| Electro-thermo-hydrodynamics(ETHD)is one of the basic research subjects of electrohydrodynamics,which belongs to the interdisciplinary fields of heat transfer,electrodynamics and hydrodynamics.It describes the unique flow,heat and mass transfer process of dielectric liquids driven by Coulomb force and buoyancy force under the coupling effect of DC electric field and non-uniform temperature field.It has rich physical connotation and high academic research value.However,the coupling of multi-physical fields and the complexity of mathematical models limit its theoretical research,which hinders the application and development of heat and mass transfer technology driven by an electric field.Therefore,it is of great significance to use the linear stability method for theoretical analysis of ETHD flow.This work presents a detailed study of the linear dynamics of convective heat transfer under the action of both electric field force and buoyancy(which is called electro-thermoconvection)using both stability analysis and numerical simulations.The flow takes place in a planar layer of a dielectric fluid heated from below and is subjected to unipolar injection from above.In addition to the hydrostatic case,a cross-flow formed as Poiseuille flow is considered in both low-and high-Reynolds number(Re,a ratio between inertial effect and viscous effect)regimes to investigate the interaction between shear flow,thermal field and electric field.The main purpose is to study and display the linear stability of electro-thermo-convection and deeply understand its physical mechanism.This paper briefly introduces the theory of electro-thermo-convection.The control equations of perturbations of linear system are derived and converted into eigenvalue problems by using wave-like hypothesis.Furthermore,the energy norm of linear system is derived.The Chebyshev collocation method and other numerical methods are introduced.In addition,the stability analysis code is fully verified.Modal stability analysis focuses on the long-term behavior of perturbations.In this work,the neutral stability curves in different planes are plotted by means of modal stability analysis,and the linear stability thresholds of flow instability are obtained.In addition,the influences of parameters in ETHD system on the linear critical values are studied.Besides,the impact of the cross-flow on the property of the linearized system and the effects of the electric field and thermal field on the canonical channel flow are studied.Furthermore,some important modal analysis results are explained in detail by using asymptotic energy analysis.Non-modal stability analysis looks for the maximum perturbation energy growth in the whole time range when considering all the allowable initial conditions.In this paper,the influences of parameters in the system on the transient energy growth,especially the maximum transient growth,are studied comprehensively by using the non-modal method.Besides,the impact of cross-flow on short-term effect is studied.In addition,the liftup mechanism is proved to be the dominant mechanism of energy growth in high-Re regime.Furthermore,the synergistic interaction of electric field and thermal field on transient growth is explored.The optimal initial conditions and optimal responses are presented.Moreover,this paper resorts to transient energy analysis to deeply understand the non-modal results and energy transfer process.In this work,the lattice Boltzmann model of electro-thermo-convection between two parallel plates is expanded.Linear stability thresholds and transient energy growth are obtained by direct numerical simulation.A good agreement between the stability analyses and numerical simulations is observed,which further verifies the results obtained by theoretical analysis.In addition,numerical simulation is applied to supplement the results of linear stability analysis.Besides,the final steady distributions of temperature,space charge and the velocity are shown in three dimensions by numerical simulation. |
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