前缘曲率对三维边界层内被激发出非定常横流模态的影响研究

陆昌根; 沈露予

doi:10.7498/aps.67.20181343

摘要

三维边界层感受性问题是三维边界层层流向湍流转捩的初始阶段，是实现三维边界层转捩预测与控制的关键环节.在高湍流度的环境下，非定常横流模态的失稳是导致三维边界层流动转捩的主要原因；但是，前缘曲率对三维边界层感受性机制作用的研究也是十分重要的课题之一.因此，本文采用直接数值模拟方法研究在自由来流湍流作用下具有不同椭圆形前缘三维（后掠翼平板）边界层内被激发出非定常横流模态的感受性机制；揭示不同椭圆形前缘曲率对三维边界层内被激发出非定常横流模态的扰动波波包传播速度、传播方向、分布规律、感受性系数以及分别提取获得一组扰动波的幅值、色散关系和增长率等关键因素的影响；建立在不同椭圆形前缘曲率情况下，三维边界层内被激发出非定常横流模态的感受性问题与自由来流湍流的强度和运动方向变化之间的内在联系；详细分析了不同强度各向异性的自由来流湍流在激发三维边界层感受性机制的物理过程中起着何种作用等.通过上述研究将有益于拓展和完善流动稳定性理论，为三维边界层内层流向湍流转捩的预测与控制提供依据.

关键词:

Abstract

Three-dimensional boundary-layer receptivity is the first stage of the laminar-turbulent transition in a three-dimensional boundary layer, and also a key issue for predicting and controlling the laminar-turbulent transition in the three-dimensional boundary layer. At a high turbulence level, the three-dimensional boundary-layer instability in the transition is caused mainly by the unsteady cross-flow vortices. And the leading-edge curvature has a significant influence on three-dimensional boundary-layer receptivity. In view of this, the direct numerical simulation is utilized in this paper to study the mechanism of receptivity to exciting unsteady cross-flow vortices in the three-dimensional (swept-plate) boundary layer with various elliptic leading edges. In order to solve the Navier-Stokes equation numerically, a modified fourth-order Runge-Kutta scheme is introduced for discretization in time; high-order compact finite difference schemes are utilized for discretization in the x-and y-direction; and Fourier transform is used in the z-direction. The pressure Helmholtz equation is solved by a fourth-order iterative scheme. Additionally, the numerical calculation is performed in the curvilinear coordinate system via Jaccobi transform. And the elliptic equation technique is used to gene-rate the body-fitted mesh. The effect of leading-edge curvature on the propagation speed and direction, distribution and receptivity coefficient of the excited unsteady cross-flow vortex wave packet, and the amplitude, dispersion relation and growth rate of the extracted unsteady cross-flow vortex are revealed. In addition, the inner link among the receptivity to unsteady cross-flow vortex, intensity, and direction of free-stream turbulence is established. Furthermore, the receptivity to anisotropic free-stream turbulence is also analyzed in detail. The numerical results indicate that the more intense receptivity to the unsteady cross-flow vortex wave packets is triggered with a smaller leading-edge curvature; whereas, the less intense receptivity is triggered with a greater leading-edge curvature. The receptivity to the unsteady cross-flow vortex wave packets in different curvatures are also found to vary with the angle of free-stream turbulence. Moreover, the anisotropic degree of free-stream turbulence can affect the excitation of the unsteady cross-flow vortex obviously. Through the above study, a further step can be taken to understand the prediction and control of laminar-turbulent transition in the three-dimensional boundary layer and also improve the theory of the hydrodynamic stability.

Keywords:

作者及机构信息

1.
南京信息工程大学海洋科学学院, 南京 210044

通信作者: 陆昌根, cglu@nuist.edu.cn

基金项目: 国家自然科学基金（批准号：11472139）、江苏省高等学校自然科学研究面上项目（批准号：17KJB130008）和江苏高校优势学科建设工程（PAPD）资助的课题.

Authors and contacts

1.
School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China

Corresponding author: Lu Chang-Gen, cglu@nuist.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11472139), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant No. 17KJB130008), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

参考文献

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[9]	Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[10]	Schrader L U, Brandt L, Mavriplis C 2010 J. Fluid. Mech. 653 245
[11]	Tempelmann D, Schrader L U, Hanifi A, et al. 2011 6th AIAA Theoretical Fluid Mechanics Conference Honolulu, Hawaii, USA, June 27-30, 2011 p3294
[12]	Tempelmann D, Schrader L U, Hanifi A 2012 J. Fluid. Mech. 711 516
[13]	Borodulin V I, Ivanov A V, Kachanov Y S 2013 J. Fluid. Mech. 716 487
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[16]	Lin R S, Malik M R 1997 J. Fluid. Mech. 333 125
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[18]	Hoffmann K A, Chiang S T 2000 Computational Fluid Dynamics (Vol. I) (Kansas: Engineering Education System) p358
[19]	Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 349
[20]	Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292

施引文献

[1]	Saric W S, Reed H L, Edward W B 2003 Annu. Rev. Fluid. Mech. 35 413
[2]	Bippes H 1999 Prog. Aerosp. Sci. 35 363
[3]	Radeztsky R H, Reibert M S, Saric W S 1999 AIAA J. 37 1370
[4]	Deyhle H, Bippes H 1996 J. Fluid. Mech. 316 73
[5]	Reibert M S, Saric W S 1997 28th Fluid Dynamics Conference Snowmass Village, CO, USA, June 29-July 2, 1997 p1816
[6]	Kurz H B E, Kloker M J 2014 J. Fluid. Mech. 755 62
[7]	Bertolotti F P 2000 Phys. Fluid. 12 1799
[8]	Collis S S, Lele S K 1999 J. Fluid. Mech. 380 141
[9]	Schrader L U, Brandt L, Henningson D S 2009 J. Fluid. Mech. 618 209
[10]	Schrader L U, Brandt L, Mavriplis C 2010 J. Fluid. Mech. 653 245
[11]	Tempelmann D, Schrader L U, Hanifi A, et al. 2011 6th AIAA Theoretical Fluid Mechanics Conference Honolulu, Hawaii, USA, June 27-30, 2011 p3294
[12]	Tempelmann D, Schrader L U, Hanifi A 2012 J. Fluid. Mech. 711 516
[13]	Borodulin V I, Ivanov A V, Kachanov Y S 2013 J. Fluid. Mech. 716 487
[14]	Shen L Y, Lu C G 2016 Acta Phys. Sin. 65 014703 (in Chinese)[沈露予, 陆昌根 2016 65 014703]
[15]	Lu C G, Shen L Y 2017 Acta Phys. Sin. 66 204702 (in Chinese)[陆昌根, 沈露予 2017 66 204702]
[16]	Lin R S, Malik M R 1997 J. Fluid. Mech. 333 125
[17]	Shen L Y, Lu C G 2018 Acta Phys. Sin. 67 184703 (in Chinese)[沈露予, 陆昌根 2018 67 184703]
[18]	Hoffmann K A, Chiang S T 2000 Computational Fluid Dynamics (Vol. I) (Kansas: Engineering Education System) p358
[19]	Shen L Y, Lu C G 2016 Appl. Math. Mech. 37 349
[20]	Zhang Y, Zaki T, Sherwin S, Wu X 2011 6th AIAA Theortical Fluid Mechanics Conference Hawaii, USA, June 27-30, 2011 p3292

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