Convection partition and dynamics in inclined Poiseuille-Rayleigh-Bénard flow

Abstract

Since Henri Bénard first carried out experiments on convection in the fluid layer heated from below at the beginning of last century, and Lord Rayleigh first analyzed small disturbance theoretically, Rayleigh-Bénard convection has received much attention from many researchers, and has become one of the models to study the spatiotemporal structure, flow stability and dynamic characteristics of convection. The methods of studying the Rayleigh-Bénard convection are divided into experimental research, theoretical analysis and numerical simulation. With the development of computer, the research of numerical simulation has made great progress. Because the Rayleigh-Bénard convection can be accurately described by continuity equation, momentum equation and energy equation of hydrodynamics. Therefore, the numerical simulation based on hydrodynamics equations has aroused a lot of research interest. Based on the classical Rayleigh-Bénard convection, the influence of horizontal flow on the Rayleigh-Bénard convection can be studied by applying horizontal flow to one end of the horizontal cavity. On the other hand, the influence of cavity inclination on Rayleigh-Bénard convection can be studied by considering the variation of inclined angles in the cavity. Some valuable convective properties have been obtained. In order to reveal some new convection structures or phenomena, the effects of cavity inclination and through-flow on Rayleigh-Bénard convection are considered at the same time in this paper.By using the numerical simulation of the basic equations of hydrodynamics, the convection partition and dynamic characteristics of the fluid with Prandtl number <i>Pr</i> = 6.99 in the inclined cavity with through-flows are discussed. The results show that for the reduced Rayleigh number <i>r</i> = 9, the system presents uniform traveling wave convection, non-uniform traveling wave convection and single roll convection pattern at the through-flow Reynolds number <i>Re</i> = 1.5 with the increase of the inclined angle <i>θ</i> in the cavity, that for the through-flow Reynolds number <i>Re</i> = 12.5, the system presents the localized traveling wave convection, parallel flow and localized single roll convection pattern with the increase of the inclined angle <i>θ</i> in the cavity, that furthermore, the numerical simulation of different values of through-flow Reynolds number <i>Re</i> and inclined angle <i>θ</i> in the cavity shows that on the plane composed of through flow Reynolds number <i>Re</i> and inclined angle <i>θ</i> in the cavity, the convection in the inclined cavity with through-flow can be divided into six kinds of pattern regions, namely, uniform traveling wave convection region, non-uniform traveling wave convection region, single roll convection region, localized traveling wave convection region, parallel flow region, and localized single roll convection region. The characteristics of the maximum vertical velocity <i>w</i>_max and Nusselt number <i>Nu</i> of convection varying with time in different convection regions are studied. The dynamic properties of convective amplitude <i>A</i> and Nusselt number <i>Nu</i> in different convective regions varying with inclined angle <i>θ</i> in the cavity are discussed.