def mach_from_nu(nu, in_radians=True, gamma=1.4):
r"""Computes the Mach number given a Prandtl-Meyer angle, :math:`\nu`.
Uses the relation between Mach number and Prandtl-Meyer angle for
isentropic flow, to iteratively compute and return the Mach number.
Parameters
----------
nu : float
Prandtl-Meyer angle, by default in radians.
in_radians : bool, optional
When set as False, converts nu from degrees to radians.
gamma : float, optional
Specific heat ratio.
Returns
-------
M : float
Mach number corresponding to :math:`\nu`.
Raises
------
ValueError
If :math:`\nu` is 0 or negative or above the theoretical maxima based on
:math:`\gamma`.
"""
if not in_radians:
nu = np.radians(nu)
nu_max = np.pi / 2.0 * (np.sqrt((gamma + 1.0) / (gamma - 1.0)) - 1)
if nu <= 0.0 or nu >= nu_max:
raise ValueError(
"Prandtl-Meyer angle must be between (0, %f) radians." % nu_max
)
eq = implicit(PrandtlMeyerExpansion.nu)
M = sp.optimize.newton(eq, 2.0, args=(nu,))
return M
def mach_from_nu(nu, in_radians=True, gamma=1.4):
r"""Computes the Mach number given a Prandtl-Meyer angle, :math:`\nu`.
Uses the relation between Mach number and Prandtl-Meyer angle for
isentropic flow, to iteratively compute and return the Mach number.
Parameters
----------
nu : float
Prandtl-Meyer angle, by default in radians.
in_radians : bool, optional
When set as False, converts nu from degrees to radians.
gamma : float, optional
Specific heat ratio.
Returns
-------
M : float
Mach number corresponding to :math:`\nu`.
Raises
------
ValueError
If :math:`\nu` is 0 or negative or above the theoretical maxima based on
:math:`\gamma`.
"""
if not in_radians:
nu = np.radians(nu)
nu_max = np.pi / 2.0 * (np.sqrt((gamma + 1.0) / (gamma - 1.0)) - 1)
if nu <= 0.0 or nu >= nu_max:
raise ValueError(
"Prandtl-Meyer angle must be between (0, %f) radians." % nu_max)
eq = implicit(PrandtlMeyerExpansion.nu)
M = newton(eq, 2.0, args=(nu, ))
return M
def mach_from_area_ratio(A_Astar, fl=None):
"""Computes the Mach number given an area ratio asuming isentropic flow.
Uses the relation between Mach number and area ratio for isentropic flow,
and returns both the subsonic and the supersonic solution.
Parameters
----------
A_Astar : float
Cross sectional area.
fl : IsentropicFlow, optional
Isentropic flow object, default flow with gamma = 7 / 5.
Returns
-------
out : tuple of floats
Subsonic and supersonic Mach number solution of the equation.
Raises
------
ValueError
If the area ratio is less than 1.0 (the critical area is always the
minimum).
"""
if not fl:
fl = IsentropicFlow(gamma=1.4)
eq = implicit(fl.A_Astar)
if A_Astar < 1.0:
raise ValueError("Area ratio must be greater than 1")
elif A_Astar == 1.0:
M_sub = M_sup = 1.0
else:
M_sub = sp.optimize.bisect(eq, 0.0, 1.0, args=(A_Astar,))
M_sup = sp.optimize.newton(eq, 2.0, args=(A_Astar,))
return M_sub, M_sup
def mach_from_area_ratio(A_Astar, fl=None):
"""Computes the Mach number given an area ratio asuming isentropic flow.
Uses the relation between Mach number and area ratio for isentropic flow,
and returns both the subsonic and the supersonic solution.
Parameters
----------
A_Astar : float
Cross sectional area.
fl : IsentropicFlow, optional
Isentropic flow object, default flow with gamma = 7 / 5.
Returns
-------
out : tuple of floats
Subsonic and supersonic Mach number solution of the equation.
Raises
------
ValueError
If the area ratio is less than 1.0 (the critical area is always the
minimum).
"""
if not fl:
fl = IsentropicFlow(gamma=1.4)
eq = implicit(fl.A_Astar)
if A_Astar < 1.0:
raise ValueError("Area ratio must be greater than 1")
elif A_Astar == 1.0:
M_sub = M_sup = 1.0
else:
M_sub = bisect(eq, 0.0, 1.0, args=(A_Astar, ))
M_sup = newton(eq, 2.0, args=(A_Astar, ))
return M_sub, M_sup