def M(self,
p_p0=None,
rho_rho0=None,
T_T0=None,
A_Astar=None,
*args,
**kwargs):
"""
Computes Mach number when one of the arguments are specified
"""
g = self.gamma
if p_p0 is not None:
M = np.sqrt(2. * ((1. / np.power(p_p0,
(g - 1.) / g)) - 1.) / (g - 1.))
elif rho_rho0 is not None:
M = np.sqrt(2. * ((1. / np.power(rho_rho0,
(g - 1.))) - 1.) / (g - 1.))
elif T_T0 is not None:
M = np.sqrt(2. * ((1. / T_T0) - 1.) / (g - 1.))
elif A_Astar is not None:
Msub, Msup = mach_from_area_ratio(A_Astar)
M = np.array([Msub, Msup])
elif 'M' in kwargs.keys():
return kwargs['M']
else:
logger.error('Insufficient data to calculate Mach number')
return M
def test_mach_from_area_ratio_supersonic():
fl = isentropic.IsentropicFlow(1.4)
A_Astar_list = [1.0, 1.043, 1.328, 1.902, 4.441]
expected_ratios = [1.0, 1.24, 1.69, 2.14, 3.05]
mach_from_area_ratios = [
isentropic.mach_from_area_ratio(A_Astar, fl)[1] # Supersonic
for A_Astar in A_Astar_list
]
np.testing.assert_array_almost_equal(mach_from_area_ratios,
expected_ratios,
decimal=2)
def test_mach_from_area_ratio_subsonic():
fl = isentropic.IsentropicFlow(1.4)
A_Astar_list = [
np.inf,
2.4027,
1.7780,
1.0382,
1.0,
]
expected_ratios = [0.0, 0.25, 0.35, 0.8, 1.0]
mach_from_area_ratios = [
isentropic.mach_from_area_ratio(A_Astar, fl)[0] # Subsonic
for A_Astar in A_Astar_list
]
np.testing.assert_array_almost_equal(mach_from_area_ratios,
expected_ratios,
decimal=3)
def M(self, p_p0=None, rho_rho0=None,
T_T0=None, A_Astar=None, *args, **kwargs):
"""
Computes Mach number when one of the arguments are specified
"""
g = self.gamma
if p_p0 is not None:
M = np.sqrt(2. * ((1./np.power(p_p0, (g-1.)/g)) - 1.) / (g-1.))
elif rho_rho0 is not None:
M = np.sqrt(2. * ((1./np.power(rho_rho0, (g-1.))) - 1.) / (g-1.))
elif T_T0 is not None:
M = np.sqrt(2. * ((1./T_T0)-1.)/(g-1.))
elif A_Astar is not None:
Msub, Msup = mach_from_area_ratio(A_Astar)
M = np.array([Msub, Msup])
elif 'M' in kwargs.keys():
return kwargs['M']
else:
logger.error('Insufficient data to calculate Mach number')
return M
def test_mach_from_area_ratio_subsonic():
fl = isentropic.IsentropicFlow(1.4)
A_Astar_list = [
np.inf,
2.4027,
1.7780,
1.0382,
1.0,
]
expected_ratios = [
0.0,
0.25,
0.35,
0.8,
1.0
]
mach_from_area_ratios = [
isentropic.mach_from_area_ratio(A_Astar, fl)[0] # Subsonic
for A_Astar in A_Astar_list]
np.testing.assert_array_almost_equal(
mach_from_area_ratios, expected_ratios, decimal=3
)
def test_mach_from_area_ratio_supersonic():
fl = isentropic.IsentropicFlow(1.4)
A_Astar_list = [
1.0,
1.043,
1.328,
1.902,
4.441
]
expected_ratios = [
1.0,
1.24,
1.69,
2.14,
3.05
]
mach_from_area_ratios = [
isentropic.mach_from_area_ratio(A_Astar, fl)[1] # Supersonic
for A_Astar in A_Astar_list]
np.testing.assert_array_almost_equal(
mach_from_area_ratios, expected_ratios, decimal=2
)
def solve_flow(self, fl, p_0, T_0, p_B):
"""Solves the flow through the nozzle.
For the time being, it assumes isentropic flow and uses a quasi one
dimensional model.
Parameters
----------
fl : IsentropicFlow
Isentropic flow through the nozzle.
p_0 : float
Stagnation pressure at the reservoir.
T_0 : float
Stagnation temperature at the reservoir.
p_B : float
Back pressure at the exit section.
Returns
-------
M : array
Mach distribution along the nozzle.
p : array
Pressure distribution along the nozzle.
Raises
------
ValueError
If the back pressure is higher than the reservoir pressure.
Notes
-----
First of all, the function computes the isentropic conditions to
discriminate if we have fully subsonic flow, chocked flow with shock
inside nozzle or chocked fully supersonic flow.
"""
p_ratio = p_B / p_0
if p_ratio > 1.0:
raise ValueError(
"Back pressure must be lower than reservoir pressure")
# Exit and minimum area
A_e = self.A[-1]
A_min = np.min(self.A)
i_min = np.argmin(self.A)
# 1. Compute isentropic conditions at the exit
# Points 1 (subsonic) and 2 (supersonic)
M_e_1, M_e_2 = isentropic.mach_from_area_ratio(fl, A_e / A_min)
pe_p0_1 = fl.p_p0(M_e_1)
pe_p0_2 = fl.p_p0(M_e_2)
# 2. Normal shock at the exit of the nozzle
ns_e = shocks.NormalShock(M_e_2)
pe_p0_3 = pe_p0_2 * ns_e.p2_p1
# 3. Discriminate case
M = np.empty_like(self.x)
p = np.empty_like(self.x)
if pe_p0_1 <= p_ratio <= 1.0:
print("Fully subsonic flow")
# 1. Compute M_e (inverse fl.p_p0(M))
# 2. Compute area ratio from M_e (fl.A_Ac(M_e))
# 3. The area ratio in each point is A_Ac = A * Ae_Ac / Ae
# so I can compute the Mach number distribution
elif pe_p0_3 <= p_ratio < pe_p0_1:
print("Shock inside the nozzle")
# First I have to compute shock location and properties
elif p_ratio < pe_p0_3:
print("Fully isentropic subsonic-supersonic flow")
# I already have Ac = A_min, so I can directly compute the Mach
# number distribution
Ac = A_min
for i in range(i_min + 1):
M[i] = isentropic.mach_from_area_ratio(fl, self.A[i] / Ac)[0]
for i in range(i_min, len(M)):
M[i] = isentropic.mach_from_area_ratio(fl, self.A[i] / Ac)[1]
# Stagnation pressure does not change, as the flow is fully
# isentropic
p = p_0 * fl.p_p0(M)
return M, p
def test_mach_from_area_ratio_raises_error_when_ratio_is_subsonic():
with pytest.raises(ValueError):
isentropic.mach_from_area_ratio(0.9)
def test_mach_from_area_ratio_raises_error_when_ratio_is_subsonic():
with pytest.raises(ValueError):
isentropic.mach_from_area_ratio(0.9)
def solve_flow(self, fl, p_0, T_0, p_B):
"""Solves the flow through the nozzle.
For the time being, it assumes isentropic flow and uses a quasi one
dimensional model.
Parameters
----------
fl : IsentropicFlow
Isentropic flow through the nozzle.
p_0 : float
Stagnation pressure at the reservoir.
T_0 : float
Stagnation temperature at the reservoir.
p_B : float
Back pressure at the exit section.
Returns
-------
M : array
Mach distribution along the nozzle.
p : array
Pressure distribution along the nozzle.
Raises
------
ValueError
If the back pressure is higher than the reservoir pressure.
Notes
-----
First of all, the function computes the isentropic conditions to
discriminate if we have fully subsonic flow, chocked flow with shock
inside nozzle or chocked fully supersonic flow.
"""
p_ratio = p_B / p_0
if p_ratio > 1.0:
raise ValueError(
"Back pressure must be lower than reservoir pressure")
# Exit and minimum area
A_e = self.A[-1]
A_min = np.min(self.A)
i_min = np.argmin(self.A)
# 1. Compute isentropic conditions at the exit
# Points 1 (subsonic) and 2 (supersonic)
M_e_1, M_e_2 = isentropic.mach_from_area_ratio(fl, A_e / A_min)
pe_p0_1 = fl.p_p0(M_e_1)
pe_p0_2 = fl.p_p0(M_e_2)
# 2. Normal shock at the exit of the nozzle
ns_e = shocks.NormalShock(M_e_2)
pe_p0_3 = pe_p0_2 * ns_e.p2_p1
# 3. Discriminate case
M = np.empty_like(self.x)
p = np.empty_like(self.x)
if pe_p0_1 <= p_ratio <= 1.0:
print("Fully subsonic flow")
# 1. Compute M_e (inverse fl.p_p0(M))
# 2. Compute area ratio from M_e (fl.A_Ac(M_e))
# 3. The area ratio in each point is A_Ac = A * Ae_Ac / Ae
# so I can compute the Mach number distribution
elif pe_p0_3 <= p_ratio < pe_p0_1:
print("Shock inside the nozzle")
# First I have to compute shock location and properties
elif p_ratio < pe_p0_3:
print("Fully isentropic subsonic-supersonic flow")
# I already have Ac = A_min, so I can directly compute the Mach
# number distribution
Ac = A_min
for i in range(i_min + 1):
M[i] = isentropic.mach_from_area_ratio(fl, self.A[i] / Ac)[0]
for i in range(i_min, len(M)):
M[i] = isentropic.mach_from_area_ratio(fl, self.A[i] / Ac)[1]
# Stagnation pressure does not change, as the flow is fully
# isentropic
p = p_0 * fl.p_p0(M)
return M, p
