基于Helmholtz速度分解的黏势流耦合方法

针对Navier-Stokes(N-S)方程,根据Helmholtz速度分解,将流场速度分解为势流部分和非势流部分,剥离势流部分后得到黏势流耦合的变形N-S方程.变形N-S方程求解的是非势流部分速度分量,其在远场的影响较弱,故较传统计算流体动力学(CFD)方法求解N-S方程计算区域小,计算效率较高.以圆柱绕流为例,势流部分速度分量采用解析解,并在OpenFOAM平台内实现了变形N-S方程的黏势流耦合计算.对不同雷诺数下圆柱绕流进行了计算模拟,并将耦合方法计算获得的流场中的速度、压力,与文献中的试验及传统CFD等计算的结果进行仔细比较和分析,相关结果吻合良好.研究表明,该方法适用于层流和湍流模型的计算模拟,为改善黏流计算效率提供了新的途径.

Approach of Viscous/Potential Flow Based on Helmholtz Velocity Decomposition

Abstract： According to Helmholtz velocity decomposition, a modified Navier Stokes(N S) equation was obtained by decomposing the velocity into the potential flow component and the remaining one. The solution to the modified N S equation was only for the remaining velocity component which vanished in the far field. It was highly efficient to solve the modified N S equation due to the request of small computation domain. Such viscous/potential flow solver was developed on the platform of open source software OpenFOAM. The flows around a cylinder were simulated by the present method in which the analytical formula was taken as the solution to the potential flow. The calculations of the flow around a cylinder at different Reynolds numbers and the comparison of the results with the ones obtained by using the conventional computational fluid dynamics method and the experiment data were conducted. The results agree well, which indicates that the present method is suitable to solve both laminar and turbulence flow and it can improve the computational efficiency.