CAJ | 학술논문

基于圆柱坐标下Stokes流的泊松方程和双调和方程，对任意角度扇形截面流道内的流体速度分布进行解析研究。采用分离变量法得到各角度扇形截面流道的轴向速度及流函数解析表达式，并利用配置点法确定流道横截面内周向及径向速度分布规律。利用数值模拟方法分析不同雷诺数下 Stokes 方程解析解与 N-S 方程数值解之间的相对偏差。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；雷诺数Re<1的条件下，解析解与数值解相对偏差小于2%，随着雷诺数增大两者结果的偏差显著增大，但雷诺数在100以下时最大偏差不超过10%，表明本文的解析解不但可以应用在雷诺数极低的Stokes流，还可以应用到雷诺数较小的部分层流。
기우원주좌표하Stokes류적박송방정화쌍조화방정，대임의각도선형절면류도내적류체속도분포진행해석연구。채용분리변량법득도각각도선형절면류도적축향속도급류함수해석표체식，병이용배치점법학정류도횡절면내주향급경향속도분포규률。이용수치모의방법분석불동뢰낙수하 Stokes 방정해석해여 N-S 방정수치해지간적상대편차。연구결과표명，재저뢰낙수하선형류도내적삼유Stokes류가이분해위량개이유류동，즉압력강추동적축향류급원호외벽선전유발적선형강내절면류；류도내적축향속도화주향속도여선형각평분선성대칭분포관계，이경향속도성반대칭관계；뢰낙수Re<1적조건하，해석해여수치해상대편차소우2%，수착뢰낙수증대량자결과적편차현저증대，단뢰낙수재100이하시최대편차불초과10%，표명본문적해석해불단가이응용재뢰낙수겁저적Stokes류，환가이응용도뢰낙수교소적부분층류。
Based on the Poisson’s equation and the biharmonic equation, the fluid velocity distribution in the fan-shaped channel with different angle are studied analytically. The analytic expressions of axial velocity and stream function are obtained in the sectorial channel with different angle by the method of separation of variables, and the distributions of the circumferential and radial velocity components in the cross section of the channel are determined by the method collocation points. By numerical simulation method, the relative deviations between analytic solutions of Stokes equation and simulated solutions of N-S equation are analyzed at different Reynolds number. The conclusion indicates that the 3D Stokes flow at low Reynolds number within the fan-shaped channel can be decomposed into two 2D flows, namely the axial flow in the straight duct driven by pressure drop and the sectional flow in the fan-shaped cavity induced by circular wall rotation. In the condition of Re<1, the relative deviations between analytic solutions and simulated solutions are all less than 2%. The deviations increase greatly with Reynolds number enhancing,but maximum deviations of three velocity components are not larger than 10%as Re<100, which implies the analytic solutions can not only be used in Stokes flow at very low Reynolds number, but also be applied in laminar flow at lower Reynolds number.