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TECHNICAL PAPERS

Simulations and Measurements of Pressure Oscillations Caused by Vortex Ropes

[+] Author and Article Information
Zhengwei Wang

Department of Thermal Engineering, Tsinghua University, Beijing, P.R.C. 100084wzw@mail.tsinghua.edu.cn

Lingjiu Zhou

College of Water Conservancy and Civil Engineering, China Agricultural University, Beijing, P.R.C. 100083

J. Fluids Eng 128(4), 649-655 (Jan 20, 2006) (7 pages) doi:10.1115/1.2201631 History: Received June 23, 2004; Revised January 20, 2006

Abstract

Pressure oscillations caused by vortex rope were measured in the draft tube of a prototype Francis turbine. The three-dimensional, unsteady Reynolds-averaged Navier-Stokes equations with the RNG $κ−ϵ$ turbulence model were solved to model the flow within the entire flow path of the prototype hydraulic unit including the guide vanes, the runner, and the draft tube. The model was able to predict the pressure fluctuations that occur when operating at 67–83% of the optimum opening. The calculated frequencies and amplitudes of the oscillation show reasonable agreement with the experiment data. However, the results at 50% opening were not satisfactory. Pressure oscillations on the runner blades were found to be related to the precession of vortex ropes which caused pressure on the blades to fluctuate with frequencies of $−fn+fd$ ($fn$ is the rotational frequency and $fd$ is vortex procession frequency). The peak-to-peak amplitudes of the pressure oscillations on the blades at the lower load conditions (67% opening) were higher than at higher load conditions (83% opening). Fluctuations on the suction side tended to be stronger than on the pressure side.

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Figures

Figure 1

Francis turbine geometry (unit in mm): (a) side view of the draft tube; (b) planform of the draft tube; (c) meridian view of the runner; (d) cross section of the draft tube

Figure 2

Recording points: (a) on the blade surface; (b) on section s1 and s2; (c) on section s3; (d) on section s4

Figure 3

Measured pressure fluctuations at point s21 (without filtering)

Figure 4

Comparison of experimental data and calculated pressure fluctuations at point s21 (The measured pressure fluctuations were filtered with cutoff frequencies of 30Hz for g20-H68 and g16-H68, 8Hz for g12-H68 and g16-H75 and 10Hz for g20-H75.)

Figure 5

Flow features in the draft tube. Parts a-c are for g20-H68, (a) vortex rope; (b) velocity vectors on the middle plane of the draft tube; (c) velocity vectors in section A-A in part b. Parts d-e are for g16-H68; (d) vortex rope; (e) velocity vectors on the middle plane of the draft tube; (f) velocity vectors in section A-A in part e.

Figure 6

Pressure amplitudes at various locations in the draft tube

Figure 7

Pressure fluctuations inside the runner and the draft tube for case g16-H68

Figure 8

Examples of pressure fluctuation spectra on the blades

Figure 9

Peak-to-peak amplitudes of pressure fluctuations on blades

Figure 10

The measured dynamic stress in the blade and the pressure fluctuations in the draft tube. Sg3 was measuring point near the conjunction of the blade outlet and the crown.

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