Study On The Direct Numerical Simulation Of Droplet And Bubble Motion In Two-phase Flow In Tank

Two-phase flow widely distributed in oil and gas storage and transportation fields,such as oil and gas gathering pipeline system,oil-gas-water separation equipment and tanks.The two-phase flow process benefits while suffering pains.For instance,the multi-phase transport and oil-gas-water separation are corresponding to the pros and cons.Generally speaking,the profound understandings through intensive researches on the essential mechanism of two-phase flow are the precondition of utilizing or preventing two-phase flow effectively.Our research focuses on common motion process of droplet or bubble in tanks.The direct simulation of droplet or bubble in two-phase flow is conducted from the micro point of view based on the diffuse interface phase field method.This is a basic and theoretical research work in multi-phase field.The diffuse interface phase field method based on energy law differs from other traditional sharp interface methods.It is no need to reconstruct the interface between two phases.It is easy to extend it from 2D to 3D.It can simulate the complex fluids,like non-Newtonian fluid,viscoelastic fluid and fluid with surfactants by introducing different kinds of free energy function in the phase field model.Diffuse interface phase field model gains lots of academic attention in recent decades as a brand new two-phase flow modeling method.Given these advantages,it is of practical significance to apply it in the oil and gas storage and transportation industry.As a pioneering and basic research job,the dissertation begins with the mathematical model and derivation of related physical quantities.We compare the method with sharp interface method and do some interpretation on the physical meaning and mathematical expression of Cahn-Hilliard equation,which is the governing equation of phase field model.The paper gives the proof of energy law in continuous or discrete form in detail.Then it provides the regular numerical treatments for N-S equation and C-H equation as references.The reason for substantial section of this paper on the proof of energy law is that it is crucial for a stable and fast computation to construct a numerical scheme keeping the energy law.The detailed proof also helps engineering students to figure it out and quickly get started if they choose related topics.Besides,there is a progress on comparison of the pressure-correction scheme with SIMPLE algorithm.They are both widely used in solving N-S equation but in different fields.Mathematical researchers usually enjoy the former,the latter is more popular in industry.We use the expression in matrix-vector form to make the differences stand out and do some analyses about the consistency and matrix information according to their numerical performance.We are inspired by a modularized and splitting coding idea and implement the conjugate gradient method to solve Cahn-Hilliard equation without constructing matrix,which is not exactly the Fortran language good at.It also help us avoid complex discretization of discrete equation and a dense coefficient matrix.Part of codes in critical section will be presented in this paper.At last,we propose a novel numerical scheme based on the model with variable density and introducing mid-velocity.We use a benchmark bubble rising numerical experiment to validate it and then simulate a case with extreme density contrast to exam its stability and robustness.At the same time,There are some numerical research on deformation and broke of droplet in shear flow,the collision of droplets,the kiss bubble merging,droplet in vortex,droplet falling down and so on.These physical process is accord with the gravitational Method,coalescence method,centrifuge method.The three ones explain how the oil-gas-water separator work.The validation and analysis jobs are finished in many ways,comparing the numerical results with analytic solution,experiments results and results calculated by other commercial software.These jobs we have done provide some references for promoting the spread of this new method in oil pipeline research field and confirm the feasibility of this method.It also gives some reliable data and predicts for two phase flow experiment research.