TAFSM

Team for Advanced Flow Simulation and Modeling



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Flow Around High-Speed Trains Passing in a Tunnel

Aerodynamics plays a crucial role in the design and development of high-speed trains from the point of view of cost effectiveness, safety, comfort, and minimal impact on the environment, amongst many other factors. Trains passing each other, especially in tunnels, create pressure transients which may threaten the structural integrity of the trains and may also cause some discomfort to the passengers.

The mesh we used is rather coarse for a 3D problem with intricate geometries and therefore we attach to the results only a qualitative significance. The mesh consists of 51,584 hexahedral elements and 58,607 nodes, and results in approximately 550,000 coupled equations. To accommodate the motion of the trains we have developed a special algebraic mesh moving and remeshing scheme where elements are transplanted from regions in front of the trains to regions behind the trains when they become too distorted. The total number of nodes and elements remains fixed during the simulation.

At the start of the simulation the trains are at rest near the tunnel entrances and accelerate to 100 m/s during the first second, which is the speed at which they will pass each other. This leads to a relative Mach number of approximately 0.6 when the trains pass. We observe that as the trains gain speed, high-pressure regions develop at the front of the trains, and low-pressure regions develop at the rear.

The images below show the pressure distribution on the surface of the trains and on a cutting plane parallel to the tunnel floor. The mesh is superimposed on top of the cutting plane. The mesh generator, flow solver, and flow visualization software (based on Visual3 library and Wavefront) were developed by the T*AFSM.

References:

1. T.E. Tezduyar and T.J.R. Hughes, "Finite Element Formulations for Convection Dominated Flows with Particular Emphasis on the Compressible Euler Equations", AIAA Paper 83-0125, Proceedings of AIAA 21st Aerospace Sciences Meeting, Reno, Nevada (1983).

2. T.J.R. Hughes and T.E. Tezduyar, "Finite Element Methods for First-order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations", Computer Methods in Applied Mechanics and Engineering, 45 (1984) 217-284.

3. G.J. Le Beau and T.E. Tezduyar, "Finite Element Computation of Compressible Flows with the SUPG Formulation", Advances in Finite Element Analysis in Fluid Dynamics (eds. M.N. Dhaubhadel, M.S. Engelman and J.N. Reddy), FED-Vol. 123, ASME, New York (1991) 21-27.

4. G.J. Le Beau and T.E. Tezduyar, "Finite Element Solution of Flow Problems with Mixed-Time Integration", Journal of Engineering Mechanics, 117 (1991) 1311-1330.

5. T.E. Tezduyar, "Stabilized Finite Element Formulations for Incompressible Flow Computations", Advances in Applied Mechanics, 28 (1991) 1-44.

6. T.E. Tezduyar, M. Behr and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: I. The Concept and the Preliminary Numerical Tests", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 339-351.

7. T.E. Tezduyar, M. Behr, S. Mittal and J. Liou, "A New Strategy for Finite Element Computations Involving Moving Boundaries and Interfaces--The DSD/ST Procedure: II. Computation of Free-surface Flows, Two-liquid Flows, and Flows with Drifting Cylinders", Computer Methods in Applied Mechanics and Engineering, 94 (1992) 353-371.

8. T.E. Tezduyar, M. Behr, S. Mittal and A.A. Johnson "Computation of Unsteady Incompressible Flows with the Stabilized Finite Element Methods--Space-Time Formulations, Iterative Strategies and Massively Parallel Implementations", New Methods in Transient Analysis (eds. P. Smolinski et al.), AMD-Vol. 143, ASME, New York (1992) 7-24.

9. T. Tezduyar, "Advanced Flow Simulation and Modeling", Flow Simulation with the Finite Element Method (in Japanese), Springer-Verlag, Tokyo, Japan (1998).

10. T. Tezduyar, "CFD Methods for Three-Dimensional Computation of Complex Flow Problems", Journal of Wind Engineering and Industrial Aerodynamics, 81 (1999) 97-116.