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Research Papers: Multiphase Flows

# Cavitating Turbulent Flow Simulation in a Francis Turbine Based on Mixture Model

[+] Author and Article Information
Shuhong Liu1

State Key Laboratory of Hydro Science and Hydraulic Engineering, Tsinghua University, Beijing 100084, Chinaliushuhong@mail.tsinghua.edu.cn

Liang Zhang, Yulin Wu

State Key Laboratory of Hydro Science and Hydraulic Engineering, Tsinghua University, Beijing 100084, China

Michihiro Nishi

Department of Mechanical Engineering, Kyushu Institute of Technology, Sensui-cho 1-1, Tobata, Kitakyushu 804-8550, Japannishi@mech.kyutech.ac.jp

1

Corresponding author.

J. Fluids Eng 131(5), 051302 (Apr 13, 2009) (8 pages) doi:10.1115/1.3112382 History: Received October 20, 2007; Revised February 11, 2009; Published April 13, 2009

## Abstract

As a numerical method to study the cavitation performance of a Francis turbine, the mixture model for the cavity/liquid two-phase flow is adopted in the cavitating turbulent flow analysis together with the re-normalization group (RNG) $k-ε$ turbulence model in the present paper. The direct coupling numerical technique is used to solve the governing equations of the mixture model for the two-phase flow. Unsteady cavitating flow simulation around a hydrofoil of ALE15 is conducted as preliminary evaluation. Then, the cavitating flow in a Francis turbine is treated from the steady flow simulation since the feasibility of the cavitation model to the performance prediction of the turbine is the present major concern. Comparisons of the computational results with the model test data, i.e., the cavitation characteristics of hydraulic efficiency and the overload vortex rope at the draft tube inlet being reproduced reasonably, indicate that the present method has sufficient potential to simulate the cavitating flow in hydraulic turbines. Further, the unsteady cavitating flow simulation through the Francis turbine is conducted as well to study the pressure fluctuation characters caused by the vortex rope in the draft tube at partial load operation.

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## Figures

Figure 7

Appearance of cavity in the runner: (a) initial cavitation (σi=0.157) and (b) severe cavitation (σ=0.08)

Figure 8

Cavitated vortex rope in draft tube at large flow rate (Case 3) under σ=0.054: (a) snapshot and (b) cavitating flow simulation

Figure 9

Wall pressure fluctuation at the 1.0D1 point for Case 1 from unsteady cavitating flow analysis (σ=0.07): (a) variation in pressure with time and (b) frequency spectrum

Figure 1

The direct coupling procedure for incompressible flow

Figure 2

Cavitating flow around ALE15 hydrofoil: (a) geometry of the hydrofoil and calculation coordinate system and (b) streamlines around the hydrofoil and bubbly cloud

Figure 3

Comparison of velocity distribution at x=13 mm and z=−5 mm

Figure 4

Numerical snapshots of cavitation bubbles on the top surface of hydrofoil: (a) view in −yb and (b) view in xb

Figure 5

Model Francis turbine: (a) calculation domain, (b) interaction surfaces, and (c) survey points of pressure in draft tube

Figure 6

Cavitation characteristics of efficiency (Q11=0.99 m3/s, n11=83.4 min−1)

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