UNSTEADY CHARACTERISTICS OF THE SHOCK PROPAGATION IN A CONVERGENT SHOCK TUBE WITH SMALL ANGLE
DOI:
https://doi.org/10.20319/mijst.2018.42.4662Keywords:
Shock/boundary Interaction, Bifurcation, InstabilityAbstract
The whole evolution of the incident shock propagation in a convergent shock tube with small angle is studied in detail by using the direct numerical simulation. Specifically, the shape of the curved shock and the unsteady flow patterns which differs from the K-H instability, have been evaluated. The results show that as a disturbance of the inclined wall on the shock, the bending position of the incident shock represents periodically changed and its non-dimensional wavelength is larger when the convergent angle becomes greater, indicating a faster response to the curvature variation. At the same time, two different flow instable patterns for the shock propagation in the area reduction channel are discovered, one of which is the asymmetric shock bifurcations when the reflected shock from the collision of the right wall interacts with the boundary layer. This instability is closely related to the unsteady vortex shedding behind the bifurcated feet, resulting in the dramatic pressure fluctuation. Another pattern occurs when the reflected shocks generated by the curved incident shock impinge on the upper and lower walls. The collision position moves at a modest speed, which causes the formation of small vortices near the reflection regions.
References
Chester, W. (1953). The propagation of shock waves in a channel of non-uniform width. The Quarterly Journal of Mechanics and Applied Mathematics, 6(4), 440-452. https://doi.org/10.1093/qjmam/6.4.440
Chisnell, R. F. (1957). The motion of a shock wave in a channel, with applications to cylindrical and spherical shock waves. Journal of Fluid Mechanics, 2(3), 286-298. https://doi.org/10.1017/S0022112057000130
Daru, V., & Tenaud, C. (2009). Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme. Computers & Fluids, 38(3), 664-676. https://doi.org/10.1016/j.compfluid.2008.06.008
Davies, L., & Wilson, J. L. (1969). Influence of Reflected Shock and Boundary‐Layer Interaction on Shock‐Tube Flows. The Physics of Fluids, 12(5), I-37. https://doi.org/10.1063/1.1692625
Dowse, J., & Skews, B. (2014). Area change effects on shock wave propagation. Shock Waves, 24(4), 365-373. https://doi.org/10.1007/s00193-014-0501-z
Gaitonde, D. V. (2015). Progress in shock wave/boundary layer interactions. Progress in Aerospace Sciences, 72, 80-99. https://doi.org/10.1016/j.paerosci.2014.09.002
Gamezo, V. N., Khokhlov, A. M., & Oran, E. S. (2001). The influence of shock bifurcations on shock-flame interactions and DDT. Combustion and flame, 126(4), 1810-1826. https://doi.org/10.1016/S0010-2180(01)00291-7
Helmholtz instability on shock propagation in curved channel. In 15th International Symposium on Flow Visualization, ISFV-15, Minsk, Paper (Vol. 177).
Hui, G., De-Xun, F., Yan-Wen, M., & Xin-Liang, L. (2005). Direct numerical simulation of supersonic turbulent boundary layer flow. Chinese Physics Letters, 22(7), 1709. https://doi.org/10.1088/0256-307X/22/7/041
Igra, O., Elperin, T., Falcovitz, J., & Zmiri, B. (1994). Shock wave interaction with area changes in ducts. Shock waves, 3(3), 233-238. https://doi.org/10.1007/BF01414717
Ivanov, I. E., Dowse, J. N., Kryukov, I. A., Skews, B. W., & Znamenskaya, I. A. (2012). Kelvin-
Mark, H. (1958). The interaction of a reflected shock wave with the boundary layer in a shock tube. National Advisory Committee for Aeronautics.
Sasoh, A., Takayama, K., & Saito, T. (1992). A weak shock wave reflection over wedges. Shock Waves, 2(4), 277-281. https://doi.org/10.1007/BF01414764
Skews, B. W. (1967). The shape of a diffracting shock wave. Journal of Fluid Mechanics, 29(2), 297-304. https://doi.org/10.1017/S0022112067000825
Skews, B. W., & Kleine, H. (2007). Flow features resulting from shock wave impact on a cylindrical cavity. Journal of Fluid Mechanics, 580, 481-493. https://doi.org/10.1017/S0022112007005757
Steger, J. L., & Warming, R. F. (1981). Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. Journal of computational physics, 40(2), 263-293. https://doi.org/10.1016/0021-9991(81)90210-2
Touber, E., & Sandham, N. D. (2011). Low-order stochastic modelling of low-frequency motions in reflected shock-wave/boundary-layer interactions. Journal of Fluid Mechanics, 671, 417-465. https://doi.org/10.1017/S0022112010005811
Xin-Liang, L., De-Xun, F., Yan-Wen, M., & Hui, G. (2009). Acoustic calculation for supersonic turbulent boundary layer flow. Chinese Physics Letters, 26(9), 094701. https://doi.org/10.1088/0256-307X/26/9/094701
Weber, Y. S., Oran, E. S., Boris, J. P., & Anderson Jr, J. D. (1995). The numerical simulation of shock bifurcation near the end wall of a shock tube. Physics of Fluids, 7(10), 2475-2488. https://doi.org/10.1063/1.868691
Whitham, G. B. (1957). A new approach to problems of shock dynamics Part I Two-dimensional problems. Journal of Fluid Mechanics, 2(2), 145-171. https://doi.org/10.1017/S002211205700004X
Whitham, G. B. (1958). On the propagation of shock waves through regions of non-uniform area or flow. Journal of Fluid Mechanics, 4(4), 337-360. https://doi.org/10.1017/S0022112058000495
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