Study On Linear Stability Of Double-Diffusive Convective In A Fluid-Porous System With Viscoelastic Fluid

The problem of convection stability is a both classic and lively research topic in the field of fluid mechanics.Relevant fluid convection stability problems are involved in applications such as meteorological convection,ocean currents,sewage treatment,oil extraction and industrial material separation.This paper is mainly to analyze the convective stability of a two-layer fluid system of a fluid layer-porous medium layer which is encountered frequently in many industrial processes(solidification,filtration,catalytic reactors,etc.)or environmental situations(geothermal systems,groundwater pollution,etc.).Specifically,it is to study the effect of each control parameters such as the ratio of layer thicknesses,the ratio of thermal diffusivities,solutal Rayleigh number and viscoelastic properties of fluid on the stability of viscoelastic fluid double-diffusive convection in superposed fluid and porous layer system under high-frequency and small-amplitude vibrations.In the specific analysis process,the high-frequency vibration is combined into the static gravity field to simulate the high-frequency dynamic gravity field.The average method is used to represent the velocity,temperature and concentration fields as the sums of their components averaged over the vibration period and oscillation components,and the closed governing equations are both established respectively.The system linear dimensionless stability equations are raised using the linear perturbation method and dimensionless method.In terms of system boundary conditions,similar to the common single-layer fluid model,we adopt the upper and lower fixed temperature and concentration boundaries,the upper solid impermeable flow,and the lower free impermeable flow boundaries.The main analytical difficulties of the system is transport phenomena analysis in such configurations at the intermediate junction interface as the continuity condition of temperature,concentration and velocity,the equilibrium condition of the normal stress,and the modified tangential Beavers-Joseph velocity-slip condition.The obtained system linear dimensionless control stability ordinary differential equations and various boundary conditions are regarded as a high-order generalized eigenvalue problem.The Chebyshev spectral method is employed to linearly discretize the flow variables in the equations,the complex boundary conditions are processed by tau approximation,and the order of these variables is reduced by the D2 operator.Then the governing equations are discretized into a high-order linear generalized eigenvalue problem.And finally,the QZ algorithm is chosen to solve the high-order eigenvalue equation,filter the spurious eigenvalues,and to obtain the dominant eigenvalues of the most unstable modes in the linear stability analysis,namely the critical Rayleigh number in this paper.According to the analysis results in this paper,when the convection phenomenon occurs,smaller the ratio of layer thicknesses is,the stronger stability of upper fluid layer;larger the ratio of thermal diffusivities is,the stronger stability of upper fluid layer,and both the less reinforcing effect on the lower porous layer.When stationary convection occurs,the greater solutal Rayleigh number,the lower overall stability of the system,but its effect is mainly reflected in the lower porous layer.When the oscillatory convection occurs,the increase of the stress relaxation time parameter of viscoelastic fluid has a weakening effect on the fluid stability,and the increase of the strain retardation time parameter has a strengthening effect,and they both mainly reflect in the upper fluid layer.And compared with the oscillatory convection stability,the stability of stationary convection is higher overall.In the process of changing the governing parameters,there is a transition of the minimum critical Rayleigh number of the system neutral stability curve,that is,the region dominated by the stability of the two-layer system is transferred between the upper fluid layer and lower porous layer.The influence of each governing variable on system stability which is under gravity modulation is similar to that convection stability without modulation.But the effect of high-frequency vibration parameters on the stability of the system is mainly reflected in the stability of the upper fluid layer.In the process of other governing parameters change,the presence of high frequency vibration will amplify its effect on the stability of the upper fluid layer in the system.It is worth noting that the appropriate system parameters,the high-frequency vibration parameters may also lead to the transition of the minimum critical Rayleigh number in the neutral stability curve,specifically during the increase of the high-frequency vibration parameters,the minimum critical Rayleigh number may be transferred from the large wave number region to the wavelet number region,that is,the system stability dominant region is transferred from the upper fluid layer to the lower porous layer region.