Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

Abstract

We present simultaneous two-dimensional velocity and scalar measurements on a central vertical plane in a pure turbulent plume. We use an edge-detection algorithm to determine the edge of the plume, and compare the data obtained in both a fixed Eulerian frame and a frame relative to local coordinates defined in terms of the instantaneous plume edge. In an Eulerian frame we observe that the time-averaged distributions of vertical and horizontal velocity are self-similar, the vertical velocity being well represented by a Gaussian distribution. We condition these measurements on whether fluid is inside or outside of the plume, and whether fluid inside is mixed plume fluid or engulfed ambient fluid. We find that, on average, 5% of the total vertical volume transport occurs outside the plume and this figure rises to nearly 14% at heights between largescale coherent structures. We show that the fluxes of engulfed fluid within the plume envelope are slightly larger than the vertical transport outside the plume -indicating that ambient fluid is engulfed into the plume envelope before being nibbled across the turbulent/non-turbulent interface (TNTI) and then ultimately irreversibly mixed. Our new measurements in the plume coordinate (following the meandering fluctuating plume)show the flow within the plume and in the nearby ambient fluid is strongly influenced by whether an eddy is present locally within the plume, or absent. When an eddy is present and the plume is wide, the vertical velocities near the plume edge are small and hence all vertical transport is inside the plume. In regions where the plume is narrow † Email address for correspondence: h.burridge@imperial.ac.uk 2 H. C. Burridge, D. A. Parker, E. S. Kruger, J. L. Partridge and P. F. Linden and there is no eddy, large vertical velocities and hence transport are observed outside the plume suggesting that pressure forces associated with the eddies accelerate ambient fluid which is then engulfed into the plume. Finally, we show that observing significant vertical velocities beyond the scalar edge of the plume does not suggest that the characteristic width of the velocity distribution is greater than that of the scalar field; on the contrary, we show our observations to be consistent with a buoyancy distribution that is up to 20% wider than that of the velocity. Measurements in the plume coordinates show that the mixing of momentum across the plume results in a distribution for which the differential entropy is close to maximal and the mixing of momentum is uninhibited (i.e. not bounded) by the TNTI of the plume. Furthermore, our measurements suggest that the scalar mixing across the plume may also result in a distribution for which the differential entropy is close to maximal but, in contrast to the momentum, the scalar mixing is strictly bounded by the plume edge.

A comparison of entrainment in turbulent line plumes adjacent to and distant from a vertical wall

“…In the case of the free plume, since C P = (E R + E L )/2, it follows that the Pearson's correlation coefficient is ρ E R ,E L = 0.16. This may be compared to a free axisymmetric plume where it was found that ρ E R ,E L = 0 (Burridge et al 2017). So although the correlation between the two edges is larger than that for an axisymmetric plume, it is still small.…”

“…The red and blue dashed curves show the Gaussian best fits to data of the statistics performed with a threshold of b t /b m = 0.17 − 20% and b t /b m = 0.17 + 20%, respectively, for the wall plume and b t /b m = 0.35 − 20% and b t /b m = 0.35 + 20%, respectively, for the free plume, highlighting the insensitivity of our results to the choice of threshold. Figure 10: The probability, at a given horizontal location, of being within the plume region bounded by the outer TNTI for the free plume (solid black line) wall plume (dashed black line) and for comparison an axisymmetric plume (grey line) (Burridge et al 2017).…”

“…In order to quantify the effect of the meandering of the free plume on the large-scale engulfment we calculate the conditional vertical transport of ambient fluid, for both the free and wall plumes, by considering, separately, ambient fluid outside the TNTI envelope and engulfed but unmixed fluid. In order to calculate the fluxes of the ambient fluid we follow a method equivalent to that of Burridge et al (2017) by first defining an instantaneous step function for the outer ambient fluid…”

“…In doing so relative contributions to the entrainment coefficient may be compared between the free and wall plume. We also use methods developed by Mistry et al (2016) and Burridge et al (2017) to examine the statistics of the TNTI by both quantifying the increased meandering in a free plume and relating this to the increased length of the TNTI in the free plume. This is achieved by making simultaneous measurements of velocity and buoyancy in self-similar line plumes adjacent to and far from a vertical wall.…”

Vertically distributed wall sources of buoyancy. Part 2. Unventilated and ventilated confined spaces

“…This is due to the vertical transport of ambient fluid by the distributed wall-source plume, which is equal to Q p (z) − Q b (0, z). Significant vertical transport of ambient fluid has also been observed in both axisymmetric (Burridge et al 2017), wall and free line plumes (Parker et al 2020). The plume, therefore, transports (unmixed) ambient fluid into the stratified region.…”