Modal and non-modal stabilities of flow around a stack of plates

Theobald, R.; Mao, X.; Jaworski, A.J.; Berson, A.

Abstract

Modal and non-modal stabilities of flow around a stack of flat plates are investigated by means of asymptotic stability and transient growth analyses respectively. It is observed that over the parameters considered, both the base flow and the stabilities vary as a function of ReW2/(W−1)2, i.e. the product of the Reynolds number and the square of the expansion ratio of the stack. The most unstable modes are found to be located downstream of the recirculation bubble while the global optimal initial perturbations (resulting in maximum energy growth over the entire domain) and the weighted optimal initial perturbations (resulting in maximum energy growth in the close downstream region of the stack) concentrate around the stack end owing to the Orr mechanism. In direct numerical simulations (DNS) of the base flow initially perturbed by the modes, it is noticed that the weighted optimal initial perturbation induces periodic vortex shedding downstream of the stack much faster than the most unstable mode. This observation suggests that the widely reported vortex shedding in flow around a stack of plates, e.g. in thermoacoustic devices, is associated with perturbations around the stack end.

Citation

Theobald, R., Mao, X., Jaworski, A., & Berson, A. (2015). Modal and non-modal stabilities of flow around a stack of plates. European Journal of Mechanics - B/Fluids, 53, 113-118. https://doi.org/10.1016/j.euromechflu.2015.04.005

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2015
• Publication Date: Sep 1, 2015
• Deposit Date: Apr 23, 2015
• Publicly Available Date: Apr 23, 2015
• Journal: European Journal of Mechanics - B/Fluids
• Print ISSN: 0997-7546
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Pages: 113-118
• DOI: https://doi.org/10.1016/j.euromechflu.2015.04.005
• Keywords: Laminar wake, Flat plates, Stability.
• Public URL: https://durham-repository.worktribe.com/output/1439991