Hello,
I’m looking for evaporation heat loss correlation from water surface to almost stagnant air. The water temperature is less than saturation temperature ranging between 15 to 80 degree C. Most of the correlations I found are for quite high air velocities.
This appropriate correlation will be implemented in a UDF to simulate the heat loss from water surface.
Hope somebody can give suggestion
I recommend book "Heat transfer - a practical approach" by Y. A. Cengel. There is a whole chapter concerning evaporation to stagnant and non-stagnan air (chapter 14, and particularly 14-10). You can calculate how much water will evaporate and from it you will know the heat loss.
I think you can use VOF model which is built in most commercial CFD codes to solve your problem. The VOF assumes that all immiscible flud phases present in a control volume share the same velocity, pressure and temperature fields. very economic model!!
You can calculate surface evaporate rate(kg/sm2) without user defined programm. Water vaporization can be expressed as energy and mass source terms in energy and mass conervation equations.
Since I am not impressed by the possible answers to find in that book (present on the internet) I will give some suggestions. You are right that it is quite impossible to find correlations. If your air is really stagnant, you might try the penetration theory. If the air is moving slowing look at boundary layer theory for laminar flow or assume penetration into stagnant 'layers' using the contact time to calculate the average mass transfer coefficient. Calculate also an available correlation (turbulent flow) for the lowest velocity, extrapolate a little bit (find the slope with velocity, linear or logarithmic, and interpolate in a sensible way with the penetration theory. Good chance that you will find a reasonable value. Always check if there might be free convection (where correlations are available for 'low' velocities).
Since you explicitly mention 'less the saturation temperature' I might add that that is not true. There will be always saturation at the surface. Just find the vapour pressure at that temperature. You should calculate both heat and mass transfer, coupled by evaporation rate, to check which of the two is limiting. Be careful to use the same method to estimate the transfer coefficients (analogy heat and mass transfer).
Hello everybody, I would like to thank all of you for giving some of your valuable time to respond to my question.
Dear Soo-Jin Jeong, I’m trying to use VOF model in Fluent, however, if it works I might use it for performing a validation case but when it comes for the actual model I won’t effort the computational expenses of multiphase model, as it is such large model and limited resources I have.
Dear Rob van der Lans, as you mentioned most of the methodologies which I found in books are not useful as they are greatly underestimate the heat loss from the water surface. Right now I’m trying to follow your suggestion and start to read about boundary layer and penetration theories. I will give you an update.
Regards, Ahmed
In stagnant conditions you need to look at natural convection. Cengel provides a reasonable good introduction to the topic. Have you look at these papers?:
Ryan, Patrick J., Donald R. F. Harleman, and Keith D. Stolzenbach. ‘Surface Heat Loss from Cooling Ponds’. Water Resources Research 10, no. 5 (1974): 930–38. doi:10.1029/WR010i005p00930.
Herb, William R., Ben Janke, Omid Mohseni, and Heinz G. Stefan. ‘Ground Surface Temperature Simulation for Different Land Covers’. Journal of Hydrology 356, no. 3–4 (15 July 2008): 327–43. doi:10.1016/j.jhydrol.2008.04.020.
They use a formulation for heat transfer by evaporation that takes into account the effects of both natural and forced convection. I have used it myself I found it suitable to model evaporation from soils.
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