Lazy plumes

Hunt, Gary R.; Kaye, Nigel B.

doi:10.1017/s002211200500457x

Cited by 123 publications

(158 citation statements)

References 13 publications

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“…Thus, for small entrainment, there is a height at which the plume radius is at a minimum. This result is qualitatively similar to that obtained in the fully turbulent case by Hunt and Kaye [16].…”

Section: Asymptotic Solution For the Inviscid Plumesupporting

confidence: 91%

Inviscid and viscous models of axisymmetric fluid jets or plumes

Letchford¹,

Forbes²,

Hocking³

2012

ANZIAMJ

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The vertical rise of a round plume of light fluid through a surrounding heavier fluid is considered. An inviscid model is analysed in which the boundary of the plume is taken to be a sharp interface. An efficient spectral method is used to solve this nonlinear freeboundary problem, and shows that the plume narrows as it rises. A generalized condition is also introduced at the boundary, and allows the ambient fluid to be entrained into the rising plume. In this case, the fluid plume first narrows then widens as it rises. These features are confirmed by an asymptotic analysis. A viscous model of the same situation is also proposed, based on a Boussinesq approximation. It qualitatively confirms the widening of the plume due to entrainment of the ambient fluid, but also shows the presence of vortex rings around the interface of the rising plume.2010 Mathematics subject classification: 76D25.

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Section: Asymptotic Solution For the Inviscid Plumesupporting

confidence: 91%

Inviscid and viscous models of axisymmetric fluid jets or plumes

Letchford¹,

Forbes²,

Hocking³

2012

ANZIAMJ

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“…With a heat source included, the conservation equation for the buoyancy flux becomes (cf. (2.9)) dF dz = fF 0 z (7.10) When N = 0 (an unstratified environment), the power-law behaviour can be obtained by using a buoyancy source S = fF/z, where F (see (7.5)) and f (see (7.6)) are known functions of Ri, the special case of constant S having been examined by Hunt & Kaye (2005). In a numerical simulation, a source of buoyancy of this kind can be imposed locally by forcing the buoyancy b by an amount f wb/z.…”

Section: Entrainment At Constant Rimentioning

confidence: 99%

“…For a pure jet, which has no buoyancy, Γ (z) = 0. Plumes that have an excess of momentum at their source are called 'forced', and Γ is in the range 0 < Γ < 1; plumes that have a deficit of momentum at their source are called 'lazy', and have Γ > 1 (Hunt & Kaye 2005). Both forced and lazy plumes will transition to a pure plume (Γ = 1) as the flow develops.…”

mentioning

confidence: 99%

Energy-consistent entrainment relations for jets and plumes

2015

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We discuss energetic restrictions on the entrainment coefficient α for axisymmetric jets and plumes. The resulting entrainment relation includes contributions from the mean flow, turbulence and pressure, fundamentally linking α to the production of turbulence kinetic energy, the plume Richardson number Ri and the profile coefficients associated with the shape of the buoyancy and velocity profiles. This entrainment relation generalises the work by Kaminski et al. (J. Fluid Mech., vol. 526, 2005, pp. 361-376) and Fox (J. Geophys. Res., vol. 75, 1970, pp. 6818-6835). The energetic viewpoint provides a unified framework with which to analyse the classical entrainment models implied by the plume theories of Morton et al. , vol. 81, 1954, pp. 144-157). Data for pure jets and plumes in unstratified environments indicate that to first order the physics is captured by the Priestley and Ball entrainment model, implying that (1) the profile coefficient associated with the production of turbulence kinetic energy has approximately the same value for pure plumes and jets, (2) the value of α for a pure plume is roughly a factor of 5/3 larger than for a jet and (3) the enhanced entrainment coefficient in plumes is primarily associated with the behaviour of the mean flow and not with buoyancy-enhanced turbulence. Theoretical suggestions are made on how entrainment can be systematically studied by creating constant-Ri flows in a numerical simulation or laboratory experiment.

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“…Hunt and Kaye (2005) considered the effect of buoyancy generation on so-called 'lazy plumes', i.e. plumes with a deficit of momentum at the source compared with a pure plume with the same source buoyancy flux.…”

Section: Introductionmentioning

confidence: 99%

“…The model they developed was based on that of Morton et al (1956) and assumed Gaussian profiles within the plume. Hunt and Kaye (2005) considered a case where the buoyancy flux increased linearly with height and were able to define a length scale at which the buoyancy flux generated during ascent became equal to that released at the source.…”

Section: Introductionmentioning

confidence: 99%

Turbulent plumes with internal generation of buoyancy by chemical reaction

Campbell

Cardoso

2010

J. Fluid Mech.

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Turbulent plumes, which are seen in a wide number of industrial and natural flows, have been extensively studied; however, very little attention has been paid to plumes which have an internal mechanism for changing buoyancy. Such plumes arise in e.g. industrial chimneys, where species can react and change the density of the plume material. These plumes with chemical reaction are the focus of this study. An integral model describing the behaviour of a plume undergoing a second-order chemical reaction between a component in the plume (A) and a component in the surrounding fluid (B), which alters the buoyancy flux, is considered. The behaviour of a reactive plume is shown to depend on four dimensionless groups: the volume and momentum fluxes at the source, the parameter ε which indicates the additional buoyancy flux generated by the reaction, and γ which is a dimensionless rate of depletion of species B. Additionally, approximate analytical solutions are sought for a reactive plume rising from a point source of buoyancy when species B is in great excess.These analytical results show excellent agreement with numerical simulations. It is also shown that the behaviour of a reactive plume in the far field is equivalent to an inert plume issuing from a virtual source downstream of the real source and the dependence of the location of the virtual source on ε and γ is discussed. The effects of varying the volume flux at the source and the Morton source parameter Γ 0 are further investigated by solving the full governing equations numerically. These solutions indicate that ε is important in determining the buoyancy generated by the reaction, and the length scale over which this reaction occurs depends on γ when γ > 1. It is also shown that when the dimensionless buoyancy 1 − < ε , the reaction can cause the plume to collapse.3

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Lazy plumes

Cited by 123 publications

References 13 publications

Inviscid and viscous models of axisymmetric fluid jets or plumes

Inviscid and viscous models of axisymmetric fluid jets or plumes

Energy-consistent entrainment relations for jets and plumes

Turbulent plumes with internal generation of buoyancy by chemical reaction

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