; // From velocity triangles\n", +"Del_Tstage=(c2^2-c1^2)/(2*Cp); // Stage temperature drop\n", +"n=Del_Toverall/Del_Tstage; // Number of stages\n", +"\n", +"disp (round (n),'Number of stages n =');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: Determination_of_output_power_developed_by_the_turbine_shaft.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"N=10000; // Speed of gas turbine in rpm\n", +"T01=700+273.15; // Total head temperature at nozzle entry in kelvin\n", +"P01=4.5; //Total head pressure at nozzle entry in bar\n", +"P02=2.6; // Outlet pressure from nozzle in bar\n", +"p3=1.5;// Pressure at trbine outlet annulus in bar\n", +"M=0.5; // Mach number at outlet\n", +"alpha_2=70; // outlet nozzle angle in degrees\n", +"D=64; // Blade mean diameter in cm\n", +"m=22.5; // Mass flow rate in kg/s\n", +"eff_T=0.99; // turbine mechanical efficiency\n", +"Cp=1.147; // Specific heat in kJ/kg K\n", +"r=1.33; // Specific heat ratio\n", +"fl=0.03; // frictional loss\n", +"R=284.6; // characteristic gas constant in J/kg K\n", +"\n", +"eff_N=1-fl; // Nozzle efficiency\n", +"T_02=(P02/P01)^((r-1)/r)*T01; // Isentropic temperature after expansion\n", +"T02=T01-eff_N*(T01-T_02); // Actual temperature after expansion\n", +"c2=sqrt (2*Cp*10^3*(T01-T02)); // Absolute velocity\n", +"u=(3.14*D*10^-2*N)/60; // Mean blade velocity\n", +"// From velocity triangles\n", +"wt2=c2*sind (alpha_2)-u;\n", +"ca=c2*cosd (alpha_2);\n", +"beta_2=atand((wt2)/ca);\n", +"T3=T02/(P02/p3)^((r-1)/r); // Assuming rotor losses are negligible\n", +"c3=M*sqrt (r*R*T3); // Absolute velocity\n", +"beta_3=atand(u/c3);\n", +"ct2=c2*sind(alpha_2);\n", +"P=eff_T*m*(ct2)*u/1000; // Power developed\n", +"\n", +"disp ('degree',beta_3,'Gas angle at exit = ','degree',beta_2,'Gas angle at entry','(i).');\n", +"disp ('kW (roundoff error)',P,'Power developed = ','(ii).');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: Estimation_of_the_blade_angle_and_power_produced.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"alpha_2=65; // Nozzle discharge angle in degree\n", +"c3=300; // Absolute velocity in m/s\n", +"alpha_3=30; // in degrees\n", +"\n", +"ca2=c3*cosd (alpha_3); // Axial velocity\n", +"c2=ca2/cosd(alpha_2); // Absolute velocity\n", +"// ca3=ca2=ca and equal blade angles then\n", +"ca=ca2;\n", +"beta_2=atand((c2*sind(alpha_2)+c3*sind(alpha_3))/(2*ca)); // Blade angle\n", +"beta_3=beta_2; // equal blade angles\n", +"u=c2*sind(alpha_2)-ca2*tand(beta_2); // Mean blade velocity\n", +"// From velocity triangles\n", +"ct2=c2*sind(alpha_2);\n", +"ct3=c3*sind(alpha_3);\n", +"WT=u*(ct2+ct3)/1000; // Work done\n", +"sigma=u/c2; // optimum speed ratio\n", +"eff_B=4*(sigma*sind(alpha_2)-sigma^2);\n", +"\n", +"disp ('degree',beta_2,'Blade angle = beta_2= beta_3 = ');\n", +"disp ('kJ/kg (roundoff error)',WT,'Power Produced = ');\n", +"disp ('%',eff_B*100,'Blade efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.4: Calculation_of_blade_angle_used_and_the_mass_flow_rate_required.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"P01=7; // Pressure at inlet in bar\n", +"T01=300+273.15; // Temperature at inlet in kelvin\n", +"P02=3; // Pressure at outlet in bar\n", +"alpha_2=70; // Nozzle angle in degree\n", +"eff_N=0.9; // Isentropic efficiency of nozzle\n", +"WT=75; // Power Produced in kW\n", +"Cp=1.15; // Specific heat in kJ/kg K\n", +"r=1.33; // Specific heat ratio\n", +"\n", +"T_02=T01*(P02/P01)^((r-1)/r); // Isentropic temperature after expansion\n", +"T02=T01-eff_N*(T01-T_02); // Actual temperature after expansion\n", +"c2=sqrt (2*Cp*10^3*(T01-T02)); // Absolute velocity\n", +"// For optimum blade speed ratio\n", +"u=(c2*sind (alpha_2)/2); // Mean blade velocity\n", +"beta_2=atand((c2*sind(alpha_2)-u)/(c2*cosd(alpha_2))); // Blade angle\n", +"// From velocity triangles\n", +"ct2=c2*sind(alpha_2);\n", +"w2=c2*cosd(alpha_2)/cosd(beta_2);\n", +"w3=w2; // Equal inlet and outlet angles\n", +"beta_3=54; // in degrees\n", +"ct3=w3*sind(beta_3)-u;\n", +"m=(WT*10^3)/(u*(ct2+ct3)); // Gas mass flow rate\n", +"\n", +"disp ('degree',beta_2,'Blade angle = ');\n", +"disp ('kg/s',m,'Gas Mass Flow Rate = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5: EX11_5.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"P01=4.6; // Total head inlet pressure in bar\n", +"T01=700+273.15; // Total head inlet temperature in kelvin\n", +"P2=1.6; // Static head pressure at mean radius in bar\n", +"Dm_h=10; // Mean blade diameter/blade height\n", +"lc=0.1; // Nozzle losses coefficient\n", +"alpha_2=60; // Nozzle outlet angle in degree\n", +"Cp=1.147; // Specific heat in kJ/kg K\n", +"r=1.33; // Specific heat ratio\n", +"m=20; // Mass flow rate in kg/s\n", +"R=284.6; // characteristic gas constant in J/kg K\n", +"\n", +"T_2=T01*(P2/P01)^((r-1)/r); // Isentropic temperature after expansion\n", +"T2=(lc*T01+T_2)/(1+lc); // Actual temperature after expansion\n", +"c2=sqrt(2*Cp*10^3*(T01-T2)); // Absolute velocity\n", +"// From velocity triangles\n", +"ca=c2*cosd(alpha_2);\n", +"row=P2*10^5/(R*T2); // Density of gas\n", +"A=m/(ca*row); // Area\n", +"Dm=sqrt (A*Dm_h/3.14); // Mean Diameter\n", +"h=Dm/10; // Blade height\n", +"rm=Dm/2; // Mean radius\n", +"// At root\n", +"r_root=(Dm-h)/2;\n", +"//At the tip\n", +"r_tip=(Dm+h)/2;\n", +"// Free vorte flow\n", +"ct_mean=c2*sind (alpha_2);\n", +"// At the root\n", +"ct2_root=(ct_mean*rm)/r_root;\n", +"alpha2_root=atand(ct2_root/ca);\n", +"c2_root=ct2_root/sind (alpha2_root);\n", +"T2_root=T01-c2_root^2/(2*Cp*10^3);\n", +"// At the tip\n", +"ct2_tip=ct_mean*rm/r_tip;\n", +"alpha2_tip = atand (ct2_tip/ca);\n", +"c2_tip=ct2_tip/sind(alpha2_tip);\n", +"T2_tip=T01-c2_tip^2/(2*Cp*10^3);\n", +"\n", +"disp ('degree',alpha2_root,'Discharge angle at the root = ','m/s',c2_root,'Gas velocity at the root = ','K',T2_root,'Gas Temperature at the root = ','A the Root');\n", +"disp ('degree',alpha2_tip,'Discharge angle at the tip = ','m/s',c2_tip,'Gas velocity at the tip = ','K',T2_tip,'Gas Temperature at the tip = ','A the tip');" + ] + } +], +"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/Gas_Turbines_by_V_Ganesan/5-Ideal_Cycles_and_their_Analysis.ipynb b/Gas_Turbines_by_V_Ganesan/5-Ideal_Cycles_and_their_Analysis.ipynb new file mode 100644 index 0000000..6633ed1 --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/5-Ideal_Cycles_and_their_Analysis.ipynb @@ -0,0 +1,655 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Ideal Cycles and their Analysis" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.10: Determination_of_the_cycle_thermal_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=15+273; // Inlet temperature of air at compressor inlet in kelvin\n", +"rp=6; // Compressor pressure ratio\n", +"T3=750+273; // Maximum permissible temperature in kelvin\n", +"T5=T3; // After reheat\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"c=rp^((r-1)/r); \n", +"T2=T1*c; // Temperature at state 2\n", +"p3_p4=sqrt (rp); // For maximum expansion work\n", +"T4=T3/(p3_p4)^((r-1)/r); // Temperature at state 4\n", +"T6=T4; // As pressure ratio is same\n", +"Wc=Cp*(T2-T1); // Compressor work\n", +"WT=Cp*(T3-T4)+Cp*(T5-T6); // Turbine work\n", +"T7=T4; // Because of 100% regeneration\n", +"q=Cp*(T3-T7)+Cp*(T5-T4); // Heat supplied\n", +"WN=WT-Wc; // Net work done\n", +"eff=WN/q; // Efficiency of the plant\n", +"Wratio=WN/WT; // Work ratio\n", +"disp ('kJ/kg of air',q,'Heat supplied = ');\n", +"disp ('kW (roundoff error)',WN,'Net shaft work = ');\n", +"disp ('%',eff*100,'The cycle thermal efficiency = ');\n", +"disp (Wratio,'Work ratio = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.11: Calculation_of_Efficiency_under_conditions_giving_maximum_work.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"Tmin=5+273; // Minimum operating temperature in kelvin\n", +"Tmax=839+273; // Maximum operating temperature in kelvin \n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"eff_carnot=1-Tmin/Tmax; // Efficiency of the carnot cycle\n", +"c=1/(1-eff_carnot);\n", +"p2_p1=c^(r/(r-1)); // Pressure ratio\n", +"disp (p2_p1,'(i).Pressure ratio at which efficiency equals Carnot cycle efficiency = ');\n", +"t=Tmax/Tmin; // Temperature ratio\n", +"// Pressure ratio for maximum work is obtained when\n", +"c=sqrt (t); \n", +"p2_p1=c^(r/(r-1)); // Pressure ratio\n", +"eff=1-1/c;// Efficiency at maximum work output\n", +"disp (p2_p1,'(ii).Pressure ratio at which maximum work is obtained = ');\n", +"disp ('%',eff*100,'(iii).Efficiency at maximum work output = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.12: Comparison_of_basic_cycle_with_modified_cycles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4;// Overall pressure ratio \n", +"T1=300; // Temperature at state 1 in kelvin\n", +"T3=1000; // Temperature at state 3 in kelvin\n", +"Cp=1; // Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717; // Specific heat at constant volume in kJ/kg K\n", +"\n", +"// Basic cycle\n", +"r=Cp/Cv; // Specific heat ratio\n", +"c=rp^((r-1)/r);\n", +"t=T3/T1; // Temperature ratio\n", +"WN=Cp*T1*(t*(1-1/c)-(c-1)); // Net work output\n", +"eff=(1-1/c)*100; // Efficiency of the cycle\n", +"\n", +"// Basic cycle with heat exchanger\n", +"WN_he=WN;\n", +"eff_he=(1-c/t)*100; // Efficiency of the cycle with heat exchanger\n", +"dev_WN1=(WN_he-WN)*100/WN; //Percentage deviation of Net work from basic cycle\n", +"dev_eff1=(eff_he-eff)*100/eff; // Percentage deviation of efficiency from basic cycle\n", +"\n", +"// Basic cycle with intercooled compressor\n", +"WN_ic=(Cp*T1)*(t*(1-1/c)-2*(sqrt(c)-1));\n", +"eff_ic=(1-(((t/c)+sqrt(c)-2)/(t-sqrt(c))))*100;\n", +"dev_WN2=(WN_ic-WN)*100/WN; //Percentage deviation of Net work from basic cycle\n", +"dev_eff2=(eff_ic-eff)*100/eff; // Percentage deviation of efficiency from basic cycle\n", +"\n", +"// Basic cycle with heat exchanger and intercooled compressor\n", +"WN_iche=WN_ic;\n", +"eff_iche=(1-((2*(sqrt(c)-1))/(t*(1-1/c))))*100;\n", +"dev_WN3=(WN_iche-WN)*100/WN; //Percentage deviation of Net work from basic cycle\n", +"dev_eff3=(eff_iche-eff)*100/eff; // Percentage deviation of efficiency from basic cycle\n", +"\n", +"printf ('Cycle \t\t\t\t\t\t WN(kJ/kg) \t\tefficiency (in percentage)\t\t percentage Change in WN \t\tpercentage change in efficiency');\n", +"printf('\n\t\t\t\t\t\t(roundoff error) \t(roundoff error) \t\t\t (roundoff error)\t\t\t\t (roundoff error)');\n", +"printf ('\n\nBasci cycle \t\t\t\t\t %f \t\t\t %f\t\t\t\t\t - \t\t\t\t\t -',WN,eff);\n", +"printf ('\n\nWith Heat Exchanger \t\t\t\t %f \t\t\t %f\t\t\t\t\t %f \t\t\t %f',WN_he,eff_he,dev_WN1,dev_eff1);\n", +"printf ('\n\nWith intercooling \t\t\t\t %f \t\t\t %f\t\t\t\t\t %f \t\t\t %f',WN_ic,eff_ic,dev_WN2,dev_eff2);\n", +"printf ('\n\nWith Heat Exchanger & Intercooling \t\t %f \t\t\t %f\t\t\t\t\t %f \t\t\t %f',WN_iche,eff_iche,dev_WN3,dev_eff3);" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13: Comparison_of_Carnot_efficiency_with_Brayton_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=27+273; // Temperature at state 1 in kelvin\n", +"T3=827+273; // Temperature at state 3 in kelvin\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"t=T3/T1; // Temperature ratio\n", +"Wmax=Cp*((T3*(1-1/sqrt(t)))-T1*(sqrt(t)-1)); // Maximum work\n", +"eff_wmax=(1-1/sqrt(t)); // Efficiency of brayton cycle\n", +"Tmax=T3; Tmin=T1;\n", +"eff_carnot=(Tmax-Tmin)/Tmax; // Carnot efficiency\n", +"disp ('kJ/kg of air',Wmax,'Maximum net work per kg of air = ');\n", +"disp ('%',eff_wmax*100,'Brayton cycle efficiency = ');\n", +"disp ('%',eff_carnot*100,'Carnot cycle efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.15: Calculation_of_Improvement_in_Efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p1=1; // Pressure at state 1 in bar\n", +"T1=300; // Temperature at state 1 in kelvin\n", +"p4=5; // Pressure at state 4 in bar\n", +"T5=1250; // Temperature at state 5 in kelvin\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"rp=p4/p1; // pressure ratio\n", +"p2=sqrt (rp); // Because of perfect intercooling\n", +"c1=p2^((r-1)/r); \n", +"T2=T1*c1; // Temperature at state 2\n", +"T4=T2; T3=T1;\n", +"\n", +"Wc1=Cp*(T2-T1); // Work of compressor 1\n", +"Wc=2*Wc1; // net work of compressor\n", +"WT1=Wc;\n", +"T6=T5-(WT1/Cp); // Temperature at state 6\n", +"p5_p6=(T5/T6)^(r/(r-1)); // Pressure ratio\n", +"p6=rp/p5_p6; // Pressure at state 6\n", +"p7=p1; T7=T5;p8=p6;\n", +"T8=T7*(p7/p8)^((r-1)/r); // Temperature in state 8\n", +"WT2=Cp*(T7-T8); // Turbine 2 work\n", +"q=Cp*(T5-T4)+Cp*(T7-T6); // Heat supplied\n", +"eff=WT2/q; // Efficiency of the cycle\n", +"// With regenerator\n", +"T9=T8;\n", +"q_withregen=Cp*((T5-T9)+(T7-T6)); // Heat supplied with regenerator\n", +"eff_withregen=WT2/q_withregen; // Efficiency of the cycle with regenerator\n", +"I_eff=(eff_withregen-eff)/eff_withregen; // Percentage improvement in efficiency\n", +"\n", +"disp ('%',eff*100,'Efficiency of the cycle = ','kJ/kg',q,'Heat supplied = ','kJ/kg',WT2,'Work of turbine = ','(i). Without regenerator ');\n", +"disp ('%',eff_withregen*100,'Efficiency of the cycle = ','kJ/kg (roundoff error)',q_withregen,'Heat supplied = ','(ii). With regenerator' );\n", +"\n", +"disp ('%',I_eff*100,'Percentage improvement in efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16: Calculation_of_Efficiency_ratio_of_the_power_plants.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p1=1; // pressure at inlet in bar\n", +"T1=27+273; // Temperature at inlet in kelvin\n", +"T4=1200; // Maximum temperature in kelvin\n", +"t=T4/T1; // Temperature ratio\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"rp=t;\n", +"c=rp^((r-1)/r);\n", +"x=(1-sqrt(c)/rp)/(1-c/rp);\n", +"eff2_1=x;\n", +"r1=sqrt(rp);\n", +"r2=r1; r3=r1; r4=r1;\n", +"\n", +"disp (eff2_1,'Efficiency ratio of power plants = ');\n", +"disp (r4,'pressure ratio of LPT = ',r3,'pressure ratio of HPT = ',r2,'pressure ratio of HPC = ',r1,'pressure ratio of LPC = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.19: Determination_of_Net_power_output.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"m=30; // Mass flow rate in kg/s\n", +"p1=1; // pressure of air at compressor inlet in bar\n", +"T1=273+15; // Temperature of air at compressor inlet in kelvin\n", +"p2=10.5; // Pressure of air at compressor outlet\n", +"T_R=420; // Temperature rise due to combustion in kelvin\n", +"p4=1.2; // Pressure at turbine outlet in bar\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"T2=T1*(p2/p1)^((r-1)/r); // Temperature at state 2\n", +"T3=T2+T_R; // Temperature at state 3\n", +"p3=p2;\n", +"T4=T3/(p3/p4)^((r-1)/r);\n", +"Wc=m*Cp*(T2-T1); // Compressor work\n", +"WT=m*Cp*(T3-T4); // Turbine work\n", +"WN=WT-Wc; // Net work output\n", +"Q=m*Cp*(T3-T2); // Heat supplied\n", +"eff_th=WN/Q; // Thermal efficiency\n", +"\n", +"disp ('%',eff_th*100,'Thermal efficiency = ','kW (roundoff error)',WN,'Power output = ','kW',Q,'Heat supplied = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Calculation_of_MEP_and_Efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p1=1; // Pressure before compression in bar\n", +"T1=350; // Temperature before compression in kelvin\n", +"T3=2000; // Temperature after combustion in kelvin\n", +"rp=1.3; // Pressure ratio\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T2=T1*(rp)^((r-1)/r); // Temperature at the end of the compression\n", +"T4=T3*(1/rp)^((r-1)/r); // Temperature after expansion\n", +"Wc=Cp*(T2-T1); // Work done during compression\n", +"WT=Cp*(T3-T4); // Work done during expansion\n", +"WN=WT-Wc; // Net work done\n", +"p2=rp*p1; // Pressure at state 2\n", +"p3=p2; p4=p1; // Constant pressure process\n", +"V1=R*T1/(p1*10^5); // specific Volume at state 1\n", +"V2=R*T2/(p2*10^5); // specific Volume at state 2\n", +"V3=R*T3/(p3*10^5); // specific Volume at state 3\n", +"V4=R*T4/(p4*10^5); // specific Volume at state 4\n", +"imep=WN*10^3/(V4-V2); // Mean effective pressure\n", +"q=Cp*(T3-T2); // Heat supplied\n", +"eff=WN/q; // Efficiency of a Joule cycle\n", +"disp ('bar',imep*10^-5,'Mean effective pressure = ');\n", +"disp ('%',eff*100,'Efficiency of a Joule cycle = ');\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2: Calculation_of_Improvement_in_Efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p1=1; // Pressure before compression in bar\n", +"T1=350; // Temperature before compression in kelvin\n", +"T3=2000; // Temperature after combustion in kelvin\n", +"rp=1.3; // Pressure ratio\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T2=T1*(rp)^((r-1)/r); // Temperature at the end of the compression\n", +"T4=T3*(1/rp)^((r-1)/r); // Temperature after expansion\n", +"Wc=Cp*(T2-T1); // Work done during compression\n", +"WT=Cp*(T3-T4); // Work done during expansion\n", +"WN=WT-Wc; // Net work done\n", +"T5=T4; // For a perfect heat exchange\n", +"q=Cp*(T3-T5); // Heat added\n", +"eff2=WN/q; // Efficiency of a modified Joule cycle\n", +"eff1=0.072220534; // Efficiency of a joule cycle\n", +"disp ('%',eff2*100,'Efficiency of a modified Joule cycle = ');\n", +"disp (eff2/eff1,'Improvement in efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: calculation_of_net_power_output_of_the_cycle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=6; // Pressure ratio\n", +"T1=300; // Inlet air temperature to the compressor in kelvin\n", +"T3=577+273; // Inlet temperature of air at turbine in kelvin\n", +"Vr=240; // Volume rate in m^3/s\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"p1=1; // pressure at state 1 in bar\n", +"\n", +"T2=T1*(rp)^((r-1)/r); // Temperature at the end of the compression\n", +"T4=T3*(1/rp)^((r-1)/r); // Temperature after expansion\n", +"Wc=Cp*(T2-T1); // Work done during compression\n", +"WT=Cp*(T3-T4); // Work done during expansion\n", +"WN=WT-Wc; // Net work done\n", +"q=Cp*(T3-T2); // Heat supplied\n", +"row1=p1*10^5/(R*T1); // Density of air at state 1\n", +"P=WN*Vr*row1; // Power output\n", +"eff=WN/q; // Efficiency of a cycle\n", +"disp ('MW (roundoff error)',P/1000,'Power Output = ');\n", +"disp ('%',eff*100,'Efficiency of a cycle = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Calculation_of_Efficiency_and_work_of_compression.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=300; // Inlet air temperature to the compressor in kelvin\n", +"p1=1; // pressure at state 1 in bar\n", +"T2=475; // Temperature at discharge in kelvin\n", +"p2=5;// Pressure at state 2\n", +"T5=655; // Temperature after heat exchanger in kelvin\n", +"T3=870+273; // Temperature at he turbine inlet in kelvin\n", +"T4=450+273; // Temperature after turbine in kelvin\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"Wc=Cp*(T2-T1); // Work done during compression\n", +"WT=Cp*(T3-T4); // Work done during expansion\n", +"WN=WT-Wc; // Net work done\n", +"q=Cp*(T3-T5); // Heat supplied\n", +"eff=WN/q; // Efficiency of a cycle\n", +"\n", +"disp ('kJ/kg',WN,'(i). The output per kg of air = ');\n", +"disp ('%',eff*100,'(ii).The efficiency of the cycle = ');\n", +"disp ('kJ/kg',Wc,'(iii). The work required to drive the compressor = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Calculation_of_Thermal_Efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p1=1.4; // Pressure at state 1 in bar\n", +"T1=310; // Temperature at state 1 in kelvin\n", +"rp=5; // Pressure ratio\n", +"Tmax=1050; // Maximum temperatuer in kelvin\n", +"WN=3000; // Net output in kW\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T3=Tmax;\n", +"T2=T1*(rp)^((r-1)/r); // Temperature at the state 2\n", +"T4=T3/(rp)^((r-1)/r); // Temperature at the state 4\n", +"T5=T4; // As regenerator effectiveness in 100 %\n", +"m=WN/(Cp*((T3-T4)-(T2-T1))); // mass flow rate of air\n", +"eff=(T3-T4-T2+T1)/(T3-T5); // Efficiency of a cycle\n", +"disp ('%',eff*100,'(i). Thermal efficiency of the cycle = ');\n", +"disp ('kg/min (roundoff error)',m*60,'(ii). The mass flow rate of air per minute = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Calculation_of_Pressure_ratio_of_compressor_and_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=290; // Compressor inlet temperature in kelvin\n", +"T2=460; // Compressor outlet temperature in kelvin\n", +"T3=900+273; // Turbine inlet temperature in kelvin\n", +"T4=467+273; // Turbine outlet temperature in kelvin\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"c=T2/T1; // Temperature ratio\n", +"rpc=c^(r/(r-1)); // Compression ratio\n", +"WN=(Cp*((T3-T4)-(T2-T1))); // Specific power\n", +"T5=T4; // Assuming regenerator effectiveness to be 100%\n", +"eff=WN/(Cp*(T3-T5)); // Overall efficiency of the cycle\n", +"Wc=Cp*(T2-T1); // Work required to drive the compressor\n", +"rpt=(T3/T4)^(r/(r-1)); // Turbine pressure ratio\n", +"disp (rpt,' Turbine pressure ratio = ',rpc,' Compressor pressure ratio = ','(i).');\n", +"disp ('kJ/kg',WN,'(ii). Specific power output = ');\n", +"disp ('%',eff*100, '(iii). Overall efficiency of the cycle = ');\n", +"disp ('kJ/kg',Wc,' (iv). Work required to drive the compressor = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: Calculation_of_temperature_drop_across_the_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"nW_WT=0.563; // Ratio of net work to turbine work\n", +"T1=300; // Inlet temperature to the compressor in kelvin\n", +"eff=0.35; // Thermal efficiency of the unit\n", +"m=10; // massflow rate in kg/s\n", +"Cp=1; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"c=1/(1-eff); // For ideal simple cycle\n", +"T2=T1*c; // Temperature at state 2\n", +"Wc=Cp*(T2-T1); // Compressor work\n", +"WT=Wc/(1-nW_WT); // Turbine work\n", +"WN=WT-Wc; // Net work\n", +"q=WN/eff; // Net heat supplied per kg of air\n", +"T3=(q/Cp)+T2; // Temperature at state 3\n", +"T4=T3/c; // Temperature at state 4\n", +"T3_T4=T3-T4; // Temperature drop across the turbine\n", +"disp ('K',T3_T4,'Temperature drop across the turbine = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Calculation_of_turbine_pressure_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p=336.5; //specific power output of a turbine in kW/kg\n", +"T4=700; // Temperature at turbine outlet in kelvin\n", +"Cp=1; // Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717; // Specific heat at constant volume in kJ/kg K\n", +"\n", +"r=Cp/Cv; // Specific heat ratio\n", +"T3=T4+(p/Cp); // Temperature at turbine inlet \n", +"p3_p4=(T3/T4)^(r/(r-1)); // Pressure ratio across the turbine\n", +"disp (round(p3_p4),'Pressure ratio across the turbine = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: Estimation_of_thermal_efficiency_of_the_plant.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=300; // Minimum operating temperature in kelvin\n", +"T3=900; // Maximum operating temperature in kelvin\n", +"p1=1; // Minimum pressure in bar\n", +"p3=4; // Maximum pressure in bar\n", +"m=1600; // Mass flowrate in kg/min\n", +"r=1.4; // Specific heat ratio\n", +"Cp=1.005; // Specific heat at constant pressure in kJ/kg K\n", +"\n", +"p2=p3; p4=p1; // Constant pressure process\n", +"c=(p2/p1)^((r-1)/r); \n", +"eff=(1-1/c); // The efficiency of the cycle\n", +"t=T3/T1; // ratio of maximum and minimum temperature\n", +"W=Cp*T1*(t*(1-1/c)-(c-1)); // Work output per kg of air\n", +"P=(m/60)*W; // Shaft power available\n", +"disp ('%',eff*100,' Thermal efficiency of the plant = ');\n", +"disp ('kW (roundoff error)',P,'Shaft power available for external Load = ');" + ] + } +], +"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/Gas_Turbines_by_V_Ganesan/6-Practical_Cycles_and_their_Analysis.ipynb b/Gas_Turbines_by_V_Ganesan/6-Practical_Cycles_and_their_Analysis.ipynb new file mode 100644 index 0000000..e92b878 --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/6-Practical_Cycles_and_their_Analysis.ipynb @@ -0,0 +1,1050 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Practical Cycles and their Analysis" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.10: Plotting_variation_of_Isentropic_efficiency_over_a_range_of_pressure_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_C=0.85; // Isentropic efficiency of the compressor\n", +"rp=4; // Pressure ratio\n", +"r=1.4; // specific heat ratio\n", +"eff_pc=(((r-1)/r)*log (rp))/log (((rp^((r-1)/r)-1)/eff_C)+1);\n", +"disp ('%',eff_pc*100,'Polytropic efficiency = ');\n", +"disp ('variation of compressor efficiency with compression ratio is shown in window1');\n", +"xset('window',1);\n", +"function eff_c=f(rc)\n", +" eff_c=(rc^0.286-1)/(rc^0.326-1);\n", +"endfunction\n", +"rc=linspace (2,10,4);\n", +"plot(rc,f);\n", +"title ('variation of compressor efficiency with compression ratio','fontsize',4,'color','blue');\n", +"xlabel('compression ratio (rc)','fontsize',4,'color','blue');\n", +"ylabel ('Compressor efficiency','fontsize',4,'color','blue');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.11: EX6_11.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_pe=0.88; // Compressor and turbine polytropic efficiencies\n", +"T01=310; // Temperature at LP compressor inlet in kelvin\n", +"p01=14; // Pressure at LP compressor inlet in bar\n", +"rp=2; // Compressor pressure ratio\n", +"T03=300;// Temperature at HP compressor inlet in kelvin\n", +"m=180; // Mass flow of Helium in kg/s\n", +"Q=500; // Heat input to gas turbine in MW\n", +"T07=700; // Helium Temperature at entry to reactor channels in kelvin\n", +"P_precoller=0.34; // Pressure loss in pre-cooler and intercooler in bar\n", +"P_loss_HE=0.27; // Pressure loss in heat exchanger in bar\n", +"P_loss_RC=1.03; // Pressure loss in reactor channel in bar\n", +"eff_pc=0.88; // Polytropiic efficiency\n", +"Cp=5.19;// Specific heat at constant pressure in kJ/kg K\n", +"r=1.66; // Specific heat ratio \n", +"\n", +"n_1_n=((r-1)/r)*(1/eff_pc);\n", +"T02=T01*rp^n_1_n;\n", +"T04=T03*rp^n_1_n;\n", +"T05=((Q*10^3)/(m*Cp))+T07;\n", +"T_press_loss=P_precoller+P_loss_HE+P_loss_RC; // Total pressure loss\n", +"p05=56-T_press_loss;\n", +"p06=p01+P_precoller+P_loss_HE;\n", +"n__1_n=eff_pc*((r-1)/r);\n", +"T06=T05/(p05/p06)^n__1_n;\n", +"WC=m*Cp*((T02-T01)+(T04-T03)); // Work of compressor\n", +"WT=m*Cp*(T05-T06); // Work of Turbine\n", +"WN=WT-WC; // Net work output\n", +"eff_th=WN/(Q*10^3); // Efficiency\n", +"eff=(T07-T04)/(T06-T04); // Effectiveness\n", +"\n", +"disp ('MW (roundoff error)',WN/1000,'Power output = ');\n", +"disp ('% (roundoff error)',eff_th*100,'Thermal efficiency = ');\n", +"disp ('% (roundoff error)',eff*100,'Effectiveness = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.12: Calculation_of_the_isentropic_efficiency_of_the_turbine_and_the_mass_flow_of_air.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4; // Pressure ratio\n", +"WN=1500; // Net work output in kW\n", +"T01=25+273; // Inlet temperature in kelvin\n", +"p01=1; // Inlet pressure in bar\n", +"p03=4; // Turbine inlet pressure in bar\n", +"T03=700+273;// turbine inlet temperature in kelvin\n", +"eff_c=0.85; // Compressor efficiency\n", +"eff_over=0.21; // Overall efficiency\n", +"Cp=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"T02=T01+T01*(rp^((r-1)/r)-1)/eff_c;\n", +"Q=WN/eff_over;\n", +"m=Q/(Cp*(T03-T02));\n", +"Wn=WN/m; // Net work per kg\n", +"T04=T03-T02+T01-(Wn/Cp);\n", +"T_04=T03/rp^((r-1)/r);\n", +"eff_T=(T03-T04)/(T03-T_04);\n", +"\n", +"disp ('kg/s',m,'Mass flow rate = ');\n", +"disp ('%',eff_T*100,'Isentropic efficiency of the Turbine = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.13: Determination_of_pressure_of_the_gas_entering_the_low_pressure_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4; // Pressure ratio\n", +"eff_c=0.86; // Compressor efficiency\n", +"eff_Thp=0.84;// High pressure turbine efficiency\n", +"eff_Tlp=0.8;// Low pressure turbine efficiency\n", +"eff_M=0.92; // Mechanical efficiency\n", +"T03=660+273; // in kelvin\n", +"T05=625+273; // In kelvin\n", +"T01=15+273; // Inlet temperature in kelvin\n", +"p01=1; // Inlet pressure in bar\n", +"Cp=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio of air\n", +"eff= 0.75; // Heat exchanger effectiveness\n", +"\n", +"T_02=T01*(rp)^((r-1)/r);\n", +"T02=((T_02-T01)/eff_c)+T01;\n", +"T04=T03-((T02-T01)/eff_M);\n", +"// In HP turbine\n", +"T_04=T03-((T03-T04)/eff_Thp);\n", +"p_04=rp/(T03/T_04)^(r/(r-1));\n", +"// In LP turbine\n", +"p05=p_04;p_06=p01;\n", +"T_06=T05/(p05/p_06)^((r-1)/r);\n", +"T06=T05-(eff_Tlp*(T05-T_06));\n", +"T07=T02+eff*(T06-T02);\n", +"Q=Cp*(T03-T07+T05-T04);\n", +"Wc=Cp*(T02-T01);\n", +"WT=Cp*(T03-T04+T05-T06);\n", +"eff_th=(WT-Wc)/Q;\n", +"\n", +"disp ('bar',p_04,'(i).Pressure of gas entering low pressure turbine = ');\n", +"disp ('%',eff_th*100,'Overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.14: Calculation_of_pressure_ratio_and_cycle_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T01=38+273; // Inlet temperature of compressor in kelvin\n", +"eff_c=0.82; // Compressor efficiency\n", +"T03=650+273; // Turbine inlet temperature in kelvin\n", +"eff_T=0.8; // Turbine efficiency\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"t=T03/T01;\n", +"// For maximun specific work we know that\n", +"ropt=(sqrt (t*eff_c*eff_T))^(r/(r-1));\n", +"T_02=T01*ropt^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"T_04=T03/ropt^((rg-1)/rg);\n", +"T04=T03-eff_T*(T03-T_04);\n", +"eff_th=((Cpg*(T03-T04))-(Cpa*(T02-T01)))/(Cpg*(T03-T02));\n", +"\n", +"disp (ropt,'Optimum pressure ratio = ');\n", +"disp ('%',eff_th*100, 'Overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.15: Estimation_of_the_temperature_of_the_gases_at_entry_to_the_turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p01=1; // Stagnation pressure at entry in bar\n", +"pa=0.93; // Static pressure at entry in bar\n", +"T1=10+273;// Static temperature in entry in kelvin\n", +"p02=6; // Pressure at state 2 in bar\n", +"T02=230+273; // Temperature at state 2 in kelvin\n", +"P=5100; // Turbine output power in kW\n", +"A=0.1; // Compressor entry area in m^2\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic constant in J/kg K\n", +"T04=460+273; // Exhaust pipe temperature in kelvin\n", +"\n", +"M=sqrt (((p01/pa)^((r-1)/r)-1)/((r-1)/2));\n", +"T01=T1*(1+(r-1)/2*M^2);\n", +"T_02=T01*(p02/p01)^((r-1)/r);\n", +"eff_c=(T_02-T01)/(T02-T01);\n", +"row_s=(pa*10^5)/(R*T1);\n", +"a=sqrt (r*R*T1);\n", +"V=M*a;\n", +"m=row_s*A*V;\n", +"T03=(P/(m*Cpg))+T04;\n", +"\n", +"disp ('%',eff_c*100,'Compressor efficiency = ');\n", +"disp ('kg/s',m,'Mass flow rate = ');\n", +"disp ('K (roundoff error)',T03,'Turbine inlet stagnation temperature = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.16: Calculation_of_efficiency_and_work_ratio_of_modern_turbines_and_old_turbines.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T01=27+273; // Inlet temperature in kelvin\n", +"p01=1; // Inlet pressure in bar\n", +"rp=3; // Pressure ratio\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic constant in J/kg K\n", +"\n", +"T_02=T01*rp^((r-1)/r);\n", +"// Turbines 70 years ago\n", +"eff_c=0.65; // Compressor efficiency \n", +"eff_T=0.7; // Turbine efficiency\n", +"T03=700+273; // in kelvin\n", +"T02=T01*(1+((rp^((r-1)/r)-1)/eff_c));\n", +"T04=T03*(1-eff_T*(1-(1/rp^((rg-1)/rg))));\n", +"eff_th=(Cpg*(T03-T04)-Cpa*(T02-T01))/(Cpg*(T03-T02));\n", +"WR=(Cpg*(T03-T04)-Cpa*(T02-T01))/(Cpg*(T03-T04));\n", +"\n", +"disp (WR,'Work ratio = ',eff_th*100,'The Efficiency = ','(i).70 years ago');\n", +"\n", +"//Modern turbines\n", +"eff_c=0.85; // Compressor efficiency \n", +"eff_T=0.9; // Turbine efficiency\n", +"T03=1000+273; // in kelvin\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"T_04=T03/rp^((rg-1)/rg);\n", +"T04=T03-eff_T*(T03-T_04);\n", +"Wc=Cpa*(T02-T01);\n", +"WT=Cpg*(T03-T04);\n", +"WN=WT-Wc;\n", +"eff_th=WN/(Cpg*(T03-T02));\n", +"WR=WN/WT;\n", +"\n", +"disp (WR,'Work ratio = ','%',eff_th*100,'The Efficiency = ','(ii).Modern turbines');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.17: Determination_of_necessary_mass_flow_rate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=7; // Pressure ratio\n", +"T03=1000; // Maximum temperature in kelvin\n", +"eff_c=0.85; // Compressor efficiency\n", +"eff_T=0.9; // Turbine efficiency\n", +"T01=288; // Air entering temperature in kelvin\n", +"PN=750; // Power output in kW\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic constant in J/kg K\n", +"\n", +"// Actual cycle\n", +"T02=T01*(1+((rp^((r-1)/r)-1)/eff_c));\n", +"T04=T03*(1-(eff_T*(1-(1/rp^((r-1)/r)))));\n", +"WN_a=(Cpa*(T03-T04)-Cpa*(T02-T01));\n", +"eff_th=WN_a/(Cpa*(T03-T02));\n", +"disp ('%',eff_th*100,'The Efficiency = ','kJ/kg',WN_a,'Net work = ','(i).Actual cycles');\n", +"\n", +"// Ideal cycle\n", +"WN=Cpa*((T03*(1-(1/rp^((r-1)/r))))-T01*((rp^((r-1)/r)-1)));\n", +"eff_th=1-(1/rp^((r-1)/r));\n", +"ma=PN/WN_a;\n", +"\n", +"disp ('kg/s',ma,'Mass flow rate = ','%',eff_th*100,'The Efficiency = ','kJ/kg',WN,'Net work = ','(ii).Ideal cycles');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.18: EX6_18.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"m=5; // Mass flow rate in kg/s\n", +"p01=1; // Pressure at state 1 in bar\n", +"p02=5; // Pressure at state 2 in bar\n", +"eff_c=0.85;// Compressor efficiency\n", +"eff_Thp=0.87; // High pressure turbine efficiency\n", +"eff_Tlp=0.82; // Low pressure turbine efficiency\n", +"T03=675+273; // HP turbine inlet temperature in kelvin\n", +"eff=0.7; // Effectiveness of the heat exchanger\n", +"T01=15+273; // Temperature at state 1 in kelvin\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic constant in J/kg K\n", +"p03=p02;\n", +"\n", +"T_02=T01*(p02/p01)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"T04=T01-T02+T03;\n", +"T_04=T03-(T03-T04)/eff_Thp;\n", +"p04=p03/(T03/T_04)^(r/(r-1));\n", +"p05=p01;\n", +"T_05=T04/(p04/p05)^((r-1)/r);\n", +"T05=T04-eff_Tlp*(T04-T_05);\n", +"T0x=eff*(T05-T02)+T02;\n", +"Wlpt=Cpa*(T04-T05);\n", +"Plpt=Wlpt*m;\n", +"Q=Cpa*(T03-T0x);\n", +"eff_th=Wlpt/Q;\n", +"\n", +"disp ('Intermediate pressure p04 and temperature T04 between the two turbine stages ');\n", +"disp ('K',T04,'To4 = ','bar',p04,'P04 = ');\n", +"disp ('kW',Plpt,'Power output of LP turbine = ');\n", +"disp ('kJ/kg',Q,'Heat supplied = ');\n", +"disp ('%',eff_th*100,'The Overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.19: EX6_19.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rlp=3; // Pressure ratio\n", +"rhp=rlp;\n", +"eff_c=0.82; // Compressor efficiency\n", +"T04=650+273; // Temperature at state 4 in kelvin\n", +"T05=540+273; // Temperature at state 5 in kelvin\n", +"eff_T=0.87; // Efficiency of turbine\n", +"T01=15+273; // Temperature at compressor inlet in kelvin\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"T02=T01*(1+(rlp^((r-1)/r)-1)/eff_c);\n", +"T03=T02*(1+(rhp^((r-1)/r)-1)/eff_c);\n", +"T_06=T05/(rlp)^(2*(rg-1)/rg);\n", +"T06=T05-eff_T*(T05-T_06);\n", +"x1=1-((T02-T01)/(((Cpg/Cpa)*(T05-T06)-(T03-T02))));\n", +"x=abs (x1);\n", +"T07=T04*(1-(eff_T*(1-(1/rhp^((rg-1)/rg)))));\n", +"eff_th=(x*Cpg*(T04-T07))/((1-x)*Cpg*(T05-T03)+x*Cpg*(T04-T02));\n", +"\n", +"disp ('%',(x)*100,'Percentage of the total air intake that passes to the power turbine = ');\n", +"disp ('% (Roundoff error)',(eff_th)*100,'The overall efficiency = ');\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Calculation_of_Net_power_and_overall_efficiency_of_installation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p01=1; // Pressure at state 1 in bar\n", +"T01=30+273; // Temperature at state 1 in kelvin\n", +"p02=6; // Pressure of air after compressed in bar\n", +"eff_c=0.87; // Isentropic efficiency of compressor\n", +"T03=700+273; // Temperature at state 3 in kelvin\n", +"eff_T=0.85; // Isentropic efficiency of the turbine \n", +"CV=43.1; // calorific value of fuel in MJ/kg\n", +"ma=80; // Mass flow rate of air in kg/min\n", +"\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"T_02=T01*(p02/p01)^((r-1)/r); // from T-S diagram\n", +"T02=T01+(T_02-T01)/eff_c; // Temperature after compression\n", +"// Neglecting the addition of fuel in the combustion chamber we have mf+ma=ma\n", +"mf=(ma/60)*Cpg*(T03-T02)/(CV*10^3);\n", +"ma_mf=(ma/60)*(1/mf); // Air fuel ratio\n", +"A_F=ma_mf;\n", +"p04=p01;p03=p02;\n", +"T_04=T03*(p04/p03)^((rg-1)/rg);\n", +"T04=T03-eff_T*(T03-T_04);\n", +"WN=(ma/60)*Cpg*(T03-T04)-(ma/60)*Cpa*(T02-T01); //The net power of installation\n", +"eff_th=WN/(mf*CV*10^3); // The overall thermal efficiency\n", +"\n", +"disp (A_F,'(i).Air fuel ratio of the turbine gases = ');\n", +"disp ('K',T04,'(ii).The final temperature of exhaust gases = ');\n", +"disp ('kW',WN,'(iii).The net power of installation = ');\n", +"disp ('%',eff_th*100,'(iv).The overall thermal efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.20: Calculation_of_the_Thermal_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=2; // Pressure ratio\n", +"T01=15+273; // Inlet temperature in kelvin\n", +"p01=1; // Inlet pressure in bar\n", +"T05=700+273; // Temperature at state 5 in kelvin\n", +"T07=T05;\n", +"eff_c=0.85; // compressor efficiency\n", +"eff_T=0.85; // Turbine efficiency\n", +"eff=0.5; // Effectiveness of heat exchanger\n", +"Cp=1.147;// Specific heat at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"T03=T01;\n", +"// p02/p01=p04/p03=rp\n", +"//p04/p01=p05/p08=rp^2\n", +"T_02=T01*(rp)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"T04=T02;\n", +"T_06=T05/rp^((rg-1)/rg);\n", +"T06=T05-eff_T*(T05-T_06);\n", +"T08=T06;\n", +"T09=T04+eff*(T08-T04);\n", +"WN=Cp*(T07-T08);\n", +"Q=Cp*(2*T05-T06-T09);\n", +"eff_th=WN/Q;\n", +"\n", +"disp ('kJ/kg',WN,'Net work done = ');\n", +"disp ('%',eff_th*100,'The overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.21: Calculation_of_cycle_thermal_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T01=270+273; // Temperature at state 1 in kelvin\n", +"T03=T01;\n", +"p01=1; // Inlet pressure in bar\n", +"rp=6; // Pressure ratio\n", +"eff_c=0.85; // Compressor efficiency\n", +"T05=1150+273; // Temperature at inlet to expansion in kelvin\n", +"eff_T=0.9; // Turbine efficiency\n", +"n=1.24; // Polytropic index\n", +"R=10.05; // in kJ/kg K\n", +"\n", +"T_02=T01*rp^((n-1)/n);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"Cv=R/(n-1);\n", +"Cp=R+Cv;\n", +"Wc=2*Cp*(T02-T01);\n", +"T_06=T05/rp^((n-1)/n);\n", +"T06=T05-eff_T*(T05-T_06);\n", +"WT=2*Cp*(T05-T06);\n", +"Q=Cp*(T05-T02)+Cp*(T05-T06);\n", +"WN=WT-Wc;\n", +"eff_th=WN/Q;\n", +"\n", +"disp ('%',eff_th*100,'The Cycle efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: Calculation_of_ratio_of_compressor_to_turbine_work.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p01=1; // Air inlet pressure in bar\n", +"T01=7+273;// Air inlet temperature in kelvin\n", +"p02=4; // Pressure at state 2 in bar\n", +"eff_c=0.82;// Isentropic efficiency of compressor\n", +"T03=800+273; // Maximum temperature at the turbine inlet in kelvin\n", +"eff_T=0.85; // Isentropic efficiency of the turbine\n", +"CV=43.1; // calorific value of fuel in MJ/kg\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"LS=0.85;\n", +"mf=1; // Let assume mass of fuel to be 1 kg\n", +"\n", +"T_02=T01*(p02/p01)^((r-1)/r); // from T-S diagram\n", +"T02=T01+(T_02-T01)/eff_c; // Temperature after compression\n", +"Wc=Cpa*(T02-T01); // Work of compression\n", +"Q=Cpg*(T03-T02); // Heat supplied\n", +"p04=p01;p03=p02;\n", +"T_04=T03*(p04/p03)^((rg-1)/rg);\n", +"T04=T03-eff_T*(T03-T_04);\n", +"WT=Cpg*(T03-T04); // Turbine work\n", +"WN=WT-Wc; // Net work done\n", +"eff_th=WN/(Q/LS); // The thermal efficiency\n", +"ma_mf=(LS*CV*10^3/Q)-1; // AIR FUEL ratio\n", +"ma=mf*ma_mf;\n", +"sfc=(3600/(ma_mf*WN)); // specific fuel consumption\n", +"Wc_WT=(Wc*ma)/(WT*(ma+mf)); // work ratio\n", +"\n", +"disp ('kJ/kg of air',Wc,'(i).Compressor work = ');\n", +"disp ('kJ/kg of air',Q,'(ii).Heat supplied = ');\n", +"disp ('kJ/kg of air',WT,'(iii).Turbine work = ');\n", +"disp ('kJ/kg of air',WN,'(iv).Net work = ');\n", +"disp ('%',eff_th*100,'(v).Thermal Efficiency = ');\n", +"disp (ma_mf,'(vi).Air/Fuel ratio = ')\n", +"disp ('kg/kWh',sfc,'(vii).Specific fuel consumption =');\n", +"disp (Wc_WT,'(viii).Ratio of compressor work to turbine work = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.3: Calculation_of_effect_of_pressure_loss.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_c=0.82; // Isentropic efficency of the compressor \n", +"eff_T=0.85; // Isentropic efficency of the turbine\n", +"eff_m=0.99; // Mechanical transmission efficiency\n", +"rp=7; // Pressure ratio\n", +"T03=1000; // Maximum cycle temperature in kelvin\n", +"eff_comb=0.97; // Combustion efficiency \n", +"CV=43.1; // Calorific value in MJ/kg\n", +"ma=20; // Air mass flow rate in kg/s\n", +"eff_reg=0.75; // Regenerator effectiveness\n", +"del_P=0.1; // Regenerator gas side pressure loss in bar\n", +"T01=327; // Ambient temperature in kelvin\n", +"p01=1; // Ambient pressure in bar\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"//(i).With Regeneration and pressure loss\n", +"T_02=T01*(rp)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"p04=p01+del_P;\n", +"p03=rp/p01;\n", +"T_04=T03*(p04/p03)^((rg-1)/rg);\n", +"T04_1=T03-eff_T*(T03-T_04);\n", +"T05=T02+eff_reg*(T04_1-T02);\n", +"mf1=(ma*Cpg*(T03-T05))/(CV*10^3*eff_comb); // By neglecting the effect of change in mass flow rate due to mf in combustion chamber\n", +"p03_p04_1=p03/p04;\n", +"WT1=(ma+mf1)*Cpg*(T03-T04_1); // Turbine work\n", +"WN1=(ma+mf1)*Cpg*(T03-T04_1)-(ma*Cpa*(T02-T01)/eff_m); // Net work output\n", +"sfc1=mf1*3600/WN1; // Specifc fuel consumption\n", +"eff_th1=WN1/(mf1*CV*10^3); // Thermal efficiency\n", +"\n", +"\n", +"\n", +"//(ii).Without Regenerator and without pressure loss\n", +"\n", +"p04=p01;\n", +"T_04=T03*(p04/p03)^((rg-1)/rg);\n", +"T04_2=T03-eff_T*(T03-T_04);\n", +"mf2=(ma*Cpg*(T03-T02))/(CV*10^3*eff_comb);\n", +"WT2=(ma*Cpg*(T03-T04_2));\n", +"WN2=(ma*Cpg*(T03-T04_2))-(ma*Cpa*(T02-T01)/eff_m); // Net work output\n", +"p03_p04_2=p03/p04;\n", +"sfc2=mf2*3600/WN2; // Specific fuel consumption\n", +"eff_th2=WN2/(mf2*CV*10^3); // Thermal efficiency\n", +"\n", +"\n", +"//(iii).With Regenerator and without pressure loss\n", +"T_02=T01*(rp)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"p04=p01;\n", +"p03=rp/p01;\n", +"T_04=T03*(p04/p03)^((rg-1)/rg);\n", +"T04_3=T03-eff_T*(T03-T_04);\n", +"T05=T02+eff_reg*(T04_3-T02);\n", +"WT3=(ma*Cpg*(T03-T05));\n", +"mf3=(ma*Cpg*(T03-T05))/(CV*10^3*eff_comb); // By neglecting the effect of change in mass flow rate due to mf in combustion chamber\n", +"p03_p04_3=p03/p04;\n", +"WN3=(ma+mf3)*Cpg*(T03-T04_3)-(ma*Cpa*(T02-T01)/eff_m); // Net work output\n", +"sfc3=mf3*3600/WN3; // Specifc fuel consumption\n", +"eff_th3=WN3/(mf3*CV*10^3); // Thermal efficiency\n", +"\n", +"\n", +"printf('Quantities \t\t\t \t\tRegenerator \t\t\t\t\t\t Without');\n", +"printf ('\n\t\t\t\twith Del_P\t\twithout Del_P\t\t\t\tregenerator and Del_P');\n", +"printf ('\n\t\t\t\t(roundoff error)\t(roundoff error)\t\t\t(roundoff error)');\n", +"printf('\n\n P03/P04\t\t\t%f\t\t%f\t\t\t\t\t%f',p03_p04_1,p03_p04_3,p03_p04_2);\n", +"printf ('\n\nT04 (K)\t\t\t\t%f\t\t%f\t\t\t\t\t%f',T04_1,T04_3,T04_2);\n", +"printf ('\n\nmf (kg/s)\t\t\t%f\t\t%f\t\t\t\t\t%f',mf1,mf3,mf2);\n", +"printf ('\n\nWT (kW)\t\t\t\t%f\t\t%f\t\t\t\t\t%f',WT1,WT3,WT2);\n", +"printf ('\n\nsfc (kg/kW h)\t\t\t%f\t\t%f\t\t\t\t\t%f',sfc1,sfc3,sfc2);\n", +"printf ('\n\nefficiency (in percentage)\t%f\t\t%f\t\t\t\t\t%f',eff_th1*100,eff_th3*100,eff_th2*100);\n", +"\n", +"printf ('\n\nAs can be seen from the table that pressure loss plays a major role in the efficiency than the regenerator. \n\nHence,more care should be taken in the design to have minimum pressure loss.');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.4: Calculation_of_net_power_out_SFC_and_overall_Efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_c=0.8; // Isentropic efficiency of compression each stage\n", +"eff_CT=0.88; // Isentropic efficiency of compressor turbine\n", +"eff_PT=0.88; // Isentropic efficiency of power turbine\n", +"eff_trans=0.98; // Turbine to compressor transmission efficiency\n", +"rp=3; // Pressure ratio in each stage of compression\n", +"T08=297; // Temperature after intercooler in kelvin\n", +"ma=15; // Air mass flow in kg/s\n", +"eff_reg=0.8; // Regenerator effectiveness\n", +"del_P=0.1; // Regenerator gas side pressure loss in bar\n", +"T01=327; // Ambient temperature in kelvin\n", +"p01=1; // Ambient pressure in bar\n", +"T03=1000; // Maximum cycle temperature in kelvin\n", +"CV=43.1; // Calorific value in MJ/kg\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"p03=rp^2; // Pressre at state 3 in bar\n", +"T_07=T01*(rp)^((r-1)/r);\n", +"T07=T01+(T_07-T01)/eff_c;\n", +"WLPC=ma*Cpa*(T07-T01); // Work of low pressue compressor\n", +"T_02=T08*(rp)^((r-1)/r);\n", +"T02=T08+(T_02-T08)/eff_c;\n", +"WHPC=ma*Cpa*(T02-T08);\n", +"WC=WLPC+WHPC; // Compressor work\n", +"WCa=WC/eff_trans; // Actual compressor work\n", +"// Neglecting effect of mf\n", +"T09=T03-(WCa/(ma*Cpg));\n", +"T_09=T03-(T03-T09)/eff_PT;\n", +"p09=p03/(T03/T_09)^(rg/(rg-1));\n", +"p04=p01+del_P;\n", +"T_04=T09*(p04/p09)^((rg-1)/rg);\n", +"T04=T09-eff_PT*(T09-T_04);\n", +"WTP=ma*Cpg*(T09-T04); // Work output of power turbine\n", +"T05=T02+eff_reg*(T04-T02);\n", +"mf=(ma*Cpg*(T03-T05))/(CV*10^3);\n", +"sfc=mf*3600/(WTP);//Specifc fuel consumption\n", +"eff_th=WTP/(mf*CV*10^3); // Thermal efficiency\n", +"\n", +"\n", +"disp ('kW (roundoff error)',WTP,'Work output of power turbine = ');\n", +"disp ('kg/kW h',sfc,'Specifc fuel consumption = ');\n", +"disp ('%',eff_th*100,'Thermal efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.5: Calculation_of_the_thermal_efficiency_and_air_rate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"Wplant=1850; // Plant work output in KW\n", +"p01=1; // Ambient pressure in bar\n", +"T01=27+273; // Ambient temperature in kelvin\n", +"T03=720+273; // Maximum cycle temperature in kelvin\n", +"rp=2.5; // Pressure ratio\n", +"eff_T=0.80; // Turbine and compressor efficiency\n", +"eff_reg=0.75; // Regenerator effectiveness\n", +"eff_comb=0.98; // Combustion efficiency \n", +"CV=43.1; // Calorific value in MJ/kg\n", +"del_p=0.03; // Pressure drop\n", +"p02=6.25; // Pressure in bar\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"T_07=T01*rp^((r-1)/r);\n", +"T07=T01+(T_07-T01)/eff_T;\n", +"T02=T07;\n", +"WLPC=Cpa*(T07-T01); // Work of low pressure compressor\n", +"WHPT=WLPC;\n", +"T09=T03-WHPT/Cpg;\n", +"T_09=T03-(T03-T09)/eff_T;\n", +"p03=(1-del_p)^2*p02\n", +"p09=p03/(T03/T_09)^(rg/(rg-1));\n", +"p10=p09*(1-del_p);\n", +"T10=T03;\n", +"p04=p01+del_p;\n", +"T_04=T10*(p04/p10)^((rg-1)/rg);\n", +"T04=T10-eff_T*(T10-T_04);\n", +"Wlpt=Cpg*(T10-T04);\n", +"WN=Wlpt-WHPT;\n", +"ma=Wplant/WN;\n", +"T05=T02+eff_reg*(T04-T02);\n", +"Q=Cpg*(T03-T05+T10-T09);\n", +"eff_th=WN/Q;\n", +"WHPT_1=ma*WHPT;\n", +"Wlpt_1=ma*Wlpt;\n", +"mf=ma*Q*3600/(eff_comb*CV*10^3);\n", +"sfc=mf/Wplant;\n", +"\n", +"disp ('K',T_07,'T_07 = ');\n", +"disp ('K',T07,'T07 = ');\n", +"disp ('K',T09,'T09 = ');\n", +"disp ('K',T_09,'T_09 = ');\n", +"disp ('K',T_04,'T_04 = ');\n", +"disp ('K',T04,'T04 = ');\n", +"disp ('K',T05,'T05 = ');\n", +"disp ('bar',p03,'P03 = ');\n", +"disp ('bar',p09,'P09 = ');\n", +"disp ('bar',p10,'P10 = ');\n", +"disp ('kg/s',ma,'Mass flow rate = ');\n", +"disp ('%',eff_th*100,'The overall efficiency = ');\n", +"disp ('kg of fuel/kW h',sfc,'Specific fuel consumption = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.6: Calculation_of_Compressor_efficiency_and_the_temperature_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=11.3137; // Pressure ratio\n", +"WN=0; // Net work output\n", +"Q=476.354; // Heat added per kg of air mass in kJ\n", +"T01=300; // Inlet air total temperature in kelvin\n", +"eff_T=0.71; // turbine efficiency\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"T_02=T01*rp^((r-1)/r);\n", +"T03_T02=Q/Cpa;\n", +"T03_T_04=rp^((r-1)/r);\n", +"T04_T03=1-(eff_T*(1/T03_T_04)*(T03_T_04-1));\n", +"T04=T01+(T03_T02);\n", +"T03=T04/T04_T03;\n", +"t=T03/T01; //Temperature ratio\n", +"T02=T03-T03_T02;\n", +"eff_C=(T_02-T01)/(T02-T01); // Compressor efficiency\n", +"\n", +"disp ('%',eff_C*100,'Compressor Efficiency = ',);\n", +"disp (t,'Temperature ratio = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.7: Calculation_of_suitable_pressure_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_C=0.7042; // Efficiency of the compressor\n", +"eff_T=0.71; // Efficiency of the turbine\n", +"Q=476.354; // Head added in kJ/kg\n", +"WR=0.0544; // Work ratio\n", +"T01=300;// Total inlet temperature in kelvin\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"c_t=(1-WR)*(eff_T*eff_C);\n", +"t=((Q/(Cpg*T01))+1-1/eff_C)/(1-c_t/eff_C); // Temperature ratio\n", +"c=c_t*t;\n", +"rp=c^(r/(r-1)); // Pressure ratio\n", +"\n", +"disp (rp,'Pressure ratio = ');\n", +"disp (t,'Temperature ratio = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.8: Calculation_of_minimum_temperature_ratio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"WR=0.3; // Work ratio\n", +"rp=12; // Pressure ratio \n", +"t=4; // Temperature ratio\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"c=rp^((r-1)/r);\n", +"eff_C_T=1/((1-WR)*t/c);\n", +"tmin=c/eff_C_T;\n", +"eff=1-1/c;\n", +"\n", +"disp (tmin,'Minimum Temperature ratio = ');\n", +"disp ('%',eff*100,'Efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.9: Calculation_of_Isentropic_efficiency_of_Turbine.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"eff_pe=0.85; // Polytropic efficiency of the compressor\n", +"T_02_T01=2;\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"\n", +"rc=(T_02_T01)^(r/(r-1));\n", +"eff_C=(T_02_T01-1)/(((rc^(((r-1)/r)*(1/eff_pe)))-1)); // Compressor efficiency\n", +"eff_T=(1-(1/rc)^(eff_pe*(r-1)/r))/(1-(1/rc)^((r-1)/r)); // Turbine efficiency\n", +"\n", +"\n", +"disp ('%',eff_C*100,' Isentropic compressor efficiency = ');\n", +"disp ('%',eff_T*100,' Isentropic Turbine efficiency = ');" + ] + } +], +"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/Gas_Turbines_by_V_Ganesan/7-Jet_Propulsion_Cycles_and_Their_Analysis.ipynb b/Gas_Turbines_by_V_Ganesan/7-Jet_Propulsion_Cycles_and_Their_Analysis.ipynb new file mode 100644 index 0000000..143c27b --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/7-Jet_Propulsion_Cycles_and_Their_Analysis.ipynb @@ -0,0 +1,522 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: Jet Propulsion Cycles and Their Analysis" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: Calculation_of_exit_speed_of_the_gases_and_the_thrust_developed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"ma=(12*10^4)/3600; // Air flow rate in kg/s\n", +"T01=15+273; // Temperature in kelvin\n", +"rp=4; // pressure ratio\n", +"p01=1.03; // Pressure in bar\n", +"T02=182+273; // Temperature in kelvin\n", +"T03=815+273; // Temperature in kelvin\n", +"T04=650+273; // Temperature in kelvin\n", +"ci=800*1000/3600; // Velocity in m/s\n", +"eff_nozzle=0.90; // Nozzle efficiency\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"p03=4.12; // in bar\n", +"\n", +"eff_c=1/((T02-T01)/(T01*((rp^((r-1)/r))-1)));\n", +"eff_T=eff_c;\n", +"Wc=ma*Cpa*(T02-T01);\n", +"rp_T=(1/(1-((T03-T04)/(eff_T*T03))))^((r/(r-1)));\n", +"p04=p03/rp_T;\n", +"p04_pc=1/(1-((rg-1)/((rg+1)*eff_nozzle)))^(rg/(rg-1));\n", +"p5=p01;\n", +"T_5=T04*(p5/p04)^((rg-1)/rg);\n", +"T5=T04-eff_nozzle*(T04-T_5);\n", +"cj=sqrt(2*Cpg*10^3*(T04-T5));\n", +"F=ma*(cj-ci);\n", +"\n", +"disp ('%',eff_c*100,'Efficiency of the compressor = ');\n", +"disp ('%',eff_T*100,'Efficiency of the Turbine = ');\n", +"disp ('kW',Wc,'Compressor work = ');\n", +"disp ('m/s (roundoff error)',cj,'The exit speed of gases = ');\n", +"disp ('N (roundoff error)',F,'Thrust developed = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1: Calculation_of_Thrust_power_and_Heat_Input.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"CV=43; // Calorific value of fuel in MJ/kg\n", +"mf=0.18*9000/3600; // Fuel consumption in kg/s\n", +"F=9; // Thrust in kN\n", +"ci=500; // Aircraft velocity in m/s\n", +"ma=27; // Mass of air passing through compressor in kg/s\n", +"\n", +"A_F=ma/mf; // Air fuel ratio\n", +"PT=F*ci; // Thrust power\n", +"Q=mf*(CV*10^3); // Heat supplied\n", +"eff=PT/Q; // Overall efficiency\n", +"disp (A_F,'Air fuel ratio = ');\n", +"disp ('%',eff*100,'Overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2: Calculation_of_The_Total_Design_Thrust.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T03=1200; // Maximum turbine inblet temperature in kelvin\n", +"rc=4.25; // Pressure ratio across compressor\n", +"ma=25; // Mass flow rate in kg/s\n", +"eff_C=0.87; // Isentropic efficiency of the compressor\n", +"eff_T=0.915; // Isentropic efficiency of turbine\n", +"eff_n=0.965; // Propelling nozzle efficiency\n", +"eff_Tr=0.985; // Transmission efficiency\n", +"del_pcomb=0.21; // Combustion chamber pressure loss in bar\n", +"Cpa=1.005; // Specific heat at constant pressure of air in kJ/kg K\n", +"ra=1.4; // Specific heat ratio of air\n", +"Cpg=1.147; // Specific heat of fuel in kJ/kg K\n", +"rg=1.33; // Specific heat of fuel\n", +"T01=293; // Ambient temperature in kelvin\n", +"p01=1; // Ambient pressure in bar\n", +"A_F=50; // Air Fuel ratio\n", +"p02=rc/p01;\n", +"\n", +"T02=(T01*((rc)^((ra-1)/ra)-1)/eff_C)+T01; // Actual temperature at state 2\n", +"T04=T03-((Cpa*(T02-T01))/(eff_Tr*Cpg)); // Temperature at state 4\n", +"rt=(1/(1-((T03-T04)/(eff_T*T03))))^(1/((rg-1)/rg)); // Pressure ratio across turbine\n", +"p04=(p02-del_pcomb)/rt; // Pressure at 4\n", +"p5=p01;\n", +"T_5=T04/(p04/p5)^((rg-1)/rg); // Temperature at 5\n", +"T5=T04-eff_n*(T04-T_5); \n", +"c5=sqrt (2*Cpg*10^3*(T04-T5)); \n", +"F=ma*c5; // Total design thrust\n", +"p04_pc=1/(1-((1/eff_n)*((rg-1)/(rg+1))))^(rg/(rg-1))\n", +"pc=p04*(1/p04_pc); \n", +"Tc=T04*(1/p04_pc)^((rg-1)/rg);\n", +"R=Cpg*10^3*(rg-1)/rg;\n", +"cj=sqrt (rg*R*Tc);\n", +"row_c=(pc*10^5)/(R*Tc);\n", +"A=ma/(row_c*cj); // Area of the propelling nozzle\n", +"d=sqrt (4*A/3.14); // Diameter of the nozzle\n", +"pa=p01;\n", +"Fp=(pc-pa)*10^5*A;// Pressure thrust\n", +"Fm=ma*cj;\n", +"Ft=Fp+Fm; // Total thrust\n", +"sfc=(ma/A_F)*3600/Ft;\n", +"\n", +"disp ('N (roundoff error)',F,' Total design thrust/s = ');\n", +"disp ('N (roundoff error)',Ft,'Total thrust /s = ');\n", +"disp ('kg/ N thrust h',sfc, 'Specific fuel consumption = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3: Calculation_of_the_velocity_leaving_the_nozzle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"p03=4.5; // Pressure at turbine inlet in bar\n", +"T03=800+273; // Temperature at turbine inlet in kelvin\n", +"p04=1.75; // Pressure at turbine outlet in bar\n", +"eff_T=0.75; //Turbine efficiency\n", +"p05=1.03; // Pressure at state 5 in bar\n", +"Cp=1.05; // Specific heat at constant pressure in kJ/kg K\n", +"r=1.38; // Specific heat ratio \n", +"\n", +"T04=T03*(1-eff_T*(1-(1/(p03/p04)^((r-1)/r)))); // Temperature at state 4\n", +"cj=sqrt (2*Cp*10^3*T04*(1-(1/(p04/p05)^((r-1)/r)))); // Velocity leaving nozzle\n", +"\n", +"disp ('K',T04,'(i).Temperature of the gas entering the jet (nozzle) = ');\n", +"disp ('m/s',cj,'(ii).Velocity of gas leaving the jet = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4: Calculation_of_propulsive_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"cj=2700; // The effective jet velocity from jet engine in m/s\n", +"ci=1350; // Flight velocity in m/s\n", +"ma=78.6; // Air flow rate in m/s\n", +"\n", +"a=ci/cj;\n", +"F=ma*(cj-ci); // Thrust\n", +"P=F*ci; // Thrust power\n", +"eff_P=2*a/(a+1); // Propulsive efficiency\n", +"\n", +"disp ('N',F,'(i).Thrust = ');\n", +"disp ('MN',P/10^6,'(ii). Thrust power = ');\n", +"disp ('%',eff_P*100,'(iii). Propulsive efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5: Calculation_of_the_thrust_and_Specific_fuel_consumption.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"pa=0.458; // Ambient pressure in bar\n", +"Ta=248; // Ambient temperature in kelvin\n", +"Ci=805*1000/3600; // Speed of the aircraft in m/s\n", +"rp=4;// Pressure ratio\n", +"DelP_comb=0.21; // Combustion chamber pressure loss in bar\n", +"T03=1100; // Turbine inlet temperature in kelvin\n", +"eff_ram=0.95; // Intake duct efficiency\n", +"eff_c=0.85; // Compressor efficiency\n", +"eff_T=0.90; // Turbine efficiency\n", +"eff_m=0.99; // Mechanical efficiency of transmission\n", +"eff_nozzle=0.95; // Nozzle efficiency\n", +"CV=43; // Low calorific value in MJ/kg\n", +"Ac=0.0935; // Nozzle outlet area in m^2\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"p01=pa*(1+eff_ram*((1+Ci^2/(2*Cpa*Ta*10^3))^(r/(r-1))-1));\n", +"p02=p01*rp;\n", +"T01=Ta+Ci^2/(2*Cpa*10^3);\n", +"T02=T01+T01*(rp^((r-1)/r)-1)/eff_c;\n", +"T04=T03-(Cpa*(T02-T01))/(Cpg*eff_m);\n", +"p03=p02-DelP_comb;\n", +"T_04=T03-(T03-T04)/eff_T;\n", +"p04=p03*(T_04/T03)^(r/(r-1));\n", +"p04_pc=1/(1-(((rg-1)/(rg+1))/eff_nozzle))^(rg/(rg-1));\n", +"Tc=T04*(1/p04_pc)^((rg-1)/rg);\n", +"pc=p04/p04_pc;\n", +"row_c=(pc*10^5)/(R*Tc);\n", +"cj=sqrt (rg*R*Tc);\n", +"m=row_c*Ac*cj;\n", +"F=m*(cj-Ci)+Ac*(pc-pa)*10^5; // Total thrust\n", +"mf=(m*Cpg*(T03-T02))/(CV*10^3);\n", +"sfc=mf*3600/F; // specific fuel consumption\n", +"\n", +"disp ('N (roundoff error)',F,'Total thrust = ');\n", +"disp ('kg/N h (roundoff error)',sfc,'specific fuel consumption = ');\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6: Calculation_of_specific_power_output.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"ci=600*1000/3600; // Velocity in m/s\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"pa=0.458; // Ambient pressure in bar\n", +"Ta=-15+273; // Ambient temperature in kelvin\n", +"rp=9; // pressure ratio\n", +"T03=1200; // Maximum temperature in kelvin\n", +"eff_ram=0.9; // Intake duct efficiency\n", +"eff_c=0.89; // Compressor efficiency\n", +"eff_T=0.93; // Turbine efficiency\n", +"eff_m=0.98; // Mechanical efficiency of transmission\n", +"\n", +"cj=ci\n", +"T_01=Ta+(ci^2/(2*Cpa*10^3));\n", +"p_01=pa*(T_01/Ta)^(r/(r-1));\n", +"p01=eff_ram*(p_01-pa);\n", +"p02=rp*p01;\n", +"T01=T_01;\n", +"T_02=T01*rp^((r-1)/r);\n", +"T02=T01+(T_02-T01)/(eff_c);\n", +"T_04=T03*(1/rp)^((rg-1)/rg);\n", +"T04=T03-eff_T*(T03-T_04);\n", +"WN=Cpg*(T03-T04)-Cpa*(T02-T01)/eff_m;// net work done\n", +"eff_th=WN/(Cpg*(T03-T02)); // Thermal efficiency\n", +"\n", +"disp ('kJ/kg (roundoff error)',WN,'Net work done = ');\n", +"disp ('%',eff_th*100,'Thermal efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7: Determination_of_rate_of_fuel_consumption.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"pa=0.7; // Ambient pressure in bar\n", +"Ta=1+273; // Ambient temperature in kelvin\n", +"Ci=800*1000/3600; // Speed of the aircraft in m/s\n", +"rp=5;// Pressure ratio\n", +"eff_ram=1.00; // Intake duct efficiency\n", +"eff_c=0.85; // Compressor efficiency\n", +"eff_T=0.90; // Turbine efficiency\n", +"eff_comb=0.98; //Combustion efficiency \n", +"eff_nozzle=0.95; // Nozzle efficiency\n", +"rp_T=2.23;// Turbine pressure ratio\n", +"CV=43; // Low calorific value in MJ/kg\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.005;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.4;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"F=25000; // Thrust in N\n", +"\n", +"cj=2*Ci;\n", +"T_01=Ta+(Ci^2/(2*Cpa*10^3));\n", +"T01=T_01;\n", +"T02=T01+(T01*(((rp)^((r-1)/r))-1))/eff_c;\n", +"p_01=pa*(1+Ci^2/(2*Cpa*10^3*Ta))^(r/(r-1));\n", +"p01=eff_ram*(p_01-pa);\n", +"p02=rp*p01;\n", +"T03=(T02-T01)/(eff_T*(1-1/rp_T^((r-1)/r)));\n", +"ma=F/(cj-Ci);\n", +"// Neglecting the effect of the mass addition of fuel on the right hand side\n", +"mf=(ma*Cpa*(T03-T02))/(eff_comb*CV*10^3);\n", +"\n", +"disp ('kg/s',ma,'Mass flow rate of air = ');\n", +"disp ('kg/s (roundoff error)',mf,'Mass flow rate of fuel = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8: Calculation_of_the_take_off_thrust.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"Ta=288; // Ambient temperature in kelvin\n", +"pa=1.01; // Ambient pressure in bar\n", +"p04=2.4; // Stagnation pressure in bar\n", +"T04=1000;// Stagnation temperature in kelvin\n", +"m=23; // Mass flow rate in kg/s\n", +"rp=1.75; // Pressure ratio\n", +"eff_f=0.88 ; // Efficiency of the fan\n", +"eff_ft=0.9; // Efficiency of the fan turbine\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=284.6; // Characteristic gas constant in J/kg K\n", +"T01=Ta;\n", +"p01=pa;\n", +"pc=p04*(2/(r+1))^(r/(r-1));\n", +"// since pc>pa the nozzle will choke\n", +"Tc=T04*(2/(r+1));\n", +"row_c=pc*10^5/(R*Tc);\n", +"cj=sqrt (r*R*Tc);\n", +"A=m/(row_c*cj);\n", +"p1=pa;\n", +"F=m*cj+(A*(pc-p1)*10^5);\n", +"// For fan engine\n", +"T_02=T01*(rp)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_f;\n", +"// For cold nozzle\n", +"m_nozzle=2*m; // Flow through cold nozzle\n", +"pc1=p01*rp*(2/(r+1))^(r/(r-1));\n", +"F_cold=m_nozzle*sqrt (2*Cpa*10^3*(T02-T01));\n", +"// Fan Turbine\n", +"T05=T04-((m_nozzle*Cpa*(T02-T01))/(m*Cpg));\n", +"T_05=T04-(T04-T05)/eff_ft;\n", +"p_05=p04*(T_05/T04)^(rg/(rg-1));\n", +"pc=p_05*(2/(rg+1))^(rg/(rg-1));\n", +"F_hot=m*sqrt (2*Cpg*10^3*(T05-T01));\n", +"Takeoffthrust= F_cold + F_hot;\n", +"\n", +"disp ('m^2 (roundoff error)',A,'Nozzle Exit area = ');\n", +"disp ('N (roundoff error)',F,'Total Thrust = ');\n", +"disp ('N (roundoff error)',Takeoffthrust,'Take-off Thrust = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9: Calculation_of_thrust_provided_by_the_engine_and_the_thrust_power_developed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"ma=18.2; // Massflow rater in m/s\n", +"Mi=0.6; // Mach number \n", +"pa=0.55; // Ambient pressure in bar\n", +"Ta=255; // Ambient temperature in kelvin\n", +"rp=5; // Pressure ratio\n", +"T03=1273; // Maximum temperature in kelvin\n", +"eff_c=0.81; // Compressor efficiency\n", +"eff_T=0.85; // Turbine efficiency\n", +"eff_nozzle=0.915; // Nozzle efficiency\n", +"eff_ram=0.9; // Intake duct efficiency\n", +"CV=45870; // Low calorific value in kJ/kg\n", +"Cpa=1.005;// Specific heat of air at constant pressure in kJ/kg K\n", +"Cpg=1.147;// Specific heat of fuel at constant pressure in kJ/kg K\n", +"rg=1.33;// Specific heat ratio of fuel\n", +"r=1.4; // Specific heat ratio of air\n", +"R=284.6; // Characteristic gas constant in J/kg K\n", +"\n", +"ci=Mi*sqrt(r*R*Ta);\n", +"T_01=Ta+ci^2/(2*Cpa*10^3);\n", +"T01=T_01;\n", +"p_01=pa*(T01/Ta)^(r/(r-01));\n", +"p01=eff_ram*(p_01-pa)+pa;\n", +"p02=rp*p01;\n", +"T02=T01*(1+((rp^((r-1)/r))-1)/eff_c);\n", +"Wc=ma*Cpa*(T02-T01);\n", +"WT=Wc;\n", +"mf=ma/((CV/(Cpg*(T03-T02)))-1);\n", +"f1=mf/ma;\n", +"T04=T03-(WT/((ma+mf)*Cpg));\n", +"rp_T=(1/(1-((1-(T04/T03))/eff_T)))^(r/(r-1));\n", +"p03=p02;\n", +"p04=p03/rp_T;\n", +"p04_pc=1/(1-((rg-1)/((rg+1)*eff_nozzle)))^(rg/(rg-1));\n", +"pc=p04_pc/p04;\n", +"Tc=T04*(1/p04_pc)^((rg-1)/rg);\n", +"cj=sqrt (r*R*Tc);\n", +"row_c=pc*10^5/(R*Tc);\n", +"An=(ma+mf)/(row_c*cj);\n", +"F=(ma+mf)*cj-ma*ci+An*(pc-pa);\n", +"Fp=F*ci;\n", +"\n", +"disp ('kW (roundoff error)',Wc,'Work of compression = ');\n", +"disp ('kW (roundoff error)',WT,'Power output of the turbine = ');\n", +"disp (f1,'Fuel-Air ratio = ');\n", +"disp ('N (roundoff error)',F,'Thrust = ');\n", +"disp ('kW (roundoff error)',Fp/1000,'Thrust power = ');" + ] + } +], +"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/Gas_Turbines_by_V_Ganesan/8-Centrifugal_Compressors.ipynb b/Gas_Turbines_by_V_Ganesan/8-Centrifugal_Compressors.ipynb new file mode 100644 index 0000000..13109a2 --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/8-Centrifugal_Compressors.ipynb @@ -0,0 +1,455 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: Centrifugal Compressors" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.10: Calculation_of_the_torque_power_required_and_the_head_developed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"m=30; // mass flow rate in kg/s\n", +"N=15000; // Speed in rpm\n", +"r2=0.3; // Radius in m\n", +"D2=r2*2; // Diameter in m\n", +"w2=100; // Relative velocity in m/s\n", +"beta_1=80; // in degrees\n", +"p01=1; // Inlet pressure in bar\n", +"T01=300 // Inlet temperature in kelvin\n", +"Cp=1.005; // specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"u2=3.14*D2*N/60;\n", +"ct2=u2-(w2*cosd (beta_1));\n", +"Fr=m*ct2*r2;\n", +"P=Fr*(2*3.14*N/60);\n", +"W=u2*ct2;\n", +"P02=p01*(1+(W*10^-3/(Cp*T01)))^(r/(r-1));\n", +"\n", +"disp ('Nm',Fr,'Torque = ');\n", +"disp ('kW',P/1000,'Power = ');\n", +"disp ('bar',P02,'Head Developed = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: Calculation_of_compressor_efficiency.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"N=11500; // Speed in rpm\n", +"T01=21+273; // Inlet total temperature in kelvin\n", +"p01=1;// Inlet total pressure in bar\n", +"p02=4;// Outlet total pressure in bar\n", +"D=0.75; // impeller diameter in m\n", +"mu=0.92;// slip factor\n", +"Cp=1.005; // specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"u=3.14*D*N/60;\n", +"W=mu*u^2;\n", +"T02=W/(Cp*10^3)+T01;\n", +"T_02=T01*(p02/p01)^((r-1)/r);\n", +"eff_c=(T_02-T01)/(T02-T01);\n", +"\n", +"disp ('%',eff_c*100,'Efficiency of the compressor = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Estimation_of_the_probable_axial_width_of_the_impeller.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"m=35; // mass flow rate of air in kg/s\n", +"D=0.76; // Impeller diameter in m\n", +"N=11500; // speed in rpm\n", +"eff_c=0.8; // Efficiency of the compressor \n", +"rp=4.2; // Pressure ratio\n", +"cr=120; // Radial velocity in m/s\n", +"p01=1; // Inlet pressure in bar\n", +"T01=47+273; // Inlet temperature in kelvin\n", +"Cp=1.005; // specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T_02=T01*rp^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c;\n", +"// ignoring the effects of the velocity of flow\n", +"p02=rp/p01;\n", +"row2=p02*10^5/(R*T02);\n", +"Atip=m/(row2*cr);\n", +"AW=Atip/(3.14*D); // Axial width\n", +"\n", +"disp ('cm',AW*100,'Axial Width = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Calculation_of_theoretical_blade_angles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"D=0.15; // Inlet eye diameter in m\n", +"N=20000; // Speed in rpm\n", +"ca1=107; // Axial velocity in m/s\n", +"T01=294; // Inlet temperature in kelvin\n", +"p01=1.03; // Inlet pressure in kg/cm^2\n", +"Cp=1.005; // specific heat at constant pressure in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"u1=3.14*D*N/60;\n", +"beta_1=atand (ca1/u1);// Blade angle \n", +"cr=u1/cosd (beta_1);\n", +"a=sqrt (r*R*(T01-ca1^2/(2*Cp*10^3)));\n", +"M=cr/a; // Mach number at the tip\n", +"\n", +"disp ('degree',beta_1,'(i).Theoretical angle of the blade at this point = ');\n", +"disp (M,'(ii).Mach number of the flow at the tip of the eye = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Calculation_of_final_temperature_of_the_gases_and_the_work_done_per_kg_of_gas.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T01=0+273; // Inlet gas temperature in kelvin\n", +"p01=0.7; // Inlet pressure in bar\n", +"p02=1.05; // Delivery pressure in bar\n", +"eff_c=0.83; // Compressor efficiency\n", +"Cp=1.005;// Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717;// Specific heat at constant volume in kJ/kg K\n", +"r=1.4; // Specific heat ratio \n", +"\n", +"T_02=T01*(p02/p01)^((r-1)/r);\n", +"T02=T01+(T_02-T01)/eff_c; // Final temperature of the gas\n", +"Wc=Cp*(T02-T01); // Work of compression\n", +"\n", +"// With additional compressor\n", +"T_03=T02*(p02/p01)^((r-1)/r);\n", +"T03=T02+(T_03-T02)/eff_c; \n", +"T_03=T01*(p02/p01)^(2*(r-1)/r);\n", +"eff_overall=(T_03-T01)/(T03-T01);\n", +"\n", +"disp ('K',T02,'Final temperature of the gas = ');\n", +"disp ('kJ/kg',Wc,' Work of compression = ');\n", +"disp ('%',eff_overall*100,'Overall efficiency = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Calculation_of_impeller_diameters_and_the_width_at_the_impeller_exit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"N=12500; // Speed in rpm\n", +"m=15; // Mass flow rate in kg/s\n", +"rp=4; // Pressure ratio\n", +"eff_c=0.75; // Isentropic efficiency \n", +"mu=0.9; // Slip factor\n", +"pi=0.3; // Flow coefficient at impeller exit\n", +"D=0.15; // Hub diameter in m\n", +"ca2=150; // Axial velocity in m/s\n", +"T01=275; // Inlet temperature in kelvin\n", +"p01=1; // Inlet pressure in bar\n", +"Cp=1.005;// Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717;// Specific heat at constant volume in kJ/kg K\n", +"r=1.4; // Specific heat ratio \n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"u2=ca2/pi;\n", +"P=m*mu*u2^2/1000; // Power output\n", +"D2=u2*60/(3.14*N);\n", +"T1=T01-ca2^2/(2*Cp*10^3);\n", +"p1=p01*(T1/T01)^(r/(r-1));\n", +"row1=p1*10^5/(R*T1);\n", +"A1=m/(row1*ca2);\n", +"D1=sqrt ((A1*4/(3.14))+D^2);\n", +"p3_p1=rp;\n", +"p2=2*p1;\n", +"T_2=T1*(p2/p1)^((r-1)/r);\n", +"T2=T1+(T_2-T1)/eff_c;\n", +"row2=p2*10^5/(R*T2);\n", +"W2=(m)/(row2*ca2*3.14*D2);\n", +"\n", +"disp ('kW',P,'Power = ');\n", +"disp ('Impeller Diameters');\n", +"disp ('cm',D2*100,'D2 = ','cm (roundoff error)',D1*100,'D1 = ');\n", +"disp ('Impeller width')\n", +"disp ('cm (roundoff error)',W2*100,'W2 = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.6: Calculation_of_the_minimum_possible_depth_of_the_diffuser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"m=14; // mass flow rate in kg/s\n", +"rp=4; // pressure ratio\n", +"N=12000; // Speed in rpm\n", +"T01=288; // Inlet temperature in kelvin\n", +"p01=1.033; // Inlet pressure in bar\n", +"Cp=1.005;// Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717;// Specific heat at constant volume in kJ/kg K\n", +"r=1.4; // Specific heat ratio \n", +"R=287; // Characteristic gas constant in J/kg K\n", +"mu=0.9; // Slip factor\n", +"chi=1.04; // Power input factor\n", +"eff_c=0.8; // Compressor efficiency\n", +"\n", +"T03=(((rp^((r-1)/r))-1)*T01/eff_c)+T01;;\n", +"U=sqrt ((T03-T01)*Cp*10^3/(chi*mu));\n", +"D=U*60/(3.14*N);\n", +"\n", +"T3=T03/1.2;\n", +"c2=sqrt (r*R*T3);\n", +"ca2=sqrt (c2^2-(mu*U)^2);\n", +"T02=eff_c*(T03-T01)+T01;\n", +"Loss=T03-T02;\n", +"T2=T3-Loss/2\n", +"p2=p01*(T2/T01)^(r/(r-1));\n", +"row2=p2*10^5/(R*T2);\n", +"A=m/(row2*ca2);\n", +"Depth=A/(2*3.14*D/2);\n", +"\n", +"disp ('cm',D*100,'Overall diameter of the Impeller = ');\n", +"disp ('cm (roundoff error)',Depth*100,'Depth of the diffuser = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7: Calculation_of_impeller_and_diffuser_blade_angles_at_inlet.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"N=10000; // Speed in rpm\n", +"Q=600; // Flow rate m^2/min\n", +"rp=4; // Pressure ratio \n", +"eff_c=0.82; // Compressor efficiency\n", +"T01=293; // Inlet temperature in kelvin\n", +"p01=1.0; // Inlet pressure in bar\n", +"Cp=1.005;// Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717;// Specific heat at constant volume in kJ/kg K\n", +"r=1.4; // Specific heat ratio \n", +"R=287; // Characteristic gas constant in J/kg K\n", +"ca=60; // Axial velocity in m/s\n", +"D2_D1=2 ;// Diameter ratio\n", +"\n", +"T_03=T01*rp^((r-1)/r);\n", +"T03=T01+(T_03-T01)/eff_c;\n", +"u2=sqrt (Cp*10^3*(T03-T01));\n", +"Wc=u2^2; // Work of compression\n", +"D2=(u2*60/(3.14*N));\n", +"D1=D2/D2_D1;\n", +"T1=T01-(ca^2/(2-Cp*10^3));\n", +"p1=p01*(T1/T01)^(r/(r-1));\n", +"row1=p1*10^5/(R*T1);\n", +"Wroot=(Q/60)*(1/(ca*3.14*D1));\n", +"u1=3.14*N*D1/60;\n", +"alpha_root=atand (ca/u1);\n", +"alpha_tip= atand (ca/u2);\n", +"\n", +"disp ('(i).Power input ');\n", +"disp ('kW/kg/s',Wc/1000,'Wc = ');\n", +"disp ('(ii).Impeller Diameters');\n", +"disp ('m',D2,'D2 = ','m',D1,'D1 = ');\n", +"disp ('(iii).Impeller and diffuser blade angles at inlet');\n", +"disp ('degree',alpha_tip,'alpha_tip = ','degree',alpha_root,'alpha_root = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.8: Calculation_of_slip_factor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4; // Pressure ratio\n", +"eff_c=0.8; // Compressor efficiency \n", +"N=15000; // Speed in rpm\n", +"T01=293; // Inlet temperature in kelvin\n", +"De=0.25; // Diameter of eye in m\n", +"C1=150; // Absolute velocity in m/s\n", +"Di=0.6; // Impeller diameter in m\n", +"a1=25; // in degree\n", +"Cp=1.005;// Specific heat at constant pressure in kJ/kg K\n", +"Cv=0.717;// Specific heat at constant volume in kJ/kg K\n", +"r=1.4; // Specific heat ratio \n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T02=T01*rp^((r-1)/r);\n", +"DelT_actual=(T02-T01)/eff_c;\n", +"P=Cp*10^3*DelT_actual; // Power input\n", +"u1=3.14*De*N/60;\n", +"ct1=C1*sind (a1);\n", +"// At Exit\n", +"u2=3.14*Di*N/60;\n", +"ct2=(P+(u1*ct1))/u2;\n", +"mu=ct2/u2; // Slip factor\n", +"\n", +"disp (mu,'Slip Factor = ');\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.9: Determination_of_number_of_radial_impeller_vanes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"P=180*10^3; // Power input in J\n", +"N=15000; // Speed in rpm\n", +"a1=25; // in degrees\n", +"De=0.25; // Mean dia of the eye in m\n", +"Di=0.6;// Impeller tip diameter in m\n", +"c1=150; // Absolute air velocity at inlet in m/s\n", +"\n", +"u1=3.14*De*N/60;\n", +"u2=3.14*Di*N/60;\n", +"ct1=c1*sind (a1);\n", +"ct2=(P+(u1*ct1))/u2;\n", +"mu=ct2/u2;\n", +"z=(1.98)/(1-mu); // Number of impeller vanes\n", +"disp(z,'Number of impeller vanes using Stanitz formulae = ');" + ] + } +], +"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/Gas_Turbines_by_V_Ganesan/9-Axial_Flow_Compressors.ipynb b/Gas_Turbines_by_V_Ganesan/9-Axial_Flow_Compressors.ipynb new file mode 100644 index 0000000..17beb4c --- /dev/null +++ b/Gas_Turbines_by_V_Ganesan/9-Axial_Flow_Compressors.ipynb @@ -0,0 +1,551 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Axial Flow Compressors" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.10: Determination_of_blade_and_air_angle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"u=250; // Mean blade speed in m/s\n", +"rp=1.3; // Pressure ratio\n", +"ca=200; // Axial velocity in m/s\n", +"p01=1; // Inlet pressure in bar\n", +"T01=300; // Inlet temperature in kelvin\n", +"R1=0.5; // Degree of reaction\n", +"Cp=1.005; // Specific heat in KJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"Del_T=(rp^((r-1)/r)-1)*T01;\n", +"//tan_beta1+tan_beta2=(R*2*u/ca);\n", +"//tan_beta1-tan_beta2=(Del_T*Cp*10^3/(u*ca));\n", +"A=[1 1;1 -1]; B=[(R1*2*u/ca) ;(Del_T*Cp*10^3/(u*ca))];\n", +"tan_beta=A\B;\n", +"beta_1=atand (tan_beta(1));\n", +"beta_2=atand (tan_beta(2));\n", +"alpha_1=beta_2; alpha_2=beta_1;\n", +"\n", +"disp ('degree',beta_2,'beta2 = ','degree',beta_1,'beta1 = ');\n", +"disp ('degree',alpha_2,'alpha2 = ','degree',alpha_1,'alpha1 = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.11: Calculation_of_rotational_speed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"n=4; // Number of stage\n", +"rp=10; // Pressure ratio\n", +"eff_p_ac=0.92; // Ploytropic efficiency of axial compressor\n", +"eff_p_cc=0.83; // Polytropic efficiency of centrifugal compressor\n", +"Del_Trise=30; // Axial compressor stage temperature in kelvin\n", +"R=0.5; // Reaction stage\n", +"beta_2=20; // Outlet stator angle in degree\n", +"D=0.25; // Mean diameter of each stage in m\n", +"wf=0.8; // Work done factor\n", +"ca=150; // Axial velocity in m/s\n", +"Di=0.33; //Impeller diameter in m\n", +"mu=0.9; // Slip factor\n", +"p01=1.01; // Ambient pressure in bar\n", +"T01=288; // Ambient temperature in kelvin\n", +"pif=1.04; // Power input factor\n", +"Cp=1.005; // Specific heat in KJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"beta_1=atand (sqrt ((Cp*10^3*Del_Trise/(wf*ca^2))+(tand(beta_2)^2)));\n", +"u=ca*(tand (beta_1)+tand(beta_2));\n", +"Nac=(u/(3.14*D));\n", +"r1=(1+n*Del_Trise/T01)^(eff_p_ac*r/(r-1)); // Total pressure ratio across the axial compressor\n", +"\n", +"r2=rp/r1; // Pressure ratio across centrifugal compressor\n", +"T02=T01*r1^((r-1)/(eff_p_ac*r));\n", +"T03=T02*r2^((r-1)/(eff_p_cc*r));\n", +"Del_Tsc=T03-T02;\n", +"u=sqrt ((Del_Tsc*Cp*10^3)/(pif*mu));\n", +"Ncc=u/(3.14*Di);\n", +"\n", +"disp ('rps (roundoff error)',Nac,'Speed of the axial compressor = ');\n", +"disp ('rps (roundoff error)',Ncc,'Speed of the centrifugal compressor = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: Estimation_of_blade_angles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"n=10; // No of stages in the axial flow compressor\n", +"rp=5; // Overall pressure ratio\n", +"eff_C=0.87; // Overall isentropic efficiency\n", +"T1=15+273; // Temperature of air at inlet in kelvin\n", +"u=210; // Blade speed in m/s\n", +"ca=170; // Axial velocity in m/s\n", +"wf=1; // Work factor\n", +"r=1.33; // Specific heat ratio\n", +"Cp=1.005; // Specific heat in kJ/kg K\n", +"\n", +"Del_Tstage=(T1*(rp^((r-1)/r)-1))/(n*eff_C); // Temperature increase per stage\n", +"// By property relations and let us assume \n", +"// tan_beta1-tan_beta2=Del_Tstage*Cp/(wf*u*ca)\n", +"// tan_beta1+tan_beta2=u/ca for 50% reaction \n", +"// To solve this above equations using matrix method\n", +"a=[1,-1;1,1]; c=[(Del_Tstage*Cp*10^3/(wf*u*ca));u/ca];\n", +"b=a\c;\n", +"beta1=atand(b(1));// Blade angles at inlet\n", +"beta2=atand(b(2)); // Blade angles at outlet\n", +"\n", +"disp ('degree (roundoff error)',beta2,'Blade angle at outlet = ','degree (roundoff error)',beta1,'Blade angle at inlet = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: Calculation_of_mass_flow_rate_and_degree_of_reaction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"P1=1.0132; // Inlet air pressure in bar\n", +"T01=288; // Inlet air temperature in kelvin\n", +"ca=150; // axial velocity in m/s\n", +"dtip=60; // Tip diameter of rotor in cm\n", +"dhub=50; // Hub diameter of rotor in cm\n", +"N=100; // Speed of rotor in rps\n", +"t_angle=30; // Deflected angle of air in degree (in question it is 30.2 but in solution it is 30)\n", +"P2_P1=1.2; // Stage pressure ratio\n", +"Cp=1005; // Specific heat in J/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"u=(3.142857*(dhub+dtip)*10^-2*N)/2; // Mean blade velocity\n", +"beta_1=atand(u/ca); // Blade angle at inlet\n", +"beta_2=beta_1-t_angle; // As air is deflected by 30\n", +"// from velocity triangle\n", +"x=ca*tand(beta_2);\n", +"alpha_2=atand ((u-x)/ca);\n", +"C1=ca;\n", +"T1=T01-(C1^2/(2*Cp)); // Static temperature at inlet\n", +"P2=P1*P2_P1; // Pressure at outlet\n", +"T2=T1*(P2/P1)^((r-1)/r); // Static temperature at outlet\n", +"row_2=(P2*10^5)/(R*T2); // Density at outlet\n", +"m=3.14*(dtip^2-dhub^2)*ca*row_2*10^-4/4; // Mass flow rate\n", +"wf=1; // Work factor\n", +"P=wf*u*ca*m*(tand(beta_1)-tand(beta_2))/1000; // Power developed\n", +"R=ca*(tand(beta_1)+tand(beta_2))/(2*u); // Degree of reaction\n", +"\n", +"disp ('kg/s',m,'Mass flow rate = ');\n", +"disp('kW (Error due to more decimal values in expression)',P,'Power developed = ');\n", +"disp (R,'Degree of Reaction = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: Estimation_of_number_of_stages_of_the_compressors.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"beta_1=45; // Inlet blade angle in degree\n", +"beta_2=10; // Outlet blade angle in degree\n", +"rp=6; // Compressor pressure ratio\n", +"eff_C=0.85;// Overall isentropic efficiency\n", +"T1=37+273; // Inet static temperature in kelvin\n", +"u=200; // Blade speed in m/s\n", +"Cp=1005; // Specific heat in J/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"// (i). wf=1\n", +"wf=1; // Work factor\n", +"ca=u/(tand(beta_1)+tand(beta_2)); // Axial velocity\n", +"Del_Tstage=wf*u*ca*(tand(beta_1)-tand(beta_2))/Cp; // Stage temperature drop\n", +"Del_Toverall=(T1*(rp^((r-1)/r)-1))/eff_C; // Overall temperature drop\n", +"n=Del_Toverall/Del_Tstage; // No of stages\n", +"\n", +"disp (n,'Number of stages required = ','(i).wf = 1');\n", +"\n", +"// (ii).wf = 0.87\n", +"wf =0.87; // Work factor\n", +"ca=u/(tand(beta_1)+tand(beta_2)); // Axial velocity\n", +"Del_Tstage=wf*u*ca*(tand(beta_1)-tand(beta_2))/Cp; // Stage temperature drop\n", +"Del_Toverall=T1*(rp^((r-1)/r)-1)/eff_C; // Overall temperature drop\n", +"n=Del_Toverall/Del_Tstage; // No of stages\n", +"\n", +"disp (n,'Number of stages required = ','(ii).wf = 0.87');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: Determination_of_Mach_number_relative_to_Rotor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4; // Total head pressure ratio\n", +"eff_O=0.85; // Overall total head isentropic efficiency\n", +"T01=290; // Total head inlet temperature in kelvin\n", +"alpha_1=10; // Inlet air angle in degree\n", +"alpha_2=45; // Outlet air angle in degree\n", +"u=220; // Blade velocity in m/s\n", +"wf=0.86; // Wok done factor\n", +"R=284.6; // Characteristic gas constant in kJ/kg K\n", +"Cp=1005; // Specific heat in J/kg K\n", +"r=1.4; // Specific heat ratio\n", +"\n", +"eff_P=1/(log10(((rp^((r-1)/r)-1)/eff_O)+1)/(log10(rp)*((r-1)/r)));; \n", +"// From velocity triangle\n", +"ca=u/(tand(alpha_1)+tand(alpha_2)); // Axial velocity\n", +"Del_Tstage=wf*u*ca*(tand(alpha_2)-tand(alpha_1))/Cp; // Stage temperature rise\n", +"T02=T01*(rp)^((r-1)/(r*eff_P)); // Total head temperature \n", +"T02_T01=T02-T01; // Total temperature rise\n", +"n=T02_T01/Del_Tstage; // Total number of stages\n", +"// from velocty traingles\n", +"w1=ca/cosd(alpha_2);\n", +"c1=ca/cosd(alpha_1);\n", +"T1=T01-c1^2/(2*Cp); // Static temperature\n", +"M=w1/sqrt(r*R*T1); // Mach number at inlet\n", +"\n", +"disp (eff_P*100,'Polytropic efficiency of the compressor = ');\n", +"disp (n,'Total number of stages = ');\n", +"disp (M,'Mach number at inlet = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: Calculation_of_pressure_rise_per_blade_ring_and_the_power_input_per_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"Q=1000; // Flow rate of free air in m^3/min\n", +"P1=0.98; // Inlet pressure in bar\n", +"T1=15+273; // Inlet temperature in kelvin\n", +"Dm=0.6; // Mean diameter in m\n", +"h=6.75; // blade length in cm\n", +"CL=0.6; CD=0.05; // At zero angle of incidence\n", +"Cp=1.005; // Specific heat in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"k=1-0.1; //Blade occupys 10% of axial area\n", +"N=6000; // speed in rpm\n", +"Ac=19.25*10^-4; // Projected area in m^2\n", +"n=50;\n", +"eff_C=1; // Efficiency of compressor\n", +"\n", +"row=(P1*10^5)/(R*T1); // Density\n", +"A=k*3.14*Dm*h*10^-2; // Area of axial\n", +"ca=Q/(60*A); // Axial velocity\n", +"u=3.14*Dm*N/60; // Blade velocity\n", +"beta_1=atand(u/ca); // Blade angle at inlet\n", +"w=sqrt (ca^2+u^2); // From velocity triangle\n", +"L=CL*row*w^2*Ac/2;\n", +"D=CD*row*w^2*Ac/2;\n", +"P=(L*cosd(beta_1)+D*sind (beta_1))*u*n*10^-3; // Power input / stage\n", +"m=Q*row/60;// mass flow rate\n", +"rp=((P*eff_C/(m*Cp*T1))+1)^(r/(r-1)); // pressure ratio\n", +"P2=rp*P1; // Pressure\n", +"\n", +"disp ('kW (Roundoff error )',P,'Power input/stage = ');\n", +"disp ('bar',P2,'Pressure at outlet = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6: Determination_of_the_direction_of_the_air_entry_to_and_exit_from_the_rotor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"T1=290; // Temperature at inlet in kelvin\n", +"n=10; // Number of stages\n", +"rp=6.5; // Pressure ratio\n", +"m=3; // mass flow rate in kg/s\n", +"eff_C=0.9; // isentropic efficiency of the compression\n", +"ca=110; // Axial velocity in m/s\n", +"u=180; // Mean blade velocity in m/s\n", +"Cp=1.005; // Specific heat in kJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"T_2=(rp)^((r-1)/r)*T1; // temperature after isentropic compression\n", +"T2=((T_2-T1)/eff_C)+T1; // Temperature after actual compression\n", +"P=m*Cp*(T2-T1); // Power given to the air\n", +"Del_Tstage=(T2-T1)/n; // Temperature rise per stage\n", +"Del_ct=Cp*10^3*Del_Tstage/u; // For work done per kg of air per second\n", +"// To find blade angles let solve the following equations\n", +"// Del_ct=ca(tan beta_1-tan beta_2) for symmetrical stages\n", +"// u=ca(tan beta_1=tan beta_2) for degree of reaction = 0.5\n", +"// Solving by matrix method\n", +"A=[1,-1;1,1]; C=[Del_ct/ca;u/ca];\n", +"B=A\C;\n", +"// Blade angles at entry and exit\n", +"beta_1=atand(B(1));\n", +"beta_2=atand(B(2));\n", +"\n", +"disp ('kW (roundoff error)',P,'Power given to the air = ');\n", +"disp ('degree',beta_2,'Blade angle at exit = ','degree',beta_1,'Blade angle at inlet = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7: Calculation_of_the_rotational_speed_and_the_length_of_the_last_stage.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=4; // Overall pressure ratio\n", +"m=3; // mass flow rate in kg/s\n", +"eff_pc=0.88; // Polytropic efficiency\n", +"Del_Tstage=25; // The stagnation temperature pressure rise in kelvin\n", +"c1=165; // Absolute velocity in m/s\n", +"alpha_1=20; // air angle from axial direction in degree\n", +"wf=0.83; // Workdone factor\n", +"D=18; // Mean diameter of the last stage rotor in cm\n", +"P01=1.01; // Ambient pressure in bar\n", +"T01=288; // Ambient temperature in kelvin\n", +"Cp=1005; // Specific heat in J/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"n=1/(1-(r-1)/(r*eff_pc));\n", +"T02=T01*(rp)^((n-1)/n); // Total pressure at stage 2\n", +"Del_Toverall= T02-T01; // Overall temperature difference\n", +"Ns=Del_Toverall/Del_Tstage; // Number of stages\n", +"eff_C=((rp^((r-1)/r)-1)/(rp^((r-1)/(r*eff_pc))-1));// Efficiency of compressor\n", +"rp1=(1+(eff_C*Del_Tstage/T01))^(r/(r-1)); // Pressure ratio acrocc first stage\n", +"Del_Tstage1=Del_Toverall/Ns; // Temperature rise across stage 1\n", +"T0ls=T02-Del_Tstage1; // Temperature at inlet to last stage\n", +"rpls=(1+(eff_C*Del_Tstage1/T0ls))^(r/(r-1)); // Pressure ratio acrocc last stage\n", +"// For symmetrical blade, R=0.5\n", +"beta_2=alpha_1; \n", +"ca=c1*cosd (alpha_1); // Axial velocity\n", +"beta_1=atand(sqrt(((Cp*Del_Tstage1/(wf*ca))/ca)+(tand(beta_2))^2)); // blade angle\n", +"u=ca*(tand(beta_1)+tand(beta_2)); // mean velocity of blade\n", +"N=60*u/(3.14*D*10^-2*60); // Speed in rps\n", +"Po=rp/rpls; // Total pressure at inlet to the last stage\n", +"T0=T0ls; // Total temperature to the last stage\n", +"Tst=T0-c1^2/(2*Cp); // Static temperature\n", +"Pst=Po/(T0/Tst)^((r-1)/r); // Static pressure\n", +"row=(Pst*10^5)/(R*Tst); // Density\n", +"h=m/(ca*row*3.14*D*10^-2);// Length of last stage\n", +"\n", +"disp (Ns,'Number of stages = ');\n", +"disp (rp1,'Pressure ratio across first stage = ');\n", +"disp (' (roundoff error)',rpls,'Temperature at inlet to last stage = ');\n", +"disp ('degree (roundoff error)',beta_1,'beta1=' );\n", +"disp ('rps (roundoff error)',N,'Speed = ');\n", +"disp ('cm (roundoff error)',h*100,'Length of last stage = ');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.8: Calculation_of_the_stage_stagnation_pressure_ratio_and_the_power_input.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"N=6000; // Speed in rpm\n", +"Del_rise=20; // Stagnation temperature rise in kelvin\n", +"wf=0.93; // Work done factor eff_c=0.89; // Isentropic efficiency of the state \n", +"c1=140; // Inlet velocity in m/s\n", +"p01=1.01; // Ambient pressure in bar\n", +"T01=288; // Ambient temperature in kelvin\n", +"M1=0.95; // Mach number\n", +"Cp=1.005; // Specific heat in J/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"H_T_ratio=0.6; // Hub tip ratio in \n", +"eff_s=0.89; // Stage efficiency\n", +"T1=T01-c1^2/(2*Cp*10^3);\n", +"w1=M1*sqrt (r*R*T1);\n", +"beta_1=acosd (c1/w1);\n", +"u=w1*sind (beta_1);\n", +"beta_2=atand (tand(beta_1)-((Cp*10^3*Del_rise)/(u*wf*c1)));\n", +"p1=p01/(T01/T1)^(r/(r-1));\n", +"row_1=(p1*10^5)/(R*T1);\n", +"Rtip=60*u/(2*3.14*N);\n", +"Rroot=H_T_ratio*Rtip;\n", +"Rm=(Rtip+Rroot)/2;\n", +"h=Rtip-Rroot;\n", +"m=row_1*2*3.14*Rm*h*c1;\n", +"rp=(1+(eff_s*Del_rise)/(T01))^(r/(r-1));\n", +"P=m*Cp*Del_rise;\n", +"uroot=2*3.14*Rroot*N/60;\n", +"beta_1root=atand (uroot/c1);\n", +"beta_2root=atand (tand (beta_1root)-((Cp*10^3*Del_rise)/(wf*uroot*c1)));\n", +"\n", +"disp ('degree',beta_2,'beta 2 = ','degree',beta_1,'beta 1 = ','Rotor air angles at tip:','m',Rtip,'Tip Radius = ','(i). ');\n", +"disp ('kg/s (Roundoff error)',m,'Mass flow rate = ','(ii).');\n", +"disp ('kW',P,'Power input = ',rp,'Stagnation pressure ratio = ','(iii).');\n", +"disp ('degree',beta_2root,'beta 2 = ','degree',beta_1root,'beta 1 = ','Rotor air angles at root sections','(iv).');\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.9: EX9_9.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"rp=1.35; // Actual pressure ratio\n", +"DelT_rise=30; // Actual temperature rise in K\n", +"beta_1=47; // Inlet blade angle in degree\n", +"beta_2=15; // Outlet blade angle in degree\n", +"u=225; // Peripheral velocity in m/s\n", +"ca=180; // Axial velocity in m/s\n", +"T01=27+273; // Ambient temperature in kelvin\n", +"Cp=1.005; // Specific heat in KJ/kg K\n", +"r=1.4; // Specific heat ratio\n", +"R=287; // Characteristic gas constant in J/kg K\n", +"\n", +"eff_s=(rp^((r-1)/r)-1)*T01/DelT_rise;\n", +"wf=(DelT_rise*Cp*10^3)/(u*ca*(tand(beta_1)-tand(beta_2)));\n", +"\n", +"disp ('%',eff_s*100,'Stage Efficiency = ');\n", +"disp (wf,'Work done factor = ');" + ] + } +], +"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 +} |