Decoupling The Role Of Inertia And Gravity On Particle Dispersion

Turbulent gas flows laden with small, dense particles are encountered in a wide number of important applications in both industrial settings and aerodynamics applications. Particle interactions with the underlying turbulent flow are exceedingly complex and, consequently, difficult to accurately model. The difficulty arises primarily due to the fact that response of a particle to the local environment is dictated by turbulence properties in the reference frame moving with the particle (particle-Lagrangian). The particleLagrangian reference frame is in turn dependent upon the particle relaxation time (time constant) as well as gravitational drift. The combination of inertial and gravitational effects in this frame complicates our ability to accurately predict particle-laden flows since measurements in the particle-Lagrangian reference frame are difficult to obtain. Therefore, in this work we will examine separately the effects of inertia and gravitational drift on particle dispersion through a combination of physical and numerical experiments. In this study, particle-Lagrangian measurements will be obtained in physical experiments using stereo image velocimetry. Gravitational drift will be varied in the variable-g environments of the NASA DC-9 and in the zero-g environment at the drop tower at NASA-Lewis. Direct numerical simulations will be used to corroborate the measurements from the variable-g experiments. We expect that this work will generate new insight into the underlying physics of particle dispersion and will, in turn, lead to more accurate models of particle transport in turbulent flows. Introduction In modeling particle-laden flow, one must have a fundamental understanding of how the particle responds to local turbulence. Defining this turbulence is probably the greatest difficulty in deriving an accurate model. The difficulty arises from the fact that each particle navigates a unique path through the flow: a path dictated by its inertia and gravitational drift. This path, dubbed the particle-Lagrangian reference frame, is neither the purely Lagrangian path of a fluid point, nor the conventional stationary Eulerian reference frame. Particle inertia affects the turbulence experienced by the particle as particles are flung from one fluid neighborhood to another, and gravity affects the path by pulling the particle through the turbulence. To accurately model the behavior of the particle, one must decouple the effects of the gravitational drift from those resulting from the inertia of the particle: this is the goal of the proposed research. If one imagines a turbulent fluid field consisting of a random assortment of various size eddies, then the turbulence can be partially characterized by a power spectrum: a measure of the distribution of the turbulent kinetic energy among these eddies. The behavior of an individual particle will depend on how quickly a particle can respond to these fluctuations in the fluid velocity. For instance, small (high frequency) eddies will have little effect Decoupling the Role of Inertia and Gravity on Particle Dispersion 1 on particles with slow response times (large time constants) and, conversely, large (low frequency) eddies will have little difficulty in influencing all but the most sluggish particles. The apparent frequency of the eddy experienced by the particle, however, will be a function of the particle velocity. Similar to an acoustic Doppler shift, as the particle moves through an eddy, the frequency it responds to will be a function of the particle velocity as well. Finally, to further complicate modeling, as it crosses the eddies due to its gravitational drift, it moves from one fluid neighborhood to another. This is known as the “crossing-trajectories” effect1, and plays an active role in the particle dispersion2.