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 becomes 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.

Wall boiling can be controlled in CFX-Pre from:

  • The domain details view, on the Boundary Models tab.

  • The boundary details view for a wall boundary, on the following tabs:

    • The Boundary Details tab, which has the Wall Boiling Model > Option setting

    • The Fluid Pair Values tab, which is available when, on the Boundary Details tab, Wall Boiling Model > Option is set to RPI Model

    • The Fluid Values tab, which has fluid-specific settings related to wall boiling.

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

The following topics are discussed:

 
7.15.3.2.1. RPI Model

The RPI model for near-wall boiling can be controlled by several settings 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.

  • 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.

    • Delta Function

      The Delta Function option is available only when using the MUSIG/IMUSIG approach for the dispersed phase; there must be at least one polydispersed fluid in the fluid pair.

      Specify a value for Delta Diameter. The size group with the nearest diameter will have its size fraction equation influenced by the RPI boiling model, resulting in the production of bubbles within that size group.

    • Distribution Function

      The Distribution Function option is available only when using the MUSIG/IMUSIG approach for the dispersed phase; there must be at least one polydispersed fluid in the fluid pair.

      Specify a CEL function for Distribution Function. Given a diameter, this function must evaluate to the probability (between 0 and 1) that a newly departing bubble has that diameter. The integral of the probability over all diameters must be one. For example, you could specify that bubbles with diameters between 1 mm and 5 mm are equally likely, and that no other diameters are allowed, by using the following CEL expression:

      if (Fluid1|Fluid2.Bubble departure diameter < 1[mm], 0, if (Fluid1|Fluid2.Bubble departure diameter < 5[mm], 0.25, 0))

      The CFX-Solver discretizes this probability function into groups corresponding to the defined size groups.

  • Bubble Departure Temperature enables you to specify the bubble departure temperature. The available options are:

    • User Defined

      With this option, you can define the bubble departure temperature using an expression.

    • Saturation Temperature

      With this option (which is the default), the bubble departure temperature is made equal to the saturation temperature.

    • Superheat Fraction

      With this option, the bubble departure temperature is made equal to the saturation temperature plus the specified fraction of the superheat.

  • 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.

  • Flux Transfer Model enables you to model heat transfer from the wall to the phase in contact with the wall. The only available option, Convective, requires Critical Vol. Frac. to be set to a value for the critical volume fraction of the applicable fluid. Whenever the volume fraction of that fluid is greater than the critical value, the simulation allows convective heat transfer to that fluid.

    With the vapor volume fraction below the critical level for the vapor phase, the wall is treated as if it is covered by a liquid film. Above the critical level, the liquid film is assumed to break down rapidly, leaving the wall exposed to the vapor so that some of the wall heat flux contributes directly to convective heating of the vapor phase.

    The default value of Critical Vol. Frac. for a gas is 1.0, which models the vapor near the wall as being saturated, with no part of the wall heat flux contributing to superheating of the vapor phase.

    For details, see Area Influence Factors in the CFX-Solver Theory Guide and Convective Heat Transfer in the CFX-Solver Theory Guide.

  • Fluid-specific Wall Boiling Model settings, which are found in the domain details view on the Boundary Models tab and in the boundary details view on the Fluid Values tab, enable you to specify information about the boundary layer temperature via Boundary Layer Liquid Temperature settings. The available options are:

    • Fixed Yplus, which 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.

    • User Line Cloud Average

      This option uses a line averaged liquid temperature as set up in the specified line cloud for calculating the liquid quenching flux and the bubble departure diameter. When setting up the line averaging for the liquid temperature in the line cloud, the distance over which the average is taken should be based on the bubble departure diameter.

      The variable <liquid name>.Temperature must be available in the list of variables for line averaging, as specified under Line Variables List in the settings of the specified user line cloud.

      For details on user line clouds, see User Line Cloud in the CFX-Pre User's Guide.

Note:  If you are using the User Defined option for any of these settings, and any of these user-defined settings use CEL expressions that involve wall superheat, then it is important to specify the temperature using the Tsuperheat variable and not the phase-specific temperature variables such as water.Temperature.

 
7.15.3.2.2. Using a 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. A 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. For this reason, when a wall boiling model is active, the recommended option for the Wall Contact Model setting (see Wall Contact Model in the CFX-Pre User's Guide) is Use Wall Boiling Fraction. This option applies the same wall contact values computed for the energy equation to all other equations, making the overall simulation consistent. Other wall contact models are still available, although not recommended, for backwards compatibility. However, when using other wall contact models, the wall contact values used for energy are different from those used for the rest of the equations.

Wall boiling must be switched on explicitly for the walls at which it is expected to occur. On the Boundary Details tab for a boundary, set Wall Boiling Model > Option to one of the following values:

  • None

    No wall boiling model is applied at the wall.

  • From Domain

    A boiling model is applied at the wall using the boiling model settings of the domain.

  • RPI Model

    The RPI model is used to model wall boiling on the wall. The primary details of the wall boiling model are defined on the domain form, but these may be overridden on the wall boundary by using settings on the boundary’s Fluid Pair Values tab.

A wall boiling model cannot be used:

  • For a laminar continuous phase.

    Laminar dispersed phases are permitted only if they do not have convective heat transfer with the wall.

  • On a boundary where the continuous phase has a free slip wall condition.

  • In conjunction with the MUSIG model.

  • 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.