Experimental investigation of a line plume in a filling box
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Experimental investigation of a line plume in a filling box Romana Akhter1 · Nigel B. Kaye1 Received: 15 July 2019 / Accepted: 3 July 2020 © The Author(s) 2020
Abstract A series of experiments were conducted to quantify the dynamics of a filling box driven by a line plume that spans the full width of the enclosure. Three configurations were tested namely symmetric (centrally located plume), wall-bounded (plume attached to an end wall), and asymmetric. The front movement for the symmetric and wall-bounded configurations was well described by the standard filling box model. The front movement results indicate that the typical value of the entrainment coefficient (𝛼) for an unconfined plume ( 𝛼 = 0.16 ) could be used to accurately predict the front movement for both the centrally located plume and the wall-attached plume. This is in contrast to other studies that suggest that wall-bounded plumes have a significantly lower entrainment coefficient. The standard filling box model broke down for the asymmetric configuration. As the plume was closer to one wall than the other, the plume outflows that spread out and reflected off the end walls returned to the plume at different times. This created a pressure imbalance across the plume that caused the plume to bend sharply toward the nearest wall. Analysis of the plume outflow as a constant flux gravity current showed that the outflow velocity scaled on the cube root of the plume buoyancy flux per unit width f , a result confirmed by further experiments. This result was used to quantify the time at which the plume bends and the standard filling box model breaks down. Keywords Line plume · Filling box model · Buoyancy · Entrainment coefficient · Gravity current Abbreviations C Co-efficient for the volume flux f Buoyancy flux per unit width ( m3/s3) 𝜆 Fraction of the total length to the right of the plume L Length of the tank (m) z Vertical distance from the plume source to the interface (m) F Plume buoyancy flux ( m4/s3) H Height of the tank (m) * Romana Akhter [email protected]; [email protected] Nigel B. Kaye [email protected] 1
Glenn Department of Civil Engineering, Clemson University, Clemson, SC 29631, USA
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Environmental Fluid Mechanics
g′ Reduced gravity (m/s2) g Gravitational acceleration ((m/s2) 𝜌s Density of the saltwater (kg/m3) 𝜌f Density of the freshwater (kg/m3) W Width of the tank (m) q Volume flux per unit width ( m2/s) Δ𝜌 Density difference (kg/m3) 𝛼 Entrainment co-efficient Q Flow rate (m3/s) R Rotameter reading for flow rate (m3/s) Qplume Volume flux of the plume ( m3/s) hl Height from the source to the interface layer at left-hand-side (m) hr Height from the source to the interface layer at right-hand-side (m) hi Interface height over time for a particular side (m) t Time (s) Tfill.i Filling time for a particular side i (s) Tfill.l Filling time for left-hand-side (s) Tfill.r Filling time for right-hand-side (s) 𝜏 Non-dimensional time parameter (s/s) 𝜏i Non-dimensional time para
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