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]
}
Nu_func_le_laminar = Nu_laminar_developed_constant_wall_temp_square
Nu_func_le_turbulent = Nu_DB
Nu_func_tp = Nu_Kandlikar_NBD_CBD_dryout
# Design parameters
p = 5e5 # Pressure through channel [Pa]
m_dot = 200e-6 # [kg/s]
A_channel = 1e-6 # [m^2] Channel cross sections
D_h = 1e-6 * np.array((100, 200, 500)) # [m] Hydraulic diameters
# Mass flux calculated for reference
G = m_dot / A_channel # [kg/(m^2*s)] Mass flux
print("Mass flux: {:3.1f} kg/(m^2*s)".format(G))
# Saturatoin conditions
rho_l = fp.get_liquid_density_at_psat(
p_sat=p) # [kg/m^3] Liquid density at saturation point
rho_g = fp.get_vapour_density_at_psat(
p_sat=p) # [kg/m^3] Vapour density at saturation point
mu_l = fp.get_liquid_saturation_viscosity(
p_sat=p) # [Pa*s] Viscosity at liquid saturatoin point (for Re_le)
Bo = fp.get_Bond_number(p_sat=p, L_ref=D_h) # [-] Bond number
# Calculate two-phase Nusselt number
x = np.linspace(start=0, stop=1, num=10000)
D_iter = np.nditer(D_h, flags=['c_index'])
Nu_tp_laminar = np.zeros(
(np.size(D_h), np.size(x)
)) # [-] Storing two-phase Nusselt numbers for assumed laminar flow
Nu_tp_turbulent = np.zeros_like(
Nu_tp_laminar
) # [-] Storing two-phase Nusselt numbers for assumed turbulent flow
## File to show the effect of the density and homogeneous assumption on void fraction and density
import numpy as np
import matplotlib.pyplot as plt
import thermo.two_phase as tp
from thermo.prop import FluidProperties
# Select propellant
fp = FluidProperties("water")
x = np.linspace(start=0, stop=1,num=1000)
p = 1e5*np.array((1,5,10)) # [Pa] Saturation pressure
rho_g = fp.get_vapour_density_at_psat(p_sat=p)
rho_l = fp.get_liquid_density_at_psat(p_sat=p)
p_iter = np.nditer(p, flags=['c_index'])
alpha = np.zeros((np.size(p),np.size(x)))
print(alpha.shape)
# Calculate void fraction for different pressures p
for p in p_iter:
alpha[p_iter.index] = tp.homogenous_void_fraction(x=x, rho_g=rho_g[p_iter.index], rho_l=rho_l[p_iter.index]) # [-] Void fraction
# Plot it!
plt.figure()
p_iter.reset()
for p in p_iter: