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Numerical investigation of the flow over a two-dimensional square cylinder with a synthetic jet generated by different exciting signals

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Abstract

The flow around a square cylinder with a synthetic jet positioned at the rear surface is numerically investigated with unsteady Reynolds-averaged Navier–Stokes (URANS) method. Different exciting signals are utilized to generate the synthetic jets, including the square signal, triangle signal, sinusoidal signal and the varying duty-cycle signal. The wake vortices evolution and the frequency characteristic are analyzed for all the cases. In the case with the square signal, the vortex shedding pattern is not essentially changed due to the deficiency of the synthetic jet strength. The synchronization at half of the exciting frequency is observed for both of the sinusoidal and triangle signal, where the alternative deflection of the jet vortex pairs is detected correspondingly. The complete synchronization is discovered in the case with the duty-cycle \(k=2\) signal, where the wake is symmetrical and totally controlled by the synthetic jets. The drag coefficient is calculated to contrast the control efficiency of different signals. The most satisfactory control performance is achieved in the case with the duty cycle \(k=2\) signal as well, where a \(33.71\%\) of drag reduction is realized compared to that without control.

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Abbreviations

\(C_{{\text{d}}}\) :

Drag coefficient

\(C_\mu\) :

Momentum coefficient

D :

Side length of the square cylinder (mm)

\(f_{{\text{e}}}\) :

Excitation frequency (Hz)

\(f_0\) :

Natural vortex shedding frequency (Hz)

\(\nu\) :

Kinematic viscosity coefficient

Re:

Reynolds number

St:

Strouhal number

T :

Period (s)

\(U_\infty\) :

Velocity of the incoming flow (m/s)

\(U_0\) :

Characteristic velocity of the synthetic jets (m/s)

\(U_\text{e}\) :

Amplitude of the sinusoidal signal

\(U_\text{p}\) :

Peak velocity the exciting signal

u(t):

Streamwise velocity at the jet orifice (m/s)

u :

Streamwise velocity fluctuations (m/s)

v :

Vertical velocity fluctuations (m/s)

w :

Width of the slot (mm)

\(\omega _{{\text{z}}}\) :

Spanwise vorticity (1/s)

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11721202).

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  1. Fluid Mechanics Key Laboratory of Education Ministry, Beihang University, Beijing, 100191, China

    Yiran Lu & Jinjun Wang

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  1. Yiran Lu
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  2. Jinjun Wang
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Correspondence to Jinjun Wang.

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Lu, Y., Wang, J. Numerical investigation of the flow over a two-dimensional square cylinder with a synthetic jet generated by different exciting signals. J Vis 27, 59–73 (2024). https://doi.org/10.1007/s12650-023-00952-0

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