Effects Of Head Loss,Surface Tension,Viscosity And Density Ratio On The Kelvin Helmholtz Instabilities

Fluid instability is an important problem in fluid mechanics and usually occurs at the interface of different fluids.There are three typical interface instabilities:Rayleigh-Taylor(RT)instability,Richtmyer-Meshkoy(RM)instability and Kelvin-Helmholtz(KH)instability.These instabilities play a key role in many fields,such as plasma,magnetic fluid,astrophysics,and inertial confinement fusion(ICF)and so forth.KH instability is in a laminar quiescent state when it begins to evolve until external perturbations are added to the fluid interface,and the interface begins to be disturbed,and the amplitude of the disturbance increases exponentially with time.Affected by the tangential directional force,the interface gradually rolls up in the direction of the flow of the fluid with high velocity.As the disturbance increases,eventually the vortex phenomenon occurs at the interface of the two fluids.In the process of studying the growth of KH instability,researchers initially regarded the fluid as an ideal fluid.The fluid was assumed to be incompressibe,inviscid and surface tension free.Later on,it was discovered that the fluid viscosity,surface tension and other factors also have a great impact on KH instability.Therefore,many numerical simulations,experiments and theoretical studies have been carried out on the effects of these factors on the KH instability.However,for the real fluids,the mechanical energy loss due to the changes of interface or flow velocity during fluid flows will also affect KH instability.This loss was named as head loss.Up to know,the research of the impact of head loss on the KH instability is rare.The concept,properties and dynamic equations of fluid are briefly introduced in the first chapter.In the second chapter,three kinds of interfacial instability and the formation of turbulence are briefly discussed.In the third chapter,firstly,the research progress of KH instability is reviewed.Secondly,two typical practical pipeline models are established,one model is the straight pipeline with different cross-sections,and the other model is the bend pipeline.Then,based on the above models and the boundary conditions of the upper and lower fluids in the pipeline,the governing equations of fluid dynamics are listed,and the analytical expressions of the relative tangential velocity of fluid and the growth rate of KH instability are presented.Finally,the effects of head loss,surface tension,viscosity,density ratio and other factors on KH instability are systematically studied.Through the systematic study of the effects of head loss,surface tension,viscosity and fluid density ratio,it is found that: for the straight pipe with different cross-sections,the relative tangential velocity of fluid decreases with the increase of head loss,viscosity and density ratio of upper and lower fluid,but it increases with the increase of surface tension;the growth rate of KH instability decreases with the increase of head loss and surface tension,but it increases with the increase of density ratio of upper and lower fluid.The higher the height of fluid interface is,the more the head loss reduces the relative tangential velocity and the growth rate of KH instability.For the bend pipeline,the critical tangential velocity decreases with the increase of head loss,viscosity and density ratio of upper and lower fluid,but it increases with the increase of surface tension;the growth rate of KH instability increases with the increase of head loss and density ratio of upper and lower fluid,but it decreases with the increase of surface tension.At the elbow angle ?=80,the effect of head loss on the KH instability reaches the maximum.The research results of this thesis provide a guidance for the moving law of real fluid in different types of pipelines and the design of pipelines for fluids in engineering.