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_subsonic(AsAc):
"""Compute Nozzle Pressure Ratio to get a choked but subsonic 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.MachSub_Sigma(AsAc))
def set_NPR(self, NPR):
""" Define Nozzle Pressure Ratio (inlet Ptot over outlet Ps) for this case
:param NPR: NPR value (>1)
"""
self.NPR = NPR
defg.set_gamma(self._gam)
if NPR < self.NPR0: # flow is fully subsonic
_Ms = Is.Mach_PiPs(NPR)
_M = mf.MachSub_Sigma(self.section * mf.Sigma_Mach(_Ms) /
self.section[-1])
_Pt = 0. * _M + NPR
_Ps = _Pt / Is.PiPs_Mach(_M)
else:
# compute Mach, assumed to be subsonic before throat, supersonic after
_Minit = 0. * self.section + .5
_Minit[self.ithroat:] = 2.
_M = mf.Mach_Sigma(self.section / self.section[self.ithroat],
Mach=_Minit)
_Pt = NPR + 0. * _M
# CHECK, there is a shock
# analytical solution for Ms, losses and upstream Mach number of shock wave
Ms = nz.Ms_from_AsAc_NPR(self.AsoAc, NPR)
Ptloss = Is.PiPs_Mach(Ms) / NPR
Msh = sw.Mn_Pi_ratio(Ptloss)
#
if NPR < self.NPRsw: # throat is choked, there may be a shock
# redefine curves starting from 'ish' index (closest value of Msh in supersonic flow)
ish = np.abs(_M - Msh).argmin()
_M[ish:] = mf.MachSub_Sigma(
self.section[ish:] * mf.Sigma_Mach(Ms) / self.section[-1])
_Pt[ish:] = Ptloss * NPR
_Ps = _Pt / Is.PiPs_Mach(_M)
#
self._M = _M
self._Pt = _Pt
self._Ps = _Ps
return
def set_NPR(NPR):
if NPR < NPR0:
_Ms = Is.Mach_PiPs(NPR, gamma=self.model.gamma)
self._M = mf.MachSub_Sigma(self.AsoAc * mf.Sigma_Mach(Ma_col) /
self.AsoAc[-1],
gamma=self.model.gamma)
self._Pt = 0. * coord_x + 1.
self._Ps = _Pt / Is.PiPs_Mach(self._M, gamma=self.model.gamma)
elif NPR < NPRsw:
_M = mf.Mach_Sigma(Noz_AoAc, Mach=_Minit)
#
# analytical solution for Ms, losses and upstream Mach number of shock wave
Ms = nz.Ms_from_AsAc_NPR(target_AoAc, NPR)
Ptloss = Is.PiPs_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(_M - Msh).argmin()
_M[ish:] = mf.MachSub_Sigma(Noz_AoAc[ish:] * mf.Sigma_Mach(Ms) /
target_AoAc)
_Pt[ish:] = Ptloss
_Ps = _Pt / Is.PiPs_Mach(_M)
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
from flowdyn.xnum import *
from flowdyn.integration import rk3ssp
import flowdyn.modelphy.euler as euler
import flowdyn.modeldisc as modeldisc
import flowdyn.solution.euler_nozzle as sol
gam = 1.4
bctype = "outsub_rh"
ncell = 100
nit_super = 1000
nit_tot = 10000
# expected Mach number at exit when supersonic ; defines As/Ac ratio
Msup = 1.8
AsAc = mf.Sigma_Mach(Msup, gam)
Msub = mf.MachSub_Sigma(AsAc, gam)
NPRsup = Is.PtPs_Mach(Msup, gam)
NPRsub = Is.PtPs_Mach(Msub, gam)
res = {}
meshsim = mesh.unimesh(ncell=ncell, length=10.0)
def S(x): # section law, throat is at x=5
return 1 + (AsAc - 1.0) * (1.0 - np.exp(-0.5 * (x - 2.0)**2))
model = euler.nozzle(gamma=gam, sectionlaw=S)
nozz = sol.nozzle(model, S(meshsim.centers()), NPR=NPRsup)
finit = nozz.fdata(meshsim)
print(NPRsup, AsAc, Msup, Msub)
def test_MachSub_Sigma(AsAc):
mach = mf.MachSub_Sigma(AsAc)
assert (mach < 1)
assert mf.Sigma_Mach(mach) == pytest.approx(AsAc, rel=1.e-6)