Mechanism of three-dimensional boundary-layer receptivity

doi:10.1007/s10483-017-2232-7

Abstract

Abstract:

Boundary-layer receptivity is always a hot issue in laminar-turbulent transition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept flat-plate boundary layer is a typical three-dimensional flow. Study of its receptivity is important both in theory and applications. In this paper, a freestream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space discretization. On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer (the infinite back-swept flat-plate boundary layer) by free-stream turbulence is studied numerically. If so, effects of the level and the direction of free-stream turbulence on the three-dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.

Key words: viscoelastic fluid, annular pipe, analytical solution, three-dimensional boundary layer, receptivity, free-stream turbulence

2010 MSC Number:

76D05
76F65

Luyu SHEN, Changgen LU. Mechanism of three-dimensional boundary-layer receptivity. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1213-1224.

TrendMD

References

[1] Saric, W. S., Reed, H. L., and White, E. B. Stability and transition of three-dimensional boundary layers. Annual Review of Fluid Mechanics, 35, 413-440(2003)
[2] Lu, C. G. and Shen, L. Y. Numerical study on boundary-layer receptivity with localized wall blowing/suction (in Chinese). Acta Physica Sinica, 64, 224702(2015)
[3] Shen, L. Y. and Lu, C. G. Boundary-layer receptivity under the interaction of free-stream turbulence and localized wall roughness. Applied Mathematics and Mechanics (English Edition), 37, 349-360(2016) DOI 10.1007/s10483-016-2037-6
[4] Shen, L. Y. and Lu, C. G. Local receptivity in non-parallel boundary layer. Applied Mathematics and Mechanics (English Edition), 37, 929-940(2016) DOI 10.1007/s10483-016-2092-9
[5] Lu, C. G. and Shen, L. Y. Numerical study of leading-edge receptivity on the infinite-thin flat-plat boundary layer (in Chinese). Acta Physica Sinica, 65, 194701(2016)
[6] Shen, L. Y. and Lu, C. G. Receptivity of the steady cross-flow vortices in the three-dimensional boundary layer (in Chinese). Acta Physica Sinica, 66, 014703(2017)
[7] Xu, G. L. and Fu, S. The instability and control of compressible cross flows (in Chinese). Advances in Mechanics, 42, 262-273(2012)
[8] Bippes, H. Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Progress in Aerospace Sciences, 35, 363-412(1999)
[9] Schrader, L. U., Brandt, L., and Henningson, D. S. Receptivity mechanisms in three-dimensional boundary-layer flows. Journal of Fluid Mechanics, 618, 209-241(2009)
[10] Schrader, L. U., Brandt, L., Mavriplis, C., and Henningson, D. S. Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge. Journal of Fluid Mechanics, 653, 245-271(2009)
[11] Tempelmann, D., Schrader, L. U., Hanifi, A., Brandt, L., and Henningson, D. S. Numerical study of boundary-layer receptivity on a swept wing. AIAA Paper, 3294, 1-13(2011)
[12] Tempelmann, D., Schrader, L. U., Hanifi, A., Brandt, L., and Henningson, D. S. Swept wing boundary-layer receptivity to localized surface roughness. Journal of Fluid Mechanics, 711, 516-544(2012)
[13] Borodulin, V. I., Ivanov, A. V., Kachanov, Y. S., and Roschektaev, A. P. Receptivity coefficients at excitation of cross-flow waves by free-stream vortices in the presence of surface roughness. Journal of Fluid Mechanics, 716, 487-527(2013)
[14] Shen, L. Y., Lu, C. G., Wu, W. G., and Xue, S. F. A high-order numerical method to study threedimensional hydrodynamics in a natural river. Advances in Applied Mathematics and Mechanics, 7, 180-195(2015)
[15] Lu, C. G., Cao, W. D., Zhang, Y., and Peng, J. Large eddies induced by local impulse at wall of boundary layer with pressure gradients. Progress in Natural Science, 18, 873-878(2008)
[16] Zhang, Y. M., Zaki, T., Sherwin, S., and Wu, X. S. Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence. 6th AIAA Theoretical Fluid Mechanics Conference, Honolulu, Hawaii (2011)
[17] Kurian, T., Fransson, J. H. M., and Alfredsson, P. H. Boundary layer receptivity to free-stream turbulence and surface roughness over a swept flat plate. Physics of Fluids, 23, 034107(2011)