A Turbulent Model for Gas-Particle Jets

This work is concerned with turbulent diffusion in gas-particle flows. The cases studied correspond to dilute flows and small Stokes number, this implies that the mean velocity of the particles is very similar to that of the fluid element. The classical $k-ε$ method is used to model the gas-phase, modified with additional terms for the k and ε equations, that takes into account the effect of particles on the carrier phase. The additional dissipation term included in the equation for k is due to the slip between phases at an intermediate scale, far from both the Kolmogorov and the integral scales. This term has a proportionality constant equal to 3/2 of Kolmogorov constant, $C0.$ In this paper, a value of 3.0 has been used for this constant as suggested by Du et al., 1995, “Estimation of the Kolmogorov Constant $C0$ for the Langarian Structure Using a Second-Order Lagrangian Model of Grid Turbulence,” Phys. Fluids 7, (12), pp. 3083–3090. The additional source term for the ε equation is taken as proportional to $ε/k,$ as is usually done. In all experiments analyzed the particles increased the dissipation of turbulent kinetic energy. A comparison is made between the results obtained with the model proposed in this work and the experiments of Shuen et al., 1985, “Structure of Particle-Laden Jets: Measurements and Predictions,” AIAA Journal, 23, No. 3, and Hishida et al., 1992, “Experiments on Particle Dispersion in a Turbulent Mixing Layer,” ASME Journal of Fluids Engineering, 119, pp. 181–194. [S0098-2202(00)02103-9]