Self-Preserving Properties of Unsteady Round Buoyant Turbulent Plumes and Thermals in Still Fluids
01 Oct 2003-Journal of Heat Transfer-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 125, Iss: 5, pp 821-830
TL;DR: In this paper, the authors investigated the self-preserving properties of round buoyant turbulent starting plumes and starting jets in unstratified environments with dye-containing salt water sources injected vertically downward into still fresh water within a windowed tank.
Abstract: The self-preserving properties of round buoyant turbulent starting plumes and starting jets in unstratified environments. The experiments involved dye-containing salt water sources injected vertically downward into still fresh water within a windowed tank. Time-resolved images of the flows were obtained using a CCD camera. Experimental conditions were as follows: source diameters of 3.2 and 6.4 mm, source/ambient density ratios of 1.070 and 1,150, source Reynolds numbers of 4,000-11,000, source Froude numbers of 10-82, volume of source fluid for thermals comprising cylinders having the same cross-sectional areas as the source exit and lengths of 50-382 source diameters, and stream-wise flow penetration lengths up to 110 source diameters and 5.05 Morton length scales from the source. Near-source flow properties varied significantly with source properties but the flows generally became turbulent and then became self-preserving within 5 and 20-30 source diameters from the source, respectively. Within the self-preserving region, both normalized streamwise penetration distances and normalised maximum radial penetration distances as functions of time were in agreement with the scaling relationships for the behavior of self-preserving round buoyant turbulent flows to the following powers: time to the 3/4 power for starting plumes and to the 1/2 power for thermals. Finally, the virtual origins of thermals were independent of source fluid volume for the present test conditions.
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TL;DR: This survey, although extensive cannot include every paper; some selection is necessary, is intended to encompass the English language heat transfer papers published in 2003, including some translations of foreign language papers.
106 citations
Cites methods from "Self-Preserving Properties of Unste..."
...The self-preserving properties of round buoyant turbulent plumes were observed in still fluids [558] and in a uniform cross-flow [559] using a water channel, a CCD camera and tracer dye....
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...[558] F....
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TL;DR: In this article, the authors compare the results of laboratory fluid dynamics experiments with theoretical models of turbulent entrainment in two-phase buoyant plumes and thermals to estimate the amount of mixing between the iron core of a planetesimal or planetary embryo and the molten silicates in a magma pool formed by its impact with a growing planet during accretion.
85 citations
Cites result from "Self-Preserving Properties of Unste..."
...Experiments on non-buoyant ‘puffs’ (turbulent isolatedmasses of fluid with initial momentum) suggest that the magnitude of the entrainment coefficient is very similar to that measured for turbulent thermals (Diez et al., 2003; Richards, 1965), and we therefore assume that α remains constant, whether the evolution of the turbulent mass is governed by its initial momentum or its buoyancy....
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...…of fluid with initial momentum) suggest that the magnitude of the entrainment coefficient is very similar to that measured for turbulent thermals (Diez et al., 2003; Richards, 1965), and we therefore assume that α remains constant, whether the evolution of the turbulent mass is governed…...
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TL;DR: In this paper, a density-based solver for compressible supersonic flow, astroFoam, is developed based on the OpenFOAM library, which performs large-eddy simulations of highly underexpanded jets with nozzle pressure ratios from 5.60 to 11.21 at a Reynolds number around 105.
Abstract: High-pressure jet injection into quiescent air is a challenging fluid dynamics problem in the field of aerospace engineering. Although plenty of experimental, theoretical, and numerical studies have been conducted to explore this flow, there is a dearth of literature detailing the flow evolution and instability characteristics, which is vital to the mixing enhancement design and jet noise reduction. In this paper, a density-based solver for compressible supersonic flow, astroFoam, is developed based on the OpenFOAM library. Large-eddy simulations of highly underexpanded jets with nozzle pressure ratios from 5.60 to 11.21 at a Reynolds number around 105 are carried out with a high-resolution grid. A grid-convergence study has been conducted to confirm the fidelity of the large-eddy simulation results. The large-eddy simulation results have also been validated against available literature data in terms of the time-averaged near-field properties of underexpanded jets. The turbulent transition processes are r...
46 citations
Cites background from "Self-Preserving Properties of Unste..."
...[65] measured unsteady round buoyant turbulent plumes and thermals jets for Reynolds numbers ranging from 4000 to 11,000, and their photographs showed that W∕z t decreases rapidly with increasing streamwise distance in the near field (y∕D < 20) and then reaches a constant 0....
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TL;DR: In this article, the characteristics of Boussinesq and non-Boussineq starting forced plumes were investigated, and two distinct periods in the transient plume penetration are identified, namely, the period of flow development (PFD) and period of developed flow (PDF).
Abstract: The characteristics of Boussinesq and non-Boussinesq starting forced plumes were investigated in this study. Two distinct periods in the transient plume penetration are identified, namely, the period of flow development (PFD) and period of developed flow (PDF). Similarity solutions are developed in PDF by incorporating the behaviour of an isolated buoyant vortex ring and recent laboratory results on the trailing forced plume, and the temporal variation of the penetration rate is derived during the different phases of jet-like, transitional and plume-like flow. To verify the similarity solutions, experiments were conducted on vertical starting forced plumes using combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) with refractive index matching. The discharge Reynolds number was varied from 3773 to 7403 and the range of excess densities (Δ 0 =(ρ ∞ -ρ 0 )/ρ ∞ , where ρ 0 and ρ ∞ . are initial plume and ambient density, respectively) from 2.77 % to 25.07 %. The experimental results revealed distinct differences between plumes having an initial density difference of larger or smaller than 15 % due to the non-Boussinesq effects. Thus, the value of 15% was employed as an approximate criterion to divide the plumes into Boussinesq versus non-Boussinesq cases. The measured penetration rates and the mean centreline axial velocity of the Boussinesq starting forced plumes agreed well with the analytical predictions at the fully developed stage. However, the behaviour was substantially more complex for the non-Boussinesq plumes. In the transient records, it was noted that the time scales for the penetration of the starting plumes and the velocity development in the trailing forced plume were similar, but the time scale for the Gaussian profile to become self-similar was somewhat longer.
39 citations
Cites background or methods or result from "Self-Preserving Properties of Unste..."
...Figure 9 shows the values of α′ to be approximately 0.16±0.03 in PDF, in reasonable agreement with Diez et al. (2003) and Turner (1962) who obtained 0.16 and 0.18 for starting plumes, respectively....
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...This combination of fresh and saline water is commonly adopted for experimentation on forced plumes within the Boussinesq range (e.g. Wang & Law 2002; Diez et al. 2003)....
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...The −1/4 time behaviour for starting plumes is also supported by the recent analysis of Diez et al. (2003)....
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...0 in this figure following the suggestion by Diez et al. (2003). It can be seen that although the time exponent can be fitted to be 3/4, the coefficient Cz does not appear to be a constant....
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...03 in PDF, in reasonable agreement with Diez et al. (2003) and Turner (1962) who obtained 0....
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TL;DR: In this article, the effect of different initial conditions numerically by solving the unsteady Reynolds-averaged Navier-Stokes equations with a two-equation turbulence closure was investigated.
Abstract: A round thermal is formed when an element of buoyant fluid is released instantaneously into a quiescent ambient. Although the thermal spreading rate is of primary importance to mathematical modeling, the reported values in the literature vary greatly. To identify possible factors affecting the thermal spreading rate, we investigated the effect of different initial conditions numerically by solving the unsteady Reynolds-averaged Navier–Stokes equations with a two-equation turbulence closure. The initial aspect ratio (i.e. length-to-diameter ratio) of the thermal was varied between 0.125–4.0, and the initial density differences was changed from 1 to 10 %. Results show that the spreading rate is greatly affected by the initial aspect ratio, which also explains the variations in earlier reported values. Following the numerical study, an analytical model using buoyant vortex ring theory is developed to predict the spreading rate of a thermal. The predictions show good agreement with the results from both the numerical simulations and previous experimental studies. Another simple analytical model is also presented to approximate the thermal induced flow, and is validated using the numerical simulations.
30 citations
References
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23 Feb 1973
TL;DR: In this article, the authors introduce linear internal waves and herar flows in a stratified fluid and double-diffusive convection in stably stratified fluids, and show that the shear flows can produce turbulence.
Abstract: Preface 1. Introduction and preliminaries 2. Linear internal waves 3. Finite amplitude motions in stably stratified fluids 4. Instability and the production of turbulence 5. Turbulent shear flows in a stratified fluid 6. Buoyant convection from isolated sources 7. Convection from heated surfaces 8. Double-diffusive convection 9. Mixing across density interfaces 10. Internal mixing processes Bibliography and author index Recent publications Subject index.
2,722 citations
TL;DR: In this article, the authors developed a theory of convection from maintained and instantaneous sources of buoyancy, 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.
Abstract: 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.
2,408 citations
TL;DR: In this article, a review of the progress in relation to how jets and plumes interact with environmental factors, such as density stratification or uniform motion of the ambient fluid is presented.
Abstract: Turbulent jets are fluid flows produced by a pressure drop through an orifice. Their mechanics, although studied for over fifty years, has recently received research attention that has resulted in a much improved understanding of the process by which they entrain surrounding fluid. Turbulent plumes are fluid motions whose primary source of kinetic energy and momentum flux is body forces derived from density inhomogeneities. Plumes have not been studied in the same detail as jets but nevertheless there have been some recent gains in the understanding of their mechanics. In this article we will review this progress, especially in relation to how jets and plumes interact with environmental factors, such as density stratification or uniform motion of the ambient fluid. As will become evident, many problems remain and, in some circumstances, we simply cannot describe precisely what does occur. In such cases we will try to provide current references and suggest approaches for future research.
617 citations