Dispersion of Heavy Particles by Turbulent Motion

Accurate prediction of heavy particle dispersion in turbulent flows requires a simultaneous consideration of particle's inertia and particle's drift velocity. A mathematically simple and physically comprehensive analysis was developed to solve the dispersion statistics of heavy particles in a homogeneous and isotropic turbulent flow. Normalized particle diffusivity, rms fluctuating velocity, and Lagrangian integral time were related by algebraic equations to three dimensionless parameters: the inertia parameter, the drift parameter, and the turbulence structure parameter. When the drift parameter is large, dispersion scales are very sensitive to the inertia parameter. Heavy particles were found to disperse faster than fluid elements if the inertia parameter controls the dispersion and slower than fluid elements if the drift parameter governs the dispersion. This finding explains previous “contradictory” dispersion data observed in experimental measurements. Not only the particle time respective but also the particle velocity scale in the direction normal to the drift were shown to be less than their respective values in the direction parallel to the drift due to the effect of fluid continuity. Use of nonlinear drag law in the analysis was made possible by using an effective inertia and an effective drift. Results of the analysis were compared with numerical simulation and other analytical studies.