Medial Axis Transform Method For Meridional Shape Design Of Pump Impellers

Meridional shape design, the focus of this thesis, is the basis and essential part of pump design. The philosophy and objective of meridional shape design are discussed for centrifugal pumps, and for the first time the numerous design methods are grouped into several geometric ones, whose advantages and disadvantages are discussed from the flowing perspective. Then the three requirements for an excellent meridional shape design method are first drawn, stimulating this study.For the first time the medial axis transform (MAT) method is introduced into meridional shape design. By MAT, derivation is done with the uniform vector and scalar descriptions of hub and shroud contours which constitute a meridional shape, and with the approximate and exact formulas of cross-section area based on the assumption that cross sections of meridional shape are circular arcs. Taylor expansions are used to analyze the approximate conditions of the two formula for cross-section area. Two independent variables in the cross-section area formula, two independent equations are in need, one is given by the expected distribution of cross-section area, and the other by constraint equation. Curvature and Cartesian expressions of hub and shroud contours are derived with MAT to facilitate geometric constrains. The pressure balance equation is also derived to apply flowing constraint. Then the meridional shape design system is built up based on MAT.The statistical method is also first presented based on MAT on the whole meridional dimensions. By contrast, conventional methods can only apply for statistics on several critical meridional dimensions, revealing some general guidance for meridional shape design. Instead of taking statistics on apparent meridional dimensions, this novel method views hub and shroud contours as two independent variables and takes statistics on their equivalent variables by MAT. A series of industrial centrifugal pumps are explored to illustrate this method. All the variables relating with MAT are extracted, showing smooth curves without striking features of the locus and radius of inscribed circles, while the curves of α and θ emerging striking segmented feature and each segment can be well fitted by a linear line or a parabola. Thus statistics is taken on segment points and fitting coefficients of each segment, realizing statistics on the whole meridional contour by inverse MAT. All variables under statistics are nondimensionalized and averaged to reduce sample error.The basis of meridional shape design through cross-section area calculation is first explored by comparison of mean meridional velocity distributions of designed and CFD calculated. Various cases are explored to compare the distributions between expected, designed, designed with blade thickness modification, CFD calculated with area-weighted average, and CFD calculated with massflow-weighted average. Results showing1) if the design of blade angle is reasonable, flowing in meridional channel can be assumed to be one-dimensional even for mixed-flow pumps;2) blade thickness can not be neglected in meridional shape design, for which the cross-section area should be modified by a blocking coefficient relating with blade thickness;3) for compressible flow, the mean meridional velocity should be modified with a coefficient relating with local compression;4) even for mixed-flow pumps, meridional cross sections can be viewed as circular arcs.The integrated meridional shape design of impeller and guide vanes for reactor coolant pump (RCP) is studied. This process is illustrated utilizing the hydraulic design point of AP1000RCP. Two kinds of designs are explored considering blade thickness or not. Results show that:1) if blade thickness is ignored in design, the calculated meridional velocity by CFD undergoes sudden changes at the leading or trailing edges of impeller and guide vanes due to the sudden extraction or expantion of cross section area;2) if blade thickness is considered in design, the calculated meridional velocity by CFD is quite smooth and fit well with the expected distribution;3) CFD results show the sudden change of meridional velocity at leading or trailing edge has little effect on hydraulic efficiency;4) the comparision of calculated meridiaonal velocity distribution with that of designed shows visually the rationality of vane angle distribution;5) the suggested procedure can be well applied in meridional shape designs for RCPs.