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Estimation of turbulent energy dissipation in the boundary layer using Smoke Image Velocimetry

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Abstract

Turbulent energy dissipation in the turbulent boundary layer has been estimated experimentally. Dissipation has been derived from dynamics of two-component instantaneous velocity vector fields measured by an optical method. Smoke Image Velocimetry technique based on digital processing of smoke visualization of flow and adapted to relatively large smoke displacement between two consecutive video frames has been employed. The obtained dissipation profiles have been compared with measurements by multi-sensor hot-wire anemometers, stereo PIV, Tomo-3D-PTV with VIC+, and DNS results.

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Abbreviations

I :

Pixel intensity

k :

Frame number

L :

Distance between the channel inlet and the measurement area (m)

N x :

Interrogation window length (pixel)

N y :

Interrogation window height (pixel)

S ii :

Strain-rate tensor components

U :

Velocity (m/s)

U ∞ :

Free-stream velocity (m/s)

U 99 :

0.99 U ∞

\( \bar{U}_{99} \) :

Average velocity in the boundary layer (m/s)

u′ :

Fluctuating component of velocity vector (m/s)

u τ :

Dynamic velocity (m/s)

Δi :

Window displacement along x coordinate

Δj :

Window displacement along y coordinate

Δx :

Distance between the points at which U is measured (m)

δ :

Boundary layer thickness at 0.99 U ∞ (m)

δ x :

Distance between the points at which U is measured allowing for the approximation scheme (m)

ε :

Turbulent energy dissipation

θ :

Momentum thickness (m)

λ K :

Kolmogorov length scale (m)

υ :

Kinematic viscosity coefficient (m2/s)

Φ :

Functional of window similarity

Re :

Reynolds number based on 2δ and \( \bar{U}_{99} \)

Re τ :

Reynolds number based on δ and u τ

Re θ :

Reynolds number based on θ and U θ

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Acknowledgements

This study was supported by the Russian Science Foundation (Project no. 16-19-10336). The authors would like to thank the anonymous reviewers for their insightful comments on the manuscript.

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Authors and Affiliations

  1. Kazan Scientific Center of the Russian Academy of Sciences, Kazan, 420111, Russia

    N. I. Mikheev, A. E. Goltsman, I. I. Saushin & O. A. Dushina

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  1. N. I. Mikheev
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  2. A. E. Goltsman
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  3. I. I. Saushin
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  4. O. A. Dushina
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Correspondence to O. A. Dushina.

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Mikheev, N.I., Goltsman, A.E., Saushin, I.I. et al. Estimation of turbulent energy dissipation in the boundary layer using Smoke Image Velocimetry. Exp Fluids 58, 97 (2017). https://doi.org/10.1007/s00348-017-2379-x

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