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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—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.
Sprays and Droplets
The term spray modeling refers to a subset of discrete phase particle modeling that describes the breakup of a continuous liquid into droplets. A number of industrial processes rely on turning quantities of liquid into vapor. One of the most common examples is liquid fueled combustion.
Secondary Breakup
Liquid droplets sometimes break up under the action of non-uniform surface forces that are induced by their motion relative to the continuous phase. This phenomenon is known as secondary breakup. Simcenter STAR-CCM+ provides a set of models that are used for the break-up of liquid droplets in a gaseous stream.
Reitz-Diwakar Breakup Model
The Reitz-Diwakar breakup model is based on observed length- and time-scales of droplet breakup.

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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.
- 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.
  - Particle Equations of Motion
    The conservation equation of momentum for a particle is written in the Lagrangian framework. The change in momentum is balanced by surface and body forces that act on the particle.
  - Wall-Bound Droplets
    Wall-bound droplets are a type of Lagrangian phase that is bound to the wall. This phase type is used to model droplets that slide along solid surfaces. The component of the particle equation of motion that is tangential to the surface is used to force the motion of the droplet along the surface.
  - Particle Heat and Mass Transfer
    If the dispersed phase is volatile, soluble, or reactive, mass transfer occurs between the phases. This mass transfer is accompanied by interphase heat transfer. Heat transfer can also take place because of the interphase temperature differences. Interphase mass transfer causes size changes in the dispersed material particles.
  - Two-Way Coupling with the Continuous Phase
    In Simcenter STAR-CCM+, you can simulate the interactions between the dispersed phase and the continuous phase as one-way coupling or two-way coupling. The coupling refers to the way that momentum, heat, and mass are exchanged between the phases.
  - Particle Injection
    Particles enter the computational domain through injectors at one or more discrete locations. An injector defines the size and the velocity vector distribution of the particles, and for unsteady simulations, the frequency. For heat and mass transfer effects, particle temperature and composition are also specified.
  - Sprays and Droplets
    The term spray modeling refers to a subset of discrete phase particle modeling that describes the breakup of a continuous liquid into droplets. A number of industrial processes rely on turning quantities of liquid into vapor. One of the most common examples is liquid fueled combustion.
    - Primary Atomization
      Primary atomization refers to the process of forcing liquid through a small orifice at a high pressure, resulting in a fine spray of liquid droplets. The injection velocity, that is, the velocity of the liquid as it exits the nozzle and enters the computational domain, is one of the most important parameters in a spray calculation. It strongly influences the atomization and break-up process, the spray penetration, the inter-phase transfer processes, and also the inter-droplet and droplet-wall interactions.
    - Secondary Breakup
      Liquid droplets sometimes break up under the action of non-uniform surface forces that are induced by their motion relative to the continuous phase. This phenomenon is known as secondary breakup. Simcenter STAR-CCM+ provides a set of models that are used for the break-up of liquid droplets in a gaseous stream.
      - KHRT Breakup Model
        The KHRT Breakup model combines two submodels, one based on Kelvin-Helmholtz (KH) theory and one based on Rayleigh-Taylor (RT) theory. Both breakup submodels consider the growth of instabilities on a droplet and provide expressions for their wavelength and frequency.
      - Reitz-Diwakar Breakup Model
        The Reitz-Diwakar breakup model is based on observed length- and time-scales of droplet breakup.
      - TAB Distortion and Breakup Model
        The Taylor analogy breakup (TAB) model is based on Taylor's analogy. The analogy represents a distorting droplet as a damped spring-mass system; it considers only the fundamental mode of oscillation of the droplet. The displacement and velocity of the mass in the spring-mass system correspond to representative distortion and rate of distortion quantities for the droplet.
      - SSD Breakup Model
        In the Stochastic Secondary Droplet (SSD) breakup model, breakup is a random process unrelated to original droplet size. This results in a log-normal distribution of droplet diameters in the long time limit.
      - User-Defined Breakup Model
        The User-Defined Breakup model lets you generate child parcels at secondary breakup events based on a breakup regime map you define. The breakup process is random, but properties like particle diameter are determined the same way for every droplet. The droplets do not have parent-child relationships after breakup events. This method is similar to the Stochastic Secondary Droplet (SSD) Breakup model.
    - Droplet Flash Boiling
      Flash boiling is the rapid phase change (vaporization) of a pressurized fluid entering ambient conditions below its vapor pressure.
    - Collision and Coalescence
      Simcenter STAR-CCM+ uses a host cell approach to detect collisions. Two parcels can collide only if they are in the same cell. Simcenter STAR-CCM+ uses the faster of the following collision algorithms to detect collisions in any particular cell. The following algorithms are available:
    - Wall Impingement
      The impact of particles on rigid solid surfaces produce a variety of effects. These effects depend on the particle size, velocity, material, and the nature of the surface. A liquid droplet, for example, can stick, bounce, or splash. The liquid that is deposited on the wall can retain the droplet form or it can merge into a fluid film.
  - Particle Porosity
    Simcenter STAR-CCM+ also provides the optional Lagrangian model, Particle Porosity, which allows you to define how the porosity of particles which burn internally changes through the course of a particle reaction.
  - Discrete Element Method
    The discrete element method (DEM) is designed for modeling the granular flow of materials such as sand, food particles, powders, capsules, and slurries. These flows are characterized by a high particle density where the inter-particle interaction is of importance.
  - Erosion
    In Simcenter STAR-CCM+, erosion modeling predicts the rate of erosion from particle impact on solid walls. Erosion rate is defined as the mass of wall material removed per unit area per unit time.
  - Passive Scalar Interactions
    There are two forms of Lagrangian/Eulerian interaction between passive scalar values: volume-weighted and area-weighted. Passive scalars can also interact between DEM particles.
  - Solution Methodology
    This section describes the methodology that is used to solve the system of equations that the Lagrangian Multiphase and the Lagrangian Phase models generate.
  - Multiphase—Lagrangian Approach Bibliography
- 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.

Reitz-Diwakar Breakup Model

The Reitz-Diwakar breakup model is based on observed length- and time-scales of droplet breakup.

The Reitz-Diwakar breakup model, [689] and [690], assumes that breakup occurs in one of two possible modes:

“bag” breakup, in which the non-uniform pressure field around the droplet causes it to expand in the low-pressure wake region and eventually disintegrate when surface tension forces are overcome
“stripping” breakup, in which liquid is sheared or stripped from the droplet surface

In either case, [689] and [690], theoretical studies provide a criterion for the onset of break-up and concurrently an estimate of the stable droplet diameter $D_{s}$ and the characteristic time-scale $τ_{b}$ of the breakup process. The droplet diameter decreases according to:

Figure 1. EQUATION_DISPLAY

\frac{d D_{p}}{d t} = \frac{D_{s} - D_{p}}{τ_{b}}

(3105)

in which $D_{s}$ is the stable diameter and $τ_{b}$ the breakup time-scale. Both $D_{s}$ and $τ_{b}$ depend on the active breakup regime.

Bag Breakup

The first breakup regime, bag breakup, is caused by the droplet expanding into the low-pressure wake region behind it, and eventually disintegrating when surface tension forces are overcome. It is assumed to be possible if

Figure 2. EQUATION_DISPLAY

W e > W e_{c r i t}

(3106)

with $W e_{c r i t} = 12$ the default. The stable diameter is obtained by making Eqn. (3106) an equality. The characteristic time-scale for this breakup regime is

Figure 3. EQUATION_DISPLAY

τ_{b} = \frac{C_{b 2} D_{p}}{4} \sqrt{\frac{ρ_{l} D_{p}}{σ}}

(3107)

Stripping Breakup

The second breakup regime, stripping breakup, is caused by liquid being sheared or stripped from the droplet surface. It is assumed to be possible if Eqn. (3106) is satisfied and additionally

Figure 4. EQUATION_DISPLAY

W e > max ({2 C}_{s 1} R e^{0.5}, W e_{c r i t})

(3108)

The default value for $C_{s 1}$ is 0.5. The stable diameter is obtained by making Eqn. (3108) an equality. The characteristic time-scale for this breakup regime is

Figure 5. EQUATION_DISPLAY

τ_{b} = \frac{C_{s 2}}{2} \sqrt{\frac{ρ_{l}}{ρ}} \frac{D_{p}}{| v_{s} |}

(3109)

The default value for $C_{s 2}$ is 20. When both Eqn. (3106) and Eqn. (3108) are satisfied, the regime with the smallest characteristic time-scale dominates.