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diff --git a/Fundamentals_of_Turbomachinery_by_W_W_Peng/11-Wind_Turbines.ipynb b/Fundamentals_of_Turbomachinery_by_W_W_Peng/11-Wind_Turbines.ipynb new file mode 100644 index 0000000..3bb4661 --- /dev/null +++ b/Fundamentals_of_Turbomachinery_by_W_W_Peng/11-Wind_Turbines.ipynb @@ -0,0 +1,225 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: Wind Turbines" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: WT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"Pe=1.5\n", +"Eg=0.96//generator efficiency\n", +"Em=0.94//transmission efficiency\n", +"P=Pe/(Eg*Em)\n", +"printf('\n The power is equal to %0.3f MW',P)\n", +"disp('After converting to W the magnitude of power is equal to 1.662*10^6 W')\n", +"\n", +"Cp=0.47//from figure 11.10\n", +"V=13\n", +"rho=1.222\n", +"disp(' Since P=Cp(0.5*rho*A*V^3),thus on substituting the values we get P=630.9A')\n", +"A=P*10^6/(Cp*0.5*rho*V^3)// Since P=Cp*(0.5*rho*A*V^3)\n", +"printf(' On substituing the value of P in P=630.9A we get A equal to %g',A)\n", +"\n", +"disp('After rounding off,the area is equal to 2634.7m^2')\n", +"Ar=2634.7//rounded off A\n", +"//A=R^2*pi\n", +"R=sqrt(A/%pi)\n", +"printf(' The Radius is equal to %g m',R)\n", +"\n", +"disp('After rounding off the,area is equal to 28.9m')\n", +"Rr=28.9//rounded off\n", +"D=2*Rr\n", +"printf(' The Diameter is equal to %g m',D)\n", +"\n", +"omega=(V/R)*5.3// In the book diameter has been incorrectly substituted in place of radius(R). That is the reason why this particular answer doesn't match with the one given in the book.\n", +"printf('\n Omega is equal to %0.2f rad/s',omega)\n", +"N=(omega*30)/%pi//since N is proportional to omega and the answer for omega doesnt match with the answer given in the book(because of the aforementioned reason), the answer of N doesn't match either.\n", +"printf('\n RPM is equal to %g rpm',N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: WT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"V= 40*(5280/3600)\n", +"printf('V is equal to %0.2f ft/s',V)\n", +"N=80\n", +"omega=(N*%pi)/30\n", +"printf('\n\nomega is equal to %0.2f rad/s',omega)\n", +"rt=15\n", +"rh=1\n", +"Vt=(rt*omega)/V//tip velocity ratio\n", +"printf('\n\nThe tip velocity ratio is equal to %0.2f ',Vt)\n", +"\n", +"Zb=12/Vt\n", +"printf('\n \n Optimum number of blades is equal to %0.2f ',Zb)\n", +"disp('On approximating,the optimum number of blades is equal to 5')\n", +"\n", +"rm=[(rt^2+rh^2)/2]^0.5\n", +"printf('\nThe mean radius is equal to %0.2f ft',rm)\n", +"\n", +"Um=rm*omega\n", +"printf('\n\nThe blade peripheral velocity at the mean radius is equal to %0.1f ft/s',Um)\n", +"\n", +"disp('Assuming V1=V')\n", +"beta_1=(atan(Um/V))*180/%pi\n", +"printf('\nThe relative flow angle at the inlet is equal to %0.1f degrees',beta_1)\n", +"\n", +"beta_2=65\n", +"tanbetam=0.5*(tan(beta_1*%pi/180)+tan(beta_2*%pi/180))\n", +"printf('\n\nThe value of tan of beta m is equal to %0.3f ',tanbetam)\n", +"beta_m=(atan(tanbetam))*180/%pi\n", +"printf('\n \n Mean relative flow angle (betam) is equal to %0.2f degrees',beta_m)\n", +"\n", +"Wm=V/cos(beta_m*%pi/180)\n", +"printf('\n\nThe relative flow velocity (Wm) is equal to %0.1f ft/s',Wm)\n", +"\n", +"rho=0.0763\n", +"gc=32.2\n", +"c=1.2\n", +"Cl=0.28\n", +"Cd=0.015\n", +"F_um=(rho*Wm^2*c*(Cl*cos(beta_m*%pi/180)-Cd*sin(beta_m*%pi/180))/(2*32.2))\n", +"printf('\n\nThe tangential force (Fum), is equal to %0.2f lb/ft',F_um)\n", +"\n", +"delta_r=14//rt-rh=deltar\n", +"Z_br=5//approximated value of Zb\n", +"P_s=rm*F_um*delta_r*omega*Z_br/550\n", +"printf('\n\nPs is approximately equal to %0.1f hp',P_s)\n", +"\n", +"A=%pi*rt^2\n", +"A_r=707//rounding of A=706.9 to 707\n", +"P_smax=((8/27)*(rho/gc)*707*58.67^3)/550\n", +"printf('\n\nFrom the actuator theory,the maximum possible shaft power will be equal to %0.1f hp.',P_smax)\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: WT.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear all; clc;\n", +"\n", +"V= 40//in mph\n", +"V=58.9//in mph\n", +"//more accurately\n", +"V= 40*(5280/3600)\n", +"a=0.27\n", +"V1=V*(1-a)\n", +"printf('V1 is equal to %0.1f ft/s',V1)\n", +"\n", +"N=60\n", +"D=50\n", +"U=(N*%pi/30)*(D/2)\n", +"printf('\nU is equal to %0.1f ft/s',U)\n", +"\n", +"//from velocity triangle\n", +"A=90+45\n", +"printf('\nA is equal to %g degrees',A)\n", +"\n", +"//from cosine law\n", +"W=(U^2+V1^2-2*U*V1*cos(A*%pi/180))^0.5\n", +"printf('\nW is equal to %0.1f ft/s',W)\n", +"\n", +"//from sine law\n", +"sinB=V1*(sin(A*%pi/180))/W\n", +"printf('\nsinB is equal to %0.4f ft/s',sinB)\n", +"\n", +"B=asin(sinB)*180/%pi\n", +"printf('\nB is equal to %0.1f degrees',B)\n", +"\n", +"setting_angle=85\n", +"alpha=B-(90-setting_angle)\n", +"printf('\nalpha is equal to %0.1f degrees',alpha)\n", +"\n", +"//from figure\n", +"Cl=0.58\n", +"Cd=0.027\n", +"rho=0.0763\n", +"gc=32.2\n", +"c=1.2\n", +"Wr=189.8//rounded off W\n", +"Fu=rho*Wr^2*c*(Cl*sin(B*%pi/180)-Cd*cos(B*%pi/180))/(2*gc)\n", +"printf('\nFu is equal to %0.3f lb/ft',Fu)\n", +"\n", +"disp('After rounding off the tangential force (Fu) is equal to 3.38 lb/ft')" + ] + } +], +"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 +} |