Influence of wavy surfaces on coherent structures in a turbulent flow |
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Authors: | Simon Kuhn Carsten Wagner Philipp Rudolf von Rohr |
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Institution: | (1) Institute of Process Engineering, ETH Zurich, Sonneggstrasse 3, 8092 Zurich, Switzerland |
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Abstract: | We describe how outer flow turbulence phenomena depend on the interaction with the wall. We investigate coherent structures
in turbulent flows over different wavy surfaces and specify the influence of the different surface geometries on the coherent
structures. The most important contribution to the turbulent momentum transport is attributed to these structures, therefore
this flow configuration is of large engineering interest. In order to achieve a homogeneous and inhomogeneous reference flow
situation two different types of surface geometries are considered: (1) three sinusoidal bottom wall profiles with different
amplitude-to-wavelength ratios of α = 2a/Λ = 0.2 (Λ = 30 mm), α = 0.2 (Λ = 15 mm), and α = 0.1 (Λ = 30 mm); and (2) a profile consisting of two superimposed sinusoidal
waves with α = 0.1 (Λ = 30 mm). Measurements are carried out in a wide water channel facility (aspect ratio 12:1). Digital
particle image velocimetry (PIV) is performed to examine the spatial variation of the streamwise, spanwise and wall-normal
velocity components in three measurement planes. Measurements are performed at a Reynolds number of 11,200, defined with the
half channel height h and the bulk velocity U
B. We apply the method of snapshots and perform a proper orthogonal decomposition (POD) of the streamwise, spanwise, and wall-normal
velocity components to extract the most dominant flow structures. The structure of the most dominant eigenmode is related
to counter-rotating, streamwise-oriented vortices. A qualitative comparison of the eigenfunctions for different sinusoidal
wall profiles shows similar structures and comparable characteristic spanwise scales Λ
z
= 1.5 H in the spanwise direction for each mode. The scale is observed to be slightly smaller for α = 0.2 (Λ = 15 mm) and slightly
larger for α = 0.2 (Λ = 30 mm). This scaling for the flow over the basic wave geometries indicates that the size of the largest
structures is neither directly linked to the solid wave amplitude, nor to the wavelength. The characteristic spanwise scale
of the dominant eigenmode for the developed flow over the surface consisting of two superimposed waves reduces to 0.85 H. However, a scale in the order of 1.3 H is identified for the second mode. The eigenvalue spectra for the superimposed waves is much broader, more modes contribute
to the energy-containing range. The turbulent flow with increased complexity of the bottom surface is characterized by an
increased number of dominant large-scale structures with different spanwise scales. |
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Keywords: | |
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