12.9.2. Leidenfrost Temperature Considerations

In the Lagrangian Wall Film (LWF) model, the wall film vaporization rate equation (Equation 12–275 for the diffusion controlled model, Equation 12–282 for the convection-diffusion controlled model, and Equation 12–291 and Equation 12–292 for the film boundary layer model) assumes that the liquid film is in full contact with the wall. When the wall film temperature reaches the boiling point, a boiling rate is computed; however, the assumption still is that the liquid film fully covers the wall surface.

The LWF boiling rate equation (Equation 12–283 and Equation 12–284 for constant-temperature walls and heat-flux walls, respectively) gives a linear dependence of the boiling rate on the wall temperature. However, liquid film boiling phenomena are much more complex, and the rate of heat transfer from the hot wall to the film deviates from the linear dependence as the temperature difference between the wall and the liquid film increases. This deviation is caused by vapor pockets that develop between the hot wall surface and the boiling film, which significantly affect both the heat transfer and the hydrodynamic characteristics of the film boiling process. The limiting condition in which the insulating vapor layer fully covers the hot wall is known as the Leidenfrost point.

Fluent deals with wall surface boiling phenomena in the context of the multiphase models, in particular in Wall Boiling Models. However, in the context of the LWF model, the prediction of the Leidenfrost point is important for assessing the adequacy of the LWF boiling rate and avoiding unphysical results.

12.9.2.1. Default Wall Temperature Limiter

In Ansys Fluent, a default limit for the wall temperature is a sum of the liquid film boiling point and the temperature difference between the wall and the liquid film :

(12–205)

where the default is 50 K.

12.9.2.2. Leidenfrost Temperature Reporting

During the LWF computation, Ansys Fluent calculates the Leidenfrost temperature and compares it to the wall temperature. If the wall temperature is above the Leidenfrost temperature, Fluent issues a warning. Note that the calculation of the Leidenfrost point is for information only and is not used to limit the wall temperature in the calculation.

For an isothermal surface, the Leidenfrost temperature can be approximated as a function of the liquid critical temperature and the liquid surface tension [51]:

(12–206)

where is the solid density, and is the solid atomic number. The last term in Equation 12–206 introduces a correction for the solid-liquid surface tension effects.

Knowing and the heat transfer properties of the solid surface, the Leidenfrost temperature can be calculated as:

(12–207)

where is liquid film temperature (K), is the complementary error function, and

where 
= solid thermal conductivity (W/m-K)
= solid density (kg/m3)
= solid heat capacity (J/kg-K)