Numerical Simulation Of The Flow With Moving Contact Line Involving Complex Geometry Substrate And Fluid-structure Interaction

Flows with moving contact line widely exist in nature, life and engineering. The research about the phenomena and mechanism in these flows is important in science and applications. However, the study of direct numerical simulations is still lack because of the challenges, such as moving contact line, complex geometry solid substrates and fluid-structure interaction. In this thesis, a series of numerical methods based on the Cartesian mesh are developed to solve the flows. Based on these methods, some topics on the flows with moving contact line are studied. The results and conclusions are briefly given as follows:(1) An etching multi-block method is developed to solve the multi-phase flow on the substrate with a corner. This method combines a diffuse interface model, a ge-ometric formulation moving contact line model and a multi-block method. The diffuse interface model and geometric formulation moving contact line model can consider two-phase flows with a large density ratio and moving contact line. The multi-block method allows natural communications between the connected sub-domains and the efficient parallel computation. The performance of the etching multi-block method is tested by simulating flows past a square cylinder and drops dripping from a pore. The etching multi-block method is used to study the prob-lem of drops dripping from a pore. We find that:with the contact line pinning on the corner, four periodic dripping modes appear with the increasing of We number - dripping with satellites, single periodic dripping, double periodic drip-ping and jetting; while with the contact line moving freely, the periodic dripping modes are hard to appear, but only dripping with many satellites at small We number.(2) We develop a diffuse interface-immersed boundary method to simulate the flows with moving contact lines on the curved substrate. The method is based on Carte-sian mesh and combines an immersed boundary method with a three-component diffuse-interface model and a characteristic moving contact lines model. The immersed boundary method is able to accurately enforce the no-slip boundary condition at the solid surface, thereby circumventing the penetration of the gas and the liquid into the solid by convection. On the other hand, using the three-component diffuse-interface model can prevent the gas and liquid from infiltrating into the solid substrate through the diffusive fluxes during the interface evolution. A combination of these two methods appears to effectively conserve the mass of the phases in the computation. The characteristic moving contact line model not only allows the contact lines to move on the curved boundaries, but makes the gas-liquid interface to intersect the solid object at an angle in consistence with the prescribed contact angle, even with the variation of surface tangent at the solid substrate. A series of cases are simulated to validate the diffuse interface-immersed boundary method:interface shapes of drops on a circular cylinder at equilibrium, drop spreading on a flat substrate, drop impact on a sphere and the penetration process of a two-dimensional drop into a porous substrate. We use the diffuse interface-immersed boundary method to study the problem of water entry. Three modes appear in order as the increasing of the contact angle:complete immersion, bubble entrapment and cavity formation. Meanwhile, we also find the effects of We number, the larger We number, the more easily cavity formation mode appears.(3) A interface fluid-structure interaction method is developed to simulate the flow with interaction between liquid interfaces and solid objects. The method is based on the diffuse interface-immersed boundary method and consist of a hybrid cap-illary force model. The hybrid capillary force model can compute the capillary-force exerted on the objects by interfaces accurately. In this hybrid model, a diffuse interface model is used for the interface profile out of equilibrium, and a sharp interface model for the interface profile at equilibrium. We simulate a series of cases to test the interface fluid-structure interaction method:the sinking of a circular cylinder with a constant velocity, the drop on a sphere at equilibrium, the sinking of a circular cylinder half immersed in water due to gravity, head-on colli-sion between a drop and a solid sphere, and the self-assembly process of multiple floating cylinders on water surface. Based on the good agreements with the for-mer experimental results, we use the interface fluid-structure interaction method to investigate the impacting onto water surface of a sphere with the density larger than water, and two modes are found, sinking and bouncing. We focus on the ef-fects of the wetting condition (contact angle) of the sphere and the width of pool. The corresponding scaling laws are constructed:in the pool with enough width, the critical transition condition between sinking and bouncing is affected by the wetting condition of the sphere,0, We～sin(θ/2)4:while in the pool with the width less than double diameter of the sphere, it is also affected by the width of the pool, L, We～(C(θ, k)L+D(k)L-1)2. where k is the only fitting parameter. The theoretical analysis and the numerical simulations agree well.(4) We develop a dual mesh method with moving contact line to improve the resolu- tion of interface, and a multi-grid method to solve the pressure Poisson equation efficiently. The test results show that both of the methods are exact and efficient, and can speed up over 80%.