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_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]
}
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
for D in D_iter:
## 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: