# Modeling of aerodynamic particle interaction

Sammanfattning: The purpose of the current study is to investigate the effect of particle-pair interaction for various separation distances and angular positions. The results obtained are used in a particle-laden turbulent jet flows in order to improve the existing Lagrangian Particle Tracking (LPT) models. In the first part, a detailed numerical study of particle interaction is carried out by varying the separation distances and angular positions between two-spherical-particles for wide range of Reynolds numbers. Different factors like drag, lift, wake structures, flow patterns and shedding frequencies are investigated. Volume of Solid (VOS) method based on Volume of Fluid (VOF) is used to represent the particles. Separation distances Do between the particles is varied from 1.5 to 12D (D being diameter of particle) and the angle is varied from 0 to 180. A wide range of Reynolds numbers from 10 to 600 are used. Independent of Reynolds number, greatest reduction in drag of trailing sphere is observed in tandem position i.e. when placed in the wake of leading or reference sphere and the effect can be seen even up to large separation distances of 12D. However in all positions other than tandem, the interaction effects can only be observed up to Do = 6D. The change in separation distance and angular position also affects both the magnitude and the direction of lift force. As the angular position is changed from 0 to 90, the direction of the lift force between two spheres changes from attraction to repulsion. The wake structures and flow are substantially altered at small separation distances of Do < 3D. Keeping the separation distance constant, increasing the Reynolds number upto 200 results in a delay in recovery of the sphere drag when placed in tandem arrangement. For a Reynolds number of 250, the downstream sphere undergoes greater reduction in drag upto Do less than equal to 3D and early recovery for Do > 3D compared to Re less than equal to 200. In the unsteady region i.e Re > 275-280, increasing the Reynolds number from 300 to 600 results in a greater reduction of drag of the downstream sphere at small separation distances i.e. Do < 2D and also a faster recovery of the drag for Do > 2D. Lift, wake structures and shedding frequencies are also observed to be strongly dependent on the separation distance and angular positions of particles. The results indicate the importance of particle interaction in the modeling of multi-phase flows even in the case of rather dilute flows, i.e. large inter-particle distances. This emphasis the need of including the drag and the lift forces in modeling multi-phase flows with Lagrangian Particle Transport (LPT). Based on separation distance and angle, drag and lift corrections are tabulated for different Reynolds number from 10 to 600. The corrections are incorporated in two-phase turbulent jet flows as a modifying factors for drag and lift forces in particle equation of motion. The effect of aerodynamic interaction is then analyzed by varying the Stokes numbers and mass loadings. The aerodynaimc effect is largely dependent on Stokes number and particle number density and is effective in dilute flows with void fraction on the order of 10^{-4}. The effect on particle dynamics is only observed in the radial direction at Stokes number of 314 and 50 resulting in enhanced dispersion of the particles. However, at a relatively low Stokes number flow (10), the effect is found in the axial direction also. In addition particles gain high radial velcoities which results in more dispersion compared to cases excluding aerodynamic interaction. The rms of axial velcoity fluctuations for the continuous phase along the axis of the jet is found to be large, resulting in faster decay of the axial velocity and higher radial velcoity in three-way case. The results will help in understanding and improving the current multi-phase models.

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