def compute(self,conditions):
"""This computes the output values from the input values according to
equations from the source.
Assumptions:
Constant polytropic efficiency and pressure ratio
Source:
https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/
Inputs:
conditions.freestream.
isentropic_expansion_factor [-]
specific_heat_at_constant_pressure [J/(kg K)]
pressure [Pa]
stagnation_pressure [Pa]
stagnation_temperature [K]
gas_specific_constant [J/(kg K)]
mach_number [-]
self.inputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
Outputs:
self.outputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
stagnation_enthalpy [J/kg]
mach_number [-]
static_temperature [K]
static_enthalpy [J/kg]
velocity [m/s]
static_pressure [Pa]
area_ratio [-]
Properties Used:
self.
pressure_ratio [-]
polytropic_efficiency [-]
pressure_recovery [-]
"""
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.gas_specific_constant
Mo = conditions.freestream.mach_number
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
eta_rec = self.pressure_recovery
#Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in*pid*eta_rec
Tt_out = Tt_in*(pid*eta_rec)**((gamma-1)/(gamma)*etapold)
ht_out = Cp*Tt_out
#compute the output Mach number, static quantities and the output velocity
Mach = np.sqrt((((Pt_out/Po)**((gamma-1)/gamma))-1)*2/(gamma-1))
#Remove check on mach numbers from expansion nozzle
i_low = Mach < 10.0
#initializing the Pout array
P_out = 1.0 *Mach/Mach
#Computing output pressure and Mach number for the case Mach <1.0
P_out[i_low] = Po[i_low]
Mach[i_low] = np.sqrt((((Pt_out[i_low]/Po[i_low])**((gamma[i_low]-1.)/gamma[i_low]))-1.)*2./(gamma[i_low]-1.))
#Computing the output temperature,enthalpy, velocity and density
T_out = Tt_out/(1.+(gamma-1.)/2.*Mach*Mach)
h_out = Cp*T_out
u_out = np.sqrt(2.*(ht_out-h_out))
rho_out = P_out/(R*T_out)
#Computing the freestream to nozzle area ratio (mainly from thrust computation)
area_ratio = (fm_id(Mo,gamma)/fm_id(Mach,gamma)*(1/(Pt_out/Pto))*(np.sqrt(Tt_out/Tto)))
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = Mach
self.outputs.static_temperature = T_out
self.outputs.density = rho_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = area_ratio
def compute(self,conditions):
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.universal_gas_constant
Mo = conditions.freestream.mach_number
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
#Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in*pid
Tt_out = Tt_in*pid**((gamma-1)/(gamma)*etapold)
ht_out = Cp*Tt_out
#compute the output Mach number, static quantities and the output velocity
Mach = np.sqrt((((Pt_out/Po)**((gamma-1)/gamma))-1)*2/(gamma-1))
T_out = Tt_out/(1+(gamma-1)/2*Mach**2)
h_out = Cp*T_out
u_out = np.sqrt(2*(ht_out-h_out))
#Checking from Mach numbers below, above 1.0
i_low = Mach < 1.0
i_high = Mach >=1.0
#initializing the Pout array
P_out = 1.0 *Mach/Mach
#Computing output pressure and Mach number for the case Mach <1.0
P_out[i_low] = Po[i_low]
Mach[i_low] = np.sqrt((((Pt_out[i_low]/Po[i_low])**((gamma-1)/gamma))-1)*2/(gamma-1))
#Computing output pressure and Mach number for the case Mach >=1.0
Mach[i_high] = 1.0*Mach[i_high]/Mach[i_high]
P_out[i_high] = Pt_out[i_high]/(1+(gamma-1)/2*Mach[i_high]**2)**(gamma/(gamma-1))
#Computing the output temperature,enthalpy, velocity and density
T_out = Tt_out/(1+(gamma-1)/2*Mach**2)
h_out = Cp*T_out
u_out = np.sqrt(2*(ht_out-h_out))
rho_out = P_out/(R*T_out)
#Computing the freestream to nozzle area ratio (mainly from thrust computation)
area_ratio = (fm_id(Mo)/fm_id(Mach)*(1/(Pt_out/Pto))*(np.sqrt(Tt_out/Tto)))
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = Mach
self.outputs.static_temperature = T_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = area_ratio
def compute_limited_geometry(self,conditions):
"""This is a variable geometry nozzle component that allows
for supersonic outflow. all possible nozzle conditions, including
overexpansion and underexpansion.
Assumptions:
Constant polytropic efficiency and pressure ratio
Source:
https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/
https://web.stanford.edu/~cantwell/AA210A_Course_Material/AA210A_Course_Notes/
Inputs:
conditions.freestream.
isentropic_expansion_factor [-]
specific_heat_at_constant_pressure [J/(kg K)]
pressure [Pa]
stagnation_pressure [Pa]
stagnation_temperature [K]
gas_specific_constant [J/(kg K)]
mach_number [-]
self.inputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
Outputs:
self.outputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
stagnation_enthalpy [J/kg]
mach_number [-]
static_temperature [K]
static_enthalpy [J/kg]
velocity [m/s]
static_pressure [Pa]
Properties Used:
self.
pressure_ratio [-]
polytropic_efficiency [-]
max_area_ratio [-]
min_area_ratio [-]
"""
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.gas_specific_constant
Mo = conditions.freestream.mach_number
To = conditions.freestream.temperature
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
max_area_ratio = self.max_area_ratio
min_area_ratio = self.min_area_ratio
# Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in*pid
Tt_out = Tt_in*pid**((gamma-1.)/(gamma)*etapold)
ht_out = Cp*Tt_out
# Method for computing the nozzle properties
#-- Initial estimate for exit area
area_ratio = (max_area_ratio + min_area_ratio)/2.
#-- Compute limits of each possible flow condition
subsonic_pressure_ratio = pressure_ratio_isentropic(area_ratio, gamma, True)
nozzle_shock_pressure_ratio = pressure_ratio_shock_in_nozzle(area_ratio, gamma)
supersonic_pressure_ratio = pressure_ratio_isentropic(area_ratio, gamma, False)
supersonic_max_Area = pressure_ratio_isentropic(max_area_ratio, gamma, False)
supersonic_min_Area = pressure_ratio_isentropic(min_area_ratio, gamma, False)
#-- Compute the output Mach number guess with freestream pressure
#-- Initializing arrays
P_out = np.ones_like(Pt_out)
A_ratio = area_ratio*np.ones_like(Pt_out)
M_out = np.ones_like(Pt_out)
# Establishing a correspondence between real pressure ratio and limits of each flow condition
# Determine if flow is within subsonic/sonic range
i_sub = Po/Pt_out >= subsonic_pressure_ratio
# Detemine if there is a shock in nozzle
i2 = Po/Pt_out < subsonic_pressure_ratio
i3 = Po/Pt_out >= nozzle_shock_pressure_ratio
i_shock = np.logical_and(i2,i3)
# Determine if flow is overexpanded
i4 = Po/Pt_out < nozzle_shock_pressure_ratio
i5 = Po/Pt_out > supersonic_min_Area
i_over = np.logical_and(i4,i5)
# Determine if flow is supersonic
i6 = Po/Pt_out <= supersonic_min_Area
i7 = Po/Pt_out >= supersonic_max_Area
i_sup = np.logical_and(i6,i7)
# Determine if flow is underexpanded
i_und = Po/Pt_out < supersonic_max_Area
#-- Subsonic and sonic flow
P_out[i_sub] = Po[i_sub]
M_out[i_sub] = np.sqrt((((Pt_out[i_sub]/P_out[i_sub])**((gamma[i_sub]-1.)/gamma[i_sub]))-1.)*2./(gamma[i_sub]-1.))
A_ratio[i_sub] = 1./fm_id(M_out[i_sub],gamma[i_sub])
#-- Shock inside nozzle
P_out[i_shock] = Po[i_shock]
M_out[i_shock] = np.sqrt((((Pt_out[i_shock]/P_out[i_shock])**((gamma[i_shock]-1.)/gamma[i_shock]))-1.)*2./(gamma[i_shock]-1.))
A_ratio[i_shock] = 1./fm_id(M_out[i_shock],gamma[i_shock])
#-- Overexpanded flow
P_out[i_over] = supersonic_min_Area[i_over]*Pt_out[i_over]
M_out[i_over] = np.sqrt((((Pt_out[i_over]/P_out[i_over])**((gamma[i_over]-1.)/gamma[i_over]))-1.)*2./(gamma[i_over]-1.))
A_ratio[i_over] = 1./fm_id(M_out[i_over],gamma[i_over])
#-- Isentropic supersonic flow, with variable area adjustments
P_out[i_sup] = Po[i_sup]
M_out[i_sup] = np.sqrt((((Pt_out[i_sup]/P_out[i_sup])**((gamma[i_sup]-1.)/gamma[i_sup]))-1.)*2./(gamma[i_sup]-1.))
A_ratio[i_sup] = 1./fm_id(M_out[i_sup],gamma[i_sup])
#-- Underexpanded flow
P_out[i_und] = supersonic_max_Area[i_und]*Pt_out[i_und]
M_out[i_und] = np.sqrt((((Pt_out[i_und]/P_out[i_und])**((gamma[i_und]-1.)/gamma[i_und]))-1.)*2./(gamma[i_und]-1.))
A_ratio[i_und] = 1./fm_id(M_out[i_und],gamma[i_und])
#-- Calculate other flow properties
T_out = Tt_out/(1.+(gamma-1.)/2.*M_out*M_out)
h_out = Cp*T_out
u_out = M_out*np.sqrt(gamma*R*T_out)
rho_out = P_out/(R*T_out)
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = M_out
self.outputs.static_temperature = T_out
self.outputs.rho = rho_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = A_ratio
def compute(self, conditions):
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.universal_gas_constant
Mo = conditions.freestream.mach_number
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
#Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in * pid
Tt_out = Tt_in * pid**((gamma - 1) / (gamma) * etapold)
ht_out = Cp * Tt_out
#compute the output Mach number, static quantities and the output velocity
Mach = np.sqrt(
(((Pt_out / Po)**((gamma - 1) / gamma)) - 1) * 2 / (gamma - 1))
#Checking from Mach numbers below, above 1.0
i_low = Mach < 1.0
i_high = Mach >= 1.0
#initializing the Pout array
P_out = 1.0 * Mach / Mach
#Computing output pressure and Mach number for the case Mach <1.0
P_out[i_low] = Po[i_low]
Mach[i_low] = np.sqrt(
(((Pt_out[i_low] / Po[i_low])**((gamma - 1) / gamma)) - 1) * 2 /
(gamma - 1))
#Computing output pressure and Mach number for the case Mach >=1.0
Mach[i_high] = 1.0 * Mach[i_high] / Mach[i_high]
P_out[i_high] = Pt_out[i_high] / (
1 + (gamma - 1) / 2 * Mach[i_high]**2)**(gamma / (gamma - 1))
#Computing the output temperature,enthalpy, velocity and density
T_out = Tt_out / (1 + (gamma - 1) / 2 * Mach**2)
h_out = Cp * T_out
u_out = np.sqrt(2 * (ht_out - h_out))
rho_out = P_out / (R * T_out)
#Computing the freestream to nozzle area ratio (mainly from thrust computation)
area_ratio = (fm_id(Mo) / fm_id(Mach) * (1 / (Pt_out / Pto)) *
(np.sqrt(Tt_out / Tto)))
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = Mach
self.outputs.static_temperature = T_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = area_ratio
def compute(self, conditions):
"""This computes the output values from the input values according to
equations from the source.
Assumptions:
Constant polytropic efficiency and pressure ratio
Source:
https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/
Inputs:
conditions.freestream.
isentropic_expansion_factor [-]
specific_heat_at_constant_pressure [J/(kg K)]
pressure [Pa]
stagnation_pressure [Pa]
stagnation_temperature [K]
gas_specific_constant [J/(kg K)]
mach_number [-]
self.inputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
Outputs:
self.outputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
stagnation_enthalpy [J/kg]
mach_number [-]
static_temperature [K]
static_enthalpy [J/kg]
velocity [m/s]
static_pressure [Pa]
area_ratio [-]
Properties Used:
self.
pressure_ratio [-]
polytropic_efficiency [-]
pressure_recovery [-]
"""
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.gas_specific_constant
Mo = conditions.freestream.mach_number
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
eta_rec = self.pressure_recovery
#Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in * pid * eta_rec
Tt_out = Tt_in * (pid * eta_rec)**((gamma - 1) / (gamma) * etapold)
ht_out = Cp * Tt_out
#compute the output Mach number, static quantities and the output velocity
Mach = np.sqrt(
(((Pt_out / Po)**((gamma - 1) / gamma)) - 1) * 2 / (gamma - 1))
#Remove check on mach numbers from expansion nozzle
i_low = Mach < 10.0
#initializing the Pout array
P_out = 1.0 * Mach / Mach
#Computing output pressure and Mach number for the case Mach <1.0
P_out[i_low] = Po[i_low]
Mach[i_low] = np.sqrt((((Pt_out[i_low] / Po[i_low])**(
(gamma[i_low] - 1.) / gamma[i_low])) - 1.) * 2. /
(gamma[i_low] - 1.))
#Computing the output temperature,enthalpy, velocity and density
T_out = Tt_out / (1. + (gamma - 1.) / 2. * Mach * Mach)
h_out = Cp * T_out
u_out = np.sqrt(2. * (ht_out - h_out))
rho_out = P_out / (R * T_out)
#Computing the freestream to nozzle area ratio (mainly from thrust computation)
area_ratio = (fm_id(Mo, gamma) / fm_id(Mach, gamma) *
(1 / (Pt_out / Pto)) * (np.sqrt(Tt_out / Tto)))
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = Mach
self.outputs.static_temperature = T_out
self.outputs.density = rho_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = area_ratio
def compute_limited_geometry(self, conditions):
"""This is a variable geometry nozzle component that allows
for supersonic outflow. all possible nozzle conditions, including
overexpansion and underexpansion.
Assumptions:
Constant polytropic efficiency and pressure ratio
Source:
https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/
https://web.stanford.edu/~cantwell/AA210A_Course_Material/AA210A_Course_Notes/
Inputs:
conditions.freestream.
isentropic_expansion_factor [-]
specific_heat_at_constant_pressure [J/(kg K)]
pressure [Pa]
stagnation_pressure [Pa]
stagnation_temperature [K]
gas_specific_constant [J/(kg K)]
mach_number [-]
self.inputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
Outputs:
self.outputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
stagnation_enthalpy [J/kg]
mach_number [-]
static_temperature [K]
static_enthalpy [J/kg]
velocity [m/s]
static_pressure [Pa]
Properties Used:
self.
pressure_ratio [-]
polytropic_efficiency [-]
max_area_ratio [-]
min_area_ratio [-]
"""
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.gas_specific_constant
Mo = conditions.freestream.mach_number
To = conditions.freestream.temperature
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
max_area_ratio = self.max_area_ratio
min_area_ratio = self.min_area_ratio
# Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in * pid
Tt_out = Tt_in * pid**((gamma - 1.) / (gamma) * etapold)
ht_out = Cp * Tt_out
# Method for computing the nozzle properties
#-- Initial estimate for exit area
area_ratio = (max_area_ratio + min_area_ratio) / 2.
#-- Compute limits of each possible flow condition
subsonic_pressure_ratio = pressure_ratio_isentropic(
area_ratio, gamma, True)
nozzle_shock_pressure_ratio = pressure_ratio_shock_in_nozzle(
area_ratio, gamma)
supersonic_pressure_ratio = pressure_ratio_isentropic(
area_ratio, gamma, False)
supersonic_max_Area = pressure_ratio_isentropic(
max_area_ratio, gamma, False)
supersonic_min_Area = pressure_ratio_isentropic(
min_area_ratio, gamma, False)
#-- Compute the output Mach number guess with freestream pressure
#-- Initializing arrays
P_out = np.ones_like(Pt_out)
A_ratio = area_ratio * np.ones_like(Pt_out)
M_out = np.ones_like(Pt_out)
# Establishing a correspondence between real pressure ratio and limits of each flow condition
# Determine if flow is within subsonic/sonic range
i_sub = Po / Pt_out >= subsonic_pressure_ratio
# Detemine if there is a shock in nozzle
i2 = Po / Pt_out < subsonic_pressure_ratio
i3 = Po / Pt_out >= nozzle_shock_pressure_ratio
i_shock = np.logical_and(i2, i3)
# Determine if flow is overexpanded
i4 = Po / Pt_out < nozzle_shock_pressure_ratio
i5 = Po / Pt_out > supersonic_min_Area
i_over = np.logical_and(i4, i5)
# Determine if flow is supersonic
i6 = Po / Pt_out <= supersonic_min_Area
i7 = Po / Pt_out >= supersonic_max_Area
i_sup = np.logical_and(i6, i7)
# Determine if flow is underexpanded
i_und = Po / Pt_out < supersonic_max_Area
#-- Subsonic and sonic flow
P_out[i_sub] = Po[i_sub]
M_out[i_sub] = np.sqrt((((Pt_out[i_sub] / P_out[i_sub])**(
(gamma[i_sub] - 1.) / gamma[i_sub])) - 1.) * 2. /
(gamma[i_sub] - 1.))
A_ratio[i_sub] = 1. / fm_id(M_out[i_sub], gamma[i_sub])
#-- Shock inside nozzle
P_out[i_shock] = Po[i_shock]
M_out[i_shock] = np.sqrt((((Pt_out[i_shock] / P_out[i_shock])**(
(gamma[i_shock] - 1.) / gamma[i_shock])) - 1.) * 2. /
(gamma[i_shock] - 1.))
A_ratio[i_shock] = 1. / fm_id(M_out[i_shock], gamma[i_shock])
#-- Overexpanded flow
P_out[i_over] = supersonic_min_Area[i_over] * Pt_out[i_over]
M_out[i_over] = np.sqrt((((Pt_out[i_over] / P_out[i_over])**(
(gamma[i_over] - 1.) / gamma[i_over])) - 1.) * 2. /
(gamma[i_over] - 1.))
A_ratio[i_over] = 1. / fm_id(M_out[i_over], gamma[i_over])
#-- Isentropic supersonic flow, with variable area adjustments
P_out[i_sup] = Po[i_sup]
M_out[i_sup] = np.sqrt((((Pt_out[i_sup] / P_out[i_sup])**(
(gamma[i_sup] - 1.) / gamma[i_sup])) - 1.) * 2. /
(gamma[i_sup] - 1.))
A_ratio[i_sup] = 1. / fm_id(M_out[i_sup], gamma[i_sup])
#-- Underexpanded flow
P_out[i_und] = supersonic_max_Area[i_und] * Pt_out[i_und]
M_out[i_und] = np.sqrt((((Pt_out[i_und] / P_out[i_und])**(
(gamma[i_und] - 1.) / gamma[i_und])) - 1.) * 2. /
(gamma[i_und] - 1.))
A_ratio[i_und] = 1. / fm_id(M_out[i_und], gamma[i_und])
#-- Calculate other flow properties
T_out = Tt_out / (1. + (gamma - 1.) / 2. * M_out * M_out)
h_out = Cp * T_out
u_out = M_out * np.sqrt(gamma * R * T_out)
rho_out = P_out / (R * T_out)
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = M_out
self.outputs.static_temperature = T_out
self.outputs.rho = rho_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = A_ratio
def compute(self, conditions):
""" This computes the output values from the input values according to
equations from the source.
Assumptions:
Constant polytropic efficiency and pressure ratio
If pressures make the Mach number go negative, these values are corrected
Source:
https://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/
Inputs:
conditions.freestream.
isentropic_expansion_factor [-]
specific_heat_at_constant_pressure [J/(kg K)]
pressure [Pa]
stagnation_pressure [Pa]
stagnation_temperature [K]
specific_gas_constant [J/(kg K)]
mach_number [-]
self.inputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
Outputs:
self.outputs.
stagnation_temperature [K]
stagnation_pressure [Pa]
stagnation_enthalpy [J/kg]
mach_number [-]
static_temperature [K]
static_enthalpy [J/kg]
velocity [m/s]
static_pressure [Pa]
area_ratio [-]
denisty [kg/m^3]
Properties Used:
self.
pressure_ratio [-]
polytropic_efficiency [-]
"""
#unpack the values
#unpack from conditions
gamma = conditions.freestream.isentropic_expansion_factor
Cp = conditions.freestream.specific_heat_at_constant_pressure
Po = conditions.freestream.pressure
Pto = conditions.freestream.stagnation_pressure
Tto = conditions.freestream.stagnation_temperature
R = conditions.freestream.gas_specific_constant
Mo = conditions.freestream.mach_number
#unpack from inputs
Tt_in = self.inputs.stagnation_temperature
Pt_in = self.inputs.stagnation_pressure
#unpack from self
pid = self.pressure_ratio
etapold = self.polytropic_efficiency
#Method for computing the nozzle properties
#--Getting the output stagnation quantities
Pt_out = Pt_in * pid
Tt_out = Tt_in * pid**((gamma - 1) / (gamma) * etapold)
ht_out = Cp * Tt_out
# A cap so pressure doesn't go negative
Pt_out[Pt_out < Po] = Po[Pt_out < Po]
#compute the output Mach number, static quantities and the output velocity
Mach = np.sqrt(
(((Pt_out / Po)**((gamma - 1) / gamma)) - 1) * 2 / (gamma - 1))
#Checking from Mach numbers below, above 1.0
i_low = Mach < 1.0
i_high = Mach >= 1.0
#initializing the Pout array
P_out = 1.0 * Mach / Mach
#Computing output pressure and Mach number for the case Mach <1.0
P_out[i_low] = Po[i_low]
Mach[i_low] = np.sqrt((((Pt_out[i_low] / Po[i_low])**(
(gamma[i_low] - 1.) / gamma[i_low])) - 1.) * 2. /
(gamma[i_low] - 1.))
#Computing output pressure and Mach number for the case Mach >=1.0
Mach[i_high] = 1.0 * Mach[i_high] / Mach[i_high]
P_out[i_high] = Pt_out[i_high] / (
1. + (gamma[i_high] - 1.) / 2. * Mach[i_high] * Mach[i_high])**(
gamma[i_high] / (gamma[i_high] - 1.))
# A cap to make sure Mach doesn't go to zero:
if np.any(Mach <= 0.0):
warn('Pressures Result in Negative Mach Number, making positive',
RuntimeWarning)
Mach[Mach <= 0.0] = 0.001
#Computing the output temperature,enthalpy, velocity and density
T_out = Tt_out / (1 + (gamma - 1) / 2 * Mach * Mach)
h_out = Cp * T_out
u_out = np.sqrt(2 * (ht_out - h_out))
rho_out = P_out / (R * T_out)
#Computing the freestream to nozzle area ratio (mainly from thrust computation)
area_ratio = (fm_id(Mo, gamma) / fm_id(Mach, gamma) *
(1 / (Pt_out / Pto)) * (np.sqrt(Tt_out / Tto)))
#pack computed quantities into outputs
self.outputs.stagnation_temperature = Tt_out
self.outputs.stagnation_pressure = Pt_out
self.outputs.stagnation_enthalpy = ht_out
self.outputs.mach_number = Mach
self.outputs.static_temperature = T_out
self.outputs.density = rho_out
self.outputs.static_enthalpy = h_out
self.outputs.velocity = u_out
self.outputs.static_pressure = P_out
self.outputs.area_ratio = area_ratio