9. EVAPORATION Namelist (Experimental)

This namelist applies a special boundary heat flux that models heat loss due to the evaporation of a material. Its intended use is in the simulation of additive manufacturing or welding processes where the heat source can produce localized surface temperatures approaching and exceeding the vaporization temperature.

The heat flux due to evaporation,

\[q_{\text{evap}} = L \dot{m},\]

is expressed in terms of the evaporated mass flux \(\dot{m}\) and latent heat of vaporization \(L\). The mass flux (mass per unit area per unit time) is determined from the Hertz-Knudsen equation [1]

\[\dot{m} = \lambda p_v(T)\sqrt{\frac{M}{2\pi R T}}\]

where \(M\) is the molar mass of the evaporating material, \(R\) is the universal gas constant, \(p_v\) is the vapor pressure of the material at temperature \(T\), and \(\lambda\) is an empirical constant that corrects for the condensation of a portion of the vaporized atoms. The vapor pressure is given by the Clausius-Claperyon equation [2]

\[p_v(T) = p_0 \exp\Bigl[\frac{ML}{R}\Bigl(\frac1{T}-\frac1{T_0}\Bigr)\Bigr]\]

where \(p_0\) is the pressure of the ambient atmosphere, and \(T_0\) is the vaporization temperature at that pressure.

Caution

This model is only compatible with problems using Kelvin for temperature.

If any other problem units differ from SI units, the value of the universal gas constant \(R\) must be redefined accordingly using the gas_constant variable of the PHYSICAL_CONSTANTS namelist.

Namelist Usage

Required/Optional:

Optional

Single/Multiple Instances:

Single

9.1. Namelist Variables

face_set_ids

A list of face set IDs that define the portion of the boundary where the evaporation model will be applied.

Default:

none

vaporization_heat

The latent heat of vaporization \(L\) (energy per unit mass).

Default:

none

vaporization_temp

The vaporization temperature \(T_0\) (K) at the ambient pressure.

Default:

none

molar_mass

The molar mass \(M\) of the evaporating material (mass per mole).

Default:

none

ambient_pressure

The pressure of the ambient atmosphere \(p_0\) (force per unit area).

Default:

\(1.01325\times10^5~\text{N}/\text{m}^2\) (1 atm)

condensation_factor

The empirical constant \(\lambda\) that accounts for the condensation of vaporized atoms.

Default:

\(0.1\)

Note:

For evaporation in a vacuum \(\lambda=1\), but at 1 atm of pressure the Hertz-Knudsen equation overestimates the mass flux by an order of magnitude. [1]