def temperature_from_stagnation_temperature(g, T, M):
""" T = stagnation_temperature(g,Tt,M): compute temperature from stagnation temperature and Mach for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
Tt = stagnation temperature (required) (floats)
M = Mach number (required) (floats)
Outputs: T = absolute temperature (floats)
"""
return Tt / f_of_M(g, M)
def stagnation_temperature(g, T, M):
""" Tt = stagnation_temperature(g,T,M): compute stagnation temperature for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
T = absolute temperature (required) (floats)
M = Mach number (required) (floats)
Outputs: Tt = stagnation temperature (floats)
"""
return T * f_of_M(g, M)
def temperature_from_stagnation_temperature(g,T,M):
""" T = stagnation_temperature(g,Tt,M): compute temperature from stagnation temperature and Mach for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
Tt = stagnation temperature (required) (floats)
M = Mach number (required) (floats)
Outputs: T = absolute temperature (floats)
"""
return Tt/f_of_M(g,M)
def stagnation_temperature(g,T,M):
""" Tt = stagnation_temperature(g,T,M): compute stagnation temperature for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
T = absolute temperature (required) (floats)
M = Mach number (required) (floats)
Outputs: Tt = stagnation temperature (floats)
"""
return T*f_of_M(g,M)
def area_ratio_from_mach(g, M):
""" M = mach_from_area_ratio(g,area_ratio,branch="supersonic"): get M from A/A* and gamma for a 1D ideal gas flow
Inputs: g = ratio of specific heats (required) (float)
M = Mach number (required) (float)
Outputs: area_ratio = A/A* (float)
"""
n = (g + 1) / (2 * (g - 1))
c = ((g + 1) / 2)**n
return 1 / (c * M / f_of_M(g, M)**n)
def stagnation_pressure(g, p, M):
""" pt = stagnation_pressure(g,p,M): compute stagnation pressure for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
p = absolute pressure (required) (floats)
M = Mach number (required) (floats)
Outputs: pt = stagnation pressure (floats)
"""
n = g / (g - 1)
return p * f_of_M(g, M)**n
def area_ratio_from_mach(g,M):
""" M = mach_from_area_ratio(g,area_ratio,branch="supersonic"): get M from A/A* and gamma for a 1D ideal gas flow
Inputs: g = ratio of specific heats (required) (float)
M = Mach number (required) (float)
Outputs: area_ratio = A/A* (float)
"""
n = (g+1)/(2*(g-1))
c = ((g+1)/2)**n
return 1/(c*M/f_of_M(g,M)**n)
def pressure_from_stagnation_pressure(g,pt,M):
""" p = pressure_from_stagnation_pressure(g,pt,M): compute pressure from stagnation pressure and Mach for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
pt = stagnation pressure (required) (floats)
M = Mach number (required) (floats)
Outputs: p = absolute pressure (floats)
"""
n = g/(g-1)
return pt/(f_of_M(g,M)**n)
def stagnation_pressure(g,p,M):
""" pt = stagnation_pressure(g,p,M): compute stagnation pressure for a 1D ideal gas
Inputs: g = ratio of specific heats (required) (float)
p = absolute pressure (required) (floats)
M = Mach number (required) (floats)
Outputs: pt = stagnation pressure (floats)
"""
n = g/(g-1)
return p*f_of_M(g,M)**n
def dRdM(M, g, area_ratio, c, n):
f = f_of_M(g, M)
return -c * (-n * M * (g - 1) * M / (f**(n + 1)) + 1 / f**n)
def R(M, g, area_ratio, c, n):
return 1 / area_ratio - c * M / f_of_M(g, M)**n
def dRdM(M,g,area_ratio,c,n):
f = f_of_M(g,M)
return -c*(-n*M*(g-1)*M/(f**(n+1)) + 1/f**n)
def R(M,g,area_ratio,c,n):
return 1/area_ratio - c*M/f_of_M(g,M)**n