Scalar mixing from a concentrated source in turbulent channel flow

Abstract

The mixing of a scalar (temperature) emitted from a concentrated line source in fully developed high-aspect-ratio turbulent channel flow is studied. The motivation for the work is to study the effect of the inhomogeneity on the scalar dispersion. It is most readily carried out in a flow that is inhomogeneous in only one direction, i.e. channel flow. Experiments were performed at two Reynolds numbers ($\hbox{\it Reacute;\,{\equiv}\,\langle U(y=h)\rangle h/\nu\,{=}\,10\,400$ and 22800), three wall-normal source locations ($y_s/h\,{=}\,0.067$, 0.17 and 1.0) and six downstream distances ($4.0 \,{\le}\, x/h \,{\le}\,22.0$). Both the mean and r.m.s. temperature profiles were found to be described well by truncated Gaussian distributions. In contrast to homogeneous flows, (i) the growth rates of the mean profile widths did not exhibit power law behaviours, (ii) the centres of the r.m.s. profiles were found to drift towards the centre of the channel for plumes emanating from off-centreline source locations and (iii) the r.m.s. profiles showed no tendency towards double peaks far downstream, as are observed in homogeneous flows. For near-wall source locations, the probability density function (PDF) of the scalar fluctuations evolved from a quasi-Gaussian distribution near the wall to a strongly positively skewed PDF (with a large spike at the cold-fluid temperature) for transverse locations away from the wall. Increasing the Reynolds number was found to improve the mixing, even though this decreases the amount of time for which the scalar can mix (owing to the more rapid advection). For the centreline source location, the PDF shape was, in general, more spiked, indicating the importance of the flapping of the plume in this case. The effect of the meandering of the plume was less significant when the plume was bounded by the wall. Second- and third-order velocity–temperature correlations were presented. The differences in their profiles for the near-wall and centreline source locations were distinct.

Large-Eddy Simulation of Dispersion from Line Sources in a Turbulent Channel Flow

“…There is a considerable literature on dispersion in various turbulent fields, including homogeneous isotropic turbulence and both homogeneous and inhomogeneous turbulent shear flows. Excellent reviews on some of these are given by Sreenivasan (1991), Warhaft (2000), Shraiman and Siggia (2000) and Lavertu and Mydlarski (2005). A brief overview is given below, by way of introduction to the specific situation considered in the present paper.…”

“…Experiments in inhomogeneous flows are more limited, but include investigation of dispersion from a line source in a channel flow (Lavertu and Mydlarski, 2005) and a point source in a boundary layer flow (Fackrell and Robins, 1982). The latter conducted experiments with both ground-level and elevated sources.…”

“…advection, production, diffusion and dissipation) in the variance transport equation. Lavertu and Mydlarski (2005) used a nominally two dimensional fully developed turbulent channel flow at two different Reynolds number, Re = 10,400 and 22,800 (based on channel halfwidth, h, and the mean velocity at the channel centre, U). Scalar mixing from line sources placed at three different wall-normal locations was studied.…”

“…Bakosi et al (2007) developed the IECM (Interaction by Exchange with the Conditional Mean) model to obtain the joint PDF of the velocity and scalar. The first and second moments of the scalar from two line sources at y s /h = 0.067 and 1 in a high-aspect-ratio channel flow at a Reynolds number (based on h and the friction velocity u τ ) Re τ = 1080 were compared with the experiments of Lavertu and Mydlarski (2005). Comments on these comparisons will be made later (in §4.2.1, 4.2.2 and 4.2.3).…”

“…This is discussed in §3 after details of the numerical methods are presented in §2. The major part of the work -simulations of the experiments of Lavertu and Mydlarski (2005) (thermal dispersion from three line sources in a fully developed channel flow at Re τ = 520) -is contained in §4. This includes consideration of the mean and fluctuating scalar fields, along with eddy diffusivities which would be difficult to obtain from laboratory experiments.…”