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.
Unsteady separation of jet branch by cutout of rotating Pelton bucket
As a part of boundaries for a free curved surface of a Pelton bucket, the cutout is indispensable to secure the smooth entrance of the unsteady inflow of water jet into the rotating bucket. The cutout of the rotating bucket unsteadily separates a free jet into two branches in both space and time: the impinging branch landing on the relevant bucket surface, and the flow-off branch separated by the cutout toward the preceding bucket. In order to investigate the unsteady jet separation by the cutout three-dimensionally, a semicircular free jet was discretized into 641 nodes of boundary-fitted grids. The position P of impinging jet branch landing on the bucket surface was acquired with the relative velocity W and the water depth D at each node. The trailing edge surface of the flow-off jet branch was simultaneously computed unsteadily. The complicate unsteady interaction of the bucket cutout with the branched free jets was clarified visually with the 3D view of illustrations in order to research the unsteady hydraulic performance of Pelton turbines in space and time.
Effect of stress conditions on collapse deformation behavior of a rockfill material
A set of saturated and dry-saturated large-scale triaxial tests were conducted in order to explore the effects of stress conditions on the saturation-induced collapse deformation behavior of a rockfill material. Specimens were tested in different confining pressures and for dry-saturated tests the specimens were submerged in various shear stress levels. The results indicate that in all of the dry-saturated tests a sudden reduction in the volume of the specimens was observed during the submerging process. The ratio of the minimum axial strength of a submerged specimen (at the end of the saturation process) to the shear strength of the specimen before saturation is defined as the coefficient of stress recovery, Csr. Results of the dry-saturated tests showed that this ratio increases as the confining pressure increases and decreases by increasing the shear stress level. According to the results of dry-saturated tests the values of internal friction angle reduction caused by saturation (Δϕc), the ratio of the elasticity modulus of the material after saturation to its elasticity modulus in dry condition, i.e., Ewet/Edry, and also the saturation induced sudden volumetric strain (εvc) decrease as the confining pressure increases. However the shear stress level does not have any meaningful effect on the variation of Dfc, Ewet/Edry and (εvc).