Study on the Eulerian dispersed phase equations in non-uniform turbulent two-phase flows: discussion and comparison with experiments

Abstract

Abstract The work presented here analyses the underlying mechanisms in the continuum equations for non-colliding particles in dilute non-uniform two-phase flows. The study is carried out for axisymmetric particle-laden gas jets, which constitute a good example of non-uniform flow. Equations of radial and axial momentum and turbulent kinetic energy for the particulate phase are divided into their basic terms and analysed separately. As a result, for high inertia particles, the modelling of the `interaction terms' (terms due to gas–particle interaction) reveals itself as the crucial point, as long as they drive the existing equilibrium in the Eulerian particle equations. The hypotheses used to model the dispersed phase Reynolds stresses are in accordance with the previous theoretical work of Reeks (Reeks, M.W., 1993. On the constitutive relations for dispersed particles in non-uniform flows I: Dispersion in a simple shear flow. Phys. Fluids A 5, 750–761): the normal stresses in the streamwise direction are enhanced over the corresponding ones in the other directions and the former prevail over the shear stresses in the limit of great inertia particles, too. This particle Reynolds stress modelling is found to be directly related with the correct prediction of the dispersion of the corresponding volume fraction profile, α d , in the considered experiments. Moreover, the information obtained from the balance of present contributions in the radial momentum equation confirms a previously used closure of radial relative velocity as proportional to the gradient of particle void fraction (Ishii, M., 1975. Thermo-fluid dynamic theory of two-phase flow, Eyrolles; Lee, S.L., Wiesler, M.A., 1986. Theory on transverse migration of particles in a turbulent two-phase suspension flow due to turbulent diffusion. Int. J. Multiphase Flow 12, 99–111; Simonin, O., 1990. Eulerian formulation for particle dispersion in turbulent two-phase flows. In: Proceedings of the 5th Workshop on Two-Phase Flow Predictions, Erlangen, Germany). This effect is the ultimate responsible for the spreading of α d along the jet. Comparisons of numerical calculations with the experiments of Mostafa et al. (Mostafa, A.A., Mongia, H.C., McDonell, V.G., Samuelsen, G.S., 1989. Evolution of particle laden jet flows: A theoretical and experimental study. AIAA J. 27, 167–183) are provided showing reasonable agreement in all available variables, included the particulate normal Reynolds stresses.