Buoyancy effects in fluids

Buoyancy effects in fluids

Many environmental flows are either driven by or strongly influenced by density differences. Many of these are associated with either natural hazards (e.g. wildfire plumes and volcanic plumes) or man-made hazards (e.g. industrial plumes and dense gas leaks). Density difference can also be used to drive air flows in buildings  and reduce building energy consumption.

Plume theory

There is a vast literature on the behavior of plumes formed by the continuous release of buoyant fluid into an environment that is either stratified or unstratified, and/or quiescent or flowing. A recent collaboration with Matthew Scase of Nottingham University (UK) examined the far-field behavior of plumes in a power-law stratification, plumes with internal buoyancy changes due to chemical reactions, and plumes with time varying source buoyancy. We showed that the far-field behavior in all these flows can be established algebraically by re-writing the plume equations in terms of the local plume Richardson number and radius (Kaye & Scase 2011).

Ali Tohidi has investigated the behavior of plumes in a power-law boundary layer velocity profile. Ali has established the scaling of the momentum and volume fluxes with distance along the plume centerline and we are working to establish the criteria for when it is important to include the boundary layer velocity profile in a trajectory model.

A recent sabbatical in Australia led to a collaboration with Prof. Paul Cooper on vertically distributed sources of buoyancy. We investigated the impact of non-ideal source and boundary conditions on the plume formed by a source of buoyancy distributed over a vertical surface. We showed that the source conditions play a role in the plume structure at all heights and that failure to account for source conditions can lead to miss-measurement of the plumes entrainment coefficient.

Dense gas dispersion 

Dense gas release in urban areas is a major hazard. There are several examples of chlorine tankers rupturing in urban areas over the past few years. Plans for large scale carbon sequestration will require the transportation significant quantities of CO2 through pipes that could be released into built up areas in the case of a pipe leak.

Zahra Baratian-Ghorghi investigated the flushing of a finite release of dense gas from a simple urban canyon. The rate of flushing depends on the flow Richardson number and the canyon geometry (Baratain-Ghorghi & Kaye 2013). For low Richardson number (relatively low density or high wind speed) the density of the gas plays no role in the dispersion rate. However, as the Richardson number increases vertical mixing is suppressed and the canyon becomes strongly stratified during the flushing (Baratain-Ghorghi & Kaye 2013). The transition from a continuously stratified canyon to a canyon with a sharp two-layer stratification occurred at the peak in the mixing efficiency of the flow (Baratain-Ghorghi & Kaye 2012). Zahra also ran a series of steady-state flushing
experiments in which there was a continuous release of dense fluid at the canyon base. Zahra showed that the mixing rate measured using the finite release technique and the continuous release technique results in the same result. She then developed a two parameter entrainment model to quantify both the interfacial mixing and skimming of dense fluid across the top of the density interface (Baratain-Ghorghi & Kaye 2013).

Building ventilation

There are two standard reduced order models for natural ventilation. The first is for isolated heat sources in a ventilated room (Linden et al. 1990) in which a steady-state two-layer stratification forms. The second is for distributed heat sources in which the room remains well mixed at all heights (Gladstone & Woods 2001). Both these models make simplifying assumptions such as adiabatic walls, idealized heat sources, and no mixing across stable density interfaces.

My research is interested in how these models behave under non-ideal situations. For example, The Linden et al. (1990) model assumes a point source of buoyancy as the heat source. However, if the heat source is distributed over a finite area then the height of the interface in the two-layer stratification will be closer to the floor and may cause thermal discomfort (Kaye & Hunt 2010). The influence of interfacial mixing on the stratification in a room was investigated with Morris Flynn and we showed that the interface thickness at full room scale will be substantially larger than is observed in small scale salt bath experiments (Kaye & Flynn 2010).

I have also collaborated with Malcolm Cook and others to perform CFD validation studies of prior small scale ventilation experiments (Kaye et al. 2009, Durrani et al. 2013).