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.
NATURAL BASIS VECTORS ON 3-D FREE SURFACE WITH SINGULAR NODES
Since a Pelton bucket has the geometry of complicated 3-D free-curved surface,it is necessary to apply the non-orthogonal curvilinear coordinate system for the boundary-fitted grids (BFG)to perform the accurate flow analysis of Pelton turbines.This paper presents how to acquire the natural basis vector g at the each grid node of the given BFG.Through the process of acquiring g, we found that there are three singular nodes on a boundary curve of the bucket brim.Special attention was required to obtain the reliable natural basis vectors for the singular nodes to complete a whole BFG.
Numerical Prediction of Dynamic Performance of Pelton Turbine
Different from the reaction turbines, the hydraulic performance of Pelton turbine is dynamic due to the unsteady flow in the rotating buckets in time and space. The dynamic energy efficiency of bucket ηEB and power efficiency of bucket ηPB within a short period can be predicted from the dynamic flow pattern of the free-surface sheet flow in the rotating bucket, whereas the dynamic discharge efficiency of bucket ηQB is defined as the resident discharge in the bucket at the respective moment. Under the operation of higher unit speed nDH than the optimum one, the power efficiency of bucket is deteriorated by the jet interference with the rear surface of bucket ΔPrear at the first stage of the dynamic performance, as well as the loss power due to the spilt flow from the cutout of bucket at the later stage of performance. Based on the dynamic performance prediction presented, the future possibility of the quantitative investigation for the negative scale effect of Pelton turbines was discussed.