The Velocity-Concentration Relationship in Turbulent Mass Transfer to a Wall
Campbell, Jay Allan
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https://hdl.handle.net/2142/66647
Description
Title
The Velocity-Concentration Relationship in Turbulent Mass Transfer to a Wall
Author(s)
Campbell, Jay Allan
Issue Date
1981
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
The relationship between the concentration field and the velocity field during fully-developed mass transfer from a turbulently flowing fluid to a solid boundary was investigated in this study. The investigation was limited to cases of high Schmidt number in which the concentration boundary layer is completely contained within the viscous sublayer.
The approach taken in this study is a radical departure from the classical methods of looking at mass transfer. The classical approach involves postulating a mechanism which depends on the definition of a fictitious quantity (eg. film thickness or renewal period). In this study, direct solutions of the mass balance equation were sought. These solutions reveal a picture of mass transfer much different from those proposed in the past. Furthermore, a real, measurable property of the velocity was identified which governs mass transfer.
The concentration boundary layer was found to be a region where time and length scales change with distance from the wall. Very close to the wall, where convection is negligible, the relatively long time scale of diffusion predominates. Only those velocity fluctuations with time scales similar to that of the diffusion will affect the mass transfer in this region. This time scale corresponds to frequencies much lower than those of the most energetic velocity fluctuations. A low frequency inflow will result in a period of high mass transfer and a low frequency outflow will result in a period of low mass transfer. As one moves away from the wall, higher frequencies of the velocity will affect the concentration field. However, those frequencies will only have a small effect on the overall mass transfer rate. The picture that emerges is that the concentration boundary layer will appear to act as a low-pass filter in selecting those velocity fluctuations to which it will respond. Experimental velocity and mass transfer measurements and a linear analysis were carried out to confirm this picture.
It is concluded that the property of the velocity field of most importance in the transport of mass is the low frequency portion of the normal velocity spectrum, W(,(beta))(0). This suggests that mass transfer rates can be predicted from a real, measurable property of the turbulence.
The results of numerical solutions of the mass balance equation predict a dimensionless mass transfer coefficient which varies as
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
where S is the Schmidt number and K and W(,(beta))(0) have been made dimensionless with the friction velocity and the kinematic viscosity. This is in excellent agreement with experimental measurements.
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