Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes (e.g., Tollmien-Schlichting (T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward-and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step (BFS) always has a greater impact than a forward-facing step (FFS). These facts agree with most of the previous investigations. However, one numerical study (WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192-197 (2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results.
Ming DONG, Anyong ZHANG
. Scattering of Tollmien-Schlichting waves as they pass over forward-/backward-facing steps[J]. Applied Mathematics and Mechanics, 2018
, 39(10)
: 1411
-1424
.
DOI: 10.1007/s10483-018-2381-8
[1] WU, X. and DONG, M. A local scattering theory for the effects of isolated roughness on boundarylayer instabity and transition:transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68-108(2016)
[2] REYNOLDS, G. A. and SARIC, W. S. Experiments on the stability of the flat-plate boundary layer with suction. AIAA Journal, 24, 202-207(1986)
[3] REED, H. L. and NAYFEH, A. H. Numerical-perturbation technique for stability of flat-plate boundary layers with suction. AIAA Journal, 24, 208-214(1986)
[4] MASAD, J. A. and NAYFEH, A. H. Laminar flow control of subsonic boundary layers by suction and heat-transfer strips. Physics of Fluids A:Fluid Dynamics, 4, 1259-1272(1992)
[5] MASAD, J. A. Transition in flow over heat transfer strips. Physics of Fluids, 4, 1259-1272(1992)
[6] BALAKUMAR, P., ZHAO, H., and ATKINS, H. Stability of hypersonic boundary layers over a compression corner. AIAA Journal, 43, 760-767(2005)
[7] EGOROV, I., NOVIKOV, A., and FEDOROV, A. Numerical modeling of the disturbances of the separated flow in a rounded compression corner. Fluid Dynamics, 41, 39-49(2006)
[8] NOVIKOV, A., EGOROV, I., and FEDOROV, A. Numerical simulation of three-dimensional wave packet in supersonic flow over a compression corner. The 45th AIAA Fluid Dynamics Conference, AIAA, Dallas, TX (2015)
[9] WANG, Y. X. and GASTER, M. Effect of surface steps on boundary layer transition. Experiments in Fluids, 39, 679-686(2005)
[10] EPPINK, J. L., WLEZIEN, R. W., KING, R. A., and CHOUDHARI, M. Interaction of a backward-facing step and crossflow instabilities in boundary-layer transition. AIAA Journal, 56, 1-12(2017)
[11] WORNER, A., RIST, U., and WAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192-197(2003)
[12] COSTANTINI, M., RISIUS, S., and KLEIN, C. Experimental investigation of the effect of forwardfacing steps on boundary layer transition. Procedia IUTAM, 14, 152-162(2015)
[13] EDELMANN, C. A. and RIST, U. Impact of forward-facing steps on laminar-turbulent transition in transonic flows without pressure gradient. The 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA, Grapevine, TX (2013)
[14] SMITH, F. T. Laminar flow over a small hump on flat plate. Journal of Fluid Mechanics, 57, 903-824(1973)
[15] SMITH, F. T. On the non-parallel flow stability of the Blasius boundary layer. Proceedings of the Royal Society A:Mathematical Physical and Engineering Sciences, 366, 91-109(1979)
[16] SMITH, F. T. On the first-mode instability in subsonic, supersonic or hypersonic boundary layers. Journal of Fluid Mechanics, 198, 127-153(1989)
[17] STEWARTSON, K. Multistructured boundary layers on flat plates and related bodies. Advances in Applied Mechanics, 14, 145-239(1974)
[18] El-MISTIKAWA, T. M. A. Subsonic triple deck flow past a flat plate with an elastic stretch. Applied Mathematical Modelling, 34, 1238-1246(2010)
Email Alert
RSS