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{
"metadata": {
"name": "",
"signature": "sha256:9f892b4a818165ad52b348800d0ffa60b6a3224f73f3dcda15a72be66b12ba9f"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER12:LINEARIZED SUPERSONIC FLOW"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E01 : Pg 395"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import pi,sqrt\n",
"alpha = 5*pi/180; # angle of attack\n",
"M_inf = 3; # freestream mach number\n",
"\n",
"# from eq.(12.23)\n",
"c_l = 4*alpha/sqrt(M_inf**2 - 1);\n",
"\n",
"# from eq.(12.24)\n",
"c_d = 4*alpha**2/sqrt(M_inf**2 - 1);\n",
"\n",
"print\"The cl and cd according to the linearized theory are:cl =\", round(c_l,2)\n",
"print\"The cl and cd according to the linearized theory are:cd =\",round(c_d,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The cl and cd according to the linearized theory are:cl = 0.12\n",
"The cl and cd according to the linearized theory are:cd = 0.01\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E02 : Pg 395"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt,pi\n",
"M_inf = 2.; # freestream mach number\n",
"rho_inf = 0.3648; # freestream density at 11 km altitude\n",
"T_inf = 216.78; # freestream temperature at 11 km altitude\n",
"gam = 1.4; # ratio of specific heats\n",
"R = 287.; # specific gas constant\n",
"m = 9400.; # mass of the aircraft\n",
"g = 9.8; # acceleratio due to gravity\n",
"W = m*g; # weight of the aircraft\n",
"S = 18.21; # wing planform area\n",
"# thus\n",
"a_inf = sqrt(gam*R*T_inf);\n",
"V_inf = M_inf*a_inf;\n",
"q_inf = 1./2.*rho_inf*V_inf**2.;\n",
"\n",
"# thus the aircraft lift coefficient is given as\n",
"C_l = W/q_inf/S;\n",
"\n",
"alpha = 180./pi*C_l/4.*sqrt(M_inf**2. - 1.);\n",
"\n",
"print\"The angle of attack of the wing is:\",alpha,\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The angle of attack of the wing is: 1.97493716351 degrees\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example E03 : Pg 400"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# All the quantities are expressed in SI units\n",
"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt,pi\n",
"# (a)\n",
"M_inf = 2.; # freestream mach number\n",
"rho_inf = 0.3648; # freestream density at 11 km altitude\n",
"T_inf = 216.78; # freestream temperature at 11 km altitude\n",
"gam = 1.4; # ratio of specific heats\n",
"R = 287.; # specific gas constant\n",
"m = 9400.; # mass of the aircraft\n",
"g = 9.8; # acceleratio due to gravity\n",
"W = m*g; # weight of the aircraft\n",
"S = 18.21; # wing planform area\n",
"c = 2.2; # chord length of the airfoil\n",
"alpha = 0.035; # angle of attack as calculated in ex. 12.2\n",
"T0 = 288.16; # ambient temperature at sea level\n",
"mue0 = 1.7894e-5; # reference viscosity at sea level\n",
"\n",
"# thus\n",
"a_inf = sqrt(gam*R*T_inf);\n",
"V_inf = M_inf*a_inf;\n",
"\n",
"# according to eq.(15.3), the viscosity at the given temperature is\n",
"mue_inf = mue0*(T_inf/T0)**1.5*(T0+110.)/(T_inf+110.);\n",
"\n",
"# thus the Reynolds number can be given by\n",
"Re = rho_inf*V_inf*c/mue_inf;\n",
"\n",
"# from fig.(19.1), for these values of Re and M, the skin friction coefficient is\n",
"Cf = 2.15*10**-3;\n",
"\n",
"# thus, considering both sides of the flat plate\n",
"net_Cf = 2.*Cf;\n",
"\n",
"# (b)\n",
"c_d = 4.*alpha**2./sqrt(M_inf**2. - 1.);\n",
"\n",
"print\"(a) Net Cf = \",net_Cf*1e3\n",
"print\"(b) cd =\",c_d*1e3"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Net Cf = 4.3\n",
"(b) cd = 2.82901631903\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
