A turbulent bubble breakup model with application to LES

We present a new turbulent breakup model that considers a linear combination of the critical energy obtained from the deformation energy and the force criteria. The relative velocity between the bubbles and the liquid, which affects the eddy/bubble collision rate, is introduced for the first time in a turbulent breakup model and is found to play a significant role. To extend use to a wide range of turbulent flows, a full turbulent spectrum is employed in the derivation of mean turbulent eddy velocity. A collision efficiency caused by the contact angle between bubbles and eddies is introduced and an effective eddy velocity is proposed when eddy size is larger than the bubble size. In principle, the model considers all the sizes of eddies in the turbulent flow, removing the need to limit the integration range when computing the contribution of eddy sizes to the breakup rate. Two modeling constants are calibrated with experiments, and then the model is validated against other experiments. Good agreement is found for both breakup rate and bubble size distribution in different turbulent flows. When the model is tested on large eddy simulation (LES) of bubbly homogeneous isotropic turbulence, it is found that the void fraction and the pressure are strongly negatively correlated and the bubble relative velocity is affected by pressure gradients, affecting the local bubbly flow. The predicted mean bubble size distribution is almost the same as Reynolds-averaged Navier-Stokes (RANS) when the dissipation rates are low. For high dissipation rates the bubble relative velocity increases as the pressure gradients increase, playing an important role in determining the size distribution, and supporting the rationale of adding bubble relative velocity to the turbulent breakup model.