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 Pt_ratio(Mn, gamma=defg._gamma):
"""Total pressure ration through shock wave
Args:
Mn: upstream relative normal Mach number to param
gamma: (Default value = defg._gamma)
Returns:
"""
return Ps_ratio(Mn, gamma) * Is.PtPs_Mach(downstream_Mn(
Mn, gamma)) / Is.PtPs_Mach(Mn, gamma)
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 update(self):
gc = self.gam_cold
cpc = gc*self.r_cold/(gc-1.)
self.Tt0 = self.T0*Is.TtTs_Mach(self.M0, gamma=self.gam_cold)
self.Pt0 = self.P0*Is.PtPs_Mach(self.M0, gamma=self.gam_cold)
self.V0 = self.M0*np.sqrt(gc*self.r_cold*self.T0)
self.Pt2 = self.Pt0*self.xi_inlet
self.Tt2 = self.Tt0
self.Pt3 = self.Pt2*self.OPR
self.Tt3 = self.Tt2*self.OPR**((gc-1.)/(gc*self.etapolCHP))
#self.Tt4 = Ti_4
self.Pt4 = self.Pt3*self.xi_cc
gh = self.gam_hot
cph = gh*self.r_hot/(gh-1.)
self.far = (cph*self.Tt4 - cpc*self.Tt3)/(self.xi_cc*self.Pci - cph*self.Tt4)
self.Tt45 = self.Tt4 - cpc*(self.Tt3-self.Tt2)/(self.eta_shaft*cph*(1.+self.far))
#print self.Tt3, self.Pt4, self.Tt45, self.Tt4, self.far
self.Pt45 = self.Pt4*(self.Tt45/self.Tt4)**(gh/((gh-1.)*self.etapolTHP))
def IsentropicPsratio_Mach_deflection(Mach, dev, gamma=defg._gamma):
m2 = Mach_PrandtlMeyer(PrandtlMeyer_Mach(Mach, gamma) - dev, gamma)
return Is.PtPs_Mach(Mach, gamma) / Is.PtPs_Mach(m2, gamma)
def deflection_Mach_IsentropicPsratio(Mach, Pratio, gamma=defg._gamma):
m2 = Is.Mach_PtPs(Is.PtPs_Mach(Mach, gamma) / Pratio, gamma)
return -PrandtlMeyer_Mach(Mach, gamma) + PrandtlMeyer_Mach(m2, gamma)
def InitialValues(self):
self.Pt0 = self.P0 * Is.PtPs_Mach(Mach=self.M0, gamma=self.g.gamma)
self.Tt0 = self.T0 * Is.TtTs_Mach(Mach=self.M0, gamma=self.g.gamma)
self.V0 = self.M0 * np.sqrt(self.g.gamma * self.g.r * self.T0)
self.current_stage_corps = 1
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 Ptot(self):
"""returns Total pressure"""
return self.p * Is.PtPs_Mach(self.Mach(), self._gamma)
def compute_from_pt_rtt_M(self, pt, rtt, M):
ps = pt / Is.PtPs_Mach(M, self._gamma)
rts = rtt / Is.TtTs_Mach(M, self._gamma)
self.__init__(rho=ps / rts, u=M * np.sqrt(self._gamma * rts), p=ps)
def test_stagnation_i2t():
assert Is.TtTs_Mach(2.) == Is.TiTs_Mach(2.)
assert Is.PtPs_Mach(2.) == Is.PiPs_Mach(2.)
assert Is.Mach_PiPs(3.) == Is.Mach_PtPs(3.)
assert Is.Mach_TiTs(3.) == Is.Mach_TtTs(3.)
assert Is.Velocity_MachTi(.8, 300.) == Is.Velocity_MachTt(.8, 300.)