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Flow in a concentric annular passage with a rotating inner cylinder, which is called Taylor-Couette flow, is important in industrial applications, such as electric motor which requires not only effective cooling of rotating shaft but also saving power required for the axis rotation. When the through flow is superposed, which is called Taylor-Couette-Poiseuille flow, it affects the cooling efficiency and the torque required for the axis rotation. To the authors' knowledge, previous studies have been focused on either the Nusselt number or the torque coefficient in the Taylor-Couette-Poiseuille flow. Therefore, it is difficult to estimate the through-flow effects on both of them under the same geometry and flow conditions. In this study, the through-flow effects on both the Nusselt number and the torque coefficient in the Taylor-Couette-Poiseuille flow under the same geometry and flow conditions were investigated by performing large eddy simulation. The through-flow Reynolds number, Re, was varied from 500 to 8000 under constant Taylor and Prandtl numbers of Ta=4000 and Pr=0.71, respectively. The Nusselt number and the torque coefficient had similar trend to each other with the increase of Re. They decreased by 25% for the change of Re from 0 to 1000 and were nearly constant for the change of Re from 4000 to 8000. Contribution of the advection, turbulent transport and diffusion terms to the Nusselt number and the torque coefficient were evaluated by using the equations proposed by the authors. The contribution of the advection term was nearly zero for Re from 500 to 8000, which was contrary to the case without through-flow (Re=0). As Re increased, the contribution of the turbulent transport term decreased but that of the diffusion term did not change so much. The friction factor in the axial direction varied as Re-0.75 of which power was between laminar (Re-1) and turbulent (Re-0.25) correlations in a smooth stationary pipe flow.

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.