强粘性层流理论及在粘性流计算中的应用

Strong viscous flow theory with application to computation of high Reynolds number flows

对高雷诺数流动计算 ,为了解决部分粘性项甚至全部惯性粘性项落入误差与流动物理尺度的关系问题 ,本文提出强粘性流动理论。强粘性流中至少有一个粘性项与惯性项同量阶 ,理论包含了物理尺度各向相同极限、经典边界层和多层边界层理论为其特例 ,给出了从经典边界层向物理尺度各向相同极限演化的尺度规律和粘性惯性诸项变化的量阶关系 ,阐明了粘性与惯性力强相互作用将在剪切层的法向以及流向同时“激发”小尺度结构。对粘性流计算 ,利用强粘性剪切流尺度律重新标度NS格式的修正微分方程 ,给出临界网格尺度与流动物理尺度和差分格式精度的关系 ,得到部分粘性项落入误差和计算结果为非物理数值粘性解的二个判据。并以流场中的边界层、驻点和分离点邻域计算为例说明理论的应用 ,对强粘性剪切流计算。

In order to solve several basic problems of high Reynolds number flow computations, we suggest a theory of strong viscous flow, where there exists at least one viscous term being the same order of magnitude as the inertial term in the Navier Stokes (NS) equations. Main contents are: evolution of strong viscous shear flow(SVSF) from anisotropic flow where viscous shear stress is dominating over other viscous stresses to an isotropic one where viscous shear and diffusion are of equal importance and physical scales are the same in the different directions, scale laws of SVSF evolution, an estimation of orders of magnitude of all viscous and inertial terms, critical grid scales of difference computing SVSF, two criterions of that the partial viscous terms drop into the truncated error terms of the modified differential equations of NS difference scheme and that NS computations yield nonphysical numerical viscous solutions. Physical and numerical analyses show that we should pay more attention to nonphysical numerical viscous solutions in small scale strong viscous shear flow regions.