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Theory
Simcenter STAR-CCM+ simulations are built on numerical algorithms that solve relevant laws of physics according to the conditions that the simulation defines. So that you can identify the physical laws, and understand the methods by which they are solved, Simcenter STAR-CCM+ comes with a Theory Guide.
Multiphase—Eulerian Approach
Multiphase flows, where several fluids flow in the domain of interest, play an important role in variety of industrial applications. In general, we associate phases with gases, liquids or solids and as such some simple examples of multiphase flows are: air bubbles rising in a glass of water, sand particles carried by wind, rain drops in air. The definition of phase can be generalized and applied to other fluid characteristics such as size, shape, density, and temperature.
Volume of Fluid Method
The Volume of Fluid (VOF) multiphase model implementation in Simcenter STAR-CCM+ belongs to the family of interface-capturing methods that predict the distribution and the movement of the interface of immiscible phases. This modeling approach assumes that the mesh resolution is sufficient to resolve the position and the shape of the interface between the phases.
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.

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Theory
Simcenter STAR-CCM+ simulations are built on numerical algorithms that solve relevant laws of physics according to the conditions that the simulation defines. So that you can identify the physical laws, and understand the methods by which they are solved, Simcenter STAR-CCM+ comes with a Theory Guide.
- Fundamental Equations
  Simcenter STAR-CCM+ models a range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. On a macroscopic scale, where the typical lengths are much greater than the inter-atomic distances, the discrete structure of matter can be neglected and materials can be modeled as continua. The mathematical models that describe the physics of continua are derived from fundamental laws that express conservation principles.
- Fluid Flow
  Simcenter STAR-CCM+ can simulate internal and external fluid flow across a wide range of flow regimes, and for a variety of fluid types. It solves the conservation equations for mass, momentum, and energy for general incompressible and compressible fluid flows.
- Numerical Flow Solution
  In the finite volume method, the solution domain is subdivided into a finite number of small control volumes, corresponding to the cells of a computational grid.
- Turbulence
- Transition
  The term transition refers to the phenomenon of laminar to turbulence transition in boundary layers. A transition model in combination with a turbulence model predicts the onset of transition in a turbulent boundary layer.
- Wall Treatment
  Walls are a source of vorticity in most flow problems of practical importance. Therefore, an accurate prediction of the flow across the wall boundary layer is essential.
- Wall Distance
  Wall distance is a parameter that represents the distance from a cell centroid to the nearest wall face with a non-slip boundary condition. Various physical models require this parameter to account for near-wall effects.
- Heat Transfer
  Heat transfer is the exchange of thermal energy between media at different temperatures. Heat transfers from locations of high temperature to locations of low temperature in order to reach an equilibrium state. The three main mechanisms of heat transfer are: conduction, convection, and radiation.
- Porous Media
  Porous media are continua that contain both fluid and fine-scale solid structures, for example: packed-bed chemical reactors, filters, radiators, honeycomb structures, or fibrous materials. The solid geometrical structures are too fine to be individually meshed and fully resolved by a computational grid.
- Species and Passive Scalars
  Simcenter STAR-CCM+ models the transport, the mixing, and the chemical reactions of multi-component liquids or multi-component gases by solving conservation equations for scalar variables that represent the mass fraction of each species in the mixture. This conservation equation allows for convection, diffusion, and optional source effects, and is solved in addition to the global mass continuity equation.
- Multiphase—Eulerian Approach
  Multiphase flows, where several fluids flow in the domain of interest, play an important role in variety of industrial applications. In general, we associate phases with gases, liquids or solids and as such some simple examples of multiphase flows are: air bubbles rising in a glass of water, sand particles carried by wind, rain drops in air. The definition of phase can be generalized and applied to other fluid characteristics such as size, shape, density, and temperature.
  - Eulerian Multiphase (EMP) Flow
    The two-fluid model that is referred to as the Eulerian Multiphase (EMP) model in Simcenter STAR-CCM+, and whose initial development was driven largely by nuclear industry, is generally used for modeling dispersed flows.
  - Volume of Fluid Method
    The Volume of Fluid (VOF) multiphase model implementation in Simcenter STAR-CCM+ belongs to the family of interface-capturing methods that predict the distribution and the movement of the interface of immiscible phases. This modeling approach assumes that the mesh resolution is sufficient to resolve the position and the shape of the interface between the phases.
    - High-Resolution Interface Capturing (HRIC)
      An important quality of a system of immiscible phases (for example, air and water) is that the fluids always remain separated by a sharp interface. The High-Resolution Interface Capturing (HRIC) scheme is designed to mimic the convective transport of immiscible fluid components, resulting in a scheme that is suited for tracking sharp interfaces.
    - Free Surface Mesh Refinement
      Free Surface Mesh Refinement is an Adaptive Mesh Refinement (AMR) criteria designed for VOF multiphase simulations. This method refines or coarsens cells in the volume mesh to improve the resolution of the interface between phases.
    - Surface Tension
      The surface tension force is a tensile force tangential to the interface separating two fluids. It works to keep the fluid molecules at the free surface in contact with the rest of the fluid.
    - Volume Fraction Reinitialization
      The Volume Fraction Reinitialization model allows for a dynamic modification of the free surface by sharpening or smearing the interface. This can improve the modeling and reduce computational cost.
    - Interface Sharpening through Slip Velocity Modeling
      Adding the slip velocity to the VOF method improves the modeling assumptions to allow a more physical behavior of the multiphase system in scenarios when the interface between phases is not resolved. In such cases, the VOF model behaves like the Mixture Multiphase (MMP) model, which can improve the modeling significantly and restore a sharp interface.
    - Interface Sharpening Using Temporal Subcycling
      Applying temporal sub-cycling to the transport of volume fraction can improve the resolution of the interface between two phases.
    - Interface Turbulence Damping
      At a liquid-gas interface with a high relative velocity between the phases, the large gradients in the boundary layer near the free surface can cause significant turbulence fluctuations. The Interface Turbulence Damping model accounts for this in VOF multiphase simulations.
    - Blob Shape Criteria
      When bodies of liquid break up, ligaments and droplets form where ligaments can subsequently break up into droplets. To evaluate the shape of large VOF resolved droplets and ligaments, also known as blobs, certain criteria can be applied. A blob can span multiple cells.
    - Wall Porosity
      The implementation of the VOF phase-specific wall porosity model is analogous to that of a porous baffle.
    - Free Surface Waves
      Simcenter STAR-CCM+ provides the VOF Waves model to simulate surface gravity waves on the interface between a liquid and a gas, typically the atmosphere. Application examples for VOF waves are the investigation of flow around ships or wave impact on offshore structures.
    - Evaporation and Condensation
      Evaporation is a form of vaporization, the phase change from liquid to gas, which occurs when liquid molecules or atoms with high enough kinetic energy escape through the interface between the two phases. Condensation is the reverse process of vaporization and is the phase change from gas to liquid.
    - Boiling
      Boiling is a rapid vaporization of a liquid. It typically takes place when a liquid is heated to the boiling point (saturation temperature of the liquid ). Its saturation vapor pressure then becomes equal to or larger than the pressure of the surrounding liquid.
    - Cavitation and Gas Dissolution
      When the static pressure at a particular location within a liquid falls below the saturation vapor pressure of the liquid, the liquid undergoes a phase change called cavitation. This phase change creates cavitation bubbles that are filled with the vapor of the liquid. Liquid can dissolve a gas up to a certain maximal concentration (saturation). When there are changes in the pressure or temperature (or both), the liquid can become over-saturated or under-saturated. In the over-saturated case, gas bubbles will form and grow in the liquid; in the under-saturated case the gas bubbles will shrink and disappear. For a multi-component gas phase, the bubbles of free gas are a mixture of those components that come out of the solution. The presence of dissolved and free gas in a liquid affects other properties, such as the rates of cavitation.
    - 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.
    - Melting and Solidification
      Melting is the process which changes the state of matter from solid to liquid. It takes place when a solid substance is heated to the melting temperature. The opposite process is called solidification.
    - VOF Waves Formulation
      Simcenter STAR-CCM+ provides the VOF Waves model to simulate surface gravity waves on the interface between a light fluid and a heavy fluid.
    - VOF Waves Bibliography
    - VOF Bibliography
  - Fluid Film
    Simcenter STAR-CCM+ allows you to model the distribution and transport of a thin layer of liquid—a fluid film— on solid surfaces. Application areas include vehicle rainwater management, selective catalytic reduction (SCR), and lubrication.
  - Dispersed Multiphase
    The Dispersed Multiphase (DMP) model simulates the flow of dispersed particles in a continuous phase using a Eulerian approach. As such, for simulating these types of flow, the DMP model is an alternative to using the Lagrangian Multiphase (LMP) model, which uses a Lagrangian approach.
  - Mixture Multiphase (MMP)
    The Mixture Multiphase (MMP) model assumes that the phases are miscible. It is suitable for modeling dispersed multiphase flows such as bubbly and droplet flows. Typical applications include fuel cells, boilers, and steam turbines. When simulating liquid droplets dispersed in a gas, the Mixture Multiphase (MMP) model accounts for evaporation and condensation.
- Multiphase—Lagrangian Approach
  Multiphase flows are found in a wide variety of industrial processes, some examples of which are internal combustion engines, liquid, or solid fueled combustors, spray driers, cyclone dust separators, and chemical reactors. Multiphase in this context refers to one thermodynamic phase, be it a solid, a liquid, or a gas, interacting with another distinct phase.
- Reacting Flow
  In reacting flows, chemical species mix with each other and react when conditions allow. To model these flows, Simcenter STAR-CCM+ couples species and energy transport equations with the chemistry solvers that compute the source terms.
- Internal Combustion Engines
  Numerical modeling of internal combustion engines plays an increasingly important role in improving engine design. CFD simulation of such engines can give a comprehensive insight into the wide-ranging physics of the device, such as turbulent mixing between fuel and air, the ignition, and combustion chemistry.
- Electrochemistry
  Electrochemistry is the discipline investigating relationships between electrical currents and chemical composition change in general.
- Plasma
  Plasma is a state of matter similar to a gas that is composed partially or completely of charged particles such as ions and electrons which are not bound to each other.
- Electromagnetism
  Many engineering applications, such as electric motors, electric switches, and transformers, involve electromagnetic phenomena. Electromagnetic phenomena can be modeled based on the classical theory of Electromagnetism, which describes the interaction between electrically charged particles in terms of electric fields, magnetic fields, and their mutual interaction.
- Batteries
- Solid Mechanics
  Solid Mechanics describes the behavior of a solid continuum in response to applied loads. Applied loads include body forces, surface loads, point forces, or thermal loads that result from changes in the solid temperature. Applied loads induce a stress field in the structure and can cause displacement of the structure—from an initial undeformed configuration to a deformed configuration.
- Aeroacoustics
  Computational aeroacoustics (CAA) is a branch of multiphysics modeling and simulation that involves identifying noise sources that are induced by fluid flow and propagation of the sound waves then generated.
- Finite Element Method
  The Finite Element method is a powerful tool for finding approximate solutions to continuous problems. The methodology is similar to other numerical techniques that approximate continuous partial differential equations with discrete algebraic equations.
- Mesh Motion
  In transient simulations, mesh motion is a numerical technique that allows you to update the position of the computational domain while the solvers run.
- 6-DOF Rigid Body Motion
  Simcenter STAR-CCM+ allows you to model the motion of a rigid body in response to applied forces and moments. In a rigid body, the relative distance between internal points does not change. Therefore, it is sufficient to solve the equations of motion for the center of mass of the body.
- Rotating Flow
  Rotating flow usually occurs in rotating machinery such as pumps, propellers, fans, wind turbines, and so on.
- Harmonic Balance
  Harmonic Balance equations describe periodic unsteady flows where the unsteady frequencies are known beforehand. They are suited to modeling periodically repeating flow fields that typically occur in turbomachinery such as compressors, turbines, and fans.
- Adjoint
  The adjoint method is an efficient means to predict the influence of many input parameters on some engineering quantities of interest in a simulation.
- Design Manager
  Design Manager provides an automated approach within Simcenter STAR-CCM+ to run design exploration studies. Design exploration covers both performance assessment and optimization.
- Scalars, Vectors, and Tensors
  Most physical quantities in Simcenter STAR-CCM+ are either scalars, vectors, or 2nd-order tensors.
- Solution Data Interpolation
  Many operations require interpolation of solution data between different sets of mesh points. For example, remeshing operations require interpolation of existing solution data onto a new mesh. Data interpolation also occurs at the interface between regions, where contacting boundaries exchange data. Additionally, configurable data mappers allow you to interpolate field functions and tabular data to specified meshes.
- Idealizations
  In many simulations, it is common practice to reduce the size of the computational domain using planes of symmetry, axes of rotation, periodicity, or by reducing the 3D domain to a 2D domain. However, when you calculate physical quantities using reports you generally want to account for the whole domain. You can obtain report values for the full model using idealizations.

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.

Homogeneous Relaxation Model

The Homogeneous Relaxation Model (HRM) is used for modeling vaporization mechanisms ranging from cavitation to flash boiling. This model is based on a finite rate equation for the rate of change of the vapor mass fraction with an empirical time-scale formulation.

The rate of change of vapor mass fraction is:

Figure 1. EQUATION_DISPLAY

\frac{d Y}{d t} = \frac{\bar{Y} - Y}{θ}

(2706)

where $Y$ is the vapour mass fraction, $\bar{Y}$ is the equilibrium mass fraction, and $θ$ is the relaxation time scale.

$θ$ is calculated from an empirical correlation. The most widely used empirical correlations is:

Figure 2. EQUATION_DISPLAY

θ = θ_{0} {α_{v}}^{- 0.54} ψ^{- 1.76}

(2707)

where $θ_{0}$ is a modelling constant with a value equal to $3.84 \times 10^{- 7}$ , $α_{v}$ is the vapor volume fraction, and $ψ$ is a non-dimensional pressure that is defined as:

Figure 3. EQUATION_DISPLAY

ψ = \frac{P_{s a t} - P}{P_{c r i t} - P_{s a t}}

(2708)

Eqn. (2706) is used to calculate the source terms in the vapour and the liquid volume fraction equations.