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

Influence of leading-edge curvature on excited unsteady cross-flow vortices in three-dimensional boundary-layer

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.

Three-dimensional boundary-layer receptivity is the first stage of the laminar-turbulent transition in a threedimensional 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（sweptplate） 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 generate 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.