TY - JOUR
T1 - Modal and non-modal stabilities of flow around a stack of plates
AU - Theobald, R
AU - Mao, Xuerui
AU - Jaworski, Artur
AU - Berson, A
PY - 2015/9/1
Y1 - 2015/9/1
N2 - 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.
AB - 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.
KW - flat plates
KW - laminar wake
KW - stability
UR - http://www.scopus.com/inward/record.url?scp=84929145207&partnerID=8YFLogxK
U2 - 10.1016/j.euromechflu.2015.04.005
DO - 10.1016/j.euromechflu.2015.04.005
M3 - Article
VL - 53
SP - 113
EP - 118
JO - European Journal of Mechanics, B/Fluids
JF - European Journal of Mechanics, B/Fluids
SN - 0997-7546
ER -