Energy spectra and bubble velocity distributions in pseudo-turbulence: Numerical simulations vs. experiments

Direct numerical simulations (DNS) are performed to study the behavior of a swarm of rising air bubbles in water, employing the front tracking method, which allows to handle finite-size bubbles. The swarms consist of monodisperse deformable 4 mm bubbles with a gas fraction of 5% and 15%. This paper focuses on the comparison of the liquid energy spectra and bubble velocity probability density functions (PDFs) with experimental data obtained by phase-sensitive constant-temperature anemometry (CTA) and three-dimensional particle tracking velocimetry (PTV), respectively.The numerical simulations confirm that the spectra of the velocity fluctuations driven by the rising bubbles follow a power law with slope close to −3, supporting the idea that the dissipation of the bubble wake is the origin of this spectral scaling, as previously proposed by Lance and Bataille.The computed PDFs of the bubble velocity show non-Gaussian features, as is also observed in the experiments. The agreement with experimental measurements is especially good in the peak region, whereas the tails of the experimental PDFs show more intermittency in comparison to the numerical results. This can be explained by the lack of large-scale flow structures in the simulations, and by the large difference in measurement time.

► The scaling of the energy spectra of liquid fluctuations in pseudo-turbulence is close to −3.
► This scaling is a result of bubble’s wake phenomena, which are explicitly solved by our model.
► We show that the simulation time is crucial for achieving statistical convergence in the scaling of the spectrum.
► We show that both experimental and numerical bubble velocity PDFs agree and are different from a Gaussian distribution.