A General Mixture Model And Its Application To Coastal Sediment Transport

It is of both theoretical and practical significance to develop effective numerical models for sediment laden flows.To overcome the disadvantages of limited aplicability of the classical diffusion model,and the computational inefficiency of the two-phase flow model,a mixture model which is based on a complete two-phase flow theory of the Eulerian type is developed to describe sediment laden flows.The mixture model can balance the advantages and disadvantages of the diffusion model and the two-phase flow model,and maintain the computational efficiency and accuracy at the same time.An enhanced Eulerian-Eulerian type of the two-phase flow model,which includes the continuity equation and equations of motion for both phases,along with a modified k-? model considering sediment effects on turbulence,is first developed by double averaging processes and then validated for both steady open channel flows and oscillatory flows.The fluid and sediment phases are coupled by interaction forces including drag force,lift force and virtual mass force,and the relaxation timescale of sediment is derived based on the momentum balance equations of both phases in hydrostatic condition.Based on the enhanced two-phase flow model,the relative velocity between the two phases is obtained by manipulating the momentum equations for both phases.Based on numerical experiments,formulation for the relative velocity between the two phases can thus be simplified to a practically useful form,called single-step model and prediction-correction model.The predictioncorrection model is demonstrated to have a similar accuracy as the two-phase flow modelA mixture model for general description of sediment laden flows is developed based on the Eulerian-Eulerian approach of the complete two-phase flow theory.The basic equations of the models include the mass and momentum conservation equations for the water-sediment mixture and the continuity equation for sediment concentration.The turbulent motion of the mixture is formulated for the fluid and the particles respectively.A modified k-? model is used to describe the fluid turbulence while an algebraic model is adopted for the particles.The prediction-correction model is incorporated to model the two phases' relative motion.The model is validated by suspended sediment motion in steady open channel flows,both in equilibrium and non-equilibrium state,and oscillatory flows,both in symmetric and asymmetric cases as well.The computed sediment concentrations,horizontal velocity and turbulence kinetic energy of the mixture are all shown to be in good agreement with experimental data.Then the mixture model,which incorporates the VOF method and topography change model,is applied to beach evolution problems in the near shore and satisfactory agreements can be obtained.