def set_NPR(self, NPR):
""" Define Nozzle Pressure Ratio (inlet Ptot over outlet Ps) for this case
Define Nozzle pressure ratio and compute Mach number, Ptot and Ps according to nozzle regime
:param NPR: NPR value (>1)
"""
self._Pt = np.ones_like(self.AxoAc)
if NPR < self.NPR0:
_Ms = Is.Mach_PtPs(NPR, gamma=self.gamma)
self._M = mf.MachSub_Sigma(self.AxoAc / self.AsoAc *
mf.Sigma_Mach(_Ms),
gamma=self.gamma)
self._Ps = self._Pt / Is.PtPs_Mach(self._M, gamma=self.gamma)
else:
self._M = np.ones_like(self.AxoAc)
self._M[:self.ithroat + 1] = mf.MachSub_Sigma(
self.AxoAc[:self.ithroat + 1], gamma=self.gamma)
self._M[self.ithroat + 1:] = mf.MachSup_Sigma(
self.AxoAc[self.ithroat + 1:], gamma=self.gamma)
if NPR < self.NPRsw:
# analytical solution for Ms, losses and upstream Mach number of shock wave
Ms = Ms_from_AsAc_NPR(self.AsoAc, NPR)
Ptloss = Is.PtPs_Mach(Ms) / NPR
Msh = sw.Mn_Pi_ratio(Ptloss)
# redefine curves starting from 'ish' index (closest value of Msh in supersonic flow)
ish = np.abs(self._M - Msh).argmin()
self._M[ish:] = mf.MachSub_Sigma(
self.AxoAc[ish:] * mf.Sigma_Mach(Ms) / self.AsoAc)
self._Pt[ish:] = Ptloss
self._Ps = self._Pt / Is.PtPs_Mach(self._M)
def NPR_choked_supersonic(AsAc):
"""Compute Nozzle Pressure Ratio to get a choked supersonic regime in a nozzle with As/Ac diffuser
Args:
AsAc ([real]): ratio of exit over throat surfaces
Returns:
[real]: Nozzle Pressure ratio (inlet total pressure over exit static pressure)
"""
return Is.PtPs_Mach(mf.MachSup_Sigma(AsAc))
def NPR_shock_at_exit(AsAc):
"""Compute Nozzle Pressure Ratio to get a choked, supersonic regime but shock at exit in a nozzle with As/Ac diffuser
Args:
AsAc ([real]): ratio of exit over throat surfaces
Returns:
[real]: Nozzle Pressure ratio (inlet total pressure over exit static pressure)
"""
Msup = mf.MachSup_Sigma(AsAc)
Msh = sw.downstream_Mn(Msup)
return Is.PtPs_Mach(Msh) / sw.Pi_ratio(Msup)
def _NPR_Ms_list(AsAc):
"""
Computes all NPR limits and associated exit Mach number
internal function
:param AsAc: ratio of section at exit over throat
:return: result NPR and Mach numbers
:Example:
>>> import aerokit.aero.MassFlow as mf ; mf.Sigma_Mach(Is.Mach_PtPs(np.array(_NPR_Ms_list(2.)[:3:2])))
array([ 2., 2.])
.. seealso:: NPR_choked_subsonic(), NPR_choked_supersonic(), NPR_shock_at_exit()
.. note:: available for scalar or array (numpy) computations
"""
Msub = mf.MachSub_Sigma(AsAc)
NPR0 = Is.PtPs_Mach(Msub)
Msup = mf.MachSup_Sigma(AsAc)
Msh = sw.downstream_Mn(Msup)
NPRsw = Is.PtPs_Mach(Msh) / sw.Pi_ratio(Msup)
NPR1 = Is.PtPs_Mach(Msup)
return NPR0, NPRsw, NPR1, Msub, Msh, Msup
def test_MachSup_Sigma(AsAc):
mach = mf.MachSup_Sigma(AsAc)
assert (mach > 1)
assert mf.Sigma_Mach(mach) == pytest.approx(AsAc, rel=1.e-6)
