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"source": [
"CHAPTER14:ELEMENTS OF HYPERSONIC FLOW"
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"source": [
"Example E01 : Pg 440"
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"# All the quantities are expressed in SI units\n",
"import math \n",
"from math import sqrt,pi,sin,cos\n",
"M1 = 8.; # mach number\n",
"alpha = 15.*pi/180.; # anlge of attack\n",
"theta= alpha;\n",
"gam = 1.4;\n",
"# (a)\n",
"# for M = 8\n",
"v1 = 95.62*pi/180.;\n",
"v2 = v1 + theta;\n",
"# from Appendix C\n",
"M2 = 14.32;\n",
"# from Appendix A, for M1 = 8 and M2 = 14.32\n",
"p_ratio = 0.9763e4/0.4808e6;\n",
"# from eq.(11.22)\n",
"Cp2 = 2/gam/M1**2*(p_ratio - 1);\n",
"# for M1 = 8 and theta = 15\n",
"b = 21*pi/180;\n",
"Mn_1 = M1*sin(b);\n",
"# for this value of Mn,1, from appendix B\n",
"p_ratio2 = 9.443;\n",
"# thus\n",
"Cp3 = 2./gam/M1**2.*(p_ratio2 - 1.);\n",
"c_n = Cp3 - Cp2;\n",
"c_l = c_n*cos(alpha);\n",
"c_d = c_n*sin(alpha);\n",
"L_by_D = c_l/c_d;\n",
"print\"The exact results from the shock-expansion theory are:\"\n",
"print\"Cp2 =\",Cp2\n",
"print\"Cp3 = \",Cp3\n",
"print\" cl =\",c_l\n",
"print\"cd =\",c_d\n",
"print\"L/D =\",L_by_D\n",
"# (b)\n",
"# from Newtonian theory, by eq.(14.9)\n",
"Cp3 = 2.*sin(alpha)**2;\n",
"Cp2 = 0;\n",
"c_l = (Cp3 - Cp2)*cos(alpha);\n",
"c_d = (Cp3 - Cp2)*sin(alpha);\n",
"L_by_D = c_l/c_d;\n",
"print\"\\n(b) The results from Newtonian theory are:\"\n",
"print\"Cp2 =\",Cp2\n",
"print\"Cp3 =\",Cp3\n",
"print\"cl =\",c_l\n",
"print\"cd =\",c_d\n",
"print\"L/D =\",L_by_D"
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"text": [
"The exact results from the shock-expansion theory are:\n",
"Cp2 = -0.0218681754368\n",
"Cp3 = 0.188459821429\n",
" cl = 0.203161244164\n",
"cd = 0.054436891307\n",
"L/D = 3.73205080757\n",
"\n",
"(b) The results from Newtonian theory are:\n",
"Cp2 = 0\n",
"Cp3 = 0.133974596216\n",
"cl = 0.129409522551\n",
"cd = 0.0346751770605\n",
"L/D = 3.73205080757\n"
]
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