def test_simple_input(self):
A = 1
m_dot = 1
rho = 1
exp = 1
res = chamber.velocity_from_mass_flow(A=A, m_dot=m_dot, rho=rho)
self.assertEqual(exp, res)
A = 2
exp = 0.5
res = chamber.velocity_from_mass_flow(A=A, m_dot=m_dot, rho=rho)
self.assertEqual(exp, res)
rho = 5
exp = 0.1
res = chamber.velocity_from_mass_flow(A=A, m_dot=m_dot, rho=rho)
self.assertEqual(exp, res)
m_dot = 100
exp = 10
res = chamber.velocity_from_mass_flow(A=A, m_dot=m_dot, rho=rho)
self.assertEqual(exp, 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
def chamber_performance_from_Nu(Nu_func, T_inlet, T_chamber, T_ref, T_wall,
p_ref, m_dot, A_channel, L_ref,
fp: FluidProperties):
""" Function that calculates the power consumption and heating area for a specific chamber
Args:
Nu_func (-): Nusselt function, that implement the emperical relation of choice
T_inlet (K): Chamber inlet temperature
T_chamber (K): Chamber outlet temperature (same as T_chamber for IRT)
T_ref (K): Reference temperature for the Nusselt relation and flow similary parameters
T_wall (K): Wall temperature
p_ref (Pa): Chamber pressure (no pressure drop assumed)
m_dot (kg/s): Mass flow
A_channel (m^2): Cross-sectional area of the chamber, through which the fluid flows
L_ref (m): Reference length for Nusselt relation and flow similarty parameters
fp (FluidProperties): Object from which Fluid Properties are determined
Returns:
dictionary with heater area, power required to heat up flow and Nusselt number
"""
## Make sure all parameters are calculated at the same reference state (including velocity!)
# Pr and Re parameters needed for most Nusselt relation
rho_ref = fp.get_density(T=T_ref, p=p_ref) # [kg/m^3] Reference density
u_ref = velocity_from_mass_flow(
A=A_channel, m_dot=m_dot,
rho=rho_ref) # [m/s] Speed at reference state
print("u_ref {} m/s".format(u_ref))
Re_ref = fp.get_Reynolds_from_mass_flow(
T=T_ref, p=p_ref, L_ref=L_ref, m_dot=m_dot,
A=A_channel) # [-] Reynolds number at reference state
Pr_ref = fp.get_Prandtl(T=T_ref,
p=p_ref) # [-] Prandtl number at reference state
# Now the Nusselt can be determined
Nusselt = Nu_func(args={
'Re': Re_ref,
'Pr': Pr_ref
}) # [-] Nusselt number at given state (used for plotting purposes)
Stanton = Stanton_from_Nusselt_func_and_velocity(
Nu_func=Nu_func,
m_dot=m_dot,
A=A_channel,
T_ref=T_ref,
p_ref=p_ref,
L_ref=L_ref,
fp=fp) # [-] Stanton number at reference state
h_conv = h_conv_from_Stanton(Stanton=Stanton,
u=u_ref,
T_ref=T_ref,
p_ref=p_ref,
fp=fp)
# Now determine how much energy must be convected
delta_h = ideal_enthalpy_change(T_inlet=T_inlet,
p_inlet=p_ref,
T_outlet=T_chamber,
p_outlet=p_ref,
fp=fp) # [J/kg]
Q_dot = required_power(
m_dot=m_dot, delta_h=delta_h) # [W] Required power to achieve delta_h
A_heater = required_heater_area(Q_dot=Q_dot,
h_conv=h_conv,
T_wall=T_wall,
T_ref=T_ref) # [m^2]
assert (A_heater > 0)
# Return a dictionary with interesting values
return {
'A_heater': A_heater,
'Q_dot': Q_dot,
'Nusselt': Nusselt,
'Re_ref': Re_ref,
'Pr_ref': Pr_ref
}
m_dot = td['m_dot'] / td['channel_amount'] # [kg/s] Mass flow
h_channel = td['h_channel'] # [m] Channel height/depth
w_channel = td['w_channel'] # [m] Channel width
L_channel = td['L_channel'] # [m] Channel length
T_outlet = td['T_chamber'] # [K] Outlet of channel
p_inlet = td['p_inlet'] # [Pa]
p_outlet = p_inlet # [Pa] Outlet pressure (assumed roughly equal to inlet)
T_inlet = td['T_inlet'] # [K]
# Geometry calculations
D_h = hydraulic_diameter_rectangular(
w_channel=w_channel, h_channel=h_channel) # [m] Hydraulic diameter
A_channel = w_channel * h_channel
# Inlet conditions
rho_inlet = fp.get_density(T=T_inlet, p=p_inlet) # [kg/m^3]
u_inlet = velocity_from_mass_flow(A=A_channel, m_dot=m_dot, rho=rho_inlet)
# Outlet conditions
rho_outlet = fp.get_density(T=T_outlet, p=p_outlet)
u_outlet = velocity_from_mass_flow(A=A_channel, m_dot=m_dot, rho=rho_outlet)
Re_outlet = fp.get_Reynolds_from_mass_flow(T=T_outlet,
p=p_outlet,
L_ref=D_h,
m_dot=m_dot,
A=A_channel)
print("\n\nTHRUSTER NAME: {}".format(td['name']))
print("\n --- GEOMETRY ---")
print("Channel length: {:4.3f} mm".format(L_channel * 1e3))
print("Hydraulic diameter: {:4.3f} um".format(D_h * 1e6))
print("L/D: {:3.2f} ".format(L_channel / D_h))
w_channel_min = 0.5e-5 # [m] Minimum channel width
w_channel_max = 5e-5 # [m] Maximum channel width
w_channel = np.linspace(
start=w_channel_min,
stop=w_channel_max) # [m] Range of channel widths to evaluate
# Calculate some basic channel geometry
A_channel = w_channel * h_channel # [m^2] Cross-sectional area of channel
Dh_channel = hydraulic_diameter_rectangular(
w_channel=w_channel,
h_channel=h_channel) # [m] Hydraulic diameter of rectangular channels
# Calculate some basic flow parameter at the inlet
rho_inlet = fp.get_density(T=T_inlet, p=p_inlet) # [kg/m^3]
u_inlet = velocity_from_mass_flow(
m_dot=m_dot, rho=rho_inlet,
A=A_channel) # [m/s] Flow velocity inside channel
# Storing results
Re_bulk = np.zeros(
(T_wall.shape[0], w_channel.shape[0])) # [-] Bulk Reynolds number
Pr_bulk = np.zeros_like(Re_bulk) # [-] Bulk Prandtl number
u_bulk = np.zeros_like(Re_bulk) # [-] Velocity under bulk condition
Nusselt = np.zeros_like(Re_bulk) # [-] Nusselt number
Stanton = np.zeros_like(Re_bulk) # [-] Stanton number
h_conv = np.zeros_like(
Re_bulk) # [W/(m^2*K)] Convective heat transfer coefficient
A_heater = np.zeros_like(
Re_bulk
) # [m^2] Heater area required to raise temperature to T_chamber with temperature T_wall
L_channel = np.zeros_like(
def calc_channel_single_phase(T, Q_dot, rho, Pr, kappa, mu, p_ref, m_dot, T_wall, D_hydr, wetted_perimeter, A_channel, Nu_func, fp: FluidProperties, wall_args=None):
""" Calculate channel length and intermediate variables by using a constant temperature step DT
Using DT should give the best accuracy for computation time
Must be a single-phase channel.
NOTE: for optimization, this calculation should be preceded by a prepatory calculations, which really only needed to be once (enthalpy, etc..)
Args:
T_0 (K): Temperature at channel entrance
T_n (K): Temperature at channel exit
steps (-): Temperature steps into which channel is divided (dT = (T_n - T_0)/steps)
p_ref (Pa): Assume pressure is constant through channel, p_ref = p_inlet
m_dot (kg/s): Mass flow
wetted_perimeter (m): Channel perimeter through which heat can be conducted
A_channel (m^2): Area through which fluid flows
fp (FluidProperties): Object to access fluid properties with
"""
u = velocity_from_mass_flow(A=A_channel, m_dot=m_dot, rho=rho) # [m/s]
# Reynold's is not calculated with FluidProperties to avoid the issues at the saturation point (which sohuld have been handled in the prepare_single_phase function)
Re = Reynolds_from_mass_flow(m_dot=m_dot, A_channel=A_channel, L_ref=D_hydr, mu=mu) # [-]
# The Nusselt number is calculated with pre-calculated Prandtl number, and the geometry-specific Reynolds number
Nu = Nu_func(args= {
"Re": Re,
"Pr": Pr,
})
# Convective heat transfer parameter
h_conv = heat_transfer_coefficient_from_Nu(Nu=Nu, kappa=kappa, L_ref=D_hydr)
# 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) # The fluid temperature keeps changing
T_wall = we['T_wall_effective'] # [K]
#print("(Effective) wall temperature (K): ")
assert(np.all(T_wall>T))
#print(T_wall-T)
# Calculate the heat flux in a channel section
A_heating = required_heater_area(Q_dot=Q_dot, h_conv=h_conv, T_wall=T_wall, T_ref=T) # [m^2] Heating area required to deliver Q_dot
assert(np.all(A_heating>=0))
assert(wetted_perimeter >0)
delta_L = A_heating / wetted_perimeter # [m] Length of channel sections to obtain A_heating
assert(np.all(delta_L>=0))
L = np.cumsum(delta_L)
# 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,
we=we,
wall_args=wall_args,
delta_L=delta_L)
# Return a dictionary with values of interest
return {
# All values are for given temperature T
'L': L, # Distance along channel at temperature T
'Nu': Nu, # [-] Nusselt number (based on L_ref)
'Re': Re, # [-] Reynolds number (based on L_ref)
'u': u, # [m/s] Flow velocity
'h_conv': h_conv, # [W/(m*K)] Convective heat transfer parameter
'delta_L': delta_L, # [m] Length of each section
'Q_bottom_plane_heat_balance': Q_bottom_plane_heat_balance, # [W] Difference in power in the bottom plane heat balance
}
w_channel = 212e-6 # [m] Channel width
channel_amount = 5 # [-]
m_dot = 0.55e-6 / channel_amount # [kg/s]
# Hydraulic diameter and area
A_channel = h_channel * w_channel # [m^2] Channel area through which fluid flows
wetted_perimeter = wetted_perimeter_rectangular(
w_channel=w_channel, h_channel=h_channel) # [m] Wetted perimeter
D_h = hydraulic_diameter(A=A_channel, wetted_perimeter=wetted_perimeter) # [m]
print("\n Hydraulic diameter: {:4.4f} um".format(D_h * 1e6))
# Determine remaining variables at inlet
rho_inlet = fp.get_density(T=T_inlet, p=p_inlet) # [kg/m^3]
cp_inlet = fp.get_cp(T=T_inlet, p=p_inlet) # [J/(kg*K)]
u_inlet = velocity_from_mass_flow(m_dot=m_dot, rho=rho_inlet,
A=A_channel) # [m/s]
mass_flux = m_dot / A_channel # [kg/(m^2*s)]
Re_Dh_inlet = fp.get_Reynolds_from_velocity(
T=T_inlet, p=p_inlet, L_ref=D_h,
u=u_inlet) # [-] Reynolds number at inlet, based on hydraulic diameter
Pr_inlet = fp.get_Prandtl(T=T_inlet, p=p_inlet) # [-] Prandtl number at inlet
print("\n----- INLET -----")
print("Density: {:4.8f} kg/m^3".format(rho_inlet))
print("C_p: {:4.8f} kJ/(kg*K)".format(cp_inlet * 1e-3))
print("Flow velocity: {:3.4f} m/s".format(u_inlet))
print("Mass flux: {:3.2f} kg/(m^2*s)".format(mass_flux))
print("Re_Dh: {:4.4f}".format(Re_Dh_inlet))
print("Pr {:4.4f}".format(Pr_inlet))
rho_outlet = fp.get_density(T=T_outlet, p=p_inlet) # [kg/m^3]