Abstract
Following the procedures developed in Chap. 2, the Fixed-Flux Model (FFM) is applied here to the stability of vertical bubbly flow. The virtual mass force and the interfacial pressure are introduced to obtain a conditionally well-posed TFM. Then a collision-induced pressure is considered and we adopt the interfacial collision force derived from the Enskog kinetic equation by Alajbegovic et al. (Chemical Engineering Communications 174: 85–133, 1999). When this force is incorporated into the FFM it removes the Kelvin–Helmholtz-type instability completely, resulting in an unconditionally well-posed model. These mechanisms are also associated with the acoustic and material wave speeds so they have an effect on the fidelity of the model. Therefore, while the pursuit of a complete TFM may be impractical, it is at least possible to obtain a well-posed model with the correct wave speeds. Finally, the nonlinear behavior of the well-posed FFM for bubbly flow, first analyzed by Park et al. (International Journal of Multiphase Flow 24: 1205–1244, 1998), is investigated with numerical simulations for stable flow and for kinematically unstable waves for conditions similar to a Guinness draught beer.
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de Bertodano, M.L., Fullmer, W., Clausse, A., Ransom, V.H. (2017). Fixed-Flux Model. In: Two-Fluid Model Stability, Simulation and Chaos. Springer, Cham. https://doi.org/10.1007/978-3-319-44968-5_5
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DOI: https://doi.org/10.1007/978-3-319-44968-5_5
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