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.
Discrete Analogue Curvature Fluctuating Widely Pelton Bucket Inner Surface by Body-Fitted Coordination
The inner surface of Pelton bucket is a free surface with cutout and the curvature fluctuating widely. The geometry eigenvalue for every data is necessary to analyze the free water sheets flow on inner bucket surface by CFD, but the Cartesian design data are inadequate. This paper presents the 3-D non- orthogonal Body-Fitted Coordinate system to discretize the free surface and achieve uniform high density grids. This paper deduces the tangential vector and unit normal vector equations for grid on 3-D Body-Fitted Coordinate system. The computed results on Body-Fitted coordination are more stable.
Representation of systems disturbed by wide band noise
In this paper, a method of handling and working with wide band noise is developed. We represent wide band noise as a distributed delay of white noise and use it to reduce a nonlinear system disturbed by wide band noise to a nonlinear system disturbed by white noise. An application of this reduction to a nonlinear filtering problem under a wide band noise disturbance is discussed.