{ "metadata": { "name": "", "signature": "sha256:f1f13cd9c3fdcfa7b8b8c8379d6bf486b07b707956742ab81238144bdac12268" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 19: Jet Propulsion and Rocket Engines" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1, page no. 873" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "\n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "Cpg = 1.13 #Specific heat of gases(in kJ/kg.K):\n", "Cpa = 1.005 \n", "rg = 1.33\n", "ra = 1.4\n", "C = 41.84*10**3 #kJ/kg of fuel\n", "T1 = 272 #Temperatures(in K):\n", "T3 = 1000\n", "nc = 0.84 #Compression efficiency:\n", "p3 = 3\n", "p2 = 3\n", "p1 = 0.5\n", "p5 = 0.4\n", "nt = 0.82 #Turbine efficiency:\n", "nn = 0.92 #Nozzle efficiency:\n", "Ca = 200 #Speed(in m/s):\n", "T2 = T1*(p2/p1)**((ra-1)/ra) #Temperature at state 2(in K):\n", "T2a = T1+(T2-T1)/nc #Temperature at state 2'(in K):\n", "Wc = Cpa*(T2a-T1) #Compressive work(in kW):\n", "r = (C-Cpg*T3)/(Cpg*T3-Cpa*T2a) #Air fuel ratio:\n", "T4a = T3-Cpa/Cpg*(T2a-T1)/(1+r) #Temperature at state 4'(in K):\n", "T4a = 810.46\n", "T4 = T3-(T3-T4a)/nt\n", "p4 = p3*(T4/T3)**(rg/(rg-1)) #Pressure of gas leaving turbine(in bar):\n", "T5 = T4a*(p5/p4)**((rg-1)/rg) #Temperature at state 5(in K):\n", "T5a = T4a-nn*(T4a-T5) #Temperature at state 5'(in K):\n", "C5a = sqrt(2*Cpg*(T4a-T5a)*10**3) #Exit jet velocity(in m/s):\n", "Ce = C5a\n", "T = (1+1/r)*Ce-Ca #Thrust per kg of air per second:\n", "\n", "#Results: \n", "print \"Power required for compressor: \",round(Wc,2),\"kW/kg\"\n", "print \"Air fuel ratio: \",round(r,2)\n", "print \"Pressure of gas leaving turbine: \",round(p4,2),\"bar\"\n", "print \"Thrust: \",round(T,2),\"N/kg/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power required for compressor: 217.55 kW/kg\n", "Air fuel ratio: 63.7\n", "Pressure of gas leaving turbine: 1.04 bar\n", "Thrust: 405.75 N/kg/s\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2, page no. 876" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "T1 = 285 #K\n", "p1 = 1 #bar\n", "T3 = 773 #K\n", "p2 = 4 #bar\n", "r = 1.4\n", "Cpa = 1.005 #kJ/kg.K\n", "CV = 43100 #kJ/kg.K\n", "T3 = 273+500 #K\n", "\n", "#Calculations:\n", "T2 = T1*(p2/p1)**((r-1)/r) #Temperature at state 2(in K):\n", "T2a = T1+1.1*(T2-T1) #Temperature at state 2'(in K):\n", "Wc = Cpa*(T2a-T1) #Work required in compressor(in kJ/kg of air):\n", "qa = Cpa*(T3-T2a) #Heat added in combustion chamber(in kJ/kg of air):\n", "r1 = CV/qa #Air fuel ratio:\n", "T5 = T3*(p1/p2)**((r-1)/r) #Temperature at state 5(in K):\n", "hd = Cpa*(T3-T5-T2a+T1) #Enthalpy drop in the nozzle(in kJ/kg of air):\n", "Ce = sqrt(2*hd*10**3) #Velocity of exit gas from nozzle(in m/s):\n", "T = (1+1/r)*Ce #Thrust(in N/kg/s):\n", "\n", "#Results: \n", "print \"Power required to drive compressor: \",round(Wc,2),\"kW/kg of air\"\n", "print \"Air-fuel ratio: \",round(r1,2)\n", "print \"Thrust: \",round(Ce,2),\"N/kg of air/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power required to drive compressor: 153.12 kW/kg of air\n", "Air-fuel ratio: 127.77\n", "Thrust: 449.34 N/kg of air/s\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3, page no. 877" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "Cpg = 1.14 #kJ/kg.K,Specific heat of gases(in kJ/kg.K):\n", "Cpa = 1.005 #kJ/kg.K,Specific heat of gases(in kJ/kg.K):\n", "nm = 0.96 #Mechanical efficiency:\n", "nc = 0.87 #Polytropic efficiency of compressor:\n", "nt = 0.90 #Turbine efficiency:\n", "nn = 0.95 #Nozzle efficiency:\n", "B = 5.5 #By pass ratio:\n", "ma = 200 #Mass flow rate of air(in kg/s):\n", "p2 = 1.5 #Pressures(in bar):\n", "p1 = 1\n", "p3 = 28\n", "pa = p1\n", "T1 = 288 #Temperatures(in K):\n", "rg = 1.33\n", "ra = 1.4\n", "CV = 43100 #kJ/kg\n", "T4 = 1573 #K\n", "\n", "#Calculations:\n", "a1 = 1/nc*(ra-1)/ra #For compression:a1 = ((ne-1)/ne)\n", "a1 = 0.328\n", "a2 = nt*(rg-1)/rg #For expansion:a2 = (nt-1)/nt\n", "a2 = 0.223\n", "T2a = T1*(p2/p1)**a1 #Temperature at state 2'(in K):\n", "T3a = T2a*(p3/p2)**a2 #Temperature at state 3'(in K):\n", "dT = nn*T2a*(1-(pa/p2)**((ra-1)/ra))#Using nozzle efficiency:\n", "C8 = sqrt(2*Cpa*10**3*dT) #Velocity at exit of nozzle(in m/s):\n", "mab = ma*B/(B+1) #Mass flow rate of bypass air(in kg/s):\n", "mca = ma-mab #Mass flow rate of hot gases(in kg/s):\n", "Tb = mab*C8/10**3 #Thrust available due to by pass air(in kN):\n", "r1 = (Cpg*T4-Cpa*T3a)/(CV-Cpg*T4) #Air fuel ratio:\n", "T5a = T4-(Cpa*(T3a-T2a)/(nm*(1+r1)*Cpg))#Temperature at state 5'(in K):\n", "T6a = (Cpg*nm*T5a-(1+B)*Cpa*(T2a-T1))/(Cpg*nm)#Temperature at state 6'(in K):\n", "p4 = p3-p2 #Pressure at state 4(in bar):\n", "p5 = p4*(T5a/T4)**(1/a2) #Pressure at state 5(in bar):\n", "p6 = p5*(T6a/T5a)**(1/a2)#Pressure at state 6(in bar):\n", "c = ((rg+1)/2)**(rg/(rg #Pressure at state 7(in bar):\n", "dT1 = nn*T6a*(1-(p7/p6)**((rg-1)/rg))#For exit nozzle(in K):\n", "C7 = sqrt(2*Cpg*10**3*dT1) #Velocity at exit of nozzle(in m/s):\n", "Tg = mca*C7/10**3 #Thrust due to hot gases(in kN):\n", "Tt = Tg+Tb #Total thrust(in kN):\n", "st = Tt/ma #Specific thrust(in kN/kg/s):\n", "sfc = r1*mca*3600/(Tt*10**3) #Specific fuel consumption(in kg/h.N):\n", "\n", "#Results: \n", "print \"Specific thrust: \",round(st,3),\"kN/kg/s\"\n", "print \"Specific fuel consumption: \",round(sfc,2),\"kg/h.N\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific thrust: 0.309 kN/kg/s\n", "Specific fuel consumption: 0.05 kg/h.N\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 4, page no. 881" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "\n", "#Variable Declaration: \n", "Ca = 277.78 #Velociy of turbojet plane(in m/s):\n", "r1 = 0.5 #Thrust to velocity ratio:\n", "m = 50 #Rate at which air enters(in kg/s):\n", "r = 52 #Air fuel ratio:\n", "LCV = 43100 #Lower calorific value of fuel:\n", "\n", "#Calculations:\n", "Ce = Ca/r1 #Jet velocity(in m/s):\n", "T = (m+m/r)*Ce-m*Ca #Thrust(in N):\n", "St = T/m #Specific thrust(in N/kg/s):\n", "P = T*Ca/10**3 #Thrust power(in kW):\n", "np = 2/(1+1/r1)*100 #Propulsive efficiency:\n", "nt = ((1+1/r)*Ce**2-Ca**2)/(2*1/r*LCV)/10 #Thermal efficiency:\n", "no = np*nt/100 #Overall efficiency:\n", "sfc = m/r*3600/(T) #Specific fuel consumption(in kg/h.N):\n", "\n", "#Results: \n", "print \"Jet velocity: \",round(Ce,2),\"m/s\"\n", "print \"Thrust: \",round(T/10**3,2),\"kN\"\n", "print \"Specific thrust: \",round(St,2),\"N/kg/s\"\n", "print \"Thrust power: \",round(P,2),\"kW\"\n", "print \"Propulsive efficiency: \",round(np,2),\"%\"\n", "print \"Thermal efficiency: \",round(nt,2),\"%\"\n", "print \"Overall efficiency: \",round(no,2),\"%\"\n", "print \"Specific fuel consumption: \",round(sfc,4),\"kg/h.N\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Jet velocity: 555.56 m/s\n", "Thrust: 14.42 kN\n", "Specific thrust: 288.46 N/kg/s\n", "Thrust power: 4006.47 kW\n", "Propulsive efficiency: 66.67 %\n", "Thermal efficiency: 14.32 %\n", "Overall efficiency: 9.55 %\n", "Specific fuel consumption: 0.24 kg/h.N\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5, page no. 882" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "p1 = 2.2 #Pressures(in bar):\n", "T1 = 220 #Temperatures(in K):\n", "T4 = 1273\n", "C1 = 260 #Velocities(in m/s):\n", "nn = 0.85 #Nozzle efficiency:\n", "nt = 0.88 #Turbine efficiency:\n", "nd = 0.90 #Diffuser efficiency:\n", "Cp = 1.005#Specific heat(in kJ/kg.K):\n", "r = 1.4 #Adiabatic index of compression:\n", "r1 = 12 #Pressure ratio:\n", "T3a = 568.635\n", "p6 = 2.2\n", "\n", "#Calculations:\n", "T2 = T1+ C1**2/(2*Cp*1000) #Temperature at state 2(in K):\n", "p2 = p1*(T2/T1)**(r/(r-1)) #Pressure at state 2(in bar):\n", "p3 = p2*r1\n", "p4 = p3\n", "T3 = T2*(p3/p2)**((r-1)/r)#Temperature at state 3(in K):\n", "T3a = T2+(T3-T2)/nn #Temperature at state 3'(in K):\n", "T5a = T4-(T3a-T2) #Temperature at state 5'(in K):\n", "T4 = T3a -T2 +T5a\n", "T5 = T4-(T4-T5a)/nt #Temperature of state 5(in K):\n", "p5 = p4*(T5/T4)**(r/(r-1)) #Pressure at state 5(in bar):\n", "T6 = T5*(p6/p5)**((r-1)/r)\n", "T2a = T1+(T2-T1)/nd #Temperature at state 2'(in K):\n", "C6 = sqrt(2*(T5-T6)*Cp*10**3) #Velocity at exit of nozzle(in m/s):\n", "\n", "#Results: \n", "print \"Velocity of exit of nozzle: \",round(C6,2),\"m/s\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Velocity of exit of nozzle: 873.41 m/s\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 6, page no. 885" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "CV = 45000 #Calorific value(in kJ/kg):\n", "T1 = 1000 #Inlet temperature(in C):\n", "T4 = T1\n", "nn = 0.9 #Nozzle efficiency:\n", "nd = 0.9 #Diffuser efficiency:\n", "nc = 0.8 #Compressive efficiency:\n", "nt = 0.8 #Turbine efficiency:\n", "Cp = 1.005 #Specific heat(in kJ/kg.K):\n", "p3 = 7.248 #bar\n", "r = 1.4\n", "p6 = 0.7\n", "R = 0.287 #Gas constant(in kJ/kg.K):\n", "T2a = 282.11 #Temperature at state 2(in K):\n", "T3a = 568.635\n", "\n", "#Calculations:\n", "p4 = p3-0.15\n", "r1 = (CV-T1*Cp)/(Cp*T1-Cp*T3a) #Air fuel ratio:\n", "T5a = T4-(T3a-T2a) #Temperature at state 5'(in K):\n", "T5 = T4-(T4-T5a)/nt #Temperature at state 5(in K):\n", "p5 = p4*(T5/T4)**(r/(r-1))\n", "T6 = T5a*(p6/p5)**((r-1)/r) #Temperature at state 6(in K):\n", "T6a = T5a-(T5a-T6)*nn #Temperature at state 6'(in K):\n", "C6 = sqrt(2*Cp*(T5a-T6a)*10**3) #Velocity at exit of nozzle(in m/s):\n", "v = 200/10 #Volume flow rate of air(in m**3/s):\n", "m = 0.7*10**2*v/(R*260) #Mass flow rate(in kg/s):\n", "St = (1+1/r1)*C6 #Specific thrust(in N/kg of air/s):\n", "Tt = m*St #Total thrust(in N):\n", "\n", "#Results: \n", "print \"Specific thrust: \",round(St,2),\"N/kg of air/s\"\n", "print \"Total thrust: \",round(Tt,2),\"N\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific thrust: 508.22 N/kg of air/s\n", "Total thrust: 9535.07 N\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 7, page no. 886" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "Cpa = 1.005 #Specific heat(in kJ/kg.K):\n", "Cpg = 1.087\n", "ra = 1.4\n", "rg = 1.33\n", "R = 0.287 #Gas constant(in kJ/kg.K):\n", "C0 = 250 #Speed of aeroplane(in m/s):\n", "C4a = 180 #Velocity at exit of turbine(in m/s):\n", "CV = 43000 #kJ/kg\n", "P = 800 #Thrust power(in kW):\n", "T0 = -20+273 #Temperatures(in K):\n", "T2 = 474.25 \n", "T3 = 973\n", "p0 = 0.3 #Pressures(in bar):\n", "p1 = 0.31\n", "nc = 0.85 #Compressor efficiency:\n", "nj = 0.90 #Jet engine efficiency:\n", "r1 = 6 #Pressure ratio:\n", "\n", "#Calculations:\n", "p5 = p0\n", "T1 = T0+C0**2/(2*Cpa*10**3)\t#Temperature at state 2(in K):\n", "T2a = T1+(T2-T1)/nc\n", "p2 = p1*r1 #Pressure at state 2(in bar):\n", "p3 = p2\n", "FA = (Cpa*T3-Cpg*T2a)/(CV-Cpa*T3) #Fuel air ratio:\n", "T4a = T3-Cpa/Cpg*(T2a-T1)/(1+FA) #Temperature at state 4'(in K):\n", "T4 = T3-(T3-T4a)/nc #Temperature at state 4(in K):\n", "p4 = p3*(T4/T3)**(rg/(rg-1)) #Pressure at state 4(in bar):\n", "T5 = T4a*(p5/p4)**((rg-1)/rg) #Temperature at state 5(in K):\n", "C5 = sqrt(2*nj*(Cpg*10**3*(T4a-T5)+C4a**2/2)) #Nozzle exit velocity(in m/s):\n", "no = (((1+FA)*C5-C0)*C0)/(FA*CV*10**3)*100 #Overall efficiency:\n", "ma = P*10**3/(((1+FA)*C5-C0)*C0) #Rate of air consumption(in kg/s):\n", "Pt = ma*(1+FA)*Cpg*(T3-T4a) #Power produced by the turbine(in kW):\n", "T5a = T4a-((C5**2-C4a**2)/(2*Cpg*10**3)) #Temperature at state 5'(in K):\n", "d5a = p5*10**2/(R*T5a) #Density of exhaust gases(in m**3/kg):\n", "Aj = ma*(1+FA)/(C5*d5a) #Jet exit area(in m**2):\n", "\n", "#Results: \n", "print \"Air-fuel ratio: \",round(1/FA,2),\":1\"\n", "print \"Rate of air consumption: \",round(ma,2),\"kg/s\"\n", "print \"Power produced by turbine: \",round(Pt,2),\"kW\"\n", "print \"Jet exit area: \",round(Aj,2),\"m**2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Air-fuel ratio: 98.67 :1\n", "Rate of air consumption: 11.99 kg/s\n", "Power produced by turbine: 2694.84 kW\n", "Jet exit area: 0.15 m**2\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8, page no. 889" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt,pi\n", "\n", "#Variable Declaration: \n", "Ca = 250 #Speed of jet plane(in m/s):\n", "d = 0.15 #Density of air(in kg/m**3):\n", "D = 6800 #Drag(in kW):\n", "np = 0.56 #Propulsive efficiency:\n", "\n", "#Calculations:\n", "Ce = 2*Ca/np-Ca #Relative velocity(in m/s):\n", "C = Ce-Ca #Absolute velocity of jet(in m/s):\n", "ma = D/(Ce-Ca) #Mass flow rate(in kg/s):\n", "v = ma/d #Volume flow rate(in m**3/s):\n", "dj = sqrt(v*4/(2*pi*Ce)) #Jet diameter(in m):\n", " \n", "#Results: \n", "print \"Jet diamter: \",round(dj*100,1),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Jet diamter: 33.8 cm\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 9, page no. 889" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", "\n", "#Variable Declaration: \n", "R = 0.287 #Gas constant(in kJ/kg.K):\n", "r1 = 0.4 #Density ratio:\n", "Cp = 1.005 #Specific heat(in kJ/kg.K):\n", "d = 0.018 #Drag coefficient:\n", "Ce = 550 #Jet velocity(in m/s):\n", "A = 20 #Wing area(in m**2):\n", "Ca = 900*1000/3600 #Speed of aeroplane(in m/s):\n", "d1 = 1.01325*10**2/(R*288) #Density of STP(in kg/m**3):\n", "d2 = r1*d1 #Density of air at altitude(in kg/m**3):\n", "T = d*A*d2*Ca**2/2 #Thrust on aeroplane:\n", "ma = T/(Ce-Ca) #Mass flow rate(in kg/s):\n", "St = T/ma #Specific thrust(in N/kg of air):\n", "\n", "#Results: \n", "print \"Specific thrust: \",round(St),\"N/kg of air\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific thrust: 300.0 N/kg of air\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10, page no. 890" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "from __future__ import division\n", " \n", "from math import sqrt\n", "\n", "#Variable Declaration: \n", "Ca = 250 #Speed of air craft(in m/s):\n", "m = 55 #Mass flow rate(in kg/s):\n", "r = 85 #Air fuel ratio:\n", "nc = 0.96 #Combustion efficiency:\n", "CV = 43000 #Lower calorific value(in kJ/kg):\n", "dh = 220 #Isentropic enthalpy change(in kJ/kg):\n", "n = 0.95 #Velocity coefficient:\n", "\n", "#Calculations:\n", "Ce = n*sqrt(2*dh*10**3)#Jet velocity(in m/s):\n", "Ce = 615.67\n", "St = 400.67 #Specific thrust per kg of air(in N/kg air):\n", "r1 = 1/r*3600*m #Fuel flow rate(in kg/hr):\n", "sfc = r1/(St*m) #Specific fuel consumption(in kg/N.hr):\n", "P = m*(Ce-Ca)*Ca/10**3 #Thrust power(in kW):\n", "Pp = m*(Ce**2-Ca**2)/2/10**3 #Propulsive power(in kW):\n", "np = P/Pp*100 #Propulsive efficiency:\n", "no = P/(m/r*CV*nc)*100 #Overall efficiency:\n", "\n", "#Results: \n", "print \"Propulsive power: \",round(Pp,2),\"kW\"\n", "print \"Propulsive efficiency: \",round(np,2),\"%\"\n", "print \"Overall efficiency: \",round(no,2),\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Propulsive power: 8705.11 kW\n", "Propulsive efficiency: 57.76 %\n", "Overall efficiency: 18.82 %\n" ] } ], "prompt_number": 22 } ], "metadata": {} } ] }