Turbulent fountains in a stratified fluid

Bloomfield, Lynn J.; Kerr, Ross C.

doi:10.1017/s0022112097008252

Cited by 105 publications

(198 citation statements)

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“…Morton 1959) to more modern developments (e.g. Bloomfield & Kerr 1998;Kaye & Hunt 2006;Carazzo et al 2010). The application of plume theory to established fountains, i.e.…”

Section: Introductionmentioning

confidence: 99%

Entrainment by turbulent fountains

Burridge

Hunt

2016

J. Fluid Mech.

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Experimental measurements of entrainment by turbulent fountains from circular sources in quiescent uniform environments are presented. Our results span almost four orders of magnitude in the source Froude number (0.004 Fr 0 25) and thereby encompass the entrainment across all classes of fountain behaviour identified to date. We identify scalings for the entrained volume flux Q E , in terms of Fr 0 and the source volume flux Q 0 , within a number of distinct Froude number bands corresponding to each class of fountain. Additionally we identify a distinct class of new behaviour, as yet unreported, for Fr 0 0.1.

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“…Morton 1959) to more modern developments (e.g. Bloomfield & Kerr 1998;Kaye & Hunt 2006;Carazzo et al 2010). The application of plume theory to established fountains, i.e.…”

Section: Introductionmentioning

confidence: 99%

Entrainment by turbulent fountains

Burridge

Hunt

2016

J. Fluid Mech.

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“…For these turbulent fountains, the momentum of the rising denser fluid is reduced gradually by the negative buoyancy until the flow first comes to rest at an initial height above the source. After that, the flow falls back as an annular plunging plume around the upward flow and this downflow continues to mix with the ambient while also interacting turbulently with the upflow which restricts the rise of further fluid and therefore reduces the initial fountain height to a final value which is observed to be related to the momentum and buoyancy fluxes at the source (Campbell & Turner 1989;Baines, Turner & Campbell 1990;Bloomfield & Kerr 1998). The schematic drawing in figure 1 by Baines et al (1990), Baines, Corriveau & Reedman (1993) is very instructive for understanding this process.…”

Section: Introductionmentioning

confidence: 99%

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

Lin

Armfield

2000

J. Fluid Mech.

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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 has been investigated. The evolution of the transient fountain flow has been analysed and two distinct stages 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 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.

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“…There have been many experimental, analytical and numerical studies on turbulent fountains in the past decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and a brief discussion of these studies was presented by Lin and Armfield [17]. For fountains with a weak source, the discharge momentum of the fountains is less than the negative buoyancy and the flow is characterized by Fr 1:0.…”

Section: Introductionmentioning

confidence: 99%

The Reynolds and Prandtl number dependence of weak fountains

Lin

Armfield

2003

Computational Mechanics

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The effect of the Prandtl number (Pr) and the Reynolds number (Re) on the behaviour of weak laminar axisymmetric and plane fountains has been studied using dimensional and scaling analyses and direct numerical simulation. For Fr $ 1.0 and assuming viscous effects are important, the analysis shows that for both the axisymmetric and plane fountains, y m $ FrRe À1=2 , where Fr is the Froude number defined at the fountain source and y m is the non-dimensionalized fountain height. These scalings are also valid for the non-dimensionalized fountain width. The analyses also shows s ms $ Fr 2 , where s ms is the non-dimensionalized time scale for the fountain flow in the fountain core to reach steady state, and using this time scale Dy T $ Fr(RePr) À1=2 , where Dy T is the nondimensionalized thickness of the temperature layer on the symmetry axis over which the fountain fluid temperature changes from the inlet value to that of the ambient fluid. All these scalings have been quantified by the direct numerical simulations, hence confirming in certain ranges the phenomenological scaling obtained in this paper. IntroductionFountains occur with jets when the buoyancy force acting on the jet, as a result of a density difference between the jet fluid and the surrounding ambient fluid, acts in the opposite direction to that of the jet flow. Thus both dense jets projected upwards into a less dense medium, and less dense jets projected downwards into a more dense medium, will produce fountains. Considering only the upward projected dense flow, the jet will penetrate to a finite height, with the fluid then falling back as a plunging plume. In cases where the jet source lies on a solid boundary the plunging plume falls to the boundary and then forms a gravity intrusion travelling away from the main fountain flow.For fountains with a strong source, the flow becomes turbulent quite close to the source. The discharge momentum is relatively larger than the negative buoyancy and the flow is characterized by Fr > 1.0 where Fr is the Froude number at the fountain source, defined as the ratio of inertia to buoyant forces as follows:where M 0 and B 0 are the specific momentum flux and specific buoyant flux, V 0 the discharge velocity, and X 0 the radius of the orifice at the fountain source for an axisymmetric fountain or the half-width of the slot at the source for a plane fountain. When the discharge velocity at the source is uniform, M 0 and B 0 are calculated by:for axisymmetric fountains andfor plane fountains, where r 0 is the reduced gravity between the fountain and the ambient fluid at the source. Therefore, for a uniform discharge velocity at the source for both axisymmetric and plane fountains, Fr is calculated as followsFor the strong fountains the fountain top, plunging plume and intrusion flow are distinct features. There have been many experimental, analytical and numerical studies on turbulent fountains in the past decades [1-16] and a brief discussion of these studies was presented by Lin and Armfield [17]. For fountains with ...

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Turbulent fountains in a stratified fluid

Cited by 105 publications

References 9 publications

Entrainment by turbulent fountains

Entrainment by turbulent fountains

Direct simulation of weak axisymmetric fountains in a homogeneous fluid

The Reynolds and Prandtl number dependence of weak fountains

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