S.W. Armfield

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.

Finite difference solutions of the Navier-Stokes equations on staggered and non-staggered grids

Abstract Finite difference schemes for the Navier-Stokes equations are considered, with particular attention to the discretization of the pressure gradient and divergence terms. It is demonstrated that the relation between these terms is the principal reason for the use of the conventional staggered mesh with SIMPLE and other schemes. The important factors in the differencing are that it should lead to an elliptic scheme that satisfies the integrability constraint. The SIMPLE scheme automatically satisfies these two constraints. A non-staggered mesh scheme that also satisfies these constraints has been developed. Comparisons between it and a SIMPLE scheme for natural convection in a cavity indicate that the schemes have equivalent accuracy. For the non-uniform mesh used in this problem the non-staggered scheme is more efficient. It is expected that this increase in efficiency would be greater for adaptive and multi-grid algorithms.

Vortex shedding suppression for flow over a circular cylinder near a plane boundary

In this study, the Navier-Stokes equations and the pressure Poisson equation for two-dimensional time-dependent viscous flows are solved with a finite difference method in a curvilinear coordinate system. With this numerical procedure, the vortex shedding flow past a circular cylinder near a wall is investigated. The flow is calculated for a broad range of gap ratios for different Reynolds numbers ranging from 80 to 1000. Based on the numerical solutions, the vortex shedding is observed using various methods, and the mechanism for the vortex shedding suppression at small gap ratios is analyzed. The critical gap ratio at which the vortex shedding is suppressed is identified at different Reynolds numbers.

Direct simulation of natural convection cooling in a vertical circular cylinder

Abstract The transient processes of cooling-down and stratifying an initially homogeneous fluid by natural convection in a vertical circular cylinder have been investigated numerically. The transient flow patterns are identified by the visualization of the transient evolving processes in the cylinder. The results show that vigorous flow activities concentrate mainly in the vertical thermal boundary layer along the sidewall and in the horizontal region which is the lower part of the domain where the cold intrusion flow is embedded. The transient flow patterns at the unsteady and quasi-steady stages are analysed, including the activities of the travelling waves in the vertical thermal boundary layer along the sidewall and the cold intrusions in the horizontal region. A scaling analysis is used to characterize the development of the vertical thermal boundary layer on the sidewall and the stratification in the cylinder. It is found that the numerical solutions agree very well with the scaling results.

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 weak axisymmetric fountains in a homogeneous fluid

The weak axisymmetric fountain that results from the injection of a dense fluid upwards into a large container of homogeneous fluid of lower density is studied numerically. Using a time-accurate finite volume code, the behaviour of fountains with both a uniform and a parabolic profile of the discharge velocity at the source have been investigated. The evolution of the transient fountain flow has been analysed and two distinct stages of evolution have been identified. The time series of the passage of the fountain front has been presented and the initial, temporary and final characteristic fountain heights have been determined and scaled with the Froude number at the source. At steady state, the final fountain height and the fountain width are found to be the height and horizontal length scales which provide the full parameterization of the fountain flow in the fountain core. The vertical velocity and temperature on the symmetry axis have been scaled with the height scale and an explicit correlation is also obtained for the former. The radial distributions of both the vertical and horizontal velocities in the zone of self similarity in the fountain core at steady state have been scaled with the two length scales and empirical correlations have been obtained.

Natural convection cooling of rectangular and cylindrical containers

Abstract Scalings are obtained for the development of unsteady natural convection, both in rectangular and vertical circular containers, and are validated by comparison with results obtained using direct numerical simulation. It is found that the numerical results agree well with the scalings. Three main stages of flow evolution are identified and the differences at each of these stages between the rectangular and cylindrical geometries are quantified. It is shown that in the flow regimes considered there is a difference in thermal boundary layer thickness; that the horizontal intrusion layer has a uniform thickness for the rectangular flow, but increases towards the symmetry axis for the cylindrical flow; and that the rate of stratification is much faster for the cylindrical geometry.

Large Eddy Simulation of a Propagating Turbulent Premixed Flame

A large eddy simulation of a turbulent premixed flame propagatingthrough a chamber containing a square obstruction is presented anddiscussed. The governing equations for compressible, reacting flowsare Favre filtered and turbulence closure is achieved using thedynamic Smagorinsky subgrid model. A simple flame surface densitymodel based on the flamelet concept is employed for the subgrid scalereaction rate. The simulation gives very good agreement with experimentalresults for the speed and the shape of the flame as it propagates throughthe chamber. The peak pressures, however, are underpredicted by20–30%. Reasons for this are discussed and it is concluded that amore sophisticated combustion model is required for complex flowssuch as this one, if a more accurate prediction of the pressureis to be achieved.

Low-Reynolds-number fountain behaviour

Experimental evidence for previously unreported fountain behaviour is presented. It has been found that the first unstable mode of a three-dimensional round fountain is a laminar flapping motion that can grow to a circling or multimodal flapping motion. With increasing Froude and Reynolds numbers, fountain behaviour becomes more disorderly, exhibiting a laminar bobbing motion. The transition between steady behaviour, the initial flapping modes and the laminar bobbing flow can be approximately described by a function FrRe2/3 =C. The transition to turbulence occurs at Re > 120, independent of Froude number, and the flow appears to be fully turbulent at Re ≈2000. For Fr > 10 and Re 120, sinuous shear-driven instabilities have been observed in the rising fluid column. For Re 120 these instabilities cause the fountain to intermittently breakdown into turbulent jet-like flow. For Fr 10 buoyancy forces begin to dominate the flow and pulsing behaviour is observed. A regime map of the fountain behaviour for 0.7Fr 100 and 15Re 1900 is presented and the underlying mechanisms for the observed behaviour are proposed. Movies are available with the online version of the paper.

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.