扇形流道内Stokes流动特性的数值模拟

Numerical Simulation of Stokes Flow Characteristics in the Fan-shaped Duct

针对低雷诺数下外壁旋转的扇形截面流道内的流动特性进行数值模拟,得到不同扇形角度下的速度、涡量及流函数的分布规律.研究结果表明:在低雷诺数下扇形流道内的三维Stokes流可以分解为两个二维流动,即压力降推动的轴向流及圆弧外壁旋转诱发的扇形腔内截面流;流道内的轴向速度和周向速度与扇形角平分线成对称分布关系,而径向速度成反对称关系;随着扇形角度的减小,流道内会出现多个涡流区域,各涡流区域内的速度场、涡量场及流函数均具有自相似性,说明外壁旋转的扇形流道内的流体具有混沌运动特征;雷诺数相同的情况下,流道内的涡量随着扇形角度的减小而增大,表明小角度扇形截面流道有利于流体的混合.

The flowcharacteristics of the fan-shaped duct with rotating circular wall at lowReynolds number is simulated,and the patterns of the velocity,vorticity and stream function are obtained at various sector angles. The results showthat the 3D Stokes flowat lowReynolds number within the sector duct can be decomposed into two 2D flows,namely the axial flowin the straight duct driven by pressure drop and the sectional flowin the fan-shaped cavity induced by circular lid rotation. Axial velocity and circumferential velocity within the duct is symmetrical about sector bisector,while radial velocity is anti-symmetrical.With the decrease of sector angle,more and more vortex regions emerge in the sector duct,and the velocity field,vorticity field or stream function in the vortex regions isself-similar to each other,which shows that the fluid flowin the fan-shaped duct withrotating outer wall is of chaotic characteristics. Under the same Reynolds number,vorticity in the duct rises with the decrease of the sector angle,which implies that the small angle fan-shaped channel is good for fluid mixing.