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{
"metadata": {
"name": "",
"signature": "sha256:b0248b236fb77321aca1aa897efa31136042f1022b99d1754ff155338956fea7"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter9-Aerothermo-dynamics of Gas Turbines "
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg537"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calcualte inlet velocity and the exit double mach number and nozzle torque per unit mass flow rate \n",
"Tt1=1800.\n",
"M1=0.55\n",
"alfa1=0.\n",
"gm=1.33\n",
"Cp=1157.\n",
"alfa2=60.\n",
"T1=Tt1/(1.+(gm-1)*M1**2/2.)\n",
"a1=((gm-1.)*Cp*T1)**(1/2.)\n",
"C1=a1*M1\n",
"C2=C1/math.cos(alfa2/57.3)\n",
"Tt2=Tt1\n",
"T2=Tt2-C2**2/(2*Cp)\n",
"a2=((gm-1)*Cp*T2)**(1/2)\n",
"M2=C2/a2\n",
"Ct2=C1*math.tan(alfa2/57.3)\n",
"r=0.35\n",
"t=0-r*Ct2\n",
"print\"%s %.4f %s\"%(\"(a)Inlet velocity C1 in m/s :\",C1,\"\")\n",
"print\"%s %.4f %s\"%(\"(b)The exit absolute Mach no. M2 :\",M2,\"\")\n",
"print\"%s %.4f %s\"%(\"(c)Nozzle torque per unit mass flow rate for r1=r2=0.35m :\",t,\"\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)Inlet velocity C1 in m/s : 444.9857 \n",
"(b)The exit absolute Mach no. M2 : 889.8525 \n",
"(c)Nozzle torque per unit mass flow rate for r1=r2=0.35m : -269.7102 \n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the nozzle exit flow angle\n",
"print(\"Example 9.2\")\n",
"M2=1.0 ##i.e choked\n",
"Tt2=1800.\n",
"gm=1.33\n",
"C1=445.\n",
"Cp=1157.\n",
"T2=Tt2/(1.+(gm-1.)*M2**2/2.)\n",
"a2=((gm-1.)*Cp*T2)**(1/2.) \n",
"M2=1\n",
"C2=M2*a2\n",
"alfa2=math.acos(C1/C2)*180/math.pi\n",
"print\"%s %.4f %s\"%(\"Nozzle exit flow angle if M2=1 in degrees:\",alfa2,\"\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Example 9.2\n",
"Nozzle exit flow angle if M2=1 in degrees: 54.5931 \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ex3-pg538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate axial velocity and rotor velocity and degree of reaction at this radius\n",
"C1=411.\n",
"alfa2=60.\n",
"C2=800.\n",
"W2=450.\n",
"alfa3=13.\n",
"C3=411.\n",
"Cz2=C2*math.cos(60/57.3)\n",
"Cz3=C3*math.cos(13/57.3)\n",
"Ct2m=Cz3*math.tan(60/57.3)\n",
"Wt2m=(450.**2.-400**2.)**(1/2.)\n",
"Um=Ct2m-Wt2m\n",
"Ct3=C3*math.sin(13/57.3)\n",
"Rm=1-(Ct2m+Ct3)/(2.*Um)\n",
"print\"%s %.4f %s\"%(\"(a)The axial velocities up- and downstream of the rotor in m/s:\",Cz2,\"c\")\n",
"print'%.4f'%(Cz3)\n",
"print\"%s %.4f %s\"%(\"(b)The rotor velocity Um in m/s:\",Um,\"\")\n",
"print\"%s %.4f %s\"%(\"(c)The degree of reaction at this radius :\",Rm,\"\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The axial velocities up- and downstream of the rotor in m/s: 400.0534 c\n",
"400.4676\n",
"(b)The rotor velocity Um in m/s: 487.3515 \n",
"(c)The degree of reaction at this radius : 0.1936 \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg553"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the loss of turbine efficiency due to tip clearance\n",
"Cd=0.5\n",
"bm=-20.\n",
"r=1.25\n",
"phi=0.5\n",
"chi=1.\n",
"t=0.02\n",
"\n",
"De=Cd*t*r*(1-(chi/phi)*math.tan(bm/57.3))**(1/2.)\n",
"print\"%s %.4f %s\"%(\"Loss of the turbine efficiency (eta0 times) :\",De,\"\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Loss of the turbine efficiency (eta0 times) : 0.0164 \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ex5-pg560"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate gas static temperature and adibatic wall temperature on the nozzle for a turbulent boundary layer \n",
"Tt=1700. ##total gas temp at exit\n",
"gm=1.33 ##gamma\n",
"Cp=1157. ##in J/kg.K\n",
"M2=1. ##local gas Mach no.\n",
"Pr=0.71 ## Prandtl no.\n",
"W2=455. ## gas speed relative to rotor\n",
"Tg=Tt/(1.+(gm-1)*(M2**2)/2.)\n",
"print\"%s %.3f %s \"%(\"The gas static temperature Tg in K:\",Tg,\"\")\n",
"a2=((gm-1)*Cp*Tg)**(1/2.)\n",
"C2=a2\n",
"r=Pr**(1/3.)\n",
"Taw=Tg+Pr**(1/3.)*C2**2./(Cp)\n",
"print\"%s %.3f %s \"%(\"The adiabatic wall temperatue Taw on the nozzle for a turbulent boundary layer in K:\",Taw,\"\")\n",
"Ttr=Tg+(W2**2)/(2*Cp)\n",
"Tawl=Tg+Pr**(1/2)*C2**2/(Cp)\n",
"print\"%s %.3f %s \"%(\"The adiabatic wall temperature on the nozzle for a laminar boundary layer in K: \",Tawl,\"\")\n",
"print\"%s %.3f %s \"%(\"The rotor temperature of the gas on the rotor in K:\",Ttr,\"\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The gas static temperature Tg in K: 1459.227 \n",
"The adiabatic wall temperatue Taw on the nozzle for a turbulent boundary layer in K: 1888.820 \n",
"The adiabatic wall temperature on the nozzle for a laminar boundary layer in K: 1940.773 \n",
"The rotor temperature of the gas on the rotor in K: 1548.694 \n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg564"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate cooling fraction\n",
"T0=288. ##in K\n",
"p0=100. ##in kPa\n",
"Tt3=800. ##in K\n",
"gm=1.4\n",
"Cpc=1.0045 ##kJ/Kg.K\n",
"pc=25.\n",
"ec=0.9\n",
"Tt4=2000. ##in K\n",
"gmc=1.33\n",
"Cpg=1.188 ##kJ/Kg.K\n",
"Stg=0.005 ##Gas-side Stanton no.\n",
"Taw=2000. ##in K\n",
"ptg=2.5 ##in Mpa\n",
"Tawd=1200. ## desired temp. in K\n",
"d=2. ##thickness of internally cooled wall in mm\n",
"bms=2. ##blade mean solidity in HPT\n",
"kw=14.9 ##in W/m.K\n",
"Twc=870. ##in K\n",
"S=1/2. ##S=Stc/Stg\n",
"e=(Cpc/Cpg)*S*(Twc-Tt3)/(Tt4-Tawd)\n",
"print\"%s %.4f %s\"%(\"Cooling fraction :\",e,\"\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Cooling fraction : 0.0370 \n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
