利用等位函數法模擬2D黏性駐波

Numerical Study of two-dimensional Viscous Standing Wave Using Level Set Method

梁興杰(Shin-Jye Liang) ； 林慶緯(Cing-Wei Lin) ； 林家賢(Jia-Sian Lin)

《海洋工程學刊》 5卷1期 (2005/10) Pp. 51-66

https://doi.org/10.6266/JCOE.2005.0501.04

摘要

本研究中，我們發展一數值模式，利用描述不可壓縮流體運動之Navier-Stokes方程式與介面運動之Hamilton-Jacobi方程式，以求解自由液面流流場；將自由液面流轉換為固定計算網格之二相流系統，氣相與液相以等位函數之「正」、「負」符號區分，零等位函數表示自由液面，氣相與液相之密度與黏滯係數以平滑之等位函數描述之；氣相與液相之流場統一以壓力校正法SIMPLE求解，介面運動以等位函數法捕捉。我們將模式應用於雷諾數Re=20與200之2D黏性駐波模擬，計算結果並與線性解(Wu，et al.，2001)比較。此外，我們探討Re=200時，不同氣相與液相密度比（ρ(下標 a)/ρ(下標 l)=1/10，1/100與1/1.000）與黏滯係數比（µ(下標 a)/µ(下標 l)=0.4429/44.29，4.429/44.29與44.29/44.29）對自由液面流流場，與數值方法質量守恆誤差之影響。計算結果顯示，當氣體與液體之密度比與黏滯性比較小時，氣體對於自由液面流的影響可以忽略，因此，數值解接近Wu，etal.(2001)之線性解；當氣體與液體的密度比與黏滯性比較大時，則需要考慮氣體對自由液面流的影響，此時黏性駐波的振幅和相位角會受氣體重力與黏滯性的影響，而與Wu，et al.(2001)線性解有差異。

關鍵字

壓力校正法 ； 等位函數法 ； 黏性駐波

並列摘要

A two-dimensional finite-volume model that couples the incompressible Navier-Stokes equations with the Hamilton-Jacobi equation for free-surface flows was developed. The free surface flow is converted into a two-phase flow system on a fixed grid in which gas and liquid are represented by the positive and negative level set function, and the free surface is implicitly expressed by the zero level set function. Pressure correction method (SIMPLE) was used to solve the two-phase flow system. Level set method was employed to capture the evolution of interface. The developed model was applied to simulate tow-dimensional viscosity standing waves with Re=20 and 200. Computed results were compared with the linear solution which considers the interaction of free surface and viscosity (Wu, et al., 2001). The effect of density ratio and viscosity ratio of air and liquid (ρ(subscript a)/ρ(subscript l)=1/10, 1/100 and 1/1,000; µ(subscript a)/µ(subscript l)=0.4429/44.29, 4.429/44.29 and 44.29/44.29) on the free surface flows were also investigated. Computed results revealed that when the ratio of density and viscosity of gas and liquid is small, the influence of gas on free-surface flow is negligible, therefore, the numerical solution agreed well with the linearized asymptotic solution of Wu, et al. (2001); When the ratio of density and viscosity of gas and liquid is large, the influence of gas on the free-surface flow needs to be considered. The amplitude and phase angle of the viscous standing wave was affected by the gravity and viscosity of gas.

並列關鍵字

Pressure correction method ； level set method ； viscous standing wave