Flow visualisation and fundamental aspects of two-dimensional turbulent plumes
Understanding the behaviour of turbulent, buoyant plumes is fundamental to modelling a multitude of fluid dynamics problems, for example, indoor airflows. Specifically, this thesis focuses on the turbulent plumes which develop above sources which directly supply buoyancy, but zero momentum, to the fluid. Sources of this type are particularly relevant to modelling the convective flows driven by underfloor heating in rooms. Indeed this form of heating underpinned the interest of the financial sponsor of the research presented herein. Remarkably, whilst the subject of a considerable body of research, this work begins by uncovering the fact that the far-field plume that forms above a heated plate is not well modelled by existing plume theory. The principle means of flow visualisation employed in this research to observe these plumes is shadowgraphy. Perhaps surprisingly, much of the underpinning theory of this method has, to date, been restricted to the case where the flow field of interest is illuminated by collimated light (i.e. illuminating light rays are parallel to each other). This is despite the fact that practical light sources produce a beam of light which diverges. The turbulent convective flow in the vicinity of a uniformly heated semi-infinite plate is investigated experimentally and theoretically. Guided by bespoke experimental observations, governing equations representing the conservation of mass, momentum and energy for this geometry are posed. On making the Boussinesq assumption, it is demonstrated that a so-called `horizontal plume' grows linearly from the plate edge. It is shown that in this near-plate region the mean horizontal velocity and mean buoyancy scale proportionally and inverse proportionally to the cube root of the distance from the plate edge, respectively. A theoretical model for the far-field flow above a uniformly heated two-dimensional plate is developed by considering the merger of two 'horizontal plumes', which grow linearly from both edges of the two-dimensional plate. New experimental data is combined with the analytical model to identify an 'apparent source', from which the results of classic plume theory can be applied. As a result, the applicability of existing analytical plume theory is extended to an entire class of buoyancy sources to which it previously could not be applied; namely, finite area sources that supply zero momentum to the fluid, for example heated surfaces. The new ability to model the convective flow above a heated surface is a fundamental step towards developing accurate, analytical predictive models for the environmental conditions resulting from underfloor heating. Whilst this was of particular interest to the financial sponsor, the wider applications encompass modelling the flow that develops from any two-dimensional area source of buoyancy including the convective flow above long sections of road heated by the sun, or the cool plumes that descend below chilled ceiling beams, for example. In order to aid the interpretation of thermal plumes visualised using the shadowgraph method, including those of interest herein, existing shadowgraph models are extended to the practical case where diverging incident light is used to illuminate the flow field. Contrary to the standard case where collimated incident light is used this results in shadowgrams which contain information about the spatial gradients of the refractive index field in three, rather than two, directions. The role of a co-flowing ambient fluid on the behaviour of turbulent planar plumes is then examined. Conservation equations are derived and their solution demonstrates that the plume behaviour is governed by a plume source Richardson number and a non-dimensional co-flow strength. For planar plumes emanating into a quiescent, unstratified environment there is single source Richardson number that results in an invariant local Richardson number at all heights. This result is extended to the case where a co-flow is present and it is demonstrated that this dynamical invariance is achieved for any pair of scaled source Richardson number and co-flow strength that sum to unity. It is also demonstrated that under certain conditions, the co-flow reduces the dilution of a plume, in some cases causing a concentration of buoyancy. A potential application of which is delivering cool air from a chilled beam at ceiling level, to occupants within a room, whilst minimising the dilution (and warming) of this air.
Buoyancy, Plume, Shadowgraph, Turbulence
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