Lateral dispersion from a concentrated line source in turbulent channel flow

Abstract

The dispersion of a passive scalar (temperature) from a concentrated line source in fully developed, high-aspect-ratio turbulent channel flow is studied herein. The line source is oriented in the direction of the inhomogeneity of the velocity field, resulting in a thermal plume that is statistically three-dimensional. This configuration is selected to investigate the lateral dispersion of a passive scalar in an inhomogeneous turbulent flow (i.e. dispersion in planes parallel to the channel walls). Measurements are recorded at six wall-normal distances (y/ h = 0.10, 0.17, 0.33, 0.50, 0.67 and 1.0), six downstream positions (x/ h = 4.0, 7.4, 10.8, 15.2, 18.6 and 22.0) and a Reynolds number of Re ≡ U y = h h/ν = 10 200 (Re τ ≡ u * h/ν = 502). The lateral mean temperature excess profiles were found to be well represented by Gaussian distributions. The rootmean-square (r.m.s.) profiles, on the other hand, were symmetric, but non-Gaussian. Consistent with homogeneous flows (and in contrast to the work of Lavertu & Mydlarski (J. Fluid Mech., vol. 528, 2005, p. 135) studying transverse dispersion in the same flow), (i) the downstream growth rate of the centreline mean temperature excess, centreline r.m.s. temperature fluctuation and half-width of the mean and r.m.s. temperature profiles followed a power law evolution in the downstream direction, and (ii) the r.m.s. profiles evolved from single-peaked to double-peaked profiles far downstream. By comparing the measured ratios of the centreline r.m.s. temperature fluctuation to the mean temperature excess to the ratios measured in other flows, it was hypothesized that the mean-flow shear, as well as the turbulence intensity, played an important, cooperative role in increasing the mixedness of the flow. The probability density functions (PDFs) were quasi-Gaussian near the wall as well as for largeenough downstream distances. Closer to both the source and the channel centreline, the PDFs were better approximated by exponential distributions, with a sharp peak corresponding to the free-stream temperature. For intermediate downstream distances, the PDFs of the lateral dispersion were better mixed than analogous PDFs of the transverse dispersion, consistent with the mixedness measurements.

Measurements of turbulent diffusion in uniformly sheared flow

“…This value is equal to the value reported by Webster et al, within the range of 0.55 to 0.76 reported by Lepore & Mydlarski (2011), and comparable to the value 0.83 fitted by us to the data of Karnik & Tavoularis. When comparing measurements in the present plume to those from the literature, it is also important to consider the state of growth of each plume with respect to the local size of the turbulent eddies which convect and diffuse the scalar field. The lengthscale ratio σ 2 L 22,2 may be chosen as a measure of relative plume growth.…”

“…The present plume differs from the one studied by Warhaft (1984), Karnik & Tavoularis (1989), and Lepore & Mydlarski (2011) in an important aspect: the former originated from essentially a point source, whereas the latter originated from a line-source and was two-dimensional on the mean. In a line-source plume, strong scalar fluctuations would be introduced mainly by transverse motions (i.e., in a direction parallel to the mean scalar gradient), whereas in a point-source plume, motions in all directions on a transverse plane may introduce strong scalar fluctuations.…”

“…All present profiles of c ′ (see figure 7b) were single-peaked, unlike some of the profiles presented by Warhaft (1984), Karnik & Tavoularis (1989), Rahman & Webster (2005), and Lepore & Mydlarski (2011), which were double-peaked. Karnik & Tavoularis attributed the presence of double peaks in the near-source profiles to the particular shape of the thermal wake of the heated ribbon used, a feature that is absent in the present experiments.…”

“…Examples of investigations of turbulent diffusion in the environment include early observations of anti-aircraft shell-bursts (Roberts 1923;Sutton 1932) and plumes of lycopodium spores released in the atmosphere (Hay & Pasquill 1959) and dyes released in a lake (Csanady 1963). Examples of relevant laboratory studies include investigations of diffusion behind a line source in grid turbulence (Warhaft 1984;Anand & Pope 1985;Stapountzis et al 1986), a line source in uniformly sheared flow (Tavoularis & Corrsin 1981;Karnik & Tavoularis 1989), a line source in channel flow (Lepore & Mydlarski 2011), a point source in uniformly sheared flow (Nakamura et al 1986), and a point source in channel flows (Webster et al 2003;Rahman & Webster 2005). In these actual turbulent flows, the turbulent kinetic energy and lengthscale would generally evolve downstream and so would the diffusivities of superimposed scalar plumes.…”

“…Strong scalar intermittency is specific to the present plume, which is relatively slender and also contains a dye with an extremely small molecular diffusivity. These specific conditions differentiate the present configuration from thermal plumes in wind tunnels (e.g., Tavoularis & Corrsin 1981;Karnik & Tavoularis 1989;Lepore & Mydlarski 2011). The values at each pixel of all recorded instantaneous concentration maps were averaged to produce the corresponding mean concentration maps.…”