We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of Elena and Schiestel [1, 2] widely validated in various rotor-stator cavities with throughflow [3-5] and heat transfer [6]. To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of Escudier and Gouldson [7] in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k − ε model of Naser [8]. Then, the second order model is applied for a large range of rotational Reynolds (3744 ≤ Re i ≤ 37443) and Prandtl numbers (0.01 ≤ P r ≤ 12), flow rate coefficient (0 ≤ Cw ≤ 30000) in a very narrow cavity of radius ratio s = Ri/Ro = 0.961 and aspect ratio L = (R o − R i)/h = 0.013, where R i and R o are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the flow control parameters Rei, Cw and P r.

The present study considers the numerical modeling of the turbulent flow inside a rotor-stator cavity subjected or not to a superimposed throughflow. Extensive numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are performed mainly in the case of turbulent flows with merged boundary layers known as turbulent torsional Couette flows and belonging to regime III of Daily and Nece (1960). The RSM model has already shown its capability of predicting accurately the mean and turbulent fields in various rotating disk configurations (Poncet, 2005;Poncet et al., , 2008. For the first time, a detailed mapping of the hydrodynamic flow over a wide range of rotational Reynolds numbers (180 000 ≤ Re ≤ 10 000 000), aspect ratios of the cavity (0.02 ≤ G ≤ 0.05), and flow rate coefficients (−10000 ≤ C w ≤ 10000) is here provided in the turbulent torsional Couette flow regime.