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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
Materials
Material models simulate substances, including various mixtures.
Setting Material Properties Methods
After the selection of an Equation of State model or a Viscous Regime, the Material Properties manager node becomes fully populated with material property nodes, which can be accessed through their properties.
Equilibrium Speed of Sound
This method of calculating the speed of sound applies in a wide range of compressible fluids in equilibrium states—that is, with properties dependent only on temperature and pressure.

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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
- Defining Physics Workflow
  Simcenter STAR-CCM+ contains a wide range of physics models and methods for the simulation of single- and multi-phase fluid flow, heat transfer, turbulence, solid stress, dynamic fluid body interaction, aeroacoustics, and related phenomena. These physics models are all selected using a physics continuum.
- Setting Up Physics
  This section provides information on how to set up physics models in STAR-CCM+.
- Running Physics Simulations
  This part of the documentation describes preparation and procedures for running a Simcenter STAR-CCM+ simulation.
- Motion
  In general, motion can be defined as the change in position of a body with respect to a certain reference frame.
- Space
  The primary function of the Space models in Simcenter STAR-CCM+ is to provide methods for computing and accessing mesh metrics. Examples of mesh metrics include cell volume and centroid, face area and centroid, cell and face indexes, and skewness angle.
- Time
  The primary function of the time models in Simcenter STAR-CCM+ is to provide solvers that control the iteration and/or unsteady time-stepping.
- Mesh Motion and Adaption
  Many simulations that involve motion or geometry change require you to move or deform the mesh. Other simulations require localized mesh adaption in order to achieve an accurate solution.
- Materials
  Material models simulate substances, including various mixtures.
  - Modeling a Single-Component Material
    To model a single-component material, that is, a pure substance, activate either the Gas, Liquid, or Solid model by selecting the appropriate radio button in the Material section of the model selection dialog.
  - Modeling a Multi-Component Mixture
    A multi-component mixture is a miscible mixture of two or more pure substances in the same phase.
  - Modeling Multi-Component Solids
    Some simulations require you to model many solid parts of different materials.
  - Modeling a Multiphase Mixture
    A multiphase mixture is a fluid that is composed of multiple phases: an immiscible mixture of two or more pure substances in either the gas or liquid phase.
  - Setting Material Properties Methods
    After the selection of an Equation of State model or a Viscous Regime, the Material Properties manager node becomes fully populated with material property nodes, which can be accessed through their properties.
    - Material Property Node Properties
      This section lists the settings for various material property nodes.
    - Plotting Variable Material Properties
      When you work with a material property that uses a polynomial function, you can generate an approximate plot preview of the values before you run the simulation.
    - Using Constant Values
      Generally, most material property values are specified as constants.
    - Using Field Functions
      Field functions can be used to create non-standard functions for material properties.
    - Using Polynomial in T
      This polynomial function is available for certain material properties.
    - Log Polynomial in T Reference
      You can specify the thermal conductivity of gas species as a function of temperature by using the Log Polynomial in T method. The Log Polynomial in T method is available only when an ECFM combustion model is selected in Simcenter STAR-CCM+ In-cylinder and when either the Mass-Weighted Mixture or Mathur-Saxena Averaging method is used to specify mixture thermal conductivity.
    - Using Thermodynamic Polynomial Data
      Thermodynamic Polynomial Data provides seven (or nine) coefficients—five (or seven) coefficient polynomial curve fits for specific heat $C_{p}$ , a coefficient polynomial curve fit for static enthalpy $h$ , and a coefficient polynomial curve fit for entropy $S$ .
    - Using IAPWS-IF97
      The IAPWS-IF97 (International Association for the properties of Water and Steam, Industrial Formulation 1997) specification provides the formulation by which various thermodynamic properties of water and steam are calculated from pressure and temperature.
    - Using Sutherland’s Law
      The Sutherland’s law function is available for various material properties.
    - Using Table (Reaction Time)
      A (Reaction Time) table has a column of Reaction Time values that specify the physical time of the reaction, in seconds, of each point (row) in the table.
    - Using Table(T)
      A (T) table has a column of temperature values and a column of data values.
    - Table, Cp (T) Reference
      A Cp (T) table has a column of temperature values and a column of specific heat values.
    - Using Table (T,c)
      The Table (T,c) method is available for specifying liquid electrolyte properties when using the Concentrated Electrolyte or the Li-Ion Battery Cell models. The table lists corresponding values of temperature and concentration for the given material properties.
    - Using Table (T,P)
      A (T,P) table consists of three columns, one for the material property itself, and two additional columns that give corresponding values of temperature and absolute pressure. STAR-CCM+ interpolates the material property value from the table.
    - Using the Density Table Method for Density Derivatives
      When density is defined by a table of data in temperature (or temperature and pressure for compressible flows), Simcenter STAR-CCM+ can numerically differentiate the table of data for density.
    - Using the Enthalpy Table Method for Enthalpy Derivatives
      This material property method is available for specifying specific heat when the enthalpy is defined by a table of values in temperature or in temperature and pressure. This method can also be used to specify the enthalpy pressure derivative when enthalpy is defined by a table of values in temperature and pressure.
    - Using the Enthalpy Difference Method for Latent Heat of Vaporization
      This material property method is available for specifying latent heat of vaporization when certain models are active.
    - Using Table(B,H) Method for Permeability
      The Table (B,H) method provides a stable iterative scheme for setting the magnetic permeability of a material using $B$ - $H$ curves. With this method, you provide a table of discrete ( $B$ , $H$ ) values. Simcenter STAR-CCM+ interpolates the imported values and constructs a continuous $B$ - $H$ curve.
    - Using Tabular Data
      The tabular data method is used to provide values of a material property. The multi-dimensional bilinear interpolation method is used for interpolating between data points in the table.
    - Using the Power Law
      The Power law function is available for various material properties.
    - Using the Temperature Shift Factors
      When temperature effects are present, the non-Newtonian liquid models use horizontal and vertical shift factors $a_{T}$ and $b_{T}$ to adjust viscosity with temperature.
    - Using the Non-Newtonian Generalized Models
      To model a non-Newtonian liquid, Simcenter STAR-CCM+ supports three methods.
    - Using the Schmidt Number
      The Schmidt number function is available for specifying molecular diffusivity of components in a mixture.
    - Using a Volume-Weighted Mixture
      The volume-weighted mixture function is for non-ideal gas multicomponent mixtures.
    - Using the Mass-Weighted Mixture
      The mass-weighted mixture method calculates a given mixture property by mass-weighting the component property values.
    - Using the Lewis Number
      The Lewis number $L_{e}$ is defined as the ratio of thermal diffusion to mass diffusion $D_{m}$ .
    - Using the PPDF Table
      The PPDF Table method interpolates property values from the PPDF table. The Molecular Weight and Specific Heat material properties of the mixture use this method.
    - Using the PCFM Method
      The PCFM method becomes active when the Partially-Premixed Coherent Flame Model (PCFM) is used. The Molecular Weight and Specific Heat material properties of the mixture use this method.
    - Using the Mixture Method for Critical Temperature and Pressure
      The Mixture method calculates the critical temperature and pressure of a mixture.
    - Using the Mixture Method for Molecular Weight
    - Using the Mixture Method for Surface Tension
    - Using the Mathur-Saxena Averaging Method for Dynamic Viscosity
      This method becomes available when the multi-component gas model is used. Selecting this method provides the choice of the Chapman-Enskog method for Dynamic Viscosity on the Mixture Component level.
    - Using the Chapman-Enskog Method for Dynamic Viscosity
      This method becomes available for single- and multi-component gases once an energy model is included. This method is also activated when the Mathur-Saxena Averaging method is selected for dynamic viscosity.
    - Using the Refutas Method for Dynamic Viscosity
      This method becomes available when the Multi-Component Liquid model is included and density is calculated using the Volume Weighted Mixture method.
    - Using the Mathur-Saxena Averaging Method for Thermal Conductivity
      The Mathur-Saxena Averaging method for thermal conductivity is a specification of the Multi-Component Mathur-Saxena Averaging Property method $〈 Φ 〉$ ; see [eqnlink].
    - Using the Kinetic Theory Method for Thermal Conductivity
      The Kinetic Theory method calculates the thermal conductivity of an individual gas component using kinetic theory.
    - Using the Elemental Composition Method
      In order to calculate the molecular weight of a molecule, this method is used to describe its elemental composition.
    - Using the Anisotropic Method
      The Anisotropic method is available in two forms: as a placeholder object to indicate that an anisotropic approach to a material property is being used in a tensor node under Regions, or as a tensor node under a material property of a physics model.
    - Using the Viscosity Method
    - Using the Thermal Conductivity Method
    - Using the Gas Kinetics Method for Specific Heat
      This method becomes available with single- and multi-component gases, together with the Ideal Gas, Constant Density, or Thermal Non-Equilibrium Ideal Gas models, or with any of the Real Gas models: Peng-Robinson, Redlich-Kwong, Soave-Redlich-Kwong, Modified Soave-Redlich-Kwong, and Van der Waals).
    - Using the Antoine Equation
      The Antoine equation is available for the Saturation Pressure material property.
    - Using the Wagner Equation
      The Wagner equation is available for the Saturation Pressure material property.
    - Using the Clausius-Clapeyron Method
      The Clausius-Clapeyron method uses the Clapeyron equation and the assumption of an ideal gas equation of state for the vapor to relate the latent heat of vaporization to the saturation pressure.
    - Using the Heat of Formation
      The Heat of Formation is the heat that is evolved when 1 kilogram of the substance is formed from its elements in their respective standard states [J/kg].
    - Using the Leidenfrost Temperature
      The Leidenfrost temperature is the temperature at which the Leidenfrost effect appears. This effect creates a vapor barrier between liquid and solid phases, reducing heat transfer and adhesion.
    - Using the Standard State Temperature
      The Standard State Temperature is the temperature at which the standard state of a substance is defined. The commonest choice is 298.15 K (25.00 C).
    - Using the Binary Diffusion Coefficient Method for Molecular Diffusivity
      This method uses specified binary diffusion coefficients between the components of the mixture to calculate a molecular diffusivity for each component that is diffusing into the mixture as a whole.
    - Using the Kinetic Theory Method for Molecular Diffusivity
      The Kinetic Theory method calculates the molecular diffusivity of an individual component using kinetic theory.
    - Using the Component Molecular Diffusivities Method for Molecular Diffusivity
      This method allows you to specify the molecular diffusivity of separate components in a multi-component mixture, for cases where the other methods are not sufficient to predict it accurately.
    - Using the Nernst-Einstein Method for Charged Species
      The Nernst-Einstein method can be set to determine the mobility of charged species from the diffusivity, or the diffusivity from the mobility.
    - Using the Electrochemical Species method for Electrical Conductivity
      When using the Electrodynamic Potential model, to obtain a consistent setup for applications which require electroneutrality, specify the Electrical Conductivity Method as Electrochemical Species.
    - Using the Thermal Diffusion Coefficient
      When the Soret Effect option is selected, you must specify the thermal diffusion coefficient for each component.
    - Equilibrium Speed of Sound
      This method of calculating the speed of sound applies in a wide range of compressible fluids in equilibrium states—that is, with properties dependent only on temperature and pressure.
    - Materials Bibliography
  - Material Databases
    The material database node within the Tools > Material Databases node contains the objects that represent the information from the material database.
- Fluid Flow
  Many engineering design projects require you to predict the effect of flowing fluids on containing structures or immersed objects. While you can analyse simple scenarios with hand calculations, complex scenarios require you to apply numerical methods for accurate solutions.
- Viscous Flow
  Viscous Flow is a finite element approach for use with viscoelastic materials and other highly viscous non-Newtonian fluids, such as liquid plastics and rubber, dough and similar foodstuffs, molten glass, and mud. Viscoelastic materials resemble elastic materials, but also exhibit viscous effects, rebounding slowly from deformations.
- Passive Scalars
  Passive scalars are user-defined variables of arbitrary value, assigned to fluid phases or individual particles. They are passive because they do not affect the physical properties of the simulation. An intuitive way to think of passive scalars is as tracer dye in a fluid, but with numerical values instead of colors, and with no appreciable mass or volume.
- Heat Transfer
  Heat transfer is the study of energy in transit due to a temperature difference in a medium or between media. Heat transfer extends thermodynamic analysis through the study of the modes of energy transfer and through development of relations to calculate energy transfer rates.
- Species
  This chapter provides information about the chemical species models in Simcenter STAR-CCM+. A species model is activated whenever a multi-component liquid or multi-component gas is chosen from the Material model section of the Physics Model Selection dialog.
- Porous Media
  Simcenter STAR-CCM+ allows you to simulate the transport of a fluid or energy (e.g. heat, electrical charge) through porous materials using the concept that the action of the porous media can be represented using appropriate loss (or 'diffusion') coefficients.
- Adjoint
  The adjoint method is an efficient means to predict the influence of many design parameters and physical inputs on some engineering quantity of interest, that is, on the engineering objective of the simulation. In other words, it provides the sensitivity of the objective (output) with respect to the design variables (input).
- Fans and Blowers
  Simcenter STAR-CCM+ provides models for axial and radial fans where classical fan laws apply.
- Virtual Disk Model
  The virtual disk model is based upon the principle of representing propellers, turbines, rotors, fans, and so on, as an actuator disk. The actuator disk treatment is practical when you are concerned about the influence of the rotor/propeller behavior on the flow rather than knowing about the detailed interactions between the flow and the blades of the rotating device.
- Turbulence
  Most fluid flows of engineering interest are characterized by irregularly fluctuating flow quantities.
- 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 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.
- Radiation
  The Radiation Model is the gateway, or entry point to all of the radiation modeling capabilities of Simcenter STAR-CCM+. This section describes Simcenter STAR-CCM+’s radiation modeling.
- Aeroacoustics
  Aeroacoustics investigates the aerodynamic generation of sound.
- Reacting Flow
  Simcenter STAR-CCM+ provides a selection of models that you can use to simulate a wide range of reacting flow applications.
- Internal Combustion Engines
  In an internal combustion engine (ICE), for example a gasoline engine, the process of combustion takes place in a cylinder (or cylinders) within the engine. The working fluid is a fuel and oxidizer mixture (usually air), which reacts to form combustion products.
- Multiphase Flow
  Multiphase flow is a term which refers to the flow and interaction of several phases within the same system where distinct interfaces exist between the phases. Simcenter STAR-CCM+ considers flow options where phases coexist as: gas bubbles in liquid, liquid droplets in gas, and/or solid particles in gas or liquid, and/or (large scale) free surface flows.
- Dynamic Fluid Body Interaction
  Dynamic Fluid Body Interaction (DFBI) in Simcenter STAR-CCM+ allows you to simulate the motion of a 6-DOF body with the displacement and rotation resulting from the defined mechanical and multiphysics interaction (flow, DEM, solid stress, EMAG).
- Harmonic Balance
  Some unsteady flows have a regularly repeating flow pattern, that is, they are time-periodic. Consider the flow from a fan blade passing across the entrance to a duct. Measurements of the instantaneous flow just within the duct would show a regularly repeating pattern. If the flow disturbances are sufficiently large, and propagate to the end of the duct, measurements of the unsteady flow at any point within the duct show repeating patterns. Such time-periodic patterns can be expressed using Fourier series.
- Solid Stress
  Simcenter STAR-CCM+ allows you to model the response of a solid continuum to applied loads, including mechanical loads and thermal loads that result from changes in the solid temperature.
- Electromagnetism
  Simcenter STAR-CCM+ allows you to model engineering applications involving electromagnetic phenomena. Example applications are electric motors, electric switches, and transformers, which can be modeled based on the classical theory of Electromagnetism.
- Electrochemistry
  Electrochemistry is the study of chemical reactions which occur due to an imposed electrical charge, or a difference in electrical potential at a boundary between a conductor–such as a metal–and an electrolyte. Simcenter STAR-CCM+ provides models that allow you to simulate batteries, corrosion, etching, and other electrochemical reactions.
- Electric Circuits
  Electrical circuits are conducting loops of interconnected electrical components, such as batteries, power sources, resistors, and inductors.
- 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.
- Batteries
  You can simulate batteries in Simcenter STAR-CCM+ using battery cells and battery cycling procedures that are defined either directly in Simcenter STAR-CCM+, or in the external software package Simcenter Battery Design Studio.
- Casting
  Casting simulations are performed using transient multiphase simulations using the VOF model with solidification. Conjugate heat transfer is applied between the solidifying melt and the solid mold.
- Region Sources
  This section provides some guidelines on how to use region sources for some common problems.
- Cell Quality Remediation
  The Cell Quality Remediation model helps you get solutions on a poor-quality mesh. This model identifies poor-quality cells, using a set of predefined criteria, such as Skewness Angle exceeding a certain threshold. Once these cells and their neighbors have been marked, the computed gradients in these cells are modified in such a way as to improve the robustness of the solution.
- Guidelines for Applying Simcenter STAR-CCM+
  This part of the documentation provides guidelines on applying Simcenter STAR-CCM+ models to your applications.
- Common Solvers Reference
  In Simcenter STAR-CCM+, solvers compute the solution during the simulation run.

Equilibrium Speed of Sound

This method of calculating the speed of sound applies in a wide range of compressible fluids in equilibrium states—that is, with properties dependent only on temperature and pressure.

This method gives the speed of sound $c$ in terms of density derivatives:

Figure 1. EQUATION_DISPLAY

c^{2} = \frac{1}{{(\frac{\partial ρ}{\partial P})}_{T} - \frac{T}{ρ^{2} C_{p}} {(\frac{\partial ρ}{\partial T})}_{P}^{2}}

(177)

where $C_{p}$ is specific heat and density $ρ$ is a function of temperature $T$ and pressure $P$ .