# Scholarly Works - BP Institute

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Item Open Access On turbulent particle fountains(Cambridge University Press (CUP), 2016) Mingotti, N; Woods, AW; Mingotti, Nicola [0000-0001-9579-0145]Show more We describe new experiments in which particle-laden turbulent fountains with source Froude numbers $20>Fr_{0}>6$ are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio $U$ of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain ($U\ll 1$) or becomes a fully separated flow ($U\geqslant 1$). In the single-phase limit, a fountain with momentum flux $M$ and buoyancy flux $B$ oscillates about the mean height, $h_{m}=(1.56\pm 0.04)M^{3/4}B^{-1/2}$, as fluid periodically cascades from the maximum height, $h_{t}=h_{m}+{\rm\Delta}h$, to the base of the tank. Experimental measurements of the speed $u$ and radius $r$ of the fountain at the mean height $h_{m}$, combined with the conservation of buoyancy, suggest that $Fr(h_{m})=u(g^{\prime }r)^{-1/2}\approx 1$. Using these values, we find that the classical scaling for the frequency of the oscillations, ${\it\omega}\sim BM^{-1}$, is equivalent to the scaling $u(h_{m})/r(h_{m})$ for a fountain supplied at $z=h_{m}$ with $Fr=1$ (Burridge & Hunt, J. Fluid Mech., vol. 728, 2013, pp. 91–119). This suggests that the oscillations are controlled in the upper part of the fountain where $Fr\leqslant 1$, and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where $Fr=1$, and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which $Fr=1$: instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.Show more Item Open Access On the transport of heavy particles through a downward displacement-ventilated space(Cambridge University Press (CUP), 2015) Mingotti, N; Woods, AW; Mingotti, Nicola [0000-0001-9579-0145]Show more We investigate the transport of relatively heavy, small particles through a downward displacement-ventilated space. A flux of particles is supplied to the space from a localised source at a high level and forms a turbulent particle-laden plume which descends through the space. A constant flow of ambient fluid which does not contain particles is supplied to the space at a high level, while an equal amount of fluid is vented from the space at a low level. As a result of the entrainment of ambient fluid into the particle plume, a return flow is produced in the ambient fluid surrounding the plume in the lower part of the space. At steady state, particles are suspended by this return flow. An interface is formed which separates the ambient fluid in the lower part of the space, which contains particles, from the particle-free ambient fluid in the upper part of the space. New laboratory experiments show that the concentration of particles in the ambient fluid below the interface is larger than the average concentration of particles in the plume fluid at the level of the interface. Hence, as the plume fluid crosses the interface and descends through the particle-laden fluid underneath, it becomes relatively buoyant and forms a momentum-driven fountain. If the fountain fluid impinges on the floor, it then spreads radially over the surface until lifting off. We develop a quantitative model which can predict the height of the interface, the concentration of particles in the lower layer, and the partitioning of the particle flux between the fraction which sediments over the floor and that which is ventilated out of the space. We generalise the model to show that when particles and negatively buoyant fluid are supplied at the top of the space, a three-layer stratification develops in the space at steady state: the upper layer contains relatively low-density ambient fluid in which no particles are suspended; the central layer contains a mixture of ambient and plume fluid in which no particles are suspended; and the lower layer contains a suspension of particles in the same mixture of ambient and plume fluid. We quantify the heights of the two interfaces which separate the three layers in the space and the concentration of particles in suspension in the ambient fluid in the lower layer. We then discuss the relevance of the results for the control of airborne infections in buildings. Our experiments show that the three-layer stratification is subject to intermittent large-scale instabilities when the concentration of particles in the plume at the source is sufficiently small, or the rate of ventilation of the space is sufficiently large: we describe the transient concentration of particles in the space during one of these instabilities.Show more Item Open Access On the transport of heavy particles through an upward displacement-ventilated space(Cambridge University Press (CUP), 2015) Mingotti, N; Woods, AW; Mingotti, Nicola [0000-0001-9579-0145]Show more We explore the transport of heavy particles through an upward displacement-ventilated space. The space incorporates a localised source of buoyancy which generates a turbulent buoyant plume. The plume fluid is contaminated with a small concentration of particles, which are subject to gravitational settling. A constant flow of uncontaminated fluid is supplied at a low level into the space, while an equal amount of fluid is vented from the space at a high level. At steady state, a two-layer density stratification develops associated with the source of buoyancy. New laboratory experiments are conducted to explore how particles are transported by this flow. The experiments identify that the upper layer may either become well-mixed in particles or it may develop a vertical stratification in particle concentration, with the particle concentration decreasing with height. We develop a quantitative model which identifies that such stratification develops for larger particle setting speeds, or smaller ventilation rates. In accord with our experiments, the model predicts that the number of particles extracted from the space through the high-level vent is controlled by the magnitude of the particle stratification in the upper layer, and this in turn depends on the particle settling speed relative to the ventilation speed and also the cross-sectional area and height of the space. We compare the predictions of the model with measurements of the flux of particles vented from the space for a range of operating conditions. We explore the relevance of the model for the removal of airborne contaminants by displacement ventilation in hospital rooms, and we discuss how contamination is propagated in the room as a result of lateral mixing of pathogens in the upper layer.Show more Item Open Access Multiple steady states in exchange flows across faults and the dissolution of CO_{2}(Cambridge University Press (CUP), 2015) Woods, Andrew W; Hesse, Marc; Berkowitz, Rachel; Chang, Kyung WonShow more We develop a model of the steady exchange flows which may develop between two aquifers at different levels in the geological strata and across which there is an unstable density stratification, as a result of their connection through a series of fractures. We show that in general there are multiple steady exchange flows which can develop, depending on the initial conditions, and which may involve a net upwards or downwards volume flux. We also show that there is a family of equilibrium exchange flows with zero net volume flux, each characterised by a different interlayer flux of buoyancy. We present experiments which confirm our simplified model of the exchange flow. Such exchange flows may supply unsaturated water from a deep aquifer to drive dissolution of a structurally trapped pool of geologically stored $\text{CO}_{2}$, once the water in the aquifer containing the trapped pool of $\text{CO}_{2}$ has become saturated in $\text{CO}_{2}$, and hence relatively dense. Such exchange flows may also lead to cross-contamination of aquifer fluids, which may be of relevance in assessing risks of geological storage systems.Show more Item Open Access Buoyancy-driven dispersion in a layered porous rock(Cambridge University Press (CUP), 2015) Farcas, Adrian; Woods, Andrew WShow more AbstractWe investigate the longitudinal dispersion of a passive tracer by a gravity-driven flow in a porous medium consisting of a series of independent horizontal layers connected to a constant pressure source. We show that in a formation of given vertical extent, the total flux is only weakly dependent on the number of layers, and is very similar to that in a single layer of the same total depth. However, although the flow speed in each layer is approximately uniform, the speed gradually increases with layer depth. As a result, if a pulse of tracer is released in the flow it will migrate more rapidly through the lower layers, leading to longitudinal dispersion of the tracer. Eventually, the location of the tracer in the different layers may become separated in space so that a sufficiently distant observation well would detect a series of discrete pulses of tracer rather than the original coherent input, as would occur in a single permeable layer. For a constant pressure source, at long times, the standard deviation of the longitudinal distribution of tracer asymptotes to a fraction of order 0.1 of the position of the centre of mass, depending on the number of layers and the overpressure of the source.Show more Item Open Access Linear estimation of flux sensitivity to uncertainty in porous media(Cambridge University Press (CUP), 2015) Evans, AJ; Caulfield, CP; Woods, AW; Caulfield, Colm-cille [0000-0002-3170-9480]Show more We derive an integral expression for the flux of a single-phase fluid through a porous medium with prescribed boundary conditions. Taking variations with respect to the parameters of a given permeability model yields an integral expression for the sensitivity of the flux. We then extend the method to consider linear changes in permeability. This yields a linearised flux expression which is independent of changes in the pressure field that result from the changes in the permeability. For demonstration purposes, we first consider an idealised layered porous medium with a point source and point sink. We show how the effects of changes in permeability are affected by the position of the source and sink relative to the layered structure as well as the layer height and orientation of the layered structure. The results demonstrate that, even in a simple porous system, flux estimates are sensitive to the way in which the permeability is represented. We derive relationships between the statistical moments of the flux and of the permeability parameters which are modelled as random variables. This allows us to estimate the number of permeability parameters that should be varied in a fully nonlinear calculation to determine the variance of the flux. We demonstrate application of the methods to permeability fields generated through fast Fourier transform and kriging methods. We show that the linear estimates for the variability in flux show good agreement with fully nonlinear calculations for sufficiently small standard deviations in the underlying permeability.Show more