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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.
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.
Circumferential Heat Flux Averaging Formulation

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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.
  - Conduction
    Heat conduction is the transfer of internal energy through interactions between the microscopic particles that compose a conducting substance. Energy flows in the direction of high temperature to low temperature as those particles in high temperature regions are more energetic than their low temperature neighbors.
  - Convection
    Convective heat transfer is the transfer of thermal energy by the combined effects of random molecular motion (diffusion) within the fluid, and the overall movement of the fluid from one place to another. In engineering practice, it is used to provide specific temperature changes.
  - Thermal Boundary Conditions
    When you are simulating non-isothermal flow, you are required to specify how the energy flow across wall boundaries is determined. Simcenter STAR-CCM+ provides various options such as defining an adiabatic wall, prescribing a fixed wall temperature, or assuming convective flow at the external side of the boundary.
  - Conjugate Heat Transfer
    A conjugate heat transfer (CHT) problem is solved across a contact interface, where different materials, such as fluid and solid or a porous medium and solid, exist on the two sides of the defined interface.
  - Thermal Radiation
    Thermal radiation is the emission of electromagnetic waves from all matter that has a temperature greater than absolute zero, and represents a conversion of thermal energy into electromagnetic energy. The thermal motion of charged particles in matter results in charge-acceleration and dipole oscillation. This behavior drives the electrodynamic generation of coupled electric and magnetic fields, which cause the emission of thermal radiation.
  - Solar Radiation
    Thermal radiative exchange with the solar environment includes both direct and diffuse components.
  - Thermal Comfort
    Human beings are endothermic homeotherms who maintain a constant body core temperature under different thermal disorders by regulating their internal body temperature with physiological and behavioral actions. The constant core body temperature is maintained within a narrow range between 36 °C – 38 °C (normal range at rest) and up to 41 °C for heavy exercise which is controlled by the thermoregulatory center in the hypothalamus.
  - Fully Developed Flow and Energy
    Fully developed flows occur in long tubes or tube banks. For simple flows without heat transfer or transported scalars, all flow variables except pressure can be treated as periodic. Pressure is typically modeled with a jump condition at the interface that compensates for the streamwise pressure drop through the system. When energy is present, a fully developed situation can be deemed to occur if the profiles of temperature and/or enthalpy become self-similar when using an appropriate scaling. In these cases, the self-similarity relations can be used to rescale the temperature profile from the interface boundary at the outflow to use at the inflow interface boundary.
  - Circumferential Heat Flux Averaging Formulation
    - A Body Spinning in an Interfacing Medium
      In this case, a solid body spins rapidly in an interfacing fluid medium. Convection, conduction, and radiation operate within in the fluid. Conduction and radiation operate within the solid. The interface is opaque to radiation.
    - A Body Spinning in a Meshless Region
      In this case, a solid or fluid body spins rapidly in a region without mesh, with no medium between the body and its environment, represented in the following figure by an external boundary. The body and the external environment interact only by thermal radiation between their boundaries, across the empty meshless region.
  - Energy Averaging for Rotating Fluids with Stationary Wall Boundaries
    For rotating machinery simulations, Simcenter STAR-CCM+ provides the option to model the rotating fluid by using a moving (rotating) reference frame. Typically, the fluid rotates with the reference frame at a specified rotational speed, and the stationary shroud is modeled as a wall boundary residing on another reference frame, which is stationary. Due to the rotation of the fluid (and associated blades), the heat transfer profile at the stationary wall boundary needs to be averaged. The circumferential averaging takes place on radial bins. To calculate the averaged heat flux on the internal side of a rotating fluid region and the averaged thermal effect on the surrounding stationary wall boundary, consider the observer placed on the stationary boundary and looking inside the rotating internal medium.
  - Boiling
    Boiling is a rapid vaporization of a liquid. It typically takes place when a liquid is heated up to temperatures that exceed the boiling temperature of the liquid. For single-component liquids that are in contact with walls at temperatures that exceed the boiling temperature of the liquid, boiling models simulate the effect of the latent heat of vaporization without simulating vapor.
  - Moisture Boiling
    The Moisture Boiling model represents a simple approach to model the effect of moisture boiling in porous solids on temperature. The model takes into account the effect of latent heat of vaporization when moisture inside a porous solid evaporates due to the solid heating up to temperatures that exceed the boiling temperature of the moisture as in, for example, gravity die casting applications.
  - Heat Transfer Bibliography
- 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.
- 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.

Circumferential Heat Flux Averaging Formulation

Simcenter STAR-CCM+ bases the averaging of heat flux around the circumference of a spinning body on either of two cases:

A body spinning in an interfacing medium.
A body spinning in a meshless region, interacting across the body boundary.

Both cases use the following conditions:

The body in question is axisymmetric, with little or no circumferential variation in any properties, physical conditions, or geometry.
Differences between the angular velocity of the axisymmetric body and any other bodies in the system are either very large or very small.
Interface boundaries and wall boundaries between the rotating region and the surroundings are opaque. (The model does not allow radiative heat transfer between rotating and non-rotating regions.)