CFD application cases involving particle-laden flows (pt 3)

CASE 3: Turbulence Modulation in Gas-Solid Two-Phase Jets
Two-phase flows, in which discrete particles are dispersed within a continuous gas or liquid phase, are of interest in many engineering applications. Examples of such applications are fuel sprays in combustion engines and burners, solids transport in a process plant, solid particles in exhaust plumes, etc. The majority of practical applications are turbulent, and whilst many models are available for simulating the fluid turbulence, the most commonly used turbulence model is the k-ε model. The presence of a second, dispersed phase within a turbulent flow can have significant effect on both the turbulence and mean field. As the mass loading ratio, defined as the mass flow rate of the dispersed phase to that of the continuous phase, is increased, the effect of the particles on the carrier-fluid’s turbulent transport of mass, momentum, and energy becomes more pronounced, and this can have a significant effect on the flow system.

Two-phase systems can be modelled via an Eulerian-Lagrangian (GENTRA) or Eulerian-Eulerian description. As we have seen with the dust-catcher example, GENTRA simulates the solid phase by following the trajectories of all the particles. The Eulerian–Eulerian approach models treats both phases as continua, and so the solid phase is modelled as a second continuous interpenetrating fluid. In PHOENICS, this approach is called IPSA (Inter-Phase Slip Analyser).

This case study considers the near-field development of a submerged turbulent round jet of air laden with solid particles, as studied experimentally by Modarress et al. [1984]. The jet issues into a low-velocity free stream and the nozzle-to-stream velocity ratio is 205. The discharge Reynolds number is 13,300, the density ratio is 2538, the particle-to-air mass-flow ratio is 0.85, and the particle diameter is 50 μm. This case has been simulated by Hamill and Malin [1991] using GENTRA, but here IPSA is used to compute the two-phase flow of gas and particles. Two calculations are made, one with the standard k-ε model, and one with the modified k-ε model of Mostafa-Mongia [1988], which allows for gas turbulence modulation due to the presence of particles. This is done by introducing source terms in the turbulence-model transport equations. Alternative and more recent formulations of the turbulence-modulation source terms have been used by Yan et al [2006] and Messa & Malavasi [2014] for other applications.

Turbulence modulation may cause an increase or a decrease in the turbulence level of the carrier phase depending on the ratio of the particle diameter to turbulent integral length scale. Particles suppress turbulence if the ratio is less than about 0.1, and the opposite effect is observed if the ratio is greater than this value. The round-jet measurements showed than an increasing the mass loading of particles reduces the turbulence and jet spreading.
Figures 8 and 9 show respectively gas axial-velocity contour plots for the standard k-ε model and the Mostafa-Mongia k-ε model. The latter damps the turbulence leading to a narrower jet with a reduced spreading rate and reduced rate of decay of the centre-line velocity.

The predicted jet half-width spreading rates associated with each of the foregoing contour plots are as follows: 0.087 and 0.054 for the standard and modified k-ε models, respectively. A simulation without particles produced a spreading rate of 0.1, which is somewhat higher than the measured value of 0.086. This is the so-called round-jet anomaly, which may be cured by modifying the model coefficients, as done by Hamill and Malin (1991), or by introducing a vortex-stretching source term into the ε-transport equation. The suppression of turbulence by the addition of particles is in agreement with the experimental findings of Modarress et al (1984).

Hamill and Malin (1991) reported a spreading rate of 0.041 for a particle laden jet using GENTRA with a mass-flow ratio of 0.85. This is similar to the present result of 0.054 using IPSA and unmodified turbulence-model model coefficients. No experimental spreading rates were reported by Modaress et al (1984), and further work is needed to validate the model against measurements of the mean velocity and turbulence profiles, as well as the centre-line velocity decay.

References

• Hamill,I.S., Malin, M.R., “Turbulence Modulation due to the presence of particles”, CHAM Ltd., PHOENICS J, Vol.4, Supp.II, p212 (1991).
• Messa, G.V., Malavasi, S., “Numerical prediction of dispersed turbulent liquid-solid flows in vertical pipes”, J.Hyd.Reseacrh, Vol.52, No.5, 684-692 (2014).
• Modarress,M., Tan, H., Elghobashi, S., “Two-component LDA measurement in a two-phase turbulent jet”, AIAA Journal Vol.22 No.5, 624-630 (1984).
• Mostafa, A.A. and Mongia, H.C., “On the interaction of particles and turbulent fluid flow. Int. J. Heat Mass Transfer, 31(10), 2063–2075 (1988).
• Yan, F., Lightstone, M.F., Wood, P.E., “A mathematical model of turbulence modulation in particle-laden flows”, Int. J. CFD, Vol.20, No.1, 37-44 (2006).