Calculation and analysis of a ventilation and cooling scheme for aircraft brake assembly

The slow cooling of brake assembly of civil aircraft is one of the major constraints on the operational efficiency of the aircraft. Aiming at the engineering problem of brake carbon heatpacks in flight cooling, this article proposes a ventilation and cooling scheme for aircraft brake assembly, which is based on the original configuration of the main landing gear compartment of the aircraft. By adding the design of the intake duct and exhaust grille, external cooling airflow is introduced to cool the brake carbon heatpacks during flight. This article confirms the cooling effect through simulation calculations and experimental data. This article can provide a reference for the ventilation and cooling design of civil aircraft brake assembly.

experimental data.This article can provide a reference for the ventilation and cooling design of civil aircraft brake assembly.

Ventilation and Cooling Scheme
The ventilation and cooling scheme for brake assembly proposed in this article is based on the original configuration of the aircraft's main landing gear compartment, by the design of the intake duct and exhaust grille, and by introducing external cooling airflow to cool the brake assembly during the flight phase.The following two factors should be considered:  The intake and exhaust ports should have a positive ventilation effect, minimize the impact of intake on aerodynamic resistance and external flow field stability, and achieve a good ventilation and cooling effect. There should be a diverter upstream of the intake to prevent the discharged flammable liquid from being sucked into the intake duct again.Considering the above factors, the ventilation and cooling scheme for the brake assembly proposed in this article contains the intake system and the exhaust system, which can be seen from Figure 1 and Figure 2. The intake system includes an intake duct and a diverter, which introduce external airflow through the intake duct to achieve ventilation and cooling for brake assembly.The intake duct takes into account both aerodynamic resistance and ventilation effect.The front end of the diverter is designed with an arc shape to ensure the discharged flammable liquid flows towards both ends of the arc, with a certain pressure relief effect to prevent the formation of local high-pressure zones and prevent flammable liquid from crossing the top of the diverter and entering the compartment.The exhaust system uses a grille to exhaust the cooled air outside the aircraft.

Simulation calculation analysis
This article selects typical conditions and obtains boundary conditions such as external flow rate and pressure through joint simulation of internal and external flow fields.Then, a temperature engineering calculation model of the brake assembly is established based on the brake assembly, and the cooling effect of the brake assembly under design conditions is calculated.In Equation (1),  is the conservation variable,  is the convection term [1] , and  is a viscosity term, whose expression is Equation (2): where  is the fluid heat conduction coefficient [2] , and the expression of  is Equation (3): The pressure parameter  is determined by the equation of Ideal Gas Low: , 4 Among Equation (4) value of  is taken as 1.4. [3]1.2.Numerical method.The discretization equation [4] of the finite volume method is used for numerical calculation, and the Navier-Stokes equation is integrated into the control body V [5] .Through the Gaussian integral, the volume integral is converted into the control body surface integral: The semi-discretization equation of grid unit  can be achieved from the above Equation ( 5): where  is the unit adjacent to the calculation unit.For discretization, Equation ( 6) implicit scheme is to solve the solution [6] .The convection items are all in Roe format [7] , and the viscous flux is calculated by the DDG method [8] .The Least-Squares method is used for gradient reconstruction [9] , and the difference format in the calculation is the Second Order Upwind.The turbulence calculation uses the Reynolds time mean method.The instantaneous variables in the flow field are divided into mean value time  and mean value fluctuation  :    7 The Reynolds time mean value of  is: where  is defined as any moment,  is defined as the time interval.Ventilation calculation uses the SST k- turbulence model [10] .

Numerical calculation.
This article uses ANSA to draw Mesh, which is shown in Figure 3.As shown, the fluid area mesh is a block structure mesh, and the number of the mesh is 4 600 000.The thickness of the first mesh boundary layer is 0.5 mm.The growth rate of grid encryption along the wall direction method is 1.2.The physical models selected for simulation calculation are shown in Table 1.  4 shows the streamline diagram near the intake duct.It can be seen that the fluid entering the main landing gear compartment through the intake duct still has a velocity greater than 50 m/s when it first enters the main landing gear compartment.After entering the main landing gear compartment, gas forms a reflux inside the compartment, and the airflow path is distributed in various areas of the main landing gear compartment.According to the calculation results of the flow field, the unilateral inlet flow rate is about 0.28 kg/s, and the total inlet flow rate is 0.56 kg/s.Figure 5 shows the flow rate of the inlet gas.It can be seen that the diverter intake duct, which is 18 mm higher than the skin surface, introduces external high-speed airflow into the interior of the main landing gear compartment, which allows the airflow that has just entered the main landing gear compartment to still have a high flow rate.

Engineering Calculation of Brake Assembly Temperature
After take-off, the brakes are retracted into the landing gear compartment, and the external airflow enters the compartment through the front intake duct of the landing gear compartment to cool the brake assembly.The cooled airflow is discharged through the rear exhaust grille.The high-temperature heat source component of the brake assembly is the brake carbon heatpacks, which gradually transfer its heat to the outside through convection heat transfer into the airflow, self-radiation heat transfer, and heat conduction of the brake carbon heatpacks to the surrounding connecting structures, in order to achieve cooling.
The airflow velocity and flow rate near the brake assembly are obtained through Section 3.1, and the temperature of the brake assembly is calculated and analyzed for engineering purposes.The gas in the compartment and brake carbon heatpacks are taken as research objects, and a dynamic heat balance model is established, as shown in Equations ( 9) and (10).
Taking the gas in the compartment as the research object.Taking brake carbon heatpacks as the research object:

MATMA-2023
The left side of Equation ( 9) shows the variation of the average internal energy of the compartment over time, while the right side shows the heat flow through the skin, wall panels, and carbon, which exchanges heat with the main landing gear compartment through ventilation.The left side of Equation (10) shows the change in internal energy of the carbon heatpacks over time, while the right side shows the heat dissipated by the brake carbon heatpacks through heat transfer.
During the flight, the convective heat transfer between the aircraft structure and the external environment is forced convection.The reference temperature for convective heat transfer is related to the external static atmospheric temperature and speed of the aircraft.It is calculated by Equation (11): where γ is the temperature recovery coefficient and is taken as 0.9.r is the ratio of air specific pressure heat capacity to specific constant capacity heat capacity and is taken as 1.4.The typical mission profile described above is the input, and the cooling time curves of the upper and lower brake carbon heatpacks calculated at ground ambient temperatures of 0℃, 30℃, and 55℃ are shown in Figure 6.Table 3 shows the maximum temperature of the brakes after landing after a typical short-range profile of 68 minutes at a brake dispatch temperature of 300℃.6 and Table 3 that the average temperature drops of carbon heatpacks are 50.5℃,45.5℃, and 42℃ when the external ambient temperatures are 0℃, 30℃, and 55℃, respectively, and the effect of ventilation and cooling scheme for Aircraft Brake assembly is relatively significant.

Conclusion
To solve the cooling problem of brake assembly, this article proposes a ventilation and cooling scheme for aircraft brake assembly, including intake, diverter, and exhaust grille.The ventilation and cooling effect of this scheme is calculated and analysed through numerical simulation of the flow field and temperature engineering calculation.The conclusions are as follows:  This ventilation scheme has a positive ventilation effect.The diverter intake design, which is 18 mm higher than the fuselage skin, effectively introduces high-speed airflow into the main landing gear compartment.Under the drainage effect of the intake, the fluid forms a reflux at a higher speed in the compartment, greatly improving the internal ventilation effect of the compartment. This ventilation scheme takes into account both aerodynamic resistance loss and ventilation effect, and can introduce cooling air with a total flow rate of about 0.56 kg/s into the main landing gear compartment to ventilate and cool the brake assembly. According to the engineering calculation of the temperature of the ventilated brake assembly, this scheme reduces the temperature of the brake carbon heatpacks by an additional 42℃~50.5℃,which can effectively alleviate the operational impact caused by the high temperature of the brake assembly.

Figure 1 .
Figure 1.Overview of Ventilation and Cooling Scheme for Aircraft Brake assembly.

Figure 2 .
Figure 2. Intake system and exhaust system.

3. 1 .
Joint simulation calculation of internal and external flow fields 3.1.1.Governing equation.Navier-Stokes equation of the three-dimensional Cartesian coordinate system to be solved in the fluid area is as below:

Figure 3 .
Figure 3. Mesh of main landing gear compartment.

Figure 4 .
Figure 4. Streamline diagram of Main landing gear compartment.

Figure 5 .
Figure 5. Inlet flow rate of main landing gear compartment.

Figure 6 .
Figure 6.Temperature-time curve of upper and lower carbon heatpacks.

Table 1 .
Physical models.Allmaras Turbulence As the harsh temperature of the brake assembly usually happens during short-range mission profiles, this article selects a typical short-range mission profile of an aircraft with a cruising altitude of 29,200 feet, cruising Mach of 0.74, angle of attack of 2.11° as the calculation condition.The calculation boundary conditions are shown in Table2.

Table 3 .
Carbon temperature Comparison of two schemes at landing.