Streamwise dispersion and mixing in quasi-two-dimensional steady turbulent jets

Landel, Julien R. and Caulfield, C. P. and Woods, Andrew W. (2012) Streamwise dispersion and mixing in quasi-two-dimensional steady turbulent jets. Journal of Fluid Mechanics, FirstV. pp. 1-47. DOI 10.1017/jfm.2012.388

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Abstract

We investigate experimentally and theoretically the streamwise transport and dispersion properties of steady quasi-two-dimensional plane turbulent jets discharged vertically from a slot of width into a fluid confined between two relatively close rigid boundaries with gap . We model the evolution in time and space of the concentration of passive tracers released in these jets using a one-dimensional time-dependent effective advection–diffusion equation. We make a mixing length hypothesis to model the streamwise turbulent eddy diffusivity such that it scales like , where is the streamwise coordinate, is the jet width, is the maximum time-averaged vertical velocity. Under these assumptions, the effective advection–diffusion equation for , the horizontal integral of the ensemble-averaged concentration, is of the form , where is time, (the advection parameter) and (the dispersion parameter) are empirical dimensionless parameters which quantify the importance of advection and dispersion, respectively, and is the source momentum flux. We find analytical solutions to this equation for in the cases of a constant-flux release and an instantaneous finite-volume release. We also give an integral formulation for the more general case of a time-dependent release, which we solve analytically when tracers are released at a constant flux over a finite period of time. From our experimental results, whose concentration distributions agree with the model, we find that and , for both finite-volume releases and constant-flux releases using either dye or virtual passive tracers. The experiments also show that streamwise dispersion increases in time as . As a result, in the case of finite-volume releases more than 50 % of the total volume of tracers is transported ahead of the purely advective front (i.e. the front location of the tracer distribution if all dispersion mechanisms are ignored and considering a ‘top-hat’ mean velocity profile in the jet); and in the case of constant-flux releases, at each instant in time, approximately 10 % of the total volume of tracers is transported ahead of the advective front.

Item Type: Article
Uncontrolled Keywords: 2012AREP; IA64; BPI;
Subjects: 99 - Other
Divisions: 99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: FirstV
Page Range: pp. 1-47
Identification Number: 10.1017/jfm.2012.388
Depositing User: Sarah Humbert
Date Deposited: 27 Oct 2012 12:52
Last Modified: 23 Jul 2013 10:05
URI: http://eprints.esc.cam.ac.uk/id/eprint/2615

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