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TECHNICAL PAPERS

# Numerical Simulation of Vortex Shedding and Lock-in Characteristics for a Thin Cambered Blade

[+] Author and Article Information
Baoshan Zhu1

State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing 100084, P.R.C.bszhu@mail.tsinghua.edu.cn

Jun Lei, Shuliang Cao

State Key Laboratory of Hydroscience and Engineering, Department of Thermal Engineering, Tsinghua University, Beijing 100084, P.R.C.

1

Corresponding author.

J. Fluids Eng 129(10), 1297-1305 (Apr 28, 2007) (9 pages) doi:10.1115/1.2776964 History: Received July 04, 2006; Revised April 28, 2007

## Abstract

In this paper, vortex-shedding patterns and lock-in characteristics that vortex-shedding frequency synchronizes with the natural frequency of a thin cambered blade were numerically investigated. The numerical simulation was based on solving the vorticity-stream function equations with the fourth-order Runge–Kutta scheme in time and the Chakravaythy–Oscher total variation diminishing (TVD) scheme was used to discretize the convective term. The vortex-shedding patterns for different blade attack angles were simulated. In order to confirm whether the vortex shedding would induce blade self-oscillation, numerical simulation was also carried out for blade in a forced oscillation. By changing the pitching frequency and amplitude, the occurrence of lock-in at certain attack angles was determined. Inside the lock-in zone, phase differences between the blade’s pitching displacement and the torque acting on the blade were used to infer the probability of the blade self-oscillation.

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## Figures

Figure 6

Vortex patterns at f∕fs=1.0 and Am=2.0 in a cycle T: (a) T∕4, (b) T∕2, (c) 3T∕4, and (d) T

Figure 7

Lift and drag coefficients at f∕fs=1.0 and Am=2.0

Figure 8

Time variations for lift force and torque: (a) α=−8.3deg and (b) α=13.7deg

Figure 10

Calculated streamline contours in a cycle: α=−8.3deg

Figure 11

Calculated streamline contours in a cycle: α=13.7deg

Figure 12

Variation of averaged torque and vortex-shedding frequency with attack angle α: (a) α=−8.3deg and (b) α=13.7deg

Figure 1

The tested thin cambered blade with maximum camber y∕c=0.038 at x∕c=0.40 and blade thickness t∕c=0.036 at x∕c=0.27

Figure 2

Figure 3

Comparison of streamline for Re=3000 at T=5.0: (a) present method, grid density 120×150, ΔT=0.005; (b) present method, grid density 180×220, ΔT=0.0025; and (c) flow visualization by Bouard and Coutanceau (18)

Figure 4

Comparison of drag coefficient: Re=3000

Figure 5

Time variation in lift and drag coefficients: Re=3000

Figure 9

Instantaneous flow patterns for α=−8.3deg: (a) calculated streamline at T=14.40; (b) flow visualization (3)

Figure 13

Calculated streamline contours in an oscillation cycle for α¯=−8.3deg, Δα=5.0deg: (a) St∕Sts=0.92 and (b) St∕Sts=0.68

Figure 14

Time histories of the oscillation displacement Δαsin(2πft) and torque Cm on the blade for α¯=−8.3deg, Δα=5.0deg: (a) St∕Sts=0.92 and (b) St∕Sts=0.68

Figure 15

Lock-in boundaries for two different attack angles: (a) α¯=−8.3deg and (b) α¯=−4.3deg

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