Water evaporation and condensation in air with radiation: the self-similar Spalding model

[+] Author and Article Information
M. Q. Brewster

Department of Mechanical Science and Engineering University of Illinois Urbana, IL 61801

1Corresponding author.

ASME doi:10.1115/1.4036075 History: Received August 23, 2016; Revised February 17, 2017


Several simple ways of improving the accuracy of Spalding model predictions over common textbook conventions for air/water evaporation/condensation problems are illustrated using open-literature examples. First is the choice of thermodynamic reference state for enthalpy evaluation. The common practice of choosing the steam table reference point (0.01°C) with water-vapor enthalpy of hfg (2501 kJ/kg) and air enthalpy of zero introduces an enthalpy mismatch between air and water vapor that unnecessarily compromises accuracy. Second is judicious choice of the blowing factor in high-rate mass transfer situations. The laminar boundary layer blowing factor is more accurate than the common stagnant-film (Couette flow) blowing factor for flat-plate flow and may be more accurate for a cylinder in crossflow under laminar conditions, as illustrated by the example of air leak effect on steam condenser tube performance. Third is radiation modeling, often a problematic or ignored feature in this type of problem. Two common, but opposite, assumptions about radiation participation in water—transparent interface and opaque interface—are shown to be equivalent for most purposes. A methodology is introduced for modeling true interfacial absorption/emission associated with phase change if/when the amount of this effect becomes known well enough to justify its inclusion. The importance of including radiation is illustrated by several examples: cloud droplet evaporation-condensation, sweat cooling, and the wet-bulb psychrometer. Fourth is inaccuracy introduced by unnecessarily setting Lewis number to unity.

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