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The Aerodynamics Analysis and Optimization Design of Evacuated Tube Transportation [Sensors & Transducers (Canada)](Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: The maximum economic speed is hard to exceed 400 km/h when high-speed trains run in the atmosphere. ETT (Evacuated Tube Transportation) will be the perfect fast vehicle on land. Taking high speed train set as a model, using Pro/E, the parameterized model of ETT was established. Analyzing the train actual boundary condition, based on FLUENT software and the turbulence model, considering multi - field coupling condition which involved the outer flow field, the aerodynamic drag field and velocity field, the numerical simulation and computation was finished. Furthermore, the laws of many parameters affect air - resistance and aero - lift were researched. By use of fuzzy multi - criteria evaluation model, the main parameters of system were optimized. The works can provide the feasibility basis for ETT. Copyright © 2013 IFSA. Keywords: ETT, Aerodynamics, Multi-field coupling, Optimization design. (ProQuest: ... denotes formulae omitted.) 1. Introduction With people demand for high speed transportation is more and more, the increasing shortage of such resources as oil, coal, it is very necessary to develop the high speed, environmental protection and efficient ground transport for the future society development. The fundamental limit factor of the top economic speed is the dense atmosphere, and overcoming aerodynamic drag is the main difficulty. Research showed that the aerodynamic resistance is directly proportional to the square of the speed. The aerodynamic resistance will be more than 80 % of all resistance as a vehicle travels running above 400 km/h [1]. ETT as the next generation vehicle, in theory, on the ground, it can achieve the same effect as an aircraft flying at an attitude of about 10,000 meters. However, because of the limits of technical and economic conditions, the less related research, and ETT aerodynamic problems, at present, there are two main ideas about ETT abroad. The one is the ETT system of Company et3.com in the United States and the other is Switzerland ultra-high-speed subway (Swiss metro). Company Et3.com only introduced the overall idea of ETT. Swiss metro engineering research contains high speed vehicle and its aerodynamics, the vacuum is limited to 0.1 bars and the running speed is 400-500 km/h. Domestic scholar only Zhang Yao-ping, Zhou Xiao, Yao Ying-feng, et al., carried out the numerical analysis of aerodynamic drag [2]. They haven't analyzed multi - fields coupling of the ETT system, also haven't optimized parameter. This paper mainly just carried out the researches. 2. Aerodynamics Analysis Based on Pro/E, to take high-speed train for model reference, the system parametric model was built. Under the condition of multi - fields coupling, using the FLUENT software to simulate air flow, the aerodynamic numerical simulation analysis of train was completed. And the paper researched the laws of such parameters as the atmospheric pressure in evacuated tube, travel speed, the locomotive's geometry and traintube dimension ratio affect air - resistance and aero - lift. 2.1. Parameterized Modeling of the System ETT train aerodynamic performance is bound up with the train apparent structure. The train streamline part and body transition curvature directly affect the aerodynamic performance. Good head surface design can effectively reduce the air resistance, pressure wave and aerodynamic noise at run time [3]. Because the real detail of bottom and outside surface of train is complex, in order to simplify the calculation, the train model is appropriately simplified on the premise of no affecting the result [4]. This paper used three trains model to simulate and analyze, i.e. a section head train (17.5 m), a middle train (25 m) and a tail train (17.5 m). ETT system's physical model was established under Pro/E (Fig. 1). It can provide analysis model for the next step study on such system parameter as the tube blocking ratio and body curvature impacting on system's aerodynamics under the coupling ultra high speed air flow field with aerodynamic drag field. 2.2. Meshing and Building the Boundary Conditions The paper supposed that train has smooth geometry, didn't consider the wheels, the rails and the sleepers, and simplified ballast bed into smooth and flat. Under the conditions not to affect the flowing near the train, select the limited length to instead of infinitely long evacuated tube, at the same time satisfy enough far distance from the boundary of the calculation area to the train surface, that made the air flow had little impact on the flow of the regional boundary when the train is running. The paper established an evacuated tube of 120 m, and the each distance is 30 m both the head and the tail train far from the import and export boundary of evacuated tube. To import the ETT system model into the ICEM CFD and to mesh the train and evacuated tub, to define entrance speed, export evacuated pressure in calculation region in tube and the boundary conditions of ETT (Fig. 2). By use of unstructured tetrahedral to mesh ETT, at the same time, check the mesh quality in order to meeting the computing requirements, at last, software CFD can output meshing file of ETT [5]. 2.3. To Establish and Calculate the Steady Turbulent Model 2.3.1. To Establish the Steady Turbulent Model The air flow field around train has obvious the turbulent flow characteristic such as boundary layer separating, wake flow. Turbulence is a kind of highly complex and unsteady 3-D flow with the track of rambling, mutual crisscrossing, rapidly changing and irregular rotation with time. The various physical parameters, such as speed, pressure, etc., have random changes with time and space. Currently, in engineering calculation of turbulent flow, the numerical calculation uses mainly Reynolds averaging method. In order to reduce amount of calculation, the calculation only considers the large scale average flow and closed turbulence model [6]. Due to that high Reynolds number flow field calculation is difficult to converge, and this paper adopts different running speed and tube pressure and different Mach number under various working conditions. Therefore not to take into account the compressibility of air, and all state was dealt with as incompressible. The basic control equations for incompressible flow as formula (1): ...(1) where ui is the flow field speed around the train, and respectively represent velocity components of three directions along the coordinate x, y, z; xi respectively represent the three coordinate directions. The law of momentum conservation is also the fundamental law which all flow system must be complied with. The law can be expressed as: the fluid momentum's change rate to time is equal to the sum of the outside forces to effect on small element, expression is: ...(2) where ui or ui respectively represent the velocity component of flow field along the x, y, z; Xi or Xrespectively represent the three coordinate directions. p is air density; p is pressure; p is kinematic viscosity coefficient; t is time. The airflow's Reynolds number is greater than 105 in vacuum tube. So its inner flow field can be calculated by use of k - £ turbulence model. This model is the most widely used in turbulence models. Two transfer equations allow determining independently the velocity and turbulence scale. Standard k - £ model is semi-empirical model which was established by the turbulent kinetic energy k and its dissipation term £. Among them, the equation k is a precise equation, and equation £ derived from empirical formulas. The k - £ turbulence model is a kind of eddy viscosity model [7]. It distinguishes mainly from Baldwin-Lomax algebraic model lying in the turbulent viscosity coefficient which includes some historical effects. Equation k for the turbulent kinetic energy: ...(3) Equation s for the turbulence consumption rate: ...(4) Among them, p is the laminar viscosity coefficient; Cx = 1.44 , C2 = 1.92, <Jk = 1.0, <Je = 1.3 , and they are respectively the empirical constant. And turbulent viscosity coefficient pt can be expressed as the function equation of k and £ : ...(5) where pt is the turbulent viscosity coefficient; k is the turbulent kinetic energy; £ is the turbulent dissipation rate; Cu is turbulent flow constant and it usually takes C = 0.09 * To build a set of enclosed equations by use of the continuous equation, Reynolds equation, turbulent viscosity coefficient equation, equation k and equation £, combine with certain initial boundary conditions, the actual problem can be numerically simulated. 23.2. Calculation and Analysis First of all, to set the solving controller, due to application scope of pressure solver covering from low pressure incompressible flow to the compression stream, also less needed memory, flexible solving process, convergence rate being much higher than that in the density solver, so the solving was based on the pressure solution. Fluid was selected air material; solid train material was selected aluminum alloy. Because it is difficult to research train running high speed in the tube, thus it assumed that trains were still at a standstill in the tube, and by using of air relatively flowing to instead of train travel in the tube. Tube pressure is the key issues to decide system parameters, and it is directly related to speed. Flying in the high altitude of 9000 - 12000 m, the air pressure is about 20 - 30 kpa, and 1000 km/h is the most economic speed. Air resistance will increase with the speed increasing, but decrease with the pressure decreasing. If train speed was selected for 600 - 1000 km/h, tube pressure should be around 10 kpa. The pressure is the same as that in 10000 - 15000 m high altitude. I.e. the high altitude condition can be created on the ground. In China, the ETT strategic orientate to 600 - 1000 km/h ground traffic [1]. So this article take 800 km/h as entrance air velocity, and the export gauge pressure was set to 0. The initial tube pressure was set as 0.2 bars. It was assumed that the tube wall and train for smooth surface. Entrance and export's turbulent kinetic energy k and turbulence dissipation rate £ was set as: k - \ (m2/s2), e = 1 (m2/s2). Solving condition monitor was set. Governing equations were discretized with second order upstream scheme. With pressure - correction algorithm (SIMPLE), to choose the steady state solution, ETT system was numerically studied. By observing to aerodynamic resistance curves and the convergence conditions of train lift curves, the finally calculate results of steady state can be gotten. 3. Results Analysis 3.1. Aerodynamic Drag Analysis in the Outer Flow Field After calculation of Fluent fluid model, head curvature can be gotten 0.15, blocking ratio is 0.1, the speed rate is 800 km/h. The train head surface stress distribution nephogram and the rear surface pressure distribution nephogram under the condition of tube pressure of 0.2 bars were shown as follow (Fig. 3, Fig. 4): It can be found from Fig. 3 and Fig. 4 that the pressure gradient of head part is obvious. And the pressure at the end of this part is the biggest in the train. On its upside and two sides, pressure values were decreased from positive to negative. On the top and side cambered surface of the transiting regions from the head to body are pale green areas. They have the maximum pressure changes, and the peak of negative pressure. This is mainly due to the transition curvature changes which are from the head to body. It makes the fluid flow faster, and sharp reduces pressure in this area. At the middle train, its body, middle and tail, roof and side wall surface are basically negative air pressure. The pressure of middle train has small absolute value; also, the pressure variation is not obvious. Near the head and wake of tail train, due to the influence of the flow around, the absolute value of pressure is slightly larger, but the pressure changes is small, isobar is sparse. And pressure gradient is small. Head of tail train has a small positive pressure, which is due to the influence of air viscosity and tail vortex. The analysis results show that the simplified model is rationality. 3.2. Analysis of Velocity Streamlines in the Outer Flow Field The velocity vector distributions of the train symmetry plane are shown in Fig. 5 and Fig. 6. The train front nose is the stagnation point; the pressure reaches the maximum and velocity is low. Along the train surface, air velocity increases gradually. In the negative pressure zones of head and tail, air velocity reaches the maximum value; the pressure change reaches the maximum. And there have obvious negative pressure. The pressure, speed is relatively stable in the middle of the train surface. At the end of the train, the eddy turbulence was generated due to high speed, and it caused negative vacuum in the front and rear of the train, i.e., there exists pressure difference. 4. Optimization Design and Analysis 4.1. Impact Analysis of System Physical Model From Fig. 3 and Fig. 4, it can be found that transition curvatures of the body have great influence on the aerodynamic performance of the train. By modifying the parameters of train physical model, to design 5 groups of different body transition curvatures, and by analyzing the corresponding aerodynamic performance, it can be gotten that the change laws of train aerodynamic drag and the aerodynamic lift with the body transition curvature changes (Fig. 7), so as to better choose a reasonable train model. Fig. 7 shows that the train aerodynamic drag increases slightly with the increase of body transition curvature. However, the influence on train aerodynamic lift is small. It can be seen, at the time of choose train model, this impact on the aerodynamic drag should be appropriately considered. In order to reduce the aerodynamic drag of the train, this paper selected train model which body transition curvature is 0.15. 4.2. Impact Analysis of Train - Tube Dimension Ratio Train - tube dimension ratio means the ratio of train cross-sectional area to the tube sectional area. In previous preliminary computation of flow field, train - tube dimension ratio was assumed as 0.1. Through adjusting tube diameter, the size of the ratio can be changed. Also by selecting five different sets of train - tube dimension ratio, analyzing the train aerodynamic performance, it can gotten that the aerodynamic lift change laws with the changes of train - tube dimension ratio. Based on this, the appropriate ratio can be selected. It can be seen from the Fig. 8, when the train - tube dimension ratio is less than 0.1, the changes of train aerodynamic drag and lift are flat. However when the ratio is bigger than 0.1, the forces are enlargement and changes are rapid. Comprehensive considering the economy and applicability, the train - tube dimension ratio of ETT is chosen as 0.1. 4.3. Impact Analysis of Velocity, Tube Pressure This article used the ANSYS Workbench platform, analyzed the influence factors and laws of the velocity and tube pressure of ETT. Considering computer hardware level, the train speed is given as 600-1000 km/h, tube pressure is in the range of 1013.5-3039.5 Pa. Computer selects automatically ten samples to calculate, the analysis results of ten sets of data are shown below in Fig. 9. By the nonparametric regression model, the laws of the tube pressure and train speed impacting on train aerodynamic drag is as follow (Fig. 10 and Fig. 11): From Fig. 10, it can be seen that the train aerodynamic drag is the square relationship with the tube pressure. With the increase of the pressure, the air becomes dense, train aerodynamic drag increase rapidly. Fig. 11 also shows the train aerodynamic drag is the square relationship with the speed. This is consistent with actual situation [8]. 4.4. Optimization Model and Results Aerodynamic drag is the main resistance during train running. It is mainly because of the friction and the pressure difference between trains and air. And the pressure difference is connected with the value of the aerodynamic lift. The greater the aerodynamic lift is, the greater the drag of pressure difference is. Train speed and the vacuum degree of ETT system will directly affect the train aerodynamic drag and aerodynamic lift. Using the workbench, under both the friction and the pressure difference, the balance chart of three relations was established which include speed, vacuum degree and aerodynamic drag (Fig. 12). The x-axis represents the train speed, the y-axis represents vacuum degree in tube, z-axis represents the train aerodynamic drag. Green squares in the chart represent the best feasibility area. Fuzzy multi-criteria is an evaluation method which apply fuzzy mathematical into multi-criteria evaluation. Because of the complexity of the actual engineering problems, adding to multi-field coupling ETT is necessary to consider such fuzzy information, as the fuzzy speed, the fuzzy material, the fuzzy boundary conditions, the system fuzziness itself, etc. In the process of multi-objective optimization, firstly, to find out the optimal solution of sub-targets constraints, and to blur each sub-goal function by use of the optimal solutions, then to calculate the intersection, the intersection is the optimal solution of multi-objective optimization problem. Through fuzzy multi-criteria evaluation method, based on the optimum space filling model and nonparametric regression model, to establish the approximate relationship between the objective function and design variables, take maximum train speed, minimum train aerodynamic drag and maximum aerodynamic lift as main goal, set speed and vacuum range as the constraint conditions, the system fuzzy multi-criteria evaluation mathematic optimization model was built. In the model, the train speed and tube vacuum were set for fuzzy constraints, and train resistance and aerodynamic lift for design variables [9]. ...(6) Among them, xl and x2 are the design variables, and indicate respectively the aerodynamic resistance and lift; f(X) is objective function of train speed; M[ and Mux are upper and lower limit of tube vacuum degree; Tilde (~) indicates that the formula contains fuzzy information. This paper used the optimization design tool which was including two modules both Response Surface and Goal Driven Optimization. Because space filling model was very suitable for the occasion which contained no random error and emphasized the deviation of control system test, this paper selected the best space filling design. The three sets of solutions had been obtained, which targets included maximum train speed, minimum train aerodynamic drag and maximum aerodynamic lift. It could be also seen from the Fig. 13, candidate A is the optimal solution, vacuum optimization results is 1077.1 Pa, train running speed is 987.7 km/h, the aerodynamic drag of the train is 5302.2 N, and the aerodynamic lift is 793.2 N. In order to verify the optimal solutions, a set of optimization result was re-substituted into the Fluent for flow field calculation. The aerodynamic drag of train is 5213.6 N; the aerodynamic lift is 680.17 N. The numerical results were approximate with that of the optimization model. It indicates that the model is reasonable. 5. Conclusion As ETT system parametric modeling, Pro/E facilitates the study of model parameters impacting on train speed and the aerodynamic drag under multifield coupling. It improves convenience for quick determining reasonable parameter design of ETT system. Based on the standard k - 8 turbulence model, internal turbulence flow field in ETT system were simulated and calculated those can be gotten: (1) The aerodynamic resistance increases with the increase of transition curvature of streamlined body. And in according to the comparative analysis, when the transition curvature is 0.15, the economy and applicability are better. (2) It can not be ignored that the train - tube dimension ratio impact on the train resistance. The resistance grows linear with train - tube dimension ratio increase. Since the change range of train cross-sectional area is small, it can only increase the tube section to reduce the growing, which will increase the project cost, affect its operating costs. (3) Train aerodynamic drag and lift increase rapidly with the increases of train speed. Similarly, it will be also increased with the tube pressure increases quickly. Using the fuzzy multi-criteria evaluation, building the mathematical optimization model, based on the best space filling model and nonparametric regression model, the objective function is established. The optimal scheme is: train running speed is 987.7 km/h, tube vacuum degree is 1077.1 Pa, the aerodynamic drag is 5213.6 N, and the aerodynamic lift is 680.17 N. Acknowledgements This work is supported in part by the Science Foundation of Education Department in Jiangxi province China, 2012 (No. GJJ12287). Reference 1. Zhi-yun Shen, On developing high-speed evacuated tube transportation in China, Journal of Southwest Jiaotong University, No. 40,2005, pp. 133-137. 2 Xiao Zhou, Yao-Ping Zhang, Ying-Feng Yao, Numerical simulation on the aerodynamic drag of high-speed train in evacuated tube, Science Technology and Engineering, No. 8, 2008, pp. 1626-1628. 3 Dayou Ma, Jiaqi Sun, Vibration and noise control engineering handbook, Mechanical Industry Press, Beijing, 2002, 137 p. 4 Hong-Qi Tian, Guang-Jun Gao, The analysis and evaluation on the aerodynamic behavior of 270 km/h High-speed Train, China Railway Science, No. 24, 2003, pp. 14-18. 5 Bingbing Ji, Jinping Chen, Grid division technology example explanation with ANSYS ICEM CFD, China Water Conservancy and Hydropower Press, Beijing, 2012. 6 Guangzhong Wu, Tingting Song, Yi Zhang, FLUENT basic entry and case, Electronic Industry Press, Beijing, 2012. 7 Minggao Li, Ming Li, ANSYS 13.0 flow field analysis techniques and application Examples, China Machine Press, Beijing, 2012. 8 Li-Ming Duan, Zheng-Yu Duan, Xin Xin, Bi-Ning Guo, The noise characteristic of certain MU trains on passenger line, Railway Energy Saving & Environmental Protection & Occupational Safety and Health, No. 2,2012, pp. 260-263. 9 Yi-Nan Lai, Bin-Di You, Yi-Xin Song, Xian-Li Liu, Fuzzy finite element optimization of complicated mechanical structure, Journal of Harbin Institute of Technology, No. 4, 2009, pp. 164-168. 1,2 Zhaoping TANG,1 Jin QIN,2 Jianping SUN 1 School of Traffic & Transportation Engineering, Central South University, Changsha 410075, China 2 School of Information Engineering, East China Jiao Tong University, Nanchang 330013, China 1 Tel.: (086) 731-82655446,2 Tel: (086) 791-87046242 E-mail: [email protected], [email protected], sunjianping@ ecjtu.jx.cn Received: 20 July 2013 /Accepted: 25 October 2013 /Published: 30 November 2013 (c) 2013 International Frequency Sensor Association |