ORCID Profile
0000-0002-0780-0911
Current Organisations
USDA Agricultural Research Service
,
University of Bristol
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Publisher: Cambridge University Press (CUP)
Date: 10-02-2002
DOI: 10.1017/S0022112001006917
Abstract: By experiments and supporting computations we investigate two methods of transport enhancement in two-dimensional open cellular flows with inertia. First, we introduce a spatial dependence in the velocity field by periodic modulation of the shape of the wall driving the flow this perturbs the steady-state streamlines in the direction perpendicular to the main flow. Second, we introduce a time dependence through transient acceleration–deceleration of a flat wall driving the flow surprisingly, even though the streamline portrait changes very little during the transient, there is still significant transport enhancement. The range of Reynolds and Reynolds–Strouhal numbers studied is 7.7[les ] Re [les ]46.5 and 0.52[les ] ReSr [les ]12.55 in the spatially dependent mode and 12[les ] Re [les ]93 and 0.26[les ] ReSr [les ]5.02 in the time-dependent mode. The transport is described theoretically via lobe dynamics. For both modifications, a curve with one maximum characterizes the various transport enhancement measures when plotted as a function of the forcing frequency. A qualitative analysis suggests that the exchange first increases linearly with the forcing frequency and then decreases as 1/ Sr for large frequencies.
Publisher: AIP Publishing
Date: 03-1999
DOI: 10.1063/1.166398
Abstract: The algorithm of Reference 1992 is presented as a method for identification of invariant reduced-order manifolds for stable systems which exhibit dynamics with a time-scale separation. While this method has been published previously in the literature, theoretical justification for the algorithm was not presented in the original work. Here, it will be shown rigorously that the algorithm correctly identifies the slow manifold. Before the theoretical results are presented, a brief background on the behavior of singularly perturbed systems is presented. The algorithm of Reference 1992 is then introduced. This method will be applied to two different ex les, a distillation column and a two-phase chemical reactor. For each of these ex les, the resulting reduced-order description will be compared to other standard methods of producing reduced-order models. In addition, some preliminary thoughts on how this method can be used to form reduced-order models are presented.
Publisher: AIP Publishing
Date: 20-10-2006
DOI: 10.1063/1.2357333
Abstract: Flockerzi and Heineken [Chaos 16, 048101 (2006)] present two ex les with the goal of elucidating issues related to the Maas and Pope method for identifying low dimensional “slow” manifolds in systems with a time-scale separation. The goal of their first ex le is to show that the result claimed by Rhodes et al. [Chaos 9, 108-123 (1999)] that the Maas and Pope algorithm identifies the slow invariant manifold in the situation in which there is finite time-scale separation is incorrect. We show that their arguments result from an incomplete understanding of the situation and that, in fact, their ex le supports, and is completely consistent with, the result in Rhodes et al.. Their second ex le claims to be a counterex le to a conjecture in Rhodes et al. that away from the slow manifold the criterion of Maas and Pope [Combust. Flame 88, 239-264 (1992)] will never be fulfilled. While this conjecture may indeed be false, we argue that it is not clear that the ex le presented by Flockerzi and Heineken is indeed a counterex le.
Location: United States of America
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Stephen Wiggins.