def m_from_critical_entropy(ep, flag="sub", gamma=1.4):
"""
Compute the Mach number given Fanno's Critical Entropy Parameter (s*-s)/R.
Parameters
----------
ep : array_like
Fanno's Critical Entropy Parameter (s*-s)/R. If float, list, tuple is given as
input, a conversion will be attempted.
Must be (s* - s) / R >= 0.
flag : string
Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
if np.any(ep < 0):
raise ValueError("It must be (s* - s) / R >= 0.")
# func = lambda M, r: r - Critical_Entropy_Parameter.__no_check(M, gamma)
func = lambda M, r: r - np.log((1 / M) * ((1 + ((gamma - 1) / 2) * M**2) / (1 + ((gamma - 1) / 2)))**((gamma + 1) / (2 * (gamma - 1))))
return apply_bisection(ep, func, flag=flag)
def m_from_prandtl_meyer_angle(angle, gamma=1.4):
"""
Compute the Mach number given the Prandtl Meyer angle.
Parameters
----------
angle : array_like
Prandtl Meyer angle [degrees].
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
M : array_like
Mach Number.
"""
nu_max = (np.sqrt((gamma + 1) / (gamma - 1)) - 1) * 90
assert np.all(angle >= 0) and np.all(
angle <= nu_max
), "Prandtl-Meyer angle must be between 0 and {}".format(nu_max)
angle = np.deg2rad(angle)
func = lambda M, a: a - (np.sqrt((gamma + 1) / (gamma - 1)) * np.arctan(
np.sqrt((gamma - 1) / (gamma + 1) *
(M**2 - 1))) - np.arctan(np.sqrt(M**2 - 1)))
return apply_bisection(angle, func, flag="sup")
def m_from_critical_total_pressure_ratio(ratio, flag="sub", gamma=1.4):
"""
Compute the Mach number given Fanno's Critical Total Pressure Ratio P0/P0*.
Parameters
----------
ratio : array_like
Fanno's Critical Total Pressure Ratio P0/P0*. If float, list, tuple is given as
input, a conversion will be attempted. Must be P0/P0* > 1.
flag : string
Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
if np.any(ratio < 1):
raise ValueError("It must be P/P* > 1.")
# func = lambda M, r: r - Critical_Total_Pressure_Ratio.__no_check(M, gamma)
func = lambda M, r: r - (1 / M) * ((1 + ((gamma - 1) / 2) * M**2) / ((gamma + 1) / 2))**((gamma + 1) / (2 * (gamma - 1)))
return apply_bisection(ratio, func, flag=flag)
def m_from_critical_area_ratio(ratio, flag="sub", gamma=1.4):
"""
Compute the Mach number given the Isentropic Critical Area Ratio A/A*.
Parameters
----------
ratio : array_like
Isentropic Critical Area Ratio A/A*. If float, list, tuple is given as input,
a conversion will be attempted. Must be A/A* >= 1.
flag : string
Can be either 'sub' (subsonic) or 'sup' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
assert np.all(ratio >= 1), "Area ratio must be A/A* >= 1."
func = lambda M, r: r - (((1 + (gamma - 1) / 2 * M**2) / (
(gamma + 1) / 2))**((gamma + 1) / (2 * (gamma - 1)))) / M
# func = lambda M, r: r - Critical_Area_Ratio.__no_check(M, gamma)
return apply_bisection(ratio, func, flag=flag)
def m_from_critical_entropy(ratio, flag="sub", gamma=1.4):
"""
Compute the Mach number given Rayleigh's Critical Entropy (s*-s)/R.
Parameters
----------
ratio : array_like
Rayleigh's Critical Critical Entropy (s*-s)/R. If float, list, tuple
is given as input, a conversion will be attempted.
Must be (s*-s)/R >= 0.
flag : string
Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
assert np.all(ratio >= 0), "It must be (s*-s)/R >= 0."
# func = lambda M, r: r - Critical_Entropy_Parameter.__no_check(M, gamma)
func = lambda M, r: r - (-gamma / (gamma - 1) * np.log(M**2 * (
(gamma + 1) / (1 + gamma * M**2))**((gamma + 1) / gamma)))
# TODO: need to adjust the extreme of the range where to apply bisection.
# If I try M_From_Critical_Entropy(1000) I get:
# ValueError: f(a) and f(b) must have different signs
return apply_bisection(ratio, func, flag=flag)
def m_from_critical_total_pressure_ratio(ratio, flag="sub", gamma=1.4):
"""
Compute the Mach number given Rayleigh's Critical Total Pressure Ratio P0/P0*.
Parameters
----------
ratio : array_like
Rayleigh's Critical Total Pressure Ratio P0/P0*. If float, list, tuple
is given as input, a conversion will be attempted.
If flag='sub', it must be 1 <= P0/P0* < P0/P0*(M=0).
Else, P0/P0* >= 1.
flag : string
Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
if flag == "sub":
upper_lim = critical_total_pressure_ratio(0, gamma)
assert np.all(ratio >= 1) and np.all(
ratio < upper_lim), "It must be 1 <= P0/P0* < {}".format(upper_lim)
else:
assert np.all(ratio >= 1), "It must be P0/P0* >= 1"
# func = lambda M, r: r - Critical_Total_Pressure_Ratio.__no_check(M, gamma)
func = lambda M, r: r - (1 + gamma) / (1 + gamma * M**2) * (
(1 + (gamma - 1) / 2 * M**2) / ((gamma + 1) / 2))**(gamma /
(gamma - 1))
return apply_bisection(ratio, func, flag=flag)
def m1_from_total_pressure_ratio(ratio, gamma=1.4):
""" Compute M1 from the total pressure ratio.
Parameters
----------
ratio : array_like
Total Pressure Ratio. If float, list, tuple is given as input,
a conversion will be attempted. Must be 0 <= P02/P01 <= 1.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Upstream Mach number M1.
"""
assert np.all(ratio >= 0) and np.all(ratio <= 1), (
"The total pressure ratio must be " + "0 <= P02/P01 <= 1")
func = lambda M1, r: r - (
(gamma + 1) * M1**2 /
(2 + (gamma - 1) * M1**2))**(gamma / (gamma - 1)) * (
(gamma + 1) / (2 * gamma * M1**2 - gamma + 1))**(1 / (gamma - 1))
return apply_bisection(ratio, func, "sup")
def m_from_critical_friction(fp, flag="sub", gamma=1.4):
"""
Compute the Mach number given Fanno's Critical Friction Parameter 4fL*/D.
Parameters
----------
fp : array_like
Fanno's Critical Friction Parameter 4fL*/D. If float, list, tuple is given as
input, a conversion will be attempted.
If flag="sub", it must be fp >= 0.
Else, 0 <= fp <= ((gamma + 1) * np.log((gamma + 1) / (gamma - 1)) - 2) / (2 * gamma)
flag : string
Can be either 'sub' (subsonic) or 'super' (supersonic). Default to 'sub'.
gamma : float
Specific heats ratio. Default to 1.4. Must be > 1.
Returns
-------
out : ndarray
Mach Number.
"""
if flag == "sub":
assert np.all(fp >= 0), 'It must be fp >= 0.'
else:
upper_lim = ((gamma + 1) * np.log(
(gamma + 1) / (gamma - 1)) - 2) / (2 * gamma)
print(upper_lim)
assert np.all(fp >= 0) and np.all(
fp <= upper_lim), 'It must be 0 <= fp <= {}'.format(upper_lim)
# TODO: when solving the supersonic case, and ratio -> upper limit,
# I get: ValueError: f(a) and f(b) must have different signs
# need to be dealt with!
# func = lambda M, r: r - Critical_Friction_Parameter.__no_check(M, gamma)
func = lambda M, r: r - (((gamma + 1) / (2 * gamma)) * np.log(
((gamma + 1) / 2) * M**2 / (1 + ((gamma - 1) / 2) * M**2)) +
(1 / gamma) * (1 / M**2 - 1))
return apply_bisection(fp, func, flag=flag)
