Convective instability and transient growth in flow over a backward-facing step
Convective instability and transient growth in flow over a backward-facing step
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DOI：
10.1017/s0022112008001109
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发表时间：
2007-11
影响因子：
3.7
通讯作者：
H. Blackburn;D. Barkley;S. Sherwin
中科院分区：
文献类型：
--
作者：
H. Blackburn;D. Barkley;S. Sherwin
本文给出了在膨胀比为2的矩形后台阶几何结构中二维和三维最佳线性扰动对二维流动的瞬态能量增长。雷诺数的基础上的台阶高度和峰值流入速度被认为是在0-500的范围内，这是低于三维渐近不稳定的发病值。众所周知，该流动具有很强的局部对流不稳定性，在Re = 500时，计算的最大线性瞬态能量增长值为80×103量级。在二维情况下，在任何时间间隔内都没有增长的临界雷诺数被确定为Re = 57.7。最大瞬时增长的能量分布的质心位置通常位于定常基流的所有停滞/再附着点的下游。次优瞬态模式也进行了计算和讨论。弱非线性效应的直接研究表明，非线性稳定在Re = 500。最佳三维扰动的展向波长为10阶台阶高度。虽然它们的生长比二维情况略大，但它们在性质上大致相似。当全非线性系统的入流受到白色噪声扰动时，在下游通道中对应于最大线性瞬态增长的位置处观察到窄带随机速度扰动。该响应的中心频率与根据预测的最佳扰动的流向波长和平均平流速度计算的中心频率相匹配。驱动流的响应和最佳扰动之间的联系进一步证明了响应能量到速度分量的分区。
Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components.