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diff --git a/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb new file mode 100644 index 00000000..3ac70f6e --- /dev/null +++ b/Fluid_Mechanics,Thermodynamics_of_Turbomachinery_by_S.L.Dixon/Chapter4_YZTImEN.ipynb @@ -0,0 +1,294 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:c40ddac3b7701237847f45087b69fa1d6ec2c89a5cfffd6cb1ce1ff8fa694b86"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter4-Axial-flow Turbines:Two-dimensional Theory"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex1-pg101"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "phi = 0.4;\n",
+ "epsilon = 28.6;##in deg\n",
+ "\n",
+ "##calculations\n",
+ "alpha2 = (180./math.pi)*math.atan(1./phi);##in deg\n",
+ "zeta = 0.04*(1+ 1.5*(alpha2/100.)**2);\n",
+ "eta = 1 + (phi**2)*(zeta*((1./math.cos(math.pi*alpha2/180.))**2) +0.5);\n",
+ "\n",
+ "##results\n",
+ "print'%s %.2f %s'%('The efficiency = ',1/eta,'');\n",
+ "print('This value appears to be the same as the peak value of efficiency curve.\\n');\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The efficiency = 0.86 \n",
+ "This value appears to be the same as the peak value of efficiency curve.\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex2-pg105"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "alpha2 = 70.;##in deg\n",
+ "p01 = 311.;##in kPa\n",
+ "T01 = 850.;##in degC\n",
+ "p3 = 100.;##in kPa\n",
+ "eff_tot_stat = 0.87;\n",
+ "U = 500.;##in m/s\n",
+ "Cp = 1.148;##in kJ/(kgC)\n",
+ "gamma = 1.33;\n",
+ "\n",
+ "##Calculations\n",
+ "delW = eff_tot_stat*Cp*(T01+273.15)*(1.-(p3/p01)**((gamma-1.)/gamma));##specific work\n",
+ "cy2 = delW*1000./U;##in m/s\n",
+ "c2 = cy2/math.sin(math.pi*alpha2/180.);##in m/s\n",
+ "T2 = (T01+273.15) - 0.5*(c2**2)/(Cp*1000.);##Nozzle exit temperature in K\n",
+ "M2 = c2/math.sqrt(gamma*287.*T2);##Nozzle exit mach number\n",
+ "cx = c2*math.cos(math.pi*alpha2/180.);##axial velocity in m/s\n",
+ "eff_tot_tot = 1./((1./eff_tot_stat)-((cx**2)/(2.*1000.*delW)));##Total to total efficiency\n",
+ "R = 1. - 0.5*(cx/U)*math.tan(math.pi*alpha2/180.);##stage reaction\n",
+ "\n",
+ "##results\n",
+ "print'%s %.2f %s'%('(i) The specific work done =',delW,' kJ/kg.\\n');\n",
+ "print'%s %.2f %s'%('(ii) The Mach number leaving the nozzle = ',M2,'');\n",
+ "print'%s %.2f %s'%('(iii) The axial velocity = .\\n',cx,'m/s');\n",
+ "print'%s %.2f %s'%('(iv) The total-to-total efficiency = .\\n',eff_tot_tot,'');\n",
+ "print'%s %.2f %s'%('(v) The stage reaction = .\\n',R,'');\n",
+ "\n",
+ "\n",
+ "##there are small errors in the answers given in the book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i) The specific work done = 275.24 kJ/kg.\n",
+ "\n",
+ "(ii) The Mach number leaving the nozzle = 0.96 \n",
+ "(iii) The axial velocity = .\n",
+ " 200.36 m/s\n",
+ "(iv) The total-to-total efficiency = .\n",
+ " 0.93 \n",
+ "(v) The stage reaction = .\n",
+ " 0.45 \n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg106"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "H_b = 5.0;##average bladeaspect ratio for the stage\n",
+ "t_c = 0.2;##max. blade thickness to chord ratio\n",
+ "Re = 1*10**5;##average Reynolds number\n",
+ "cx = 200.;##in m/s\n",
+ "cy2 = 552.;##in m/s\n",
+ "U = 500.;##in m/s\n",
+ "c2 = 588.;##in m/s\n",
+ "delW = 276.;##in kJ\n",
+ "c3 = 200.;##in m/s\n",
+ "Cp = 1.148;##in kJ/(kgC)\n",
+ "T2 = 973.;##in K\n",
+ "T01 = 1123.;##in K\n",
+ "alpha1 = 0.;##in deg\n",
+ "alpha2 = 70.;##in deg\n",
+ "\n",
+ "##calculations\n",
+ "eps = alpha1 + alpha2;##in deg\n",
+ "zetaN = 0.04*(1. + 1.5*(eps/100.)**2);\n",
+ "zetaN1 = (1.+zetaN)*(0.993 + 0.021/H_b) - 1;\n",
+ "beta2 = (180./math.pi)*math.atan((cy2-U)/cx);\n",
+ "beta3 = (180./math.pi)*math.atan(U/cx);\n",
+ "epsR = beta2 + beta3;\n",
+ "zetaR = 0.04*(1. + 1.5*(epsR/100.)**2);\n",
+ "zetaR1 = (1.+zetaR)*(0.975 + 0.075/H_b) - 1;\n",
+ "w3_U = math.sqrt(1.+(cx/U)**2);\n",
+ "eff_ts = 1./(1. + (zetaR1*w3_U + zetaN1*((c2/U)**2) + (cx/U)**2)/(2.*cy2/U));\n",
+ "T3 = T01 - (delW*1000. + 0.5*c3**2.)/(Cp*1000.);\n",
+ "eff_ts1 = 1/(1. + (zetaR1*(w3_U)**2 + (T3/T2)*zetaN1*((c2/U)**2.) + (cx/U)**2.)/(2.*cy2/U));\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s'%('The total-to static efficiency = ',eff_ts,'');\n",
+ "print('\\n The result is very close to the value assumed in first example.')\n",
+ "print'%s %.2f %s'%('\\n The total-to-static efficiency after including the temperature ratio in the equation = ',eff_ts1,'');\n",
+ "\n",
+ "##there are small errors in the answers given in the book\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total-to static efficiency = 0.87 \n",
+ "\n",
+ " The result is very close to the value assumed in first example.\n",
+ "\n",
+ " The total-to-static efficiency after including the temperature ratio in the equation = 0.87 \n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg119"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#calculate the\n",
+ "\n",
+ "##given data\n",
+ "T02 = 1200.;##in K\n",
+ "p01 = 4.0;##in bar\n",
+ "dt = 0.75;##tip diameter in m\n",
+ "hb = 0.12;##blade height in m\n",
+ "v = 10500.;##shaft speed in rev/min\n",
+ "R = 0.5;##degree of reaction at mean radius\n",
+ "phi = 0.7;##flow coefficient\n",
+ "psi = 2.5;##stage loading coefficient\n",
+ "eff_noz = 0.96;##Nozzle efficiency\n",
+ "Cp = 1160.;##in kJ/(kgC)\n",
+ "gamma = 1.33;\n",
+ "Rg = 287.8;##specific gas constant\n",
+ "A2 = 0.2375;##in m^2\n",
+ "K = 2/3.;##stress taper factor\n",
+ "rho = 8000.;##in kg/m^3\n",
+ "\n",
+ "##calculations\n",
+ "beta3 = (180./math.pi)*math.atan((0.5*psi + R)/phi);\n",
+ "beta2 = (180./math.pi)*math.atan((0.5*psi - R)/phi);\n",
+ "alpha2 = beta3;\n",
+ "alpha3 = beta2;\n",
+ "rm = (dt-hb)/2.;\n",
+ "Um = (v/30.)*math.pi*rm;\n",
+ "cx = phi*Um;\n",
+ "c2 = cx/(math.cos(alpha2*math.pi/180.));\n",
+ "T2 = T02 - 0.5*(c2**2)/Cp;\n",
+ "p2 = p01*((1-((1.-(T2/T02))/eff_noz))**(gamma/(gamma-1.)));\n",
+ "mdot = ((p2*10**5)/(Rg*T2))*A2*cx;\n",
+ "Ut = (v/30.)*math.pi*0.5*dt; \n",
+ "sig_rho = K*0.5*(Ut**2)*(1-((dt-2.*hb)/dt)**2);\n",
+ "sig1 = rho*sig_rho;\n",
+ "Tb = T2 + 0.85*((cx/math.cos(beta2*math.pi/180.))**2.)/(2.*Cp);\n",
+ "\n",
+ "##Results\n",
+ "print'%s %.2f %s %.2f %s'%('(i)The relative and absolute angles for the flow: \\n beta3 = ',beta3,' deg' and 'beta2 = ',beta2,' deg.');\n",
+ "print'%s %.2f %s %.2f %s'%(' alpha2 = ',alpha2,' deg' and 'alpha3 = ',alpha3,'deg.');\n",
+ "print'%s %.2f %s'%('\\n (ii) The velocity at nozzle exit = ',c2,' m/s');\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of ',eff_noz,''and ': \\n T2 = ',T2,'K'and '\\n p2 =',p2,' bar');\n",
+ "print'%s %.2f %s' %('\\n and mass flow = ',mdot,'kg/s');\n",
+ "print'%s %.2f %s %.2f %s '%('\\n (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \\n the blade material density is ',rho,' kg/m2'and ' =',sig1/(10**6),' MPa');\n",
+ "print'%s %.2f %s'%('\\n (v) The approximate average mean blade temperature is Tb = ',Tb,' K');\n",
+ "\n",
+ "\n",
+ "\n",
+ "#\n",
+ "\n",
+ "##there are very small errors in the answers given in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(i)The relative and absolute angles for the flow: \n",
+ " beta3 = 68.20 beta2 = 46.97 deg.\n",
+ " alpha2 = 68.20 alpha3 = 46.97 deg.\n",
+ "\n",
+ " (ii) The velocity at nozzle exit = 652.82 m/s\n",
+ "\n",
+ " (iii)The static temperature and pressure at nozzle exit assuming a nozzle efficiency of 0.96 1016.30 \n",
+ " p2 = 1.99 bar \n",
+ "\n",
+ " and mass flow = 39.10 kg/s\n",
+ "\n",
+ " (iv)The rotor blade root stress assuming the blade is tapered with a stress taper factor K of 2/3 and \n",
+ " the blade material density is 8000.00 = 243.74 MPa \n",
+ "\n",
+ " (v) The approximate average mean blade temperature is Tb = 1062.56 K\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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