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]
}
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