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
# Range of Reynolds numbers to consider
Reynolds = np.logspace(start=0, stop=2.8)
D_hydraulic = np.logspace(start=-4.93, stop=-2.93)
A_channel = D_hydraulic**2
Reynolds_2 = fp.get_Reynolds_from_mass_flow(T=T_liquid,
p=p,
L_ref=D_hydraulic,
m_dot=m_dot,
A=A_channel)
# Range of hydraulic diameter that fit this Reynolds number
#w_channel = 2*m_dot/( Reynolds_100 * mu_liquid ) - h_c # [m]
#A_channel = h_c * w_channel # [m^2]
#D_hydraulic = basic.chamber.hydraulic_diameter_rectangular(w_channel=w_channel,h_channel=h_c) # [m]
#Reynolds_check = fp.get_Reynolds_from_mass_flow(T=T_liquid, p=p, L_ref=D_hydraulic, m_dot=m_dot, A=A_channel) # [-]
Bond = fp.get_Bond_number(p_sat=p, L_ref=D_hydraulic) # [m]
# Prandtl number in both reference states
Pr_liquid = fp.get_Prandtl(T=T_liquid, p=p) # [-]
Pr_gas = fp.get_Prandtl(T=T_gas, p=p) # [-]
# Conductivity in reference state
conductivity_liquid = fp.get_thermal_conductivity(T=T_liquid, p=p)
Nu_DB_liquid = np.zeros_like(Reynolds)
Nu_DB_gas = np.zeros_like(Reynolds)
Nu_Kandlikar_liquid = np.zeros_like(Reynolds)
#Nu_Kandlikar_gas = np.zeros_like(Reynolds)
# Calculate Nusselt number for different relations
# Iterare over Reynolds numbers
# print(Reynolds)
# iter_Re = np.nditer(Reynolds, flags=['c_index'])
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:
i = D_iter.index
# Flow parameters for entire flow as a liquid
Re_le = Reynolds_from_mass_flow(
def calc_homogenous_transition(p_sat, x, alpha, T_sat, rho_l, rho_g, rho, m_dot, mu_l, mu, Pr, Pr_l, kappa, kappa_l, Q_dot, T_wall, D_hydr, wetted_perimeter, A_channel, Nu_func_tp, Nu_func_le, Nu_func_dryout, fp: FluidProperties, wall_args=None):
"""[summary]
Args:
p_sat ([type]): [description]
x ([type]): [description]
alpha ([type]): [description]
T_sat ([type]): [description]
rho_l ([type]): [description]
rho_g ([type]): [description]
rho ([type]): [description]
m_dot ([type]): [description]
mu_l ([type]): [description]
mu ([type]): [description]
Pr ([type]): [description]
Pr_l ([type]): [description]
kappa ([type]): [description]
kappa_l ([type]): [description]
Q_dot ([type]): [description]
T_wall ([type]): [description]
D_hydr ([type]): [description]
wetted_perimeter ([type]): [description]
A_channel ([type]): [description]
Nu_func_tp ([type]): [description]
Nu_func_le ([type]): [description]
Nu_func_dryout ([type]): [description]
fp (FluidProperties): [description]
wall_args ([type], optional): [description]. Defaults to None.
Returns:
[type]: [description]
"""
# Calculate flow velocity
# Homogenous assumption means that liquid and gas velocity are equal, so one of two must be calculated.
# Alpha (void fraction) has already been calculated to satisfy this condition
# For both velocities there will be some issues with a singularity at (x=0, alpha =0) or (x=1, alpha=1), but the overal density rho does not have this problem
#u_l = (m_dot / A_channel) * ( 1 - x ) / (rho_l * ( 1- alpha )) # [m/s]
#u_g = (m_dot / A_channel) * x / (rho_g * alpha) # [m/s]
u = (m_dot / A_channel) / rho # [m/s]
## Calculate flow similarity/two-phase parameters that can only be known as soon as the geometry is known
## NOTE: mu is some form of weighted average and there are several ways to weight it (prepare_ function has the method)
Re = Reynolds_from_mass_flow(m_dot=m_dot, A_channel=A_channel, L_ref=D_hydr, mu=mu) # [-]
# Bond number
Bo = fp.get_Bond_number(p_sat=p_sat,L_ref=D_hydr) # [-] Bond number
# Nusselt number for entire flow as liquid (often used for two-phase relations)
# NOTE: _le is often used as subscript, but _l might sometimes mean something else, such as G(1-x) * L / (A * mu_l). _le does NOT scale with (1-x) and is G * L / ( A * mu_l )
Re_le = Reynolds_from_mass_flow(m_dot=m_dot, A_channel=A_channel, L_ref=D_hydr, mu=mu_l) # [-] Use viscosity of liquid phase to get Re_le
args_le = { 'Re': Re_le,
'Pr': Pr_l}
Nu_le = Nu_func_le(args=args_le) # [-] Nusselt number as if entire flow was liquid.
args_dryout = {
'Re': Re,
'Pr': Pr,
'kappa': kappa,
'kappa_l': kappa_l,
}
Nu_dryout = Nu_func_dryout(args=args_dryout)
## Actual Nusselt number
args = { 'Re': Re,
'Pr': Pr_l,
'Bo': Bo,
'rho_g': rho_g,
'rho_l': rho_l,
'x': x,
'Nu_le': Nu_le,
'Nu_dryout': Nu_dryout,
}
Nu = Nu_func_tp(args=args) # [-] Two-phase Nusselt number
# The Nusselt number is calculated in relation to liquid thermal conducitvity only
h_conv = heat_transfer_coefficient_from_Nu(Nu=Nu, kappa=kappa_l, L_ref=D_hydr) # [W/(m^2 * K)] Heat transfer coefficient
# For backwards compatability with test code, effect of wall temperature thickness can be activate separetly and is off by default
we = None # Pass nothing to end result, if no wall arguments are passed
if wall_args is not None: # If no information about wall is provided, skip this part
# Call function to get dictionary of relevant wall effect parameters
we = calc_wall_effect_parameters(\
h_conv=h_conv,
w_channel_spacing=wall_args['w_channel_spacing'],
kappa_wall=wall_args['kappa_wall'], # Thermal conductivity of the wall
h_channel=wall_args['h_channel'], # NOTE: these arguments were not already passed to this function, due to earlier design choices
w_channel=wall_args['w_channel'],
T_wall_top=T_wall, # The temperature of the top is simply the heater temperature at the top, which was earlier set to T_wall
T_wall_bottom=wall_args['T_wall_bottom'], # IMPORTANT: The bottom wall temperature is the one that must be guessed or iterated towards!
T_fluid=T_sat) # The fluid temperature is equal
T_wall = we['T_wall_effective'] # [K]
# print("(Effective) wall temperature (K): ")
# print(T_wall)
# NOTE: T_wall may be replaced if T_wall is changed due to calculated wall effects
A_heater = required_heater_area(Q_dot=Q_dot, h_conv=h_conv, T_wall=T_wall, T_ref=T_sat) # [m^2] Required heater area to heat up section with Q_dot
delta_L = A_heater / wetted_perimeter # [m] Required channel section length for heating area
#assert(np.all(delta_L>0))
L = np.cumsum(delta_L) # [m] Cumulative channel length of two-phase section
# Note, now the channel length is known, the heat transfer in the plane of the bottom wall can be calculated (which must be equal to radiation heat loss)
# This is only necessary if wall effects are taken into account
Q_bottom_plane_heat_balance = None # [W] Is None unless calculated to prevent use if not actually calculated
if we is not None:
Q_bottom_plane_heat_balance = calc_bottom_plane_heat_balance(
h_conv=h_conv,
T_fluid=T_sat,
we=we,
wall_args=wall_args,
delta_L=delta_L)
return {
'L': L,
'delta_L': delta_L,
'u': u,
'rho': rho,
'Re': Re,
'Nu': Nu,
'Nu_le': Nu_le,
'h_conv': h_conv,
'Q_bottom_plane_heat_balance': Q_bottom_plane_heat_balance,
}