def total_power_single_channel(T_wall, w_channel, Nu_func, T_inlet, T_chamber,
T_ref, p_ref, m_dot, h_channel,
w_channel_margin, emmisivity, fp):
""" 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 (-): Nusselt function
T_inlet (K): Chamber inlet temperature
T_chamber (K): Chamber outlet temperature (same as T_c in IRT)
T_ref (K): Reference temperature for the Nusselt relation and flow similary parameters
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
emmisivity (-) Emmisivity of the chamber material (for calculation of radation losses)
fp (- ): [description]
"""
## NOTE: just a test, assumptions are a bit sloppy, and this is just to test optimization approach at this stage
A_channel = w_channel * h_channel # [m^2] Channel area
print("A_channel: {}".format(A_channel))
wetted_perimeter = wetted_perimeter_rectangular(
w_channel=w_channel, h_channel=h_channel
) # [m] Distance of channel cross-section in contact with fluid
print("wetted_perimeter: {}".format(wetted_perimeter))
# Reference length is hydraulic diameter
D_hydraulic = hydraulic_diameter_rectangular(
w_channel=w_channel, h_channel=h_channel) # [m] Hydraulic diameter
cp = chamber_performance_from_Nu(Nu_func=Nu_func,
T_inlet=T_inlet,
T_chamber=T_chamber,
T_ref=T_ref,
T_wall=T_wall,
p_ref=p_ref,
m_dot=m_dot,
A_channel=A_channel,
L_ref=D_hydraulic,
fp=fp)
## Assume single-sided heater heat chamber material through-out at T-wall, and all along the wetted perimeter heat flows equally to teh propellant
A_heater = cp['A_heater'] # [m^2]
assert (A_heater > 0)
L_channel = A_heater / wetted_perimeter # [m] Required length of channel to achieve required heat flow
print("L_channel: {}".format(L_channel))
A_chip = required_chip_area(
L_channel=L_channel,
w_channel=w_channel,
w_channel_margin=w_channel_margin
) # [m^2] Assume radiation occurs from silicon on just a single side of the heater
print("A_microheater: {}".format(A_chip))
P_radiation = radiation_loss(T=T_wall, A=A_chip,
emmisivity=emmisivity) # [W] Radiation loss
P_total = P_radiation + cp[
'Q_dot'] # [W] Total power consumption, the variable to minimize
print("Heat loss {}".format(P_radiation / P_total))
return P_total
def test_simple_input(self):
h = 1
w = 1
exp = 4
res = chamber.wetted_perimeter_rectangular(w_channel=w, h_channel=h)
self.assertEqual(res, exp)
h = 4
exp = 10
res = chamber.wetted_perimeter_rectangular(w_channel=w, h_channel=h)
self.assertEqual(res, exp)
w = 2
exp = 12
res = chamber.wetted_perimeter_rectangular(w_channel=w, h_channel=h)
self.assertEqual(res, exp)
def rectangular_multi_channel_homogenous_calculation(channel_amount, prepared_values, Nusselt_relations, pressure_drop_relations, w_channel, h_channel, m_dot, T_wall, p_inlet, fp: FluidProperties, area_ratio_contraction=None, wall_args=None):
"""Same as full_homogenous_calculation, but with channels combined
Args:
channel_amount (-): Number of channels
prepared_values (dict): Dictionary with prepared thermodynamic variables
Nusselt_relations (dict): Nusselt relations for different phases
pressure_drop_relations (dict): Pressure drop relations for different phases and effects
A_channel (m^2): Area of a single channel
wetted_perimeter (m): Circumference of a single channel (fot heat flux purposes)
D_hydraulic (m): Reference for Reynolds numbers etc...
m_dot (kg/s): mass flow
T_wall (K): Wall temperature
p_ref (Pa): Pressure through channel
fp (FluidProperties): Object to access propellant properties with
Returns:
Results {}: Return results which are relevant for optimization
"""
m_dot_channel = m_dot / channel_amount # [kg/s] Mass flow for a single channel
A_channel = w_channel * h_channel # [m^2] Area of a single channel
D_hydraulic = hydraulic_diameter_rectangular(w_channel=w_channel, h_channel=h_channel) # [m]
wetted_perimeter = wetted_perimeter_rectangular(w_channel=w_channel, h_channel=h_channel) # [m]
# dP_contraction = None # [Pa] Contraction pressure drop is set to None by default, so it raises obvious errors if one attemps to use it without calculating it before (0 would hide errors)
# # Contraction losses must be calculated here, as this pressure drop does significantly affect heat transfer
# if pressure_drop_relations is not None:
# if 'contraction' in pressure_drop_relations:
# area_ratio_contraction = w_channel*channel_amount / w_inlet_manifold # [-]
# dP_contraction = calc_contraction_loss(dP_func=pressure_drop_relations['contraction'])
# Simulation of the flow resulting in desired channel length
res = full_homogenous_calculation(
prepared_values=prepared_values,
Nusselt_relations=Nusselt_relations,
pressure_drop_relations=pressure_drop_relations,
A_channel=A_channel,
wetted_perimeter=wetted_perimeter,
D_hydraulic=D_hydraulic,
m_dot=m_dot_channel,
T_wall=T_wall,
p_ref=p_inlet,
fp=fp,
area_ratio_contraction=area_ratio_contraction,
wall_args=wall_args,
)
return res
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
m_dot=m_dot, h_channel=h_channel, w_channel_margin=w_channel_margin,\
emmisivity=emmissivity, fp=fp)
print(x_result)
# Found optimum
T_superheat = x_result.x[0] # [K]
w_channel = x_result.x[1] # [m]
# Chamber performance following from optimum
T_wall = T_chamber + T_superheat # [K] Wall temperature
A_channel = w_channel * h_channel # [m^2] Channel area
mass_flux = m_dot / A_channel # [kg/m^2] Used as reference for validity of many relations in micro-channel studies
print("A_channel: {}".format(A_channel))
wetted_perimeter = wetted_perimeter_rectangular(
w_channel=w_channel, h_channel=h_channel
) # [m] Distance of channel cross-section in contact with fluid
print("wetted_perimeter: {}".format(wetted_perimeter))
# Reference length is hydraulic diameter
D_hydraulic = hydraulic_diameter_rectangular(
w_channel=w_channel, h_channel=h_channel) # [m] Hydraulic diameter
cp = zD.chamber_performance_from_Nu(Nu_func=Nu_func, T_inlet=T_inlet, T_chamber=T_chamber,\
T_ref=T_bulk, T_wall=T_wall, p_ref=p_inlet, m_dot=m_dot, A_channel=A_channel, L_ref=D_hydraulic, fp=fp)
L_channel = cp['A_heater'] / w_channel # [m]
print("L_channel: {:3.4f} mm".format(L_channel * 1e3))
print("mass_flux: {}".format(mass_flux))
print("Mass flow: {:3.4f} mg/s".format(m_dot * 1e6))
## Print all results
print(ep)
'p_exit'] # [Pa] Nozzle exit pressure
# Calculate ideal power
h_inlet = fp.get_enthalpy(T=T_inlet,
p=p_chamber) # [J/kg] Enthalpy at chamber inlet
delta_h = h_chamber - h_inlet # [J/kg] Enthalpy change between inlet and chamber
Pt_ideal = m_dot * delta_h # [W] Total ideal power consumption (no heat losses)
## Plot the results
fig, axs = plt.subplots(5, 2)
# Render the mass flow and throat width as a function of temperature and area ratios
w_throat = A_throat / h_channel # [m] Throat width, determined by assuming channel depth
# Find out the hydraulic diameter for a rectangular channel
wetted_perimeter = wetted_perimeter_rectangular(
w_channel=w_throat, h_channel=h_channel) # [m] Wetted perimeter
D_hydraulic_throat = hydraulic_diameter(
A=A_throat, wetted_perimeter=wetted_perimeter) # [m] Hydraulic diameter
# Numpy and CoolProp don't play nicely together, so iterate over each element to calculate Reynolds's number
it_AR.reset()
for AR in it_AR:
it_T = np.nditer(T_chamber, flags=['c_index'])
for T in it_T:
# Calculate Reynolds number at throat
Re_throat[it_AR.index][it_T.index] = fp.get_Reynolds_from_velocity(T=T_throat[it_AR.index][it_T.index], p=p_throat[it_AR.index][it_T.index], \
L_ref=D_hydraulic_throat[it_AR.index][it_T.index], u=u_throat[it_AR.index][it_T.index]) # [-] Reynolds number at throat
it_AR.reset()
for AR in it_AR:
# Left side of plot
axs[0][0].plot(T_chamber,
