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Technical Briefs

# Medial Axis Transform Method for Shape Design of Hub and Shroud Contours of Impellers

[+] Author and Article Information
Pengfei Wang, Xiaodong Ruan, Xin Fu

State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China

Jun Zou1

State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, Chinajunzou@zju.edu.cn

1

Corresponding author.

J. Fluids Eng 133(3), 034502 (Mar 15, 2011) (4 pages) doi:10.1115/1.4003689 History: Received September 14, 2010; Revised February 19, 2011; Published March 15, 2011; Online March 15, 2011

## Abstract

A novel method of designing hub and shroud contours is presented. The method, based on the medial axis transform theory in differential geometry, gives a uniform description of hub and shroud contours and the formula of cross section area. Through solving the formula of cross section area with an additional constraint, the hub and shroud contours can be determined numerically. The constraint is exposed through a curvature equation, which allows the medial axis or hub (shroud) contour to be a certain form. Using this method, various optimization criteria relating to the cross section area can be conveniently introduced into the design.

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## Figures

Figure 3

(a) The given distribution of incline angle α (left), which comprises four linear segments; the desired distribution of cross section area (right, dash line), which comprises two linear segments; and the distribution of cross section area of approached contours (right, solid line). (b) The calculated contours of hub and shroud (hollow dots); the approached contours (solid lines).

Figure 1

Sketch of the medial axis and hub and shroud contours

Figure 2

(a) The calculated hub and shroud contours (hollow dots) and the approached contours (solid line); (b) the profile of mean meridional velocity of calculated (hollow dots) and approached (solid line) contours. All are in SI units.

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