Theoretical, Numerical and Experimental Investigation of the Flow in Rotor-Stator Cavities with Application to a Centrifugal Pump

In the present work, the complex flow in rotor-stator cavities is investigated by means of analytical, numerical and experimental approaches. This kind of flow can be found in nearly all kinds of turbomachinery in the side chambers located between the rotating impeller and the stationary casing. The flow conditions in these small side gaps have a strong impact on the overall losses (disk friction and leakage) and thus the efficiency of the machine. Many more effects are related to the side chamber flow such as the resulting axial force on the impeller, rotordynamic issues or acoustic resonances. The present manuscript is structured into three parts. In the first part, a new one-dimensional flow model is derived on the basis of a simplified model of the side chamber flow which allows the determination of the radial tangential velocity distribution as the major flow parameter. Related parameters such as the radial pressure distribution or the frictional resistance can then be calculated thereafter. The underlying, fundamental differential equation is derived from two different approaches. First, the derivation is shown emerging from the Navier-Stokes equations in cylindrical coordinates by applying several simplifications. Secondly, the principal of conservation of angula momentum is applied to a small cylindrical volume element located between a rotating and a stationary disk. Based on a substantial literature review, it is assumed in the derivation that a boundary layer flow structure with two boundary layers on the rotating and the stationary wall, separated by an inviscid core region, establishes. The flow model accounts for the influence of the outer cylindrical wall by means of an additional correction function. Moreover, a new approach for the determination of the friction factors is introduced based on the logarithmic law of the wall whereas usually the empirical resistance law according to Blasius is employed by most researchers. Comparisons with available experimental data from the literature as well as two other well-known flow models demonstrate an improvement of the achievable results. Furthermore, the flow model is successfully applied for two practical cases namely a centrifugal pump of low specific speed with volute casing (hydraulic turbomachine) and a radial compressor (thermal turbomachine). In the second part, numerical flow solutions obtained with commercial CFD solvers are compared to experimental data from the literature. The investigations focuse on the prediction of the mean flow quantities and confirm the previous assumptions concerning the flow fields encountered in rotor-stator cavities. The numerical results clearly highlight the complexity of the encountered flow patterns. Even the prediction of the flow created by an enclosed rotating disk can become severly difficult with respect to turbulence modeling due to transition from laminar to turbulent flow. Furthermore, the results confirm the superior impact of an external through-flow on the flow field. Based on the previous experiences, the flow in a complete centrifugal pump including both side chambers and the volute casing is simulated with CFD. The numerical results are supported by measurements of the radial static pressure distributions in the side chambers and the delivery head at three different operating conditions (partload, design flow rate and overload). On this occasion, an impeller either with or without balancing holes to reduce the resulting axil thrust is used. Balancing holes lead to a radial inward directed leakage flow in the rearside chamber which strongly influences the flow conditions. A very good agreement between measured and computed delivery heads for all three operating points is found which confirms an (overall) accurate modeling of the flow with CFD. In the front side chamber, the predicted radial static pressure distributions consistently compare well to the measured ones while somewhat greater discrepancies are present in the rearside chamber. Due to different axial gap widths in the side chambers, the encountered flow structures are inherently different. In the front side chamber, the axial spacing is wide enough to allow the formation of two boundary layers with core region. In the rearside chamber, the boundary layers are merged due to the significantly smaller axial spacing. Generally, a strong coupling in terms of mass and momentum exchange between the side chambers and the flow in the adjacent components such as the volute or the impeller outlet can be observed. A characteristic feature of the present pump is the inhomogenous tangential pressure built up in the volute which is found in all investigated configurations but with different markedness. Due to the close coupling, this strongly influences the flow in the side chambers. If an impeller without balancing holes is used, the secondary flow field at the impeller outlet drifts towards the suction side of the pump and increases the entering angular momentum flux in the frontside chamber. Furthermore, the omission of the balancing holes leads to the creation of a three-dimensional, counter rotating wake region in the narrow rearside chamber. This effect can also be recognized from the measurements as well as the difference in the flow regimes. The application of the previously derived flow model yields good results in the front side chamber while the dissimilar shear flow in the rearside chamber requires the implementation of a modified approach from the literature.