非饱和带水–气二相流数值模拟研究

Study on numerical model for water-air two-phase flow in unsaturated soil

为了真实反映非饱和带中流体(水和气)的运移规律和渗透特性,将非饱和带中的孔隙水和孔隙气作为研究对象,基于水-气二相流理论,建立了水-气二相流数学模型。该模型采用积分形式的有限差分法对控制方程进行离散,在应用Newton-Raphson迭代方法得到相应的线性方程组的基础上,编制了三维计算程序SEEP2P。通过对土坝稳定渗流和降雨入渗情况的计算分析,得出稳定状态的渗流可以近似采用单相流模型来模拟,降雨入渗下的非稳定渗流问题采用水-气二相流模型来模拟更加符合实际。采用水-气二相流模型模拟得到水相、气相的流动状态,为定量研究孔隙气压力对入渗水流的影响提供了有效途径。

To simulate the fluids （water and air） flowing through unsaturated soils, a numerical model for water-air two-phase flow through unsaturated soil was developed. Water and air phases were assumed to occupy the entire pores of porous media simultaneously. Flow of water and air through unsaturated soils could be explained by balance equations of mass and extended Darcy＇s law in unsaturated soils. An integral finite difference algorithm was presented for numerically solving the governing equations of water-air two-phase flow in saturated-unsaturated porous media. Nonlinearities were handled by the Newton-Raphson iteration. A computer code named SEEP2P was developed by the authors to perform fluids flow simulation in saturated-unsaturated soils. Examples were presented to demonstrate the capabilities of the model. It was indicated that the single-phase approach to unsaturated flow was accurate enough for steady state seepage, but the multiphase flow of air and water must be considered in unsteady state seepage like rainfall infiltration problem. And flow of water and air simulated by numerical model of water-air two-phase flow could be used to quantitatively analyze the influence of air pressure on infiltration of water into soil.