Two-phase Flow Models And Their Applications To Sediment Transport

The importance to develop an accurate and generally applicable two-phase flow model for sediment-laden flow has been emphasized ever-increasingly in the past decades.In the present study,an Eulerian-Lagrangian two-phase flow model is improved for suspended sediment,and an Eulerian-Eulerian two-fluid model is developed for large eddy simulations of sediment laden flows with the Smoothed Particle Hydrodynamics(SPH)method applied.In the improved Eulerian-Lagrangian model,the Reynolds averaged Navier-Stokes equations together with the k-? turbulence model are applied to the water phase.In the RANS equations and equations for k and ?,sediment volume concentration is included to take into account the effect of sediment on the water.In the model,the solid phase is regarded as a dispersed phase,and the velocity of a sand particle is divided into a time-averaged and a fluctuating term.The time-averaged velocity of a sand particle is computed by the equation of motion,and the fluctuating term of the sand velocity due to the turbulent flow is evaluated by the Eddy Interaction Model(EIM).The EIM is enhanced considering the effect of the wake behind the particle to improve the accuracy of the Eulerian-Lagrangian model in simulating the suspension of sediment.The Eulerian-Lagrangian model is simplified for suspended sediment in dilute flows,and the simplified model is applied to sediment suspension under steady and uniform flow condition in a two-dimensional open channel.The profiles of sediment concentration under different sand diameter conditions are compared,and the effect of sand diameter on sediment turbulent dispersion coefficient is studied.It is shown that the EulerianLagrangian two-phase flow model coupled with the enhanced EIM performs very well in simulating the suspension of sediment under more general conditions of particle size.In the developed SPH two-fluid model,the governing equations of the two phases are obtained by spatially filtering the Favre averaged basic equations.The Smagorinsky model is used to compute the sub-particle scale(SPS)stress of the two phases,and it is assumed that the Smagorinsky coefficient of the sediment phase equals to that of the water.The model includes the drag force for the interaction force between the two phases and relates the viscosity of the solid phase to inter-granular stress.The effect of sediment on the sub-particle scale turbulence is also modeled with a correction function of sediment concentration added to the formula of the flow eddy viscosity.The sediment-laden flow is divided into SPH particles,which move with the water velocity and carry the quantities of sediment concentration,sediment velocity,and water mass concentration.The spatially filtered governing equations are rewritten into SPH forms,and formulated and solved using the SPH method.The Eulerian-Eulerian two-fluid model is applied to sediment dumping,and the variation of the width,settling velocity,and concentration of the sand cloud is studied.It is concluded from the comparison of computed results with measured data that the developed SPH two-fluid model performs well in simulating the motion of the sand cloud.