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Experiments on asymmetric vortex pair interaction with the ground

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Abstract

The interaction between the asymmetric vortex pair and the ground was experimentally investigated in a closed-circuit water channel for the current study. Particle image velocimetry tests were conducted to achieve the velocity measurements of flow fields at various crossflow planes. The vortex pair, with the reference circulation Reynolds number ReΓ ≈ 4490, was tested with various initial heights (h0/b0 = 1.5, 1.0 and 0.5) and circulation ratios (λ = 0.36:1, 1:0.36, 0.6:1, 1:0.6), with it being found that according to different interaction effects, the trajectory and merger of the vortex pair could be significantly affected. As the primary vortex pair approached the ground, a high turbulent kinetic energy region was observed between the secondary and primary vortical structures, which suggests violent interaction and accelerated circulation decay of the primary vortex. In addition, depending on the distribution of secondary vorticity and image vortices to the moving coordinate system, merging-promoting or -inhibiting effects were observed, which eventually affected the evolution of the primary vortex pair.

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Abbreviations

a :

Vortex core radius

b :

Vortex separation

b 0 :

Initial vortex separation

c :

Root chord length

d L :

Distance between γS and VL

d R :

Distance between γS and VR

h :

Height of the primary vortex

h 0 :

Initial height of the primary vortex

M :

Number of streamwise locations

m i :

Intersection of the ξ axis and the maximum vorticity line

N S :

Number of γS

n j :

Intersection of the η axis and the maximum vorticity line

PIV:

Particle image velocimetry

r :

Pearson coefficients

TKE:

Normalized turbulent kinetic energy

U ∞ :

Free-stream velocity

U I :

Accumulated net induced velocities

u I :

Relative velocity component along the ξ axis induced by γS

u IL :

Induced velocity component on the VL from γS

u IL,ξ :

Magnitude of uIL along the ξ axis

u IR :

Induced velocity component on the VR from γS

u IR,ξ :

Magnitude of uIR along the ξ axis

\(u_{y}^{{\prime }}\) :

Velocity fluctuation in the direction of the y-axis

\(u_{z}^{{\prime }}\) :

Velocity fluctuation in the direction of the z-axis

V L :

Primary left vortex

V R :

Primary right vortex

x :

Streamwise coordinate

y :

Lateral (spanwise) coordinate

y S :

Lateral (spanwise) coordinate of γS

z :

Vertical coordinate

z L :

Vertical coordinate of VL

z R :

Vertical coordinate of VR

z S :

Vertical coordinate of γS

Γ :

Circulation of the primary vortex

Γ 0 :

Initial primary vortex circulation

Γ L :

Circulation of VL

Γ R :

Circulation of VR

Γ ref :

Reference circulation

γ S :

Arbitrary circulation element of secondary vorticity

θ L :

Orientation angles between the ξ axis (positive direction) and uIL

θ R :

Orientation angles between the ξ axis (positive direction) and uIR

λ :

Circulation ratio

ν :

Kinematic viscosity

ξ–η :

Moving coordinate

σ :

Area of the circulation element of secondary vorticity

ω S :

Vorticity intensity of γS

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China, under Grant Numbers 11850410440, 11772033 and 117221202.

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Authors and Affiliations

  1. Key Laboratory of Aero-Acoustics Ministry of Industry and Information Technology (Lu Shijia Laboratory), Beihang University (BUAA), Beijing, 100191, People’s Republic of China

    Qingmin Chen, Tianxiang Hu & Peiqing Liu

  2. Key Laboratory of Fluid Mechanics Ministry of Education, Beihang University, Beijing, 100191, People’s Republic of China

    Yue Liu, Qiulin Qu & Hao Guo

  3. Department of Automotive and Aeronautical Engineering, Hamburg University of Applied Sciences, Hamburg, Germany

    Rinie A. D. Akkermans

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  1. Qingmin Chen
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  2. Tianxiang Hu
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  3. Peiqing Liu
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  4. Yue Liu
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  7. Rinie A. D. Akkermans
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Correspondence to Tianxiang Hu.

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Chen, Q., Hu, T., Liu, P. et al. Experiments on asymmetric vortex pair interaction with the ground. Exp Fluids 61, 150 (2020). https://doi.org/10.1007/s00348-020-02987-7

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