def sigmaSonic(Mach, gamma=1.4):
""" computes the shock angle for a downstream SONIC Mach number
"""
M2 = np.square(Mach)
ka = gamma-3+M2*(gamma+1)
kb = (gamma+1)*(np.square(M2-3)+gamma*np.square(M2+1))
return degree.asin(np.sqrt((ka+np.sqrt(kb))/(4*gamma*M2)))
def weaksigma_Mach_deflection(Mach, deflection, gamma=1.4):
ka = (1. + .5*(gamma+1.)*Mach**2)*degree.tan(deflection)
kb = 1. - Mach**2
kc = (1. + .5*(gamma-1.)*Mach**2)*degree.tan(deflection)
kd = (ka**2/3. - kb)/3.
ke = 2.*ka**3/27. - ka*kb/3. + kc
if ke**2 - 4.*kd**3 > 0:
print "no weak shock wave solution"
return degree.asin(1./Mach)
else:
phi = math.acos(-.5*ke/math.sqrt(kd**3))
kf = 2.*math.sqrt(kd)*math.cos(phi/3.) - ka/3.
return degree.atan(1./kf)
def sigma_Mach_deflection(Mach, deflection, gamma=1.4):
def local_f(sig):
return deflection_Mach_sigma(Mach, sig, gamma)
return IterativeSolve.secant_solve(local_f, deflection, degree.asin(1./Mach)+deflection)
def deflection_Mach_ShockPsratio(Mach, Pratio, gamma=1.4):
return deflection_Mach_sigma(Mach, degree.asin(Mn_Ps_ratio(Pratio, gamma)/Mach), gamma)