Numerical Study On Solid-liquid Slip Using The Discrete Unified Gas Kinetic Scheme

The slip on superhydrophobic surfaces has the effect of drag reduction,which has been widely recognized and paid attention to.It has a good application prospect in tools and equipment involving solid-liquid interface,such as torpedo,autonomous underwater vehicle(AUV)and submarine.Mesoscopic simulation plays an important role in studying how the slip on the surface of macroscopic objects with micro/nano structures affects the flow.In recent years,the Discrete Unified Gas Kinetic Scheme(DUGKS)is a competitive mesoscopic method with strong ability to capture multi-scale flows in different flow regime,which is also suitable for liquids in continuum flows.The construction of numerical model of the solid-liquid slip in the DUGKS is new and challenging.To characterize the slip phenomenon observed in the experiment and establish the relationship between micro scale and macro scale in the simulation,two kinds of strategies are adopted to construct the numerical model of the slip using the DUGKS,which can be applied to predict and study the influence and effect of the slip.One strategy is to introduce slip boundary conditions coupled with the Navier’s slip model to determine the unknown distribution function at the boundary,where the slip length measured in the experiment can be used as the input parameter.This strategy is suitable for the solid wall boundary in Euler grids.The other strategy is to introduce the liquid-solid interaction to approximate the hydrophobic repulsive force of the solid wall.In the DUGKS coupled with the immersed boundary method,this strategy is used to study the slip on the complex solid wall boundary of moving objects.In addition,to improve the reliability of results with the non-slip condition,new schemes of corner and straight boundary conditions for the DUGKS are proposed and validated.The main conclusions are summarized as follows:(1)Compared with the untreated corner,the proposed corner boundary condition satisfies the conservation relation,which can improve the accuracy and convergence efficiency.The new schemes of non-slip straight boundary conditions have higher accuracy than the original schemes respectively.Among them,the new moment-based scheme has the best performance,which is relatively more suitable for the DUGKS.(2)The improved tangential momentum accommodation coefficient(TMAC)scheme has higher accuracy in the DUGKS.The TMAC as a two-dimensional slip boundary condition is applied to the flow around a square cylinder,the flow around a delta wing,the nanofluid in a channel with surface mounted blocks.The results show that the slip makes the flow tends to be stable due to the effect of delaying flow separation,reducing the vortex shedding frequency.The slip has drag reduction effect on the square cylinder and the delta wing.The drag reduction rate of blocks in pure water decreases with increasing Reynolds number,but the change of drag reduction rate is affected by nanoparticles,which does not show a linear trend,especially for higher Re.(3)The new three-dimensional anisotropic slip boundary condition is based on the assumption of nonlinear velocity distribution,which has higher accuracy than the bounceback and specular reflection scheme.The results of square cavity flow driven by upper and lower walls with orthogonal oscillation show that the anisotropic slip applied to the single wall has a greater impact on the flow and enhances the mixing of 3D flows,compared with the pure slip applied to the upper and lower walls.The results of lid-driven rectangular cavity flow show that the influence of slip on the top wall-normal velocity is the least for streamwise,spanwise and top wall-normal velocity components.The effect of the anisotropic slip on the flow is greater than that of the streamwise/spanwise slip,and the effect of the streamwise slip on the flow is greater than that of the spanwise slip.(4)The DUGKS coupled with immersed boundary method is proposed and validated by two numerical tests.Its effectiveness in solving the fluid-structure interaction problem of underwater vehicle is futher validated by a self-designed experiment.Then the liquidsolid interaction force is introduced to solve the multiscale flow problem of constructing the slip model of moving objects,which is validated by the experiment with the slip condition.Futhermore,the proposed methods are applied to study the influence of the slip on the motion of an AUV model.The results show that the slip can reduce the drag,which can improve the speed and endurance of the AUV model.The drag reduction effect of the slip mainly contributes to the stage of accelerated motion.The slip induced by larger fluid-solid interaction has a greater effect on the drag reduction and velocity improvement.