I am simulating the evaporation of a static droplet using the lattice boltzmann method. The ambiguity for me is that, the temperature of the drop remains constant during the evaporation and after finishing the evaporation process, it starts to increase. Please see the attached page for more details/figures about the problem. Do you think this behavior of temperature is true?
Your initial droplet temperature is too high to see the expected behaviour, you can start with 0.5 and see what's going on.
Dear Ahmed
the behavior of temperature is the same even with lower initial temperature.
Note: when i set a small value for initial temperature, the evaporation did not happen. so, I added a source term to all nodes to supply necessary heat for evaporation ...again the behavior is the same, i.e. the temperature is fixed in droplet during the evaporation (but the evaporation rate is high) ... also, the temperature of the vapor increases because of the source term during the evaporation...
So, the temperature you got is not correct. the early time of droplet time is usually spent in heating up the droplet to the wet bulb temperature then the evaporation takes place. please see my papers with Sergei Sazhin
thanks for your paper .. I will double check the temperature calculation
Your liquid phase must remains at saturation temperature until all is evaporated, simply because liquid phase above Tsat and below Psat does not exit: it is a gas phase
http://www.mae.wvu.edu/~smirnov/mae320/figs/F3-8.jpg
Dear Jean-Yves
thanks for the point. so, do you believe the results are ok? and what is your expectation for the temperature behavior within a bubble?
Your gas temperature should decrease with time because it gives energy to the droplet (Latent heat) to evaporate, meanwhile the droplet temperature should increase until reaching Tsat and remain at Tsat until all has become gas phase (unless there is not enough energy in the gas to convert all the liquid mass, some liquid will remain). Usually plotting the results on a PT diagram could help checking if your results makes sense accoring to the V-L equilibrium.
http://www.learnthermo.com/images/ch02/Lesson-B/2B-8-PT-diagram.png
Phase change is a constant temperature, constant pressure process. The only thing that changes during phase change is the density of the fluid. As has been mentioned by Jean-Yves, the gas temperature will drop as it transfers heat to the liquid droplet until it reaches the saturation temperature and then stays there until it is vaporized.
If it is a solution you will have to look a McCabe-Thiele type of methods and T-x-y diagrams to look how the fractionation happens. However it is not called critical temperature but dew and bubble curves temperatures
http://eq-comp.com/data/uploads/images/BINARY-IMG2.jpg
http://www.chem.mtu.edu/~tbco/cm2110/cm205_txy_16.gif
See the following:
Clark, C. R.: “Adsorption and Desorption of Light Paraffirric Hydrocarbons in Dry and Water-Saturated Sand-Clay Packs: Studies to Determine the Effect of These Phenomena on the P-V-T Behavior of Natural Gasea and Gas Condensates in the Reservoir, ” PhD thesis, U. of Kansas, Lawrence (1969).
Sadykh-Zade, E. S., Mamedov, J. G. and Rafibejli,N. M.: “Determination of the Dynamic Pressure of the Beginning of Condensation in the Presence of a porous Medium,’’ Net’i Gaz. (1963) VO1. 12, 268-270.
Nice explanation is already given by Jean-Yves and Kidambi Sreenivas. Droplet surface consumes latent heat from the droplet core until saturation temperature is reached and also sensible heat (depends on 'h') from the surroundings. Therefore droplet temperature initially reduces to a minimum as indicated by T=2000. As the time passes, the size of the droplet decreases and also the heat capacity of the droplet. Further the vapor pressure is increasing in the surroundings due to evaporation which may require higher saturation temperature for evaporation.Due to the sensible heat transfer from the surroundings the droplet temperature rises with time as a result of thermal equilibrium being maintained. Therefore the graph shows that modelling is capturing the trend of droplet temperature during evaporation.
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