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

Wang, Pengfei; Ruan, Xiangyan; Zou, Jun; Fu, Xin

doi:10.1115/1.4003689

Cited by 7 publications

(15 citation statements)

References 10 publications

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“…Instead of geometrically designing the meridional channel with linear lines and circular arcs, an important medial axis transform theory was firstly proposed by Choi et al [12], which was subsequently extended to meridional shape design by Zou et al [13] and Wang et al [14]. In succession, Wang et al [15] adopted the medial axis method in his study and had designed the meridional shapes with different inlet conditions.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…Continually, different from the previous studies [13][14][15], research here would use the radial coordinate to take the place of the natural coordinate ; thus, becomes the independent variable in the envelope formula of the MAT theory. Comparatively, ( ), p( ), q( ), and ( ) in Figure 1 can be replaced with ( ), p( ), q( ), and ( ).…”

Section: Simplification Of Envelope Formula In Mat Theorymentioning

confidence: 99%

“…Taking the envelope formula of the medial axis transform (MAT) theory [12][13][14][15] into consideration, research here transformed it into another simple manner controlled by the independent variable of the radial coordinate. Then based on the transformed envelope formula, the circular equation, and the cross section area equation, two kinds of mathematical constraints which had the corresponding solutions for the shape design were introduced.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…In [14,15], the distribution of the cross section area ( ) can be taken as a previous settled variable, so that the variable ( ) can still be taken as a known variable before the meridional channel design in this study. However, in the other design conditions [13], the previous given cross section area ( ) can also be replaced with some other design variables, for instance, the volume flow rate , the mean meridional velocity , and the blockage factor , but actually, the distribution of ( ) can be settled down previously with the following equation:…”

Section: The Cross Section Area Equationmentioning

confidence: 99%

“…where can be got from the simulation result or the experienced formula [14] ( = + , where and are the constants determined by the inlet and outlet variables). is closed to 1 and can be ignored sometimes; moreover, it can also be calculated from some experienced formulas [11].…”

Section: The Cross Section Area Equationmentioning

confidence: 99%

See 4 more Smart Citations

Derivation of the Mathematical Approach to the Radial Pump’s Meridional Channel Design Based on the Controlment of the Medial Axis

Wang

Xie

2017

Mathematical Problems in Engineering

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The meridional channel is the base for designing the radial pumps, and a new design approach is proposed here. Different from the previous studies, research here tries to establish the design model simply controlled with the radial coordinate. With the combination of a series of mathematical equations, the new design approach can shape the meridional contours directly by using the initial design variables. As for the mathematical constraint in the new design approach, it was presented in two forms, and each form had its corresponding solution. For the first form (Constraint I), the midpoints of the design points on the hub and shroud contours were thought to be located on the medial axis, and the PSO algorithm was adopted to search for the suitable results. Continually, to accelerate the design process, the second form (Constraint II) to simplify the mathematical constraint was added, and the explicit mathematical expressions calculating the coordinates on the hub and shroud contours were deduced. Finally, to check out the feasibility of the design approach in engineering, it was applied to redesign some typical meridional channels proposed by previous studies, and, through comparative analysis, the effectiveness of the new approach was evaluated and demonstrated.

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