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.
The EU Legal Framework for the Enforcement of Consumer Law
The European Union (EU) is special in that it is a multi-level system in which, principally, consumer law can be adopted at the EU level but it is enforced at the level of the Member States. Nevertheless, the EU has over time developed an ever denser legal framework for the enforcement of consumer law by the Member States. It is this legal framework that this contribution focuses upon.