Turbulent transport and entrainment in jets and plumes: A DNS study

Abstract

We present a direct numerical simulation (DNS) data set for a statistically axisymmetric turbulent jet, plume, and forced plume in a domain of size 40r0×40r0×60r0, where r0 is the source diameter. The data set supports the validity of the Priestley-Ball entrainment model in unstratified environments (excluding the region near the source) [Priestley and Ball, Q. J. R. Meteor. Soc. 81, 144 (1955)], which is corroborated further by the Wang-Law and Ezzamel et al. experimental data sets [Wang and Law, J. Fluid Mech. 459, 397 (2002); Ezzamel et al., J. Fluid Mech. 765, 576 (2015)], the latter being corrected for a small but influential coflow that affected the statistics. We show that the second-order turbulence statistics in the core region of the jet and the plume are practically indistinguishable from each other, although there are significant differences near the plume edge. The DNS data indicate that the turbulent Prandtl number is about 0.7 for both jets and plumes. For plumes, this value is a result of the difference in the ratio of the radial turbulent transport of radial momentum and buoyancy. For jets, however, the value originates from a different spread of the buoyancy and velocity profiles, in spite of the fact that the ratio of radial turbulent transport terms is approximately unity. The DNS data do not show any evidence of similarity drift associated with gradual variations in the ratio of buoyancy profile to velocity profile widths

The turbulent Prandtl number in a pure plume is 3/5

“…Chen & Rodi 1980;Pietri et al 2000;Wang & Law 2002;Ezzamel et al 2015;van Reeuwijk et al 2016, and the experimental data in table 1). For jets it is well established that the observation Sc T < 1 is consistent with the ratio ϕ of the width of the scalar profile to the width of the velocity profile being greater than one (Chen & Rodi 1980;van Reeuwijk et al 2016). A similar approach has been used to explain why Pr T < 1 in plumes (Carazzo, Kaminski & Tait 2006;Ezzamel et al 2015).…”

“…Entrainment determines the rate at which passive and active scalars are diluted as a plume mixes with its surroundings (van Reeuwijk et al 2016) and therefore provides a conceptual and physical link between several plume integrals relating to scalar transport. Whilst van reported consistency requirements for entrainment from momentum and energy conservation, the present work focuses on entrainment relations that can be derived from scalar transport budgets.…”

“…Experiments and direct simulations indicate that the turbulent Schmidt number Sc T and the turbulent Prandtl number Pr T in jets and plumes, respectively, are less than one (see e.g. Chen & Rodi 1980;Pietri et al 2000;Wang & Law 2002;Ezzamel et al 2015;van Reeuwijk et al 2016, and the experimental data in table 1). For jets it is well established that the observation Sc T < 1 is consistent with the ratio ϕ of the width of the scalar profile to the width of the velocity profile being greater than one (Chen & Rodi 1980;van Reeuwijk et al 2016).…”

“…Ezzamel, Salizzoni & Hunt 2015, and references therein) and, more recently, numerical simulations (e.g. Plourde et al 2008;van Reeuwijk et al 2016). In spite of the vast quantity of data that have been…”

Turbulence Measurement of Vertical Dense Jets in Crossflow

“…The mixing of discharged fluids with a surrounding natural fluid is of primary concern for a wide range of engineering and environmental applications, i.e., the discharge of wastewater in receiving natural water bodies, the ascending motions of thermals in the atmosphere, the dynamic of volcanic eruption columns, the fuel injection in combustion chambers, the engineering propulsion systems, the propagation of smoke in free or enclosed spaces [1]. Brine discharge from desalination plants, as an example, is the concern of many countries around the world.…”