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30.4 Alphabetical Listing of Field Variables and Their Definitions

Below, the variables listed in Tables  30.3.1- 30.3.13 are defined. For some variables (such as residuals) a general definition is given under the category name, and variables in the category are not listed individually. When appropriate, the unit quantity is included, as it appears in the Quantities list in the Set Units panel.

Abs (C-H) Spanwise Coordinate   (in the Grid... category) is the dimensional coordinate in the spanwise direction, from casing to hub. Its unit quantity is length.

Abs (H-C) Spanwise Coordinate   (in the Grid... category) is the dimensional coordinate in the spanwise direction, from hub to casing. Its unit quantity is length.

Abs Meridional Coordinate   (in the Grid... category) is the dimensional coordinate that follows the flow path from inlet to outlet. Its unit quantity is length.

Abs Pitchwise Coordinate   (in the Grid... category) is the dimensional coordinate in the circumferential (pitchwise) direction. Its unit quantity is angle.

Absolute Pressure    (in the Pressure... category) is equal to the operating pressure plus the gauge pressure. See Section  8.14 for details. Its unit quantity is pressure.

Absorbed Radiation Flux (Band-n)    (in the Wall Fluxes... category) is the amount of radiative heat flux absorbed by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux.

Absorbed Visible Solar Flux, Absorbed IR Solar Flux    (in the Wall Fluxes... category) is the amount of solar heat flux absorbed by a semi-transparent wall for a visible or infrared (IR) radiation.

Absorption Coefficient    (in the Radiation... category) is the property of a medium that describes the amount of absorption of thermal radiation per unit path length within the medium. It can be interpreted as the inverse of the mean free path that a photon will travel before being absorbed (if the absorption coefficient does not vary along the path). The unit quantity for Absorption Coefficient is length-inverse.

Acoustic Power    (in the Acoustics... category) is the acoustic power per unit volume generated by isotropic turbulence (see Equation  21.2-10). It is available only when the Broadband Noise Sources acoustics model is being used. Its unit quantity is power per volume.

Acoustic Power Level (dB)    (in the Acoustics... category) is the acoustic power per unit volume generated by isotropic turbulence and reported in dB (see Equation  21.2-13). It is available only when the Broadband Noise Sources acoustics model is being used.

Active Cell Partition    (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file. See Section  31.5.4 for more information.

Adaption...   includes field variables that are commonly used for adapting the grid. For information about solution adaption, see Chapter  26.

Adaption Function    (in the Adaption... category) can be either the Adaption Space Gradient or the Adaption Curvature, depending on the settings in the Gradient Adaption panel. For instance, the Adaption Curvature is the undivided Laplacian of the values in temporary cell storage. To display contours of the Laplacian of pressure, for example, you first select Static Pressure, click the Compute (or Display) button, select Adaption Function, and finally click the Display button.

Adaption Iso-Value    (in the Adaption... category) is the desired field variable function.

Adaption Space Gradient    (in the Adaption... category) is the first derivative of the desired field variable.


 \vert e_{i1} \vert = (A_{\rm cell})^\frac{r}{2} \vert \nabla f\vert (30.4-1)

Depending on the settings in the Gradient Adaption panel, this equation will either be scaled or normalized. Recommended for problems with shock waves (i.e., supersonic, inviscid flows). For more information, see Section  26.4.1.

Adaption Curvature    (in the Adaption... category) is the second derivative of the desired field variable.


 \vert e_{i2} \vert = (A_{\rm cell})^\frac{r}{2} \vert \nabla ^2 f\vert (30.4-2)

Depending on the settings in the Gradient Adaption panel, this equation will either be scaled or normalized. Recommended for smooth solutions (i.e., viscous, incompressible flows). For more information, see Section  26.4.1.

Adiabatic Flame Temperature   (in the Premixed Combustion... category) is the adiabatic temperature of burnt products in a laminar premixed flame ( $T_b$ in Equation  16.2-24). Its unit quantity is temperature.

Arrhenius Rate of Reaction-n    (in the Reactions... category) is given by the following expression (see Equation  14.1-8 for definitions of the variables shown here):


\hat{R}_r = {\Gamma} \left(k_{f,r} \prod_{j=1}^{N_r} \left[C_... ... \prod_{j=1}^{N_r} \left[C_{j,r} \right]^{\eta''_{j,r}} \right)

The reported value is independent of any particular species, and has units of kgmol/m $^3$-s.

To find the rate of production/destruction for a given species $i$ due to reaction $r$, multiply the reported reaction rate for reaction $r$ by the term $M_i (\nu''_{i,r} - \nu'_{i,r})$, where $M_i$ is the molecular weight of species $i$, and $\nu''_{i,r}$ and $\nu'_{i,r}$ are the stoichiometric coefficients of species $i$ in reaction $r$.

Angular Coordinate    (in the Grid... category) is the angle between the radial vector and the position vector. The radial vector is obtained by transforming the default radial vector (y-axis) by the same rotation that was applied to the default axial vector (z-axis ). This assumes that, after the transformation, the default axial vector (z-axis) becomes the reference axis. The angle is positive in the direction of cross-product between reference axis and radial vector.

Abs. Angular Coordinate    (in the Grid... category) is the absolute value of the Angular Coordinate defined above.

Axial Coordinate    (in the Grid... category) is the distance from the origin in the axial direction. The axis origin and (in 3D) direction is defined for each cell zone in the Fluid or Solid panel. The axial direction for a 2D model is always the $z$ direction, and the axial direction for a 2D axisymmetric model is always the $x$ direction. The unit quantity for Axial Coordinate is length.

Axial Pull Velocity    (in the Solidification/Melting... category) is the axial-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity.

Axial Velocity    (in the Velocity... category) is the component of velocity in the axial direction. (See Section  30.2 for details.) For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. Its unit quantity is velocity.

Axial-Wall Shear Stress    (in the Wall Fluxes... category) is the axial component of the force acting tangential to the surface due to friction. Its unit quantity is pressure.

Beam Irradiation Flux (Band-b)    (in the Wall Fluxes... category) is specified as an incident heat flux ( $W/m^2$) for each wavelength band.

Boundary Cell Distance    (in the Adaption... category) is an integer that indicates the approximate number of cells from a boundary zone.

Boundary Normal Distance    (in the Adaption... category) is the distance of the cell centroid from the closest boundary zone.

Boundary Volume Distance    (in the Adaption... category) is the cell volume distribution based on the Boundary Volume, Growth Factor, and normal distance from the selected Boundary Zones defined in the Boundary Adaption panel. See Section  26.3 for details.

Cell Children    (in the Adaption... category) is a binary identifier based on whether a cell is the product of a cell subdivision in the hanging-node adaption process (value = 1) or not (value = 0).

Cell Element Type    (in the Cell Info... category) is the integer cell element type identification number. Each cell can have one of the following element types:

  triangle       1
  tetrahedron    2
  quadrilateral  3
  hexahedron     4
  pyramid        5
  wedge          6

Cell Equiangle Skew    (in the Grid... category) is a nondimensional parameter calculated using the normalized angle deviation method, and is defined as


 \max \left[ \frac{q_{\rm max} - q_e}{180 - q_e}, \frac{q_e - q_{\rm min}}{q_e} \right] (30.4-3)

where


$q_{\rm max}$ = largest angle in the face or cell
$q_{\rm min}$ = smallest angle in the face or cell
$q_e$ = angle for an equiangular face or cell
    (e.g., 60 for a triangle and 90 for a square)

A value of 0 indicates a best case equiangular cell, and a value of 1 indicates a completely degenerate cell. Degenerate cells (slivers) are characterized by nodes that are nearly coplanar (collinear in 2D). Cell Equiangle Skew applies to all elements.

Cell Equivolume Skew    (in the Grid... category) is a nondimensional parameter calculated using the volume deviation method, and is defined as


 \frac{\mbox{optimal-cell-size} - \mbox{cell-size}}{\mbox{optimal-cell-size}} (30.4-4)

where optimal-cell-size is the size of an equilateral cell with the same circumradius. A value of 0 indicates a best case equilateral cell and a value of 1 indicates a completely degenerate cell. Degenerate cells (slivers) are characterized by nodes that are nearly coplanar (collinear in 2D). Cell Equivolume Skew applies only to triangular and tetrahedral elements.

Cell Id   (in the Cell Info... category) is a unique integer identifier associated with each cell.

Cell Info...   includes quantities that identify the cell and its relationship to other cells.

Cell Partition    (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells.

Cell Refine Level    (in the Adaption... category) is an integer that indicates the number of times a cell has been subdivided in the hanging node adaption process, compared with the original grid. For example, if one quad cell is split into four quads, the Cell Refine Level for each of the four new quads will be 1. If the resulting four quads are split again, the Cell Refine Level for each of the resulting 16 quads will be 2.

Cell Reynolds Number    (in the Velocity... category) is the value of the Reynolds number in a cell. (Reynolds number is a dimensionless parameter that is the ratio of inertia forces to viscous forces.) Cell Reynolds Number is defined as


 {\rm Re} \equiv \frac{\rho u d}{\mu} (30.4-5)

where $\rho$ is density, $u$ is velocity magnitude, $\mu$ is the effective viscosity (laminar plus turbulent), and $d$ is Cell Volume $^{1/2}$ for 2D cases and Cell Volume $^{1/3}$ in 3D or axisymmetric cases.

Cell Squish Index    (in the Grid... category) is a measure of the quality of a mesh, and is calculated from the dot products of each vector pointing from the centroid of a cell toward the center of each of its faces, and the corresponding face area vector as


 \max_i \left[1 - \frac{\vec{A}_i \cdot \vec{r}_{c0/xf_i}}{\vert\vec{A}_i\vert\vert\vec{r}_{c0/xf_i}\vert}\right] (30.4-6)

Therefore, the worst cells will have a Cell Squish Index close to 1.

Cell Surface Area    (in the Adaption... category) is the total surface area of the cell, and is computed by summing the area of the faces that compose the cell.

Cell Volume    (in the Grid... category) is the volume of a cell. In 2D the volume is the area of the cell multiplied by the unit depth. For axisymmetric cases, the cell volume is calculated using a reference depth of 1 radian. The unit quantity of Cell Volume is volume.

2D Cell Volume    (in the Grid... category) is the two-dimensional volume of a cell in an axisymmetric computation. For an axisymmetric computation, the 2D cell volume is scaled by the radius. Its unit quantity is area.

Cell Volume Change    (in the Adaption... category) is the maximum volume ratio of the current cell and its neighbors.

Cell Wall Distance    (in the Grid... category) is the distribution of the normal distance of each cell centroid from the wall boundaries. Its unit quantity is length.

Cell Warpage    (in the Adaption... category) is the square root of the ratio of the distance between the cell centroid and cell circumcenter and the circumcenter radius:


 \mbox{warpage} = \sqrt{\frac{\vert\vec{r}_{\rm centroid} - \vec{r}_{\rm circumcenter}\vert}{R_{\rm circumcenter}}} (30.4-7)

Cell Zone Index    (in the Cell Info... category) is the integer cell zone identification number. In problems that have more than one cell zone, the cell zone ID can be used to identify the various groups of cells.

Cell Zone Type    (in the Cell Info... category) is the integer cell zone type ID. A fluid cell has a type ID of 1, a solid cell has a type ID of 17, and an exterior cell (parallel solver) has a type ID of 21.

Contact Resistivity    (in the Solidification/Melting... category) is the additional resistance at the wall due to contact resistance. It is equal to $R_c(1-\beta)/h$, where $R_c$ is the contact resistance, $\beta$ is the liquid fraction, and $h$ is the cell height of the wall-adjacent cell. The unit quantity for Contact Resistivity is thermal-resistivity.

Critical Strain Rate    (in the Premixed Combustion... category) is a parameter that takes into account the stretching and extinction of premixed flames ( $g_{\rm cr}$ in Equation  16.2-16). Its unit quantity is time-inverse.

Custom Field Functions...    are scalar field functions defined by you. You can create a custom function using the Custom Field Function Calculator panel. All defined custom field functions will be listed in the lower drop-down list. See Section  30.5 for details.

Damkohler Number    (in the Premixed Combustion... category) is a nondimensional parameter that is defined as the ratio of turbulent to chemical time scales.

Density...   includes variables related to density.

Density    (in the Density... category) is the mass per unit volume of the fluid. Plots or reports of Density include only fluid cell zones. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. The unit quantity for Density is density.

Density All    (in the Density... category) is the mass per unit volume of the fluid or solid material. Plots or reports of Density All include both fluid and solid cell zones. The unit quantity for Density All is density.

Derivatives...    are the viscous derivatives. For example, dX-Velocity/dx is the first derivative of the $x$ component of velocity with respect to the $x$-coordinate direction. You can compute first derivatives of velocity, angular velocity, and pressure in the pressure-based solver, and first derivatives of velocity, angular velocity, temperature, and species in the density-based solvers.

Diameter    (in the Properties... category) is the diameter of particles, droplets, or bubbles of the secondary phase selected in the Phase drop-down list. Its unit quantity is length.

Diffusion Coef. of Scalar-n    (in the User Defined Scalars... category) is the diffusion coefficient for the $n$th user-defined scalar transport equation. See the separate UDF manual for details about defining user-defined scalars.

Discrete Phase Model...   includes quantities related to the discrete phase model. See Chapter  22 for details about this model.

DPM Absorption Coefficient    (in the Discrete Phase Model... category) is the absorption coefficient for discrete-phase calculations that involve radiation ( $a$ in Equation  13.3-1). Its unit quantity is length-inverse.

DPM Accretion    (in the Discrete Phase Model... category) is the accretion rate calculated at a wall boundary:


 R_{\rm accretion} = \sum^{N}_{p=1} \frac{\dot{m}_p}{A_{\rm face}} (30.4-8)

where $\dot{m}_p$ is the mass flow rate of the particle stream, and $A_{\rm face}$ is the area of the wall face where the particle strikes the boundary. This item will appear only if the optional erosion/accretion model is enabled. See Section  22.11.5 for details. The unit quantity for DPM Accretion is mass-flux.

DPM Burnout    (in the Discrete Phase Model... category) is the exchange of mass from the discrete to the continuous phase for the combustion law (Law 5) and is proportional to the solid phase reaction rate. The burnout exchange has units of mass-flow.

DPM Concentration    (in the Discrete Phase Model... category) is the total concentration of the discrete phase. Its unit quantity is density.

DPM Emission    (in the Discrete Phase Model... category) is the amount of radiation emitted by a discrete-phase particle per unit volume. Its unit quantity is heat-generation-rate.

DPM Enthalpy Source    (in the Discrete Phase Model... category) is the exchange of enthalpy (sensible enthalpy plus heat of formation) from the discrete phase to the continuous phase. The exchange is positive when the particles are a source of heat in the continuous phase. The unit quantity for DPM Enthalpy Source is power.

DPM Erosion    (in the Discrete Phase Model... category) is the erosion rate calculated at a wall boundary face:


 R_{\rm erosion} = \sum^{N}_{p=1} \frac{\dot{m}_p f(\alpha)} {A_{\rm face}} (30.4-9)

where $\dot{m}_p$ is the mass flow rate of the particle stream, $\alpha$ is the impact angle of the particle path with the wall face, $f(\alpha)$ is the function specified in the Wall panel, and $A_{\rm face}$ is the area of the wall face where the particle strikes the boundary. This item will appear only if the optional erosion/accretion model is enabled. See Section  22.11.5 for details. The unit quantity for DPM Erosion is mass-flux.

DPM Evaporation/Devolatilization    (in the Discrete Phase Model... category) is the exchange of mass, due to droplet-particle evaporation or combusting-particle devolatilization, from the discrete phase to the evaporating or devolatilizing species. If you are not using the non-premixed combustion model, the mass source for each individual species ( DPM species-n Source, below) is also available; for non-premixed combustion, only this sum is available. The unit quantity for DPM Evaporation/Devolatilization is mass-flow.

DPM Mass Source    (in the Discrete Phase Model... category) is the total exchange of mass from the discrete phase to the continuous phase. The mass exchange is positive when the particles are a source of mass in the continuous phase. If you are not using the non-premixed combustion model, DPM Mass Source will be equal to the sum of all species mass sources ( DPM species-n Source, below); if you are using the non-premixed combustion model, it will be equal to DPM Burnout plus DPM Evaporation/Devolatilization. The unit quantity for DPM Mass Source is mass-flow.

DPM Scattering    (in the Discrete Phase Model... category) is the scattering coefficient for discrete-phase calculations that involve radiation ( $\sigma_s$ in Equation  13.3-1). Its unit quantity is length-inverse.

DPM Sensible Enthalpy Source   (in the Discrete Phase Model... category) is the exchange of sensible enthalpy from the discrete phase to the continuous phase. The exchange is positive when the particles are a source of heat in the continuous phase. Its unit quantity is power.

DPM species-n Source   (in the Discrete Phase Model... category) is the exchange of mass, due to droplet-particle evaporation or combusting-particle devolatilization, from the discrete phase to the evaporating or devolatilizing species. (The name of the species will replace species-n in DPM species-n Source.) These species are specified in the Set Injection Properties panel, as described in Section  22.12.4. The unit quantity is mass-flow. Note that this variable will not be available if you are using the non-premixed combustion model; use DPM Evaporation/Devolatilization instead.

DPM Swirl Momentum Source   (in the Discrete Phase Model... category) is the exchange of swirl momentum from the discrete phase to the continuous phase. This value is positive when the particles are a source of momentum in the continuous phase. The unit quantity is force.

DPM X, Y, Z Momentum Source   (in the Discrete Phase Model... category) are the exchange of $x$-, $y$-, and $z$-direction momentum from the discrete phase to the continuous phase. These values are positive when the particles are a source of momentum in the continuous phase. The unit quantity is force.

Dynamic Pressure    (in the Pressure... category) is defined as $q \equiv \frac{1}{2} \rho v^2$. Its unit quantity is pressure.

Eff Diff Coef of species-n   (in the Species... category) is the sum of the laminar and turbulent diffusion coefficients of a species into the mixture:


D_{i,m} + \frac{\mu_t}{\rho {{\rm Sc}_t}}

(The name of the species will replace species-n in Eff Diff Coef of species-n.) The unit quantity is mass-diffusivity.

Effective Prandtl Number    (in the Turbulence... category) is the ratio $\mu_{\rm eff} c_p / k_{\rm eff}$, where $\mu_{\rm eff}$ is the effective viscosity, $c_p$ is the specific heat, and $k_{\rm eff}$ is the effective thermal conductivity.

Effective Thermal Conductivity    (in the Properties... category) is the sum of the laminar and turbulent thermal conductivities, $k + k_t$, of the fluid. A large thermal conductivity is associated with a good heat conductor and a small thermal conductivity with a poor heat conductor (good insulator). Its unit quantity is thermal-conductivity.

Effective Viscosity    (in the Turbulence... category) is the sum of the laminar and turbulent viscosities of the fluid. Viscosity, $\mu$, is defined by the ratio of shear stress to the rate of shear. Its unit quantity is viscosity.

Enthalpy    (in the Temperature... category) is defined differently for compressible and incompressible flows, and depending on the solver and models in use.

For compressible flows,


 H = \sum_j Y_j H_j (30.4-10)

and for incompressible flows,


 H = \sum_j Y_j H_j + \frac{p}{\rho} (30.4-11)

where $Y_j$ and $H_j$ are, respectively, the mass fraction and enthalpy of species $j$. (See Enthalpy of species-n, below). For the pressure-based solver, the second term on the right-hand side of Equation  30.4-11 is included only if the pressure work term is included in the energy equation (see Section  13.2.1). For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. For all species models, the Enthalpy plots consist of the thermal (or sensible) plus chemical energy. The unit quantity for Enthalpy is specific-energy.

Enthalpy of species-n   (in the Species... category) is defined differently depending on the solver and models options in use. The quantity:


 H_j = \int^{T}_{T_{{\rm ref},j}} c_{p,j}\; dT + h_j^{0} (T_{{\rm ref},j}) (30.4-12)

where $h_j^{0} (T_{{\rm ref},j})$ is the formation enthalpy of species $j$ at the reference temperature $T_{{\rm ref},j})$, is reported only for non-adiabatic PDF cases, or if the density-based solver is selected. The quantity:


 h_j = \int^{T}_{T_{\rm ref}} c_{p,j}\; dT (30.4-13)

where $T_{\rm ref} = 298.15 K$, is reported in all other cases. The unit quantity for Enthalpy of species-n is specific-energy.

Entropy    (in the Temperature... category) is a thermodynamic property defined by the equation
 \Delta S \equiv \int_{\rm rev} \frac{\delta Q}{T} (30.4-14)

where "rev'' indicates an integration along a reversible path connecting two states, $Q$ is heat, and $T$ is temperature. For compressible flows, entropy is computed using the equation
 s = c_v \left[ \frac{p/p_{\rm ref}}{(\rho / \rho_{\rm ref})^\gamma} - 1 \right] (30.4-15)

where $c_v$ is computed from $R/(\gamma -1)$, and the reference pressure and density are defined in the Reference Values panel. For incompressible flow, the entropy is computed using the equation
 s = c_p \left(\frac{T}{T_{\rm ref}} - 1\right) (30.4-16)

where $c_p$ is the specific heat at constant pressure and $T_{\rm ref}$ is defined in the Reference Values panel. The unit quantity for entropy is specific-heat.

Existing Value    (in the Adaption... category) is the value that presently resides in the temporary space reserved for cell variables (i.e., the last value that you displayed or computed).

Face Handedness    (in the Grid... category) is a parameter that is equal to one in cells that are adjacent to left-handed faces, and zero elsewhere. It can be used to locate mesh problems.

Face Squish Index    (in the Grid... category) is a measure of the quality of a mesh, and is calculated from the dot products of each face area vector, and the vector that connects the centroids of the two adjacent cells as


 1 - \frac{\vec{A}_i \cdot \vec{r}_{c0/c1}}{\vert\vec{A}_i\vert\vert\vec{r}_{c0/c1}\vert} (30.4-17)

Therefore, the worst cells will have a Face Squish Index close to 1.

Fine Scale Mass Fraction of species-n    (in the Species... category) is the term $Y^{*}_i$ in Equation  14.1-31.

Fine Scale Temperature    (in the Temperature... category) is the temperature of the fine scales, which is calculated from the enthalpy when the reaction proceeds over the time scale ( $\tau^{*}$ in Equation  14.1-30), governed by the Arrhenius rates of Equation  14.1-8. Its unit quantity is temperature.

Fine Scale Transfer Rate    (in the Species... category) is the transfer rate of the fine scales, which is equal to the inverse of the time scale ( $\tau^{*}$ in Equation  14.1-30). Its unit quantity is time-inverse.

1-Fine Scale Volume Fraction   (in the Species... category) is a function of the fine scale volume fraction ( $\xi^{*}$ in Equation  14.1-29). The quantity is subtracted from unity to make it easier to interpret.

Fvar Prod   (in the Pdf... category) is the production term in the mixture fraction variance equation solved in the non-premixed combustion model (i.e., the last two terms in Equation  15.2-5).

Fvar2 Prod   (in the Pdf... category) is the production term in the secondary mixture fraction variance equation solved in the non-premixed combustion model. See Equation  15.2-5.

Gas Constant (R)    (in the Properties... category) is the gas constant of the fluid. Its unit quantity is specific-heat.

Granular Conductivity    (in the Properties... category) is equivalent to the diffusion coefficient in Equation  23.5-75. For more information, see Section  23.5.8. Its unit quantity is kg/m-s.

Granular Pressure...   includes quantities for reporting the solids pressure for each granular phase ( $p_s$ in Equation  23.5-44). See Section  23.5.5 for details. Its unit quantity is pressure. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Granular Temperature...   includes quantities for reporting the granular temperature for each granular phase ( $\Theta_s$ in Equation  23.5-75). See Section  23.5.8 for details. Its unit quantity is $m^2/s^2$. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Grid...    includes variables related to the grid.

Grid X-Velocity, Grid Y-Velocity, Grid Z-Velocity    (in the Velocity... category) are the vector components of the grid velocity for moving-grid problems (rotating or multiple reference frames, mixing planes, or sliding meshes). Its unit quantity is velocity.

HCN Density    (in the NOx... category) is the mass per unit volume of HCN. The unit quantity is density. The HCN Density will appear only if you are modeling fuel NOx. See Section  20.1.5 for details.

Helicity    (in the Velocity... category) is defined by the dot product of vorticity and the velocity vector.
 H = ( \nabla \times \vec{V} ) \cdot \vec{V} (30.4-18)

It provides insight into the vorticity aligned with the fluid stream. Vorticity is a measure of the rotation of a fluid element as it moves in the flow field.

Incident Radiation    (in the Radiation... category) is the total radiation energy, $G$, that arrives at a location per unit time and per unit area:


 G = \int_{\Omega = 4 \pi} I d\Omega (30.4-19)

where $I$ is the radiation intensity and $\Omega$ is the solid angle. $G$ is the quantity that the P-1 radiation model computes. For the DO radiation model, the incident radiation is computed over a finite number of discrete solid angles, each associated with a vector direction. The unit quantity for Incident Radiation is heat-flux.

Incident Radiation (Band n)    (in the Radiation... category) is the radiation energy contained in the wavelength band $\Delta \lambda$ for the non-gray DO radiation model. Its unit quantity is heat-flux.

Internal Energy    (in the Temperature... category) is the summation of the kinetic and potential energies of the molecules of the substance per unit volume (and excludes chemical and nuclear energies). Internal Energy is defined as $e = c_v T$. Its unit quantity is specific-energy.

Jet Acoustic Power    (in the Acoustics... category) is the acoustic power for turbulent axisymmetric jets (see Equation  21.2-14). It is available only when the Broadband Noise Sources acoustics model is being used.

Jet Acoustic Power Level (dB)    (in the Acoustics... category) is the acoustic power for turbulent axisymmetric jets, reported in dB (see Equation  21.2-27). It is available only when the Broadband Noise Sources acoustics model is being used.

Lam Diff Coef of species-n    (in the Species... category) is the laminar diffusion coefficient of a species into the mixture, $D_{i,m}$. Its unit quantity is mass-diffusivity.

Laminar Flame Speed   (in the Premixed Combustion... category) is the propagation speed of laminar premixed flames ( $U_l$ in Equation  16.2-4). Its unit quantity is velocity.

LEE Self-Noise X-Source, LEE Self-Noise Y-Source, LEE Self-Noise Z-Source    (in the Acoustics... category ) are the self-noise source terms in the linearized Euler equation for the acoustic velocity component (see Equation  21.2-32). They are available only when the Broadband Noise Sources acoustics model is being used.

LEE Shear-Noise X-Source, LEE Shear-Noise Y-Source, LEE Shear-Noise Z-Source    (in the Acoustics... category ) are the shear-noise source terms in the linearized Euler equation for the acoustic velocity component (see Equation  21.2-32). They are available only when the Broadband Noise Sources acoustics model is being used.

LEE Total Noise X-Source, LEE Total Noise Y-Source, LEE Total Noise Z-Source    (in the Acoustics... category ) are the total noise source terms in the linearized Euler equation for the acoustic velocity component (see Equation  21.2-32). The total noise source term is the sum of the self-noise and shear-noise source terms. They are available only when the Broadband Noise Sources acoustics model is being used.

Lilley's Self-Noise Source    (in the Acoustics... category ) is the self-noise source term in the linearized Lilley's equation (see Equation  21.2-36), available only when the Broadband Noise Sources acoustics model is being used.

Lilley's Shear-Noise Source    (in the Acoustics... category ) is the shear-noise source term in the linearized Lilley's equation (see Equation  21.2-36), available only when the Broadband Noise Sources acoustics model is being used.

Lilley's Total Noise Source    (in the Acoustics... category ) is the total noise source term in the linearized Lilley's equation (see Equation  21.2-36). The total noise source term is the sum of the self-noise and shear-noise source terms, available only when the Broadband Noise Sources acoustics model is being used.

Liquid Fraction    (in the Solidification/Melting... category) is the liquid fraction $\beta$ computed by the solidification/melting model:


\beta = \frac{\Delta H}{L} = 0 \;\;\ \ \ {\rm if}\ \ \; T < T_{\rm solidus}


\beta = \frac{\Delta H}{L} = 1 \;\;\ \ \ {\rm if}\ \ \; T > T_{\rm liquidus}


 \beta = \frac{\Delta H}{L} = \frac{T-T_{\rm solidus}}{T_{\rm... ...;\;\ \ \ {\rm if}\ \ \; T_{\rm solidus} < T < T_{\rm liquidus} (30.4-20)

Mach Number    (in the Velocity... category) is the ratio of velocity and speed of sound.

Mass fraction of HCN, Mass fraction of NH3, Mass fraction of NO, Mass fraction of N2O   (in the NOx... category) are the mass of HCN, the mass of NH $_3$, the mass of NO, and the mass of N $_2$O per unit mass of the mixture (e.g., kg of HCN in 1 kg of the mixture). The Mass fraction of HCN and the Mass fraction of NH3 will appear only if you are modeling fuel NOx. See Section  20.1.5 for details.

Mass fraction of nuclei   (in the Soot... category) is the number of particles per unit mass of the mixture (in units of particles $\times 10^{15}$/kg) The Mass fraction of nuclei will appear only if you use the two-step soot model. See Section  20.3 for details.

Mass fraction of soot   (in the Soot... category) is the mass of soot per unit mass of the mixture (e.g., kg of soot in 1 kg of the mixture). See Section  20.3 for details.

Mass fraction of species-n    (in the Species... category) is the mass of a species per unit mass of the mixture (e.g., kg of species in 1 kg of the mixture).

Mean quantity-n   (in the Unsteady Statistics... category) is the time-averaged value of a solution variable (e.g., Static Pressure). See Section  25.17.4 for details.

Meridional Coordinate   (in the Grid... category) is the normalized (dimensionless) coordinate that follows the flow path from inlet to outlet. Its value varies from $0$ to $1$.

Mixture Fraction Variance    (in the Pdf... category) is the variance of the mixture fraction solved for in the non-premixed combustion model. This is the second conservation equation (along with the mixture fraction equation) that the non-premixed combustion model solves. (See Section  15.2.1.)

Modified Turbulent Viscosity    (in the Turbulence... category) is the transported quantity $\tilde{\nu}$ that is solved for in the Spalart-Allmaras turbulence model (see Equation  12.3-1). The turbulent viscosity, $\mu_t$, is computed directly from this quantity using the relationship given by Equation  12.3-2. Its unit quantity is viscosity.

Molar Concentration of species-n    (in the Species... category) is the moles per unit volume of a species. Its unit quantity is concentration.

Mole fraction of species-n    (in the Species... category) is the number of moles of a species in one mole of the mixture.

Mole fraction of HCN, Mole fraction of NH3, Mole fraction of NO, Mole fraction of N2O   (in the NOx... category) are the number of moles of HCN, NH $_3$, NO, and N $_2$O in one mole of the mixture. The Mole fraction of HCN and the Mole fraction of NH3 will appear only if you are modeling fuel NOx. See Section  20.1.5 for details.

Mole fraction of soot    (in the Soot... category) is the number of moles of soot in one mole of the mixture.

Molecular Prandtl Number    (in the Properties... category) is the ratio $c_p \mu_{\rm lam}/k_{\rm lam}$.

Molecular Viscosity    (in the Properties... category) is the laminar viscosity of the fluid. Viscosity, $\mu$, is defined by the ratio of shear stress to the rate of shear. Its unit quantity is viscosity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list. For granular phases, this is equivalent to the solids shear viscosity $\mu_s$ in Equation  23.5-62.

NH3 Density, NO Density, N2O Density    (in the NOx... category) are the mass per unit volume of NH $_3$, NO and N $_2$O. The unit quantity for each is density. The NH3 Density will appear only if you are modeling fuel NOx. See Section  20.1.5 for details.

NOx...   contains quantities related to the NOx model. See Section  20.1 for details about this model.

Partition Boundary Cell Distance    (in the Grid... category) is the smallest number of cells which must be traversed to reach the nearest partition (interface) boundary.

Partition Neighbors    (in the Cell Info... category) is the number of adjacent partitions (i.e., those that share at least one partition boundary face (interface)). It gives a measure of the number of messages that will have to be generated for parallel processing.

Pdf...   contains quantities related to the non-premixed combustion model, which is described in Chapter  15.

Phases...   contains quantities for reporting the volume fraction of each phase. See Chapter  23 for details.

Pitchwise Coordinate   (in the Grid... category) is the normalized (dimensionless) coordinate in the circumferential (pitchwise) direction. Its value varies from $0$ to $1$.

Preconditioning Reference Velocity   (in the Velocity... category) is the reference velocity used in the coupled solver's preconditioning algorithm. See
Section  25.5.2 for details.

Premixed Combustion...   contains quantities related to the premixed combustion model, which is described in Chapter  16.

Pressure...    includes quantities related to a normal force per unit area (the impact of the gas molecules on the surfaces of a control volume).

Pressure Coefficient    (in the Pressure... category) is a dimensionless parameter defined by the equation


 C_p = \frac{(p - p_{\rm ref})}{q_{\rm ref}} (30.4-21)

where $p$ is the static pressure, $p_{\rm ref}$ is the reference pressure, and $q_{\rm ref}$ is the reference dynamic pressure defined by $\frac{1}{2} \rho_{\rm ref} {v_{\rm ref}}^2$. The reference pressure, density, and velocity are defined in the Reference Values panel.

Product Formation Rate    (in the Premixed Combustion... category) is the source term in the progress variable transport equation ( $S_c$ in Equation  16.2-1). Its unit quantity is time-inverse.

Production of k    (in the Turbulence... category) is the rate of production of turbulence kinetic energy (times density). Its unit quantity is turb-kinetic-energy-production. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Progress Variable    (in the Premixed Combustion... category) is a normalized mass fraction of the combustion products ( $c=1$) or unburnt mixture products ( $c=0$), as defined by Equation  16.2-2.

Properties...   includes material property quantities for fluids and solids.

Rate of NO    (in the NOx... category) is the overall rate of formation of NO due to all active NO formation pathways (e.g., thermal, prompt, etc.).

Rate of Nuclei    (in the Soot... category) is the overall rate of formation of nuclei.

Rate of N2OPath NO    (in the NOx... category) is the rate of formation of NO due to the N2O pathway only (only available when N2O pathway is active).

Rate of Prompt NO    (in the NOx... category) is the rate of formation of NO due to the prompt pathway only (only available when prompt pathway is active).

Rate of Reburn NO    (in the NOx... category) is the rate of formation of NO due to the reburn pathway only (only available when reburn pathway is active).

Rate of SNCR NO    (in the NOx... category) is the rate of formation of NO due to the SNCR pathway only (only available when SNCR pathway is active).

Rate of Soot    (in the Soot... category) is the overall rate of formation of soot mass.

Rate of Thermal NO    (in the NOx... category) is the rate of formation of NO due to the thermal pathway only (only available when thermal pathway is active).

Rate of Fuel NO    (in the NOx... category) is the rate of formation of NO due to the fuel pathway only (only available when fuel pathway is active).

Rate of USER NO    (in the NOx... category) is the rate of formation of NO due to user defined rates only (only available when UDF rates are added).

Radial Coordinate    (in the Grid... category) is the length of the radius vector in the polar coordinate system. The radius vector is defined by a line segment between the node and the axis of rotation. You can define the rotational axis in the Fluid panel. (See also Section  30.2.) The unit quantity for Radial Coordinate is length.

Radial Pull Velocity    (in the Solidification/Melting... category) is the radial-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity.

Radial Velocity    (in the Velocity... category) is the component of velocity in the radial direction. (See Section  30.2 for details.) The unit quantity for Radial Velocity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Radial-Wall Shear Stress   (in the Wall Fluxes... category) is the radial component of the force acting tangential to the surface due to friction. Its unit quantity is pressure.

Radiation...   includes quantities related to radiation heat transfer. See Section  13.3 for details about the radiation models available in FLUENT.

Radiation Heat Flux    (in the Wall Fluxes... category) is the rate of radiation heat transfer through the control surface. It is calculated by the solver according to the specified radiation model. Heat flux out of the domain is negative, and heat flux into the domain is positive. The unit quantity for Radiation Heat Flux is heat-flux.

Radiation Temperature    (in the Radiation... category) is the quantity $\theta_R$, defined by


 \theta_R = (\frac{G}{4 \sigma})^{1/4} (30.4-22)

where $G$ is the Incident Radiation. The unit quantity for Radiation Temperature is temperature.

Rate of Reaction-n    (in the Reactions... category) is the effective rate of progress of $n$th reaction. For the finite-rate model, the value is the same as the Arrhenius Rate of Reaction-n. For the eddy-dissipation model, the value is equivalent to the Turbulent Rate of Reaction-n. For the finite-rate/eddy-dissipation model, it is the lesser of the two.

Reactions...   includes quantities related to finite-rate reactions. See Chapter  14 for information about modeling finite-rate reactions.

Reflected Radiation Flux (Band-n)    (in the Wall Fluxes... category) is the amount of radiative heat flux reflected by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux.

Reflected Visible Solar Flux, Reflected IR Solar Flux    (in the Wall Fluxes... category) is the amount of solar heat flux reflected by a semi-transparent wall for a visible or infrared (IR) radiation.

Refractive Index    (in the Radiation... category) is a nondimensional parameter defined as the ratio of the speed of light in a vacuum to that in a material. See Section  13.3.6 for details.

Relative Axial Velocity    (in the Velocity... category) is the axial-direction component of the velocity relative to the reference frame motion. See Section  30.2 for details. The unit quantity for Relative Axial Velocity is velocity.

Relative Humidity    (in the Species... category) is the ratio of the partial pressure of the water vapor actually present in an air-water mixture to the saturation pressure of water vapor at the mixture temperature. FLUENT computes the saturation pressure, $p$, from the following equation [ 302]:


 \ln \left( \frac{p}{p_c} \right) = \left( \frac{T_c}{T} -1 ... ... \sum_{i=1}^8 F_i \left[ a \left(T-T_p \right) \right] ^ {i-1} (30.4-23)


where $p_c$ = $\phantom{-}$22.089 MPa
  $T_c$ = $\phantom{-}$647.286 K
  $F_1$ = $-7.4192420$
  $F_2$ = $\phantom{-}2.9721000 \times 10^{-1}$
  $F_3$ = $-1.1552860 \times 10^{-1}$
  $F_4$ = $\phantom{-}8.6856350 \times 10^{-3}$
  $F_5$ = $\phantom{-}1.0940980 \times 10^{-3}$
  $F_6$ = $-4.3999300 \times 10^{-3}$
  $F_7$ = $\phantom{-}2.5206580 \times 10^{-3}$
  $F_8$ = $-5.2186840 \times 10^{-4}$
  $a$ = $\phantom{-}$0.01
  $T_p$ = $\phantom{-}$338.15 K

Relative Length Scale (DES)    (in the Turbulence... category) is defined by
 Ls = Ls_{rans} - Ls_{les} (30.4-24)

where $Ls_{rans}$ is an RANS-based length scale, and $Ls_{les}$ is an LES-based length scale. All of the cells inside the domain in which $Ls > 0$ belong to the LES region, and all of the cells inside the domain in which $Ls < 0$ belong to the RANS region.

Relative Mach Number    (in the Velocity... category) is the nondimensional ratio of the relative velocity and speed of sound.

Relative Radial Velocity   (in the Velocity... category) is the radial-direction component of the velocity relative to the reference frame motion. (See Section  30.2 for details.) The unit quantity for Relative Radial Velocity is velocity.

Relative Swirl Velocity   (in the Velocity... category) is the tangential-direction component of the velocity relative to the reference frame motion, in an axisymmetric swirling flow. (See Section  30.2 for details.) The unit quantity for Relative Swirl Velocity is velocity.

Relative Tangential Velocity   (in the Velocity... category) is the tangential-direction component of the velocity relative to the reference frame motion. (See Section  30.2 for details.) The unit quantity for Relative Tangential Velocity is velocity.

Relative Total Pressure    (in the Pressure... category) is the stagnation pressure computed using relative velocities instead of absolute velocities; i.e., for incompressible flows the dynamic pressure would be computed using the relative velocities. (See Section  30.2 for more information about relative velocities.) The unit quantity for Relative Total Pressure is pressure.

Relative Total Temperature    (in the Temperature... category) is the stagnation temperature computed using relative velocities instead of absolute velocities. (See Section  30.2 for more information about relative velocities.) The unit quantity for Relative Total Temperature is temperature.

Relative Velocity Angle    (in the Velocity... category) is similar to the Velocity Angle except that it uses the relative tangential velocity, and is defined as


 \tan^{-1} \left(-\frac{\mbox{relative-tangential-velocity}} {\mbox{axial-velocity}}\right) (30.4-25)

Its unit quantity is angle.

Relative Velocity Magnitude    (in the Velocity... category) is the magnitude of the relative velocity vector instead of the absolute velocity vector. The relative velocity ( $\vec{w}$) is the difference between the absolute velocity ( $\vec{v}$) and the grid velocity. For simple rotation, the relative velocity is defined as
 \vec{w} \equiv \vec{v} - \vec{\Omega} \times \vec{r} (30.4-26)

where $\vec{\Omega}$ is the angular velocity of a rotating reference frame about the origin and $\vec{r}$ is the position vector. (See also Section  30.2.) The unit quantity for Relative Velocity Magnitude is velocity.

Relative X Velocity, Relative Y Velocity, Relative Z Velocity   (in the Velocity... category) are the $x$-, $y$-, and $z$-direction components of the velocity relative to the reference frame motion. (See Section  30.2 for details.) The unit quantity for these variables is velocity.

Residuals...    contains different quantities for the pressure-based and density-based solvers:

In the density-based solvers, this category includes the corrections to the primitive variables pressure, velocity, temperature, and species, as well as the time rate of change of the corrections to these primitive variables for the current iteration (i.e., residuals). Corrections are the changes in the variables between the current and previous iterations and residuals are computed by dividing a cell's correction by its physical time step. The total residual for each variable is the summation of the Euler, viscous, and dissipation contributions. The dissipation components are the vector components of the flux-like, face-based dissipation operator.

In the pressure-based solver, only the Mass Imbalance in each cell is reported (unless you have requested others, as described in Section  25.18.1). At convergence, this quantity should be small compared to the average mass flow rate.

RMS quantity-n    (in the Unsteady Statistics... category) is the root mean squared value of a solution variable (e.g., Static Pressure). See Section  25.17.4 for details.

Rothalpy    (in the Temperature... category) is defined as


 I = h + \frac{w^2}{2} - \frac{u^2}{2} (30.4-27)

where $h$ is the enthalpy, $w$ is the relative velocity magnitude, and $u$ is the magnitude of the rotational velocity $\vec{u} = \vec{\omega} \times \vec{r}$.

Scalar-n   (in the User Defined Scalars... category) is the value of the $n$th scalar quantity you have defined as a user-defined scalar. See the separate UDF manual for more information about user-defined scalars.

Scalar Dissipation   (in the Pdf... category) is one of two parameters that describes the species mass fraction and temperature for a laminar flamelet in mixture fraction spaces. It is defined as


 \chi = 2 D {\vert{\nabla } f \vert}^2 (30.4-28)

where $f$ is the mixture fraction and $D$ is a representative diffusion coefficient (see Section  15.3.2 for details). Its unit quantity is time-inverse.

Scattering Coefficient    (in the Radiation... category) is the property of a medium that describes the amount of scattering of thermal radiation per unit path length for propagation in the medium. It can be interpreted as the inverse of the mean free path that a photon will travel before undergoing scattering (if the scattering coefficient does not vary along the path). The unit quantity for Scattering Coefficient is length-inverse.

Secondary Mean Mixture Fraction    (in the Pdf... category) is the mean ratio of the secondary stream mass fraction to the sum of the fuel, secondary stream, and oxidant mass fractions. It is the secondary-stream conserved scalar that is calculated by the non-premixed combustion model. See Section  15.2.1.

Secondary Mixture Fraction Variance    (in the Pdf... category) is the variance of the secondary stream mixture fraction that is solved for in the non-premixed combustion model. See Section  15.2.1.

Sensible Enthalpy    (in the Temperature... category) is available when any of the species models are active and displays only the thermal (sensible) enthalpy.

Skin Friction Coefficient    (in the Wall Fluxes... category) is a nondimensional parameter defined as the ratio of the wall shear stress and the reference dynamic pressure
 C_f \equiv \frac{\tau_w}{\frac{1}{2} \rho_{\rm ref} {v^2_{\rm ref}}} (30.4-29)

where $\tau_w$ is the wall shear stress, and $\rho_{\rm ref}$ and $v_{\rm ref}$ are the reference density and velocity defined in the Reference Values panel. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Solar Heat Flux    (in the Wall Fluxes... category) is the rate of solar heat transfer through the control surface. Heat flux out of the domain is negative and heat flux into the domain is positive.

Solidification/Melting...   contains quantities related to solidification and melting.

Soot...   contains quantities related to the Soot model, which is described in Section  20.3.

Soot Density    (in the Soot... category) is the mass per unit volume of soot. The unit quantity is density. See Section  20.1.5 for details.

Sound Speed    (in the Properties... category) is the acoustic speed. It is computed from $\sqrt{\frac{\gamma p}{\rho}}$. Its unit quantity is velocity.

Spanwise Coordinate   (in the Grid... category) is the normalized (dimensionless) coordinate in the spanwise direction, from hub to casing. Its value varies from $0$ to $1$.

species-n Source Term   (in the Species... category) is the source term in each of the species transport equations due to reactions. The unit quantity is always kg/m $^3$-s.

Species...   includes quantities related to species transport and reactions.

Specific Dissipation Rate (Omega)    (in the Turbulence... category) is the rate of dissipation of turbulence kinetic energy in unit volume and time. Its unit quantity is time-inverse.

Specific Heat (Cp)    (in the Properties... category) is the thermodynamic property of specific heat at constant pressure. It is defined as the rate of change of enthalpy with temperature while pressure is held constant. Its unit quantity is specific-heat.

Specific Heat Ratio (gamma)    (in the Properties... category) is the ratio of specific heat at constant pressure to the specific heat at constant volume.

Stored Cell Partition    (in the Cell Info... category) is an integer identifier designating the partition to which a particular cell belongs. In problems in which the grid is divided into multiple partitions to be solved on multiple processors using the parallel version of FLUENT, the partition ID can be used to determine the extent of the various groups of cells. The active cell partition is used for the current calculation, while the stored cell partition (the last partition performed) is used when you save a case file. See Section  31.5.4 for more information.

Static Pressure    (in the Pressure... category) is the static pressure of the fluid. It is a gauge pressure expressed relative to the prescribed operating pressure. The absolute pressure is the sum of the Static Pressure and the operating pressure. Its unit quantity is pressure.

Static Temperature    (in the Temperature... and Premixed Combustion... categories) is the temperature that is measured moving with the fluid. Its unit quantity is temperature.

Note that Static Temperature will appear in the Premixed Combustion... category only for adiabatic premixed combustion calculations. See Section  16.3.7.

Strain Rate    (in the Derivatives... category) relates shear stress to the viscosity. Also called the shear rate ( $\dot{\gamma}$ in Equation  8.4-17), the strain rate is related to the second invariant of the rate-of-deformation tensor $\overline{\overline{D}}$. Its unit quantity is time-inverse. In 3D Cartesian coordinates, the strain rate, $S$, is defined as


$\displaystyle S^2$ $\textstyle =$ $\displaystyle \left[\frac{\partial u}{\partial x}\left(\frac{\partial u}{\parti... ...ft(\frac{\partial u}{\partial z} +\frac{\partial w}{\partial x}\right)\right] +$  
    $\displaystyle \left[\frac{\partial v}{\partial x}\left(\frac{\partial v}{\parti... ...ft(\frac{\partial v}{\partial z} +\frac{\partial w}{\partial y}\right)\right] +$  
    $\displaystyle \left[\frac{\partial w}{\partial x}\left(\frac{\partial w}{\parti... ...left(\frac{\partial w}{\partial z} +\frac{\partial w}{\partial z}\right)\right]$ (30.4-30)

For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Stream Function    (in the Velocity... category) is formulated as a relation between the streamlines and the statement of conservation of mass. A streamline is a line that is tangent to the velocity vector of the flowing fluid. For a 2D planar flow, the stream function, $\psi$, is defined such that
 \rho u \equiv \frac{\partial \psi}{\partial y} \; \; \; \; \; \; \rho v \equiv - \frac{\partial \psi}{\partial x} (30.4-31)

where $\psi$ is constant along a streamline and the difference between constant values of stream function defining two streamlines is the mass rate of flow between the streamlines.

The accuracy of the stream function calculation is determined by the text command /display/set/n-stream-func.

Stretch Factor    (in the Premixed Combustion... category) is a nondimensional parameter that is defined as the probability of unquenched flamelets ( $G$ in Equation  16.2-13).

Subgrid Filter Length    (in the Turbulence... category) is a mixing length for subgrid scales of the LES turbulence model (defined as $L_S$ in Equation 12.9-16).

Subgrid Kinetic Energy    (in the Turbulence... category) is the turbulence kinetic energy per unit mass of the unresolved eddies, $k_s$, calculated using the LES turbulence model. It is defined as


 k_s = \frac{\nu_t^2}{L_s^2} (30.4-32)

Its unit quantity is turbulent-kinetic-energy.

Subgrid Turbulent Viscosity    (in the Turbulence... category) is the turbulent (dynamic) viscosity of the fluid calculated using the LES turbulence model. It expresses the proportionality between the anisotropic part of the subgrid-scale stress tensor and the rate-of-strain tensor. (See Equation   12.9-8.) Its unit quantity is viscosity.

Subgrid Turbulent Viscosity Ratio    (in the Turbulence... category) is the ratio of the subgrid turbulent viscosity of the fluid to the laminar viscosity, calculated using the LES turbulence model.

Surface Acoustic Power    (in the Acoustics... category) is the Acoustic Power per unit area generated by boundary layer turbulence (see Equation  21.2-31). It is available only when the Broadband Noise Sources acoustics model is being used. Its unit quantity is power per area.

Surface Acoustic Power Level (dB)    (in the Acoustics... category) is the Acoustic Power per unit area generated by boundary layer turbulence, and represented in dB (see Equation  21.2-31). It is available only when the Broadband Noise Sources acoustics model is being used.

Surface Cluster ID   (in the Radiation... category) is used to view the distribution of surface clusters in the domain. Each cluster has a unique integer number (ID) associated with it.

Surface Coverage of species-n    (in the Species... category) is the amount of a surface species that is deposited on the substrate at a specific point in time.

Surface Deposition Rate of species-n    (in the Species... category) is the amount of a surface species that is deposited on the substrate. Its unit quantity is mass-flux.

Surface dpdt RMS    (in the Acoustics... category) is the RMS value of the time-derivative of static pressure ( $\partial p/\partial t$). It is available when the Ffowcs-Williams & Hawkings acoustics model is being used.

Surface Heat Transfer Coef.    (in the Wall Fluxes... category), as defined in FLUENT, is given by the equation
 h_{\rm eff} = \frac{q}{T_{\rm wall} - T_{\rm ref}} (30.4-33)

where $q$ is the combined convective and radiative heat flux, $T_{\rm wall}$ is the wall temperature, and $T_{\rm ref}$ is the reference temperature defined in the Reference Values panel. Please note that $T_{\rm ref}$ is a constant value that should be representative of the problem. Its unit quantity is the heat-transfer- coefficient.

Surface Incident Radiation    (in the Wall Fluxes... category) is the net incoming radiation heat flux on a surface. Its unit quantity is heat-flux.

Surface Nusselt Number    (in the Wall Fluxes... category) is a local nondimensional coefficient of heat transfer defined by the equation


 {\rm Nu} = \frac{h_{\rm eff} L_{\rm ref}} {k} (30.4-34)

where $h_{\rm eff}$ is the heat transfer coefficient, $L_{\rm ref}$ is the reference length defined in the Reference Values panel, and $k$ is the molecular thermal conductivity.

Surface Stanton Number    (in the Wall Fluxes... category) is a nondimensional coefficient of heat transfer defined by the equation


 {\rm St} = \frac{h_{\rm eff}}{\rho_{\rm ref} v_{\rm ref} c_p} (30.4-35)

where $h_{\rm eff}$ is the heat transfer coefficient, $\rho_{\rm ref}$ and $v_{\rm ref}$ are reference values of density and velocity defined in the Reference Values panel, and $c_p$ is the specific heat at constant pressure.

Swirl Pull Velocity    (in the Solidification/Melting... category) is the tangential-direction component of the pull velocity for the solid material in a continuous casting process. Its unit quantity is velocity.

Swirl Velocity    (in the Velocity... category) is the tangential-direction component of the velocity in an axisymmetric swirling flow. See Section  30.2 for details. The unit quantity for Swirl Velocity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Swirl-Wall Shear Stress   (in the Wall Fluxes... category) is the swirl component of the force acting tangential to the surface due to friction. Its unit quantity is pressure.

Tangential Velocity    (in the Velocity... category) is the velocity component in the tangential direction. (See Section  30.2 for details.) The unit quantity for Tangential Velocity is velocity.

Temperature...    indicates the quantities associated with the thermodynamic temperature of a material.

Thermal Conductivity    (in the Properties... category) is a parameter ( $k$) that defines the conduction rate through a material via Fourier's law ( $q = -k \nabla T$). A large thermal conductivity is associated with a good heat conductor and a small thermal conductivity with a poor heat conductor (good insulator). Its unit quantity is thermal-conductivity.

Thermal Diff Coef of species-n    (in the Species... category) is the thermal diffusion coefficient for the $n$th species ( $D_{T,i}$ in Equations  8.9-1, 8.9-3, and 8.9-7). Its unit quantity is viscosity.

Time Step    (in the Residuals... category) is the local time step of the cell, $\Delta t$, at the current iteration level. Its unit quantity is time.

Time Step Scale    (in the Species... category) is the factor by which the time step is reduced for the stiff chemistry solver (available in the density-based solver only). The time step is scaled down based on an eigenvalue and positivity analysis.

Total Energy    (in the Temperature... category) is the total energy per unit mass. Its unit quantity is specific-energy. For all species models, plots of Total Energy include the sensible, chemical and kinetic energies. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Total Enthalpy    (in the Temperature... category) is defined as $H + \frac{1}{2}v^2$ where $H$ is the Enthalpy, as defined in Equation  13.2-7, and $v$ is the velocity magnitude. Its unit quantity is specific-energy. For all species models, plots of Total Enthalpy consist of the sensible, chemical and kinetic energies. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Total Enthalpy Deviation   (in the Temperature... category) is the difference between Total Enthalpy and the reference enthalpy, $H + \frac{1}{2}v^2 - H_{\rm ref}$, where $H_{\rm ref}$ is the reference enthalpy defined in the Reference Values panel. However, for non-premixed and partially premixed models, Total Enthalpy Deviation is the difference between Total Enthalpy and total adiabatic enthalpy (total enthalpy where no heat loss or gain occurs). The unit quantity for Total Enthalpy Deviation is specific-energy. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Total Pressure    (in the Pressure... category) is the pressure at the thermodynamic state that would exist if the fluid were brought to zero velocity and zero potential. For compressible flows, the total pressure is computed using isentropic relationships. For constant $c_p$, this reduces to:


 p_0 = p {\left[ 1 + \frac{\gamma - 1}{ 2 } {\rm M}^2 \right]}^{\gamma/(\gamma - 1)} (30.4-36)

where $p$ is the static pressure, $\gamma$ is the ratio of specific heats, and M is the Mach number. For incompressible flows (constant density fluid), we use Bernoulli's equation, $p_0 = p + p_{\rm dyn}$, where $p_{\rm dyn}$ is the local dynamic pressure. Its unit quantity is pressure.

Total Surface Heat Flux    (in the Wall Fluxes... category) is the rate of total heat transfer through the control surface. It is calculated by the solver according to the boundary conditions being applied at that surface. By definition, heat flux out of the domain is negative, and heat flux into the domain is positive. The unit quantity for Total Surface Heat Flux is heat-flux.

Total Temperature    (in the Temperature... category) is the temperature at the thermodynamic state that would exist if the fluid were brought to zero velocity. For compressible flows, the total temperature is computed from the total enthalpy using the current $c_p$ method (specified in the Materials panel). For incompressible flows, the total temperature is equal to the static temperature. The unit quantity for Total Temperature is temperature.

Transmitted Radiation Flux (Band-n)    (in the Wall Fluxes... category) is the amount of radiative heat flux transmitted by a semi-transparent wall for a particular band of radiation. Its unit quantity is heat-flux.

Transmitted Visible Solar Flux, Transmitted IR Solar Flux    (in the Wall Fluxes... category) is the amount of solar heat flux transmitted by a semi-transparent wall for a visible or infrared radiation.

Turbulence...   includes quantities related to turbulence. See Chapter  12 for information about the turbulence models available in FLUENT.

Turbulence Intensity    (in the Turbulence... category) is the ratio of the magnitude of the RMS turbulent fluctuations to the reference velocity:


 I = \frac{\sqrt{\frac{2}{3} k}} {v_{\rm ref}} (30.4-37)

where $k$ is the turbulence kinetic energy and $v_{\rm ref}$ is the reference velocity specified in the Reference Values panel. The reference value specified should be the mean velocity magnitude for the flow. Note that turbulence intensity can be defined in different ways, so you may want to use a custom field function for its definition. See Section  30.5 for more information.

Turbulent Dissipation Rate (Epsilon)    (in the Turbulence... category) is the turbulent dissipation rate. Its unit quantity is turbulent-energy-diss-rate. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Turbulent Flame Speed   (in the Premixed Combustion... category) is the turbulent flame speed computed by FLUENT using Equation  16.2-4. Its unit quantity is velocity.

Turbulent Kinetic Energy (k)    (in the Turbulence... category) is the turbulence kinetic energy per unit mass defined as


 k = \frac{1}{2}\overline{u'_i u'_i} (30.4-38)

Its unit quantity is turbulent-kinetic-energy. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Turbulent Rate of Reaction-n    (in the Reactions... category) is the rate of progress of the $n$th reaction computed by Equation  14.1-26 or 14.1-27. For the "eddy-dissipation'' model, the value is the same as the Rate of Reaction-n. For the "finite-rate'' model, the value is zero.

Turbulent Reynolds Number (Re_y)    (in the Turbulence... category) is a nondimensional quantity defined as


 \frac{\rho d \sqrt{k}}{\mu_{\rm lam}} (30.4-39)

where $k$ is turbulence kinetic energy, $d$ is the distance to the nearest wall, and $\mu_{\rm lam}$ is the laminar viscosity.

Turbulent Viscosity    (in the Turbulence... category) is the turbulent viscosity of the fluid computed using the turbulence model. Its unit quantity is viscosity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Turbulent Viscosity Ratio    (in the Turbulence... category) is the ratio of turbulent viscosity to the laminar viscosity.

udm-n   (in the User Defined Memory... category) is the value of the quantity in the $n$th user-defined memory location.

Unburnt Fuel Mass Fraction   (in the Premixed Combustion... category) is the mass fraction of unburnt fuel. This function is available only for non-adiabatic models.

Unsteady Statistics...   includes mean and root mean square (RMS) values of solution variables derived from transient flow calculations.

User Defined Memory...   includes quantities that have been allocated to a user-defined memory location. See the separate UDF Manual for details about user-defined memory.

User-Defined Scalars...   includes quantities related to user-defined scalars. See the separate UDF Manual for information about using user-defined scalars.

UU Reynolds Stress    (in the Turbulence... category) is the $\overline{u^{'2}}$ stress.

UV Reynolds Stress   (in the Turbulence... category) is the $\overline{u^{'} v^{'}}$ stress.

UW Reynolds Stress   (in the Turbulence... category) is the $\overline{u^{'} w^{'}}$ stress.

Variance of Species   (in the NOx... category) is the variance of the mass fraction of a selected species in the flow field. It is calculated from Equation  20.1-110.

Variance of Species 1, Variance of Species 2   (in the NOx... category) are the variances of the mass fractions of the selected species in the flow field. They are each calculated from Equation  20.1-110.

Variance of Temperature   (in the NOx... category) is the variance of the normalized temperature in the flow field. It is calculated from Equation  20.1-110.

Velocity...    includes the quantities associated with the rate of change in position with time. The instantaneous velocity of a particle is defined as the first derivative of the position vector with respect to time, $d \vec{r}/dt$, termed the velocity vector, $\vec{v}$.

Velocity Angle    (in the Velocity... category) is defined as follows:

For a 2D model,


 \tan^{-1} \left(\frac{\mbox{y-velocity-component}} {\mbox{x-velocity-component}}\right) (30.4-40)

For a 2D or axisymmetric model,


 \tan^{-1} \left(\frac{\mbox{radial-velocity-component}} {\mbox{axial-velocity-component}}\right) (30.4-41)

For a 3D model,


 \tan^{-1} \left(\frac{\mbox{tangential-velocity-component}} {\mbox{axial-velocity-component}}\right) (30.4-42)

Its unit quantity is angle.

Velocity Magnitude    (in the Velocity... category) is the speed of the fluid. Its unit quantity is velocity. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Volume fraction    (in the Phases... category) is the volume fraction of the selected phase in the Phase drop-down list.

Vorticity Magnitude    (in the Velocity... category) is the magnitude of the vorticity vector. Vorticity is a measure of the rotation of a fluid element as it moves in the flow field, and is defined as the curl of the velocity vector:
 \xi = \nabla \times \vec{V} (30.4-43)

VV Reynolds Stress   (in the Turbulence... category) is the $\overline{v^{'2}}$ stress.

VW Reynolds Stress   (in the Turbulence... category) is the $\overline{v^{'} w^{'}}$ stress.

Wall Fluxes...    includes quantities related to forces and heat transfer at wall surfaces.

Wall Func. Heat Tran. Coef.    is defined by the equation


 h_{\rm eff} = \frac{\rho C_p C_{\mu}^{1/4} k_{p}^{1/2}}{T^*} (30.4-44)

where $C_p$ is the specific heat, $k_p$ is the turbulence kinetic energy at point $P$, and $T^*$ is defined in Equation  12.10-5.

Wall Shear Stress    (in the Wall Fluxes... category) is the force acting tangential to the surface due to friction. Its unit quantity is pressure. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Wall Temperature (Inner Surface)    (in the Temperature... category) is the temperature on the inner surface of a wall (corresponding to the side of the wall surface away from the adjacent fluid or solid cell zone). Note that wall thermal boundary conditions are applied on this surface. See also Figure  7.13.2. The unit quantity for Wall Temperature (Inner Surface) is temperature.

Wall Temperature (Outer Surface)   (in the Temperature... category) is the temperature on the outer surface of a wall (corresponding to the side of the wall surface toward the adjacent fluid or solid cell zone). Note that wall thermal boundary conditions are applied on the Inner Surface. See also Figure  7.13.2. The unit quantity for Wall Temperature (Outer Surface) is temperature.

Wall Yplus    (in the Turbulence... category) is a nondimensional parameter defined by the equation


 y^+ = \frac{\rho u_\tau y_P } {\mu} (30.4-45)

where $u_\tau = \sqrt{\tau_w / \rho_w}$ is the friction velocity, $y_P$ is the distance from point $P$ to the wall, $\rho$ is the fluid density, and $\mu$ is the fluid viscosity at point $P$. See Section  12.10 for details. For multiphase models, this value corresponds to the selected phase in the Phase drop-down list.

Wall Ystar    (in the Turbulence... category) is a nondimensional parameter defined by the equation


 y^* = \frac{\rho C_{\mu}^{1/4} k_P^{1/2} y_P}{\mu} (30.4-46)

where $k_P$ is the turbulence kinetic energy at point $P$, $y_P$ is the distance from point $P$ to the wall, $\rho$ is the fluid density, and $\mu$ is the fluid viscosity at point $P$. See Section  12.10 for details.

WW Reynolds Stress   (in the Turbulence... category) is the $\overline{w^{'2}}$ stress.

X-Coordinate, Y-Coordinate, Z-Coordinate    (in the Grid... category) are the Cartesian coordinates in the $x$-axis, $y$-axis, and $z$-axis directions respectively. The unit quantity for these variables is length.

X Face Area, Y Face Area, Z Face Area   (in the Grid... category) are the components of the boundary face area vectors stored in the adjacent boundary cells. The face area calculations are done as in X Surface Area, Y Surface Area, Z Surface Area (see below), except the area values in the cells with more than one boundary face are not summed to obtain the cell values. Instead, the area value relative to the last visited face of each cell is taken as the cell value.

The face area calculation can be restricted to a set of zones. Your zone selection can be made from the Boundary Zones list contained in the Boundary Adaption panel. The face areas will be calculated only on the zones selected, and in order to make your selection active, you need to click the Mark button in the Boundary Adaption panel. Note that if the Boundary Zones list is empty, all boundary zones will be used.

X Pull Velocity, Y Pull Velocity, Z Pull Velocity   (in the Solidification/Melting... category) are the $x$, $y$, and $z$ components of the pull velocity for the solid material in a continuous casting process. The unit quantity for each is velocity.

X Surface Area, Y Surface Area, Z Surface Area   (in the Grid... category) are the components of the boundary face area vectors stored in the adjacent boundary cells. The surface area is accumulated from all boundary faces adjacent to the boundary cell. For each boundary face zone, the component of the face area in the relevant direction ( $x$, $y$, or $z$) is added to the cell value of the adjacent cell. For those cells having more than one boundary face, the cell value is the sum (accumulation) of all the boundary face area values. In most circumstances, the X Surface Area, Y Surface Area, Z Surface Area are used for flux and surface integration. In the few instances where area accumulation must be avoided, you can mark the zones of interest and use X Face Area, Y Face Area, Z Face Area (see above) for flux and integral calculations.

X Velocity, Y Velocity, Z Velocity    (in the Velocity... category) are the components of the velocity vector in the $x$-axis, $y$-axis, and $z$-axis directions, respectively. The unit quantity for these variables is velocity. For multiphase models, these values correspond to the selected phase in the Phase drop-down list.

X-Vorticity, Y-Vorticity, Z-Vorticity    (in the Velocity... category) are the $x$, $y$, and $z$ components of the vorticity vector.

X-Wall Shear Stress, Y-Wall Shear Stress, Z-Wall Shear Stress    (in the Wall Fluxes... category) are the $x$, $y$, and $z$ components of the force acting tangential to the surface due to friction. The unit quantity for these variables is pressure. For multiphase models, these values correspond to the selected phase in the Phase drop-down list.


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