Two-fluid model simulations of a bubbly vertical jet are presented. The purpose of these simulations is to assess the modeling of turbulence dispersion and lift forces in a free shear flow. Although turbulence dispersion forces have previously been validated using simpler canonical flows and microscopic particles or bubbles, there was a need to asses the model performance for larger bubbles in more turbulent flows. This method, of validating two-fluid models in flows of increasing complexity has the advantage of excluding, or at least minimizing, the possibility of cancellation of errors when modeling several forces. In a companion paper (see Part-II), the present two-fluid model is extended to a boundary layer in which forces induced by the presence of a wall are important. The turbulent dispersion models used herein are based on the application of a kinetic transport equation, similar to Boltzmann’s equation, to obtain the turbulent diffusion force for the dispersed phase [1, 2]. They have already been constituted and validated for the case of particles in homogeneous turbulence and jets  and for microscopic bubbles in grid generated turbulence and mixing layers . It was found that it is possible to simulate the experimental data in Ref.  (See Figures-1 to 4) for a bubbly jet with 1 mm diameter bubbles. Good agreement is obtained using the model of Brucato et al.  for the modulation of the drag force by the liquid phase turbulence and a constant lift coefficient, CL. However, little sensitivity is observed to the value of the lift coefficient in the range 0 < CL < 0.29.
The Modeling of Lift and Dispersion Forces in Two-Fluid Model Simulations: Part I — Jet Flows
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Lopez de Bertodano, M, Moraga, FJ, Drew, DA, & Lahey, RT, Jr. "The Modeling of Lift and Dispersion Forces in Two-Fluid Model Simulations: Part I — Jet Flows." Proceedings of the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. Volume 1: Fora, Parts A, B, C, and D. Honolulu, Hawaii, USA. July 6–10, 2003. pp. 1787-1792. ASME. https://doi.org/10.1115/FEDSM2003-45557
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