def Madapt_from_AsAc_NPR(AsAc, NPR):
"""
Computes Mach number for pressure adapted flow of a nozzle given As/Ac and NPR
This method checks the NPR to define regime and computes Mach number in jet. The switch between
overexpanded jet and underexpanded jet is
:param AsAc: ratio of section at exit over throat
:param NPR: ratio of total pressure at inlet over 'expected' static pressure at exit
:return: result Mach number at exit
:Example:
>>> print round(Ms_from_AsAc_NPR(2.636, 1.5), 8) # case with shock in diffuser
0.32586574
.. seealso::
.. note:: NOT available for array (numpy) computations
"""
NPR0, NPRsw, NPR1, Msub, Msh, Msup = _NPR_Ms_list(AsAc)
if (NPR < NPR0):
Ms = Is.Mach_PtPs(NPR)
elif (NPR > NPR1): # under expanded flow
Ms = Is.Mach_PtPs(NPR)
elif (NPR > NPRsw): # shock wave in jet
Ms = sw.downstreamMach_Mach_ShockPsratio(Msup, NPR1 / NPR)
else:
gmu = defg._gamma - 1.
K = NPR / AsAc / ((defg._gamma + 1.) / 2)**(
(defg._gamma + 1.) / 2 / gmu)
Ms = np.sqrt((np.sqrt(1. + 2. * gmu * K * K) - 1.) / gmu)
return Ms
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 update(self):
gg.base.update(self)
gh = self.gam_hot
cph = gh * self.r_hot / (gh - 1.)
self.Pt9 = np.maximum(self.Pt45 * self.xi_nozzle, self.P0)
self.M9 = Is.Mach_PtPs(self.Pt9 / self.P0, gamma=self.gam_hot)
self.V9 = Is.Velocity_MachTi(self.M9,
self.Tt45,
r=self.r_hot,
gamma=self.gam_hot)
def stage_9(self):
if self.current_stage_corps == 5:
self.Tt9 = self.Tt5
self.Pt9 = self.Pt5 * self.xi_tuy
self.P9 = self.P0
self.M9 = Is.Mach_PtPs(self.Pt9 / self.P9, self.g_fuel.gamma)
self.V9 = Is.Velocity_MachTi(self.M9, self.Tt9, self.g_fuel.r,
self.g_fuel.gamma)
self.F_c = self.m_c * (self.V9 - self.V0)
self.current_stage_corps = 9
def stage_19(self):
if self.current_stage_fan == 13:
self.Pt19 = self.Pt13 * self.xi_tuy
self.Tt19 = self.Tt13
self.P19 = self.P0
self.M19 = Is.Mach_PtPs(self.Pt19 / self.P19, self.g.gamma)
self.V19 = Is.Velocity_MachTi(self.M19, self.Tt19, self.g.r,
self.g.gamma)
self.F_f = self.m_f * (self.V19 - self.V0)
self.current_stage_fan = 19
def compute_from_pt_rtt_p(self, pt, rtt, p):
"""Init state from Ptot r.Ttot and Ps (velocity sign is arbitrary and positive)
Args:
pt ([float]): [description]
rtt ([float]): [description]
p ([float]): [description]
"""
M = Is.Mach_PtPs(pt / p, self._gamma)
rts = rtt / Is.TtTs_Mach(M, self._gamma)
self.__init__(rho=p / rts, u=M * np.sqrt(self._gamma * rts), p=p)
def update(self):
tj.turbojet_opt.update(self)
gh = self.gam_hot
cph = gh*self.r_hot/(gh-1.)
Wsp_mono = (1.-(self.Pt45/self.P0*self.xi_nozzle)**(-(gh-1.)*self.etapolTBP/gh))*self.Tt45*cph*(1.+self.far)
self.Tt5 = self.Tt45 - Wsp_mono*self.fanpower_ratio/cph/(1.+self.far)
self.Pt5 = self.Pt45*(self.Tt5/self.Tt45)**(gh/((gh-1.)*self.etapolTBP))
# core nozzle
self.Pt9 = self.Pt5 * self.xi_nozzle
self.M9 = Is.Mach_PtPs(self.Pt9/self.P0, gamma=self.gam_hot)
self.V9 = Is.Velocity_MachTi(self.M9, self.Tt5, r=self.r_hot, gamma=self.gam_hot)
# fan
gc = self.gam_cold
cpc = gc*self.r_cold/(gc-1.)
#print self.bpr, cpc
self.Tt17 = self.Tt2 + self.eta_shaft*Wsp_mono*self.fanpower_ratio/(self.bpr*cpc)
self.Pt17 = self.Pt2*(self.Tt17/self.Tt2)**((gc*self.etapolfan)/(gc-1.))
# bypass nozzle
self.Tt19 = self.Tt17
self.Pt19 = self.Pt17*self.xi_nozzle
self.M19 = Is.Mach_PtPs(self.Pt19/self.P0, gamma=gc)
self.V19 = Is.Velocity_MachTi(self.M19, self.Tt19, r=self.r_cold, gamma=gc)
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 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.)