def test_table(self): # Page 1410 of Span2000 fp = FluidProperties("nitrogen") pressure = 1e5 # 1 bar of pressure molar_mass = 0.02801348 # [kg/mol] also from Span2000 # T in, enthalpy out # Enthalpy taken in J/mol from table in_out = ((300, 8717.7, 0), (330, 9593.0, -1), (450, 13105, -1), (600, 17564, -1), (1000, 30135, -2)) for T, h, places in in_out: res_h = fp.get_enthalpy(T=T, p=pressure) self.assertAlmostEqual( res_h, h / molar_mass, places=places ) # Must be divided by molar mass as CoolProp gives enthalpy for J/kg # Testing again, but for another pressure pressure = 1e6 in_out = ((300, 8662.5, -1), (320, 9253.6, -1), (400, 11612, -1), (550, 16060, -2), (800, 23728, -2), (1000, 30152, -2)) for T, h, places in in_out: res_h = fp.get_enthalpy(T=T, p=pressure) self.assertAlmostEqual( res_h, h / molar_mass, places=places ) # Must be divided by molar mass as CoolProp gives enthalpy for J/kg
def prepare_single_phase_liquid(T_inlet, steps, p_ref, m_dot, fp: FluidProperties): """ Prepare numpy arrays for calculating channel length in a liquid single-phase section of a channel. NOTE: This is done to avoid recalculating arrays that are not dependent on channel geometry, therefore speeding up optimizations.\ After all, during optimization the geometry is what varies.\ Also it also ensure that temperature endpoint and enthalpy cleanly match with saturation temperature in the correct phase Args: T_inlet (K): Inlet temperature steps (-): Amount steps of dT taken to reach saturation temperature T_sat (dT = (T_sat-T_inlet)/2) p_ref (Pa): Pressure assumed constant along channel, equal to inlet pressure m_dot (kg/s): Mass flow fp (FluidProperties): Object to access propellant properties with """ T_sat = fp.get_saturation_temperature(p=p_ref) # [K] Saturation temperature assert ( T_inlet < T_sat) # Check input assert (steps > 1) # Temperature and other intermediate variable in channel section i=0...n T, dT = np.linspace(start=T_inlet, stop=T_sat, num=steps,retstep=True) # [K] Temperature T_i (also returns steps between sections) # 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 last values must be replaced with the correct values for the saturated liquid 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[-1] = fp.get_saturation_enthalpy_liquid(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[-1] = fp.get_liquid_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[-1] = fp.get_saturation_Prandtl_liquid(p_sat=p_ref) # [-] Saturation Prandtl # Thermal conductivity kappa = fp.get_thermal_conductivity(T=T, p=p_ref) # [W/(m*K)] Conductivity kappa[-1] = fp.get_liquid_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[-1] = fp.get_liquid_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 calc_P_delta_h(T_in,T_out,m_dot,p_chamber): """Calculate power required to raise temperature of flow with mass flow m_dot Arguments: T_in {K} -- Inlet temperature T_out {K} -- Outlet temperature m_dot {kg/s} -- Mass flow p_chamber {Pa} -- Chamber pressure Returns: {W} - Required power """ # Check if outlet state is gaseous fp = FluidProperties("water") outlet_phase = fp.get_phase(T=T_out,p=p_chamber) if not (outlet_phase == "gas" or outlet_phase == "supercritical_gas"): print(fp.get_phase(T=T_out,p=p_chamber)) raise ValueError("Assumed outlet temperature is not not in gas phase") Delta_h = fp.get_enthalpy(T=T_out, p=p_chamber) - fp.get_enthalpy(T=T_in, p=p_chamber) return m_dot*Delta_h
def run2(): #Calcuate heating efficiency of heaters in literature m_dot = 0.83e-6 # [kg/s] mass flow T_in = 24+273.15 # [K] Inlet temperature T_out = 426.65 # [K] Outlet temperature p = 5.15e5 # [Pa] Pressure P_total = 8.19 # [W] Total electrical power fp = FluidProperties("water") # Specific enthalpy at inlet and outlet h_in = fp.get_enthalpy(T=T_in, p=p) # [J/kg] Inlet h_out = fp.get_enthalpy(T=T_out, p=p) # [J/kg] Outlet P_delta_h = m_dot*(h_out-h_in) # [W] Power raising enthalpy efficiency = P_delta_h/P_total # [-] print("Exit phase: {}".format(fp.get_phase(T=T_out,p=p))) print("P_delta_h: {:1.2f} W".format(P_delta_h)) print("Micro-heater efficiency: {:1.2f} ".format(efficiency)) print("T_in = {:3.0f} K \t\t T_out = {:3.0f} K".format(T_in,T_out)) print("Mass flow = {:2.2f} mg/s".format(m_dot*1e6))
def ideal_enthalpy_change(T_inlet, p_inlet, T_outlet, p_outlet, fp: FluidProperties): """Returns specific enthalpy change based on simple chamber inlet and outlet conditions. This should give the power the micro-heater must transfer in ideal conditions with no heat losses. In addition returns a warning if the final state is not gaseous. Arguments: T_inlet {K} -- Inlet temperature p_inlet {Pa} -- Inlet pressure T_outlet {K} -- Outlet temperature p_outlet {Pa} -- Outlet pressure fp {object} -- FluidProperties object Returns: delta_h {J/(kg*K)} -- """ h_inlet = fp.get_enthalpy(T=T_inlet, p=p_inlet) h_outlet = fp.get_enthalpy(T=T_outlet, p=p_outlet) outlet_phase = fp.get_phase(T=T_outlet,p=p_outlet) if not (outlet_phase == 'gas' or outlet_phase == 'supercritical_gas'): print("Warning: Phase at chamber exit is not gaseous but {}".format(outlet_phase)) return h_outlet-h_inlet
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
# Iterate over all possible combinations of area ratio and chamber temperature to find the mass flow and area ratio that finds according to basic IRT for AR in it_AR: it_T = np.nditer(T_chamber, flags=['c_index']) for T in it_T: # Store mass flow, throat area and other results ep = IRT.engine_performance_from_F_and_T(F_desired=F, p_chamber=p_chamber, T_chamber=float(T), AR_exit=float(AR), p_back=p_back, fp=fp) m_dot[it_AR.index][it_T.index] = ep['m_dot'] # [kg/s] Mass flow A_throat[it_AR.index][it_T.index] = ep['A_throat'] # [m^2] Throat area Isp[it_AR.index][it_T.index] = ep['Isp'] # [s] Specific impulse h_chamber[it_AR.index][it_T.index] = fp.get_enthalpy( T=float(T), p=p_chamber) # [J/kg] Enthalpy at chamber inlet # Throat stuff T_throat[it_AR.index][it_T.index] = ep[ 'T_throat'] # [K] Throat temperature p_throat[it_AR.index][it_T.index] = ep[ 'p_throat'] # [Pa] Throat pressure u_throat[it_AR.index][it_T.index] = ep[ 'u_throat'] # [K] Throat velocity Pr_throat[it_AR.index][it_T.index] = fp.get_Prandtl( T=ep['T_throat'], p=ep['p_throat']) # [-] Prandtl number in throat mu_throat[it_AR.index][it_T.index] = fp.get_viscosity( T=ep['T_throat'], p=ep['p_throat']) # [Pa*s] Dynamic viscosity in the throat # Nozzle exit stuff T_exit[it_AR.index][it_T.index] = ep[ 'T_exit'] # [K] Nozzle exit temperature