/usr/share/pyshared/gastables/RayleighFlow.py is in python-gastables 0.3-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 | """ Python module for flow properties of perfect gases with heat transfer
In Rayleigh flow, heat addition increases the entropy and takes the process
towards the choking conditions, (M = M* = 1). This behaviour imposes a limit
to heat addition, therefore for a given initial Mach number there is a fixed
value of the maximum possible heat transfer (Qmax).
Assumptions:
1) One dimensional flow with Heat transfer
2) Constant area duct
3) Perfect gas with constant specific heats and molecular weights
"""
"""
* Copyright (C) 2006 Varun Hiremath.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* Authors: Varun Hiremath, Venkattraman A
* Version 0.2
"""
from scipy import optimize
from math import *
class RayleighFlow :
def __init__(self, g= 1.4):
""" g is the value of gamma (ratio of specific heats), default = 1.4
"""
self.g = g
def get_P_by_Pstar_from_M(self, M):
"""Returns the value of p/p* at Mach number M"""
return (1+self.g)/(1+self.g*M**2)
def get_Po_by_Postar_from_M(self, M):
"""Returns the value of po/po* at Mach number M"""
return (1+self.g)/(1+self.g*M**2)*(2*(1+(self.g-1)/2*M**2)/(self.g+1))**(self.g/(self.g-1))
def get_T_by_Tstar_from_M(self, M):
"""Returns the value of T/T* at Mach number M"""
return ((1+self.g)/(1+self.g*M**2))**2*M**2
def get_To_by_Tostar_from_M(self, M):
"""Returns the value of To/To* at Mach number M"""
return 2*(1+self.g)*M**2*(1+(self.g-1)/2*M**2)/(1+self.g*M**2)**2
def get_rho_by_rhostar_from_M(self, M):
"""Returns the value of rho/rho* at Mach number M"""
return (1+self.g*M**2)/(1+self.g)/M**2
def get_Qmax_by_CpT_from_M(self, M):
"""Returns the value of Qmax/CpT* at Mach number M"""
return (M**2-1)**2/2/(self.g+1)/M**2
def get_M_from_P_by_Pstar(self, P_by_Pstar):
"""Returns Mach number M at p/p* equal to P_by_Pstar"""
if P_by_Pstar > self.get_P_by_Pstar_from_M(0.0001) :
raise Exception('Value of P/P* should be greater than 0 and less than %s' % self.get_P_by_Pstar_from_M(0.0001))
else:
return (((1+self.g)/P_by_Pstar-1)/self.g)**0.5
def get_Po_by_Postar_from_P_by_Pstar(self, P_by_Pstar):
"""Returns po/po* at p/p* equal to P_by_Pstar"""
M = self.get_M_from_P_by_Pstar(P_by_Pstar)
return self.get_Po_by_Postar_from_M(M)
def get_T_by_Tstar_from_P_by_Pstar(self, P_by_Pstar):
"""Returns T/T* at p/p* equal to P_by_Pstar"""
M = self.get_M_from_P_by_Pstar(P_by_Pstar)
return self.get_T_by_Tstar_from_M(M)
def get_To_by_Tostar_from_P_by_Pstar(self, P_by_Pstar):
"""Returns To/To* at p/p* equal to P_by_Pstar"""
M = self.get_M_from_P_by_Pstar(P_by_Pstar)
return self.get_To_by_Tostar_from_M(M)
def get_rho_by_rhostar_from_P_by_Pstar(self, P_by_Pstar):
"""Returns rho/rho* at p/p* equal to P_by_Pstar"""
M = self.get_M_from_P_by_Pstar(P_by_Pstar)
return self.get_rho_by_rhostar_from_M(M)
def get_Qmax_by_CpT_from_P_by_Pstar(self, P_by_Pstar):
"""Returns Qmax/CpT at p/p* equal to P_by_Pstar"""
M = self.get_M_from_P_by_Pstar(P_by_Pstar)
return self.get_Qmax_by_CpT_from_M(M)
def get_M_from_Po_by_Postar(self, Po_by_Postar):
"""Returns Mach number M at po/po* equal to Po_by_Postar"""
if Po_by_Postar < 1.0:
raise Exception('Value of Po/Po* should be greater than 1')
else:
if Po_by_Postar < self.get_Po_by_Postar_from_M(0.001):
return (optimize.bisect(lambda M : self.get_Po_by_Postar_from_M(M) - Po_by_Postar, 0.001, 1.0),optimize.bisect(lambda M : self.get_Po_by_Postar_from_M(M) - Po_by_Postar, 1.0, 100.0))
else:
return optimize.bisect(lambda M : self.get_Po_by_Postar_from_M(M) - Po_by_Postar, 1.0, 100.0)
def get_P_by_Pstar_from_Po_by_Postar(self, Po_by_Postar =1.4):
"""Returns p/p* from po/po* equal to Po_by_Postar"""
M = self.get_M_from_Po_by_Postar(Po_by_Postar)
return (self.get_P_by_Pstar_from_M(M[0]),self.get_P_by_Pstar_from_M(M[1]))
def get_T_by_Tstar_from_Po_by_Postar(self, Po_by_Postar):
"""Returns T/T* at po/po* equal to Po_by_Postar"""
M = self.get_M_from_Po_by_Postar(Po_by_Postar)
return (self.get_T_by_Tstar_from_M(M[0]),self.get_T_by_Tstar_from_M(M[1]))
def get_To_by_Tostar_from_Po_by_Postar(self, Po_by_Postar):
"""Returns To/To* at po/po* equal to Po_by_Postar"""
M = self.get_M_from_Po_by_Postar(Po_by_Postar)
return self.get_To_by_Tostar_from_M(M)
def get_rho_by_rhostar_from_Po_by_Postar(self, Po_by_Postar):
"""Returns rho/rho* at po/po* equal to Po_by_Postar"""
M = self.get_M_from_Po_by_Postar(Po_by_Postar)
return (self.get_rho_by_rhostar_from_M(M[0]),self.get_rho_by_rhostar_from_M(M[1]))
def get_Qmax_by_CpT_from_Po_by_Postar(self, Po_by_Postar):
"""Returns Qmax/CpT at po/po* equal to Po_by_Postar"""
M = self.get_M_from_Po_by_Postar(Po_by_Postar)
return (self.get_Qmax_by_CpT_from_M(M[0]),self.get_Qmax_by_CpT_from_M(M[1]))
def get_M_from_T_by_Tstar(self, T_by_Tstar):
"""Returns M at T/T* equal to T_by_Tstar"""
if T_by_Tstar > self.get_T_by_Tstar_from_M(1/sqrt(self.g)):
raise Exception('Value of T/T* should be less than %s' % self.get_T_by_Tstar_from_M(1/sqrt(self.g)))
else:
return (optimize.bisect(lambda x : self.get_T_by_Tstar_from_M(x) - T_by_Tstar, 0.001, 1.0/sqrt(self.g)),optimize.bisect(lambda x : self.get_T_by_Tstar_from_M(x) - T_by_Tstar, 1.0/sqrt(self.g), 100.0))
def get_P_by_Pstar_from_T_by_Tstar(self, T_by_Tstar):
"""Returns p/p* at T/T* equal to T_by_Tstar"""
M = self.get_M_from_T_by_Tstar(T_by_Tstar)
return (self.get_P_by_Pstar_from_M(M[0]),self.get_P_by_Pstar_from_M(M[1]))
def get_Po_by_Postar_from_T_by_Tstar(self, T_by_Tstar):
"""Returns po/po* at T/T* equal to T_by_Tstar"""
M = self.get_M_from_T_by_Tstar(T_by_Tstar)
return (self.get_Po_by_Postar_from_M(M[0]),self.get_Po_by_Postar_from_M(M[1]))
def get_To_by_Tostar_from_T_by_Tstar(self, T_by_Tstar):
"""Returns To/To* at T/T* equal to T_by_Tstar"""
M = self.get_M_from_T_by_Tstar(T_by_Tstar)
return (self.get_To_by_Tostar_from_M(M[0]),self.get_To_by_Tostar_from_M(M[1]))
def get_rho_by_rhostar_from_T_by_Tstar(self, T_by_Tstar):
"""Returns rho/rho* at T/T* equal to T_by_Tstar"""
M = self.get_M_from_T_by_Tstar(T_by_Tstar)
return (self.get_rho_by_rhostar_from_M(M[0]),self.get_rho_by_rhostar_from_M(M[1]))
def get_Qmax_by_CpT_from_T_by_Tstar(self, T_by_Tstar):
"""Returns Qmax/CpT at T/T* equal to T_by_Tstar"""
M = self.get_M_from_T_by_Tstar(T_by_Tstar)
return (self.get_Qmax_by_CpT_from_M(M[0]),self.get_Qmax_by_CpT_from_M(M[1]))
def get_M_from_To_by_Tostar(self, To_by_Tostar):
"""Returns M at To/To* equal to To_by_Tostar"""
if To_by_Tostar > 1.0:
raise Exception('Value of To/To* should be less than 1')
else:
if To_by_Tostar > self.get_To_by_Tostar_from_M(1000.0):
return (optimize.bisect(lambda x : self.get_To_by_Tostar_from_M(x) - To_by_Tostar, 0.001, 1.0),optimize.bisect(lambda x : self.get_To_by_Tostar_from_M(x) - To_by_Tostar, 1.0, 1000.0))
else:
return optimize.bisect(lambda x : self.get_To_by_Tostar_from_M(x) - To_by_Tostar, 0.001, 1.0)
def get_P_by_Pstar_from_To_by_Tostar(self, To_by_Tostar):
"""Returns p/p* at To/To* equal to To_by_Tostar"""
M = self.get_M_from_To_by_Tostar(To_by_Tostar)
return (self.get_P_by_Pstar_from_M(M[0]),self.get_P_by_Pstar_from_M(M[1]))
def get_Po_by_Postar_from_To_by_Tostar(self, To_by_Tostar):
"""Returns po/po* at To/To* equal to To_by_Tostar"""
M = self.get_M_from_To_by_Tostar(To_by_Tostar)
return (self.get_Po_by_Postar_from_M(M[0]),self.get_Po_by_Postar_from_M(M[1]))
def get_T_by_Tstar_from_To_by_Tostar(self, To_by_Tostar):
"""Returns T/T* at To/To* equal to To_by_Tostar"""
M = self.get_M_from_To_by_Tostar(To_by_Tostar)
return (self.get_T_by_Tstar_from_M(M[0]),self.get_T_by_Tstar_from_M(M[1]))
def get_rho_by_rhostar_from_To_by_Tostar(self, To_by_Tostar):
"""Returns rho/rho* at To/To* equal to To_by_Tostar"""
M = self.get_M_from_To_by_Tostar(To_by_Tostar)
return (self.get_rho_by_rhostar_from_M(M[0]),self.get_rho_by_rhostar_from_M(M[1]))
def get_Qmax_by_CpT_from_To_by_Tostar(self, To_by_Tostar):
"""Returns Qmax/CpT at To/To* equal to To_by_Tostar"""
M = self.get_M_from_To_by_Tostar(To_by_Tostar)
return (self.get_Qmax_by_CpT_from_M(M[0]),self.get_Qmax_by_CpT_from_M(M[1]))
def get_M_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns Mach number M at rho/rho* equal to rho_by_rhostar"""
return (1.0/((1+self.g)*rho_by_rhostar - self.g))**0.5
def get_P_by_Pstar_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns p/p* at rho/rho* equal to rho_by_rhostar"""
M = self.get_M_from_rho_by_rhostar(rho_by_rhostar)
return self.get_P_by_Pstar_from_M(M)
def get_Po_by_Postar_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns po/po* at rho/rho* equal to rho_by_rhostar"""
M = self.get_M_from_rho_by_rhostar(rho_by_rhostar)
return self.get_Po_by_Postar_from_M(M)
def get_T_by_Tstar_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns T/T* at rho/rho* equal to rho_by_rhostar"""
M = self.get_M_from_rho_by_rhostar(rho_by_rhostar)
return self.get_T_by_Tstar_from_M(M)
def get_To_by_Tostar_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns To/To* at rho/rho* equal to rho_by_rhostar"""
M = self.get_M_from_rho_by_rhostar(rho_by_rhostar)
return self.get_To_by_Tostar_from_M(M)
def get_Qmax_by_CpT_from_rho_by_rhostar(self, rho_by_rhostar):
"""Returns Qmax/CpT at rho/rho* equal to rho_by_rhostar"""
M = self.get_M_from_rho_by_rhostar(rho_by_rhostar)
return self.get_Qmax_by_CpT_from_M(M)
def get_M_from_Qmax_by_CpT(self, Qmax_by_CpT):
"""Returns M at Qmax/CpT equal to Qmax_by_CpT"""
return sqrt((Qmax_by_CpT*(self.g+1) + 1) + sqrt(((self.g+1)*Qmax_by_CpT+1)**2 - 1))
|