RCAIDE.Library.Methods.Aerodynamics.Common.Drag.cooling_drag
cooling_drag#
- cooling_drag(state, settings, geometry)[source]#
Computes cooling drag coefficient based on heat exchanger operation and air flow through cooling ducts.
- Parameters:
state (Data) –
- Flight conditions and energy state containing:
- conditions.freestream.densityfloat
Freestream air density [kg/m³]
- conditions.freestream.velocityfloat
Freestream velocity [m/s]
- conditions.freestream.pressurefloat
Freestream static pressure [Pa]
- conditions.energy.coolant_linesdict
- Dictionary of coolant line results indexed by coolant line tag
- coolant_line_tagdict
- Dictionary of heat exchanger results indexed by heat exchanger tag
- heat_exchanger_tagData
- Heat exchanger operation results containing:
- air_mass_flow_ratefloat
Mass flow rate of air through heat exchanger [kg/s]
- pressure_diff_airfloat
Pressure differential across heat exchanger [Pa]
settings (dict) – Analysis settings and parameters
geometry (Data) –
- Vehicle geometry containing:
- reference_areafloat
Reference area for drag coefficient calculation [m²]
- networkslist
- List of propulsion networks containing coolant lines
- coolant_lineslist
- List of coolant line objects with heat exchangers
- tagstr
Unique identifier for the coolant line
- heat_exchangerslist
- List of heat exchanger objects containing:
- tagstr
Unique identifier for the heat exchanger
- atmospheric_air_inlet_to_outlet_area_ratiofloat
Ratio of inlet to outlet area for atmospheric air [unitless]
- duct_lossesfloat
Duct efficiency factor accounting for losses [unitless]
- minimum_air_speedfloat
Minimum air speed required for heat exchanger operation [m/s]
- Returns:
Results are stored in state.conditions.aerodynamics.coefficients.drag.cooling.total
- Return type:
None
Notes
This function calculates the drag penalty associated with cooling system operation, including the momentum deficit caused by air flow through heat exchangers and the pressure forces on duct surfaces. The calculation accounts for variable inlet areas based on required cooling flow rates.
- Major Assumptions
Density across the duct is equal to freestream density
Inlet area varies based on required cooling flow rate
Duct losses are characterized by a single efficiency factor
Heat exchanger operation ceases below minimum air speed
Theory
The cooling drag is calculated from momentum and pressure forces:
\(F_{cooling} = \dot{m}_{air}(V_{exit} \eta_{duct} - V_{\infty}) + A_{outlet} \eta_{duct}(P_{exit} - P_{\infty})\)
- where:
\(\dot{m}_{air}\) is the air mass flow rate through the heat exchanger [kg/s]
\(V_{exit}\) is the exit velocity [m/s]
\(V_{\infty}\) is the freestream velocity [m/s]
\(\eta_{duct}\) is the duct efficiency factor
\(A_{outlet}\) is the outlet area [m²]
\(P_{exit}\) is the exit pressure [Pa]
\(P_{\infty}\) is the freestream pressure [Pa]
The inlet area is determined from mass flow requirements:
\(A_{inlet} = \frac{\dot{m}_{air}}{\rho_{\infty} V_{\infty}}\)
The exit velocity and pressure are calculated as:
\(V_{exit} = \frac{\dot{m}_{air}}{\rho_{\infty} A_{outlet}}\)
\(P_{exit} = \frac{1}{2}\rho_{\infty}[(1+\eta_e)V_{exit}^2 - V_{\infty}^2] + P_{\infty} - \Delta P_{HEX}\)
where \(\eta_e = 0.5(1 - A_{outlet}/A_{inlet})\) is the expansion efficiency.
The cooling drag coefficient is:
\(C_{D,cooling} = \frac{F_{cooling}}{\frac{1}{2}\rho_{\infty} V_{\infty}^2 S_{ref}}\)
Definitions
- ‘Cooling Drag’
Additional drag caused by the momentum deficit and pressure forces associated with air flow through cooling systems.
- ‘Duct Losses’
Efficiency factor accounting for frictional and form losses in the cooling air ductwork.
References
[1] Brelje, B., Jasa, J., Martins, J., & Gray, J. (2019). “Development of a conceptual-level thermal management system design capability in OpenConcept.”