A dissipation transport equation for the carrier phase turbulence in particle-laden flow is derived from fundamental principles. The equation is obtained by volume averaging the same equation used for single phase flows. This process yields three additional terms that reflect the effect of the particles; these terms are evaluated assuming Stokes flow around the particles. Two of the terms reduce to zero and only one term remains which is identified as the production of dissipation due to the particles. The dissipation equation for the standard k-ε model is reformulated to include the additional term. The equation is then applied to the case of particles falling in an initially quiescent fluid and experimental data are used to evaluate the empirical coefficients. The ratio of the coefficient for the production of dissipation (due to the presence of particles) to the coefficient for the dissipation of dissipation is found to correlate well with the relative Reynolds number.
Volume Average Turbulence Dissipation Equation for Multiphase Flow
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Schwarzkopf, JD, Crowe, CT, & Dutta, P. "Volume Average Turbulence Dissipation Equation for Multiphase Flow." Proceedings of the ASME 2008 International Mechanical Engineering Congress and Exposition. Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C. Boston, Massachusetts, USA. October 31–November 6, 2008. pp. 1827-1832. ASME. https://doi.org/10.1115/IMECE2008-67455
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