Numerical Simulation of Airflow Velocity and Temperature Distribution in an Aircraft Cabin

In this work, a computational fluid dynamics (CFD) model is established to calculate the airflow distribution in the cabin of a single-channel Boeing 737-800 airplane. The RNG k-ε model, considering the calculation of turbulence kinetic energy and its rate of dissipation, is adopted to solve turbulence problems in physical field simulation. The proposed three-dimensional model is able to consider the particular physical factors and spatial structures, which can simulate the detailed distributions of complex physical fields, compared with the one-dimensional lumped parameter model. The velocity and temperature fields under different air supply velocities are then numerically investigated. The calculation results show that when the air velocity at the top air supply inlet is 1.4 m/s, the velocity and temperature distribution inside the cabin can both meet the comfort requirements of humans in the airworthiness standards. The results from this work can help to design an aircraft environmental control system.


Introduction
With the rapid development of civil aviation, airplane has been the preferred means of transportation for an increasing number of passengers [1].The thermal comfort has become a significant factor for passengers to choose airlines [2].As a typical enclosed space, the aircraft cabin has the characteristics of limited space, high occupancy, low airspeed, and low humidity, where the distribution of airflow directly affects the thermal comfort of passengers [2].Therefore, the research on the prediction of cabin airflow distribution is of great significance for real-time control of aircraft environmental control system [3][4].
Researchers have conducted numerical simulations and predictive analysis of the airflow distribution within the aircraft cabin using computational fluid dynamics (CFD) methods [5][6][7][8].Zhang and Chen [7] numerically studied the airflow distribution in the dual-channel Boeing 767 airplane.The simulation results show that the personalized system has the lowest CO 2 concentration and relatively lower air temperature, providing the best air quality.Mboreha et al. [8] developed a CFD model for the Boeing 767-300 airplane.The calculation results indicate that the ventilation system with distributed air inlets results in a more uniform airflow distribution and lower overall temperature inside the cabin.
The above studies demonstrate that using CFD methods can accurately predict the airflow distribution in the aircraft cabin.In this work, a CFD model is established to calculate the airflow distribution in the cabin of a Boeing 737-800 airplane.The influences of air supply velocity on the velocity and temperature fields are then numerically investigated.The results from this work can provide useful guidance for the design of aircraft environmental control systems.

Physical Model
A physical model of the cabin of a single-channel Boeing 737-800 airplane is established, as shown in Fig. 1.Due to the complexity of the internal structure of the cabin, the factors that have little impact on the airflow distribution are simplified, including the use of simplified human models and the omission of lights.The length, width, and height are 3.23 m, 1.88 m, and 2.18 m, respectively.There are two rows of seats, each with six seats symmetrically distributed.Besides, four rows of air supply inlets are set up, two on the top and two on the side wall.The top air supply inlet is in the form of an interval-type slit air supply, with a total of eleven air supply inlets on each side.The length and width of each top air supply inlet are 87 mm and 15 mm, respectively.The length of side wall air supply inlet is equal to the length of cabin, and the width is 10 mm.The air outlet is located at the bottom of the side wall of the cabin, with a length equal to the length of cabin and a width of 330 mm.

Grid Division
Due to the irregularities of the cabin internal structure, seats, and human models, a non-structural tetrahedral grid is used for grid division.The number of grids in the entire cabin physical model is approximately 1.38 million, and the grid quality is above 0.3.The global grid size is 70 mm.Besides, local refinement is applied to the human body, top air supply inlets, side wall air supply inlets, and air outlets, with grid sizes of 40 mm, 5 mm, 3 mm, and 40 mm, respectively.

Boundary Condition
Considering the complexity of the heat transfer in the cabin and the irregularity of the boundary, the boundary conditions are simplified: (1) The top air supply inlet is defined as the velocity inlet boundary, with a temperature of 292.15K and a velocity of 1.4 m/s.(2) The side wall air supply inlet is also defined as the velocity inlet boundary, with a temperature of 292.15K and a velocity of 0.7 m/s.(3) The air outlet is defined as the outflow boundary.(4) The ceiling, side wall, and floor are defined as the constant temperature wall boundaries.The temperatures for these boundaries are determined based on experimental measurements, which are 295.15K,296.15K, and 297.15K respectively [9].(5) The front wall, rear wall and seats are defined as the adiabatic wall boundaries.The RNG k- model is adopted [10][11][12], where turbulence kinetic energy and its rate of dissipation are calculated from equations ( 1) and ( 2

Sampling Section and Sampling Point
To study the airflow distribution inside the cabin, data from one transverse sampling section, one longitudinal sampling section, and 25 sampling points are selected.A transverse sampling section is taken between two rows of seats, with a distance of 150 mm from the back of the seat.Four columns of 25 sampling points are taken on the transverse sampling section, as shown in Fig.

Velocity Field
The airflow velocity field inside the cabin is numerically studied.Fig. 3 show the velocity field of the transverse and longitudinal sampling sections when the air velocity at the top air supply inlet is 1.4 m/s.The fresh air supplied from the top air supply inlets flows towards the center under the influence of the fresh air supplied from the side wall air supply inlets.After reaching the floor surface, most of the air flows along the floor and is eventually discharged from the air outlet out of the cabin.A small portion of the air moves upwards because of the reflection on the floor surface combined with the thermal plume phenomenon of passengers.The fresh air supplied from the side wall air supply inlets flows towards the ceiling along the side wall surface under the influence of the upward-moving airflow mentioned above.For the transverse sampling section, the airflow velocity in the middle aisle area is relatively high, with a maximum velocity of approximately 1.43 m/s.The airflow velocity in the passenger area is relatively uniform, ranging from 0 to 0.24 m/s.At the longitudinal sampling section, the velocities at the floor and the ceiling are significantly higher than that at the intermediate height.In the passenger area, the airflow velocity at the foot and knee is relatively high, with the maximum velocity of approximately 0.26 m/s.The airflow velocity at the chest and head is relatively low, with the maximum velocity of only about 0.08 m/s.Fig. 4 shows the velocity distribution at all sampling points when the air velocity at the top air supply inlet is 1.4 m/s.For the passenger area, i.e., the sampling points on Line A, Line B, and Line C, the velocity generally first decreases and then increases from the floor to the ceiling.For the middle aisle area, i.e., the sampling points on Line D, the velocity generally first increases and then decreases from the floor to the ceiling.The highest velocity among the sampling points is 0.26 m/s, located at the position of 1.09 m on Line D in the middle aisle area, while the lowest velocity is 0.03 m/s, located at the position of 1.09 m on Line B and Line C in the passenger area.The velocities around the passengers are all lower than 0.2 m/s, which meets the comfort requirements of human in the airworthiness standards.Fig. 5 presents the airflow velocity of the sampling points at the feet (A1, B1, C1) and head (A4, B4, C4) of passengers under different velocities at the top air supply inlet.As the air velocity increases, the velocities of the sampling points at the foot and head show an increasing trend.Within the scope of the study, the velocities of the sampling points at the head are all lower than 0.2 m/s.However, when the air supply velocity is higher than 1.8 m/s, the velocity at the sampling point C1 is higher than 0.3 m/s, which will have a certain influence on the comfort of passenger.

Temperature Field
The temperature field inside the cabin is then numerically studied.Fig. 6 show the temperature field of the transverse and longitudinal sampling sections when the air velocity at the top air supply inlet is 1.4 m/s.As shown in the Fig. 6, the temperatures near the top air supply inlet, the middle aisle area, and the floor surface are relatively low, while the temperatures near the passenger area and the side wall are relatively high, because the fresh air with lower temperature is blown into the cabin from the top air supply inlet.For the horizontal sampling section, the temperature in the middle aisle area is relatively low, with a minimum temperature of about 289.2K, while the temperature in the passenger area is relatively high, with a minimum temperature of approximately 291.9K.At the longitudinal sampling section, the temperatures at the floor and the ceiling are slightly higher than that at the intermediate height.For the passenger area, the temperatures at the foot and knee are relatively lower, with a minimum temperature of about 291.8K, while the temperatures at the chest and head are slightly higher, with a minimum temperature of approximately 292.1K.Fig. 7 presents the temperature distribution at all sampling points when the air velocity at the top air supply inlet is 1.4 m/s.For the sampling points on Line B and Line C, which are far away from the side wall, the temperature generally increases first and then decreases from the floor to the ceiling.For the sampling points on Line A and Line D, the temperature gradually increases from the floor to the ceiling.The highest temperature among the sampling points is about 294.1K, located at a position of 2.1 m on Line D, due to its proximity to the higher temperature ceiling.The lowest temperature is about 291.9K, located at a position of 0.1 m on Line B, Line C, and Line D, due to the lower temperature fresh air blowing from the top to the floor.The maximum vertical temperature difference in the passenger area is located on Line A, which is about 0.7K, and the minimum vertical temperature difference is located on Line B, which is only about 0.2K.Besides, the maximum horizontal temperature difference is located between Line A and Line B, which is about 0.6K.Both the vertical and horizontal temperature differences in the passenger area can meet the comfort requirements of human in the airworthiness standards.the temperatures of sampling points at the foot and generally show a decreasing trend.Within the scope of the study, when the air supply velocity is 1.2 m/s, the maximum vertical temperature difference in the passenger area is located on Line A, which is about 1.1K, and the maximum horizontal temperature difference between Line A and Line B in the passenger area is approximately 0.9K .

Conclusions
The airflow velocity and temperature distributions in the cabin of a Boeing 737-800 airplane are numerically investigated in this work.Besides, the influences of air supply velocity on the airflow velocity and temperature fields are studied.The main conclusions are summarized as follows: (1) A three-dimensional CFD model based on the RNG k-ε model is developed to calculate the airflow velocity and temperature fields.( 2) Compared with the one-dimensional lumped parameter model, the developed three-dimensional model can provide the detailed distributions of the physical fields inside the cabin, which can help to design an aircraft environmental control system.(3) The computational cost of the three-dimensional model is relatively high, and it requires a longer simulation time.Replacing CFD model with the trained Artificial Neural Network (ANN) model can enhance computational efficiency and reduce simulation time, which will be our future effort.

Figure 1 .
Figure 1.Physical model of the cabin of a single-channel Boeing 737-800 airplane.

Figure 2 .
Figure 2. Distribution diagram of sampling points.

Figure 3 .
Figure 3.The velocity field of the transverse and longitudinal sampling sections.

Figure 4 .
Figure 4. Airflow velocity distribution at all sampling points.

Figure 5 .
Figure 5. Airflow velocity versus velocity at the top air supply inlet.

Figure 6 .
Figure 6.The temperature field of the transverse and longitudinal sampling sections.

Figure 7 .
Figure 7. Temperature distribution at all sampling points.

Figure 8 .
Figure 8. Temperature versus velocity at the top air supply inlet.

Fig. 8
Fig.8presents the temperature of the sampling points at the feet (A1, B1, C1) and head (A4, B4, C4) of passengers under different velocities at the top air supply inlet.As the air supply velocity increases, ):