def prepare_homogenous_transition(p, m_dot, steps, fp: FluidProperties):
x = np.linspace(start=0, stop=1, num=steps) # [-] Vapour quality range
## NOTE: subscript sat for sat has been dropped for readability
# Calculate saturation parameters at edges
T_sat = fp.get_saturation_temperature(p=p) # [K] Saturation temperature
rho_l = fp.get_liquid_density_at_psat(p_sat=p) # [kg/m^3]
rho_g = fp.get_vapour_density_at_psat(p_sat=p) # [kg/m^3] Gas saturation density
# Void fraction is precalculated because it allow for simple evaluation of velocity when geometry changes
alpha = tp.homogenous_void_fraction(x=x, rho_g=rho_g, rho_l=rho_l) # [-] Void fraction
rho = tp.mixture_density(alpha=alpha, rho_g=rho_g, rho_l=rho_l) # [kg/m^3] Mixture density of two-phase flow
# Mean viscosity has no obvious way to be calculated and as such, a relation must simply be chosen [10.42] from Carey2008 is used.
mu_l = fp.get_liquid_saturation_viscosity(p_sat=p) # [Pa*s]
mu_g = fp.get_gas_saturation_viscosity(p_sat=p) # [Pa*s]
mu = tp.mean_viscosity(mu_g=mu_g, mu_l=mu_l, rho_l=rho_l, rho_g=rho_g, x=x) # [Pa*s]
# Thermal conductivity at saturation
kappa_l = fp.get_liquid_saturation_conductivity(p_sat=p) # [W/(m*K)]
kappa_g = fp.get_gas_saturation_conductivity(p_sat=p) # [W/(m*K)]
# Mean conductivity
kappa = tp.mean_conductivity(kappa_g=kappa_g, kappa_l=kappa_l, rho_l=rho_l, rho_g=rho_g, x=x) # [W/(m^2*K)]
# Prandtl numbers at saturation,
Pr_l = fp.get_saturation_Prandtl_liquid(p_sat=p) # [-]
Pr_g = fp.get_saturation_Prandtl_gas(p_sat=p) # [-]
# Mean Prandtl
Pr = tp.mean_Prandtl(Pr_g=Pr_g, Pr_l=Pr_l, rho_l=rho_l, rho_g=rho_g, x=x) # [-]
# Saturation enthalpies
h_sat_liquid = fp.get_saturation_enthalpy_liquid(p=p) # [J/kg]
h_sat_gas = fp.get_saturation_enthalpy_gas(p=p) # [J/kg]
# Enthalpy as function of vapour quality x
h = h_sat_liquid + (h_sat_gas-h_sat_liquid) * x # [J/kg] Saturation enthalpy as flow quality increases
delta_h = delta_enthalpy_per_section(h=h) # [J/kg] Enthalpy difference per section
Q_dot = required_power(m_dot=m_dot, delta_h=delta_h) # [W] Heating power required to increase enthalpy in each sections
return {
'x': x,
'alpha': alpha,
'T_sat': T_sat,
'rho': rho,
'rho_l': rho_l,
'rho_g': rho_g,
'mu': mu,
'mu_l': mu_l,
'mu_g': mu_g,
'Pr_l': Pr_l,
'Pr_g': Pr_g,
'Pr': Pr,
'kappa_l': kappa_l,
'kappa_g': kappa_g,
'kappa': kappa,
'h': h,
'Q_dot': Q_dot,
}
def prepare_single_phase_liquid(T_inlet, steps, p_ref, m_dot, fp: FluidProperties):
""" Prepare numpy arrays for calculating channel length in a liquid single-phase section of a channel.
NOTE: This is done to avoid recalculating arrays that are not dependent on channel geometry, therefore speeding up optimizations.\
After all, during optimization the geometry is what varies.\
Also it also ensure that temperature endpoint and enthalpy cleanly match with saturation temperature in the correct phase
Args:
T_inlet (K): Inlet temperature
steps (-): Amount steps of dT taken to reach saturation temperature T_sat (dT = (T_sat-T_inlet)/2)
p_ref (Pa): Pressure assumed constant along channel, equal to inlet pressure
m_dot (kg/s): Mass flow
fp (FluidProperties): Object to access propellant properties with
"""
T_sat = fp.get_saturation_temperature(p=p_ref) # [K] Saturation temperature
assert ( T_inlet < T_sat) # Check input
assert (steps > 1)
# Temperature and other intermediate variable in channel section i=0...n
T, dT = np.linspace(start=T_inlet, stop=T_sat, num=steps,retstep=True) # [K] Temperature T_i (also returns steps between sections)
# The reference temperature for heat transfer calculations
# The first value [0] should not be important. The heat transfer calculated at i is between i-1 and i
# So, from T[i-1] to T[i]. So, if there reference temperature is the average dT/2 must SUBTRACTED
#T_ref = T - dT/2 # [K] Reference temperature for heat transfer calculations
## Get all thermodynamic values that can be precalculated
# NOTE: all last values must be replaced with the correct values for the saturated liquid state
# Before the values are replaced, sometimes an error is thrown because the values are close to the saturation point
# That, or NaNs and infinites show up. This shouldn't be a problem, unless the second-to-last points also start getting close to the saturation point
# Enthalpy
h = fp.get_enthalpy(T=T, p=p_ref) # [J/kg] Enthalpy
h[-1] = fp.get_saturation_enthalpy_liquid(p=p_ref) # [J/kg] Saturation enthalpy at T_n = T_sat
# Heating power required in section to increase temp by dT. Use enthalpy difference
delta_h = delta_enthalpy_per_section(h=h) # [J/kg] Enthalpy difference per section
Q_dot = required_power(m_dot=m_dot, delta_h=delta_h) # [W]
# Density
rho = fp.get_density(T=T, p=p_ref) # [kg/m^3] Density
rho[-1] = fp.get_liquid_density_at_psat(p_sat=p_ref) # [kg/m^3] Saturation density
# Prandtl number
Pr = fp.get_Prandtl(T=T, p=p_ref) # [-] Prandtl number
Pr[-1] = fp.get_saturation_Prandtl_liquid(p_sat=p_ref) # [-] Saturation Prandtl
# Thermal conductivity
kappa = fp.get_thermal_conductivity(T=T, p=p_ref) # [W/(m*K)] Conductivity
kappa[-1] = fp.get_liquid_saturation_conductivity(p_sat=p_ref) # [W/(m*K)] Saturation conductivity
# Viscosity
mu = fp.get_viscosity(T=T, p=p_ref) # [Pa*s] Viscosity
mu[-1] = fp.get_liquid_saturation_viscosity(p_sat=p_ref) # [Pa*s] Saturation viscosity
return {\
"T":T, # [K]
"dT": dT, # [K]
"rho": rho, # [kg/m^3]
"h": h, # [J/kg]
"Q_dot": Q_dot, # [W]
"Pr": Pr, # [-]
"kappa": kappa, # [W/(m*K)]
"mu": mu, # [Pa*s]
}
def plotSaturationCurve():
fp = FluidProperties("water")
p_sat = np.linspace(start=0.01e5, stop=10.0e5, num=100) # [P] Pressure
T_sat = fp.get_saturation_temperature(p_sat) # [K]
plt.figure()
plt.plot(T_sat, p_sat * 1e-5)
plt.xlabel("Saturation temperature - $T_{{sat}}$ [K]")
plt.ylabel("Saturation pressure - $p_{{sat}}$ [bar]")
plt.grid()
plt.title("Saturation curve for water")
plt.tight_layout()
def prepare_single_phase_gas(T_outlet, steps, p_ref, m_dot, fp: FluidProperties):
T_sat = fp.get_saturation_temperature(p=p_ref) # [K] Saturation temperature
assert (T_outlet > T_sat)
assert (steps > 1)
# Temperature and other intermediate variable in channel section i=0...n
T, dT = np.linspace(start=T_sat, stop=T_outlet, num=steps, retstep=True) # [K] Temperature T_i
# The reference temperature for heat transfer calculations
# The first value [0] should not be important. The heat transfer calculated at i is between i-1 and i
# So, from T[i-1] to T[i]. So, if there reference temperature is the average dT/2 must SUBTRACTED
#T_ref = T - dT/2 # [K] Reference temperature for heat transfer calculations
## Get all thermodynamic values that can be precalculated
# NOTE: all first values must be replaced with the correct values for the saturated gas state
# Before the values are replaced, sometimes an error is thrown because the values are close to the saturation point
# That, or NaNs and infinites show up. This shouldn't be a problem, unless the second-to-last points also start getting close to the saturation point
# Enthalpy
h = fp.get_enthalpy(T=T, p=p_ref) # [J/kg] Enthalpy
h[0] = fp.get_saturation_enthalpy_gas(p=p_ref) # [J/kg] Saturation enthalpy at T_n = T_sat
# Heating power required in section to increase temp by dT. Use enthalpy difference
delta_h = delta_enthalpy_per_section(h=h) # [J/kg] Enthalpy difference per section
Q_dot = required_power(m_dot=m_dot, delta_h=delta_h) # [W]
# Density
rho = fp.get_density(T=T, p=p_ref) # [kg/m^3] Density
rho[0] = fp.get_vapour_density_at_psat(p_sat=p_ref) # [kg/m^3] Saturation density
# Prandtl number
Pr = fp.get_Prandtl(T=T, p=p_ref) # [-] Prandtl number
Pr[0] = fp.get_saturation_Prandtl_gas(p_sat=p_ref) # [-] Saturation Prandtl
# Thermal conductivity
kappa = fp.get_thermal_conductivity(T=T, p=p_ref) # [W/(m*K)] Conductivity
kappa[0] = fp.get_gas_saturation_conductivity(p_sat=p_ref) # [W/(m*K)] Saturation conductivity
# Viscosity
mu = fp.get_viscosity(T=T, p=p_ref) # [Pa*s] Viscosity
mu[0] = fp.get_gas_saturation_viscosity(p_sat=p_ref) # [Pa*s] Saturation viscosity
return {\
"T":T, # [K]
"dT": dT, # [K]
"rho": rho, # [kg/m^3]
"h": h, # [J/kg]
"Q_dot": Q_dot, # [W]
"Pr": Pr, # [-]
"kappa": kappa, # [W/(m*K)]
"mu": mu, # [Pa*s]
}
def two_phase_single_channel(T_wall,
w_channel,
Nu_func_gas,
Nu_func_liquid,
T_inlet,
T_chamber,
p_ref,
m_dot,
h_channel,
fp: FluidProperties,
print_info=True):
""" Function that calculates the total power consumption of a specific chamber, in order to optimize the chamber
Args:
T_wall (K): Wall temperature
w_channel (m): Channel width
Nu_func_gas (-): Nusselt function for gas phase
Nu_func_liquid (-) Nusselt function for liquid phase
T_inlet (K): Chamber inlet temperature
T_chamber (K): Chamber outlet temperature (same as T_c in IRT)
p_ref (Pa): Reference pressure for the Nusselt relation and flow similary parameters (same as inlet pressure as no pressure drop is assumed)
m_dot (kg/s): Mass flow
h_channel (m): Channel height
w_channel_margin (m): The amount of margin around the chamber for structural reasons. Important because it also radiates heat
fp (- ): [description]
print_info(Bool): for debugging purposes
"""
# Calculate saturation temperature, to determine where transition from gas to liquid occurs
T_sat = fp.get_saturation_temperature(p=p_ref) # [K]
# Sanity check on input
assert (T_chamber > T_sat)
assert (T_wall > T_chamber)
# Calculate the two reference temperatures for the separated phases
T_bulk_gas = (T_sat + T_chamber) / 2 # [K] Bulk temperature gas phase
T_bulk_liquid_multi = (
T_inlet +
T_sat) / 2 # [K] Bulk temperature of liquid and multi-phase flow
# Calculate the density at these reference points
rho_bulk_gas = fp.get_density(T=T_bulk_gas, p=p_ref) # [kg/m^3]
rho_bulk_liquid_multi = fp.get_density(T=T_bulk_liquid_multi,
p=p_ref) # [kg/m^3]
# Channel geometry
A_channel = w_channel * h_channel # [m^2] Area through which the fluid flows
wetted_perimeter = wetted_perimeter_rectangular(
w_channel=w_channel, h_channel=h_channel
) # [m] Distance of channel cross-section in contact with fluid
D_hydraulic = hydraulic_diameter_rectangular(
w_channel=w_channel, h_channel=h_channel) # [m] Hydraulic diameter
# Flow similarity parameters (for debugging and Nu calculatoin purposes)
Re_bulk_gas = fp.get_Reynolds_from_mass_flow(
m_dot=m_dot, p=p_ref, T=T_bulk_gas, L_ref=D_hydraulic,
A=A_channel) # [-] Bulk Reynolds number in the gas phase
Re_bulk_liquid_multi = fp.get_Reynolds_from_mass_flow(
m_dot=m_dot,
p=p_ref,
T=T_bulk_liquid_multi,
L_ref=D_hydraulic,
A=A_channel) # [-] Bulk Reynolds number in the liquid/multi-phase
Pr_bulk_gas = fp.get_Prandtl(
T=T_bulk_gas, p=p_ref) # [-] Prandtl number in the gas phase
Pr_bulk_liquid_multi = fp.get_Prandtl(
T=T_bulk_liquid_multi,
p=p_ref) # [-] Prandtl number in liquid/multi-phase
Bo_sat = fp.get_Bond_number(
p_sat=p_ref, L_ref=D_hydraulic
) # [-] Bond number at saturation pressure (assumed to be p_ref)
# Calculate Nusselt number in both sections
args_gas = {
'Re': Re_bulk_gas, # Arguments for Nusselt function (gas phase)
'Pr': Pr_bulk_gas,
'Bo': Bo_sat,
}
args_liquid_multi = { # Arguments for Nusselt function (liquid/multi phase)
'Re': Re_bulk_liquid_multi,
'Pr': Pr_bulk_liquid_multi,
'Bo': Bo_sat,
}
Nu_gas = Nu_func_gas(args=args_gas)
Nu_liquid_multi = Nu_func_liquid(args=args_liquid_multi)
# Calculate Stanton number in both sections
St_gas = Stanton_from_Nusselt_and_velocity(
Nu=Nu_gas,
T_ref=T_bulk_gas,
p_ref=p_ref,
L_ref=D_hydraulic,
m_dot=m_dot,
A=A_channel,
fp=fp) # [-] Stanton number in gas phase
St_liquid_multi = Stanton_from_Nusselt_and_velocity(
Nu_liquid_multi,
T_ref=T_bulk_liquid_multi,
p_ref=p_ref,
L_ref=D_hydraulic,
m_dot=m_dot,
A=A_channel,
fp=fp) # [-] Stanton number in liquid phase
# Calculate velocity for convection parameter (bulk temp used as reference for phase)
u_bulk_gas = velocity_from_mass_flow(
A=A_channel, m_dot=m_dot,
rho=rho_bulk_gas) # [m/s] Velocity at the gas bulk reference state
u_bulk_liquid_multi = velocity_from_mass_flow(
A=A_channel, m_dot=m_dot, rho=rho_bulk_liquid_multi
) # [m/s] Velocity at the liquid/multi-phase bulk reference state
# Convective parameter
h_conv_gas = h_conv_from_Stanton(
Stanton=St_gas, u=u_bulk_gas, T_ref=T_bulk_gas, p_ref=p_ref, fp=fp
) # [W/(m^2*K)] Convective heat transfer coefficient at bulk gas state
h_conv_liquid_multi = h_conv_from_Stanton(
Stanton=St_liquid_multi,
u=u_bulk_liquid_multi,
T_ref=T_bulk_liquid_multi,
p_ref=p_ref,
fp=fp
) # [W/(m^2*K)] Convective heat transfer coefficient at bulk liquid/multi-phase state
# Required specific enthalpy change for heating the separate sections
h_outlet = fp.get_enthalpy(
T=T_chamber, p=p_ref) # [J/kg] Specific enthalpy at the outlet
h_sat_gas = fp.get_saturation_enthalpy_gas(
p=p_ref) # [J/kg] Specific enthalpy of saturated gas
h_inlet = fp.get_enthalpy(T=T_inlet, p=p_ref) # [J/kg]
# Required specific enthalpy increases
delta_h_gas = h_outlet - h_sat_gas # [J/kg] Enthalpy increase needed to go from saturated gas to outlet enthalpy
delta_h_liquid_multi = h_sat_gas - h_inlet # [J/k] Enthalpy increase needed to go from inlet enthalpy to saturated gas
# Required power for those enthalpy changes at the given mass flow
Q_dot_gas = required_power(m_dot=m_dot, delta_h=delta_h_gas) # [W]
Q_dot_liquid_multi = required_power(m_dot=m_dot,
delta_h=delta_h_liquid_multi) # [W]
# Required heater area to achieve the required power
A_heater_gas = required_heater_area(Q_dot=Q_dot_gas,
h_conv=h_conv_gas,
T_wall=T_wall,
T_ref=T_bulk_gas) # [m^2]
A_heater_liquid_multi = required_heater_area(
Q_dot=Q_dot_liquid_multi,
h_conv=h_conv_liquid_multi,
T_wall=T_wall,
T_ref=T_bulk_liquid_multi) # [m^2]
# Required length to achieve desired area
L_channel_gas = A_heater_gas / wetted_perimeter # [m] Length of channel after gas is saturated
L_channel_liquid_multi = A_heater_liquid_multi / wetted_perimeter # [m] Length of channel after heater
L_channel = L_channel_gas + L_channel_liquid_multi # [m]
L_hydrodynamic_entrance = D_hydraulic * Re_bulk_liquid_multi * 0.04 # [m] Hydrodynamic entrance to estimate if the flow is fully developed
assert (h_outlet > h_sat_gas)
assert (h_sat_gas > h_inlet)
if (print_info):
print("\n--- SPECIFIC ENTHALPY AT DIFFERENT STATIONS ---")
print("h_outlet: {:4.3f} J/kg".format(h_outlet))
print("h_sat_gas: {:4.3f} J/kg".format(h_sat_gas))
print("h_inlet: {:4.3f} J/kg".format(h_inlet))
print("\n --- REQUIRED POWER ---")
print("Q_dot_gas: {:2.5f} W".format(Q_dot_gas))
print("Q_dot_liquid_multi: {:2.5f} W".format(Q_dot_liquid_multi))
print("\n --- BULK GAS PHASE PARAMETERS --- ")
print("u: {:3.2f} m/s".format(u_bulk_gas))
print("Nu: {}".format(Nu_gas))
print("Re: {}".format(Re_bulk_gas))
print("Pr: {}".format(Pr_bulk_gas))
print("St: {}".format(St_gas))
print("Bo_sat: {}".format(Bo_sat))
print("\n --- BULK LIQUID/MULTI-PHASE PARAMETERS ---")
print("u: {:3.4f} m/s".format(u_bulk_liquid_multi))
print("Nu: {}".format(Nu_liquid_multi))
print("Re: {}".format(Re_bulk_liquid_multi))
print("Pr: {}".format(Pr_bulk_liquid_multi))
print("St: {}".format(St_liquid_multi))
print("\n --- CHARACTERISTIC GEOMETRIC VALUES --- ")
print("Hydrodynamic entance length: {:3.3f} micron".format(
L_hydrodynamic_entrance * 1e6))
print("Hydraulic diameter: {:3.3f} micron".format(D_hydraulic * 1e6))
print("L/D: {:4.2f} ".format(L_channel / D_hydraulic))
print("L/X_T {:4.2f}".format(L_channel / L_hydrodynamic_entrance))
print("\n --- RESULTING GEOMETRY ---")
print("Total length: {:3.3f} mm".format(L_channel * 1e3))
print("Length (liquid/multi): {:3.3f} mm".format(
L_channel_liquid_multi * 1e3))
print("Length (gas): {:3.4f} mm".format(L_channel_gas * 1e3))
print("Relative length (gas) {:3.3f} \%".format(L_channel_gas /
L_channel * 100))
## Return a dictionary with results and interesting intermediate values
res = {
"L_channel": L_channel, # [m] Total length of channel
"D_hydraulic": D_hydraulic, # [m] Hydraulic diameter of channel
"Nu_liquid_multi":
Nu_liquid_multi, # [-] Nusselt number of liquid/multi-phase flow
"Pr_bulk_liquid_multi":
Pr_bulk_liquid_multi, # [-] Prandlt number of liquid/multi-phase flow
"Re_bulk_liquid_multi":
Re_bulk_liquid_multi, # [-] Reynolds number of liquid/multi-phase flow
"St_liquid_multi":
St_liquid_multi, # [-] Stanton number of liquid/multi-phase flow
"h_conv_liquid_multi":
h_conv_liquid_multi, # [W/(m^2*K)] Heat transfer coefficient
"A_heater_liquid_multi":
A_heater_liquid_multi, # [m^2] Required heater area for liquid/multi-phase flow
"L_channel_liquid_multi":
L_channel_liquid_multi, # [m] Length of channel to get required heater area
"u_bulk_liquid_multi":
u_bulk_liquid_multi, # [m/s] Bulk flow velocity of liquid/multi-phase flow
"rho_bulk_liquid_multi":
rho_bulk_liquid_multi, # [kg/m^3] Bulk density of liquid/multi-phase flow
"T_bulk_liquid_multi":
T_bulk_liquid_multi, # [K] Bulk temperature of liquid/multi-phase flow
"delta_h_liquid_multi":
delta_h_liquid_multi, # [J/kg] Enthalpy change from inlet to saturated gas
"Q_dot_liquid_multi":
Q_dot_liquid_multi, # [W] Power required for enthalpy change
## Same thing but for gas values
"Nu_gas": Nu_gas, # [-]
"Pr_bulk_gas": Pr_bulk_gas, # [-]
"Re_bulk_gas": Re_bulk_gas, # [-]
"St_gas": St_gas, # [-]
"h_conv_gas": h_conv_gas, # [W/(m^2*K)]
"A_heater_gas": A_heater_gas, # [m^2]
"L_channel_gas": L_channel_gas, # [m]
"u_bulk_gas": u_bulk_gas, # [m/s]
"rho_bulk_gas": rho_bulk_gas, # [kg/m^3]
"T_bulk_gas": T_bulk_gas, # [K]
"delta_h_gas": delta_h_gas, # [J/kg]
"Q_dot_gas": Q_dot_gas, # [W]
}
return res
w_channel = td['w_channel'] # [m] Channel width
T_inlet = td['T_inlet'] # [K] Inlet temperature
T_wall = td['T_wall'] # [K] Wall temperature
p_inlet = td['p_inlet'] # [Pa] Inlet pressure
m_dot = td['m_dot'] # [kg/s] Mass flow (through all channels if multiple)
channel_amount = td['channel_amount'] # [-] Amount of channels
h_channel = td['h_channel'] # [m] Channel height/depth
fp = FluidProperties(
td['propellant']) # Object from which fluid properties can be accessed
# Calculate mass flow for one single channel
m_dot_channel = m_dot / channel_amount # [kg/s] Mass flow through one single channel
## Chamber temperature is unknown, so instead a range is chosen from T_sat + 1 to T_wall-1
T_sat = fp.get_saturation_temperature(p=p_inlet) # [K]
T_chamber = np.linspace(start=T_sat + 1, stop=T_wall - 1, num=250) # [K]
it = np.nditer(T_chamber, flags=['c_index'])
L_channel_1 = np.zeros_like(T_chamber) # [m]
L_channel_2 = np.zeros_like(T_chamber) # [m]
L_channel_3 = np.zeros_like(T_chamber) # [m]
for T in it:
## First set of Nusselt relations
res_1 = zD.two_phase_single_channel( T_wall=T_wall, w_channel=w_channel, Nu_func_gas=Nu_func_gas_1, Nu_func_liquid=Nu_func_liquid_1,\
T_inlet=T_inlet, T_chamber=float(T), p_ref=p_inlet, m_dot=m_dot_channel,\
h_channel=h_channel, fp=fp,print_info=False)
# Store results
L_channel_1[it.index] = res_1['L_channel']
def calc_and_plot_thruster(td, axs_to_plot):
# For Cen the chamber temperature is unknown, so a range is taken instead
# seem inconsitent with saturation temperatures and/or reported wall temperatures
T_wall = td['T_wall'] # [K] Wall temperature
w_channel = td['w_channel'] # [m] Channel width
T_inlet = td['T_inlet'] # [K] Inlet temperature
p_inlet = td['p_inlet'] # [Pa] Inlet pressure
m_dot = td['m_dot'] # [kg/s] Mass flow (through all channels if multiple)
channel_amount = td['channel_amount'] # [-] Amount of channels
h_channel = td['h_channel'] # [m] Channel height/depth
fp = FluidProperties(td['propellant']) # Object from which fluid properties can be accessed
# Calculate mass flow for one single channel
m_dot_channel = m_dot/channel_amount # [kg/s] Mass flow through one single channel
# Chamber temperature is unknown, so a range is taken
T_sat = fp.get_saturation_temperature(p=p_inlet) # [K]
T_chamber = np.linspace(start=T_sat+1, stop=T_wall-1, num=250) # [K]
# Geometric values
wetted_perimeter = basic.chamber.wetted_perimeter_rectangular(w_channel=w_channel, h_channel=h_channel) # [m] Wetted perimeter of channel
A_channel = w_channel*h_channel # [m^2] Cross-sectional through which fluid flows
D_hydraulic = basic.chamber.hydraulic_diameter_rectangular(w_channel=w_channel, h_channel=h_channel) # [m] Hydraulic diameter
# Preparation functions calculations many intermediate values that are known before geometry is known
# Storing the length results in here, one for each set of Nusselt relations
L_1 = np.zeros_like(T_chamber) # [m] Total channel length
L_2 = np.zeros_like(L_1)
# Loop to calculate the channel length with each wall temperature
it_T = np.nditer(T_chamber, flags=['c_index']) # [K] Wall temperature
T_chamber_guess = None # [K] Stores chamber temperature when actual length is first reached (in laminar case).
for T in it_T:
prepared_values = oneD.full_homogenous_preparation(
T_inlet=T_inlet,
T_outlet=T, # <---- Iterated variable
m_dot=m_dot_channel,
p_ref=p_inlet,
steps_l=steps_l,
steps_tp=steps_tp,
steps_g=steps_g,
fp=fp)
# results_1 = oneD.full_homogenous_calculation(
# prepared_values=prepared_values,
# Nusselt_relations=Nusselt_relations_1,
# A_channel=A_channel,
# wetted_perimeter=wetted_perimeter,
# D_hydraulic=D_hydraulic,
# m_dot=m_dot,
# T_wall=T_wall,
# p_ref=p_inlet,
# fp=fp
# )
results_2 = oneD.full_homogenous_calculation(
prepared_values=prepared_values,
Nusselt_relations=Nusselt_relations_2,
A_channel=A_channel,
wetted_perimeter=wetted_perimeter,
D_hydraulic=D_hydraulic,
m_dot=m_dot_channel,
T_wall=T_wall, # <--- Iterated variable
p_ref=p_inlet,
fp=fp
)
# First time the length crosses the actual length, store the value
if (T_chamber_guess == None) and (results_2['L_total'] > td['L_channel']): # results_2 stores laminar results
T_chamber_guess = T # [K]
# L_1[it_T.index] = results_1['L_total']
L_2[it_T.index] = results_2['L_total']
## Print info about thruster, including, estimated chamber temperature for laminar relations
print("Thruster name: {}".format(td['name']))
print("Estimated chamber temperature: {:3.2f} K".format(T_chamber_guess))
axs_to_plot.set_title("$\\dot{{m}}={:1.2f}$ mg/s, $p={:1.2f}$ bar".format(m_dot*1e6,p_inlet*1e-5))
# axs_to_plot.plot(T_chamber,L_1*1e3, label="Turbulent")
axs_to_plot.plot(T_chamber,L_2*1e3, label="Laminar")
axs_to_plot.hlines(td['L_channel']*1e3, xmin=T_chamber[0], xmax=T_chamber[-1], linestyle='dashed', color='red', label="Real length")
axs_to_plot.grid()
axs[1][0].plot(T_chamber, w_throat[it_AR.index, :] * 1e6)
axs[2][0].plot(T_chamber, Isp[it_AR.index, :])
axs[3][0].plot(T_chamber, Pt_ideal[it_AR.index, :])
axs[4][0].plot(T_throat[it_AR.index, :], mu_throat[it_AR.index, :])
# Right side of plot
axs[0][1].plot(T_chamber, D_hydraulic_throat[it_AR.index, :] * 1e6)
axs[1][1].plot(T_chamber, Re_throat[it_AR.index, :])
axs[2][1].plot(T_chamber, Pr_throat[it_AR.index, :])
axs[3][1].plot(T_throat[it_AR.index, :], p_throat[it_AR.index, :] * 1e-5)
axs[4][1].plot(T_exit[it_AR.index, :], p_exit[it_AR.index, :] * 1e-5)
# Plot saturation curve on the throat pressure plot to check for condensation
# Some calculations in here are to put proper bound on the plot
T_sat_max = fp.get_saturation_temperature(
p=1.1 * np.max(p_throat)
) #fp.get_critical_temperature() # [K] Get saturation temperature at 1.1 times p_throat
T_sat = np.linspace(
start=np.min(T_throat), stop=T_sat_max,
num=50) # [K] Evenly spaced temperature from inlet temp to critical temp
p_sat = fp.get_saturation_pressure(
T=T_sat) # [Pa] Saturation pressures matching the temps
# Plot it on the throat pressure curve
axs[3][1].plot(T_sat, p_sat * 1e-5, label="Saturation curve")
# Again, but with bounds for exit pressures and temperature, to keep plot nice
T_sat_max_2 = fp.get_saturation_temperature(
p=1.1 * np.max(p_exit)
) #fp.get_critical_temperature() # [K] Get saturation temperature at 1 bar
T_sat_2 = np.linspace(
start=np.min(T_exit), stop=T_sat_max_2,