An experimental investigation of the potential of empirical correlations derived based on Dalton’s law and similarity theory to predict evaporation rate from still water surface

Abstract

This paper investigates the applicability of two approaches (similarity theory and Dalton’s law) in predicting the evaporation rate. The results of this study showed that conventional Dalton’s based models could not be used to predict the evaporation rate at all convection regimes. Thus, a new formula as a function of vapor density difference was developed to predict evaporation rate at natural turbulent convection. However, still, it cannot get an acceptable result. Also, another two formulas were developed to predict the evaporation rate at forced and mixed convection regimes after considering the nonlinear relationship between the evaporation rate and the vapor pressure difference. The evaporation rate is proportional to the exponent (n) of the partial vapor pressure difference. This exponent was written as a function of the higher-order polynomial of air velocity to get a good match between experimental results and predicted value, and satisfactory results were achieved. Similarity theory is an analogy between heat and mass transfer methods used to predict the evaporation rate from the still free water surface. The results show that the evaporation rate obtained from the similarity method is much larger than the actual evaporation rate. The similarity theory considers the effect of the vapor density difference. Thus, it can be observed that the experimental results and similarity method results are in good agreement at natural turbulent convection. It is noteworthy that the similarity theory cannot predict the evaporation rate from the still water surface at forced convection. In this convection regime, the evaporated water surface is not completely smooth, which violates the assumption of the similarity theory. A nonlinear regression analysis was conducted to evaluate the empirical correlation of the Sherwood number for mixed convection under turbulent conditions with the exponent n as a logarithmic function of the ratio $(\frac{G r m}{R e^{2}})$ , then derived a new formula that can be used to evaluate evaporation rate at mixed convection regime, and the results are in good agreement with the experimental results. The laboratory measurements are made using the large wave tank-wind tunnel combination to control wind speed.

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