Chapter 27. Field Function De nitions · Chapter 27. Field Function De nitions You must select...

Chapter 27. Field Function Definitions

You must select flow variables for a number of tasks in FLUENT. Thevalues are computed and placed in temporary memory that is allocatedfor storing the results for each cell. For example, the Compute com-mand associated with a panel that contains the field variable drop-downlist calculates the values of the selected function and places them intotemporary storage.

Sections 27.1 and 27.2 provide some general information related to thefield variables. In Section 27.3, the variables are listed by category inTables 27.3.1–27.3.14. These tables will also indicate when each variablewill be available. Section 27.4 contains an alphabetical listing of thevariables along with their definitions. All variables appear as they wouldin the variable selection drop-down lists that are contained in many ofthe FLUENT panels. Section 27.5 explains how you can calculate yourown field function.

• Section 27.1: Node and Cell Values

• Section 27.2: Velocity Reporting Options

• Section 27.3: Field Variables Listed by Category

• Section 27.4: Alphabetical Listing of Field Variables and TheirDefinitions

• Section 27.5: Custom Field Functions

27.1 Node and Cell Values

Two types of field values are available for postprocessing: node valuesand cell values. For the following discussion, “surface” refers to a col-lection of facets, lines or points that are created and manipulated in the

c© Fluent Inc. November 28, 2001 27-1

Field Function Definitions

Surface menu. In most cases, these surfaces are created by computingintersections of constant isovalues with the domain cells or with existingsurfaces.

27.1.1 Cell Values

FLUENT stores most variables in cells. For postprocessing, the entireregion contained within the cell has this value. A surface cell value isthe value of the cell that has been intersected by a surface facet or line, orthat contains a surface point. Since surface facets and lines are createdfrom the intersection of isovalues and the existing grid cells, this is aunique definition. On a boundary, the cell value is the value in the celladjacent to the boundary.

27.1.2 Node Values

Node values are explicitly defined or obtained by averaging the cell data.Various boundary conditions impose values of field variables at the do-main boundaries, so grid node values on these boundary zones are definedexplicitly. In addition, for several variables (e.g., node coordinates) ex-plicit node values are available at all nodes. For most variables, however,the grid node values are computed by averaging the data of all the cellsthat share the node.

Computation of node values is performed in two steps:

1. Values at all nodes are initialized to the average of the surroundingcell values.

2. At boundaries, these node values are overwritten with the bound-ary values (if available). (Variables for which explicit node valuesare available at boundaries are indicated by bnv in Tables 27.3.1–27.3.14.)

For example, in Figure 27.1.1, the value at node n1 will be computedfrom the average of the values in the surrounding cells (c1–c6), and thevalue at node n2 will be the specified boundary value (not the average

27-2 c© Fluent Inc. November 28, 2001

27.2 Velocity Reporting Options

c3c4

c5

c6c1

c2

n1

n2c7

boundary

Figure 27.1.1: Computing Node Values

of the values in cells c1, c6, and c7), if there are explicit boundary valuesavailable for the variable in question.

Note that explicit boundary node values are not available for custom!field functions.

The values of the nodes on surfaces are interpolated from the grid nodedata by linear interpolation. For zone surfaces the nodes on the surfaceand the zone correspond, so the values are identical. For isofacets andisolines, the values are interpolated from the grid nodes on the faceintersected by the isovalue. For isopoints, the value is interpolated fromall the grid nodes of the cell containing the point.


The following methods are available for reporting velocities:

• Cartesian velocities: These velocities are based on the Cartesiancoordinate system used by the geometry. To report Cartesian ve-locities, select X Velocity, Y Velocity, or Z Velocity. This is the mostcommon type of velocity reported.

• Cylindrical velocities: These velocities are the axial, radial, andtangential components based on the following coordinate systems:



– For axisymmetric problems, in which the rotation axis mustbe the x axis, the x direction is the axial direction and the ydirection is the radial direction. (If you model axisymmetricswirl, the swirl direction is the tangential direction.)

– For 2D problems involving a single cell zone, the z directionis the axial direction, and its origin is specified in the Fluidpanel.

– For 3D problems involving a single cell zone, the coordinatesystem is defined by the rotation axis and origin specified inthe Fluid panel.

– For problems involving multiple zones (e.g., multiple referenceframes or sliding meshes), the coordinate system is defined bythe rotation axis specified in the Fluid (or Solid) panel for the“reference zone”. The reference zone is chosen in the ReferenceValues panel, as described in Section 26.8. Recall that for 2Dproblems, you will specify only the axis origin; the z directionis always the axial direction.

For all of the above definitions of the cylindrical coordinate system,positive radial velocities point radially out from the rotation axis,positive axial velocities are in the direction of the rotation axisvector, and positive tangential velocities are based on the right-hand rule using the positive rotation axis.

To report cylindrical velocities, select Axial Velocity, Radial Veloc-ity, etc. Figure 27.2.1 illustrates the cylindrical velocities availablefor different types of domains: For 3D problems, you can reportaxial, radial, and tangential velocities. For 2D problems, radial andtangential velocities are available. For axisymmetric problems, youcan report axial and radial velocities, and if you are modeling ax-isymmetric swirl you can also report the swirl velocity (which isequivalent to the tangential velocity).

• Relative velocities: These velocities are based on the coordinatesystem and motion of a moving reference frame. They are usefulwhen you are modeling your flow using a rotating reference frame,a mixing plane, multiple reference frames, or sliding meshes. (SeeChapter 9 for information about modeling flow in moving zones.)



axial

radial

tangential(swirl)

axial

radialtangential

radial

tangential

rotation axis

rotation axis origin

rotation axis

Figure 27.2.1: Cylindrical Velocity Components in 3D, 2D, and Axisym-metric Domains

To report relative velocities, select Relative X Velocity, Relative YVelocity, Relative Radial Velocity, etc. (Note that you can reportrelative velocities for both Cartesian and cylindrical components.)

If you are using a single rotating reference frame, the relative ve-locity values will be reported with respect to the moving frame. Ifyou are using multiple reference frames, mixing planes, or slidingmeshes, you will need to specify the frame to which you want thevelocities to be relative by choosing the appropriate cell zone asthe Reference Zone in the Reference Values panel (see Section 26.8).The axis of rotation for each cell zone is defined in the associatedFluid panel or Solid panel. (See Section 6.17.1 or 6.18.1 for details.)

Note that if your problem does not involve any moving zones, rel-ative and absolute velocities will be equivalent.

Note that relative velocities can also be used to compute stagnationquantities (total pressure and total temperature), and that the cylindri-cal coordinate systems described in the second item above are used fordefining the Axial Coordinate and Radial Coordinate as well.



27.3 Field Variables Listed by Category

In Tables 27.3.1–27.3.14, the following restrictions apply to marked vari-ables:

2d available only for 2D flows2da available only for 2D axisymmetric flows (with or without swirl)

2dasw available only for 2D axisymmetric swirl flows3d available only for 3D flowsbnv node values available at boundariescpl available only in the coupled solverscv available only for cell values (Node Values option turned off)dil not available with full multicomponent diffusiondo available only when the discrete ordinates radiation model is used

dpm available only for coupled discrete phase calculationsdtrm available only when the discrete transfer radiation model is used

e available only for energy calculationsedc available only with the EDC model for turbulence-chemistry

interactionemm available only when the Eulerian multiphase model is usedewt available only with the enhanced wall treatmentgran available only if a granular phase is presenth2o available only when the mixture contains waterid available only when the ideal gas law is enabled for densityke available only when one of the k-ε turbulence models is usedkw available only when one of the k-ω turbulence models is usedles available only when the LES turbulence model is used

melt available only when the melting and solidification model is usedmix available only when the multiphase mixture model is usedmp available only for multiphase modelsnox available only for NOx calculationsnp not available in parallel solversnv uses explicit node value functionp available only in parallel solversp1 available only when the P-1 radiation model is used



pdf available only for non-premixed combustion calculationspmx available only for premixed combustion calculationsppmx available only for partially premixed combustion calculations

r available only when the Rosseland radiation model is usedrad available only for radiation heat transfer calculationsrc available only for finite-rate reactions

rsm available only when the Reynolds stress turbulence model is useds2s available only when the surface-to-surface radiation model is usedsa available only when the Spalart-Allmaras turbulence model is usedseg available only in the segregated solversp available only for species calculationssr available only for surface reactions

soot available only for soot calculationsstat available only with data sampling for unsteady statisticsstcm available only for stiff chemistry calculations

t available only for turbulent flowsturbo available only when a turbomachinery topology has been definedudm available only when a user-defined memory location is useduds available only when a user-defined scalar is usedv available only for viscous flows

Table 27.3.1: Pressure and Density Categories

Category VariablePressure... Static Pressure (bnv, nv)

Pressure CoefficientDynamic PressureAbsolute Pressure (bnv, nv)Total Pressure (bnv, nv)Relative Total Pressure

Density... DensityDensity of phase-n (mp)Density All



Table 27.3.2: Velocity Category

Category VariableVelocity... Velocity Magnitude (bnv, nv)

X Velocity (bnv, nv)Y Velocity (bnv, nv)Z Velocity (3d, bnv, nv)Swirl Velocity (2dasw, bnv, nv)Axial Velocity (2da or 3d)Radial VelocityStream Function (2d, nv)Tangential VelocityMach Number (id)Relative Velocity Magnitude (bnv, nv)Relative X Velocity (bnv, nv)Relative Y Velocity (bnv, nv)Relative Z Velocity (3d, bnv, nv)Relative Axial Velocity (2da)Relative Radial Velocity (2da)Relative Swirl Velocity (2dasw, bnv, nv)Relative Tangential Velocity (2d or 3d)Relative Mach Number (id)Grid X-Velocity (nv)Grid Y-Velocity (nv)Grid Z-Velocity (3d, nv)Velocity AngleRelative Velocity AngleVorticity Magnitude (v)Helicity (v, 3d)X-Vorticity (v, 3d)Y-Vorticity (v, 3d)Z-Vorticity (v, 3d)Cell Reynolds Number (v)Preconditioning Reference Velocity (cpl)



Table 27.3.3: Velocity Category (Multiphase-Specific Variables)

Category VariableVelocity... phase-n Velocity Magnitude (mp)

phase-n X Velocity (mp)phase-n Y Velocity (mp)phase-n Z Velocity (3d, mp)phase-n Axial Velocity (2da or 3d; mp)phase-n Radial Velocity (mp)phase-n Swirl Velocity (2dasw, mp, bnv, nv)phase-n Stream Function (2d, mp, nv)



Table 27.3.4: Temperature, Radiation, and Solidification/Melting Cate-gories

Category VariableTemperature... Static Temperature (e, nv)

Total Temperature (e, bnv, nv)Enthalpy (e, nv)Enthalpy of phase-n (e, nv, mp)Total Enthalpy of phase-n (e, nv, mp)Total Enthalpy Deviation of phase-n (e, nv, mp)Total Energy of phase-n (e, nv, mp)Relative Total Temperature (e)Rothalpy (e, nv)Fine Scale Temperature (edc, nv)Wall Temperature (Outer Surface) (e, v, cv)Wall Temperature (Inner Surface) (e, v, cv)Total Enthalpy (e)Total Enthalpy Deviation (e)Entropy (e)Total Energy (e)Internal Energy (e)

Radiation... Absorption Coefficient (r, p1, do, or dtrm)Scattering Coefficient (r, p1, or do)Refractive Index (do)Radiation Temperature (p1 or do)Incident Radiation (p1 or do)Incident Radiation (Band n) (do (non-gray))Surface Cluster ID (s2s)

Solidification/ Liquid Fraction (melt)Melting... Contact Resistivity (melt)

X Pull Velocity (melt (if calculated))Y Pull Velocity (melt (if calculated))Z Pull Velocity (melt (if calculated), 3d)Axial Pull Velocity (melt (if calculated), 2da)Radial Pull Velocity (melt (if calculated), 2da)Swirl Pull Velocity (melt (if calculated), 2dasw)



Table 27.3.5: Turbulence Category

Category VariableTurbulence... Turbulent Kinetic Energy (k) (ke, kw, or rsm; bnv, nv)

phase-n Turbulent Kinetic Energy (ke, emm)UU Reynolds Stress (rsm)VV Reynolds Stress (rsm)WW Reynolds Stress (rsm)UV Reynolds Stress (rsm)UW Reynolds Stress (rsm, 3d)VW Reynolds Stress (rsm, 3d)Turbulence Intensity (ke, kw, or rsm)Turbulent Dissipation Rate (Epsilon) (ke or rsm; bnv, nv)phase-n Turbulent Dissipation Rate (ke, emm)Specific Dissipation Rate (Omega) (kw)Production of k (ke, kw, or rsm)phase-n Production of k (ke, emm)Modified Turbulent Viscosity (sa)Turbulent Viscosity (t)phase-n Turbulent Viscosity (t, emm)Effective Viscosity (t)Turbulent Viscosity Ratio (ke, kw, rsm, or sa)Subgrid Turbulent Kinetic Energy (les)Subgrid Turbulent Viscosity (les)Subgrid Effective Viscosity (les)Subgrid Turbulent Viscosity Ratio (les)Effective Thermal Conductivity (t, e)Effective Prandtl Number (t, e)Wall Ystar (ke, kw, or rsm; cv)Wall Yplus (t, cv)phase-n Wall Yplus (t, cv, emm)Turbulent Reynolds Number (Re y) (ke or rsm; ewt)



Table 27.3.6: Species, Reactions, Pdf, and Premixed Combustion Categories

Category VariableSpecies... Mass fraction of species-n (sp, pdf, or ppmx; nv)

Mole fraction of species-n (sp, pdf, or ppmx)Concentration of species-n (sp, pdf, or ppmx)Lam Diff Coef of species-n (sp, dil)Eff Diff Coef of species-n (t, sp, dil)Thermal Diff Coef of species-n (sp)Enthalpy of species-n (sp)species-n Source Term (rc, cpl)Surface Deposition Rate of species-n (sr)Relative Humidity (sp, pdf, or ppmx; h2o)Time Step Scale (sp, stcm)Fine Scale Mass fraction of species-n (edc)Fine Scale Transfer Rate (edc)1-Fine Scale Volume Fraction (edc)

Reactions... Rate of Reaction-n (rc)Arrhenius Rate of Reaction-n (rc)Turbulent Rate of Reaction-n (rc, t)

Pdf... Mean Mixture Fraction (pdf or ppmx; nv)Secondary Mean Mixture Fraction (pdf or ppmx; nv)Mixture Fraction Variance (pdf or ppmx; nv)Secondary Mixture Fraction Variance (pdf or ppmx; nv)Fvar Prod (pdf or ppmx)Fvar2 Prod (pdf or ppmx)Scalar Dissipation (pdf or ppmx)

Premixed Progress Variable (pmx or ppmx; nv)Combustion... Damkohler Number (pmx or ppmx)

Stretch Factor (pmx or ppmx)Turbulent Flame Speed (pmx or ppmx)Static Temperature (pmx or ppmx)Product Formation Rate (pmx or ppmx)Laminar Flame Speed (pmx or ppmx)Critical Strain Rate (pmx or ppmx)Adiabatic Flame Temperature (pmx or ppmx)Unburnt Fuel Mass Fraction (pmx or ppmx)



Table 27.3.7: NOx, Soot, and Unsteady Statistics Categories

Category VariableNOx... Mass fraction of NO (nox)

Mass fraction of HCN (nox)Mass fraction of NH3 (nox)Mole fraction of NO (nox)Mole fraction of HCN (nox)Mole fraction of NH3 (nox)Concentration of NO (nox)Concentration of HCN (nox)Concentration of NH3 (nox)Variance of Temperature (nox)Variance of Species (nox)Variance of Species 1 (nox)Variance of Species 2 (nox)

Soot... Mass fraction of soot (soot)Mass fraction of nuclei (soot)

Unsteady Statistics... Mean quantity-n (stat)RMS quantity-n (stat)



Table 27.3.8: Phases, Discrete Phase Model, Granular Pressure, and Gran-ular Temperature Categories

Category VariablePhases... Volume fraction of phase-n (mp)Discrete Phase Model... DPM Mass Source (dpm)

DPM Erosion (dpm, cv)DPM Accretion (dpm, cv)DPM X Momentum Source (dpm)DPM Y Momentum Source (dpm)DPM Z Momentum Source (dpm, 3d)DPM Swirl Momentum Source (dpm, 2dasw)DPM Sensible Enthalpy Source (dpm, e)DPM Enthalpy Source (dpm, e)DPM Absorption Coefficient (dpm, rad)DPM Emission (dpm, rad)DPM Scattering (dpm, rad)DPM Burnout (dpm, sp, e)DPM Evaporation/Devolatilization (dpm, sp, e)DPM Concentration (dpm)DPM species-n Source (dpm, sp, e)

Granular Pressure... phase-n Granular Pressure (emm, gran)Granular Temperature... phase-n Granular Temperature (emm, gran)



Table 27.3.9: Properties, Wall Fluxes, User Defined Scalars, and User De-fined Memory Categories

Category VariableProperties... Molecular Viscosity (v)

Molecular Viscosity of phase-n (v, mp)Diameter of phase-n (mix or emm)Thermal Conductivity (e, v)Specific Heat (Cp) (e)Specific Heat Ratio (gamma) (id)Gas Constant (R) (id)Molecular Prandtl Number (e, v)Mean Molecular Weight (seg, pdf)Sound Speed (id)

Wall Fluxes... Wall Shear Stress (v, cv)phase-n Wall Shear Stress (v, cv, emm)X-Wall Shear Stress (v, cv)Y-Wall Shear Stress (v, cv)Z-Wall Shear Stress (v, 3d, cv)phase-n X-Wall Shear Stress (v, cv, emm)phase-n Y-Wall Shear Stress (v, cv, emm)phase-n Z-Wall Shear Stress (v, 3d, cv, emm)Axial-Wall Shear Stress (2da, cv)Radial-Wall Shear Stress (2da, cv)Swirl-Wall Shear Stress (2dasw, cv)Skin Friction Coefficient (v, cv)phase-n Skin Friction Coefficient (v, cv, emm)Total Surface Heat Flux (e, v, cv)Radiation Heat Flux (rad, cv)Surface Incident Radiation (do, cv)Surface Heat Transfer Coef. (e, v, cv)Surface Nusselt Number (e, v, cv)Surface Stanton Number (e, v, cv)

User Defined Scalars... Scalar-n (uds, nv)Diffusion Coef. of Scalar-n (uds)

User Defined Memory... udm-n (udm)



Table 27.3.10: Cell Info, Grid, and Adaption Categories

Category VariableCell Info... Cell Partition (np)

Active Cell Partition (p)Stored Cell Partition (p)Cell Id (p)Cell Element TypeCell Zone TypeCell Zone IndexPartition Neighbors

Grid... X-Coordinate (nv)Y-Coordinate (nv)Z-Coordinate (3d, nv)Axial Coordinate (nv)Radial Coordinate (nv)X Surface AreaY Surface AreaZ Surface Area (3d)X Face AreaY Face AreaZ Face Area (3d)Cell Equiangle SkewCell Equivolume SkewCell Volume2D Cell Volume (2da)Cell Wall DistanceFace HandednessFace Squish IndexCell Squish Index



Table 27.3.11: Grid Category (Turbomachinery-Specific Variables) andAdaption Category

Category VariableGrid... Meridional Coordinate (nv, turbo)

Abs Meridional Coordinate (nv, turbo)Spanwise Coordinate (nv, turbo)Abs (H-C) Spanwise Coordinate (nv, turbo)Abs (C-H) Spanwise Coordinate (nv, turbo)Pitchwise Coordinate (nv, turbo)Abs Pitchwise Coordinate (nv, turbo)

Adaption... Adaption FunctionExisting ValueBoundary Cell DistanceBoundary Normal DistanceBoundary Volume Distance (np)Cell Volume ChangeCell Equiangle SkewCell Equivolume SkewCell Surface AreaCell WarpageCell ChildrenCell Refine Level



Table 27.3.12: Residuals Category

Category VariableResiduals... Mass Imbalance

Pressure Residual (cpl)X-Velocity Residual (cpl; 2d or 3d)Y-Velocity Residual (cpl; 2d or 3d)Z-Velocity Residual (cpl, 3d)Axial-Velocity Residual (cpl, 2da)Radial-Velocity Residual (cpl, 2da)Swirl-Velocity Residual (cpl, 2dasw)Temperature Residual (cpl, e)Species-n Residual (cpl, sp)



Table 27.3.13: Derivatives Category

Category VariableDerivatives... Strain Rate (v)

dX-Velocity/dxdY-Velocity/dxdZ-Velocity/dx (3d)dAxial-Velocity/dx (2da)dRadial-Velocity/dx (2da)dSwirl-Velocity/dx (2dasw)d species-n/dx (cpl, sp)dX-Velocity/dydY-Velocity/dydZ-Velocity/dy (3d)dAxial-Velocity/dy (2da)dRadial-Velocity/dy (2da)dSwirl-Velocity/dy (2dasw)d species-n/dy (cpl, sp)dX-Velocity/dz (3d)dY-Velocity/dz (3d)dZ-Velocity/dz (3d)d species-n/dz (cpl, sp, 3d)dOmega/dx (2dasw)dOmega/dy (2dasw)dp-dX (seg)dp-dY (seg)dp-dZ (seg, 3d)



Table 27.3.14: Derivatives Category (Multiphase-Specific Variables)

Category VariableDerivatives... Strain Rate of phase-n (v, emm)

phase-n dX-Velocity/dX (v, emm)phase-n dY-Velocity/dX (v, emm)phase-n dZ-Velocity/dX (v, emm, 3d)phase-n dAxial-Velocity/dX (v, emm, 2da)phase-n dRadial-Velocity/dX (v, emm, 2da)phase-n dX-Velocity/dY (v, emm)phase-n dY-Velocity/dY (v, emm)phase-n dZ-Velocity/dY (v, emm, 3d)phase-n dAxial-Velocity/dY (v, emm, 2da)phase-n dRadial-Velocity/dY (v, emm, 2da)phase-n dX-Velocity/dZ (v, emm, 3d)phase-n dY-Velocity/dZ (v, emm, 3d)phase-n dZ-Velocity/dZ (v, emm, 3d)phase-n Granular Pressure G 0 cmpn (emm, gran)phase-n Granular Pressure G 1 cmpn (emm, gran)phase-n Granular Pressure G 2 cmpn (emm, gran, 3d)


27.4 Alphabetical Listing of Field Variables and Their Definitions

27.4 Alphabetical Listing of Field Variables and TheirDefinitions

Below, the variables listed in Tables 27.3.1–27.3.14 are defined. Forsome variables (such as residuals) a general definition is given under thecategory name, and variables in the category are not listed individually.When appropriate, the unit quantity is included, as it appears in theQuantities list in the Set Units panel.

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

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

Abs Meridional Coordinate (in the Grid... category) is the dimensionalcoordinate that follows the flow path from inlet to outlet. Its unitquantity is length.

Abs Pitchwise Coordinate (in the Grid... category) is the dimensional co-ordinate in the circumferential (pitchwise) direction. Its unit quan-tity is angle.

Absolute Pressure (in the Pressure... category) is equal to the operatingpressure plus the gauge pressure. See Section 7.12 for details. Itsunit quantity is pressure.

Absorption Coefficient (in the Radiation... category) is the property of amedium that describes the amount of absorption of thermal radia-tion per unit path length within the medium. It can be interpretedas the inverse of the mean free path that a photon will travel beforebeing absorbed (if the absorption coefficient does not vary alongthe path). The unit quantity for Absorption Coefficient is length-inverse.

Active Cell Partition (in the Cell Info... category) is an integer identifierdesignating the partition to which a particular cell belongs. In



problems in which the grid is divided into multiple partitions tobe solved on multiple processors using the parallel version of FLU-ENT, the partition ID can be used to determine the extent of thevarious groups of cells. The active cell partition is used for the cur-rent calculation, while the stored cell partition (the last partitionperformed) is used when you save a case file. See Section 28.4.3 formore information.

Adaption... includes field variables that are commonly used for adaptingthe grid. For information about solution adaption, see Chapter 23.

Adaption Function (in the Adaption... category) is the undivided Lapla-cian of the values in temporary cell storage. For example, to dis-play contours of the Laplacian of pressure, you first select StaticPressure, click the Compute (or Display) button, select AdaptionFunction, and finally click the Display button.

Adiabatic Flame Temperature (in the Premixed Combustion... category) isthe adiabatic temperature of burnt products in a laminar premixedflame (Tb in Equation 15.2-21). Its unit quantity is temperature.

Arrhenius Rate of Reaction-n (in the Reactions... category) is given bythe following expression (see Equation 13.1-7 for definitions of thevariables shown here):

Rr = Γ

kf,r

Nr∏j=1

[Cj,r]η′

j,r − kb,r

Nr∏j=1

[Cj,r]η′′

j,r

The reported value is independent of any particular species, andhas units of kgmol/m3-s.

To find the rate of production/destruction for a given species i dueto reaction r, multiply the reported reaction rate for reaction r bythe term Mi(ν ′′i,r−ν ′i,r), where Mi is the molecular weight of speciesi, and ν ′′i,r and ν ′i,r are the stoichiometric coefficients of species i inreaction r.

Axial Coordinate (in the Grid... category) is the distance from the originin the axial direction. The axis origin and (in 3D) direction is



defined for each cell zone in the Fluid or Solid panel. The axialdirection for a 2D model is always the z direction, and the axialdirection 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 acontinuous casting process. Its unit quantity is velocity.

Axial Velocity (in the Velocity... category) is the component of velocity inthe axial direction. (See Section 27.2 for details.) Its unit quantityis velocity.

phase-n Axial Velocity (in the Velocity... category) is the component ofvelocity in the axial direction for the nth phase. (The name of thephase will replace phase-n). Its unit quantity is velocity.

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

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

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

Boundary Volume Distance (in the Adaption... category) is the cell vol-ume distribution based on the Boundary Volume, Growth Factor,and normal distance from the selected Boundary Zones defined inthe Boundary Adaption panel. See Section 23.3 for details.

Cell Children (in the Adaption... category) is a binary identifier based onwhether 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 elementtype identification number. Each cell can have one of the followingelement types:



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

Cell Equiangle Skew (in the Grid... and Adaption... categories) is a nondi-mensional parameter calculated using the normalized angle devia-tion method, and is defined as

max[qmax − qe180 − qe

,qe − qmin

qe

](27.4-1)

whereqmax = largest angle in the face or cellqmin = smallest angle in the face or cellqe = 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 of1 indicates a completely degenerate cell. Degenerate cells (slivers)are characterized by nodes that are nearly coplanar (collinear in2D). Cell Equiangle Skew applies to all elements.

Cell Equivolume Skew (in the Grid... and Adaption... categories) is anondimensional parameter calculated using the volume deviationmethod, and is defined as

optimal-cell-size − cell-sizeoptimal-cell-size

(27.4-2)

where optimal-cell-size is the size of an equilateral cell with thesame circumradius. A value of 0 indicates a best case equilateralcell and a value of 1 indicates a completely degenerate cell. De-generate cells (slivers) are characterized by nodes that are nearlycoplanar (collinear in 2D). Cell Equivolume Skew applies only totriangular and tetrahedral elements.



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

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

Cell Partition (in the Cell Info... category) is an integer identifier desig-nating the partition to which a particular cell belongs. In problemsin which the grid is divided into multiple partitions to be solvedon multiple processors using the parallel version of FLUENT, thepartition ID can be used to determine the extent of the variousgroups of cells.

Cell Refine Level (in the Adaption... category) is an integer that indicatesthe number of times a cell has been subdivided in the hanging nodeadaption process, compared with the original grid. For example, ifone quad cell is split into four quads, the Cell Refine Level for eachof the four new quads will be 1. If the resulting four quads aresplit again, the Cell Refine Level for each of the resulting 16 quadswill be 2.

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

Re ≡ ρud

µ(27.4-3)

where ρ is density, u is velocity magnitude, µ is the effective viscos-ity (laminar plus turbulent), and d is Cell Volume1/2 for 2D casesand Cell Volume1/3 in 3D or axisymmetric cases.

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

maxi

[1 −

~Ai · ~rc0/xfi

| ~Ai||~rc0/xfi|

](27.4-4)



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

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

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

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

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

Cell Wall Distance (in the Grid... category) is the distribution of the nor-mal distance of each cell centroid from the wall boundaries. Itsunit quantity is length.

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

warpage =

√|~rcentroid − ~rcircumcenter|

Rcircumcenter(27.4-5)

Cell Zone Index (in the Cell Info... category) is the integer cell zone iden-tification 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 typeID. 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.

Concentration of species-n (in the Species... category) is the mass perunit volume of a species. Its unit quantity is density.



Concentration of HCN, Concentration of NH3, Concentration of NO (in theNOx... category) are the mass per unit volume of HCN, NH3 andNO. The unit quantity for each is density. The Concentration ofHCN and the Concentration of NH3 will appear only if you aremodeling fuel NOx. See Section 17.1.5 for details.

Contact Resistivity (in the Solidification/Melting... category) is the addi-tional resistance at the wall due to contact resistance. It is equalto Rc(1 − β)/h, where Rc is the contact resistance, β is the liquidfraction, and h is the cell height of the wall-adjacent cell. The unitquantity for Contact Resistivity is thermal-resistivity.

Critical Strain Rate (in the Premixed Combustion... category) is a pa-rameter that takes into account the stretching and extinction ofpremixed flames (gcr in Equation 15.2-13). Its unit quantity istime-inverse.

Custom Field Functions... are scalar field functions defined by you. Youcan create a custom function using the Custom Field Function Cal-culator panel. All defined custom field functions will be listed inthe lower drop-down list. See Section 27.5 for details.

Damkohler Number (in the Premixed Combustion... category) is a nondi-mensional parameter that is defined as the ratio of turbulent tochemical time scales.

Density... includes variables related to density.

Density (in the Density... category) is the mass per unit volume of thefluid. Plots or reports of Density include only fluid cell zones. Theunit quantity for Density is density.

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

Density of phase-n (in the Density... category) is the mass per unit vol-ume of the nth phase. Its unit quantity is density.



Derivatives... are the viscous derivatives. For example, dX-Velocity/dxis the first derivative of the x component of velocity with respectto the x-coordinate direction. You can compute first derivativesof velocity, angular velocity, and pressure in the segregated solver,and first derivatives of velocity, angular velocity, temperature, andspecies in the coupled solvers.

Diameter of phase-n (in the Properties... category) is the diameter of par-ticles, droplets, or bubbles of secondary phase n. Its unit quantityis length.

Diffusion Coef. of Scalar-n (in the User Defined Scalars... category) is thediffusion coefficient for the nth user-defined scalar transport equa-tion. See the separate UDF manual for details about defining user-defined scalars.

Discrete Phase Model... includes quantities related to the discrete phasemodel. See Chapter 19 for details about this model.

DPM Absorption Coefficient (in the Discrete Phase Model... category) isthe absorption coefficient for discrete-phase calculations that in-volve radiation (a in Equation 11.3-1). Its unit quantity is length-inverse.

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

Raccretion =N∑

p=1

mp

Aface(27.4-6)

where mp is the mass flow rate of the particle stream, and Aface isthe area of the wall face where the particle strikes the boundary.This item will appear only if the optional erosion/accretion modelis enabled. See Section 19.7.6 for details. The unit quantity forDPM Accretion is mass-flux.

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



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

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

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

Rerosion =N∑

p=1

mpf(α)Aface

(27.4-7)

where mp is the mass flow rate of the particle stream, α is theimpact angle of the particle path with the wall face, f(α) is thefunction specified in the Wall panel, and Aface is the area of thewall face where the particle strikes the boundary. This item willappear only if the optional erosion/accretion model is enabled. SeeSection 19.7.6 for details. The unit quantity for DPM Erosion ismass-flux.

DPM Evaporation/Devolatilization (in the Discrete Phase Model... cate-gory) is the exchange of mass, due to droplet-particle evaporationor combusting-particle devolatilization, from the discrete phase tothe evaporating or devolatilizing species. If you are not using thenon-premixed combustion model, the mass source for each indi-vidual species (DPM species-n Source, below) is also available; fornon-premixed combustion, only this sum is available. The unitquantity for DPM Evaporation/Devolatilization is mass-flow.

DPM Mass Source (in the Discrete Phase Model... category) is the to-tal exchange of mass from the discrete phase to the continuousphase. The mass exchange is positive when the particles are a



source of mass in the continuous phase. If you are not using thenon-premixed combustion model, DPM Mass Source will be equalto the sum of all species mass sources (DPM species-n Source, be-low); if you are using the non-premixed combustion model, it willbe 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 scatter-ing coefficient for discrete-phase calculations that involve radiation(σs in Equation 11.3-1). 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 thecontinuous phase. The exchange is positive when the particles area source of heat in the continuous phase. Its unit quantity is power.

DPM species-n Source (in the Discrete Phase Model... category) is the ex-change of mass, due to droplet-particle evaporation or combusting-particle devolatilization, from the discrete phase to the evaporat-ing or devolatilizing species. (The name of the species will replacespecies-n in DPM species-n Source.) These species are specified inthe Set Injection Properties panel, as described in Section 19.9.5.The unit quantity is mass-flow. Note that this variable will not beavailable if you are using the non-premixed combustion model; useDPM Evaporation/Devolatilization instead.

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

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

Dynamic Pressure (in the Pressure... category) is defined as q ≡ 12ρv

2.Its unit quantity is pressure.



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

Di,m +µt

ρSct

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

Effective Prandtl Number (in the Turbulence... category) is the ratioµeffcp/keff , where µeff is the effective viscosity, cp is the specificheat, and keff is the effective thermal conductivity.

Effective Thermal Conductivity (in the Properties... category) is the sumof the laminar and turbulent thermal conductivities, k+ kt, of thefluid. A large thermal conductivity is associated with a good heatconductor and a small thermal conductivity with a poor heat con-ductor (good insulator). Its unit quantity is thermal-conductivity.

Effective Viscosity (in the Turbulence... category) is the sum of the lam-inar and turbulent viscosities of the fluid. Viscosity, µ, is definedby the ratio of shear stress to the rate of shear. Its unit quantityis viscosity.

Enthalpy (in the Temperature... category) is defined differently for com-pressible and incompressible flows, and depending on the solverand models in use.

For compressible flows,

H =∑j

YjHj (27.4-8)

and for incompressible flows,

H =∑j

YjHj +p

ρ(27.4-9)

where Yj and Hj are, respectively, the mass fraction and enthalpyof species j. (See Enthalpy of species-n, below). For the segregated



solver, the second term on the right-hand side of Equation 27.4-9is included only if the pressure work term is included in the en-ergy equation (see Section 11.2.1). For adiabatic non-premixedcombustion cases, Enthalpy reports the adiabatic value based onthe local mean mixture fraction. The unit quantity for Enthalpy isspecific-energy.

Enthalpy of phase-n (in the Temperature... category) is the enthalpy (de-fined above) of the nth phase. Its unit quantity is specific-energy.

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

Hj =∫ T

Tref,j

cp,j dT + h0j (Tref,j) (27.4-10)

where h0j(Tref ,j) is the formation enthalpy of species j at the ref-

erence temperature Tref,j), is reported only for non-adiabatic PDFcases, or if the coupled solver is selected. The quantity:

hj =∫ T

Tref

cp,j dT (27.4-11)

where Tref = 298.15K, is reported in all other cases. The unitquantity for Enthalpy of species-n is specific-energy.

Entropy (in the Temperature... category) is a thermodynamic propertydefined by the equation

∆S ≡∫rev

δQ

T(27.4-12)

where “rev” indicates an integration along a reversible path con-necting two states, Q is heat, and T is temperature. For compress-ible flows, entropy is computed using the equation

s = cv

[p/pref

(ρ/ρref)γ− 1

](27.4-13)



where cv is computed from R/(γ − 1), and the reference pressureand density are defined in the Reference Values panel. For incom-pressible flow, the entropy is computed using the equation

s = cp

(T

Tref− 1

)(27.4-14)

where cp is the specific heat at constant pressure and Tref is definedin the Reference Values panel. The unit quantity for entropy isspecific-heat.

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

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

Face Squish Index (in the Grid... category) is a measure of the qualityof a mesh, and is calculated from the dot products of each facearea vector, and the vector that connects the centroids of the twoadjacent cells as

1 −~Ai · ~rc0/c1

| ~Ai||~rc0/c1|(27.4-15)

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 theterm Y ∗

i in Equation 13.1-30.

Fine Scale Temperature (in the Temperature... category) is the tempera-ture of the fine scales, which is calculated from the enthalpy whenthe reaction proceeds over the time scale (τ∗ in Equation 13.1-29),governed by the Arrhenius rates of Equation 13.1-7. Its unit quan-tity is temperature.

Fine Scale Transfer Rate (in the Species... category) is the transfer rateof the fine scales, which is equal to the inverse of the time scale (τ∗

in Equation 13.1-29). Its unit quantity is time-inverse.



1-Fine Scale Volume Fraction (in the Species... category) is a functionof the fine scale volume fraction (ξ∗ in Equation 13.1-28). Thequantity is subtracted from unity to make it easier to interpret.

Fvar Prod (in the Pdf... category) is the production term in the mixturefraction variance equation solved in the non-premixed combustionmodel (i.e., the last two terms in Equation 14.1-5).

Fvar2 Prod (in the Pdf... category) is the production term in the sec-ondary mixture fraction variance equation solved in the non-premixedcombustion model. See Equation 14.1-5.

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

Granular Pressure... includes quantities for reporting the solids pressurefor each granular phase.

phase-n Granular Pressure (in the Granular Pressure... category) is thesolids pressure for granular phase n (ps in Equation 20.4-45). SeeSection 20.4.4 for details. Its unit quantity is pressure.

Granular Temperature... includes quantities for reporting the granular tem-perature for each granular phase.

phase-n Granular Temperature (in the Granular Temperature... category)is the granular temperature for granular phase n (Θs in Equa-tion 20.4-56). See Section 20.4.6 for details. Its unit quantity istemperature.

Grid... includes variables related to the grid.

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

Helicity (in the Velocity... category) is defined by the dot product ofvorticity and the velocity vector.

H = (∇× ~V ) · ~V (27.4-16)



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

Incident Radiation (in the Radiation... category) is the total radiationenergy, G, that arrives at a location per unit time and per unitarea:

G =∫Ω=4π

IdΩ (27.4-17)

where I is the radiation intensity and Ω is the solid angle. Gis the quantity that the P-1 radiation model computes. For theDO radiation model, the incident radiation is computed over afinite number of discrete solid angles, each associated with a vectordirection. The unit quantity for Incident Radiation is heat-flux.

Incident Radiation (Band n) (in the Radiation... category) is the radiationenergy contained in the wavelength band ∆λ for the non-gray DOradiation model. Its unit quantity is heat-flux.

Internal Energy (in the Temperature... category) is the summation of thekinetic and potential energies of the molecules of the substance (inthe absence of chemical or nuclear reactions) per unit volume. Itis defined as e = cvT . Its unit quantity is specific-energy.

Lam Diff Coef of species-n (in the Species... category) is the laminar dif-fusion coefficient of a species into the mixture, Di,m. Its unit quan-tity is mass-diffusivity.

Laminar Flame Speed (in the Premixed Combustion... category) is thepropagation speed of laminar premixed flames (Ul in Equation 15.2-4).Its unit quantity is velocity.

Liquid Fraction (in the Solidification/Melting... category) is the liquidfraction β computed by the solidification/melting model:

β =∆HL

= 0 if T < Tsolidus



β =∆HL

= 1 if T > Tliquidus

β =∆HL

=T − Tsolidus

Tliquidus − Tsolidusif Tsolidus < T < Tliquidus

(27.4-18)

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

Mass fraction of HCN, Mass fraction of NH3, Mass fraction of NO (in theNOx... category) are the mass of HCN, the mass of NH3, and themass of NO per unit mass of the mixture (e.g., kg of HCN in1 kg of the mixture). The Mass fraction of HCN and the Massfraction of NH3 will appear only if you are modeling fuel NOx. SeeSection 17.1.5 for details.

Mass fraction of nuclei (in the Soot... category) is the number of particlesper unit mass of the mixture (in units of particles ×1015/kg) TheMass fraction of nuclei will appear only if you use the two-step sootmodel. See Section 17.2 for details.

Mass fraction of soot (in the Soot... category) is the mass of soot perunit mass of the mixture (e.g., kg of soot in 1 kg of the mixture).See Section 17.2 for details.

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

Mean quantity-n (in the Unsteady Statistics... category) is the time-averag-ed value of a solution variable (e.g., Static Pressure). See Sec-tion 22.15.3 for details.

Meridional Coordinate (in the Grid... category) is the normalized (dimen-sionless) 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 themixture fraction solved for in the non-premixed combustion model.This is the second conservation equation (along with the mixturefraction equation) that the non-premixed combustion model solves.(See Section 14.1.2.)

Modified Turbulent Viscosity (in the Turbulence... category) is the trans-ported quantity ν that is solved for in the Spalart-Allmaras turbu-lence model (see Equation 10.3-1). The turbulent viscosity, µt, iscomputed directly from this quantity using the relationship givenby Equation 10.3-2. Its unit quantity is viscosity.

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

Mole fraction of HCN, Mole fraction of NH3, Mole fraction of NO (in theNOx... category) are the number of moles of HCN, NH3, and NOin one mole of the mixture. The Mole fraction of HCN and the Molefraction of NH3 will appear only if you are modeling fuel NOx. SeeSection 17.1.5 for details.

Molecular Prandtl Number (in the Properties... category) is the ratiocpµlam/klam.

Molecular Viscosity (in the Properties... category) is the laminar viscosityof the fluid. Viscosity, µ, is defined by the ratio of shear stress tothe rate of shear. Its unit quantity is viscosity.

Molecular Viscosity of phase-n (in the Properties... category) is the lami-nar viscosity of the nth phase. Its unit quantity is viscosity.

NOx... contains quantities related to the NOx model. See Section 17.1for details about this model.

Partition Boundary Cell Distance (in the Grid... category) is the small-est number of cells which must be traversed to reach the nearestpartition (interface) boundary.

Partition Neighbors (in the Cell Info... category) is the number of adjacentpartitions (i.e., those that share at least one partition boundary



face (interface)). It gives a measure of the number of messagesthat will have to be generated for parallel processing.

Pdf... contains quantities related to the non-premixed combustion model,which is described in Chapter 14.

Phases... contains quantities for reporting the volume fraction of eachphase. See Chapter 20 for details.

Pitchwise Coordinate (in the Grid... category) is the normalized (dimen-sionless) coordinate in the circumferential (pitchwise) direction. Itsvalue varies from 0 to 1.

Preconditioning Reference Velocity (in the Velocity... category) is the ref-erence velocity used in the coupled solver’s preconditioning algo-rithm. See Section 22.4.2 for details.

Premixed Combustion... contains quantities related to the premixed com-bustion model, which is described in Chapter 15.

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

Pressure Coefficient (in the Pressure... category) is a dimensionless pa-rameter defined by the equation

Cp =(p − pref)qref

(27.4-19)

where p is the static pressure, pref is the reference pressure, andqref is the reference dynamic pressure defined by 1

2ρrefvref2. The

reference pressure, density, and velocity are defined in the ReferenceValues panel.

Product Formation Rate (in the Premixed Combustion... category) is thesource term in the progress variable transport equation (Sc inEquation 15.2-1). Its unit quantity is time-inverse.

Production of k (in the Turbulence... category) is the rate of productionof turbulence kinetic energy (times density). Its unit quantity isturb-kinetic-energy-production.



phase-n Production of k (in the Turbulence... category) is the rate of pro-duction of turbulent kinetic energy (times density) for the nthphase. Its unit quantity is turb-kinetic-energy-production.

Progress Variable (in the Premixed Combustion... category) is a normal-ized mass fraction of the combustion products (c = 1) or unburntmixture products (c = 0), as defined by Equation 15.2-2.

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

Radial Coordinate (in the Grid... category) is the length of the radius vec-tor in the polar coordinate system. The radius vector is defined bya line segment between the node and the axis of rotation. You candefine the rotational axis in the Fluid panel. (See also Section 27.2.)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 acontinuous casting process. Its unit quantity is velocity.

Radial Velocity (in the Velocity... category) is the component of velocityin the radial direction. (See Section 27.2 for details.) The unitquantity for Radial Velocity is velocity.

phase-n Radial Velocity (in the Velocity... category) is the component ofvelocity in the radial direction for the nth phase. Its unit quantityis velocity.

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

Radiation... includes quantities related to radiation heat transfer. SeeSection 11.3 for details about the radiation models available inFLUENT.

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



Radiation Temperature (in the Radiation... category) is the quantity θR,defined by

θR = (G

4σ)1/4 (27.4-20)

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

Rate of Reaction-n (in the Reactions... category) is the effective rate ofprogress of nth reaction. For the finite-rate model, the value is thesame as the Arrhenius Rate of Reaction-n. For the eddy-dissipationmodel, the value is equivalent to the Turbulent Rate of Reaction-n.For the finite-rate/eddy-dissipation model, it is the lesser of thetwo.

Reactions... includes quantities related to finite-rate reactions. See Chap-ter 13 for information about modeling finite-rate reactions.

Refractive Index (in the Radiation... category) is a nondimensional pa-rameter defined as the ratio of the speed of light in a material tothat in vacuum. See Section 11.3.6 for details.

Relative Axial Velocity (in the Velocity... category) is the axial-directioncomponent of the velocity relative to the reference frame motion.See Section 27.2 for details. The unit quantity for Relative AxialVelocity is velocity.

Relative Humidity (in the Species... category) is the ratio of the par-tial pressure of the water vapor actually present in an air-watermixture to the saturation pressure of water vapor at the mixturetemperature. FLUENT computes the saturation pressure, p, fromthe following equation [190]:

ln(p

pc

)=(Tc

T− 1

)×

8∑i=1

Fi [a (T − Tp)]i−1 (27.4-21)



where pc = 22.089 MPaTc = 647.286 KF1 = −7.4192420F2 = 2.9721000 × 10−1

F3 = −1.1552860 × 10−1

F4 = 8.6856350 × 10−3

F5 = 1.0940980 × 10−3

F6 = −4.3999300 × 10−3

F7 = 2.5206580 × 10−3

F8 = −5.2186840 × 10−4

a = 0.01Tp = 338.15 K

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

Relative Radial Velocity (in the Velocity... category) is the radial-directioncomponent of the velocity relative to the reference frame motion.(See Section 27.2 for details.) The unit quantity for Relative RadialVelocity is velocity.

Relative Swirl Velocity (in the Velocity... category) is the tangential-direc-tion component of the velocity relative to the reference frame mo-tion, in an axisymmetric swirling flow. (See Section 27.2 for de-tails.) 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 framemotion. (See Section 27.2 for details.) The unit quantity for Rela-tive Tangential Velocity is velocity.

Relative Total Pressure (in the Pressure... category) is the stagnationpressure computed using relative velocities instead of absolute ve-locities; i.e., for incompressible flows the dynamic pressure wouldbe computed using the relative velocities. (See Section 27.2 formore information about relative velocities.) The unit quantity forRelative Total Pressure is pressure.

Relative Total Temperature (in the Temperature... category) is the stag-nation temperature computed using relative velocities instead of



absolute velocities. (See Section 27.2 for more information aboutrelative velocities.) The unit quantity for Relative Total Tempera-ture is temperature.

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

tan−1(−relative-tangential-velocity

axial-velocity

)(27.4-22)

Its unit quantity is angle.

Relative Velocity Magnitude (in the Velocity... category) is the magnitudeof the relative velocity vector instead of the absolute velocity vec-tor. The relative velocity (~w) is the difference between the absolutevelocity (~v) and the grid velocity. For simple rotation, the relativevelocity is defined as

~w ≡ ~v − ~Ω × ~r (27.4-23)

where ~Ω is the angular velocity of a rotating reference frame aboutthe origin and ~r is the position vector. (See also Section 27.2.) Theunit quantity for Relative Velocity Magnitude is velocity.

Relative X Velocity, Relative Y Velocity, Relative Z Velocity (in the Veloc-ity... category) are the x-, y-, and z-direction components of thevelocity relative to the reference frame motion. (See Section 27.2for details.) The unit quantity for these variables is velocity.

Residuals... contains different quantities for the segregated and coupledsolvers:

In the coupled solvers, this category includes the corrections to theprimitive variables pressure, velocity, temperature, and species, aswell as the time rate of change of the corrections to these primi-tive variables for the current iteration (i.e., residuals). Correctionsare the changes in the variables between the current and previousiterations and residuals are computed by dividing a cell’s correc-tion by its physical time step. The total residual for each variable



is the summation of the Euler, viscous, and dissipation contribu-tions. The dissipation components are the vector components ofthe flux-like, face-based dissipation operator.

In the segregated solver, only the Mass Imbalance in each cell isreported (unless you have requested others, as described in Sec-tion 22.16.1). At convergence, this quantity should be small com-pared to the average mass flow rate.

RMS quantity-n (in the Unsteady Statistics... category) is the root meansquared value of a solution variable (e.g., Static Pressure). SeeSection 22.15.3 for details.

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

I = h+w2

2− u2

2(27.4-24)

where h is the enthalpy, w is the relative velocity magnitude, andu is the magnitude of the rotational velocity ~u = ~ω × ~r.

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

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

χ = 2D|∇f |2 (27.4-25)

where f is the mixture fraction and D is a representative diffusioncoefficient (see Section 14.4.3 for details). Its unit quantity is time-inverse.

Scattering Coefficient (in the Radiation... category) is the property of amedium that describes the amount of scattering of thermal radia-tion per unit path length for propagation in the medium. It canbe interpreted as the inverse of the mean free path that a photon



will travel before undergoing scattering (if the scattering coefficientdoes not vary along the path). The unit quantity for Scattering Co-efficient is length-inverse.

Secondary Mean Mixture Fraction (in the Pdf... category) is the meanratio 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-premixedcombustion model. See Section 14.1.2.

Secondary Mixture Fraction Variance (in the Pdf... category) is the vari-ance of the secondary stream mixture fraction that is solved for inthe non-premixed combustion model. See Section 14.1.2.

Skin Friction Coefficient (in the Wall Fluxes... category) is a nondimen-sional parameter defined as the ratio of the wall shear stress andthe reference dynamic pressure

Cf ≡ τw12ρrefv

2ref

(27.4-26)

where τw is the wall shear stress, and ρref and vref are the referencedensity and velocity defined in the Reference Values panel.

phase-n Skin Friction Coefficient (in the Wall Fluxes... category) is theskin friction coefficient (defined above) for the nth phase.

Solidification/Melting... contains quantities related to solidification andmelting.

Soot... contains quantities related to the Soot model, which is describedin Section 17.2.

Sound Speed (in the Properties... category) is the acoustic speed. It iscomputed from

√γpρ . Its unit quantity is velocity.

Spanwise Coordinate (in the Grid... category) is the normalized (dimen-sionless) 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 ineach of the species transport equations due to reactions. The unitquantity is always kg/m3-s.

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

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

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

Specific Heat Ratio (gamma) (in the Properties... category) is the ratioof specific heat at constant pressure to the specific heat at constantvolume.

Stored Cell Partition (in the Cell Info... category) is an integer identifierdesignating the partition to which a particular cell belongs. Inproblems in which the grid is divided into multiple partitions tobe solved on multiple processors using the parallel version of FLU-ENT, the partition ID can be used to determine the extent of thevarious groups of cells. The active cell partition is used for the cur-rent calculation, while the stored cell partition (the last partitionperformed) is used when you save a case file.See Section 28.4.3 formore information.

Static Pressure (in the Pressure... category) is the static pressure of thefluid. It is a gauge pressure expressed relative to the prescribedoperating pressure. The absolute pressure is the sum of the StaticPressure 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 thefluid. Its unit quantity is temperature.

Note that Static Temperature will appear in the Premixed Combus-tion... category only for adiabatic premixed combustion calcula-tions. See Section 15.3.7.



Strain Rate (in the Derivatives... category) relates shear stress to the vis-cosity. Also called the shear rate (γ in Equation 7.3-17), the strainrate is related to the second invariant of the rate-of-deformationtensor D. Its unit quantity is time-inverse. In 3D Cartesian coor-dinates, the strain rate, S, is defined as

S2 =[∂u

∂x

(∂u

∂x+∂u

∂x

)+∂u

∂y

(∂u

∂y+∂v

∂x

)+∂u

∂z

(∂u

∂z+∂w

∂x

)]+[

∂v

∂x

(∂v

∂x+∂u

∂y

)+∂v

∂y

(∂v

∂y+∂v

∂y

)+∂v

∂z

(∂v

∂z+∂w

∂y

)]+[

∂w

∂x

(∂w

∂x+∂u

∂z

)+∂w

∂y

(∂w

∂y+∂v

∂z

)+∂w

∂z

(∂w

∂z+∂w

∂z

)](27.4-27)

Strain Rate of phase-n (in the Derivatives... category) is the strain rate(defined above) of the nth phase. Its unit quantity is time-inverse.

Stream Function (in the Velocity... category) is formulated as a relationbetween the streamlines and the statement of conservation of mass.A streamline is a line that is tangent to the velocity vector of theflowing fluid. For a 2D planar flow, the stream function, ψ, isdefined such that

ρu ≡ ∂ψ

∂yρv ≡ −∂ψ

∂x(27.4-28)

where ψ is constant along a streamline and the difference betweenconstant values of stream function defining two streamlines is themass rate of flow between the streamlines.

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

Stretch Factor (in the Premixed Combustion... category) is a nondimen-sional parameter that is defined as the probability of unquenchedflamelets (G in Equation 15.2-10).

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



ks =ν2

t

L2s

(27.4-29)

Its unit quantity is turbulent-kinetic-energy.

Subgrid Turbulent Viscosity (in the Turbulence... category) is the tur-bulent (dynamic) viscosity of the fluid calculated using the LESturbulence model. It expresses the proportionality between theanisotropic part of the subgrid-scale stress tensor and the rate-of-strain tensor. (See Equation 10.7-7.) Its unit quantity is viscosity.

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

Surface Cluster ID (in the Radiation... category) is used to view the dis-tribution of surface clusters in the domain. Each cluster has aunique integer number (ID) associated with it.

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

Surface Heat Transfer Coef. (in the Wall Fluxes... category) is defined bythe equation

heff =q

Twall − Tref(27.4-30)

where q is the convective heat flux, Twall is the wall temperature,and Tref is reference temperature defined in the Reference Valuespanel. Its unit quantity is heat-transfer-coefficient.

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

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

Nu =heffLref

k(27.4-31)



where heff is the heat transfer coefficient, Lref is the reference lengthdefined in the Reference Values panel, and k is the molecular ther-mal conductivity.

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

St =heff

ρrefvrefcp(27.4-32)

where heff is the heat transfer coefficient, ρref and vref are referencevalues of density and velocity defined in the Reference Values panel,and cp is the specific heat at constant pressure.

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

Swirl Velocity (in the Velocity... category) is the tangential-directioncomponent of the velocity in an axisymmetric swirling flow. SeeSection 27.2 for details. The unit quantity for Swirl Velocity isvelocity.

phase-n Swirl Velocity (in the Velocity... category) is the tangential-direc-tion component of the velocity in an axisymmetric swirling flow forthe nth phase. Its unit quantity is velocity.

Swirl-Wall Shear Stress (in the Wall Fluxes... category) is the swirl com-ponent 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 componentin the tangential direction. (See Section 27.2 for details.) The unitquantity for Tangential Velocity is velocity.

Temperature... indicates the quantities associated with the thermody-namic temperature of a material.

Thermal Conductivity (in the Properties... category) is a parameter (k)that defines the conduction rate through a material via Fourier’slaw (q = −k∇T ). A large thermal conductivity is associated with



a good heat conductor and a small thermal conductivity with apoor heat conductor (good insulator). Its unit quantity is thermal-conductivity.

Thermal Diff Coef of species-n (in the Species... category) is the thermaldiffusion coefficient for the nth species (DT,i in Equations 7.7-1,7.7-3, and 7.7-7). Its unit quantity is viscosity.

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

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

Total Energy (in the Temperature... category) is the total energy per unitmass. Its unit quantity is specific-energy.

Total Energy of phase-n (in the Temperature... category) is the total en-ergy per unit mass of the nth phase. Its unit quantity is specific-energy.

Total Enthalpy (in the Temperature... category) is defined as H + 12v

2

where H is the Enthalpy and v is the velocity magnitude. Its unitquantity is specific-energy.

Total Enthalpy of phase-n (in the Temperature... category) is defined asH + 1

2v2 where H is the Enthalpy of phase-n and v is the phase-n

Velocity Magnitude. Its unit quantity is specific-energy.

Total Enthalpy Deviation (in the Temperature... category) is the differ-ence between Total Enthalpy and the reference enthalpy, H+ 1

2v2 −

Href , where Href is the reference enthalpy defined in the ReferenceValues panel. The unit quantity for Total Enthalpy Deviation isspecific-energy.

Total Enthalpy Deviation of phase-n (in the Temperature... category) isthe difference between Total Enthalpy of phase-n and the referenceenthalpy, H + 1

2v2 − Href , where Href is the reference enthalpy



defined in the Reference Values panel. The unit quantity for TotalEnthalpy Deviation of phase-n is specific-energy.

Total Pressure (in the Pressure... category) is the pressure at the ther-modynamic state that would exist if the fluid were brought to zerovelocity and zero potential. For compressible flows, the total pres-sure is computed using isentropic relationships. For constant cp,this reduces to:

p0 = p

[1 +

γ − 12

M2]γ/(γ−1)

(27.4-33)

where p is the static pressure, γ is the ratio of specific heats, andM is the Mach number. For incompressible flows (constant densityfluid), we use Bernoulli’s equation, p0 = p+pdyn, where pdyn is thelocal dynamic pressure. Its unit quantity is pressure.

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

Total Temperature (in the Temperature... category) is the temperature atthe thermodynamic state that would exist if the fluid were broughtto zero velocity. For compressible flows, the total temperature iscomputed from the total enthalpy using the current cp method(specified in the Materials panel). For incompressible flows, thetotal temperature is equal to the static temperature. The unitquantity for Total Temperature is temperature.

Turbulence... includes quantities related to turbulence. See Chapter 10for information about the turbulence models available in FLUENT.

Turbulence Intensity (in the Turbulence... category) is the ratio of themagnitude of the RMS turbulent fluctuations to the reference ve-locity:



I =

√23k

vref(27.4-34)

where k is the turbulence kinetic energy and vref is the referencevelocity specified in the Reference Values panel. The reference valuespecified should be the mean velocity magnitude for the flow. Notethat turbulence intensity can be defined in different ways, so youmay want to use a custom field function for its definition. SeeSection 27.5 for more information.

Turbulent Dissipation Rate (Epsilon) (in the Turbulence... category) is theturbulent dissipation rate. Its unit quantity is turbulent-energy-diss-rate.

phase-n Turbulent Dissipation Rate (in the Turbulence... category) is theturbulent dissipation rate for the nth phase. Its unit quantity isturbulent-energy-diss-rate.

Turbulent Flame Speed (in the Premixed Combustion... category) is theturbulent flame speed computed by FLUENT using Equation 15.2-4.Its unit quantity is velocity.

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

k =12u′iu′i (27.4-35)

Its unit quantity is turbulent-kinetic-energy.

phase-n Turbulent Kinetic Energy (in the Turbulence... category) is theturbulence kinetic energy per unit mass (defined above) for thenth phase. Its unit quantity is turbulent-kinetic-energy.

Turbulent Rate of Reaction-n (in the Reactions... category) is the rateof progress of the nth reaction computed by Equation 13.1-25 or13.1-26. For the “eddy-dissipation” model, the value is the sameas the Rate of Reaction-n. For the “finite-rate” model, the value iszero.



Turbulent Reynolds Number (Re y) (in the Turbulence... category) is anondimensional quantity defined as

ρd√k

µlam(27.4-36)

where k is turbulence kinetic energy, d is the distance to the nearestwall, and µlam is the laminar viscosity.

Turbulent Viscosity (in the Turbulence... category) is the turbulent vis-cosity of the fluid computed using the turbulence model. Its unitquantity is viscosity.

phase-n Turbulent Viscosity (in the Turbulence... category) is the turbu-lent viscosity of the nth phase, computed using the turbulencemodel. Its unit quantity is viscosity.

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

udm-n (in the User Defined Memory... category) is the value of the quan-tity in the nth user-defined memory location.

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

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

User Defined Memory... includes quantities that have been allocated to auser-defined memory location. See the separate UDF Manual fordetails 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 u′2 stress.

UV Reynolds Stress (in the Turbulence... category) is the u′v′ stress.



UW Reynolds Stress (in the Turbulence... category) is the u′w′ stress.

Variance of Species (in the NOx... category) is the variance of the massfraction of a selected species in the flow field. It is calculated fromEquation 17.1-86.

Variance of Species 1, Variance of Species 2 (in the NOx... category) arethe variances of the mass fractions of the selected species in theflow field. They are each calculated from Equation 17.1-86.

Variance of Temperature (in the NOx... category) is the variance of thenormalized temperature in the flow field. It is calculated fromEquation 17.1-86.

Velocity... includes the quantities associated with the rate of change inposition with time. The instantaneous velocity of a particle isdefined as the first derivative of the position vector with respect totime, d~r/dt, termed the velocity vector, ~v.

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

For a 2D model,

tan−1(

y-velocity-componentx-velocity-component

)(27.4-37)

For a 2D or axisymmetric model,

tan−1(

radial-velocity-componentaxial-velocity-component

)(27.4-38)

For a 3D model,

tan−1(

tangential-velocity-componentaxial-velocity-component

)(27.4-39)

Its unit quantity is angle.

Velocity Magnitude (in the Velocity... category) is the speed of the fluid.Its unit quantity is velocity.



phase-n Velocity Magnitude (in the Velocity... category) is the speed ofthe nth phase. Its unit quantity is velocity.

Volume fraction of phase-n (in the Phases... category) is the volume frac-tion of the nth phase.

Vorticity Magnitude (in the Velocity... category) is the magnitude of thevorticity vector. Vorticity is a measure of the rotation of a fluidelement as it moves in the flow field, and is defined as the curl ofthe velocity vector:

ξ = ∇× ~V (27.4-40)

VV Reynolds Stress (in the Turbulence... category) is the v′2 stress.

VW Reynolds Stress (in the Turbulence... category) is the v′w′ stress.

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

Wall Shear Stress (in the Wall Fluxes... category) is the force acting tan-gential to the surface due to friction. Its unit quantity is pressure.

phase-n Wall Shear Stress (in the Wall Fluxes... category) is the forceacting tangential to the surface due to friction on the nth phase.Its unit quantity is pressure.

Wall Temperature (Inner Surface) (in the Temperature... category) is thetemperature on the inner surface of a wall (corresponding to theside of the wall surface away from the adjacent fluid or solid cellzone). Note that wall thermal boundary conditions are applied onthis surface. See also Figure 6.13.2. The unit quantity for WallTemperature (Inner Surface) is temperature.

Wall Temperature (Outer Surface) (in the Temperature... category) is thetemperature on the outer surface of a wall (corresponding to theside of the wall surface toward the adjacent fluid or solid cell zone).Note that wall thermal boundary conditions are applied on theInner Surface. See also Figure 6.13.2. The unit quantity for WallTemperature (Outer Surface) is temperature.



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

y+ =ρuτyP

µ(27.4-41)

where uτ =√τw/ρw is the friction velocity, yP is the distance from

point P to the wall, ρ is the fluid density, and µ is the fluid viscosityat point P . See Section 10.8 for details.

phase-n Wall Yplus (in the Turbulence... category) is the value of y+

computed (as defined above) using the turbulence kinetic energy,density, and viscosity of the nth phase.

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

y∗ =ρC

1/4µ k

1/2P yP

µ(27.4-42)

where kP is the turbulence kinetic energy at point P , yP is thedistance from point P to the wall, ρ is the fluid density, and µ isthe fluid viscosity at point P . See Section 10.8 for details.

WW Reynolds Stress (in the Turbulence... category) is the w′2 stress.

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

X Face Area, Y Face Area, Z Face Area (in the Grid... category) are thecomponents of the boundary face area vectors accumulated to theboundary cells, for the zones selected in the Boundary Zones listcontained in the Boundary Adaption panel. The face areas are cal-culated only on the zones selected, and in order to make your selec-tion active, you need to click on the Mark button in the BoundaryAdaption panel. Note that if the Boundary Zones list is empty, allboundary zones will be used. The face area calculations are doneas in X Surface Area, Y Surface Area, Z Surface Area (see below),



except the area values in the cells with more than one boundaryface are not summed to obtain the cell values. Instead, the areavalue relative to the last visited face of each cell (resulting fromyour selection of Boundary Zones) is taken as the cell value.

X Pull Velocity, Y Pull Velocity, Z Pull Velocity (in the Solidification/Melt-ing... category) are the x, y, and z components of the pull velocityfor the solid material in a continuous casting process. The unitquantity 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 accumulatedto the boundary cells. The surface area is accumulated for allboundary faces. For each boundary face zone, the component ofthe face area in the relevant direction (x, y, or z) is accumulatedas the cell value of the adjoining cell. For those cells having morethan one boundary face, the cell value is the sum (accumulation)of all the face area values. In most circumstances, the X SurfaceArea, Y Surface Area, Z Surface Area are used for flux and surfaceintegration. In the few instances where area accumulation mustbe avoided, you can mark the zones of interest and use X FaceArea, Y Face Area, Z Face Area (see above) for flux and integralcalculations.

X Velocity, Y Velocity, Z Velocity (in the Velocity... category) are the com-ponents of the velocity vector in the x-axis, y-axis, and z-axis direc-tions, respectively. The unit quantity for these variables is velocity.

phase-n X-Velocity, phase-n Y-Velocity, phase-n Z-Velocity (in the Veloc-ity... category) are the components of the velocity vector in thex-axis, y-axis, and z-axis directions for each phase. The unit quan-tity for these variables is velocity.

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 WallFluxes... category) are the x, y, and z components of the force act-ing tangential to the surface due to friction. The unit quantity forthese variables is pressure.


27.5 Custom Field Functions

phase-n X-Wall Shear Stress, phase-n Y-Wall Shear Stress, phase-n Z-WallShear Stress (in the Wall Fluxes... category) are the x, y, and z com-ponents of the force acting tangential to the surface due to frictionon the nth phase. The unit quantity for these variables is pressure.


In addition to the basic field variables provided by FLUENT (and de-scribed in Section 27.4), you can also define your own field functions tobe used in conjunction with any of the commands that use these vari-ables (contour and vector display, XY plots, etc.). This capability isavailable with the Custom Field Function Calculator panel. You can usethe default field variables, previously defined calculator functions, andcalculator operators to create new functions. (Several sample functionsare described in Section 27.5.3.)

Any field functions that you define will be saved in the case file the nexttime that you save it. You can also save your custom field functions toa separate file (as described in Section 27.5.2), so that they can be usedwith a different case file.

Note that all custom field functions are evaluated and stored in SI units.!Any solver-defined flow variables that you use in your field-function defi-nition will be automatically converted if they are not already in SI units,but you must be careful to enter constants in the appropriate units. Notealso that explicit node values are not available for custom field functions;all node values for these functions will be computed by averaging the val-ues in the surrounding cells, as described in Section 27.1.2.

27.5.1 Creating a Custom Field Function

To create your own field function, you will use the Custom Field FunctionCalculator panel (Figure 27.5.1). This panel allows you to define fieldfunctions based on existing functions, using simple calculator operators.Any functions that you define will be added to the list of default flowvariables and other field functions provided by the solver.

Define −→Custom Field Functions...



Recall that you must enter all constants in the function definition in SI!units.

Figure 27.5.1: The Custom Field Function Calculator Panel

The steps for creating a custom field function are as follows:

1. Use the calculator buttons and the Field Functions list and Selectbutton to specify the function definition, as described below. (Asyou select each item from the Field Functions list or click on a buttonin the calculator keypad, its symbol will appear in the Definitiontext entry box. You cannot edit the contents of this box directly;if you want to delete part of a function, use the DEL button on thekeypad.)

2. Specify the name of the function in the New Function Name field.

Be sure that you do not specify a name that is already used for!a standard field function (e.g., velocity-magnitude); you can seea complete list of the predefined field functions in FLUENT byselecting the display/contours text command and viewing theavailable choices for contours of.



3. Click on the Define button.

When you click on Define, the solver will create the function and add itto the list of Custom Field Functions within the drop-down list of availablefield functions. The Define push button is grayed out after you create anew function or if the Definition text entry box is empty.

Should you decide to rename or delete the function after you have com-pleted the definition, you can do so in the Field Function Definitions panel,which you can open by clicking on the Manage... push button. See Sec-tion 27.5.2 for details.

Using the Calculator Buttons

Your function definition can include many basic calculator operations(e.g., addition, subtraction, multiplication, square root). When you se-lect a calculator button (by clicking on it), the appropriate symbol willappear in the Definition text entry box. The meaning of the buttons isstraightforward; they are similar to the buttons you would find on anystandard calculator. You should, however, note the following:

• The CE/C button will clear the entire Definition and the New Func-tion Name, if you have entered one. The DEL button will deleteonly the last entry in the Definition text entry box. You can useDEL to delete characters one at a time, starting with the last oneentered.

• To obtain the inverse trigonometric functions arcsin, arccos, andarctan, click on the INV button before selecting sin, cos, or tan.

• The ABS button yields the absolute value of the number that fol-lows it, and the log button yields the natural logarithm of thefollowing number.

• The PI button represents π and the e button represents the baseof the natural logarithm system (which is approximately equal to2.71828).



Using the Field Functions List

Your function definition can also include any of the field functions definedby the solver (and listed in Section 27.4) or by you. To include one ofthese variables/functions in your function definition, select it in the FieldFunctions drop-down list and then click on the Select button below thelist. The symbol for the selected item will appear in the Definition textentry box (e.g., p will appear if you select Static Pressure).

27.5.2 Manipulating, Saving, and Loading Custom FieldFunctions

Once you have defined your field functions, you can manipulate themusing the Field Function Definitions panel (Figure 27.5.2). You can displaya function definition to be sure that it is correct, delete the function ifyou decide that it is incorrect and needs to be redefined, or give thefunction a new name. You can also save custom field functions to a fileor read them from a file. The custom field function file allows you totransfer your custom functions between case files.

To open the Field Function Definitions panel, click on the Manage... but-ton in the Custom Field Function Calculator panel.

The following actions can be performed in the Field Function Definitionspanel:

• To check the definition of a function, select it in the Field Functionslist. Its definition will be displayed in the Definition field. Thisdisplay is for informational purposes only; you cannot edit it. If youwant to change a function definition, you must delete the functionand define it again in the Custom Field Function Calculator panel.

• To delete a function, select it in the Field Functions list and clickon the Delete button.

• To rename a function, select it in the Field Functions list, enter anew name in the Name field, and click on the Rename button.

Be sure that you do not specify a name that is already used for!a standard field function (e.g., velocity-magnitude); you can see



Figure 27.5.2: The Field Function Definitions Panel

a complete list of the predefined field functions in FLUENT byselecting the display/contours text command and viewing theavailable choices for contours of.

• To save all of the functions in the Field Functions list to a file, clickon the Save... button and specify the file name in the resultingSelect File dialog box (see Section 2.1.2).

• To read custom field functions from a file that you saved as de-scribed above, click on the Load... button and specify the filename in the resulting Select File dialog box. (Custom field functionfiles are valid Scheme functions, and can also be loaded with theFile/Read/Scheme... menu item, as described in Section 3.15.)



27.5.3 Sample Custom Field Functions

When you are checking the results of your simulation, you may find ituseful to define some of the following field functions:

• To define a function that determines the ratio of static pressure toinlet total pressure, use the relationship

R =p+ pop

pto + pop(27.5-1)

where p is the static pressure calculated by the solver, pto is theinlet total pressure, and pop is the operating pressure for the prob-lem. Use the solver-defined function Static Pressure for p, and thenumerical value that you specified for Gauge Total Pressure in thePressure Inlet panel for pto. Specify the value of the operatingpressure to be the value that you set in the Operating Conditionspanel. As discussed in Section 7.12, all pressures in FLUENT aregauge pressures relative to the operating pressure. If the operat-ing pressure is zero, as is generally the case for compressible flowcalculations, the expression for the pressure ratio reduces to

PR =p

pto(27.5-2)

• To define a function that determines the critical velocity ratio v/a∗,a parameter that is sometimes used in turbomachinery calculations,use the relationship

v

a∗=[(γ + 1γ − 1

)(1 − PR(γ−1)/γ

)]1/2

(27.5-3)

In this relationship, a∗ is the critical velocity (i.e., the velocity thatwould occur for the same stagnation conditions if M = 1), γ is theratio of specific heats, and PR is the pressure ratio defined in Equa-tion 27.5-2 for which you created your own function. For γ, ratioof specific heats, select Specific Heat Ratio (gamma) in the Proper-ties... category. To include PR, select Custom Field Functions... in



the first drop-down list under Field Functions, and then select fromthe second list the function name that you assigned PR.

• Suppose you have swirling flow in a pipe, aligned with the z axis,and you want to calculate the flow rate of angular momentumthrough a cross-sectional plane:

∫ρrvθ~v · d ~A (27.5-4)

You can create a function for the product rvθ, where r is the RadialCoordinate and vθ is the Tangential Velocity. Then use the SurfaceIntegrals panel to compute the flow rate of this quantity.


Chapter 27. Field Function De nitions · Chapter 27. Field Function De nitions You must select...

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