Energy and Power Engineering, 2013, 5, 51-55

doi:10.4236/epe.2013.54B010 Published Online July 2013 (http://www.scirp.org/journal/epe)

Simulation of Unsteady Water Film Flow on Pelton Bucket

Shen Na

School of Electrical Engineering, Guangzhou College of South China University of Technology, Guangzhou, China

Email: nashen5@163.com

Received January, 2013

ABSTRACT

In order to simulate the complicated unsteady flow in Pelton bucket, it is necessary to apply the animated cartoon ap-

proach. In this paper, a free jet and the inner surface of a bucket is described by boundary fitted grid (BFG) with

non-orthogonal curvilinear coordinates. The water flow is discretized in space and time for CFD (computational fluid

dynamics). The moving grids of water film are successfully projected onto the bucket’s inner surface by a projection

algorithm. The visualization result of the jet landing on bucket’s surface and the unsteady flow in the rotating buckets in

3D verifies the effectiveness of the proposed method.

Keywords: Water Film Flow; Simulation; Projection; Pelton Bucket

1. Introduction

Different from the reaction turbines such as Francis and

Kaplan turbines, the flow in Pelton turbine is essentially

unsteady in space and time. This is the reason why the

application of CFD (computational fluid dynamics) to the

Pelton turbines is much behind other turbines. With the

continuous improvement of computer technology and

physical model, the numerical simulation of inner com-

plicated flow in Pelton turbine also becomes possible. In

1994, Kubota and Nakanishi classified the unsteady flow

in Pelton turbines for the study of the scale effect [1]. In

1998, Kubota et al. first proposed a numerical method

called “BucFlAs” which solves the unsteady quasi-2D

flow in Pelton bucket for different space/time steps indi-

vidually [2]. Liu et al. described the comparative nu-

merical analysis of the flow in buckets at different

enlarging rates of jet in 2D [3]. In 2005, Zheng, Han, et

al. discussed the unsteady interference between free wa-

ter jet and rear surface of rotating buckets in Pelton tur-

bine in quasi-3D[4].

So far, there is no paper reporting the unsteady water

film flow in rotating Pelton bucket in 3D. In this paper,

the animated cartoon approach is applied to simulate the

unsteady flow in Pelton bucket. The cross section of free

jet and the free curved surface is discretized by BFG. The

flow particles may depart from the bucket surface be-

cause of error in simulation, it is necessary to project

those particles in each moving step. A projection algo-

rithm is proposed in this paper to solve the problem, and

the example verifies the reliability of this method.

Through the simulation, the visual results of free jet

landing on the buckets and the unsteady flow water film

on bucket surface are obtained.

2. Discretization of Pelton Bucket and Free

Jet

2.1. Discretization of Complicated Bucket

Surface

The boundary of Pelton bucket consists of splitter, cutout,

end-wall and brim, respectively as shown in Figure 1.

Since all the boundary is curved, the orthogonal grids

cannot describe the surface of Pelton bucket accurately. It

is necessary to apply BFG with non-orthogonal curvilinear

coordinates. The natural basis vector and their partial dif-

ferential can be calculated accurately by differential ge-

ometry[5]. Those parameters are used in the algorithm of

projection which will be mentioned later for CFD.

Outer-brim

Splitter Cutout

End-wall

Inner-brim

Cutout-

otto

Side-

rim

*Project: Important Science and Technology Specific Projects in Zhe-

iang Province (Grant No. 2008C11057); Teaching Reform Research

Project in Guangzhou College of SCUT (Grant No. JY110319) Figure 1. Complicated curved surface of Pelton bucket.

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