/usr/lib/python2.7/dist-packages/gastables/NormalShock.py is in python-gastables 0.3-2.2.
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Assumptions:
1) One dimensional flow
2) Constant area duct
3) Perfect gas with constant specific heat and molecular weights
4) Adiabatic flow
"""
"""
* 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 *
from Isentropic import Isentropic
class NormalShock:
def __init__(self, g=1.4):
""" g is the value of gamma (ratio of specific heats), default = 1.4
"""
self.g = 1.4
self.Isentropic = Isentropic(self.g)
def get_My_from_Mx(self, Mx):
"""Returns Mach No My behind a normal shock from Mach No Mx ahead of the shock"""
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
return sqrt((2/(self.g-1) + Mx**2)/(2*self.g/(self.g-1)*Mx**2 -1))
def get_Py_by_Px_from_Mx(self, Mx):
"""Returns py/px across a normal shock from Mx """
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
return 2*self.g/(self.g+1)* Mx**2 - (self.g-1)/(self.g+1)
def get_Ty_by_Tx_from_Mx(self, Mx):
"""Returns Ty/Tx across a normal shock from Mx """
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
return (1 + (self.g-1)*0.5* Mx**2)*(2*self.g/(self.g-1)*Mx**2 - 1)/((self.g+1)**2/(self.g-1)*0.5* Mx**2)
def get_rhoy_by_rhox_from_Mx(self, Mx):
"""Returns rhoy/rhox across a normal shock from Mx"""
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
return self.get_Py_by_Px_from_Mx(Mx) / self.get_Ty_by_Tx_from_Mx(Mx)
def get_Poy_by_Pox_from_Mx(self, Mx):
"""Returns poy/pox across a normal shock from Mx"""
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
My = self.get_My_from_Mx(Mx)
return self.Isentropic.get_P_by_Po_from_M(Mx) * self.get_Py_by_Px_from_Mx(Mx) / self.Isentropic.get_P_by_Po_from_M(My)
def get_Poy_by_Px_from_Mx(self, Mx):
"""Returns poy/px across a normal shock from Mx"""
if Mx <= 1:
raise Exception("Mach No ahead of ths shock Mx should be greater than 1")
else:
My = self.get_My_from_Mx(Mx)
return self.get_Py_by_Px_from_Mx(Mx) / self.Isentropic.get_P_by_Po_from_M(My)
def get_Mx_from_My(self, My):
"""Returns Mach No Mx ahead of a normal shock from Mach No My behind the shock"""
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else:
return sqrt((1 + (self.g-1)* 0.5 * My**2)/(self.g * My**2 - (self.g-1)*0.5))
def get_Py_by_Px_from_My(self, My):
"""Returns py/px across a normal shock from My """
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else :
Mx = self.get_Mx_from_My(My)
return self.get_Py_by_Px_from_Mx(Mx)
def get_Ty_by_Tx_from_My(self, My):
"""Returns Ty/Tx across a normal shock from My """
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else :
Mx = self.get_Mx_from_My(My)
return self.get_Ty_by_Tx_from_Mx(Mx)
def get_rhoy_by_rhox_from_My(self, My):
"""Returns rhoy/rhox across a normal shock from My"""
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else :
Mx = self.get_Mx_from_My(My)
return self.get_rhoy_by_rhox_from_Mx(Mx)
def get_Poy_by_Pox_from_My(self, My):
"""Returns poy/pox across a normal shock from My"""
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else :
Mx = self.get_Mx_from_My(My)
return self.get_Poy_by_Pox_from_Mx(Mx)
def get_Poy_by_Px_from_My(self, My):
"""Returns poy/px across a normal shock from My"""
if My >= 1.0 or My <= sqrt((self.g-1)/self.g * 0.5):
raise Exception("Mach No behind a normal shock My should be between %s and 1.0" % str(sqrt((self.g-1)/self.g * 0.5)))
else :
Mx = self.get_Mx_from_My(My)
return self.get_Poy_by_Px_from_Mx(Mx)
def get_Mx_from_Ty_by_Tx(self, Ty_by_Tx):
"""Returns Mx from Ty/Tx equal to Ty_by_Tx"""
if Ty_by_Tx <= 1.0:
raise Exception("Ty/Tx must be greater than 1")
else:
a = 2*self.g*(self.g-1)
b = 4*self.g - (self.g-1)**2 - Ty_by_Tx * (self.g+1)**2
c = -2*(self.g-1)
return sqrt((-b + sqrt(b**2 - 4*a*c))/a *0.5)
def get_My_from_Ty_by_Tx(Self, Ty_by_Tx):
"""Returns Mx from Ty/Tx equal to Ty_by_Tx"""
if Ty_by_Tx <= 1.0:
raise Exception("Ty/Tx must be greater than 1")
else:
Mx = self.get_Mx_from_Ty_by_Tx(Ty_by_Tx)
return self.get_My_from_Mx(Mx)
def get_Py_by_Px_from_Ty_by_Tx(self, Ty_by_Tx):
"""Returns Py/Px from Ty/Tx equal to Ty_by_Tx"""
if Ty_by_Tx <= 1.0:
raise Exception("Ty/Tx must be greater than 1")
else:
Mx = self.get_Mx_from_Ty_by_Tx(Ty_by_Tx)
return self.get_Py_by_Px_from_Mx(Mx)
def get_Poy_by_Pox_from_Ty_by_Tx(self, Ty_by_Tx):
"""Returns poy/pox from Ty/Tx equal to Ty_by_Tx"""
if Ty_by_Tx <= 1.0:
raise Exception("Ty/Tx must be greater than 1")
else:
Mx = self.get_Mx_from_Ty_by_Tx(Ty_by_Tx)
return self.get_Poy_by_Pox_from_Mx(Mx)
def get_Poy_by_Px_from_Ty_by_Tx(self, Ty_by_Tx):
"""Returns poy/px from Ty/Tx equal to Ty_by_Tx"""
if Ty_by_Tx <= 1.0:
raise Exception("Ty/Tx must be greater than 1")
else:
Mx = self.get_Mx_from_Ty_by_Tx(Ty_by_Tx)
return self.get_Poy_by_Px_from_Mx(Mx)
def get_Mx_from_Py_by_Px(self, Py_by_Px):
"""Returns Mx from py/px equal to Py_by_Px"""
if Py_by_Px <= 1:
raise Exception("py/px must be greater than 1")
else:
return sqrt((Py_by_Px - 1)* (self.g+1)/self.g * 0.5 + 1)
def get_My_from_Py_by_Px(self, Py_by_Px):
"""Returns My from py/px equal to Py_by_Px"""
if Py_by_Px <= 1:
raise Exception("py/px must be greater than 1")
else:
Mx = self.get_Mx_from_Py_by_Px(Py_by_Px)
return self.get_My_from_Mx(Mx)
def get_Ty_by_Tx_from_Py_by_Px(self, Py_by_Px):
"""Returns Ty/Tx from py/px equal to Py_by_Px"""
if Py_by_Px <= 1:
raise Exception("py/px must be greater than 1")
else:
Mx = self.get_Mx_from_Py_by_Px(Py_by_Px)
return self.get_Ty_by_Tx_from_Mx(Mx)
def get_Poy_by_Pox_from_Py_by_Px(self, Py_by_Px):
"""Returns poy/pox from Py/Px equal to Py_by_Px"""
if Py_by_Px <= 1:
raise Exception("py/px must be greater than 1")
else:
Mx = self.get_Mx_from_Py_by_Px(Py_by_Px)
return self.get_Poy_by_Pox_from_Mx(Mx)
def get_Poy_by_Px_from_Py_by_Px(self, Py_by_Px):
"""Returns Poy/Px from Py/Px equal to Py_by_Px"""
if Py_by_Px <= 1:
raise Exception("py/px must be greater than 1")
else:
Mx = self.get_Mx_from_Py_by_Px(Py_by_Px)
return self.get_Poy_by_Px_from_Mx(Mx)
def get_Mx_from_rhoy_by_rhox(self, rhoy_by_rhox):
"""Returns Mx from rhoy/rhox equal to rhoy_by_rhox"""
if rhoy_by_rhox <=1.0 or rhoy_by_rhox >= (self.g+1)/(self.g-1):
raise Exception("rhoy/rhox should be between 1 and ",(self.g+1)/(self.g-1))
else:
return sqrt(2*rhoy_by_rhox/(self.g+1- rhoy_by_rhox*(self.g-1)))
def get_My_from_rhoy_by_rhox(self, rhoy_by_rhox):
"""Returns My from rhoy/rhox equal to rhoy_by_rhox"""
if rhoy_by_rhox <=1.0 or rhoy_by_rhox >= (self.g+1)/(self.g-1):
raise Exception("rhoy/rhox should be between 1 and ",(self.g+1)/(self.g-1))
else:
Mx = self.get_Mx_from_rhoy_by_rhox(rhoy_by_rhox)
return self.get_My_from_Mx(Mx)
def get_Ty_by_Tx_from_rhoy_by_rhox(self, rhoy_by_rhox):
"""Returns Ty/Tx from rhoy/rhox equal to rhoy_by_rhox"""
if rhoy_by_rhox <=1.0 or rhoy_by_rhox >= (self.g+1)/(self.g-1):
raise Exception("rhoy/rhox should be between 1 and ",(self.g+1)/(self.g-1))
else:
Mx = self.get_Mx_from_rhoy_by_rhox(rhoy_by_rhox)
return self.get_Ty_by_Tx_from_Mx(Mx)
def get_Poy_by_Pox_from_rhoy_by_rhox(self, rhoy_by_rhox):
"""Returns poy/pox from rhoy/rhox equal to rhoy_by_rhox"""
if rhoy_by_rhox <=1.0 or rhoy_by_rhox >= (self.g+1)/(self.g-1):
raise Exception("rhoy/rhox should be between 1 and ",(self.g+1)/(self.g-1))
else:
Mx = self.get_Mx_from_rhoy_by_rhox(rhoy_by_rhox)
return self.get_Poy_by_Pox_from_Mx(Mx)
def get_Poy_by_Px_from_rhoy_by_rhox(self, rhoy_by_rhox):
"""Returns poy/px from rhoy/rhox equal to rhoy_by_rhox"""
if rhoy_by_rhox <=1.0 or rhoy_by_rhox >= (self.g+1)/(self.g-1):
raise Exception("rhoy/rhox should be between 1 and ",(self.g+1)/(self.g-1))
else:
Mx = self.get_Mx_from_rhoy_by_rhox(rhoy_by_rhox)
return self.get_Poy_by_Px_from_Mx(Mx)
def get_Mx_from_Poy_by_Pox(self, Poy_by_Pox):
"""Returns Mx from poy/pox equal to Poy_by_Pox"""
if Poy_by_Pox <= 0 or Poy_by_Pox >= 1:
raise Exception("Poy/Pox must be between 0 and 1")
else:
return optimize.fsolve(lambda Mx: self.get_Poy_by_Pox_from_Mx(Mx) - Poy_by_Pox, 2.0)
def get_My_from_Poy_by_Pox(self, Poy_by_Pox):
"""Returns My from poy/pox equal to Poy_by_Pox"""
if Poy_by_Pox <= 0 or Poy_by_Pox >= 1:
raise Exception("Poy/Pox must be between 0 and 1")
else:
Mx = self.get_Mx_from_Poy_by_Pox(Poy_by_Pox)
return self.get_My_from_Mx(Mx)
def get_Ty_by_Tx_from_Poy_by_Pox(self, Poy_by_Pox):
"""Returns Ty/Tx from poy/pox equal to Poy_by_Pox"""
if Poy_by_Pox <= 0 or Poy_by_Pox >= 1:
raise Exception("Poy/Pox must be between 0 and 1")
else:
Mx = self.get_Mx_from_Poy_by_Pox(Poy_by_Pox)
return self.get_Ty_by_Tx_from_Mx(Mx)
def get_Py_by_Px_from_Poy_by_Pox(self, Poy_by_Pox):
"""Returns py/px from poy/pox equal to Poy_by_Pox"""
if Poy_by_Pox <= 0 or Poy_by_Pox >= 1:
raise Exception("Poy/Pox must be between 0 and 1")
else:
Mx = self.get_Mx_from_Poy_by_Pox(Poy_by_Pox)
return self.get_Py_by_Px_from_Mx(Mx)
def get_Poy_by_Px_from_Poy_by_Pox(self, Poy_by_Pox):
"""Returns poy/px from poy/pox equal to Poy_by_Pox"""
if Poy_by_Pox <= 0 or Poy_by_Pox >= 1:
raise Exception("Poy/Pox must be between 0 and 1")
else:
Mx = self.get_Mx_from_Poy_by_Pox(Poy_by_Pox)
return self.get_Poy_by_Px_from_Mx(Mx)
def get_Mx_from_Poy_by_Px(self, Poy_by_Px):
"""Returns Mx from poy/px equal to Poy_by_Px"""
if Poy_by_Px <= ((self.g+1)*0.5)**(self.g/(self.g-1)):
raise Exception("Poy/Px should be greater than",((self.g+1)*0.5)**(self.g/(self.g-1)))
else:
return optimize.fsolve(lambda Mx: self.get_Poy_by_Px_from_Mx(Mx) - Poy_by_Px, 2.0)
def get_My_from_Poy_by_Px(self, Poy_by_Px):
"""Returns My from poy/px equal to Poy_by_Px"""
if Poy_by_Px <= ((self.g+1)*0.5)**(self.g/(self.g-1)):
raise Exception("Poy/Px should be greater than",((self.g+1)*0.5)**(self.g/(self.g-1)))
else:
Mx = self.get_Mx_from_Poy_by_Px(Poy_by_Px)
return self.get_My_from_Mx(Mx)
def get_Ty_by_Tx_from_Poy_by_Px(self, Poy_by_Px):
"""Returns Mx from poy/px equal to Poy_by_Px"""
if Poy_by_Px <= ((self.g+1)*0.5)**(self.g/(self.g-1)):
raise Exception("Poy/Px should be greater than",((self.g+1)*0.5)**(self.g/(self.g-1)))
else:
Mx = self.get_Mx_from_Poy_by_Px(Poy_by_Px)
return self.get_Ty_by_Tx_from_Mx(Mx)
def get_Py_by_Px_from_Poy_by_Px(self, Poy_by_Px):
"""Returns py/px from poy/px equal to Poy_Px"""
if Poy_by_Px <= ((self.g+1)*0.5)**(self.g/(self.g-1)):
raise Exception("Poy/Px should be greater than",((self.g+1)*0.5)**(self.g/(self.g-1)))
else:
Mx = self.get_Mx_from_Poy_by_Px(Poy_by_Px)
return self.get_Py_by_Px_from_Mx(Mx)
def get_Poy_by_Pox_from_Poy_by_Px(self, Poy_by_Px):
"""Returns poy/pox from poy/px equal to Poy_by_Px """
if Poy_by_Px <= ((self.g+1)*0.5)**(self.g/(self.g-1)):
raise Exception("Poy/Px should be greater than",((self.g+1)*0.5)**(self.g/(self.g-1)))
else:
Mx = self.get_Mx_from_Poy_by_Px(Poy_by_Px)
return self.get_Poy_by_Pox_from_Mx(Mx)
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