The effects of crossing trajectories on the dispersion of particles in a turbulent flow

Abstract

The effects of ‘crossing trajectories’ and inertia on the dispersion of particles suspended in a field of grid-generated turbulence were investigated experimentally. The effect of particle trajectories crossing the trajectories of fluid elements, under the influence of a potential field (usually gravity), is to force the particles from one region of highly correlated flow to another. In this manner, particles lose velocity correlation more rapidly than the corresponding fluid points and as a result disperse less.A homogeneous decaying turbulent field was created behind a square biplanar grid in a wind tunnel. Particles were charged by a corona discharge then passed into the test section through a small plastic tube. A uniform electric field within the test section was used to simulate the effect of gravity, forcing the charged particles out of regions of correlated fluid at a higher than normal rate, therefore inducing the effects of crossing trajectories. Two sizes of glass beads (5 μm and 57 μm diameter) were employed in order to observe inertial effects. Laser-Doppler anemometry was used to measure particle mean-square displacement, autocorrelation coefficient, and mean-square velocity, from which dispersion coefficients were calculated.For the two particle sizes used in the tests, it was found that the particle diffusion coefficient, after a suitably long time from their release, was influenced primarily by the effect of crossing trajectories. Only in the particle mean-square velocity was the particle inertia seen to have any effect. The ratio of the particle relaxation time to the Kolmogoroff timescale was found to be a good indicator for the effects of particle inertia.

Lagrangian statistics for fluid particles and bubbles in turbulence

“…Yet, a full understanding of the forces that are relevant in the phenomenon is lacking. For instance, whereas strong gravity effects are known to reduce heavy particle diffusion as compared to fluid particles, the role played by inertia is less evident, even though it is often found to increase the diffusivities [11]- [13].…”

Dispersion and fall out of heavier particles

“…Fitted against wind tunnel tests of Wells and Stock (1983), the Csanady (1963) model for dispersion of larger and heavier particles than aerosols does very well against all the tests of Wells and Stokes, against wind tunnel tests of Snyder and Lumley (1971) and reasonably against the test of Csanady (1964) in the free atmosphere. The Astrup parameterization also does very well against the wind tunnel tests, but not so well against the Csanady free atmosphere tests.…”

“…Snyder and Lumley, 1971;Wells and Stock, 1983), measurements outdoor (e.g. Csanady, 1964), models tracing a number of particles describing the interaction with turbulence in different ways (e.g.…”

“…It takes the particle turbulent time scale as minimum of the fluid turbulent time scale and the fluid turbulent length scale divided by the particle free fall velocity. For the Csanady parameterization b has here not been modelled but has been fitted (b = 0.17) against the wind tunnel experiments of Wells and Stock (1983), and then tested against the wind tunnel experiments of Snyder and Lumley (1971) and the free fall experiments of Csanady (1964). The Astrup parameterization has been tested against all the experiments.…”

Two-way coupled stochastic model for dispersion of inertial particles in turbulence

“…Experiments also shed light on the multiscale interactions between the dispersed and carrier phases (Snyder & Lumley 1971;Wells & Stock 1983;Groszmann & Rogers 2004). However, in experiments, unlike in the DNS studies, it is difficult to isolate physical mechanisms that affect these multiscale interactions.…”