With the development of economy and technology, modern society is demanding more and more from travel speed, which begins looking at a way of transportation that is superspeed on the ground, beyond aircraft speed. In the dense atmosphere, the maximum economic speed of high speed vehicle should not be higher than 400 km/h[1-3]. The measured data from German TR and Japanese Shinkansen show aerodynamic drag will account for more than 80% of total drag when the train speed exceeds 400 km/h[4]. Besides, the high-speed train will cause serious problems of aerodynamic noise. This aerodynamic noise increases rapidly with 6th power to 8th power of speed[5]. In this background, the tube train transportation[6-8] emerges as the times requirement. It aims to reduce the aerodynamic drag of the train under high speed by decreasing air pressure in the tube, so then promote the train to a higher speed. Due to its advantages of environmental protection and energy conservation, it becomes the most potential development of ultra-high-speed rail transit in the future[9]. However, it also brings many new aerodynamic problems. For instance, when the high-speed train runs in a closed tube, owing to tube wall’s restrictions, and improper choice of air pressure, it will result in the aerodynamic drag of the train rising sharply. Furthermore, with the increasing speed of the train, there will appear some aerodynamic heating problems gradually. Heat quantity generated in the tube when the train runs is not as easy to radiate through the surrounding airflow as it in the open air. Instead, it is much easier to aggregate which causes higher and higher temperature in the tube. As a result, the strength of trains and the tube may be affected, which will further endanger the system’s safety[10]. Therefore, the aerodynamic problems of the tube trains are worth studying, which can provide the basis for future tube trains’ design.
In recent years, a growing number of scholars begin to research the characteristics related to aerodynamic aspects of the tube train, such as aerodynamic drag, aerodynamic noise, aerodynamic heating, etc. Zhou et al.[11] studied the influence of air pressure and running speed on the aerodynamic drag of trains. It is reported that the higher the speed of the train, the greater the reduction in aerodynamic drag will be with the decrease in air pressure. Subsequently, Zhou et al.[12] studied the effect of blockage ratio on aerodynamic drag. It is found that the greater the blockage ratio is, the greater the aerodynamic drag of the train. However, when the blockage ratio is small, the influence of its change on the drag of the train is small, but when the blockage ratio is large, the drag of the train rises sharply. Mi et al.[13] used the dynamic mesh to study the regularities of the influence of train running speed, air pressure and blockage ratio on the aerodynamic drag. The law suggests when the train is running in low air pressure, there is a good linear relationship between the aerodynamic drag and the blockage ratio. And when the air pressure is high, the linear relationship will be weakened. What’s more, the aerodynamic drag has an approximate linear relationship with the square of running speed. Chen et al.[14] analyzed these aerodynamic drag characteristics of different shapes of the head car and the tail car under different air pressures and blockage ratios. The result reflects that the air pressure in the tube of 1000 Pa and blockage ratio of 0.25 can effectively reduce aerodynamic drag. And under this air pressure, different streamlined shapes of the head car have no significant difference in reducing aerodynamic drag, but the blunt tail can reduce the aerodynamic drag more effectively. Zhang[15] calculated and compared the aerodynamic drag of trains with different blockage ratios and different air pressures in the tube, and found that for the same aerodynamic drag condition, the energy saving of vacuum pumping by reducing the cross section is greater than that by increasing the vacuum degree. Ma et al.[16] based on the evacuated tube test device, analyzed that the air pressure, running speed and the blockage ratio are three very important factors leading to the energy loss of the evacuated tube. Liu et al.[17] modeled the aerodynamic calculation model of high-speed train with the evacuated tube under low-pressure environment, studied the influence of air pressure, the blockage ratio and train’s running speed on the aerodynamic drag of the train, and gave the optimal relationship between air pressure, blockage ratio and train’s speed of the evacuated tube transportation system. Bao et al.[18] found the shape of the train body and the structure of the tube can affect the aerodynamic drag, and the blockage ratio is the main factor. In addition, Kim et al.[19] also found that when shock waves are generated during the tube train operation, the aerodynamic drag will increase dramatically. It is suggested to keep a low air pressure to alleviate the shock wave effect. Zhou et al.[20][21] further studied the shock wave’s structure and its change law of the tube train, and found that the shock wave is mainly composed of expansion wave, reflected shock and normal shock. The intensity of the normal shock wave in front of the head car experiences four states: rapid increase, initial stability, sudden decrease and final stability. Influenced by the interaction between the expansion wave and the reflected shock wave, the wake velocity decreases obviously in the opposite direction of the train’s movement. Liu et al.[22] and Zhang et al.[23] conducted a study on the aerodynamic noise of the tube train. The results showed that the greater the running speed of the train, the greater the aerodynamic noise will be produced. And when the train runs at a constant speed, the intensity of the aerodynamic noise source of the high-speed train can be reduced by decreasing the air pressure and the blockage ratio.
At present, most research on the aerodynamic aspects of the tube train is focused on the aerodynamic drag, but the research on aerodynamic heating is less. Jia et al.[24] found that when the running speed of the train and the air pressure in the tube are constant, the aerodynamic heating effect increases exponentially with the increase of the blockage ratio, and with the increase of Mach number, the maximum temperature in the flow field increases in a parabola trend. Duan[25] found that the maximum temperature increases with the decrease of the air pressure in the tube. Dong[26] found that the aerodynamic heating in the tube gradually decreases with the increase of the train running time, which is a monotonous increasing parabola. When the running time of the train is short, the aerodynamic heating increases sharply with the time. With the increase of the running time of the train, the increment of aerodynamic heating decreases gradually until it approaches a certain temperature infinitely. In the further study of aerodynamic heating, Niu et al.[10] and Zhou et al.[27] found that the aerodynamic heating effect will increase significantly when there is a shock wave in the tube. And with the increase of the blockage ratio, the choking limit formed in the flow field will intensify the aerodynamic phenomenon, which will further worsen the aerodynamic heating environment in the tube[28].
The above research shows that when the train runs at ultra-high speed in the tube, the aerodynamic heating effect will make the ambient temperature in the tube increase. If the heat quantity cannot release to the outside, the heat quantity generated when the next train passes will further increase the ambient temperature. However, the effect of the initial ambient temperature on the aerodynamic heating effect has not been studied so far. Excessive temperature in the tube may affect some equipment carried in the tube and outside the train, which may endanger the driving safety. In addition, in the study of aerodynamic heating of the tube train, most scholars adopt a two-dimensional geometric model, which makes it impossible to further observe the temperature distribution on the train surface and in the tube. In the future, most of the trains in the tube will be maglev trains[1], some types of the maglev trains’ external equipment cannot be in high temperature environment, such as the high temperature superconducting maglev of Southwest Jiaotong University[18], whose bottom contains several cryostats similar to the wheels of wheel-rail trains, which need to be far away from high temperature environment. Therefore, it is necessary to study the influence of the initial ambient temperature on the aerodynamic heating and the temperature distribution in the tube.
2. Numerical simulation
2.1 Geometric model
Currently, there is no a mature shape of the tube train, so a simplified three-dimensional geometric model of the train was used in this paper. The approximate dimensions of the tube and the train are shown in Fig. 1. The height of the train is H=3.2 m, which is defined as the flow characteristic length[17]. The total length of the train body is 24.688H, the width of the train is 1.060H, and the nose tip length of the head and tail car is 1.875H (6 m). The total length of the tube is 125H, which consists of a circular arc with a radius of 1.063H and a plane with a width of 1.407H. The distance from the bottom of the train to the bottom of the tube is about 0.156H, and the distance between the stagnation point of nose tip of the head car and the inlet is 31.250H. The blockage ratio (β) of this geometric model is about 0.28. The blockage ratio is defined as the ratio of the maximum cross-section area of the train to the cross-section area of the tube. The stagnation point of the nose tip of head car is set a the coordinate origin of the flow field.
2.2 Numerical model
When the train runs in a closed tube at a super-high speed, the flow field around the train is in a turbulent flow state. Since turbulence is the irregular motion of fluid micro-clusters, the transport of mass, momentum and energy generated by turbulent motion will be much larger than the macroscopic transport generated by molecular thermal motion, while turbulent fluctuation leads to additional energy dissipation resulting in an increase in aerodynamic heating. So, the turbulence calculation is very important for accurate prediction of aerodynamic heating. In the prediction of aerodynamic heating, the near-wall region is the region where aerodynamic heating produces heat flux exchange, and the viscosity is dominant in the boundary layer viscous sublayer[29]. Therefore, a precise prediction of the boundary layer is required. The shear stress transport (SST) k-ω turbulence model combines the advantages of k-ε turbulence model with k-ω turbulence model. It has a good ability to predict the low Reynolds number flow within the boundary layer and the fully developed turbulence flow outside the boundary layer[30]. Consequently, the SST k-ω turbulence model is used to predict aerodynamic heating in this paper. The speed of the train studied in this paper is 1000 km/h, and the corresponding Mach number is obviously higher than 0.3, so the compressibility of air needs to be considered. On the other hand, the tube is sealed, and the influence of air compressibility also needs to be considered. The flow simulation is based on the finite volume method, and the solver is the coupled implicit steady state solver with the second-order upwind discretization scheme. The AUSM+ -up scheme can be employed for solving a wide range of flow problems including incompressible to compressible. Hence, the AUSM+ -up scheme was selected to process the inviscid flux to improve the prediction accuracy of aerodynamic heating.
2.3 Boundary conditions and initial conditions
As shown in Fig. 2, a diagrammatic sketch of the tube train system is used to describe the boundary conditions of the computational domain. The inlet of the computational domain is defined as the stagnation-inlet, and the outlet is defined as the pressure-outlet. The train is set at a fixed wall with no slip. The thermal boundary conditions of the train and the tube are set at adiabatic. In this paper, we mainly study the aerodynamic heating effect of the tube train at a speed of 1000 km/h. So, the initial velocity is set at 1000 km/h. And the reference pressure is 0.1 atm (1 atm=101325 Pa) in Section 4. Since this paper studies the influence of initial ambient temperature on aerodynamic heating, the initial temperatures are set at 243 K, 293 K, 343 K and 393 K, respectively.
2.4 Mesh generation
The trim mesh and the prism mesh in STAR-CCM+ are used to divide the computational domain. The trim mesh is the main volume mesh in computational domain. For obtaining the flow field information of near-wall area more accurately, the volume mesh of near-wall area of the train surface adopts the prism mesh. The thickness of near wall prism layer is determined by y+=1, about 0.01 mm. The number of prism layers is set at 20. The prism layer stretching ratio is set at 1.4. The prism layer total thickness is set at 20 mm. The flow field near the train is complex, especially in the wake of the train. In order to ensure the accuracy of the simulation, the mesh in front of the head car and the mesh in the wake of the tail car are refined with reference to the Muld’s[31] mesh layout method. The diagrammatic sketch of the mesh refinement is shown in Fig. 3. The minimum size of the trim mesh is defined as Lmin. The mesh size of the front of the head car is Lmin. Due to the wake region of the train is longer, 3 mesh refinement blocks are arranged at the rear of the train, and the size is gradually increased from Lmin to 4Lmin. Fig. 4 shows the longitudinal section of the mesh near the train.
3 Verification
3.1 Influence of fixed wall on calculation
In the computational domain, the tube wall is very close to the train, so setting the tube wall to a fixed wall may affect the calculation results. It is necessary to make a simple discussion on whether the fixed wall has influence on the calculation results. In this part, the boundary condition of the tube wall is set at the moving wall with no slip and the fixed wall with no slip respectively and compared the two calculation results. The air pressure in the tube is 0.5 atm. The tangential velocity of the moving wall is equal to the airflow velocity. The initial ambient temperature in the tube is 293 K. The number of mesh is about 18.8 million, and the Lmin=0.05 m (approximately 0.0156H).
In this section, the drag coefficient (Cd) and pressure coefficient (CP) are defined as follows:
where Fd and P are the aerodynamic drag and the pressure measured in the flow field, respectively. And the pressure (P) in this paper represents the difference between absolute pressure and reference pressure. ρ0 is the initial density of air in the flow field. When air pressure is 0.5 atm and the ambient temperature is 293 K, the air density is about 0.602 kg/m3. v is the train speed (1000 km/h), and Strain is the maximum cross-section area of the train, which here is about 9.637 m2.
Table 1 shows the aerodynamic drag coefficients calculated by using a moving wall and a fixed wall, respectively. The difference of aerodynamic drag coefficient (Cd) between the moving wall and the fixed wall is great.
Fig. 5 shows the distribution of temperature and CP on the intersection line between the train upper surface and the xy plane, respectively. Here, the surface above the train stagnation point is defined as the upper surface, and the surface below the train stagnation point is the lower surface. It can be seen from Fig. 5 that when the boundary condition of the tube wall is the fixed wall, the distribution of temperature and CP is quite different from that of the moving wall. The reason for this difference should be that the distance from the tube wall to the train is very close, and the boundary conditions have great interference in solving the flow field around the train.
Therefore, when solving the flow field of the tube train, if the train is considered to a stationary wall, it is more reasonable to set the boundary condition of the tube to the moving wall, so that the train moves relative to the tube, which is more consistent with the actual situation. Based on this result, in the following calculations, the tube wall is all set at the moving wall.
3.2 Mesh independence verification
In order to ensure the rationality of the calculation, three different sizes of the mesh were generated to observe the influence of the number of mesh on the calculation results. Table 2 shows the details of the mesh, including the minimum size of the trim mesh Lmin and the total number of the mesh. The initial conditions in this section are the same as in Section 3.1.
Table 3 shows the Cd calculated from the coarse, medium and fine mesh, respectively. The difference of the Cd between coarse mesh and fine mesh is 0.33%; the Cd of the medium mesh is closer to that of the fine mesh, and the difference is only 0.05%.
Fig. 6 shows the distribution of temperature and CP on the intersection line between the train upper surface and the xy plane under the three types of the mesh. It can be found that both the temperature and CP of coarse and medium meshes are comparable to those of fine mesh, and the temperature and CP of medium mesh are closer to that of fine mesh. In addition, the temperature and CP curves of the coarse mesh fluctuate at the shoulder of the tail car, while those of the medium and the fine mesh are relatively gentler. Overall, the calculation results of medium and fine mesh are more reasonable. Considering that the fine mesh will spend more time and computing resource, it is a good choice to use medium mesh to achieve reasonable calculation results.