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Control of Near-wall Turbulence by Stabilizing Saddle-type Steady Flow

稳定鞍型稳流控制近壁湍流

基本信息

批准号：
13650183
负责人：
KAWAHARA Genta
金额：
$ 2.11万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

In this project we first searched for saddle-type steady flows in a plane Couette system. We obtained quiescent states of the saddle type which appeared transiently in direct numerical simulations of turbulent flow, and then the quiescent states were used as an initial guess for the Newton iteration to numerically compute three-dimensional saddle solutions to the incompressible Navier-Stokes equation. At the lowest Reynolds number for self-sustaining turbulence we have also succeeded in numerically obtaining unstable periodic motion embedded in the Couette turbulence by using the original iterative method with the aid of the direct numerical simulations. This periodic saddle is a three-dimensional periodic solution, and it represents well the regeneration cycle of near-wall coherent structures, i.e., streaks and streamwise vortices. In order to demonstrate similarities of the saddle solutions obtained in the Couette system with those in a plane Poiseuille system we next compared their … More properties with those in a fully turbulent state of these systems. It has been found in the comparison that the mean velocity and the RMS velocities in the buffer region of near-wall turbulence are in excellent agreement with the corresponding velocities of the saddle solutions.On the other hands, we introduced a porous wall into boundary-layer flow to retard a flow separation (or equivalently to enhance momentum transfer), and we observed the significant effects of the wall porosity. We also obtained analytically the unstable eigensolutions to corrugated vortex sheets, which are a model for the near-wall streaky flow, at a long-wavelength limit. In this analysis we have elucidated theoretically the destabilization mechanism of the steaks, and we have found that the saddle-type steady state appears as a nonlinearly saturated state of unstable perturbations. Furthermore, we performed the direct numerical simulations of the flow downstream of a backward-facing step, and we have shown the generation mechanism of three-dimensional vortical structures appearing downstream of the step.We have worked on the stabilization of the saddle (unstable) solutions using the Pyragas' external-force method, and in the numerical experiments of the Couette system we have succeeded in the stabilization of the periodic saddles. In this strategy we can stabilize saddle solutions by small control input. Less

在本计画中，我们首先研究了一个平面Couette系统中的鞍型定常流动。我们获得了在湍流直接数值模拟中出现的鞍型瞬态静态，然后将该静态作为牛顿迭代的初始假设，数值计算了不可压Navier-Stokes方程的三维鞍型解。在自持湍流的最低Reynolds数下，我们还成功地通过使用原始迭代方法并借助于直接数值模拟来数值获得嵌入在Couette湍流中的不稳定周期运动。这个周期鞍是一个三维周期解，它很好地代表了近壁相干结构的再生周期，即，条纹和流向涡。为了证明在Couette系统中获得的鞍解与在平面Poiffille系统中获得的鞍解的相似性，我们接下来比较了它们的 ...更多信息与这些系统的完全湍流状态下的性质。通过比较发现，近壁湍流缓冲区的平均速度和均方根速度与鞍解的相应速度吻合得很好。另一方面，我们在边界层流动中引入多孔壁以阻止流动分离（或等效地增强动量传递），并观察到壁面多孔性的显著影响。我们还得到了波纹涡面的不稳定本征解，这是一个模型的近壁条纹流，在长波长的限制。在这个分析中，我们已经从理论上阐明了牛排的失稳机制，我们已经发现，鞍型稳态出现作为一个非线性饱和状态的不稳定扰动。此外，我们还对后台阶下游的流动进行了直接数值模拟，揭示了后台阶下游三维涡结构的产生机理，并对鞍形结构的稳定性进行了研究（不稳定）的解决方案，使用皮拉加斯的外力方法，在Couette系统的数值实验中，我们成功地稳定了周期鞍。在这种策略中，我们可以通过小的控制输入稳定鞍解。少