### 7.15.3. Thermal Phase Change Model

This model describes phase change induced by interphase heat transfer; it may be used to simulate boiling and condensation, or melting and solidification. For example, it may be used to model condensation of saturated vapor bubbles in sub-cooled liquid, or evaporation of saturated bubbles in super-heated liquid. It is only applicable to phase changes of pure substances.

This section provides modeling information. For a discussion of the theory, see The Thermal Phase Change Model.

The Thermal Phase Change model requires a number of related items of information to be provided.

#### 7.15.3.1. Saturation Temperature

There are two possible ways of defining the saturation temperature:

- Using the optional parameter Saturation Temperature (on the Fluid Pair Models tab under Phase Change Model with Option set to `Thermal Phase Change`). It may be set as a constant, or an expression. If the latter, it should be defined as a function of absolute pressure.

  Note: This option will not be available if you have created a Homogeneous Binary Mixture definition.

- Alternatively, you may define a homogeneous binary material (HBM) in the Material details view. For details, see Material Details View: Homogeneous Binary Mixture in the CFX-Pre User's Guide. The HBM should consist of the two materials undergoing phase change, and the saturation conditions should be defined as material properties of the HBM.

You must use one of these methods to define the Saturation Temperature, otherwise an error will be generated. If you use both methods, then the Saturation Temperature parameter (of the `Thermal Phase Change` option) takes precedence.

#### 7.15.3.2. Wall Boiling Model

Wall boiling starts when the wall temperature achieves a temperature that is sufficiently large to initiate the activation of wall nucleation sites. This activation temperature is typically a few degrees above the saturation temperature. However, at this stage, the average temperature of the liquid in the vicinity of the heated wall is still well below the saturation temperature, hence in the sub-cooled boiling regime.

ANSYS CFX implements an RPI boiling model. Usage information is provided in RPI Model. For a theoretical discussion of this model, see Wall Boiling Model.

##### 7.15.3.2.1. RPI Model

The RPI model for near-wall boiling can be controlled by several settings in CFX-Pre (on the Fluid Pair Models tab for a domain, and on the Boundary Details tab for a wall boundary) as described next:

- Bubble Diam. Influence Factor

  Enables you to specify the bubble diameter influence factor. For details, see Partitioning of the Wall Heat Flux.

- Max. Area Frac. of Bubble Influence

  Enables you to specify the maximum area fraction of bubble influence. For details, see Area Influence Factors and Evaporation Rate.

- Fixed Yplus for Liquid Subcooling

  Enables you to specify a fixed value at which the temperature is estimated for use in the bubble departure diameter and quenching heat transfer correlations. For details, see Bubble Departure Diameter.

- Onset of Boiling Superheating

  CFX-Solver assumes that boiling starts when exceeds by more than the specified Onset value.

- Mass Source Under-Relaxation

  This factor under-relaxes only , which is the evaporation mass transfer rate per unit wall area. It is recommended that you set the Mass Source Under-Relaxation factor and the Wall Heat Flux Partitioning Under-Relaxation factor to the same value to avoid inconsistencies in the wall energy fluxes that could lead to convergence problems.

- Wall Superheating Under-Relaxation

  This factor under-relaxes only , which is the unknown in wall heat partitioning. You may specify this factor independently of any applied partitioning under-relaxation or mass source under-relaxation.

- Wall Heat Flux Partitioning Under-Relaxation

  This under-relaxation factor permits consistent relaxation of the individual heat partitions (convection to liquid, quenching, and evaporation) in order to fulfil the given wall heat flux boundary condition. It is recommended that you set the Wall Heat Flux Partitioning Under-Relaxation factor and the Mass Source Under-Relaxation factor to the same value to avoid inconsistencies in the wall energy fluxes that could lead to convergence problems.

- Bubble Departure Diameter enables you to specify the bubble departure diameter. The available options are:

  - `User Defined`

  - `Tolubinski Kostanchuk`

  For details, see Bubble Departure Diameter.

- Wall Nucleation Site Density enables you to specify the wall nucleation site density. The available options are:

  - `User Defined`

  - `Lemmert Chawla`

  For details, see Wall Nucleation Site Density.

- Bubble Detachment Frequency enables you to specify the bubble detachment frequency. The available options are:

  - `User Defined`

  - `Terminal Velocity over Departure Diameter`

  For details, see Bubble Detachment Frequency.

- Bubble Waiting Time enables you to specify the bubble waiting time. The available options are:

  - `User Defined`

  - `Proportional to Detachment Period`

  For details, see Bubble Waiting Time.

- Liquid Quenching Heat Transfer Coefficient enables you to specify the liquid quenching heat transfer coefficient. The available options are:

  - `User Defined`

  - `Del Valle Kenning`

  For details, see Quenching Heat Transfer.

Note: If you are using the `User Defined` option for any of these variables, and if any of these user-defined models are CEL expressions that use wall superheat, then it is important to use the phase-pair-based variable that describes this; for example `water | steam.Tsuperheat`. It is not appropriate to use the phase-based temperature field such as `water.Temperature` to determine this. See System Variable Prefixes in the CFX Reference Guide for a description of the use of phase-pair based variables, and Determination of the Wall Heat Flux Partition in the CFX-Solver Theory Guide for a discussion on the determination of the wall superheat.

##### 7.15.3.2.2. Using the Wall Boiling Model

Walls that have boiling may have a specified temperature, specified heat flux, or specified heat transfer coefficient. Walls that have boiling may not have fluid-specific heat transfer boundary conditions. The wall boiling model has its own algorithms for computing wall contact area fractions for each phase; for the purpose of computing wall heat transfer, any user-specified wall contact model is overridden.

Wall boiling must be switched on explicitly for the walls at which it is expected to occur. The primary details of the wall boiling model are defined on the domain form, but these may be overridden on individual walls.

Note the following restrictions when using wall boiling:

- Cannot be enabled for a laminar continuous phase. Laminar dispersed phases are permitted.

- Cannot be enabled in conjunction with the MUSIG model.

- Cannot be enabled on a boundary where the continuous phase has a Free Slip Wall condition.

- Cannot be enabled in conjunction with thermal radiation models.

#### 7.15.3.3. Latent Heat

This is not specified directly. Rather, it is obtained indirectly as the difference between the static enthalpies of the two phases. For example:

| (7–6)

Hence, it is essential that the static enthalpy fields contain the absolute enthalpies of the two phases. This should be taken care of automatically if you select materials from the materials properties data base. On the other hand, if you define your own material properties, you should ensure that the enthalpies are defined correctly by setting the following fields in the Material details view:

- Reference Temperature, T ref

- Reference Pressure, p ref.

- Reference Specific Enthalpy h ref.

Definitions of these quantities are available. For details, see Library Materials.

For example, if you know the latent heat L at a reference state (T, P), then one way of ensuring that the correct latent heat is obtained at all temperatures and pressures is to set:

| (7–7)

#### 7.15.3.4. Heat Transfer Models

In general, both phases should be assigned either the Thermal Energy or Total Energy model for heat transfer.

However, in the case of subcooled boiling, you should find that the vapor phase temperature remains fixed at saturation conditions. Hence, in the case of constant saturation conditions, it is possible to run the vapor phase as Isothermal, with Reference Temperature set equal to the vapor saturation temperature.

#### 7.15.3.5. Interphase Heat Transfer Correlations

The Thermal Phase Change Model assumes:

- That thermodynamic equilibrium prevails at the interface between the two phases. That is, that the interfacial temperature equals the saturation temperature.

- That heat transfer either side of the phase interface may be modeled by two independent heat transfer coefficients. For details, see Two Resistance Model for Fluid Specific Heat Transfer Coefficients.

Hence, the Thermal Phase Change model requires the use of the Two Resistance model for interphase heat transfer. Selection of appropriate heat transfer correlations depends on the situation being modeled. Suggestions are provided below. First, some terminology:

- A phase is said to be saturated if its temperature equals the saturation temperature.

- It is said to be subcooled if its temperature is below saturation.

- It is said to be superheated if its temperature is above saturation.

#### 7.15.3.6. Modeling Advice

##### 7.15.3.6.1. Saturated Vapor Bubbles in Subcooled or Superheated Liquid

Vapor temperature is expected to remain at saturation conditions. There is negligible resistance to heat transfer on the dispersed phase side. Hence:

- Under constant saturation conditions, you should set Zero Resistance on the dispersed phase side.

- Under variable saturation conditions, you should set a large but finite Nusselt Number (of the order of 1000) on the dispersed phase side.

The primary resistance to heat transfer is on the continuous liquid phase side. Hence:

- For spherical bubbles, you should set either the Ranz Marshall or Hughmark correlation on the continuous phase side.

- For non-spherical bubbles, you may want to replace these by a user-defined correlation for Heat Transfer Coefficient or Nusselt Number.

##### 7.15.3.6.2. Subcooled or Superheated Droplets in Saturated Vapor

The situation here is entirely the opposite to the above, as there is now negligible resistance to heat transfer on the continuous phase side. Hence:

- Under constant saturation conditions, you should set Zero Resistance on the continuous phase side.

- Under variable saturation conditions, You should set a large but finite Nusselt Number (of the order of 1000) on the continuous phase side.

The primary resistance to heat transfer is on the dispersed droplet phase side. This is a fundamentally transient phenomenon for which there are no universally established correlations.

The simplest possible model on the dispersed phase side is:

| (7–8)

This is based on the analytic solution of transient heat conduction inside a solid sphere. It assumes:

- That advection effects inside the drop may be neglected.

- That the time-dependent temperature field inside the sphere may be considered to be spatially constant.

##### 7.15.3.6.3. Superheated Vapor Bubbles in Liquid

In this case, there is significant resistance to heat transfer on both the dispersed and continuous phase sides. Hence:

- For spherical bubbles, use either the Ranz Marshall or Hughmark correlation on the continuous phase side.

- On the dispersed phase side, use a correlation appropriate to heat transfer inside a spherical fluid particle, such as the discussed above.

##### 7.15.3.6.4. Thermal Energy and Total Energy Models

- Use Thermal Energy in cases where low-speed flow exists and where viscous effects are negligible.

- Use Total Energy in the case of high-speed flow and where viscous effects are not negligible.

Note: The Incl. Viscous Work Term option should be selected for a case involving MFR (multiple frames of reference) and the Total Energy equation. For details, see The Total Energy Equation in the CFX-Solver Theory Guide.

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