Time-Dependent Oscillating Viscoelastic Rayleigh-Bénard Convection: Viscoelastic Kinetic Energy Budget Analysis

The time-dependent oscillating convection leading to the formation of reverse flowing cells is a special phenomenon induced by viscoelasticity in the Rayleigh-Bénard convection (RBC). The causes and the evolution of this overstability problem have not yet been investigated in-depth. Numerical simulations of the viscoelastic Rayleigh-Bénard convection (VRBC) have been conducted in this work with viscoelastic working fluids abiding by the nonlinear Phan-Thien-Tanner (PTT) constitutive structure in two-dimensional cavities. To understand the impact of the nonlinearity and the rheological parameters on the mechanism of the regular reverse flow numerical simulations have been performed over the range of β=(0.1,0.2) (where β=μs/μ0, μs is the solvent viscosity, μ0=μs+μp is sum of solvent viscosity μs and polymer viscosity μp) and Weissenberg number (We [0.075,0.25]), using an in-house finite-difference code. The remaining constitutive parameters of the (PTT) fluid representing elongational and slippage characteristics of the fluid were kept fixed at ϵ=0.1 and ζ=0.05, respectively. A viscoelastic kinetic-energy budget method was used to analyze the energy transport in this time-dependent reverse flow process. An original parametric analysis is developed to gain an insight into the dynamics of the reversal flow observed recently in our work, Zheng et al. [Phys. Rev. Fluids 7, 023301 (2022)2469-990X10.1103/PhysRevFluids.7.023301], as well as observed by Park and Ryu [Rheol. Acta 41, 427 (2002)0035-451110.1007/s00397-001-0223-x] and Lappa and Boaro [J. Fluid Mech. 904, A2 (2020)0022-112010.1017/jfm.2020.608]. The emergence of the reversal convection can be explained by the transfer of potential energy between flow and fluid elasticity during the reversal process. The existence of time phase differences of different potentials in the evolution drive this potential-energy transfers. © 2023 American Physical Society.