Velocity fluctuations for bubbly flows at small Re

We experimentally investigate the effect of Reynolds number (Re) on the turbulence induced by the motion of bubbles in a quiescent Newtonian fluid at small Re. The energy spectra, \(E(k)\), is determined from the decaying turbulence behind the bubble swarm obtained using particle image velocimetry (PIV). We show that when Re \(\sim\) \(O\)(100), the slope of the normalized energy spectra is no longer independent on the gas volume fraction and the \(k^{-3}\) subrange is significantly narrower, where \(k\) is the wavenumber. This is further corroborated using second-order longitudinal velocity structure function and spatial correlation of the velocity vector behind the bubble swarm. On further decreasing the bubble Reynolds number (\(O(1) < \) Re \( < O(10)\)), the signature \(k^{-3}\) of the energy spectra for the bubble induced turbulence is replaced by \(k^{-5/3}\) scaling. Thus, we provide experimental evidence to the claim by \citet{mazzitelli2003effect} that at low Reynolds numbers the normalized energy spectra of the bubble induced turbulence will no longer show the \(k^{-3}\) scaling because of the absence of bubble wake and that the energy spectra will depend on the number of bubbles, thus non-universal.