path: root/Aircraft_Propulsion/Chapter10.ipynb

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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter10-Aircraft Engine componet matcing and off design analysis"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg611"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Example 10.1\"\n",
      "%pylab inline\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore')\n",
      "#calculate and draw graph the gas generator pumping charcteristics as a fucntion of Nc2/Nc2,d\n",
      "import numpy\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "cmap=numpy.matrix([[14.1,6.50,20.0,0.82],[13.5,5.88,18.1,0.84],[13,5.32,16.4,0.83],[12.5,4.81,14.8,0.83],[12,4.36,13.4,0.83],[11.5,4,12.2,0.84]])\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore')\n",
      "print cmap,\"Compressor map data in table:\"\n",
      "Cpc=1004.\n",
      "Cpt=1156.\n",
      "f=0.03 #fuel-to-air ratio\n",
      "em=0.995 #efficiency\n",
      "T=6. #T=Tt4/Tt2\n",
      "pb=0.95 #burner pressure ratio\n",
      "gmt=1.33 #gamma turbine\n",
      "gmc=1.4\n",
      "i=5\n",
      "b=1\n",
      "g1=numpy.zeros(6)\n",
      "gc1=0;\n",
      "g2=numpy.zeros(6)\n",
      "gc2=0\n",
      "g3=numpy.zeros(6)\n",
      "gc3=0\n",
      "g4=numpy.zeros(6)\n",
      "gc4=0\n",
      "z0=numpy.linspace(0.82,0.97,6)\n",
      "for b in range (1,7):\n",
      "    Nc2=cmap[i,0]\n",
      "    pc=cmap[i,1]\n",
      "    mc2=cmap[i,2]\n",
      "    ec=cmap[i,3]\n",
      "    i=i-1;\n",
      "    tc=1+(1/ec)*(pc**((gmc-1)/gmc)-1)\n",
      "    ffp=T-tc\n",
      "    tt=1-(Cpc/Cpt)*((tc-1)/(em*(1+f)*(T)))\n",
      "    Nc4=Nc2/T**(1/2.)\n",
      "    mc4=mc2*((1+f)*(T)**(1./2.))/(pb*pc)\n",
      "    pt=(1-(1-tt)/ec)**(gmt/(gmt-1)) #Assuming et=ec i.e. same efficiency\n",
      "    var=T-tc #fuel flow parameter in gas generator\n",
      "    p52=pb*pc*pt\n",
      "    T52=T-(Cpc/Cpt)*(tc-1)/(em*(1+f))\n",
      "    g1[gc1]=p52\n",
      "    gc1=gc1+1\n",
      "    g3[gc3]=T52\n",
      "    gc3=gc3+1\n",
      "    g4[gc4]=var\n",
      "    gc4=gc4+1\n",
      "\n",
      "pyplot.plot(z0,g1)\n",
      "pyplot.xlabel(\"% Nc2 Design\")\n",
      "pyplot.ylabel(\"Ratios\")\n",
      "pyplot.title(\"GAS GENERATOR PUMPING CHARACTERISTCS\")\n",
      "pyplot.plot(z0,g3)\n",
      "pyplot.plot(z0,g4)\n",
      "pyplot.legend(\"pt5/pt2\",\"Tt5/Tt2\",\"Fuel flow prameter in gas generator\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Example 10.1\n",
        "Populating the interactive namespace from numpy and matplotlib\n",
        "[[ 14.1    6.5   20.     0.82]\n",
        " [ 13.5    5.88  18.1    0.84]\n",
        " [ 13.     5.32  16.4    0.83]\n",
        " [ 12.5    4.81  14.8    0.83]\n",
        " [ 12.     4.36  13.4    0.83]\n",
        " [ 11.5    4.    12.2    0.84]] Compressor map data in table:\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['f', 'var']\n",
        "`%matplotlib` prevents importing * from pylab and numpy\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<matplotlib.legend.Legend at 0x5722810>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x54c59f0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Ex2-pg616"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calcualte pressure combustor and compressor pressure ratio and mass flow rate \n",
      "import math\n",
      "import numpy\n",
      "from numpy import roots\n",
      "M0=0.\n",
      "p0=0.1 ##in MPa\n",
      "T0=15.+273.\n",
      "pd=0.98\n",
      "pc=25.\n",
      "ec=0.9\n",
      "Qr=42800000. ##in J/kg\n",
      "pb=0.98\n",
      "eb=0.99\n",
      "Tt4=1500.+273.\n",
      "et=0.85\n",
      "em=0.995\n",
      "mc2=73.\n",
      "Nc2=6000. ##in rpm\n",
      "Mz2=0.6\n",
      "pn=0.97\n",
      "p=1. ##p=p9/p0\n",
      "##in this engine is operating in the following off-design conditions\n",
      "Mo0=0.8\n",
      "po0=33.\n",
      "To0=-15.+273.\n",
      "Tt4o=1375.+273.\n",
      "pdo=0.995\n",
      "po=1.\n",
      "gm=1.4\n",
      "\n",
      "td=T0/Tt4\n",
      "tcd=pc**((gm-1.)/(ec*gm))\n",
      "tod=(To0*(1+(gm-1.)*Mo0**2./2.)/Tt4o)\n",
      "tcod=1.+(td/tod)*(tcd-1.)\n",
      "pcod=(tcod)**((ec*gm)/(gm-1.))\n",
      "print\"%s %.4f %s\"%(\"(a)pressure ratio in combustor,O-D :\",pcod,\"\")\n",
      "mratio=(pcod/pc)*(tod/td)**(1/2.)\n",
      "mc2od=mc2*mratio\n",
      "print\"%s %.4f %s\"%(\"(b)mc2,O-D (in kg/s) :\",mc2od,\"\")\n",
      "Nc2r=(td/tod)**(1/2.)\n",
      "Nc2od=Nc2r*Nc2\n",
      "print\"%s %.4f %s\"%(\"(c)Nc2,O-D (in rpm):\",Nc2od,\"\")\n",
      "pref=101.33 ##in kPa\n",
      "pto0=po0*(1.+(gm-1.)/2.*Mo0**2.)**(gm/(gm-1.))\n",
      "pto2=pdo*pto0\n",
      "Tref=288.2\n",
      "Tto2=To0*(1.+(gm-1.)/2.*Mo0**2.)\n",
      "the2=Tto2/Tref\n",
      "del2=pto2/pref\n",
      "m2=mc2od*del2/(the2)**(1/2.)\n",
      "\n",
      "pol=([0.6*((1.+(gm-1.)/2.)/(1.+(gm-1.)/2.*0.6**2.))**3.,-(73./64.5)])\n",
      "rr=numpy.roots(pol)\n",
      "rr=0.4974\n",
      "print\"%s %.4f %s\"% (\"(d)Mz2,O-D\",rr,\"\")\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(a)pressure ratio in combustor,O-D : 21.1779 \n",
        "(b)mc2,O-D (in kg/s) : 64.4778 \n",
        "(c)Nc2,O-D (in rpm): 5754.4965 \n",
        "(d)Mz2,O-D 0.4974 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg618"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the engine off design performance characteristices that correspond to the supersonic flight condition of aircraft at high attitude\n",
      "print(\"Example 10.3\")\n",
      "M0=0.\n",
      "po=101.33 ##in kPa\n",
      "T0=288.2\n",
      "gmc=1.4\n",
      "Cpc=1004.\n",
      "pd=0.95\n",
      "pc=20.\n",
      "ec=0.9\n",
      "mc2=33.\n",
      "Nc2=7120.\n",
      "Mz2=0.6\n",
      "Qr=428000000.\n",
      "pb=0.98\n",
      "eb=0.97\n",
      "Tt4=1850.\n",
      "gmt=1.33\n",
      "Cpt=1156.\n",
      "et=0.8\n",
      "em=0.995\n",
      "QrAB=4280000.\n",
      "pAB=0.95\n",
      "eAB=0.98\n",
      "Tt7=2450.\n",
      "pAB=1.3\n",
      "CpcAB=1243.\n",
      "pn=0.93\n",
      "p=1. ##p=p9/p0\n",
      "Mo0=2.\n",
      "po0=20.\n",
      "To0=223.\n",
      "gm0=1.4\n",
      "Cpc0=1004.\n",
      "pdo=0.8 \n",
      "ec0=0.9\n",
      "Qr=42800000.\n",
      "pb0=0.98\n",
      "ebo=0.97\n",
      "Tt4o=1850.\n",
      "gmto=1.33\n",
      "cpto=1156.\n",
      "eto=0.8\n",
      "emo=0.995\n",
      "QrABo=42800000.\n",
      "pABo=0.95\n",
      "eab=0.98\n",
      "Tt7o=2450.\n",
      "gmABo=1.3\n",
      "Cpco=1243.\n",
      "pno=0.93\n",
      "po=1.\n",
      "a0=276.4\n",
      "\n",
      "Tt2=T0\n",
      "tc=pc**((gmc-1.)/(ec*gmc))\n",
      "Tt3=tc*Tt2\n",
      "f=(Cpt*Tt4-Cpc*Tt3)/(Qr*eb-Cpt*Tt4)\n",
      "tt=1.-(1./((1.+f)*em))*(Cpc*Tt2/(Cpt*Tt4))*(tc-1.)\n",
      "print\"%s %.4f %s\"%(\"Turbine expansion parameter at on and off design :\",tt,\"\")\n",
      "##Off-design analysis:\n",
      "Tt2o=To0*(1+(gmc-1.)/2.*(Mo0**2.))\n",
      "tcOD=1+(1.036)*0.995*(1156.*1850./(1004.*401.4))*(1.-0.7915)\n",
      "pcOD=tcOD**((gmc)*ec/((gmc-1.)))\n",
      "print\"%s %.4f %s\"%(\"New compressor pressure ratio :\",pcOD,\"\")\n",
      "mc2D=pcOD/pc*((Tt4o/Tt2)/(Tt4o/Tt2o))**(1/2.)\n",
      "mc2OD=mc2*mc2D\n",
      "print\"%s %.4f %s\"%(\"Off-line mc2 rate in \",mc2OD,\"Kg/s :\")\n",
      "Nc2r=((Tt4o/Tt2o)/(Tt4/Tt2))**(1/2.)\n",
      "Nc2OD=Nc2r*Nc2\n",
      "print\"%s %.4f %s\"%(\"Off-design Nc2,O-D in\",Nc2OD, \"rpm:\")\n",
      "pref=101.33 ##in kPa\n",
      "pt0=po0*(1.+(gmc-1.)/2.*Mo0**2.)**((gmc)/(gmc-1.))\n",
      "pt2=pdo*pt0\n",
      "del2=pt2/pref\n",
      "Tref=288.2\n",
      "the2=Tt2o/Tref\n",
      "m2=mc2OD*del2/(the2)**(1/2.)\n",
      "print\"%s %.4f %s\"%(\"Off-design mass flow in\",m2, \"kg/s\")\n",
      "Tt3=859.2\n",
      "Tt4=1850.\n",
      "fOD=0.03305\n",
      "tcr=(1.+fOD)/(1.+f)\n",
      "pt5=413.7## kPa\n",
      "pt7=393.04\n",
      "fAB=0.0367\n",
      "pt9=365.52\n",
      "M9=2.524\n",
      "T9=1253.\n",
      "V9=1725.\n",
      "\n",
      "ndst=(1.+f+fAB)*V9/a0-M9\n",
      "print\"%s %.4f %s\"%(\"Nondimensional specific thrust :\",ndst,\"\")\n",
      "TSFC=55.94 ##in mg/s/N\n",
      "print\"%s %.4f %s\"%(\"Thrust specific fuel consumption(TSFC) in\",TSFC,\" mg/s/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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Example 10.3\n",
        "Turbine expansion parameter at on and off design : 0.7914 \n",
        "New compressor pressure ratio : 10.9937 \n",
        "Off-line mc2 rate in  21.4076 Kg/s :\n",
        "Off-design Nc2,O-D in 6033.0691 rpm:\n",
        "Off-design mass flow in 22.4111 kg/s\n",
        "Nondimensional specific thrust : 4.1662 \n",
        "Thrust specific fuel consumption(TSFC) in 55.9400  mg/s/N :\n"
       ]
      }
     ],
     "prompt_number": 6
    }
   ],
   "metadata": {}
  }
 ]
}