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Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction



We examine the development of a thermal plume originating from a localized heat source using direct numerical simulation. The Reynolds number of the plume, based on source diameter and the characteristic buoyancy velocity, is chosen to be 7700, which is sufficiently large so that the flow turns to a fully turbulent state. A highly resolved grid of 622 million points is used to capture the entire range of turbulent scales in the plume. Here at the source, only heat has been added with no mass or momentum addition and accordingly the vertical evolution of the mass, momentum and buoyancy fluxes computed from the simulation have been verified to follow those of a pure thermal plume. The computed vertical evolution of the time-averaged centreline velocity and temperature are in good agreement with available experimental measurements. Investigation of the time evolution of the plume shows periodic formation of vortex ring structure surrounding the main ascending column of hot fluid. The vortex ring forms very close to the heat source and even at formation it is three-dimensional. The vortex ring ascends with the plume and at an elevation of about two diameters it strongly interacts with and destabilizes the central column and subsequently a complex turbulent flow arises. Thus, relatively laminar, transitional and fully turbulent regimes of the plume evolution can be identified. In the fully turbulent regime, complex three-dimensional hairpin-like vortex structures are observed; but vestiges of the coherent vortex rolls that form close to the source can be observed in the turbulent statistics. It is shown that local entrainment consists of contraction and expulsion phases. Such instantaneous mechanisms drive the entrainment process, and the instantaneous entrainment coefficient shows large variation in both time and space with local values up to three times higher than the average entrainment level. Such findings support the view that entrainment mechanisms in plumes should be considered from an unsteady point of view. Movies are available with the online version of the paper.



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Plourde et al. supplementary movie
Movie 1. A three-dimensional isosurface of vorticity with time; a puffing mechanism, i.e. vorticity concentration, in the very close vicinity of the source is detected. The flow is computed by direct numerical simulation in a square domain of 5Dx5Dx8D (where D is the diameter of the circular heat source) and with grid resolution of 720x720x1200. The Reynolds number of the plume, based on source diameter and characteristic buoyant velocity, is 7700. Above the vertical location of the puffing phenomenon a more complex topology is observed and an intense vortical region is mainly organized as hairpin structures. These vortex structures principally populate the high-shear region that surrounds the main ascendant flow field. The hairpin vortical structures clearly interlace with each other in a complex way as is typically the case in a turbulent flow. Simulated time shown is 27 time units. The movie corresponds to figure 4 in the paper.

 Video (7.1 MB)
7.1 MB

Plourde et al. supplementary movie
Movie 2. To better emphasize structures involved in the main ascendant process, the same data were used to compute the imaginary part of the complex-conjugate eigenvalues of the local velocity gradient tensor. Structures are mainly hairpin shaped, rolling around the main ascendant flow. In addition, it is obvious that strong interactions between structures develop at the periphery of the plume where dissipation is driven by buoyancy.

 Video (7.5 MB)
7.5 MB


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