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author | Prashant S | 2020-04-14 10:25:32 +0530 |
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committer | GitHub | 2020-04-14 10:25:32 +0530 |
commit | 06b09e7d29d252fb2f5a056eeb8bd1264ff6a333 (patch) | |
tree | 2b1df110e24ff0174830d7f825f43ff1c134d1af /Fundamentals_of_Turbomachinery_by_W_W_Peng/9-Steam_Turbines.ipynb | |
parent | abb52650288b08a680335531742a7126ad0fb846 (diff) | |
parent | 476705d693c7122d34f9b049fa79b935405c9b49 (diff) | |
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diff --git a/Fundamentals_of_Turbomachinery_by_W_W_Peng/9-Steam_Turbines.ipynb b/Fundamentals_of_Turbomachinery_by_W_W_Peng/9-Steam_Turbines.ipynb new file mode 100644 index 0000000..df6f1b2 --- /dev/null +++ b/Fundamentals_of_Turbomachinery_by_W_W_Peng/9-Steam_Turbines.ipynb @@ -0,0 +1,647 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Steam Turbines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: ST.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"rm=8/12\n", +"N=7500\n", +"U=rm*N*%pi/30\n", +"printf('The peripheral velocity is calculated as U= %0.1f ft/s\n\n',U)\n", +"\n", +"disp('From equation 9.1 we have U/V1=sinα1/4')\n", +"//let x= U/V1\n", +"alpha1=70*%pi/180\n", +"x=(sin(alpha1))/4\n", +"printf('\n Thus U/V1= %0.4f',x)\n", +"\n", +"V1=U/x\n", +"printf('\n Thus V1= %0.1f ft/s',V1)\n", +"\n", +"disp('From velocity diagram at station1 we have V1sinα1-W1sinß1=U and V1cosα1=W1cosß1 or W1sinß1')\n", +"//let y= W1sinß1\n", +"V1=2228.8\n", +"U=523.6\n", +"y=V1*sin(alpha1)-U\n", +"printf('\n Hence W1sinß1= %0.1f ft/s',y)\n", +"\n", +"//Let z=W1cosß1\n", +"z=V1*cos(alpha1)\n", +"printf('\n Thus W1cosß1= %0.1f ft/s',z)\n", +"\n", +"disp('Hence tanß1=2.06')\n", +"tanbeta1=2.06\n", +"beta1=(atan(tanbeta1))*180/%pi\n", +"printf('\n Thus beta1= %0.1f degrees and W1=1746 ft/s',beta1)\n", +"\n", +"disp('At station 2 we have W2sinß2-V2sinα2=U and V2cosα2=W2cosß2,with W2=W1=1746ft/s and ß1=ß2=64.1 degrees')\n", +"//Let l=V2sinα2\n", +"l=1746*sin(64.1*%pi/180)-523.6\n", +"printf(' Thus V2sinα2=%0.0f ft/s',l)\n", +"\n", +"//m=V2cosα2\n", +"m=1746*cos(64.1*%pi/180)\n", +"printf('\n V2cosα2 %0.2f ft/s',m)\n", +"\n", +"disp('Hence tanα2=1.373')\n", +"tanalpha2=1.373\n", +"alpha2=((atan(tanalpha2)*180/%pi))\n", +"printf(' Hence α2= %0.2f degrees',alpha2)\n", +"\n", +"disp('Hence V2=1295.2 ft/s')\n", +"\n", +"disp('At station 3 we have V3sinα3-W3sinα3=U=523.6ft/s')\n", +"disp('Also W3cosß3=V3cosα3')\n", +"//let n=V3cosα3\n", +"V3=1295.2\n", +"alpha3=53.9*%pi/180\n", +"n=V3*cos(alpha3)\n", +"printf(' Thus W3cosß3= %0.1f ft/s',n)\n", +"\n", +"disp('Hence tanß3=0.685')\n", +"tanbeta3=0.685\n", +"beta3=((atan(tanbeta3))*180/%pi)\n", +"printf(' Hence ß3= %0.1f degrees',beta3)\n", +"\n", +"disp('Thus W3=925.1 ft/s')\n", +"\n", +"disp('Also W4=W3=925.1ft/s')\n", +"disp('ß4=ß3=34.4 degrees')\n", +"disp('And V4=VaV1cosß4')\n", +"beta4=34.4*%pi/180\n", +"//let y=Va*V1\n", +"y=925.0848\n", +"V4=y*cos(beta4)\n", +"printf(' Thus V4= %0.1f ft/s',V4)\n", +"disp('α4=0 degrees')\n", +"\n", +"disp('From these velocities,the energy transfers of the rotors can be calculated')\n", +"\n", +"U=523.6\n", +"V1=2228.8\n", +"alpha1=70*%pi/180\n", +"V2=1295.2\n", +"alpha2=53.9*%pi/180\n", +"delta_E1=U*(V1*sin(alpha1)+V2*sin(alpha2))\n", +"printf(' Thus delta_E1= %0.1f ((ft/s)^2)',delta_E1)\n", +"\n", +"delta_E1=1.643*(10^6)/(32.2*778)//converting units from (ft/s)^2 to Btu/lb\n", +"printf('\n On converting to Btu/lb we have delta_E1=%0.1f Btu/lb',delta_E1)\n", +"\n", +"V3=1295.2\n", +"alpha3=alpha2\n", +"delta_E2=U*(V3*sin(alpha3))\n", +"printf('\n delta_E2=%0.1f ((ft/s)^2)',delta_E2)\n", +"delta_E2=0.546*(10^6)/(32.2*778)\n", +"printf('\n On converting to Btu/lb we have delta_E2=%0.1f Btu/lb',delta_E2)\n", +"\n", +"delta_Ec=65.6+21.8\n", +"printf('\n Hence the total energy transfer is delta_Ec= %0.1f Btu/lb',delta_Ec)\n", +"disp('To compare with that calculated with equation9.3,we have delta_Ec=8*U^2')\n", +"delta_Ec=8*(U^2)\n", +"printf(' delta_Ec= %0.2f ((ft/s)^2)',delta_Ec)\n", +"delta_Ec=2.19*10^6/(32.2*778)//converting units\n", +"printf('\n On converting we have delta_Ec= %0.2f Btu/lb',delta_Ec)//answer given in the book is 87.5,however 87.42 is more accurate\n", +"\n", +"disp('The difference is due to round off error.')\n", +"disp('The static enthalpies and pressure at stations 1,2,3 and 4 are same for the ideal case and can be calculated from h1=h01-((V1)^2)/2 ')\n", +"disp('Where h01=h0i=1405Btu/lb from the Mollier diagram for p0i=3000 psia,T01=950 degrees Farenheit')\n", +"//let l=(V1^2)/2\n", +"V1=2228.8\n", +" l=(V1^2)/(2*32.2*778)\n", +"printf(' Thus (V1^2)/2 = %0.0f Btu/lb',l)\n", +"\n", +"disp('Hence we have h1=1306 Btu/lb and p1=1400psia')\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.2: ST.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"disp('To use Figure 9.8,with Qf=ΣU^2/delta_Hs=2*g_c*lambda^2*R_H')\n", +"disp('The value of R_H can be estimated with equation 8.4.')\n", +"disp('Using k=1.3 for steam and suusming ETA_p=0.90 we have ETAad=[1-(p_e/p_i)^(ETAp*(k-1)/k)]/[1-(p_e/p_i)^(k-1)/k]=0.931')\n", +"\n", +"ETA_ad=0.931\n", +"ETA_p=0.90\n", +"R_H=ETA_ad/ETA_p\n", +"printf(' R_H=ETA_ad/ETA_p= %0.3f',R_H)\n", +"\n", +"disp('For impulse stages,the optimal efficiencies occur at lambda=U/V2=sinα2/2=0.47 with alpha2=70 degrees')\n", +"QF=2*25052*(0.47^2)*1.035\n", +"printf(' So Qf can be calculated as %0.0f',QF)\n", +"\n", +"disp('From figure 9.8, the efficiency can be estimated as ETA=83%')\n", +"\n", +"disp('From the Mollier diagram in figure A1 we have hi=1525 Btu/lbm,hse=1150 Btu/lbm,with s_i=s_es=1.8Btu/lb-R')\n", +"delta_Hs=1525-1150\n", +"printf(' Hence delta_Hs=%0.0f Btu/lbm',delta_Hs)\n", +"\n", +"summation_sqr(U)=11455*375\n", +"printf('\n So we have ΣU^2=%0.0f ((ft/s)^2)',summation_sqr(U))\n", +"\n", +"disp('With 10 identical stages,we have U^2=429562')\n", +"sqr(U)=429562\n", +"U=sqrt(sqr(U))\n", +"printf(' Thus U= %0.0f ft/s',U)\n", +"\n", +"omega=3600*%pi/30\n", +"D=2*U/omega\n", +"printf('\n The turbine diameter D= %0.3f ft',D)//The answer has been incorrectly rounded off to 3.47 in the book. A more accurate answer is provided here.\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: ST.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"disp('The tangential velocity at the rotor mean radius is Um')\n", +"rm=1.5\n", +"N=3600\n", +"Um=rm*N*%pi/30\n", +"printf('Um=rm*N*pi/30= %0.1f',Um)\n", +"\n", +"disp('From the velocity diagram in figure 8.11 for the impulse stages we have delta_h0')\n", +"disp('delta_h0=delta_Et=UmVu2-UmVu3/g_c=UmVu2/g_c=2((Um)^2)/gc')\n", +"Um=565.5\n", +"gc=32.2\n", +"delta_h0=2*((Um)^2)/gc\n", +"printf('\n delta_h0= %0.0f lbf-ft/lbm=25.5 Btu/lbm',delta_h0)\n", +"\n", +"disp('From the Mollier diagram in appendix A, we have hoi=1565 Btu/lbm')\n", +"disp('For the stages with constant mean radi,we have hoi-hoe=n_s*delta_hoe or hoe=h0i-n_s*delta_hoe')\n", +"h_oe=1565-(12*25.5)\n", +"printf(' hoe= %0.0f Btu/lbm.',h_oe)\n", +"\n", +"disp('Also from ETA_ad=(hoi-hoe)/(hoi-hsoe), we have hsoe=hoi-(hoi-hoe)/ETA_ad')\n", +"h_soe=1565-306/0.85\n", +"printf(' hsoe= %0.0f Btu/lbm',h_soe)\n", +"\n", +"disp('From s_soe=Soi=1.69 Btu/(lbm-R),we have poe=50 psia and Toe=450 degrees Farenheit')\n", +"disp('Also from given efficiencies we have Ps=ETAv*ETAm*m*n_s*delta_ho')\n", +"Ps=0.92*0.90*7*12*19863/550\n", +"printf(' Ps=%0.0f hp',Ps)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: ST.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"disp('Based on the law of Willian we have m_t=0.5+CP_s')\n", +"C=(7-0.5)/2512\n", +"printf(' Where C= %0.4f lbm/(hp-s)\n',C)\n", +"\n", +"disp('So we have SR=mt/Ps=0.5/Ps+(2.6*10^-3)')\n", +"disp('And HR=Q_h*SR')\n", +"\n", +"\n", +"disp('OR at full load,')\n", +"SR_1=(0.5/2512)+(2.6*10^-3)\n", +"printf('\n SR_1= %0.4f lbm/(hp-s)=10.1 lbm/(hp-h)',SR_1)\n", +"\n", +"HR_1=1750*10.1\n", +"printf('\n HR_1=%0.0f Btu/(hp-h)',HR_1)\n", +"\n", +"\n", +"disp('at 50% load,')\n", +"SR_2=(0.5/1256)+(2.6*10^-3)\n", +"printf('\n SR_2= %0.4f lbm/(hp-s)=10.8 lbm/(hp-h)',SR_2)\n", +"\n", +"HR_2=1750*10.8\n", +"printf('\n HR_2=%0.0f Btu/(hp-h)',HR_2)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: ST.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"disp('To calculate the thermal efficiency,the units have to be consisitent. With hp=0.707 Btu/s=2545Btu/h, we have ETAth=Ps+Qe/Qin')\n", +"ETA_th=(2512*0.707+1259*7)/(7*1750)\n", +"printf(' Thus ETA_h= %0.3f',ETA_th)\n", +"\n", +"ETA_th=2512*0.707/(7*1750)\n", +"printf('\n For the simple shaft power system,we have ETA_th= %0.3f',ETA_th)\n", +"\n", +"ETA_th=2545/17675\n", +"printf('\n From the heat rate,ETA_th=2545/HR %0.3f',ETA_th)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.6: Steam_Turbines.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"disp('The enthalpies at various points have t be determined first. For the steam turbine cycle,fro the Mollier diagram or steam tables,we have h1=hf1=83.6')\n", +"\n", +"h2=83.6+(0.0185*(1000-1.5)*144)/(778*0.80)\n", +"printf(' h2=h1+nu*deltap/ETA_p =%0.1f Btu/lbm',h2)\n", +"\n", +"disp('h3=1447 Btu/lbm')\n", +"\n", +"disp('s_s4=s3=1.61 Btu/(lbm-R)')\n", +"\n", +"disp('hs4=925 Btu/lbm')\n", +"\n", +"disp('Hence from ETAst=(h3-h4)/(h3-hs4) we have h4=h3-(h3-hs4)*ETAst')\n", +"h3=1447\n", +"hs4=925\n", +"ETA_st=0.85\n", +"h4=h3-(h3-hs4)*ETA_st\n", +"printf(' h4= %0.0f Btu/lbm',h4)\n", +"\n", +"h4=1003\n", +"h2=87.9\n", +"h1=83.6\n", +"ETA_ths=[(h3-h4)-(h2-h1)]/(h3-h2)\n", +"printf('\n The thermal efficiency of the steam turbine cycle is then obtained as ETA_th,s=(Wst-Wp)/(Qin,s)=%0.4f ',ETA_ths)//it has been rounded off to 32.3 in the book\n", +"\n", +"disp('For the gas turbine cycle, an ideal gas with constant Cp is assumed for the working gas. With Cp=0.24 Btu/(lbm-R) and k=1.4 we have T6')\n", +"T5=540\n", +"//Let n=p6/p5 and m= (k-1)/k\n", +"n=15\n", +"m=0.2857\n", +"ETAc=0.82\n", +"T6=T5+[T5*({(n)^(m)}-1)]/ETAc\n", +"printf('\n T6= %0.0fR=849 degrees Farenheit',T6)\n", +"\n", +"T7=2560\n", +"//let b=(1/15)^0.2857\n", +"b=0.461\n", +"ETA_gt=0.85\n", +"T8=T7-T7*[1-b]*ETA_gt\n", +"printf('\n T8=%0.0f R= 928 degrees Farenheit',T8)\n", +"\n", +"disp('Which should be greater than T3')\n", +"T7=2560\n", +"T8=1388\n", +"T6=1309\n", +"T5=540\n", +"ETA_thg=[(T7-T8)-(T6-T5)]/(T7-T6)\n", +"printf('\n The thermal efficiency of the gas turbine is obtained as %0.3f=32.2 percent',ETA_thg)\n", +"\n", +"disp('From the energy balance equation across the HRSG,we have m_g*Cp*(T8-T9)')\n", +"disp('ms/mg=[Cp*(T8-T9)]/(h3-h2)')\n", +"//let x=ms/mg\n", +"Cp=0.24\n", +"T8=928\n", +"T9=450\n", +"h3=1447\n", +"h2=87.9\n", +"x=[Cp*(T8-T9)]/(h3-h2)\n", +"printf('\n Thus ms/mg=%0.3f',x)\n", +"\n", +"disp('Hence the thermal efficiency of the combined cycle is obtained as ETA_th,c=[(Wgt-Wc)+(ms/mg)*(Wst-Wp)]/[Cp*(T7-T6)]')\n", +"ETA_thc=[0.24*(1172-769)+0.084*(439.7)]/(0.24*1251)\n", +"printf('\n ETA_th,c= %0.3f=44.5 percent',ETA_thc)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |