Contribution of advetion, turbulent transport and diffusion terms to Nusselt number and torque coefficient in Taylor-Couette flow

Abstract

Contributions of the advection, turbulent transport and diffusion terms to the Nusselt number and the torque coefficient in the Taylor-Couette flow were evaluated. Integrating the energy equation in the Taylor-Couette flow twice gave an equation in which the Nusselt number was decomposed into the three terms which were the advection, turbulent transport and diffusion terms. Integrating twice the momentum equation with respect to the azimuthal velocity in the Taylor-Couette flow gave an equation in which the torque coefficient was decomposed into the three terms. The two equations obtained here made it possible to evaluate the contribution of the three terms to the Nusselt number and the torque coefficient. Large eddy simulation was performed to obtain the velocity and temperature fields in two cases of Taylor number, Ta=4000 and 8000. Using the above equations to this field data showed that the contribution of the advection term was the highest, more than 70% for the Nusselt number and more than 55% for the torque coefficient due to the Taylor vortex which retained the structure in the axis-normal plane. The contribution of the turbulent transport term increased with the increase of the Taylor number while the advection term decreased. The contribution of diffusion term was small and did not change so much.

Keywords

• taylor-couette flow
• nusselt number
• torque coefficient
• advection term
• turbulent transport term
• diffusion term