Homogeneous Relaxation Model Reference

The Homogeneous Relaxation Model (HRM) is used for modeling vaporization mechanisms ranging from cavitation to flash boiling.

Flash boiling is a phase change in a high temperature liquid that is depressurized below its vapor pressure. This phenomenon occurs in thermal non-equilibrium and therefore requires a finite rate model. The Homogeneous Relaxation Model (HRM) is based on a finite rate equation with an empirical time-scale formulation, so is suited to modeling flash boiling.

The Homogeneous Relaxation model may be used in the following applications:

  • Diesel and Gasoline Direct Injection (GDI) fuel injectors

    GDI fuel injectors operate at high temperatures, which makes them susceptible to flash boiling. Flash boiling (or cavitation) in the nozzle greatly influences the flow in the injector and the subsequent spray characteristics of the injector.

    The time scale depends on flow conditions such as pressure, void fraction, fuel vapor pressure, and the saturated liquid and vapor densities. For standard diesel injectors, the time-scale value is small and the vaporization is pressure-driven (that is, cavitation). However, for GDI injectors, the flow conditions and fuel properties make the time-scale value relatively large such that thermal non-equilibrium effects must be modeled.

  • Pressurized Water Reactors (PWR)

    Flash boiling of superheated water into steam

Table 1. Homogeneous Relaxation Model Reference
Model Names Homogeneous Relaxation
Multi-component Homogeneous Relaxation
Theory See Homogeneous Relaxation Model.
Provided By [phase interaction] > Models > Cavitation Models
Example Node Path Continua > Physics 1 > Models > Multiphase Interaction > Phase Interactions > [phase interaction] > Models > Homogeneous Relaxation
Requires

A VOF Multiphase simulation with the Segregated Multiphase Temperature model activated.

The appropriate liquid phase and corresponding vapor phase defined. The liquid and vapor phases must be both single-component materials or both multi-component materials.

A VOF-VOF Phase Interaction with the primary phase set to the liquid phase and the secondary phase set to the vapor phase.

In the Phase Interaction Model Selection dialog:

  • For single-component phases:
  • Cavitation Models: Homogeneous Relaxation
  • For multi-component phases:
  • Cavitation Models: Multi-component Homogeneous Relaxation
Properties Key properties are:

Time Scale Modeling Constant

Void Fraction Exponent

Dimensionless Pressure Exponent

Flash Boiling Rate Under-Relaxation Factor

See Homogeneous Relaxation Model Properties.

Activates Model Controls (child nodes)

Equilibrium Coefficient

See Multi-component Homogeneous Relaxation Model Child Nodes.

Materials

Phase Material Properties:

Critical Pressure (applies to liquid phases only)

Critical Temperature (applies to liquid phases only)

Heat of Formation

Saturation Pressure (applies to liquid phases only)

Saturation Temperature (applies to liquid phases only)

Standard State Temperature

See Homogeneous Relaxation Model Material Properties.

Field Functions

Cavitation Saturation Pressure of [Phase Interaction]

Cavitation Saturation Temperature of [Phase Interaction]

See Homogeneous Relaxation Field Functions.

Homogeneous Relaxation Model Properties

Time Scale Modeling Constant
This value is θ0 in Eqn. (2707). The default value of this modeling constant is 3.84×10−7.
Void Fraction Exponent
The exponent that is applied to the vapor void fraction, α, in Eqn. (2707). The default value is −0.54.
Dimensionless Pressure Exponent
The exponent that is applied to the non-dimensional pressure, ψ, in Eqn. (2707). The default value is −1.76.
Flash Boiling Rate Under-Relaxation Factor
The under relaxation factor that is applied to the Homogeneous Relaxation model source term. Under relaxation is recommended in cases where pressure oscillations are observed in the solution.
Connectivity

Maps the components in the liquid phase to their corresponding components in the gas phase. For multi-component phases, you select the gas component that corresponds to each liquid component. For the Homogeneous Relaxation model, you can ignore the dissolved gas components of the liquid mixture.

Applies to multi-component phases only.

Multi-component Homogeneous Relaxation Model Child Nodes

Equilibrium Coefficient
Specifies the method by which the equilibrium coefficient is found for each pair of liquid-gas components. By default, Raoult’s Law is used, as this option applies when the component is a significant fraction of the liquid mixture.

Applies to multi-component phases only.

Homogeneous Relaxation Model Material Properties

The following properties are set for single-component phases or for each component of multi-component phases.

These properties are set under [Phase] > Models > [Material (for example, Multi-Component Liquid) or Component (for example, Liquid Components > H2O)] > Material Properties when the Homogeneous Relaxation model is activated.

Critical Pressure
The pressure that is required to liquefy a material at its critical temperature, given by pcrit in Eqn. (2708). This value is required for each liquid component.
Critical Temperature
The temperature above which the material cannot be liquefied, regardless of the pressure that is applied. This value is required for each liquid component.
Heat of Formation
The heat that is evolved when 1 kilogram of the material is formed from its elements in their respective standard states [J/kg]. See Using the Heat of Formation.
Saturation Pressure

The saturation pressure p s a t is a key material property (see Eqn. (2708)). It is the pressure of each vapor component when in equilibrium with the corresponding liquid component. This value is required for each liquid component.

For multicomponent mixtures, the saturation pressure must be a function of the saturation temperature and cannot be constant.

Saturation Temperature
The temperature for a corresponding saturation pressure at which the liquid material boils to form its vapor phase.

This property is not available for multicomponent mixtures, as Simcenter STAR-CCM+ automatically calculates the saturation temperature using an iterative method.

Standard State Temperature
The temperature at which the standard state of the material is defined. See Using the Standard State Temperature.

Homogeneous Relaxation Field Functions

For both single component phases and multi-component phases:

Cavitation Saturation Pressure of [Phase Interaction]
Cavitation Saturation Temperature of [Phase Interaction]

For multi-component phases only:

Effective Mass Diffusivity of [component] in [multi-component material]
Enthalpy of [component] in [multi-component material]
Mass Fraction of [component] in [multi-component material]
Molar Concentration of [component] in [multi-component material]
Mole Fraction of [component] in [multi-component material]
Molecular Weight of [component] in [multi-component material]
Specific Heat of [component] in [multi-component material]