On the Flow Behavior in Rotor‐Stator System with Superposed Flow

Abstract

The flow between a rotor and a stator at high Reynolds number and small Ekman number is divided into three domains, two boundary layers adjacent to the discs separated by a central core. In the present work, a simple theoretical approach provides analytical solutions for the radial distribution of the core swirl ratio valid for a rotor-stator system with a superposed radial inflow rate. At first, the flow in the rotor boundary layer is assumed to behave as expressed by Owen and Rogers (1989) in the case of a turbulent flow on a rotating single disc. On the stator side, a necessary compensation flow rate must take place according to the conservation of mass. It is found that this compensation flow rate cannot be estimated with a good accuracy using the hypotheses of a stationary disc in a rotating fluid by Owen and Rogers (1989). Thus, two innovative weighting functions are tested, leading to new analytical laws relating the core swirl ratioKto the coefficient of flow rateCqrintroduced by Poncet et al. (2005). The adequacy between the theoretical solutions and numerous results of the literature is clearly improved and the discussion allows a better understanding of the flow behavior.

Investigation on the Flow in a Rotor-Stator Cavity with Centripetal Through-Flow

“…The velocity profiles at three radial positions for Re = 1.9 × 10 6 and G = 0.072 (wide gap) are shown in Figure 7 Figure 7d,e. The profiles are special, because according to the former results (such as from Poncet et al [9] and Debuchy et al [11]), the increase of | | will result in an increase of the core swirl ratio K for centripetal through-flow. Then, the tangential velocity should increase instead of decrease.…”

“…Using a two-component Laser Doppler Anemometer (LDA) system, Poncet et al [9] correlated Equation (2a) to evaluate the core swirl ratio K (the ratio of the angular velocity of the fluid to that of the disk at = 0.5) with centripetal through-flow when −0.2. Debuchy et al [11] determined Equation (2b) to calculate the values of K for a wider range −0.5 with a two-component LDA system. The results from Equation (2b) are smaller than those from Equation A number of studies, such as those by Kurokawa et al [6], Poncet et al [9], Coren et al [13], and Barabas et al [15], show that the pressure distribution along the radius of the disk can be Int.…”

“…For Batchelor type flow, the centrifugal disk boundary layer and the centripetal wall boundary layer are separated by a central core. Debuchy et al [11] derived an explicit equation for K which is valid over a wide range of C qr . Launder et al [12] provided a review of the current understanding of instability pattern that are created in rotor-stator cavities leading to transition and eventually turbulence.…”

Influence of a weak superposed centripetal flow in a rotor-stator system for several pre-swirl ratios

“…Several functions have been tested in Debuchy et al [5], the best results, whether there is a superposed flow or not, being obtained with , where is a constant. For a cavity with superposed centripetal flow, it has been shown in [5] that is proportional to the dimensionless flow parameter .…”

“…For a cavity with superposed centripetal flow, it has been shown in [5] that is proportional to the dimensionless flow parameter . Replacing eq.…”