Direct numerical simulation of Taylor-Couette flow subjected to a radial temperature gradient

Abstract

Direct numerical simulations have been performed to study the Taylor-Couette (TC) flow between two rotating, coaxial cylinders in the presence of a radial temperature gradient. Specifically, the influence of the buoyant force and the outer cylinder rotation on the turbulent TC flow system with the radius ratio η = 0.912 was examined. For the co-rotating TC flows with Rei (inner cylinder) =1000 and Reo (outer cylinder) =100, a transition pathway to highly turbulent flows is realized by increasing σ, a parameter signifying the ratio of buoyant to inertial force. This nonlinear flow transition involves four intriguing states that emerge in sequence as chaotic wavy vortex flow for σ = 0, wavy interpenetrating spiral flows for σ = 0.02 and 0.05, intermittent turbulent spirals for σ = 0.1 and 0.2, and turbulent spirals for σ = 0.4. Overall, the fluid motion changes from a centrifugally driven flow regime characterized by large-scale wavy Taylor vortices (TVs) to a buoyancy-dominated flow regime characterized by small-scale turbulent vortices. Commensurate changes in turbulence statistics and heat transfer are seen as a result of the weakening of large-scale TV circulations and enhancement of turbulent motions. Additionally, the influence of variation of the outer cylinder rotation, −500 < Reo < 500 in presence of buoyancy (σ = 0.1) with Rei = 1000, has been considered. Specifically, it is demonstrated that this variation strongly influences the azimuthal and axial mean flows with a weaker influence on the fluctuating fluid motions. Of special interest, here are the turbulent dynamics near the outer wall where a marked decrease of turbulence intensity and a sign inversion of the Reynolds stress Rrz are observed for the strongly counter-rotating regimes (Reo = − 300 and −500). To this end, it has been shown that the underlying flow physics for this drastic modification are associated with the modification of the correlation between the radial and axial fluctuating motions. In turn, the intriguing effects of this modification on the mean axial flow, turbulent statistics, force balance, and dynamic processes such as turbulence production and dissipation are discussed.