Numerical study on viscoelastic Rayleigh-Bénard convection

Résumé

La transition de la convection d’inversion à la convection stationnaire. (b) Nous avons également étudié la RBC viscoélastique dans une cavité inclinée et vérifié l’influence de (β, We) sur la structure d’écoulement et le transfert de chaleur. Les résultats montrent que la structure d’écoulement, la capacité de transfert de chaleur et le nombre de Rayleigh critique sont presque les mêmes pour un milieu rempli des fluids á faible élasticité (β = 0.9, We = 0.1) ou newtoniens. Cependant, le processus de transition d’écoulement changera radicalement, même si l’angle d’inclinaison est petit (α < 2), lorsque le fluide est très élastique (β = 0.1, We > 0.5). (c) Des résultats préliminaires de RBC viscoélastique tridimensionnelle sont également obtenus dans cete thése, afin de voir comment le phénomène d’inversion observé en 2D se comporte dans une cavité tridimensionnelle.

mots clés

Titre traduit

Étude numérique sur la convection de Rayleigh-Bénard viscoélastique
Résumé

A direct numerical simulation (DNS) solver based on Fortran language was developed for the viscoelastic laminar Rayleigh-Bénard convection in 2D and 3D rectangular cavities. The solver considers a quasi-linear treatment to hyperbolic terms of the governing equation system to avoid numerical instability at a high Weissenberg number. The procedure of DNS solver is based on Finite difference method and includes a variety of temporal discrete schemes (such as 1-order Euler, 2-order backward differential formula), spatial discrete schemes (such as the upwind scheme, central differential scheme, and High Order Upstream Central scheme), and viscoelastic constitutive models (such as Oldroyd-B (OB) and Phan-Thien-Thanner (PTT) models). Most of the investigation in this thesis focuses on the viscoelastic RBC with the PTT model, because the PTT model is a nonlinear model that is suitable for simulating more complex viscoelastic fluids. The contents of this thesis can be divided into three parts: (a) we focused on the viscoelastic RBC in a 2:1 cavity and presented a particular regular reverse convection phenomenon in detail. At the same time, we studied the influence of different rheological parameters of viscoelastic fluid (ε, ξ, β, and We) on the flow and heat transfer characteristics. We have also discovered, for the first time, the second critical Ra corresponding to the transition from reversal convection to steady convection. (b) We also studied the viscoelastic RBC in the tilted cavity and checked the influence of (β, We) on the convection structure and heat transfer. The results show that flow structure, heat transfer capacity, and critical Rayleigh number of tilted RBC are almost the same for a medium filled with weak elasticity fluids (β = 0.9, We = 0.1) and Newtonian fluids. However, the flow pattern transition process will change dramatically, even if the inclination angle is small (α < 2), when the fluid is very elastic (β = 0.1, We > 0.5). (c) A preliminary numerical study about three-dimensional viscoelastic RBC has also started in this thesis, in order to see how the periodic convection with strong elasticity works in the 3D cavity.