A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

Closure of the Reynolds stress and scalar flux equations

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors' knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well.The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.

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A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

The present study systematically investigates through experiments the influence of Reynolds number on a plane jet issuing from a radially contoured, rectangular slot nozzle of large aspect ratio. Detailed velocity measurements were performed for a jet exit Reynolds number spanning the range 1500≤Reh≤16 500, where Reh≡Ubh/υ with Ub as the momentum-averaged exit mean velocity, h as the slot height, and υ as the kinematic viscosity. Additional centerline measurements were also performed for jets from two different nozzles in the same facility to achieve Reh=57 500. All measurements were conducted using single hot-wire anemometry to an axial distance (x) of x≤160h. These measurements revealed a significant dependence of the exit and the downstream flows on Reh despite all exit velocity profiles closely approximating a “top-hat” shape. The effect of Reh on both the mean and turbulent fields is substantial for Reh<10 000 but becomes weaker with increasing Reh. The length of the jet’s potential core, initial pri...

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The influence of Reynolds number on a plane jet

An integral technique suggested for the analysis of turbulent jets by Corrsin & Uberoi (1950) and Morton, Taylor & Turner (1956) is re-examined in an attempt to improve the description of the entrainment. It is determined that the hypothesis of Priestley & Ball (1955), that the entrainment coefficient is a linear function of the jet Richardson number, is reasonable, and that two empirically determined plume parameters are sufficient to describe the transition of buoyant jets to plumes. The results of a series of experiments in which both time-averaged velocity and time-averaged temperature profiles were recorded in a substantial number of plane turbulent buoyant jets of varying initial Richardson numbers are used to verify the basic ideas. In addition, measurements of the mean tracer flux in a series of buoyant jets indicate that as much as 40% of the transport in plumes is by the turbulent flux.

/pdf/plane-turbulent-buoyant-jets-part-1-integral-properties-3mdsxpxa6t.pdf

Plane turbulent buoyant jets. Part 1. Integral properties

Mean Temperature and Velocity in a Plane Turbulent Jet

The velocities of the flow in the vicinity of the interface, of the apparent lateral motion of the interface, and of entrainment are compared for a plane two‐dimension jet.

P. E. Jenkins

Papers

Mean Temperature and Velocity in a Plane Turbulent Jet

Interface related velocities in turbulent plane jets