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RESEARCH PAPERS: Natural and Mixed Convection

# Self-Preserving Mixing Properties of Steady Round Buoyant Turbulent Plumes in Uniform Crossflows

[+] Author and Article Information
F. J. Diez

Department of Mechanical and Aerospace Engineering,  Rutgers, The State University of New Jersey, Piscataway, NJ 08854-8058diez@rutgers.edu

L. P. Bernal, G. M. Faeth

Department of Aerospace Engineering,  The University of Michigan, Ann Arbor, MI 48109-2140

J. Heat Transfer 128(10), 1001-1011 (Jul 07, 2006) (11 pages) doi:10.1115/1.2345424 History: Received March 31, 2005; Revised July 07, 2006

## Abstract

The self-preserving mixing properties of steady round buoyant turbulent plumes in uniform crossflows were investigated experimentally. The experiments involved salt water sources injected into fresh water crossflows within the windowed test section of a water channel. Mean and fluctuating concentrations of source fluid were measured over cross sections of the flow using planar-laser-induced fluorescence which involved seeding the source fluid with Rhodamine 6G dye and adding small concentrations of ethanol to the crossflowing fluid in order to match the refractive indices of the source flow and the crossflow. The self-preserving penetration properties of the flow were correlated successfully based on the scaling analysis of Diez, Bernal, and Faeth (2003, ASME J. Heat Transfer, 125, pp. 1046–1057) whereas the self-preserving structure properties of the flow were correlated successfully based on the scaling analysis of Fischer (1979, Mixing in Inland and Coastal Waters, Academic Press, New York, pp. 315–389); both approaches involved assumptions of no-slip convection in the cross stream (horizontal) direction (parallel to the crossflow) and a self-preserving line thermal having a conserved source specific buoyancy flux per unit length that moves in the streamwise (vertical) direction (parallel to the direction of both the initial source flow and the gravity vector). The resulting self-preserving structure consisted of two counter-rotating vortices having their axes nearly aligned with the crossflow direction that move away from the source in the streamwise (vertical) direction due to the action of buoyancy. Present measurements extended up to 202 and 620 source diameters from the source in the streamwise and cross stream directions, respectively. The onset of self-preserving behavior required that the axes of the counter-rotating vortex system be nearly aligned with the crossflow direction. This alignment, in turn, was a strong function of the source/crossflow velocity ratio, $uo∕v∞$. The net result was that the onset of self-preserving behavior was observed at streamwise distances of 10–20 source diameters from the source for $uo∕v∞=4$ (the smallest value of $uo∕v∞$ considered), increasing to streamwise distances of 160–170 source diameters from the source for $uo∕v∞=100$ (the largest value of $uo∕v∞$ considered). Finally, the counter-rotating vortex system was responsible for substantial increases in the rate of mixing of the source fluid with the ambient fluid compared to axisymmetric round buoyant turbulent plumes in still environments, e.g., transverse dimensions in the presence of the self-preserving counter-rotating vortex system were 2–3 times larger than the transverse dimensions of self-preserving axisymmetric plumes at similar streamwise distances from the source.

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## Figures

Figure 1

Visualization of the penetration properties of a steady turbulent plume in a uniform crossflow (d=6.4mm,Reo=5000,ρo∕ρ∞=1.150,Fro=223,uo∕v∞=7). The upper figure is a side view; the lower figure is a top view.

Figure 2

Sketches of a steady turbulent plume in a uniform crossflow

Figure 6

Plots of the development of mean and fluctuating concentrations of source fluid in terms of self-preserving variables for transverse paths through the vortex axes over the cross section of the flow for steady turbulent plumes in crossflows

Figure 7

Plots of mean concentrations of source fluid in terms of self-preserving variables for various vertical and horizontal paths over the cross section of the flow for steady turbulent plumes in crossflows within the self-preserving region

Figure 8

Plots of rms concentration fluctuations of source fluid in terms of self-preserving variables for various vertical and horizontal paths over the cross section of the flow for steady turbulent plumes in crossflows within the self-preserving region

Figure 9

Contour plots of mean concentrations of source fluid in terms of self-preserving variables over the cross section of the flow for steady turbulent plumes in crossflows within the self-preserving region

Figure 10

Contour plots of rms concentration fluctuations of source fluid in terms of self-preserving variables over the cross section of the flow for steady turbulent plumes in crossflows within the self-preserving region

Figure 3

Flow regime map of the developing flow and self-preserving regions for steady turbulent plumes in crossflows

Figure 4

Instantaneous PLIF images of the cross section of a steady turbulent plume in a uniform crossflow (d=3.2mm, Reo=10,000, ρo∕ρ∞=1.038, Fro=223, uo∕v∞=47, (xc−xos)∕d=120, y∕d=98, and Δt=50ms between frames)

Figure 5

Streamwise and transverse penetration distances, and the transverse spacing between the vortex axes, in terms of self-preserving variables for steady turbulent plumes in crossflows

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