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Numerical Simulation of Inviscid Transient Flows in Shock Tube and its Validations

Authors: Al-Falahi Amir, Yusoff M. Z, Yusaf T

Abstract:

The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN" in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wide range of Mach number. The developed solver uses second order accurate cell-vertex finite volume spatial discretization and forth order accurate Runge-Kutta temporal integration and it is designed to simulate the flow process for similar driver/driven gases (e.g. air-air as working fluids). The solver is validated against analytical solution and experimental measurements in the high speed flow test facility. Further investigations were made on the flow process inside the shock tube by using the solver. The shock wave motion, reflection and interaction were investigated and their influence on the performance of the shock tube was determined. The results provide very good estimates for both shock speed and shock pressure obtained after diaphragm rupture. Also detailed information on the gasdynamic processes over the full length of the facility is available. The agreements obtained have been reasonable.

Keywords: shock tunnel, shock tube, shock wave, CFD.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331555

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References:


[1] Caleffi, V., Valiani, A. and Zanni, A. (2003), ÔÇÿFinite Volume Method for Simulating Extreme Flood Events in Natural Channels-, Journal of Hydraulic Research, Vol. 41, No. 2, pp. 167-177.
[2] Valiani, A., Caleffi, V. and Zanni, A. (2002), ÔÇÿCase Study: Malpasset Dam-Break Simulation using a 2D Finite Volume Method-, Journal of Hydraulics Engineering, Vol. 128, No. 5, pp. 460-472.
[3] McDonald, P.W. (1971) 'The Computation of Transonic Flow Through 2D Gas Turbine Cascades- ASME Paper No. 71-GT-89
[4] Couston, M. (1976) 'Time-Marching Finite Area Method' V.K.I. Lecture Series 84
[5] Thiaville, J.M. (1977) 'Comparison of a Finite Difference Method with a Time-Marching Method for Blade to Blade Transonic Flow Calculations' . in ÔÇÿTransonic Flow Problems in Turbomachinery-, (ed. Adamson, T.C & Platser, M.F.)
[6] Farn, C.L. and Whirlow, D.K. (1977) 'Application of Time-Dependent Finite Volume to Transonic Flow in Large Turbine' in ÔÇÿTransonic Flow Problems in Turbomachinery-, (ed. Adamson, T.C & Platser, M.F.)
[7] Denton, J.D. (1975) 'A Time Marching Method for Two- and Three- Dimensional Blade to Blade Flows' ARC R. & M. No. 3775
[8] Lerat, A. and Sides, J. (1982) 'A New Finite Volume Method for the Euler Equations with Applications to Transonic Flows' in ÔÇÿNumerical Methods in Aeronautical Fluid Dynamics-, (Ed. Roe, P.L), Academic Press, pp. 245-288
[9] Rizzi, A. and Eriksson, L.E. (1981) ÔÇÿTransfinite Mesh Generation and Damped Euler Equations Algorithm for Transonic Flow Around Wing-Body Configurations- . AIAA 5th Computational Fluid Dynamics Conference, Paulo Alto, pp. 43-68
[10] Rizzi, A. (1982) ÔÇÿDamped Euler-Equations Method to Compute Transonic Flow Around Wing-Body Combinations- AIAA Journal, Vol. 20
[11] Jameson, A., Schmidt, W. and Turkel, E. (1981) 'Numerical Solutions of the Euler Equations by Finite Volume Methods using Runge-Kutta Time Stepping Schemes' AIAA Paper No. 81-1259
[12] Jameson, A. (1982) 'Transonic Aerofoil Calculations Using the Euler Equations' Numerical Methods in Aeronautical Fluid Dynamics (P.L. Roe ed.), Academic Press, pp. 289-308
[13] Jameson, A. and Baker, T.J. (1983) 'Solution of the Euler Equations for Complex Configurations' Proc. of the AIAA 6th Computational Fluid Dynamics Conference, AIAA, New York, pp. 293-302
[14] Buratynski, E.K. and Caughey, D.A. (1986) 'An Implicit LU scheme for the Euler Equations Applied to Arbitrary Cascades' AIAA Journal, 24 (1): 39-46
[15] Dawes, W.N. (1987) 'Application of a Three-Dimensional Viscous Compressible Flow Solver to a High-Speed Centrifugal Compressor Rotor - Secondary Flow and Loss Generation' Proc. Inst. Mech. Engrs., Conf. Turbomachinery Efficiency, Prediction and Improvement, C261-87, pp. 53-61
[16] Van Leer, B. (1979) ÔÇÿTowards the Ultimate Conservative Difference Schemes. V. A Second Order Sequel to Gudunov-s Method- J. Comp. Physics, 32 : 101-36
[17] Harten, A. (1983) ÔÇÿHigh Resolution Schemes for Hyperbolic Conservation Laws- Journal of Computational Physics, 49, 357-93
[18] Harten, A. (1984) ÔÇÿOn a Class of High Resolution Total Variation Stable Finite Difference Schemes- SIAM Journal of Numerical Analysis, 21, 1-23
[19] Osher, S. (1984) ÔÇÿRiemann Solvers, the Entropy Condition and Difference Approximation- SIAM Journal Numerical Analysis, 21, pp. 217-35
[20] Osher, S. and Chakravarthy, S.R. (1984) ÔÇÿHigh Resolution Schemes and the Entropy Condition- SIAM Journal of Numerical Analysis, 21, pp. 955-84
[21] Yusoff M. Z. (1997)ÔÇÿ An improved treatment of two-dimensional Two-Phase Flow of Steam by a Runge-Kutta Method-,Ph.D. Thesis, University of Birmingham
[22] Yusoff M. Z. "A Two-Dimensional Time-Accurate Euler Solver for Turbo machinery Applications" Journal-Institution of Engineers, Malaysia Vol. 5 No. 3 1998
[23] Hirsch, C. (1990) ÔÇÿNumerical Computation of Internal and External Flows- Volume 1(Fundamentals of Numerical Discretization) and Volume 2 (Computational Methods for Inviscid and Viscous Flows), John Wiley & Sons
[24] Gustafsson, B. and Sundstrom, A. (1978) ÔÇÿIncompletely Parabolic Problem in Fluid Dynamics- SIAM Journal of Applied Mathematics, 35 (2): 343-357
[25] Pulliam, T.H. (1986) ÔÇÿArtificial Dissipation Model for the Euler Equations.- AIAA Journal , 24: 1931-1940
[26] Swanson, R.C. and Turkel, E. (1987) ÔÇÿArtificial Dissipation and Central Difference Schemes for the Euler and Navier Stokes Equation.- AIAA Paper No. 87-1101, Proc. AIAA 8th Computational Fluid Dynamics Conference, pp. 55-69
[27] Caughey, D.A. and Turkel, E. (1988) ÔÇÿEffects of Numerical Dissipation of Finite Volume Solutions of Compressible Flow Problems- AIAA Paper No. 88-0621, AIAA 26th Aerospace Sciences Meeting
[28] Bamkole, B.O. (1991) ÔÇÿA Two Step Method for Solving the Euler Equations- Internal Report, Manuf. & Mech. Eng. Dept., University of Birmingham
[29] G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys. 43 (1978) 1-31