The effects of the volute geometry on the head, efficiency, and radial force of a low specific-speed centrifugal pump were investigated focusing on off-design conditions. This paper is divided into three parts. In the first part, the three-dimensional flow inside the pump with rectangular volute was simulated using three well-known turbulence models. Simulation results were compared with the available experimental data, and an acceptable agreement was obtained. In the second part, two volute design methods, namely, the constant velocity and the constant angular momentum were investigated. Obtained results showed that in general the constant velocity method gives more satisfactory performance. In the third part, three volutes with different cross section and diffuser shape were designed. In general, it was found that circular cross section volute with radial diffuser provides higher head and efficiency. Moreover, the minimum radial force occurs at higher flowrate in circular volute geometry comparing to rectangular cross section volute.

Large radial force causes several issues in pumps, such as noise, vibration, and extra load on the bearings. To reduce the radial force, the effects of concentric volute and multivolute geometry on the head, efficiency, and radial force of a low speed centrifugal pump at off-design conditions were investigated. Commercial software with the k -ω turbulence model and automatic near wall treatment was employed for the prediction of fluid flow inside the pump. Flow simulations for three casings concentric at 180°, 270°, and 360°from the tongue showed that the 270°concentric volute generates the lowest radial force at throughout the entire range of flow rate. The triple-volute and tetravolute casings are also proposed as new volute geometries. The flow analysis of a double-volute, triple-volute, and tetravolute show that the triple-volute is the most appropriate volute geometry at off-design conditions.

In this study, we investigated the effects of volute tongue geometry variation on the head, efficiency, and radial force of a centrifugal pump. Numerical simulation modeling based on k À ! turbulence with automatic near wall treatments was used to simulate the turbulent flow. The effect of blade position with respect to the volute tongue on instantaneous pump characteristics was investigated. The parametric studies were done for cutwater gap, tongue shape, and volute tongue angle. Numerical results showed that the large cutwater gap caused lower radial force, especially at high flow rates. Investigations using various volute tongue shapes indicated that the short tongue volute decreased the radial force at design and low flow rates. Considering all aspects, the most satisfactory volute tongue angle was found to be 5 less than the outlet velocity angle of the impeller; yielding about 40% lower radial force than others at the design point.

SUMMARYThis paper reports the outcome of applying two di erent low-Reynolds-number eddy-viscosity models to resolve the complex three-dimensional motion that arises in turbulent ows in ducts with 90• bends. For the modelling of turbulence, the Launder and Sharma low-Re k-model and a recently produced variant of the cubic non-linear low-Re k-model have been employed. In this paper, developing turbulent ow through two di erent 90• bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross-section the curvature induces a strong secondary ow, while for the rectangular cross-section the secondary motion is conÿned to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross-section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross-section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean ow ÿeld, the non-linear k-model returns superior predictions of the turbulence ÿeld and also of the pressure and friction coe cients.

This paper reports the outcome of applying two different low-Re number eddy-viscosity models to resolve the complex three-dimensional motion that arises in turbulent flow in a square cross-section duct passing around a 90° bend. Flow computations have been obtained using a three-dimensional, non-orthogonal flow solver. For modeling of turbulence, the Launder and Sharma low-Re k–ε model and a recently modified version of nonlinear low-Re k–ε model that have been shown to be suitable for flow and thermal predictions in re-circulating and impinging jet flows, have been employed. A bounded version of the QUICK scheme was used for the approximation of convection in all transport equations. The numerical predictions are validated through comparisons with the reported flow measurements and are used to explain how the curvature influences the flow development. The results of the present investigation indicate that the curvature induces a strong secondary flow in the curved section of the duct. The secondary motion also persists downstream of the bend, although it slowly disappears with the main stream development. At the entrance of the curved section, the curvature alters the flow development by displacing the fluid towards the convex (inner) wall. Comparisons of the predicted stream-wise and cross-stream velocity components with the measured data indicate that both turbulence models employed in the present study can produce reasonable predictions, although the non-linear model predictions are generally closer to the measurements. Both turbulence models successfully reproduce the distribution as well as the levels of the local pressure coefficient in the curved section of the duct.

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