Session AR: Buoyancy Driven Flows

Icicles: diffusive gravity currents and phase change

The growth and melting of icicles motivates this study of diffusive gravity currents. For example, the growth of an icicle vertically downwards is mediated by convective heat transfer in the surrounding air. The flow of the buoyant air is traditionally viewed as a near-vertical boundary layer and solved using the associated partial differential boundary-layer equations. However, near the tip of the icicle gravity acts in a direction orthogonal to the primary direction of flow. This situation is exemplified by the case of buoyancy-driven flow above a cooled, finite, horizontal plate or below a heated, finite horizontal plate. We find solutions of the corresponding boundary-layer equations in the form of approximate, nonlinear, separable solutions, with the horizontal variation of the boundary-layer thickness being governed by equations similar to those for a gravity current. We exploit the structure of such solutions to compute the steady-state shape and rate of melting of an icicle.   

Mean flow influence on a gravity current in a nearly horizontal confined geometry

We study experimentally the effect of an imposed mean flow on a buoyancy-driven exchange flow of two miscible fluids of the same viscosity in a long tube, oriented close to horizontal. Measuring the front velocity, $V_f$, as a function of the mean flow velocity, $V_0$, for different density contrasts, viscosity, and inclination angles has allowed us to identify two regimes. First, for low $V_0$ the flow is dominated by the buoyancy-driven flow and the dynamics are similar to the exchange flow dynamics. Secondly, for high $V_0$ the flow is dominated by the imposed mean flow, the front velocity varies proportionally to the mean flow velocity and the ratio $V_f/V_0$ does not appear to be very sensitive to the density contrast or viscosity, but does increase as the tube gets closer to vertical. In this regime we find that the flow becomes more laminar and stable, as $V_0$ increases. This appears counter intuitive, since more energy is being injected into the system through the mean flow.   

Modified thermal theory for gravity currents on sloping boundaries

In this study we generalize the thermal theory adopted in Beghin, Hopfinger, and Britter (J. Fluid Mech. Vol. 107, 1981, p. 407) in order to account for both entrainment and detrainment effects occurring in the motion of gravity currents. We observe that although the model of Beghin et al. (1981) qualitatively captures the acceleration and deceleration phases of gravity current motion, their pure entrainment model consistently underpredicts the gravity current velocity and the distance before the maximum velocity is reached. Their model, therefore, could easily overestimate the arrival time of a gravity current generated by an instantaneous buoyancy release. We find that the effect of detrainment is to increase the predicted velocity of gravity current and extend the predicted distance before the maximum velocity is reached. The effect of detrainment is not immediately obvious, but it explains the differences between the experimental data and the model of Beghin et al. (1981). The idea presented here will lead to more investigations of gravity currents on sloping boundaries.   

Study of the Front Structures of Gravity Current Using Simultaneous PIV/PLIF Measurement

The mixing and entrainment associated with the front development of gravity current have important implications in studying of many atmospheric and oceanic flow problems. A series of laboratory experiments are performed to investigate the development of the front structure of gravity current in an apparatus in which dense fluid is introduced into a less dense environment through a locking gate. A simultaneous PIV/PLIF system is developed to measure the velocity and density fields. The dynamics and structures around the current front are examined as well as the effect of bottom inclination.   

Jets, plumes and particle-laden jets in two-dimensional environments

Results on the experimental investigation of liquid jets and plumes in a quasi Hele- Shaw cell are presented. Few experimental studies have been conducted when jets are constrained in a narrow gap whose length is two orders of magnitude smaller than the length scales of the other two dimensions. In this configuration, the dynamics shown by the jets is very rich when parameters such as the initial flow-rate and the buoyancy are changed. Furthermore, different behaviors have been observed for the front of the jet and the flow in steady state. In particular, the models for the rise of the jet and the expansion must be slightly modified between the two cases. PIV techniques have been used to measure accurately the flow field of the jets and to allow accurate comparison with the theoretical models. Finally, the results of this investigation on jets and plumes serve as a basis for more complex experiments involving particle- laden jets. A better understanding of liquid jets with varying buoyancy proves to be useful to the study of this two-phase flow.   

Instability Phenomena in Stratified, Particle-laden Flow

When a layer of particle-laden water is placed above clear water of different temperature and salinity, various instabilities may arise. Depending on the specific density configuration, distinct convection patterns (``fingering'' vs. ``leaking'') have been reported from experiments (Parsons et al. 2001, Maxworthy 1999). We present linear stability results for such situations, with a focus on the role of particle settling. The effect of the settling velocity on the temporal instability growth rates is investigated in combination with various salinity distributions. The nonlinear evolution of the resulting instability structures is studied via DNS. Using linear analysis, DNS and experimental literature we hypothesize various mechanisms in an attempt to explain the occurrence of ``leaking'' and ``fingering.'' Current nonlinear results will be presented in an effort to fully explain the ``leaking'' mode.   

Intrusion-generated internal waves in a constantly stratified fluid

Intrusive Gravity Currents (IGCs) occur when horizontal density gradients result in the intrusion of one fluid into another fluid at an intermediate depth. The vertical density stratification of the receiving fluid necessary for an IGC is also capable of supporting internal wave motion. Though many IGCs in the ocean and atmosphere propagate into a stratified fluid, traditional assessments of GC and IGC dynamics neglect energy losses to internal wave motion. We present an experimental study of the internal wave field propagating ahead of a well-mixed intrusion into a constantly stratified ambient fluid. Intrusions at various heights in the ambient fluid are examined, and synthetic schlieren imaging techniques are used to quantify wave motion ahead of the current. We note a strong influence of the level of IGC propagation on the forcing of particular supercritical wave modes, and estimate the associated energy fluxes. To construct a more balanced energy budget of intrusions into stratified environments, we compare these losses to the initial Available Potential Energy (APE) of the system and to estimates of the kinetic energy of the IGC.   

Transient adjustment of UFAD systems in demand response operations

Transient responses of a UFAD system due to Demand Response (DR) are investigated theoretically and experimentally. DR activities can be categorized by reducing thermal loads and increasing room setpoint temperature, which change the thermal environment in a room and can cause occupant thermal discomfort. By comparing the filling box time (Baines \& Turner 1968) and the replenishment time in which all the air in the enclosure is replaced by supply air, non-dimensional models of UFAD systems are proposed and validated by laboratory experiments using a salt-water analogy. Two-layer stratification in the model allows us to estimate the temporal temperature change in the occupied zone and the interface height. Various DR activities, adjusting thermal loads and room setpoint temperature, are simulated to reveal the dynamic thermal responses. This study suggests that the interfacial height quickly converges to steady state compared to occupied zone temperature. The experiments show good agreement with the theoretical predictions of DR responses.   

The role of diffusion in natural displacement ventilation

The classic natural displacement ventilation model of Linden {\it et al.} (1990) predicts the formation of a two layer stratification when a single thermal plume is introduced into a room with vents at floor and ceiling level. The model assumes that molecular diffusion plays no role in the development of the rooms ambient stratification as such diffusion is a slow process and the plume entrainment field will act to thin the interface between the warm upper layer and cool lower layer. The prediction of a sharp interface has been confirmed by small scale salt bath experiments. However, full scale measurements and CFD simulations at larger scale indicate that the interface between the two layers is not sharp but smeared out over a finite thickness. We present two simple models for predicting the thickness of the interface as a function of the room height, floor area and vent area as well as the plume buoyancy flux and the thermal diffusivity of the fluid. The interface increases in thickness with increasing room floor area and decreasing plume strength. Our model is compared to interface thickness measurements based on CFD simulations and salt bath models and is shown to agree both phenomenologically and numerically. \\[4pt] Linden, Lane-Serf, \& Smeed, (1990) `Emptying filling boxes, the fluid mechanics of natural ventilation' J. Fluid Mech. {\textbf{212}} pp. 309--335.