The Influence of Finite Rupture Times on Flow Dynamics Within Micro-Shock Tubes

The Influence of Finite Rupture Times on Flow Dynamics Within Micro-Shock Tubes

Desmond Adair Abilkaiyr Mukhambetiyar Martin Jaeger Michael Malin

Department of Mechanical & Aerospace Engineering, Nazarbayev University, Astana, Kazakhstan

School of Engineering, University of Tasmania, Hobart, Australia

CHAM Ltd, Wimbledon Village, London, U.K.

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The importance of micro-shock tubes is growing in line with recent developments of microscale technology for products like micro-heat engines and micro-propulsion systems. The flow dynamics within a micro-shock tube are different from those found in a macro shock tube, and knowledge of these dynamics is not as yet well established, as the flow within these tubes includes extra physics namely rarefaction and complex effects due to viscosity. Studies have recently been made with assumed initial condition of instantaneous diaphragm rupture producing centred shock and expansion waves. However, for a real case, the diaphragm ruptures over a finite time causing a period of partial rupture and this will change the shock characteristics. The work here reports on a series of axisymmetric numerical simulations carried out to calculate the influence of an initial finite-time diaphragm rupture. Rarefaction effects were taken into account by the use of Maxwell’s slip velocity and temperature conditions. Use of an initial finite-time diaphragm rupture boundary condition causes the forming of a non-centred shock wave downstream of the diaphragm, and, the shock propagation distance is considerably reduced by use of the finite-time rupture process.


CFD, finite rupture, micro-shock tube, Shock wave propagation, slip wall


[1] Zhang, G., Setoguchi, T. & Kim, H.D., Numerical simulation of flow characteristics to micro shock tubes. Journal of Thermal Science, 24(3), pp. 246–253, 2015.

[2] Karniadakis, G.E.M. & Beskok, A., Micro Flows Fundamentals and Simulation, Springer, New York, 2002.

[3] Duff, R.E., Shock tube performance at initial low pressure. Physics of Fluids, 2,      pp. 207–216, 1959.

[4] Mirels, H., Test time in low pressure shock tube. Physics of Fluids, 6, pp. 1201–1214, 1963.

[5] Brouillete, M., Shock waves at microscales. Shock Waves, 13, pp. 3–12, 2003.

[6] Kohsuke, T., Kazuaki, I. & Makoto, Y., Numerical investigation on transition of shock induced boundary, 47th AIAA Aerospace Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, 2009.

[7] Ngomo, D., Chaudhuri, D., Chinnayya, A. & Hadjadj, A., Numerical study of shock propagation and attenuation in narrow tubes including friction and heat losses. Comput- ers & Fluids, 39, pp. 1711–1721, 2010.

[8] Zeitoun, D.E., Burtschell, Y. & Graur, I.A., Numerical simulation of shock wave pro- pogation in micro channels using continuum and kinetic approaches. Shock Waves, 19, pp. 307–316, 2009.

[9] Mukhambetiyar, A., Jaeger, M. & Adair, D., CFD modelling of flow characteristics in micro shock tubes. Journal of Applied Fluid Mechanics, 10(4), pp. 1061–1070, 2017.

[10] Arun, K.R. & Kim, H.D., Computational study of the unsteady flow characteristics of a micro shock tube. Journal of Mechanical Science and Technology, 27(2), pp. 451–459, 2012.

[11] Hickman, R.S., Farrar, L.C. & Kyser, J.B., Behaviour of burst diaphragms in shock tubes. Physics of Fluids, 18(10), pp. 1249–1252, 1975.

[12] Outa, E., Tajima, K. & Hayakawa, K., Shock tube flow influenced by diaphragm opening (two-dimensional flow near the diaphragm), 10th International Symposium on Shock Waves and Shock Tubes, Kyoto, Japan, 14–16 July, 1975.

[13] Matsuo, S., Mohammad, M., Nakano, S. & Kim, H.D., Effect of diaphragm rupture process on flow characteristics in a shock tube using dried cellophane, Proceedings of the International Conference on Mechanical Engineering (ICME), Dhaka, 29–31 December, 2007.

[14] Cham Ltd., PHOENICS CODE 2018, Cham Ltd., Wimbledon, London, UK.

[15] Menter, F.R., Zonal two equation k- turbulence models for aerodynamic flows. AIAA Paper 93-2906, 1993.

[16] Menter, F.R., Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8), pp. 1598–1605, 1994.

[17] Sod, G.A., A survey of several finite difference methods for systems on nonlinear hyperbolic conservation laws. Journal of Computational Physics, 27, pp. 1–13, 1978.

[18] Suresh, A. & Huynh, H.T., Accurate monotonicity-preserving schemes with Runge- Kutta time stepping. Journal of Computational Physics, 136, pp. 83–99, 1997.

[19] Park, J.O., Kim, G.W. & Kim, H.D., Experimental study of the shock wave dynamics in micro shock tube. Journal of the Korean Society of Propulsion Engineers, 17(5),  pp. 54–59, 2014.

[20] Wegener, M., Sutcliffe, M. & Morgan, R., Optical study of a light diaphragm rupture process in an expansion tube. Shock Waves, 10, pp. 167–178, 2000.