Temporal variation of non-ideal plumes with sudden reductions in buoyancy flux

Scase, M. M.; Caulfield, C. P.; Dalziel, Stuart B.

doi:10.1017/s0022112008000487

Cited by 15 publications

(34 citation statements)

References 16 publications

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“…However, consistent with our interpretation of figure 2, the change in plume width is not readily discernible from the radial extent of the passive scalar field presented in figures 3 and 4 of Scase et al (2008). Only by quantifying the width of the plume with a top-hat width based on the concentration of the passive scalar do Scase et al (2008) find that the plume becomes narrower (figure 6 of their study). The interpretation and observed behaviour of the plume radius will be discussed in further detail below.…”

Section: Unsteady Plumessupporting

confidence: 66%

“…Looking at the buoyancy field and the boundary of the plume in figure 2, one does not get the impression that the width or radial extent of the plume is strongly affected by the step change in the buoyancy flux. In this regard, we note that experimental observations of a plume, whose source buoyancy flux was suddenly reduced at the source, suggested that such plumes become narrower in the vicinity of the step change (Scase et al 2008). However, consistent with our interpretation of figure 2, the change in plume width is not readily discernible from the radial extent of the passive scalar field presented in figures 3 and 4 of Scase et al (2008).…”

Section: Unsteady Plumessupporting

confidence: 64%

“…In this regard, we note that experimental observations of a plume, whose source buoyancy flux was suddenly reduced at the source, suggested that such plumes become narrower in the vicinity of the step change (Scase et al 2008). However, consistent with our interpretation of figure 2, the change in plume width is not readily discernible from the radial extent of the passive scalar field presented in figures 3 and 4 of Scase et al (2008). Only by quantifying the width of the plume with a top-hat width based on the concentration of the passive scalar do Scase et al (2008) find that the plume becomes narrower (figure 6 of their study).…”

Section: Unsteady Plumesmentioning

confidence: 85%

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Generalised unsteady plume theory

Craske

Reeuwijk

2016

J. Fluid Mech.

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We develop a generalised unsteady plume theory and compare it with a new direct numerical simulation (DNS) dataset for an ensemble of statistically unsteady turbulent plumes. The theoretical framework described in this paper generalises previous models and exposes several fundamental aspects of the physics of unsteady plumes. The framework allows one to understand how the structure of the governing integral equations depends on the assumptions one makes about the radial dependence of the longitudinal velocity, turbulence and pressure. Consequently, the ill-posed models identified by Scase & Hewitt (J. Fluid Mech., vol. 697, 2012, pp. 455-480) are shown to be the result of a non-physical assumption regarding the velocity profile. The framework reveals that these ill-posed unsteady plume models are degenerate cases amongst a comparatively large set of well-posed models that can be derived from the generalised unsteady plume equations that we obtain. Drawing on the results of DNS of a plume subjected to an instantaneous step change in its source buoyancy flux, we use the framework in a diagnostic capacity to investigate the properties of the resulting travelling wave. In general, the governing integral equations are hyperbolic, becoming parabolic in the limiting case of a 'top-hat' model, and the travelling wave can be classified as lazy, pure or forced according to the particular assumptions that are invoked to close the integral equations. Guided by observations from the DNS data, we use the framework in a prognostic capacity to develop a relatively simple, accurate and well-posed model of unsteady plumes that is based on the assumption of a Gaussian velocity profile. An analytical solution is presented for a pure straight-sided plume that is consistent with the key features observed from the DNS.

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Section: Unsteady Plumessupporting

confidence: 66%

Section: Unsteady Plumessupporting

confidence: 64%

Section: Unsteady Plumesmentioning

confidence: 85%

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Generalised unsteady plume theory

Craske

Reeuwijk

2016

J. Fluid Mech.

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“…A contribution to experimental data pertaining to unsteady plumes was made by Scase, Caulfield & Dalziel (2008), who investigated the effects of a sudden reduction in buoyancy flux. In particular, Scase et al (2008) found that source conditions 502 J.…”

mentioning

confidence: 99%

Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets

Craske

Reeuwijk

2014

J. Fluid Mech.

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We study the physics of unsteady turbulent jets using direct numerical simulation (DNS) by introducing an instantaneous step change (both up and down) in the source momentum flux. Our focus is on the propagation speed and rate of spread of the resulting front. We show that accurate prediction of the propagation speed requires information about the energy flux in addition to the momentum flux in the jet. Our observations suggest that the evolution of a front in a jet is a self-similar process that accords with the classical dispersive scaling z ∼ √ t. In the analysis of the problem we demonstrate that the use of a momentum-energy framework of the kind used by Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1955, pp. 144-157) has several advantages over the classical mass-momentum formulation. In this regard we generalise the approach of Kaminski et al. (J. Fluid Mech., vol. 526, 2005, pp. 361-376) to unsteady problems, neglecting only viscous effects and relatively small boundary terms in the governing equations. Our results show that dispersion originating from the radial dependence of longitudinal velocity plays a fundamental role in longitudinal transport. Indeed, one is able to find dispersion in the steady state, although it has received little attention because its effects can then be absorbed into the entrainment coefficient. Specifically, we identify two types of dispersion. Type I dispersion exists in a steady state and determines the rate at which energy is transported relative to the rate at which momentum is transported. In unsteady jets type I dispersion is responsible for the separation of characteristic curves and thus the hyperbolic, rather than parabolic, nature of the governing equations, in the absence of longitudinal mixing. Type II dispersion is equivalent to Taylor dispersion and results in the longitudinal mixing of the front. This mixing is achieved by a deformation of the self-similar profiles that one finds in steady jets. Using a comparison with the local eddy viscosity, and by examining dimensionless fluxes in the vicinity of the front, we show that type II dispersion provides a dominant source of longitudinal mixing.

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“…Validation of the various self-similarity-based statistically unsteady turbulent jet and plume models in Scase, Caulfield & Dalziel (2008), Musculus (2009), Scase, Aspden & Caulfield (2009) and Craske & van Reeuwijk (2015b) indicates that assumption of self-similar mean axial velocity profiles provides a useful basis for development of models in statistically unsteady jets; however, the underlying assumption that self-similarity persists as the jet decelerates has not been examined directly. On the contrary, the measurements by Borée et al (1996) indicate that the radial profiles of phase-averaged axial velocity and other velocity moments deviate from the self-similar profiles of a statistically steady jet as the jet decelerates, and that the profiles vary axially through the confined deceleration region (Borée et al 1996(Borée et al , 1997.…”

Section: Introductionmentioning

confidence: 99%

Self-similar properties of decelerating turbulent jets

2017

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The flow in a decelerating turbulent round jet is investigated using direct numerical simulation. The simulations are initialised with a flow field from a statistically stationary turbulent jet. Upon stopping the inflow, a deceleration wave passes through the jet, behind which the velocity field evolves towards a new statistically unsteady self-similar state. Assumption of unsteady self-similar behaviour leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics. Consistency between these predictions and the simulation data supports the use of the assumption of self-similarity. The mean radial velocity is predicted to reverse in direction near to the jet centreline as the deceleration wave passes, contributing to an approximately threefold increase in the normalised mass entrainment rate. The shape of the mean axial velocity profile undergoes a relatively small change across the deceleration transient, and this observation provides direct evidence in support of previous models that have assumed that the mean axial velocity profile, and in some cases also the jet spreading angle, remain approximately constant within unsteady jets.

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Temporal variation of non-ideal plumes with sudden reductions in buoyancy flux

Cited by 15 publications

References 16 publications

Generalised unsteady plume theory

Generalised unsteady plume theory

Energy dispersion in turbulent jets. Part 1. Direct simulation of steady and unsteady jets

Self-similar properties of decelerating turbulent jets

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