A new technique is described for measuring the axial mass flow rate in the turbulent jet formed when a gas in injected into a reservoir of stagnant air at uniform pressure. The jet is surrounded by a porous-walled cylindrical chamber, and air is injected through the wall until the pressure in the chamber is uniform and atmospheric, a condition which is taken to signify that the ‘entrainment appetite’ of the jet is satisfied.Measurements made with the apparatus have allowed the deduction of an entrainment law relating mass flow rate, jet momentum, axial distance and air density, regardless of the injected gas, and including the effects of buoyancy. When the injected gas burns in the jet the entrainment rate is up to 30% lower than when it does not.

Measurements of entrainment by axisymmetrical turbulent jets

The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated The Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques The entire room was fully seeded for the LDA measurements The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environmentThe results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline) The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211209400323X

Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet

When a fluid which is lighter than its surroundings is emitted by a source under a sloping roof (or a heavier fluid from a source on a sloping floor), it may flow as a relatively thin turbulent layer. The motion of this layer is governed by the rate at which it entrains the ambient fluid. A theory is presented in which it is assumed that the entrainment is proportional to the velocity of the layer multiplied by an empirical function, E(Ri), of the overall Richardson number for the layer defined by Ri = g(ρa - ρ) h/ρa V2. This theory predicts that in most practical cases the layer will rapidly attain an equilibrium state in which Ri does not vary with distance downstream, and the gravitational force on the layer is just balanced by the drag due to entrainment together with friction on the floor or roof.Two series of laboratory experiments are described from which E(Ri) can be determined. In the first, the spread of a surface jet of fluid lighter than that over which it is flowing is measured; in the second, a study is made of the flow of a heavy liquid down the sloping floor of a channel. These experiments show that E falls off rapidly as Ri increases and is probably negligible when Ri is more than about 0·8.The theoretical and experimental results allow predictions to be made of flow velocities once the rate of supply of density difference is known. An estimate is also given of the uniform velocity which the ambient fluid must possess in order to cause the motion of the layer to be reversed.

Turbulent entrainment in stratified flows

Violent respiratory events such as coughs and sneezes play a key role in transferring respiratory diseases between infectious and susceptible individuals. We present the results of a combined experimental and theoretical investigation of the fluid dynamics of such violent expiratory events. Direct observation of sneezing and coughing events reveals that such flows are multiphase turbulent buoyant clouds with suspended droplets of various sizes. Our observations guide the development of an accompanying theoretical model of pathogen-bearing droplets interacting with a turbulent buoyant momentum puff. We develop in turn discrete and continuous models of droplet fallout from the cloud in order to predict the range of pathogens. According to the discrete fallout model droplets remain suspended in the cloud until their settling speed matches that of the decelerating cloud. A continuous fallout model is developed by adapting models of sedimentation from turbulent fluids. The predictions of our theoretical models are tested against data gathered from a series of analogue experiments in which a particle-laden cloud is ejected into a relatively dense ambient. Our study highlights the importance of the multiphase nature of respiratory clouds, specifically the suspension of the smallest drops by circulation within the cloud, in extending the range of respiratory pathogens.

/pdf/violent-expiratory-events-on-coughing-and-sneezing-mvnnymz7ur.pdf

Violent expiratory events: on coughing and sneezing

The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.

Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows

Theories of convection from maintained and instantaneous sources of buoyancy are developed, using methods which are applicable to stratified body fluids with any variation of density with height; detailed solutions have been presented for the case of a stably stratified fluid with a linear density gradient. The three main assumptions involved are (i) that the profiles of vertical velocity and buoyancy are similar at all heights, (ii) that the rate of entrainment of fluid at any height is proportional to a characteristic velocity at that height, and (iii) that the fluids are incompressible and do not change volume on mixing, and that local variations in density throughout the motion are small compared to some reference density. The governing equations are derived in non-dimensional form from the conditions of conservation of volume, momentum and buoyancy, and a numerical solution is obtained for the case of the maintained source, This leads to a prediction of the final height to which a plume of light fluid will rise in a stably stratified fluid. Estimates of the constant governing the rate of entrainment are made by comparing the theory with some previous results in uniform fluids, and with the results of new experiments carried out in a stratified salt solution. For the case of an instantaneous source of buoyancy there is an exact solution; the entrainment constant is again estimated from laboratory results for a stratified fluid Finally, the analysis is applied to the (compressible) atmosphere, by making the customary substitution of potential temperature for temperature. Predictions are made of the height to which smoke plumes from typical sources of heat should rise in a still, stably stratified atmosphere under various conditions.

Turbulent gravitational convection from maintained and instantaneous sources

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Turbulent gravitational convection from maintained and instantaneous sources