Influence of a Weak Superposed Centripetal Flow in a Rotor-Stator System for Several Pre-Swirl Ratio

The present study is devoted to the influence of a superposed centripetal flow q in a rotor-stator cavity with a peripheral opening. In the literature, previous works have already shown that a weak radial inflow has no major influence near the periphery of the cavity, whereas the flow behavior is strongly modified when approaching the axis [1–2]. The challenge of this work is to give a better understanding of this phenomenon. Attention is focused on a rotor-stator system characterized by a small gap ratio G and high Reynolds number Re, so that the flow is divided into two boundary layers separated by a core region, according to the classification by Daily and Nece [3]. Until now, numerous authors obtained analytical solutions for the central core flow behavior: following the analysis performed by Schlichting [4], and assuming that the evolution of the velocity in the Ekman boundary layer corresponds to a 1/7 power law, Poncet et al. [2] proposed an analytical law predicting the evolution of the core swirl ratio K versus a local dimensionless coefficient of flow rate C_qr. Debuchy et al. [5] improved this last solution by taking into account the radial exchange of fluid outside the boundary layers. This last approach was used by Abdel Nour et al. [6] in a rotor-stator cavity without any superposed flow (isolated cavity). They obtained an original analytical law, different from the classical similitary solution proposed by Batchelor [7] in the case of infinite disc, convenient for a cavity with peripheral opening and small pre-swirl ratio. In this paper, the authors present an original analytical law in order to model the central core flow behavior in a rotor-stator cavity subjected to a very weak inflow rate (q → 0). The validity of the solution is tested with the help of: • a new set of experimental data including the radial and tangential mean velocity measured by hot-wire anemometry, • experimental results from the literature.