aero.MassFlow

In [1]:

import aerokit.aero.MassFlow   as mf
import numpy as np

import aerokit.aero.MassFlow as mf import numpy as np

Consider a nozzle in which a perfect gas is flowing ($\gamma = 1.4$ ; $r = 287$). The area of throat and exit sections are $A_\textrm{throat} = 0.1 m²$ and $A_\textrm{exit} = 0.25m²$.

Find the Mach number of the flow at the exit of the nozzle in an adapted supersonic regime.

In [2]:

A_throat = .1
A_exit = .25
sigma_Mexit = A_exit / A_throat
M_exit = mf.Mach_Sigma(sigma_Mexit)
print("The Mach number of the flow at the exit of the nozzle is M = {:.2f}.".format(M_exit))

A_throat = .1 A_exit = .25 sigma_Mexit = A_exit / A_throat M_exit = mf.Mach_Sigma(sigma_Mexit) print("The Mach number of the flow at the exit of the nozzle is M = {:.2f}.".format(M_exit))

The Mach number of the flow at the exit of the nozzle is M = 2.44.

Considering the following total pressure and total temperature of the flow $P_t = 1.07 \cdot 10^6$ Pa and $T_t = 300$ K.

Using weighted mass flow, what is the mass flow at the throat of the nozzle ?

In [3]:

M_throat = 1
m_dot_R = mf.WeightMassFlow(M_throat)
print("The weight mass flow is m_dot_R = {:.4f}".format(m_dot_R))
P_t = 1.07e6
T_t = 300.
r = 287.
m_dot = m_dot_R*(P_t*A_throat)/np.sqrt(r*T_t)
print("The mass flow is m_dot = {:.2f} kg/s".format(m_dot))

M_throat = 1 m_dot_R = mf.WeightMassFlow(M_throat) print("The weight mass flow is m_dot_R = {:.4f}".format(m_dot_R)) P_t = 1.07e6 T_t = 300. r = 287. m_dot = m_dot_R*(P_t*A_throat)/np.sqrt(r*T_t) print("The mass flow is m_dot = {:.2f} kg/s".format(m_dot))

The weight mass flow is m_dot_R = 0.6847
The mass flow is m_dot = 249.69 kg/s

The flow is now subsonic. Furthermore, the nature of the gas has changed, its specific constant is now $\gamma = 1.25$.

The Mach number at the throat is $M_\textrm{exit} = 0.85$.

Find $M_\textrm{exit}$, the Mach number at the exit of the nozzle, in this case.

In [4]:

A_throat = .1
A_exit = .25
sigma_Mthroat = mf.Sigma_Mach(.85, 1.25)
sigma_Mexit = (A_exit / A_throat)*sigma_Mthroat
M_exit = mf.MachSub_Sigma(sigma_Mexit, 1.25)
print("The Mach number of the flow at the exit of the nozzle is M = {:.2f}.".format(M_exit))

A_throat = .1 A_exit = .25 sigma_Mthroat = mf.Sigma_Mach(.85, 1.25) sigma_Mexit = (A_exit / A_throat)*sigma_Mthroat M_exit = mf.MachSub_Sigma(sigma_Mexit, 1.25) print("The Mach number of the flow at the exit of the nozzle is M = {:.2f}.".format(M_exit))

The Mach number of the flow at the exit of the nozzle is M = 0.24.