Proper orthogonal decomposition analysis of lid-driven cavity flows containing particle suspensions
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Previous experiments done on the square lid driven cavity have shown that its stability and transitional behavior, and by extension the behavior of more complex flows, can be greatly modified by introducing systematic disturbances called perturbations to its flow field. In this study, a square lid driven cavity is calculated in two-dimensional space and perturbed by means of particles suspended in the flow. The perturbations manifest as subtle changes in the flow field velocity and overall flow structure, these are caused by the particle-fluid drag interaction and the particle-particle collision interaction. To understand the nature of these changes and their ramifications particles are suspended in the base lid driven cavity flow and the base flow is subtracted to isolate the disturbances produced across the flow field. The dominant flow structures of this resultant field, referred to as the difference velocity, are then identified and characterized by means of an eigenvector and eigenvalue analysis called proper orthogonal decomposition. Relationships are then drawn between dominant eigenvectors and eigenvalues, representing the dominant perturbation modes and their contributions respectively. This is carried out at area fractions of 5%, 25%, and 50% particle suspension and Reynolds numbers of 100, 400, and 1000 in hopes of seeing over which ranges a certain mode is dominant and when/if changes in critical transitions and flow structures occur in relation to the base flow. Finally, the implications are discussed in the context of particle suspension flow behavior and recommendations for future studies are made.