John C. Patterson

Unsteady natural convection in a rectangular cavity

The problem of transient natural convection in a cavity of aspect ratio A [les ] 1 with differentially heated end walls is considered. Scale analysis is used to show that a number of initial flow types are possible, collapsing ultimately onto two basic types of steady flow, determined by the relative value of the non-dimensional parameters describing the flow. A number of numerical solutions which encompass both flow types are obtained, and their relationship to the scale analysis is discussed.

Transient features of natural convection in a cavity

Comparisons of numerical and experimental results for transient two-dimensional natural convection initiated by instantaneously heating and cooling the opposing vertical walls of a square cavity containing a stationary and isothermal fluid are presented. The good comparisons indicate that the simulation is capturing the important features of the flow. Several features are identified and discussed in detail; in particular, the presence of travelling wave instabilities on the vertical-wall boundary layers and horizontal intrusions, the existence of a rapid flow divergence in the region of the outflow of the intrusions, and the presence of cavity-scale oscillations, caused by the interaction of the intrusions with the opposing vertical boundary layer. The utilization of both numerical and experimental investigations has allowed a more complete exploitation of the available resources than would have been possible had each been conducted separately.

On the response of a reservoir sidearm to diurnal heating and cooling

During the day, the shallower regions of a reservoir sidearm absorb more heat per unit volume than the deeper parts, leading to a horizontal pressure gradient that drives a circulation in the sidearm. At night, the shallow regions cool more rapidly, leading to a circulation in the opposite direction. Since the spin-up time of a typical sidearm is at least of the same order as a day, the flow within a diurnally forced sidearm is principally an inertia–buoyancy balance. In this paper, a diurnally forced sidearm is modelled by periodically forced natural convection in a triangular cavity. The periodic forcing enters the model via an internal heating/cooling term in the temperature equation. Reservoir sidearms typically have small bottom slopes and this fact can be exploited to obtain asymptotic solutions of the resulting equations. These solutions clearly demonstrate the transition from the viscous-dominated flow in the shallows to the inertia-dominated flow in the deeper parts. In the inertia-dominated region, the flow response significantly lags the forcing. Numerical solutions of the full nonlinear problem are consistent with the asymptotic solutions.

Wave properties of natural-convection boundary layers

The thermal boundary layer on the wall of a side-heated cavity at early time is known to exhibit a complex travelling wave during growth to steady state and a similar feature is observed on isolated heated semi-infinite plates. Direct numerical solutions of the Navier-Stokes equations together with a linearized stability analysis are used to study the character of the flow at early time in detail. It is demonstrated that the cavity flow is essentially identical to the plate flow, and that for early time the flow is one-dimensional

Direct simulation of wave interactions in unsteady natural convection in a cavity

Abstract Numerical solutions for unsteady natural convection flow in a square cavity with differentially heated side walls are obtained using an implicit second-order time-accurate finite volume scheme, and briefly compared to experimental data reported elsewhere. The results predict the occurrence of a cavity scale seiche, the presence of waves in the vertical thermal boundary layer that travel from the walls into the horizontal intrusions that form on the horizontal boundaries, and a region of strong divergence at the upstream end of the intrusions. These three mechanisms are observed to interact at a Rayleigh number of 5 × 109 to produce a mixing patch in the intrusion, suggestive of a transition to turbulence. The net heat transfer and the approach to steady state are strongly influenced by the presence of the waves.

The daytime circulation and temperature structure in a reservoir sidearm

During the daylight hours, the shallow regions of a reservoir sidearm absorb more heat per unit volume than the deeper parts, leading to a nett horizontal pressure gradient that drives a circulation in the sidearm. The spin up time for a typical sidearm is of the order of or longer than a day, implying that the flow is intrinsically unsteady. In this paper, the unsteady daytime circulation and temperature structure in a reservoir sidearm is modelled by the natural convection of a fluid contained in a 2-D, triangular cavity. The absorption of solar radiation that drives the flow is modelled by Beers law and a heat flux bottom boundary condition formulated from the amount of heat that penetrates the entire local depth. Asymptotic solutions of the resulting equations are found and these reproduce some of the observed features of the daytime circulation in a reservoir sidearm.

Unsteady natural convection in a cavity with non-uniform absorption of radiation

A study of the unsteady natural convection in a cavity which was heated by the absorption of radiation entering through part of the surface is reported. While a general scaling analysis is quite complex, involving five separate timescales, most naturally occurring problems fall into just one regime, and it is only this regime which is discussed. To test the scaling, a series of laboratory experiments were performed in which the radiation parameters (surface flux and attenuation coefficient) were varied. The method by which these parameters were determined is also discussed. Numerical experiments were used to extend the parameter range, and the results of all these experiments confirmed the validity of the scaling over a range of parameters.

Natural convection in a side-heated cavity: visualization of the initial flow features

The shadowgraph technique is used for visualizing the early stages of the flow in a water-filled square cavity which is suddenly heated and cooled on the opposing sidewalls. These sidewalls are perfect heat conductors, while the top and bottom boundaries of the cavity are thermally insulating. For the first time, a clear visualization is given of the first group of waves travelling up the hot boundary layer immediately after start-up, of the initial horizontal intrusions and of the second group of waves resulting from the interaction of the incoming intrusion with the boundary layer. The properties of the waves are examined and shown to be in agreement with previous numerical predictions. Special attention is paid to the initial horizontal intrusions, and their connection to gravity currents is discussed. One feature in particular which makes these intrusions unique is the interaction with the first group of waves coming from the vertical boundary layers. This interaction together with what appears to be a thermal instability of the intrusion nose are discussed in detail.

On the stability of the near shore waters of a lake when subject to solar heating

During the day, water in a lake or reservoir absorbs solar radiation according to Beers law. As the depth decreases towards the shore, more of the radiation penetrates to the bottom, leading to a region of warmer water attached to the lower boundary which is a potentially unstable temperature profile. This situation is modelled by a fluid contained in a triangular domain with a horizontal upper surface. The fluid is subject to internal heating associated with Beers law and a bottom boundary heat flux associated with the radiation that is not absorbed by the water column. Previous work suggests that the preferred mode for the instability consists of longitudinal rolls with their axes aligned with the slope. As the bottom slope becomes small, the stability problem becomes independent of the base flow and the originally threedimensional (3-D) problem is reduced to a two-dimensional (2-D) problem between horizontal and parallel plates. A quasi-static, linear stability analysis suggests that, for geophysical parameters, the model is locally unstable in a region centred away from the shore.

Simulation of bubble plume destratification systems in reservoirs

A simple model of the dynamics of a bubble plume is incorporated in the one dimensional model of reservoir dynamics DYRESM and tested against a data set from Myponga Reservoir in South Australia. The comparisons show that the model provides a reasonably good simulation of the dynamics, and allows use of the combined model for determining the behaviour of aerators under a number of operational strategies. It is shown that a peak efficiency in excess of 15% may be achieved from a single bubble plume, and that the total efficiency of an aerator operating with a fixed airflow rate and fixed configuration over a full season may be increased markedly from 1.5% to about 5.5% by a simple control method. It is suggested that total efficiencies of the order of 15% may be achieved by more complex control strategies.