Influence of vortex street structure on the efficiency of energy separation

Abstract

Regions with reduced and increased values of total enthalpy are observed in a time-averaged flow behind a bluff body. This energy redistribution takes place both in the vortex formation region and in the developed vortex wake. The present paper focuses on studying the effect of the structure of a vortex street on the intensity of energy redistribution. Two approaches are used. The first one is direct numerical simulation of the flow behind a transversely oscillating cylinder, which is known for a variety of vortex patterns in the wake. The simulations are based on a finite element solution of the Navier-Stokes equations for a compressible perfect viscous gas. The second approach is based on simplified point vortex models for infinite periodic vortex streets, which contain a finite number of vortex chains in equilibrium. It turns out that these simple models make it possible to obtain satisfactory qualitative results, particularly if a more precise approximation of velocity fields in the vortex cores (Rankine vortices) is implemented. It is shown that the effect of energy redistribution significantly depends on the vortex structure, namely the mutual arrangement of the vortices and their intensities. The estimates of the energy separation efficiency in the time-averaged flow are obtained for the general case of an arbitrary number of chains. A more detailed analysis is performed for vortex streets with 2, 3, and 4 vortex chains.

The Eckert–Weise effect and energy separation under the flow interference behind side-by-side cylinders

“…(1987) gave the relation between the total enthalpy and the parameters of the vortex street (period of street , vortex circulation and its velocity in the reference frame fixed to the cylinder) as where time-averaged values are denoted by overbars. Aleksyuk (2019) considered a similar model in the general case of wake structures consisting of vortex chains and demonstrated quite good agreement of the obtained estimates with the numerical results considering local regions of a two-dimensional wake behind a transversely oscillating circular cylinder. Thus, having a specific structure of the wake, one can estimate total enthalpy redistribution based on simple point vortex models.…”

“…This ambiguity is related to the fact that the increase in with other parameters fixed can lead to the increase of the velocity defect simultaneously decreasing the velocity of vortices . The described model allows estimation of the intensity of energy separation for specific wake patterns, as was shown in Aleksyuk (2019) by comparison with the numerical simulations assuming a weak dependence of the wake structure on .…”

“…The idea was applied in Kurosaka et al. (1987) for the classical staggered Kármán street and further generalised in Aleksyuk (2019) for arbitrary periodic vortex wakes, which are formed by infinite chains of vortices.…”

“…In this regard, the understanding of energy separation processes in canonical problems such as a flow around cylinders with the effects of interference is of substantial importance. It allows one to model various interactions of the forming vortices with the rear part of the body surface and the structures of the formed wakes, which determines the intensity of the Eckert-Weise effect (Aleksyuk & Osiptsov 2018) and correspondingly the degree to which the total enthalpy can be lowered in the central part of the wake (Kurosaka et al 1987;Aleksyuk 2019).…”

“…It allows one to model various interactions of the forming vortices with the rear part of the body surface and the structures of the formed wakes, which determines the intensity of the Eckert–Weise effect (Aleksyuk & Osiptsov 2018) and correspondingly the degree to which the total enthalpy can be lowered in the central part of the wake (Kurosaka et al. 1987; Aleksyuk 2019).…”