I had some concerns about the logic used to calculate thermodynamic properties like pressure (of a mixture) and other properties like temperature of vapour in a condensing flow of steam in a nozzle. Also, how to calculate properties of a liquid droplet. Or can I take the properties of the droplet as the same as those of saturated condition water properties?
Regarding the Nucleation model, do I need to put some condition to start the condensation process (like minimum radius or minimum nucleation rate or minimum supersaturation ratio below which nucleation rate equation do not come into play)?
The answer depend in part on your model to calculate the nucleating steam. I assume that your model incorporates a multitude of droplets, which nucleate and then grow or shrink depending on conditions. In a nucleation model, you always need to specify the density of nucleation seeds. In homogeneous nucleation, there are models for that based on thermodynamic considerations (giving the density based on supersaturation based on the probability to find clusters of a minimal size, which grow spontaneously); these models unfortunately often are off by several orders of magnitude, requiring empirical correction factors. In heterogeneous nucleation (where seeds like dust particles are available), you have to specify this density.
The droplets will condense at the condensation temperature corresponding to the local steam pressure. The steam pressure, temperature and density needs to obey the equation of state of the steam, the steam density can be calculated from mass conservation, reducing steam mass by mass in the droplets (use number / size of all droplets).
The pressure inside the droplet will be higher than in the surrounding steam due to surface tension. Usually, this is taken into account in droplet growth models.
Dear Proferssor,
Many Thanks for replying back to my question. I would like to take the opportunity to explain the kind of model I am implementin. I am using single fluid model which was used by Prof. Sławomir Dykas and Włodzimierz Wróblewski in their publised paper of "Numerical modelling of steam condensing flow in low and high-pressure nozzles".
I this model mixture properties are used (density, velocity and energy). Also there is an assumption that an average pressure governs the flow i.e. pressure of steam and droplets are same. Also it is assumed that there is no slip condtion so the velocity of droplets and steam are equal.
I am trying to implement this model with Euler equations. What I understood from your answer is that I need to specify critical radius which is a function of supersaturation ratio. When radius is more than this radius the droplets grow other they collapse. In this model an volume averaged radius is assumed. But I did not understand how to use empirical correction factors. Can you explain a bit more about this. What kind of factor is to be used.
Also in this model I calculated mixture density from solution of Euler equation and then use mass fraction (Y) to calculate steam density. And then use density and pressure to calculate rest of properties of Steam.
In case of Droplets I calculate properties of liquid phase using Pressure and saturation condition (by specifying qulaity as 0.0 when evaluating properties).
Please indicate if I am assuming something wrong here. Also I would like to know if I have to put a condition for minimum nucleation factor J (no. of droplets/m3.s) or a minimum condition for supersaturation ratio.
Thanks and Regards
Anshuman
Dear Anshuman,
usually you assume a nucleation factor J since the values from the theories are wrong anyway. SInce J is growing extremely rapidly with temperature (several orders of magnitude in a few degrees K), an error in J will not be very critical.
The initial radius of the droplets is the critical radius. Usually the models take the growth and coalescence of droplets into account. You can ignore that the pressure inside the droplet is higher than the gas pressure, since only the gas pressure is part of your solution. Also the no-slip condition is ok. since droplets are small (< 1 micron).
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