高雷诺数紊流流动直接数值模拟方法研究

Turbulent flow is one of the most commonly fluid phenomena in practical engineering. Numerical simulation of turbulent flow at a high Reynolds number has long been one of the most difficult problems in modern fluid mechanics. Although the direct numerical solution by using N-S equations to simulate turbulent flow (DNS) is the best suitable approach, the numerical simulation currently remains at a fairly low level, only able to simulate the turbulent flow at a low Reynolds number. This research project has made a break-through of the conventional approach of using DNS method, holding that the simulation of turbulent flow dominated by large eddies can neglect the effects of small eddies, and should focus on direct numerical simulation of flow at a high Reynolds number on a coarse mesh by use of N-S equations. In this study, a discrete processing method for strong nonlinear convection flow, a numerical interpolation scheme with negligible numerical damping and no quasi-numerical oscillation, and a numerical method suitable for complex geometrical boundary are developed to realize the solution by using DNS method. In the flume tests, a physical approach, taking single-expansion scheme and double-expansion scheme for flow separation as examples, PIV velocity measuring technology will be adopted to obtain instantaneous flow domain and pressure pulsation characteristic values so as to provide a basis to verify the validity of the numerical approach and the accuracy of the simulation. The two approaches, physical and numerical, will finally be used jointly to study flow at different Reynolds numbers and the effects of expansion ratio on flow separation, to analyze the process of flow separation and the evolution of the repeated water-touching wall area, to reveal the development of flow patterns, to analyze the pressure on the wall behind the step, the water energy variation tendency and the restoration process of the flow regime downstream of the step, and to study the characteristics of velocity variation and pressure pulsation.

紊流是工程领域最常见的流体运动，数值模拟高雷诺数复杂水流运动一直是近代流体力学中最大的难题之一。虽然直接数值解N-S方程模拟紊流(DNS)是最理想方法，但目前仅停留在较低Re数的筒单紊流模拟。 本申请项目突破传统的DNS求解观点，认为以大涡控制的复杂紊流可忽略小涡影响，着重研究较粗网格下高雷诺数流动的N-S方程直接数值模拟方法，提出适应强非线性对流项的离散处理方法、数值阻尼小而无伪数值振荡的数值插值格式以及适应复杂几何边界的数值方法，实现DNS方法求解；结合水槽试验，以单扩和双扩分离流动为例，采用高分辨率的PIV测速技术，获取瞬态流场及压力脉动特性，为数值方法有效性和计算精度检验提供依据，同时结合试验和计算结果，研究不同Re数、突扩比对分离流动特性影响，分析流动分离、再附着区域变动演变过程，揭示折冲水流发生规律，剖析坎后壁面压力及能量变化趋势及台阶下游流态恢复过程，研究流速及压力脉动特性。

紊流是工程领域最常见的流体运动，数值模拟高雷诺数复杂水流运动一直是近代流体力学中最大的难题之一。虽然直接数值解N-S方程模拟紊流(DNS)是最理想方法，但目前仅停留在较低雷诺数的简单紊流模拟。本申请项目突破传统的DNS求解观点，认为以大涡控制的复杂紊流可忽略小涡影响，着重研究较粗网格下高雷诺数流动的N-S方程直接数值模拟方法，提出适应强非线性对流项的离散处理方法、数值阻尼小而无伪数值振荡的数值插值格式以及适应复杂几何边界的数值方法，实现DNS方法求解。结合水槽试验，以后向台阶分离流动为例，研发了一套高分辨率同步PIV测速系统，获取瞬态流场，为数值方法的有效性和计算精度检验提供依据。同时结合试验和计算结果，研究后向台阶分离流动特性，分析流动分离、再附着区域演变过程。此外，揭示了后向台阶分离流动中的相干结构，为研究分离流动的非恒定特性奠定了基础。