Direct numerical simulation of turbulent scalar transport across a flat surface. (10th April 2014)

• Record Type: Journal Article
• Authors: Herlina, H.; Wissink, J. G.
• Is Part Of: Journal of fluid mechanics. Volume 744(2014:Apr.)
• Page Start: 217
• Page End: 249
• Publication Date: 2014-04-10
• Subjects: Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2014.68
• Languages: English
• ISSNs: 0022-1120

Abstract

<abstract> <title>Abstract</title> <p>To elucidate the physical mechanisms that play a role in the interfacial transfer of atmospheric gases into water, a series of direct numerical simulations of mass transfer across the air–water interface driven by isotropic turbulence diffusing from below has been carried out for various turbulent Reynolds numbers (<inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350ftv2p" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$R_T=84, 195, 507$]]></tex-math></alternatives></inline-formula>). To allow a direct (unbiased) comparison of the instantaneous effects of scalar diffusivity, in each of the DNS up to six scalar advection–diffusion equations with different Schmidt numbers were solved simultaneously. As far as the authors are aware this is the first simulation that is capable to accurately resolve the realistic Schmidt number, <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350fx7db" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\mathit{Sc}=500$]]></tex-math></alternatives></inline-formula>, that is typical for the transport of atmospheric gases such as oxygen in water. For the range of turbulent Reynolds numbers and Schmidt numbers considered, the normalized transfer velocity <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350fttgs" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$K_L$]]></tex-math></alternatives></inline-formula> was found to scale with <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350fx7k3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$R_T^{-{1/2}}$]]></tex-math></alternatives></inline-formula> and <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350ftt8g" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$\mathit{Sc}^{-{1/2}}$]]></tex-math></alternatives></inline-formula>, which indicates that the largest eddies present in the isotropic turbulent flow introduced at the bottom of the computational domain tend to determine the mass transfer. The <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350ftv14" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$K_L$]]></tex-math></alternatives></inline-formula> results were also found to be in good agreement with the surface divergence model of McCready, Vassiliadou & Hanratty (<italic>AIChE J.</italic>, vol. 32, 1986, pp. 1108–1115) when using a constant of proportionality of 0.525. Although close to the surface large eddies are responsible for the bulk of the gas transfer, it was also observed that for higher <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh350fx7n6" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$R_T$]]></tex-math></alternatives></inline-formula> the influence of smaller eddies becomes more important.</p> </abstract>