The evolution of energy in flow driven by rising bubbles - Physics > Fluid DynamicsReport as inadecuate

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Abstract: We investigate by direct numerical simulations the flow that rising bubblescause in an originally quiescent fluid. We employ the Eulerian-Lagrangianmethod with two-way coupling and periodic boundary conditions. In order to beable to treat up to 288000 bubbles, the following approximations andsimplifications had to be introduced: i The bubbles were treated aspoint-particles, thus ii disregarding the near-field interactions among them,and iii effective force models for the lift and the drag forces were used. Inparticular, the lift coefficient was assumed to be 1-2, independent of thebubble Reynolds number and the local flow field. The results suggest that largescale motions are generated, owing to an inverse energy cascade from the smallto the large scales. However, as the Taylor-Reynolds number is only in therange of 1, the corresponding scaling of the energy spectrum with an exponentof -5-3 cannot develop over a pronounced range. In the long term, the propertyof local energy transfer, characteristic of real turbulence, is lost and theinput of energy equals the viscous dissipation at all scales. Due to the lackof strong vortices the bubbles spread rather uniformly in the flow. Themechanism for uniform spreading is as follows: Rising bubbles induce a velocityfield behind them that acts on the following bubbles. Owing to the shear, thosebubbles experience a lift force which make them spread to the left or right,thus preventing the formation of vertical bubble clusters and therefore ofefficient forcing. Indeed, when the lift is artifically put to zero in thesimulations, the flow is forced much more efficiently and a more pronouncedenergy accumulates at large scales is achieved.

Author: Irene Mazzitelli, Detlef Lohse


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