High-order direct numerical simulations of a turbulent round impinging jet onto a rotating heated disk in a highly confined cavity

The present work reports Direct Numerical Simulations (DNS) of an impinging round jet onto a rotating heated disk in a confined rotor-stator cavity. The geometrical characteristics of the system correspond to the experimental set-up developed by [J. Pellé and S. Harmand. Heat transfer study in a rotor-stator system air-gap with an axial inflow. Applied Thermal Engineering, 29:1532-1543, 2009.]. The aspect ratio of the cavity G=h/Rd between the interdisk spacing h and the rotor radius Rd is fixed to 0.02 corresponding to a narrow-gap cavity. The axial Reynolds number Rej based on the jet characteristics is also fixed to Rej=5300, while the rotational Reynolds number ReΩ may vary to preserve the swirl parameter N∝ReΩ/Rej (0 ≤ N ≤ 2.47) between the present simulations and the experimental data of [J. Pellé and S. Harmand. Heat transfer study in a rotor-stator system air-gap with an axial inflow. Applied Thermal Engineering, 29:1532-1543, 2009.] and [T. D. Nguyen, J. Pellé, S. Harmand, and S. Poncet. PIV measurements of an air jet impinging on an open rotor-stator system. Experiments in Fluids, 53:401-412, 2012.] for comparisons. The results are discussed in terms of radial distributions of the mean velocity components and corresponding Reynolds stress tensor components. The swirl parameter does not modify the size of the recirculation bubble developed along the stator close to the pipe exit. For N ≥ 1.237, centrifugal effects at the rotor periphery are balanced by a centripetal flow along the stator. Some spiral patterns develop then in the stator boundary layer corresponding to the SRIII instability of [L. Schouveiler, P. Le Gal, and M. P. Chauve. Instabilities of the flow between a rotating and a stationary disk. Journal of Fluid Mechanics, 443:329-350, 2001.] in an enclosed cavity. The numerical results are found to agree particularly well with the experimental data in terms of the distribution of the local Nusselt number along the rotor. Finally, a correlation for its averaged value is proposed according to the swirl parameter.