The non-local nature of structure functions

Kolmogorov's two-thirds, ((Δv) 2) ∼ e 2/ 3r 2/ 3, and five-thirds, E ∼ e 2/ 3k -5/ 3, laws are formally equivalent in the limit of vanishing viscosity, v → 0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s 2/ 3, in accordance with Kolmogorov's 1941 law, and we vary the range of scales, γ = s max/s min, in any one realisation from γ = 25 to γ = 800. This is equivalent to varying the Reynolds number in an experiment from R λ = 60 to R λ = 600. While there is some evidence of a five-thirds law for g > 50 (R λ > 100), the two-thirds law only starts to become apparent when g approaches 200 (R λ ∼ 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, ((Δv) 2) takes the form of a mixed power-law, a 1+a 2r 2+a 3r 2/ 3, where a 2r 2 tracks the variation in enstrophy and a 3r 2/ 3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r 2/ 3 law by the enstrophy contribution, a 2r 2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency.

Fluid-structure interaction of three-dimensional magnetic artificial cilia

A numerical model is developed to analyse the interaction of artificial cilia with the surrounding fluid in a three-dimensional setting in the limit of vanishing fluid inertia forces. The cilia are modelled using finite shell elements and the fluid is modelled using a boundary element approach. The coupling between both models is performed by imposing no-slip boundary conditions on the surface of the cilia. The performance of the model is verified using various reference problems available in the literature. The model is used to simulate the fluid flow due to magnetically actuated artificial cilia. The results show that narrow and closely spaced cilia create the largest flow, that metachronal waves along the width of the cilia create a significant flow in the direction of the cilia width and that the recovery stroke in the case of the out-of-plane actuation of the cilia strongly depends on the cilia width. © 2012 Cambridge University Press.

A comparison of winter pre-heating requirements for natural displacement and natural mixing ventilation

In winter, natural ventilation can be achieved either through mixing ventilation or upward displacement ventilation (P.F. Linden, The fluid mechanics of natural ventilation, Annual Review of Fluid Mechanics 31 (1999) pp. 201-238). We show there is a significant energy saving possible by using mixing ventilation, in the case that the internal heat gains are significant, and illustrate these savings using an idealized model, which predicts that with internal heat gains of order 0.1 kW per person, mixing ventilation uses of a fraction of order 0.2-0.4 of the heat load of displacement ventilation assuming a well-insulated building. We then describe a strategy for such mixing natural ventilation in an atrium style building in which the rooms surrounding the atrium are able to vent directly to the exterior and also through the atrium to the exterior. The results are motivated by the desire to reduce the energy burden in large public buildings such as hospitals, schools or office buildings centred on atria. We illustrate a strategy for the natural mixing ventilation in order that the rooms surrounding the atrium receive both pre-heated but also sufficiently fresh air, while the central atrium zone remains warm. We test the principles with some laboratory experiments in which a model air chamber is ventilated using both mixing and displacement ventilation, and compare the energy loads in each case. We conclude with a discussion of the potential applications of the approach within the context of open plan atria type office buildings.

Transient Ventilation Dynamics Following a Change in Strength of a Point Source of Heat

We investigate the transient ventilation flow within a confined ventilated space, with high- and low-level openings, when the strength of a low-level point source of heat is changed instantaneously. The steady-flow regime in the space involves a turbulent buoyant plume, which rises from the point source to a well-mixed warm upper layer. The steady-state height of the interface between this layer and the lower layer of exterior fluid is independent of the heat flux, but the upper layer becomes progressively warmer with heat flux. New analogue laboratory experiments of the transient adjustment between steady states identify that if the heat flux is increased, the continuing plume propagates to the top of the room forming a new, warmer layer. This layer gradually deepens, and as the turbulent plume entrains fluid from the original warm layer, the original layer is gradually depleted and disappears, and a new steady state is established. In contrast, if the source buoyancy flux is decreased, the continuing plume is cooler than the original plume, so that on reaching the interface it is of intermediate density between the original warm layer and the external fluid. The plume supplies a new intermediate layer, which gradually deepens with the continuing flow. In turn, the original upper layer becomes depleted, both as a result of being vented through the upper opening of the space, but also due to some penetrative entrainment of this layer by the plume, as the plume overshoots the interface before falling back to supply the new intermediate layer. We develop quantitative models which are in good accord with our experimental data, by combining classical plume theory with models of the penetrative entrainment for the case of a decrease in heating. Typically, we find that the effect of penetrative entrainment on the density of the intruding layer is relatively weak, provided the change in source strength is sufficiently large. However, penetrative entrainment measurably increases the rate at which the depth of the draining layer decreases. We conclude with a discussion of the importance of these results for the control of naturally ventilated spaces.

Transient Natural Ventilation of a Room with a Distributed Heat Source

We report on an experimental and theoretical study of the transient flows which develop as a naturally ventilated room adjusts from one temperature to another. We focus on a room heated from below by a uniform heat source, with both high- and low-level ventilation openings. Depending on the initial temperature of the room relative to (i) the final equilibrium temperature and (ii) the exterior temperature, three different modes of ventilation may develop. First, if the room temperature lies between the exterior and the equilibrium temperature, the interior remains well-mixed and gradually heats up to the equilibrium temperature. Secondly, if the room is initially warmer than the equilibrium temperature, then a thermal stratification develops in which the upper layer of originally hot air is displaced upwards by a lower layer of relatively cool inflowing air. At the interface, some mixing occurs owing to the effects of penetrative convection. Thirdly, if the room is initially cooler than the exterior, then on opening the vents, the original air is displaced downwards and a layer of ambient air deepens from above. As this lower layer drains, it is eventually heated to the ambient temperature, and is then able to mix into the overlying layer of external air, and the room becomes well-mixed. For each case, we present new laboratory experiments and compare these with some new quantitative models of the transient flows. We conclude by considering the implications of our work for natural ventilation of large auditoria.