Combined Modeling Of Continuous Interfaces And Discrete Particles For Complex Multiphase Flows

Multiphase flow is a simultaneous flow of materials in different states,or materials with different properties but in the same state.In nature,regular life and industrial processes,multiphase flows are widely found,including gas-liquid,liquid-liquid,gas-solid,liquid-solid flows or a mixture of them.Gas-liquid,gas-solid or gas-liquid-solid flows always include large interface deformation,discrete particle transport and continuum-discrete transformation.For systems containing phase interfaces and eddies in very different scales,the biggest difficulty is to capture the interfaces and eddies in small scales compared to the system.The present work aims to develop a multi-scale modeling framework for such multiphase flow problems.Firstly,based on the open source package OpenFOAM,the compressive interface capturing scheme for arbitrary meshes(CICSAM)and the adaptive mesh refinement(AMR)approaches are combined with the volume of fluid(VOF)method for a high-resolution gas-liquid interface.Meanwhile,the large eddy simulation(LES)approach is adopted for directly resolving large eddies,and modeling sub-grid scale eddies using the one equation eddy viscosity model(OEEVM).The methodology is applied for simulations of cavitating flows around an axisymmetric cylinder and a Clark-Y hydrofoil,with coupling the Schnerr&Sauer equation for the mass transfer between water and vapor.On the basis of model validation,the mechanisms of vapor cloud forming and collapsing,the impact of vapor cloud shedding on drag and lift forces on underwater obstacles are investigated.Different cavitation patterns and flow structures related with drag and lift forces are identified.The results show that the proposed methodology can efficiently improve the resolution of the interface between immiscible fluids within limited computational resources.For systems containing large amounts of discrete particles,the present work uses a discrete element model(DEM)to simulate the sub-grid scale particles in a Lagrangian reference frame with coupling the continuous phase in an Eulerian reference frame.Particularly,new drag closures for polydisperse systems derived from the lattice Boltzmann method(LBM)is incorporated and compared with the traditional drag closures.The modified collision model is validated and a minimum grid-particle size ratio is determined for continuum-discrete coupling.In simulations of spout-fluidized beds,the results show that,the Gidaspow drag law predicts unsatisfied flow behaviors for the single bubble transport and spout-fluidization flow regime,while the new drag closures show better results,meanwhile,predict accurate gas-solid flow behaviors for the other conditions.Significantly,for gas-liquid-solid systems including large scale interfaces and discrete particles,an interface capturing(VOF)and discrete element modeling(DEM)combined methodology is developed for multi-scale simulations of such systems.The new solver using the VOF-DEM methodology is tested by several cases,indicating its accuracy and suitability for mixed gas-liquid-solid flows.Finally,for the system with large amounts of discrete bubbles,the interface capturing approach is also limited.Thus,the present work proposes a methodology using the discrete bubble model(DBM)and the VOF method for respectively tracking discrete bubbles and capturing continuous interfaces.The bubble aggregation and the discrete-continuum transformation on gas-liquid interface are considered and modeled.The methodology is employed for simulations of the multiphase flow in a gas-stirring ladle with the LES.The gas bubble periodic spouting,the mechanisms of slag eye forming and collapsing and slag droplet entrainment are well revealed.The bubble size evolution is validated against both the experimental measurement and the population balance model(PBM)prediction.The time-averaged slag eye size agrees well with the experiment.The methodology shows promise for modeling the discrete bubble transport as well as the interface deformation and splitting.