Representation of Two-Phase Flows by Averaging,
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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This article considers descriptors of gas-particle aggregates which represent space averaged local properties of the aggregate. It shows that such descriptors have undulations due to the finite size of the averaging volume, and derive an estimate for the bounds of the amplitude of the undulations. According to that estimates, one obtains reasonably accurate averages only if the averaging volume contains at least 30-150 particles. In terms of the size of the averaging volume this limitation means that the diameter of the volume should equal at least four to five mean distances between particle centers. A consequence for the modeling of two-phase flows through tubes is that space averaged descriptors cannot resolve the radial structure of such flows unless the mean particle distance is much smaller than one tenth of the tube diameter. This condition excludes, for instance, the use of average descriptors for radial flow resolution of some interior ballistics flows, where the particulate phase consists of propellant grains. We also derive an approximate characterization of the boundary of a particle aggregate for different sizes of the averaging volume.