def max_deflection(M_1, gamma=1.4):
"""Returns maximum deflection angle and corresponding wave angle for given
Mach number.
Parameters
----------
M_1 : float
Upstream Mach number.
gamma : float, optional
Specific heat ratio, default 7 / 5.
Returns
-------
theta : float
Maximum deflection angle.
beta : float
Corresponding wave angle.
"""
def eq(beta, M_1, gamma):
os = _ShockClass(M_1, beta, gamma)
return -os.theta
mu = mach_angle(M_1)
beta_theta_max = optimize.fminbound(eq,
mu,
np.pi / 2,
args=(M_1, gamma),
disp=0)
os = _ShockClass(M_1, beta_theta_max, gamma)
return os.theta, os.beta
def max_deflection(M_1, gamma=1.4):
"""Returns maximum deflection angle and corresponding wave angle for given
Mach number.
Parameters
----------
M_1 : float
Upstream Mach number.
gamma : float, optional
Specific heat ratio, default 7 / 5.
Returns
-------
theta : float
Maximum deflection angle.
beta : float
Corresponding wave angle.
"""
def eq(beta, M_1, gamma):
os = _ShockClass(M_1, beta, gamma)
return -os.theta
mu = mach_angle(M_1)
beta_theta_max = optimize.fminbound(eq, mu, np.pi / 2, args=(M_1, gamma), disp=0)
os = _ShockClass(M_1, beta_theta_max, gamma)
return os.theta, os.beta
def _from_deflection_angle(M_1, theta, weak, gamma):
"""Returns oblique shock given upstream Mach number and deflection angle.
"""
def eq(beta, M_1, theta, gamma):
os = _ShockClass(M_1, beta, gamma)
return os.theta - theta
theta_max, beta_theta_max = max_deflection(M_1)
if theta > theta_max:
raise ValueError("No attached solution for this deflection angle")
else:
if weak:
mu = mach_angle(M_1)
beta = optimize.bisect(eq,
mu,
beta_theta_max,
args=(M_1, theta, gamma))
else:
beta = optimize.bisect(eq,
beta_theta_max,
np.pi / 2,
args=(M_1, theta, gamma))
return _ShockClass(M_1, beta, gamma)
def test_mach_angle():
M_list = [1.1, 1.38, 2.05, 3.0, np.inf]
mu_list = [65.38, 46.44, 29.20, 19.47, 0.0]
expected_mach_angles = [np.radians(val) for val in mu_list]
mach_angles = [isentropic.mach_angle(M) for M in M_list]
np.testing.assert_array_almost_equal(mach_angles,
expected_mach_angles,
decimal=3)
def __init__(self, M_1, beta, gamma):
mu = mach_angle(M_1)
if beta < mu:
raise ValueError(
"Shock wave angle must be higher than Mach angle {:.2f}°".
format(np.degrees(mu)))
self.M_1 = M_1
self.M_1n = M_1 * np.sin(beta) if beta != 0.0 else 0.0
self.beta = beta
self.gamma = gamma
def __init__(self, M_1, beta, gamma):
mu = mach_angle(M_1)
if beta < mu:
raise ValueError(
"Shock wave angle must be higher than Mach angle {:.2f}°"
.format(np.degrees(mu)))
self.M_1 = M_1
self.M_1n = M_1 * np.sin(beta) if beta != 0.0 else 0.0
self.beta = beta
self.gamma = gamma
def theta(self):
"""Deflection angle of the shock.
"""
if self.beta == mach_angle(self.M_1) or self.beta == np.pi / 2:
theta = 0.0
else:
theta = np.arctan(
2 / np.tan(self.beta) *
(np.sin(self.beta)**2 - 1 / self.M_1 / self.M_1) /
(self.gamma + np.cos(2 * self.beta) + 2 / self.M_1 / self.M_1))
return theta
def theta(self):
"""Deflection angle of the shock.
"""
if self.beta == mach_angle(self.M_1) or self.beta == np.pi / 2:
theta = 0.0
else:
theta = np.arctan(
2 / np.tan(self.beta) *
(np.sin(self.beta) ** 2 - 1 / self.M_1 / self.M_1) /
(self.gamma + np.cos(2 * self.beta) + 2 / self.M_1 / self.M_1))
return theta
def test_mach_angle():
M_list = [1.1, 1.38, 2.05, 3.0, np.inf]
mu_list = [
65.38,
46.44,
29.20,
19.47,
0.0
]
expected_mach_angles = [np.radians(val) for val in mu_list]
mach_angles = [isentropic.mach_angle(M) for M in M_list]
np.testing.assert_array_almost_equal(mach_angles,
expected_mach_angles,
decimal=3)
def _from_deflection_angle(M_1, theta, weak, gamma):
"""Returns oblique shock given upstream Mach number and deflection angle.
"""
def eq(beta, M_1, theta, gamma):
os = _ShockClass(M_1, beta, gamma)
return os.theta - theta
theta_max, beta_theta_max = max_deflection(M_1)
if theta > theta_max:
raise ValueError("No attached solution for this deflection angle")
else:
if weak:
mu = mach_angle(M_1)
beta = sp.optimize.bisect(
eq, mu, beta_theta_max, args=(M_1, theta, gamma))
else:
beta = sp.optimize.bisect(
eq, beta_theta_max, np.pi / 2, args=(M_1, theta, gamma))
return _ShockClass(M_1, beta, gamma)
def test_mach_angle_raises_error_when_mach_is_subsonic():
with pytest.raises(ValueError) as excinfo:
isentropic.mach_angle(0.8)
assert excinfo.exconly().startswith("ValueError: "
"Mach number must be supersonic")
def test_mach_angle_raises_error_when_mach_is_subsonic():
with pytest.raises(ValueError) as excinfo:
isentropic.mach_angle(0.8)
assert excinfo.exconly().startswith("ValueError: "
"Mach number must be supersonic")
