Journal of Fluid Mechanics

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On bubble clustering and energy spectra in pseudo-turbulence

JULIÁN MARTÍNEZ MERCADOa1 c1, DANIEL CHEHATA GÓMEZa1, DENNIS VAN GILSa1, CHAO SUNa1 and DETLEF LOHSEa1

a1 Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

Abstract

Three-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulence.

(Received April 21 2009)

(Revised November 20 2009)

(Accepted November 22 2009)

(Online publication March 24 2010)

Correspondence:

c1 Email address for correspondence: j.martinezmercado@tnw.utwente.nl

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