class Engine(Turbomachine):
def __init__(self):
self.compressor = Compressor()
self.turbine = Turbine()
self.initial_guess = self.__class__.DEFAULT_PARAMS.copy()
self.cpc = 1004 # J/(kg K)
self.cpt = 1225 # J/(kg K)
self.T01 = 273.15 # K
self.P01 = 101e3 # Pa
self.R_c = (1 - 1 / self.compressor.gam) * self.cpc # from gam and cp
self.R_t = (1 - 1 / self.turbine.gam) * self.cpt
self.A8 = pi / 4 * 35e-3**2 # Measured: D8 = 45mm
self.FHV = 43e6 #J/kg Fuel lower calorific value
self.eta_combustion = 0.5
DEFAULT_PARAMS = {
'P0_ratio_c': 1.2347241010782356,
'Mb_t': 0.27072466251896482,
'MFP4': 0.15310678698124691,
'MFP3': 0.14924987675288623,
'M_flight': 0,
'mdotf': 0.0019637316313999187,
'P0_ratio_t': 0.92680225375718472,
'MFP5': 0.15451547834023707,
'Mb_c': 0.44527731422329964,
'MFP': 0.14801196525452109,
'T0_ratio_t': 0.98261102832775471,
'T0_ratio_c': 1.0669702796449636,
'T04': 840.63888888888891
}
N_FREE_PARAMS = 2
def implicit_map(
self,
M_flight, # flight mach number
MFP,
MFP3,
Mb_c,
T0_ratio_c,
P0_ratio_c, # compressor
mdotf,
T04, # burner
MFP4,
MFP5,
Mb_t,
T0_ratio_t,
P0_ratio_t # turbine
):
"""
This function implements burner, nozzle and spool dynamics and integrates it with
turbine and compressor maps
Variable balance:
12 variables
- 11 equations
--------
2 free choices (e.g. M_flight and mdotf)
"""
# Expose constants
A8 = self.A8
FHV = self.FHV
eta_combustion = self.eta_combustion
A5 = self.turbine.geom['A2']
gam_c = self.compressor.gam
gam_t = self.turbine.gam
cpc = self.cpc
cpt = self.cpt
T01 = self.T01
P01 = self.P01
R_c = self.R_c
R_t = self.R_t
### Dimensionalize everything ###
dim_params = self.dimensionalize(
M_flight, # flight mach number
MFP,
MFP3,
Mb_c,
T0_ratio_c,
P0_ratio_c, # compressor
mdotf,
T04, # burner
MFP4,
MFP5,
Mb_t,
T0_ratio_t,
P0_ratio_t # turbine
)
T02 = dim_params.T02
T03 = dim_params.T03
T05 = dim_params.T05
P02 = dim_params.P02
P03 = dim_params.P03
P04 = dim_params.P04
P05 = dim_params.P05
omega_c = dim_params.omega_c
omega_t = dim_params.omega_t
mdot2 = dim_params.mdot2
mdot3 = dim_params.mdot3
mdot4 = dim_params.mdot4
mdot5 = dim_params.mdot5
### CONSTRAINTS ###
# * Energy addition in ther burner
res_T04 = T03 + mdotf * FHV * eta_combustion / (mdot3 * cpc) - T04
# * Spool has constant speed
res_omega = omega_c - omega_t
# * Conservation of energy in the spool
res_energy = mdot2 * cpc * (T03 - T02) - mdot4 * cpt * (T04 - T05)
# * Consevation of mass in the combustor
res_mdot = mdot3 + mdotf - mdot4
# * Nozzle exit is either choked or at ambient pressure
Pa = P01 / (1 + (gam_c - 1) / 2 * M_flight**2)**(gam_c / (gam_c - 1))
MFP8 = MFP5 * A5 / A8
res_MFP_nozzle = (P05 / Pa - 1) * MFP8 - (P05 / Pa - 1) * mach2mfp(
min(1, (2 / (gam_t - 1) * ((P05 / Pa)**(
(gam_t - 1) / gam_t) - 1))**0.5) if P05 / Pa > 1 else 0, gam_t)
### remove dimensions of residuals ###
# References for removing dimensions of residuals
mdotref = (T01 * R_c)**0.5 / (P01 * gam_c**0.5 *
self.compressor.geom['A1'])
h_ref = cpc * T01
omega_ref = (gam_c * R_c * T01)**0.5 / self.compressor.geom['D2']
#remove dimensions
res_omega /= omega_ref
res_energy /= h_ref * mdotref
res_mdot /= mdotref
res_T04 /= T04
### COMPRESSOR MAP ###
res_MFP_c, res_T0_ratio_c, res_P0_ratio_c = self.compressor.implicit_map(
MFP, MFP3, Mb_c, T0_ratio_c, P0_ratio_c, tol=1e-13)
### TURBINE MAP ###
res_MFP_t, res_T0_ratio_t, res_P0_ratio_t = self.turbine.implicit_map(
MFP4, MFP5, Mb_t, T0_ratio_t, P0_ratio_t, tol=1e-13)
return (res_omega, res_energy, res_mdot, res_MFP_nozzle, res_T04,
res_MFP_c, res_T0_ratio_c, res_P0_ratio_c, res_MFP_t,
res_T0_ratio_t, res_P0_ratio_t)
def dimensionalize(
self,
M_flight, # flight mach number
MFP,
MFP3,
Mb_c,
T0_ratio_c,
P0_ratio_c, # compressor
mdotf,
T04, # burner
MFP4,
MFP5,
Mb_t,
T0_ratio_t,
P0_ratio_t # turbine
):
gam_c = self.compressor.gam
gam_t = self.turbine.gam
T01 = self.T01
P01 = self.P01
R_c = self.R_c
R_t = self.R_t
### Dimensionalize everything ###
a01 = (gam_c * R_c * T01)**0.5
a04 = (gam_t * R_t * T04)**0.5
T02 = T01
T03 = T02 * T0_ratio_c
T04 = T04
T05 = T04 * T0_ratio_t
P02 = P01
P03 = P02 * P0_ratio_c
P04 = P03
P05 = P03 * P0_ratio_t
omega_c = Mb_c * a01 / (self.compressor.geom['D2'] / 2)
omega_t = Mb_t * a04 / (self.turbine.geom['D1t'] / 2)
mdot2 = MFP * self.compressor.geom['A1'] * P01 * gam_c**0.5 / (
T01 * R_c)**0.5
mdot3 = MFP3 * self.compressor.geom['A2'] * P03 * gam_c**0.5 / (
T03 * R_c)**0.5
mdot4 = MFP4 * self.turbine.geom['A1'] * P04 * gam_t**0.5 / (T04 *
R_t)**0.5
mdot5 = MFP5 * self.turbine.geom['A2'] * P05 * gam_t**0.5 / (T05 *
R_t)**0.5
#Nozzle
MFP8 = min(MFP5 * self.turbine.geom['A2'] / self.A8,
mach2mfp(1, gam_t))
M8 = mfp2mach(MFP8, gam_t)
P8 = P05 * (1 + (gam_t - 1) / 2 * M8**2)**(-gam_t / (gam_t - 1))
T8 = T05 * (1 + (gam_t - 1) / 2 * M8**2)**(-1)
dim_params = DimensionalParameters(T02=T02,
T03=T03,
T04=T04,
T05=T05,
T8=T8,
P02=P02,
P03=P03,
P04=P04,
P05=P05,
P8=P8,
omega_c=omega_c,
omega_t=omega_t,
mdot2=mdot2,
mdot3=mdot3,
mdot4=mdot4,
mdot5=mdot5)
return dim_params
def working_line(self, T04_grid):
wline = []
params = self.initial_guess
for T04 in T04_grid:
sol = self.general_explicit_map({
'M_flight': 0,
'T04': T04
}, params)
params = sol.params
wline.append(params)
return wline
def thrust(self, **params):
gam_t = self.turbine.gam
R_t = self.R_t
MFP8 = min(params['MFP5'] * self.turbine.geom['A2'] / self.A8,
mach2mfp(1, gam_t))
mdot = params['MFP5'] * self.turbine.geom['A2'] * params[
'P05'] * gam_t**0.5 / (params['T05'] * R_t)**0.5
M8 = mfp2mach(MFP8, gam_t)
P8 = params['P05'] * (1 + (gam_t - 1) / 2 * M8**2)**(-gam_t /
(gam_t - 1))
mdot5 = params['MFP5'] * self.turbine.geom['A2'] * params[
'P05'] * gam_t**0.5 / (params['T05'] * R_t)**0.5
T8 = params['T05'] * (1 + (gam_t - 1) / 2 * M8**2)**(-1)
return mdot * M8 * (gam_t * R_t * T8)**0.5 + (
P8 - self.P01 /
(1 + (gam_t - 1) * params['M_flight']**2)**0.5) * self.A8
def ode_fun(self, t, y):
P4, mdot, omega = y
self.compressor.explicit_map(mdot, omega)
T04 = self.throtle(t, mdot, T03)
self.turbine.explicit_map(P4, omega)
P4_dot = a01**2 * (mdot - mdott)
mdotdot = A1 / Lc * (P3 - P4)
omega_dot = 1 / J * torque_t - torque_c
return P4_dot, mdotdot, omega_dot
