It is admitted that the (-5/3) law of the turbulent energy spectrum in single-phase flow changes into a law around (-8/3) in bubbly flow. The fact remains that it is difficult to understand why this (-8/3) bubbly flow law remains unchanged with various void fractions and with bubbles of different sizes. It's counterintuitive, isn't it? Maybe there is a simple explanation that escapes me?
Lance and Bataille (1991) were the first to report, from their homogeneous bubbly turbulence experiments (JFM, 1991), that the (-5/3) law of the turbulent energy spectrum in single-phase flow changes into a law around (-8/3) in bubbly flow. They analyzed the spectral equation and succeeded, by simplifying it and by developing scale analysis, to explain the phenomenon. Many experimental works followed later, in particular in pipe bubbly flows, and yielded the same result : all confirmed the existence of almost (-8/3) in bubbly flow. The same for all the exprimental investigations
Dear Readers, I am pleased to announce the latest publication of our work on turbulence and interfacial transfers in bubbly flows.
On turbulence and interfacial momentum transfer in dispersed gas-liquid flows:
(8) Combined Effects of the Turbulence and Interfacial Momentum Transfer On Two-Phase Turbulent Bubbly Flows | Request PDF (researchgate.net)
Just request.
Interesting paper: Innocenti, A., Jaccod, A., Popinet, S., & Chibbaro, S. (2021). Direct numerical simulation of bubble-induced turbulence. Journal of Fluid Mechanics, 918.Article Direct numerical simulation of bubble-induced turbulence
Abstract: We report on an investigation of bubble-induced turbulence. Bubbles of a size larger than the dissipative scale cannot be treated as pointwise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, bubble motions may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations with a volume-of-fluid method. In the first part of the work, we perform both two-dimensional and three-dimensional tests in order to determine appropriate numerical and physical parameters. We then carry out a highly resolved simulation of a three-dimensional bubble column, with a set-up and physical parameters similar to those used in laboratory experiments. This is the largest simulation attempted for such a configuration and is only possible thanks to adaptive grid refinement. Results are compared both with experiments and previous coarse-mesh numerical simulations. In particular, the one-point probability density function of the velocity fluctuations is in good agreement with experiments. The spectra of the kinetic energy show a clear k−3 scaling. The mechanisms underlying the energy transfer and notably the possible presence of a cascade are unveiled by a local scale-by-scale analysis in physical space. The comparison with previous simulations indicates to what extent simulations not fully resolved may yet give correct results, from a statistical point of view.
Interesting paper: Numerical simulations of the agitation generated by coarse-grained bubbles moving at large Reynolds number, November 2021 Journal of Fluid Mechanics 926
Article Numerical simulations of the agitation generated by coarse-g...
Abstract:
We present a numerical method for simulating the flow induced by bubbles rising at large Reynolds number. This method is useful to simulate configurations of large dimensions involving a great number of bubbles. The action that each bubble exerts on the liquid is modelled as a volume source of momentum distributed over a few mesh-grid elements. The flow in the vicinity of the bubbles is thus not finely resolved. The bubbles are treated as Lagrangian particles that move under the influence of the hydrodynamic force exerted by the liquid. The determination of this force on a given bubble requires knowledge of the liquid flow that is undisturbed by this bubble. A model is developed to accurately estimate this disturbance for large-Reynolds-number objects and get rid of any spurious self-induced effect. Thanks to that, a homogeneous swarm of rising bubbles is simulated. Comparisons with experiments show a good agreement with the flow scales larger than the bubbles, which turn out to be controlled by the interactions between bubble wakes and rather independent of unresolved smaller scales. This method can be used to study the coupling between bubble-induced agitation and large-scale motions, such as those produced in industrial bubble columns.
Interesting paper: Direct numerical simulation of deformable rising bubbles at low Reynolds numbers. November 2021, Physics of Fluids 33(11):113309 available on:
Article Direct numerical simulation of deformable rising bubbles at ...
A very recent paper on: Analysis and modeling of bubble-induced agitation from direct numerical simulation of homogeneous bubbly flows, April 2022, Physical Review Fluids 7(4) to be requested on:
Article Analysis and modeling of bubble-induced agitation from direc...
Abstract: In this study based on direct numerical simulations (DNS) of homogeneous bubbly flows, an analysis of velocity fluctuations is performed and a methodology for the development of a bubble-induced agitation (or pseudoturbulence) model is described. This process is based on the separation of two phenomena causing velocity fluctuations in the liquid: the agitation resulting from wakes and their collective interactions [wake-induced agitation (WIA)], which is our main focus, and the nonturbulent fluctuations resulting from averaged wakes and potential flows around bubbles [potential flow and averaged wake fluctuations (PWFs)]. We run DNS of fixed bubbles, with random spatial distribution, and compare the results to free-bubble simulations in order to build a model for those phenomena. The simulation of motionless bubbles allow the decomposition of the Reynolds stress transport equation to study WIA and PWFs separately. Then the main characteristics of bubbly flows are analyzed. The signature of an energy conversion from wake kinetic energy (PWFs) to turbulent kinetic energy (WIA) is observed, revealing the importance of nonlinear interactions and transfers between PWFs and WIA. A first proposal of model is made, which gives satisfactory results on our database for a wide range of bubble Reynolds numbers and is consistent with experimental observations. It is operational and can be implemented and assessed in an averaged code.
Merry Christmas to All Colleagues and Hope for Better Tomorrows for Humanity. Thoughts and compassion for the innocent victims of armed conflicts in Ukraine Palestine and everywhere else.
Open letter from the Palestinian Patriarch "from https://groupegaullistesceaux.fr/ (Own Translation from French)": Michel Sabbah, the former Latin Patriarch of Jerusalem, addressed the global public from the birthplace of Christ in Beit Lahm, through the "Palestine 100 Initiative" platform, for this year's Christmas. In a message dedicated to war-fallen Gaza, the Patriarch said, "Christmas this year, in Beit Lahm and all over the world, is a prayer to God Almighty, to stop the war in Gaza and all of Palestine. During these days, many direct their eyes and hearts to Beit Lahm, but only an hour away, they see the war in Gaza, where humans are buried beneath the rubble of their own homes, they see children beneath the rubble, they see humanity beneath the rubble."
He regarded the war as a genocide of Palestinians, adding that Palestinians and Christians witnessing the genocide during these specific times, "must recognize that Christmas this year should not be restricted to Beit Lahm solely but must traverse to every oppressed human, particularly on the Holy Land, and it makes its way to Gaza and all of Palestine, where death reigns supreme". The patriarch called for an end to the aggressive genocide in Gaza, calling on Christians around the world to support and defend the Palestinian cause. “Gaza deserves liberation, independence and peace,” the patriarch said, adding that the root causes of war and occupation must be investigated, as Gaza and Palestine have a long history of war.
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