Numerical Study On The Stability And Heat Transfer Of Electro-thermo-convection In Non-newtonian Dielectric Liquids

Electro(thermo)convection in dielectric liquids is a multidisciplinary and multi-physical coupling problem.Its applications are quite extensive,involving several important fields such as aerospace,electronics industry,and pharmaceutical industry.Due to the strong nonlinear coupling of multi-physical fields,in the unique heat and mass transfer process of the electro-thermo-convection,there are complicated flow transitions,linear and nonlinear instabilitie s,bifurcation,chaos,and other phenomena,which leads to rich physical connotations.Existing research mainly focuses on its physical phenomena in Newtonian fluids.With the discovery of the in-depth study,it is found that fluid properties have a significant impact on its instability and heat transfer mechanism.The theoretical system based on Newtonian fluids cannot be extended to the non-Newtonian fluids,which severely limits the application range of the electro-thermo-convection.Therefore,this thesis extends the study of electro(thermo)convection problems to non-Newtonian fluids.The flow evolution,instability,and heat transfer characteristic of electro(thermo)convection in non-Newtonian fluid from hydrostatic state to the onset of convection,then to unsteady convection,and finally to the chaotic state are studied.The non-Newtonian effects on instability,nonlinear flow structure evolution,and heat transfer are focused on,and the impact on a single electric plume are also investigated.The charge generation mechanism in the dielectric liquid under the action of an electric field is introduced in detail,and the basic equations of electrohydrodynamics under the unipolar charge injection mechanism in non-Newtonian fluids are clarified.The constitutive equations of two typical non-Newtonian fluids considering the viscosity variation and the elastic effect are given.A finite volume method program is developed for the steady solution of electro(thermo)convection of non-Newtonian fluids by using the special discrete schemes such as the total variation diminishing scheme and the log-conformation approach.In order to clarify the evolution dynamics of the electro(thermo)convection,a series of nonlinear dynamic analysis methods are introduced.Based on the above work,the main research contents of this thesis are summarized as follows.Firstly,the influence of viscosity variation on the electro-thermo-convection is investigated.Taking the electro-thermo-convection of the power-law non-Newtonian fluid in a square cavity as an example,the two arrangement forms of horizontal temperature gradient and horizontal electric field combination,vertical temperature gradient and vertical electric field combination are considered at the same time,and the bifurcation process and heat transfer of the system under different driving parameters are investigated.Compared with the condition in Newtonian fluids,it is found that the viscosity variation has a vital effect on the bifurcation process,and the stability phase diagram is significantly different.According to related phenomena,the mechanism of the unique bifurcation process in the power-law fluid is clarified.On this basis,the unsteady evolution process of the electro-thermo-convection is investigated,and it is found that a small power-law exponent can enhance the randomness of the flow and generate chaotic flow under a small driving parameter.A numerical study is carried out on the two-dimensional unipolar injection of the electro-convection in Oldroyd-B viscoelastic dielectric liquid,and the instability process of the system from hydrostatic solution to the onset of convection under different elastic parameters is investigated.It is found that under the rigid boundary condition,the system can form steady convection through supercritical bifurcation or form periodic oscillatory convection through Hopf bifurcation.While under the transverse free boundary,the system can form steady convection through subcritical bifurcation or supercritical bifurcation,and form periodic oscillatory convection through Hopf bifurcation.When the flow lose its stability from the Hopf bifurcation,the threshold of driving parameter corresponding to the first instability is significantly reduced relative to the Newtonian fluid.Regarding the problem of the electro-thermo-convection,it is found that no matter in Newtonian fluids or viscoelastic fluids,different charge injection directions will not change the criterion corresponding to the onset of the first instability.The electro-thermo-convection of viscoelastic fluids can also lose its stability through the Hopf bifurcation.In addition,the elastic effect promotes the transition from the steady flow to oscillatory convection.These phenomena are all closely related to the elastic parameter.Aiming at the problem of electro-convection between two plates,the influence of the elastic parameter on the flow state transition to the chaos in viscoelastic fluids is investigated,and a variety of transition processes are found.Due to the influence of the nonlinear elastic effect,the four-vortex asymmetric steady-state flow is observed through numerical simulation in a completely symmetric system,and it is found that the elastic effect can suppress or amplify the flow os cillation amplitude.The current transfer is closely related to the strength of elasticity,and it is found that the current transfer may be enhanced or suppressed.However,when the electro-convection is extended to the electro-thermo-convection,only the phenomenon that the heat transfer is suppressed is observed under all the elastic parameters considered in this thesis.Finally,taking the mode of electro-convection between the blade and the plate as an example,the influence of the elastic effect and the viscosity variation on the development process of a single electric plume and the related heat transfer process are investigated,respectively.Studies have found that elasticity can promote the development process of the electric plume,and it has been determined that the extensional and compressional process of viscoelastic molecules and the hysteresis of elastic stress are the main reasons for the above phenomenon.The viscosity variation has a vital influence on the shape and development of the electric plume.This thesis investigates and quantifies the difference between it and the Newtonian fluid.