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Transitions between smooth and rough surfaces in turbulent channel flows for d- and k-type rough elements

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Abstract

This paper presents an experimental study on the transition from smooth to rough walls, and back to the smooth one, in turbulent closed-conduit flows. These transitions cause a shift on flow velocity profiles that changes their parameters when compared to the flow over a smooth wall. Different water flow rates were imposed in a closed conduit of rectangular cross section, where rough elements consisting of cavities of d- and k-type were positioned covering a part of the bottom wall of the test section. Reynolds numbers based on the channel half-height were moderate, varying between 7800 and 9600, and the regime upstream of the rough elements was hydraulically smooth. Experimental data for this specific case remain scarce and the involved physics rests to be understood. The flow field was measured by low frequency PIV (particle image velocimetry) and by flow visualization, the latter using a continuous 0.1 W laser, a high-speed camera, and scripts written by the authors. From the instantaneous fields measured with PIV, the mean velocities, fluctuations, shear stresses, and turbulence production were computed. The results show the presence of oscillations in Reynolds stress and turbulence production, that are higher for the k-type roughness and were not shown in previous experimental works. From the high-speed movies, the angular velocities and frequencies of vortices in the cavities were computed, and the occurrence of fluid ejection from the cavities to upper layers of the flow was observed. A relation between the angular velocities of inner-cavities vortices and the oscillations in Reynolds stress and turbulence production is proposed.

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Abbreviations

B :

constant

d :

diameter (m)

\(d_\mathrm{h}\) :

hydraulic diameter (m)

f :

Darcy friction factor

f :

Frequency (Hz)

h :

Channel half height (m)

H :

Channel height (m)

k :

Height of rough elements (m)

L :

Wavelength (m)

\(l_\mathrm{v}\) :

Viscous length (m)

N :

Number of image pairs

P :

Turbulence production term (m\(^2\)/s\(^3\))

Q :

Volumetric flow rate (m\(^3\)/h)

Re :

Reynolds number based on the boundary-layer thickness

\(Re_{\mathrm{dh}}\) :

Reynolds number based on the hydraulic diameter

t :

Time (s)

u :

Longitudinal component of the velocity (m/s)

\(u_*\) :

Shear velocity (m/s)

v :

Vertical component of the velocity (m/s)

\(v_\mathrm{t}\) :

Tangential velocity (m/s)

w :

Distance between rough elements (m)

x :

Horizontal coordinate (m)

y :

Vertical coordinate (m)

\(\delta\) :

Boundary-layer thickness (m)

\(\Delta\) :

Displacement

\(\kappa\) :

von Kármán constant

\(\lambda\) :

Ratio between the projected frontal and parallel areas

\(\mu\) :

Dynamic viscosity (Pa s)

\(\nu\) :

Kinematic viscosity (m\(^2\)/s)

\(\Omega\) :

Angular velocity (rad/s)

\(\rho\) :

Specific mass (kg/m\(^3\))

\(\tau\) :

Shear stress (N/m\(^2\))

0:

Relative to the smooth surface

0:

Relative to the origin of the vertical coordinate

\(\mathrm{bla}\) :

Relative to Blasius correlation

\(\mathrm{d}\) :

Relative to the displaced coordinate system

\(\mathrm{dh}\) :

Relative to the hydraulic diameter

\(\mathrm{s}\) :

Sand equivalent

\(\mathrm{v}\) :

Relative to the viscous layer

\(+\) :

Normalized by the viscous length \(l_\mathrm{v}\) or by the shear velocity \(u_*\)

\(\overline{\quad }\) :

Averaged in time

\('\) :

Fluctuation

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Acknowledgements

The authors are grateful to ANP, Repsol, Cepetro, Labpetro, CNPq (Grant no. 400284/2016-2), and to FAPESP (Grants nos. 2012/19562-6 and 2016/13474-9) for the provided financial support.

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Authors and Affiliations

  1. School of Mechanical Engineering, UNICAMP, University of Campinas, Campinas, Brazil

    Gabriel Maltese Meletti de Oliveira & Erick de Moraes Franklin

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  1. Gabriel Maltese Meletti de Oliveira
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  2. Erick de Moraes Franklin
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Correspondence to Erick de Moraes Franklin.

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Technical Editor: Jader Barbosa Jr.

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Maltese Meletti de Oliveira, G., de Moraes Franklin, E. Transitions between smooth and rough surfaces in turbulent channel flows for d- and k-type rough elements. J Braz. Soc. Mech. Sci. Eng. 40, 187 (2018). https://doi.org/10.1007/s40430-018-1113-9

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  • DOI: https://doi.org/10.1007/s40430-018-1113-9

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