Curved Surface of Pelton Bucket Based on Differential Geometry
A 3-D free curved surface of a Pelton bucket was discretized into the 51×51 = 2,601 nodes of boundary fitted grid (BFG) for the CFD. The non-orthogonal curvilinear local frames were introduced with the natural basis vector g for the respective nodes of BFG. The natural basis vector g and its partial derivatives ∂g/∂P at each node were computed based on the differential geometry. As a result, the strong effect of the singular shape of the cutout, especially of its end-wall, on the Pelton bucket was numerically clarified and managed by the differential geometry. After the whole curved surface was approximated by the 50×50 = 2,500 local flat panels tangent to each node, the local surface area ΔS and the Gaussian curvature κ in each panel were investigated to assess the quality of the BFG.
Simulation of Unsteady Water Film Flow on Pelton Bucket
In order to simulate the complicated unsteady flow in Pelton bucket, it is necessary to apply the animated cartoon approach. In this paper, a free jet and the inner surface of a bucket is described by boundary fitted grid (BFG) with non-orthogonal curvilinear coordinates. The water flow is discretized in space and time for CFD (computational fluid dynamics). The moving grids of water film are successfully projected onto the bucket’s inner surface by a projection algorithm. The visualization result of the jet landing on bucket’s surface and the unsteady flow in the rotating buckets in 3D verifies the effectiveness of the proposed method.
多ノズルペルトン水車のジェット干渉 : 第2報,自由ジェットの流速減衰を考慮したジェット干渉度の予測 ( タ-ボ機械の内部流れと定常・否定常特性)
Jet interference brings serious deterioration of efficiency in multinozzle Pelton turbines especially in the operating region of higher unit speed and higher unit discharge. Since the jet interference is intensified by the scale effect of the specific hydraulic energy for a turbine, it is difficult to predict the jet interference of a prototype from is low-head model test results. An alternative approach for predicting prototype interference is therefore urgently required. In our 1st report, a newly proposed intensity for the jet interference based on the relative jet paths reveals a good correlation with the efficiency deterioration due to the jet interference. In the present report, the scale effect of specific energy on the jet interference intensity is investigated. The velocity coefficient of a free jet is reduced with increasing specific hydraulic energy of the turbine, because the entrainment of water droplets in the turbine housing into the free jet increases with the increase of jet flow rate, or of specific energy. Using the relative jet paths considering the decay of jet velocity, the predicted intensity of jet interference shows a good correlation with the increased deterioration of efficiency due to the scale effect of specific energy.