Particle Clustering Algorithms to Expedite Brownout Calculations
Encounters with brownout are the leading cause of human factorrelated mishaps during military rotorcraft operations, and civilian helicopters too have suffered from the problem. The suspended dust particles can also cause rapid abrasion of the rotor blades and engine wear, creating serious and costly maintenance issues. Lagrangian formulations of the flow and particles are attractive compared to fullblown CFD calculations for studying the problem of rotorcraft brownout, because these simulations are relatively inexpensive and can capture the key physics pertinent to the understanding of the phenomenon. Further information on rotorcraft brownout and its modelling can be found here. However, the Lagrangian approach involves the tracking of many billions of dust particles in space and time over relatively long times, which obviously poses several numerical and computational challenges.
The purpose of the present work was to examine clustering approaches that could potentially be used to significantly reduce the cost of Lagrangian brownout dust cloud simulations. In principle, the application of clustering methods allows groups of particles to be tracked in that the equations of particle motion are applied to the group rather than to each of the individual particles that would otherwise make up an equivalent group. Several different particleclustering approaches are possible, which may also include the adoption of declustering and reclustering strategies. A significant disadvantage of any clustering method can be with the accumulating inaccuracies in the particle trajectories, which depends on the method used to perform the clustering. However, if it can be shown that a clustering method incurs small losses in accuracy of the particle positions for significant gains in computational time, then such methods could be very powerful computational tools to help in the simulation of brownout dust clouds.
Fig. 1: Schematic showing the kmeans method of clustering and declustering.
Fig. 2: Schematic showing the Gaussian technique of particle clustering.
Fig. 3: Schematic showing a density "packet" deforming under the velocity gradients (Osiptsov's method).
Three methods were investigated,

The kmeans clustering method is based on the principle that certain sets of individual dust particles can be decomposed into smaller groups of clusters, and that the resulting equations of motion are solved only for the clusters.

The Gaussian clustering technique assumed that each particle tracked in itself represented a cluster of particle that were distributed in a Gaussian fashion.

Osiptsov's method assumed that the particles tracked were actually density packets and these density packets can be used to reconstruct the entire dust field.
Representative Results
Fig. 4: Comparison of RMS error and CPU time between clustered and actual simulations for different number of particles when using the kmeans method.
Fig. 5: Solution obtained from brownout dust field computations when using the Gaussian clustering distribution method.
Exact solution
Osiptsov's method
By direct counting
Fig. 6: Comparison of particle density maps between exact and clustered solution using Osiptsov's method.
Publications

Govindarajan, B., Leishman, J. G., and Gumerov, N. A., "ParticleClustering Algorithms for the Prediction of Brownout Dust Clouds," AIAA Journal, Vol. 51, No. 5, pp. 1,0801,094, 2013.

Govindarajan, B., "Evaluation of Particle Clustering Algorithms in the Prediction of Brownout Dust Clouds," MS Thesis, Department of Aerospace Engineering, University of Maryland, College Park, MD, 2012.