Computer simulation of turbulent mass transfer at a mobile interface

Abstract

Numerical solutions to the unaveraged mass balance equation for the case of a flat mobile interface reveal that both high-and low-frequency velocity fluctuations can contribute to mass transfer. This is in contrast to transport to a solid boundary where only low-frequency fluctuations, normal to the wall, are important. The average mass transfer coefficient is found to depend on Schmidt number to the -0.5 power, in agreement with classical theories. It is related to the velocity field in the liquid primarily through the mean-square value of the gradient of normal velocity fluctuations at the interface. SCOPEThe absorption of a slightly soluble gas in a concurrent, turbulent gas-liquid flow is controlled by flow fluctuations in the liquid through mechanisms that are not yet understood. This is a situation where the Schmidt number is large, and as a consequence the concentration boundary layer in the liquid is confined to a very thin region near the interface. Shear, caused by the gas flow, induces wave formation and also greatly enhances mass transfer rates. Mass transfer coefficients measured by Aisa et al. (1981) and McCready and Hanratty (1 984b) are about one order of magnitude larger than those found for turbulent mass transfer at a solid boundary. The fundamental problem that must be considered in order to understand mass transfer in these complex flows is how the gas and liquid velocity fields interact to control the transport rate. The work presented here addresses this question by numerically solving the unaveraged mass balance equations for a randomly varying velocity.A similar approach was taken previously by Campbell and Hanratty (1983) in their studies of mass transfer between a turbulent fluid and a solid boundary. These yielded the surprising result that mass transfer is controlled by low-frequency velocity fluctuations normal to the surface that contain only a small fraction of the turbulent energy.The principal hydrodynamic difference between the case considered here and the case considered by Campbell and Hanratty is that near a mobile boundary the velocity normal to the boundary varies linearly with distance from the boundary, rather than quadratically. The goal of this work has been to explore the consequences of this difference. CONCLUSIONS AND SIGNIFICANCEMass transfer at a mobile boundary (a clean gas-liquid interface) is found to be fundamentally different from mass transfer at an immobile boundary (a contaminated gas-liquid interface or a solid), in that velocity fluctuations of all frequencies are playing an important role. This is reflected in the equations for the massThe presentaddressof Eleni Vassiliadou is KoninklijkeShell Lab.. Amsterdam, Holland. transfer coefficient that are derived from computer experiments.The velocity normal to mobile and immobile surfaces are given respectively by u = p ( x , z, t ) y, and u = p ( x , z, t ) y', where all terms have been made dimensionless using a friction velocity and the kinematic viscosity. Campbell and Hanratty (1983) T h e importanc...

Direct numerical simulation of turbulent scalar transport across a flat surface

“…For low to moderate R T it was also found that K L /u ∞ ∝ R − 1 /2 T . The above is in agreement with the large eddy model of Fortescue & Pearson (1967), A direct comparison of K L obtained in the DNS-s and several grid-stirred experiments with the surface divergence model of McCready et al (1986) showed a very good agreement when using a constant of proportionality of 0.525.…”

“…Laboratory measurements have indeed shown β rms to be a good measure for mass transfer as it implicitly takes the surface conditions into account (Turney & Banerjee 2013). Figure 9 shows the dependency of K L on the surface divergence supporting the surface divergence model of McCready et al (1986), K L ∝ √ β rms D. It can be seen that our numerical results predict that K L = 0.525 √ β rms D which matches the trend of the experimental results in grid-stirred tanks performed by Herlina & Jirka (2008); McKenna & McGillis (2004a). The advantage of the present numerical simulation is that surface contamination is not an issue so that unbiased investigations of the effect of Sc and the turbulence levels (here described in terms of the turbulent Reynolds number R T ) can be performed.…”

“…McCready et al 1986) this linear relationship between K L and D was found to be an oversimplification of the actual transfer process. Higbie (1935) realised that the actual transfer velocity was strongly dependent on the rate at which turbulence replaced the saturated fluid near the interface by fresh fluid from below.…”

“…Theofanous et al (1976) subsequently proposed two regimes, in which the large-eddy model is valid for low R T and the small-eddy model is valid for high R T , where the critical R T is approximately 500. Finally, by performing numerical investigations, McCready et al (1986) found that the surface divergence plays an important role in the interfacial gas transfer process. The main problem of conceptual models (reviews of models can be found in e.g.…”

Isotropic-turbulence-induced mass transfer across a severely contaminated water surface

“…Theofanous et al (1976) proposed two regimes, in which the large-eddy model is valid for low R T and the small-eddy model is valid for high R T , where the critical R T is approximately 500. Another conceptual model is the surface divergence model, originating from the numerical investigation by McCready, Vassiliadou & Hanratty (1986 Kermani et al 2011;Herlina & Wissink 2014) confirmed that surface divergence provides a good measure for the transfer velocity, as surface conditions are implicitly taken into account. Recently, however, Turney & Banerjee (2013) found that the surface divergence model is not applicable when a portion of the near-surface motions hold small time scales.…”