Spalding Evaporation/Condensation Model Reference

The model is enabled only for multi-component phases. Single-component phases are not supported, but you can use multi-component phases that have only one component. For a multi-component phase, not all of the components are required to change state.

The Spalding Evaporation/Condensation model has no known incompatibilities. However, the following limitations apply:

Different energy and velocity in phases is not resolved. There can be some discrepancy in the simulation results when compared to EMP and Lagrangian evaporation/condensation.
Single-component phases are not supported. However, you can use multi-component phases that have only one component to model single-component phases.

Table 1. Spalding Evaporation/Condensation Model Reference
Theory	See Evaporation and Condensation.
Provided By	Phase Interactions > [phase interaction] > Models > Optional Models
Example Node Path	[phase interaction] > Models > Spalding Evaporation/Condensation
Requires	A Eulerian Multiphase Mixture simulation with the following models activated: Material: Multiphase, Multiphase Interaction (Selected automatically) Multiphase Model: Mixture Multiphase (MMP), (Automatically activates: Multiphase Interaction, Gradients) The appropriate liquid phase and corresponding vapor phase defined. An Multiphase Interaction with the Primary Phase set to the liquid phase and the Secondary Phase set to the vapor phase.
Properties	See Spalding Evaporation/Condensation Properties.
Activates	Physics Models	Automatically selected models: Interaction Length Scale See Interaction Length Scale Model Reference.
	Model Controls (child nodes)	See Spalding Evaporation/Condensation Child Nodes.
	Materials	Critical Temperature Heat of Formation Saturation Pressure Saturation Temperature Standard State Temperature See Materials and Methods.
	Field Functions	Saturation Pressure of [liquid component] Saturation Temperature of [liquid component] Evaporation Rate of [vapor component] See Field Functions.

Spalding Evaporation/Condensation Properties

The Spalding Evaporation/Condensation model has the following properties:

Connectivity

Maps the components in the liquid phase to their corresponding components in the gas phase.

Under-Relaxation Factor

The factor $ω$ that is used to under-relax the evaporation rate ${\dot{m}}_{p i}$ that is computed in Eqn. (2885).

The default value of $ω$ is $1$ .

Heat-Transfer Limited Mode

When activated, heat-transfer limited evaporation mode is used when applicable, that is, when the vapor at the liquid surface is saturated and subcritical. The condition for a saturated vapor is that the vapor mole fraction at the liquid surface exceeds unity. The vapor mole fraction at the liquid surface is evaluated as the ratio of the saturation pressure at the liquid surface temperature and the pressure in the surrounding gas.

When deactivated, mass diffusion limited evaporation mode is applied instead, and the vapor mole fraction at the liquid surface is fixed at 0.99999. Use this setting with care, as the diffusion-limited evaporation mass transfer rate can cause numerical instability if applied close to saturation conditions.

Spalding Evaporation/Condensation Child Nodes

The Spalding Evaporation/Condensation model has the following child nodes:

Nusselt Number

Sets the method for specifying the Nusselt number

{N u}_{p}

that is used for calculating the mass transfer conductance

g^{*}

for heat transfer limited evaporation and condensation.

In addition to the usual methods, you can use the Armenante-Kirwan correlation that is given in Eqn. (2043). The values that you can set are:

Alpha

By default, $α$ = 0.6.
Beta

By default, $β$ = 0.5.
Gamma

By default, $γ$ = 0.333333.

Sherwood Number

Sets the method for specifying the Sherwood number

{S h}_{p}

that is used for calculating the mass transfer conductance

g^{*}

for diffusion limited evaporation and condensation.

In addition to the usual methods, you can use the Armenante-Kirwan correlation that is given in Eqn. (2063). The values that you can set are the same as for the Nusselt number, above.

Interaction Length Scale

Used to define non-dimensional parameters for the phase interaction, and also to compute an interaction area density.

This value is equivalent to the droplet diameter.

See Interaction Length Scale Model Reference.

Materials and Methods

The Spalding Evaporation/Condensation model activates the following material properties:

Critical Temperature

The temperature above which a gas cannot be liquefied by pressure alone. This value is

T_{c, i}

for component

i

in Evaporation and Condensation of Droplets.

Heat of Formation

The heat that is evolved when 1 kilogram of the substance is formed from its elements in their respective standard states [J/kg].

See Using the Heat of Formation.

Saturation Pressure

The pressure of a vapor when it is in equilibrium with its liquid at a given temperature. This value is

p_{s a t}^{i}

for component

i

in Evaporation and Condensation of Droplets .

The following methods are available:

Antoine Equation

The Antoine equation for saturation pressure is based on the logarithm of the ratio $P_{s a t} / P_{a t m}$ .

See Using the Antoine Equation.
Wagner Equation

The Wagner equation provides a good fit to experimental data, but is more complex than the Antoine equation. It expresses reduced vapor pressure as a function of reduced temperature.

See Using the Wagner Equation.

Saturation Temperature

The temperature at which, for any given pressure, the gas is saturated; any further temperature reduction at fixed pressure results in condensation of the vapor to liquid. This value is

T_{s a t}^{i}

for component

i

in Evaporation and Condensation of Droplets.

In addition to the standard Constant and Field Function methods, the Iterative method is available. This method computes the saturation temperature automatically from the definition of Saturation Pressure. However, this method is available only if the Saturation Pressure changes with temperature, as is the case for the Antoine and Wagner methods.

Standard State Temperature

A reference point that is used to calculate the material properties under different conditions. The default value is 298.15 K (25.00 C).

See Using the Standard State Temperature.

Field Functions

The following field functions are available immediately:

Saturation Pressure of [liquid component]
Saturation Temperature of [liquid component]

When the Temporary Storage Retained flag is activated in the Segregated N-Phase Mixture solver, the following field function also becomes available:

Evaporation Rate of [vapor component]