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Appendix A Conventions for Data-Name Identifiers

Identifiers or names can be attached to DataArray_t entities to identify and describe the quantity being stored. To facilitate communication between different application codes, we propose to establish a set of standardized data-name identifiers with fairly precise definitions. For any identifier in this set, the associated data should be unambiguously understood. In essence, this section proposes standardized terminology for labeling CFD-related data, including grid coordinates, flow solution, turbulence model quantities, nondimensional governing parameters, boundary condition quantities, and forces and moments.

We use the convention that all standardized identifiers denote scalar quantities; this is consistent with the intended use of the DataArray_t structure type to describe an array of scalars. For quantities that are vectors, such as velocity, their components are listed.

Included with the lists of standard data-name identifiers are the fundamental units of dimensions associated with that quantity. The following notation is used for the fundamental units: M is mass, L is length, T is time, Θ is temperature, α is angle, and I is electric current. These fundamental units are directly associated with the elements of the DimensionalExponents_t structure. For example, a quantity that has dimensions ML/T corresponds to MassExponent = +1, LengthExponent = +1, and TimeExponent = -1.

Unless otherwise noted, all quantities in the following sections denote floating-point data types, and the appropriate DataType structure parameter for DataArray_t is real.

A.1 Coordinate Systems

Coordinate systems for identifying physical location are as follows:

System 3-D 2-D Cartesian (x,y,z) (x,y) or (x,z) or (y,z) Cylindrical (r,θ,z) (r,θ) Spherical (r,θ,φ) Auxiliary (ξ,η,ζ) (ξ,η) or (ξ,ζ) or (η,ζ)

Associated with these coordinate systems are the following unit vector conventions:

 x-direction: ex r-direction: er ξ-direction: eξ y-direction: ey θ-direction: eθ η-direction: eη z-direction: ez φ-direction: eφ ζ-direction: eζ

Note that er, eθ and eφ are functions of position.

We envision that one of the "standard" coordinate systems (Cartesian, cylindrical or spherical) will be used within a zone (or perhaps the entire database) to define grid coordinates and other related data. The auxiliary coordinates will be used for special quantities, including forces and moments, which may not be defined in the same coordinate system as the rest of the data. When auxiliary coordinates are used, a transformation must also be provided to uniquely define them. For example, the transform from Cartesian to orthogonal auxiliary coordinates is, where T is an orthonormal matrix (2×2 in 2-D and 3×3 in 3-D).

In addition, normal and tangential coordinates are often used to define boundary conditions and data related to surfaces. The normal coordinate is identified as n with the unit vector en.

The data-name identifiers defined for coordinate systems are listed in the following table. All represent real DataTypes, except for ElementConnectivity and ParentData, which are integer.

Data-Name Identifier Description Units CoordinateX x L CoordinateY y L CoordinateZ z L CoordinateR r L CoordinateTheta θ α CoordinatePhi φ α CoordinateNormal Coordinate in direction of en L CoordinateTangential Tangential coordinate (2-D only) L CoordinateXi ξ L CoordinateEta η L CoordinateZeta ζ L CoordinateTransform Transformation matrix (T) - InterpolantsDonor Interpolation factors - ElementConnectivity Nodes making up an element - ParentData Element parent identification -

A.2 Flowfield Solution

This section describes data-name identifiers for typical Navier-Stokes solution variables. The list is obviously incomplete, but should suffice for initial implementation of the CGNS system. The variables listed in this section are dimensional or raw quantities; nondimensional parameters and coefficients based on these variables are discussed in the section Nondimensional Parameters.

We use fairly universal notation for state variables. Static quantities are measured with the fluid at speed: static density (ρ), static pressure (p), static temperature (T), static internal energy per unit mass (e), static enthalpy per unit mass (h), entropy (s), and static speed of sound (c). We also approximate the true entropy by the function sapp = p / ργ (this assumes an ideal gas). The velocity is q = uex + vey + wez, with magnitude q = (qq)1/2. Stagnation quantities are obtained by bringing the fluid isentropically to rest; these are identified by a subscript "0". The term "total" is also used to refer to stagnation quantities.

Conservation variables are density, momentum (ρq = ρuex + ρvey + ρwez), and stagnation energy per unit volume (ρe0).

For rotating coordinate systems, u, v, and w are the x, y, and z components of the velocity vector in the inertial frame; ω is the rotation rate vector; R is a vector from the center of rotation to the point of interest; and wr = ω × R is the rotational velocity vector of the rotating frame of reference, with components wrx, wry, and wrz.

Molecular diffusion and heat transfer introduce the molecular viscosity (μ), kinematic viscosity (ν) and thermal conductivity coefficient (k). These are obtained from the state variables through auxiliary correlations. For a perfect gas, μ and k are functions of static temperature only.

The Navier-Stokes equations involve the strain tensor ( ) and the shear-stress tensor ( ). Using indicial notation, the 3-D Cartesian components of the strain tensor are, and the stress tensor is, where (x1,x2,x3) = (x,y,z) and (u1,u2,u3) = (u,v,w). The bulk viscosity is usually approximated as λ = −2μ/3.

Reynolds averaging of the Navier-Stokes equations introduce Reynolds stresses (−ρ(uv′)ave, etc.) and turbulent heat flux terms (−ρ(ue′)ave, etc.), where primed quantities are instantaneous fluctuations. These quantities are obtained from auxiliary turbulence closure models. Reynolds-stress models formulate transport equations for the Reynolds stresses directly; whereas, eddy-viscosity models correlate the Reynolds stresses with the mean strain rate,

−(uv′)ave = νt (∂u/∂y + ∂v/∂x)

where νt is the kinematic eddy viscosity. The eddy viscosity is either correlated to mean flow quantities by algebraic models or by auxiliary transport models. An example two-equation turbulence transport model is the k-ε model, where transport equations are formulated for the turbulent kinetic energy (k = [(uu′)ave + (vv′)ave + (ww′)ave] / 2) and turbulent dissipation (ε).

Skin friction evaluated at a surface is the dot product of the shear stress tensor with the surface normal: Note that skin friction is a vector.

The data-name identifiers defined for flow solution quantities are listed below.

Note that for some vector quantities, like momentum, the table only explicitly lists data-name identifiers for the x, y, and z components, and for the magnitude. It should be understood, however, that for any vector quantity with a standardized data name "Vector", the following standardized data names are also defined:

 VectorX x-component of vector VectorY y-component of vector VectorZ z-component of vector VectorR Radial component of vector VectorTheta θ-component of vector VectorPhi φ-component of vector VectorMagnitude Magnitude of vector VectorNormal Normal component of vector VectorTangential Tangential component of vector (2-D only)

Also note that some data-name identifiers used with multi-species flows include the variable string Symbol, which represents either the chemical symbol for a species, or a defined name for a mixture. See the section describing the ChemicalKineticsModel data structure for examples and a table of defined names.

Data-Name Identifier Description Units Potential Potential: ∇φ = q L2/T StreamFunction Stream function (2-D): ∇ × ψ = q L2/T Density Static density (ρ) M/L3 Pressure Static pressure (p) M/(LT2) Temperature Static temperature (T) Θ EnergyInternal Static internal energy per unit mass (e) L2/T2 Enthalpy Static enthalpy per unit mass (h) L2/T2 Entropy Entropy (s) ML2/(T2Θ) EntropyApprox Approximate entropy (sapp = p / ργ) L3γ−1/(Mγ−1T2) DensityStagnation Stagnation density (ρ0) M/L3 PressureStagnation Stagnation pressure (p0) M/(LT2) TemperatureStagnation Stagnation temperature (T0) Θ EnergyStagnation Stagnation energy per unit mass (e0) L2/T2 EnthalpyStagnation Stagnation enthalpy per unit mass (h0) L2/T2 EnergyStagnationDensity Stagnation energy per unit volume (ρe0) M/(LT2) VelocityX x-component of velocity (u = q · ex) L/T VelocityY y-component of velocity (v = q ⋅ ey) L/T VelocityZ z-component of velocity (w = q ⋅ ez) L/T VelocityR Radial velocity component (q ⋅ er) L/T VelocityTheta Velocity component in θ direction (q ⋅ eθ) L/T VelocityPhi Velocity component in φ direction (q ⋅ eφ) L/T VelocityMagnitude Velocity magnitude (q = (q ⋅ q)1/2) L/T VelocityNormal Normal velocity component (q ⋅ n) L/T VelocityTangential Tangential velocity component (2-D) L/T VelocitySound Static speed of sound L/T VelocitySoundStagnation Stagnation speed of sound L/T MomentumX x-component of momentum (ρu) M/(L2T) MomentumY y-component of momentum (ρv) M/(L2T) MomentumZ z-component of momentum (ρw) M/(L2T) MomentumMagnitude Magnitude of momentum (ρq) M/(L2T) RotatingVelocityX x-component of velocity, relative to rotating frame (urx = u − wrx) L/T RotatingVelocityY y-component of velocity, relative to rotating frame (ury = v − wry) L/T RotatingVelocityZ z-component of velocity, relative to rotating frame (urz = w − wrz) L/T RotatingMomentumX x-component of momentum, relative to rotating frame (ρurx) M/(L2T) RotatingMomentumY y-component of momentum, relative to rotating frame (ρury) M/(L2T) RotatingMomentumZ z-component of momentum, relative to rotating frame (ρurz) M/(L2T) RotatingVelocityMagnitude Velocity magnitude in rotating frame (qr = (urx + ury + urz)1/2) L/T RotatingPressureStagnation Stagnation pressure in rotating frame M/(LT2) RotatingEnergyStagnation Stagnation energy per unit mass in rotating frame ((e0)r) L2/T2 RotatingEnergyStagnationDensity Stagnation energy per unit volume in rotating frame (ρ(e0)r) M/(LT2) RotatingEnthalpyStagnation Stagnation enthalpy per unit mass in rotating frame, rothalpy L2/T2 EnergyKinetic (u2 + v2 + w2)/2 = q2/2 L2/T2 PressureDynamic ρq2/2 M/(LT2) SoundIntensityDB Sound intensity level in decibels, 10 log10(I/Iref) = 20 log10(p/pref), where I is the sound power per unit area, Iref = 10−12 watts/m2 is the reference sound power per unit area, p is the pressure wave amplitude, and pref = 2×10−5 N/m2 is the reference pressure. - SoundIntensity Sound intensity (i.e., sound power per unit area, I) M/T3 VorticityX ωx = ∂w/∂y − ∂v/∂z = ω ⋅ ex T−1 VorticityY ωy = ∂u/∂z − ∂w/∂x = ω ⋅ ey T−1 VorticityZ ωz = ∂v/∂x − ∂u/∂y = ω ⋅ ez T−1 VorticityMagnitude ω = (ω × ω)1/2 T−1 SkinFrictionX x-component of skin friction (τ ⋅ ex) M/(LT2) SkinFrictionY y-component of skin friction (τ ⋅ ey) M/(LT2) SkinFrictionZ z-component of skin friction (τ ⋅ ez) M/(LT2) SkinFrictionMagnitude Skin friction magnitude ((τ × τ)1/2) M/(LT2) VelocityAngleX Velocity angle (arccos(u/q) ∈ [0,180°]) α VelocityAngleY arccos(v/q) α VelocityAngleZ arccos(w/q) α VelocityUnitVectorX x-component of velocity unit vector (q ⋅ ex / q) - VelocityUnitVectorY y-component of velocity unit vector (q ⋅ ey / q) - VelocityUnitVectorZ z-component of velocity unit vector (q ⋅ ez / q) - MassFlow Mass flow normal to a plane (&rhoq ⋅ n) M/(L2T) ViscosityKinematic Kinematic viscosity (ν = μ/ρ) L2/T ViscosityMolecular Molecular viscosity (μ) M/(LT) ViscosityEddyKinematic Kinematic eddy viscosity (νt) L2/T ViscosityEddy Eddy viscosity (μt) M/(LT) ThermalConductivity Thermal conductivity coefficient (k) ML/(T3Θ) PowerLawExponent Power-law exponent (n) in molecular viscosity or thermal conductivity model - SutherlandLawConstant Sutherland's Law constant (Ts) in molecular viscosity or thermal conductivity model Θ TemperatureReference Reference temperature (Tref) in molecular viscosity or thermal conductivity model Θ ViscosityMolecularReference Reference viscosity (μref) in molecular viscosity model M/(LT) ThermalConductivityReference Reference thermal conductivity (kref) in thermal conductivity model ML/(T3Θ) IdealGasConstant Ideal gas constant (R = cp − cv) L2/(T2Θ) SpecificHeatPressure Specific heat at constant pressure (cp) L2/(T2Θ) SpecificHeatVolume Specific heat at constant volume (cv) L2/(T2Θ) ReynoldsStressXX Reynolds stress −ρ(u′u′)ave M/(LT2) ReynoldsStressXY Reynolds stress −ρ(u′v′)ave M/(LT2) ReynoldsStressXZ Reynolds stress −ρ(u′w′)ave M/(LT2) ReynoldsStressYY Reynolds stress −ρ(v′v′)ave M/(LT2) ReynoldsStressYZ Reynolds stress −ρ(v′w′)ave M/(LT2) ReynoldsStressZZ Reynolds stress −ρ(w′w′)ave M/(LT2) MolecularWeightSymbol Molecular weight for species Symbol - HeatOfFormationSymbol Heat of formation per unit mass for species Symbol L2/T2 FuelAirRatio Fuel/air mass ratio - ReferenceTemperatureHOF Reference temperature for the heat of formation Θ MassFractionSymbol Mass of species Symbol, divided by total mass - LaminarViscositySymbol Laminar viscosity of species Symbol M/(LT) ThermalConductivitySymbol Thermal conductivity of species Symbol ML/(T3Θ) EnthalpyEnergyRatio The ratio β = h / e = ∫TTref cp dT / ∫TTref cv dT for the mixture - CompressibilityFactor The gas constant of the mixture divided by the freestream gas constant, Z = R / R∞ - VibrationalElectronEnergy Vibrational-electronic excitation energy per unit mass L2/T2 HeatOfFormation Heat of formation per unit mass for the entire mixture, H = ∑ni=1 Yi Hi, where n is the number of species, Yi is the mass fraction of species i, and Hi is the heat of formation for species i at the reference temperature ReferenceTemperatureHOF. This requires that ReferenceTemperatureHOF be specified using the ChemicalKineticsModel data structure. L2/T2 VibrationalElectronTemperature Vibrational electron temperature Θ SpeciesDensitySymbol Density of species Symbol M/L3 MoleFractionSymbol Number of moles of species Symbol divided by the total number of moles for all species - Voltage Voltage ML2/TI ElectricFieldX x-component of electric field vector ML/TI ElectricFieldY y-component of electric field vector ML/TI ElectricFieldZ z-component of electric field vector ML/TI MagneticFieldX x-component of magnetic field vector I/L MagneticFieldY y-component of magnetic field vector I/L MagneticFieldZ z-component of magnetic field vector I/L CurrentDensityX x-component of current density vector I/L2 CurrentDensityY y-component of current density vector I/L2 CurrentDensityZ z-component of current density vector I/L2 ElectricConductivity Electrical conductivity ML/T3I2 LorentzForceX x-component of Lorentz force vector ML/T2 LorentzForceY y-component of Lorentz force vector ML/T2 LorentzForceZ z-component of Lorentz force vector ML/T2 JouleHeating Joule heating ML2/T2 LengthReference Reference length L L

A.3 Turbulence Model Solution

This section lists data-name identifiers for typical Reynolds-averaged Navier-Stokes turbulence model variables. Turbulence model solution quantities and model constants present a particularly difficult nomenclature problem - to be precise we need to identify both the variable and the model (and version) that it comes from. The list in the following table falls short in this respect.

Data-Name Identifier Description Units TurbulentDistance Distance to nearest wall L TurbulentEnergyKinetic k = [(u′u′)ave + (v′v′)ave + (w′w′)ave] / 2 L2/T2 TurbulentDissipation ε L2/T3 TurbulentDissipationRate ε/k = ω T−1 TurbulentBBReynolds Baldwin-Barth one-equation model RT - TurbulentSANuTilde Spalart-Allmaras one-equation model νSA L2/T

A.4 Nondimensional Parameters

CFD codes are rich in nondimensional governing parameters, such as Mach number and Reynolds number, and nondimensional flowfield coefficients, such as pressure coefficient. The problem with these parameters is that the definitions and conditions at which they are evaluated can vary from code to code. Reynolds number is particularly notorious in this respect.

These parameters have posed a difficult dilemma for us. Either we impose a rigid definition for each and force all database users to abide by it, or we develop some methodology for describing the particular definition that the user is employing. The first limits applicability and flexibility, and the second adds complexity. We have opted for the second approach, but we include only enough information about the definition of each parameter to allow for conversion operations. For example, the Reynolds number includes velocity, length, and kinematic viscosity scales in its definition (i.e., Re = VLR/ν. The database description of Reynolds number includes these different scales. By providing these "definition components", any code that reads Reynolds number from the database can transform its value to an appropriate internal definition. These definition components are identified by appending a "_" to the data-name identifier of the parameter.

Definitions for nondimensional flowfield coefficients follow: the pressure coefficient is defined as,

cp = (ppref) / (ρrefq2ref / 2)

where ρrefq2ref / 2 is the dynamic pressure evaluated at some reference condition, and pref is some reference pressure. The skin friction coefficient is,
cf = τ / (ρrefq2ref / 2)

where τ is the shear stress or skin friction vector. Usually, τ is evaluated at the wall surface.

The data-name identifiers defined for nondimensional governing parameters and flowfield coefficients are listed in the following table.

Data-Name Identifier Description Units Mach Mach number: M = q/c - Mach_Velocity Velocity scale (q) L/T Mach_VelocitySound Speed of sound scale (c) L/T RotatingMach Mach number relative to rotating frame: Mr = qr/c - Reynolds Reynolds number: Re = VLR/ν - Reynolds_Velocity Velocity scale (V) L/T Reynolds_Length Length scale (LR) L Reynolds_ViscosityKinematic Kinematic viscosity scale (ν) L2/T Prandtl Prandtl number: Pr = μcp/k - Prandtl_ThermalConductivity Thermal conductivity scale (k) ML/(T3Θ) Prandtl_ViscosityMolecular Molecular viscosity scale (μ) M/(LT) Prandtl_SpecificHeatPressure Specific heat scale (cp) L2/(T2Θ) PrandtlTurbulent Turbulent Prandtl number, ρνtcp/kt - SpecificHeatRatio Specific heat ratio: γ = cp/cv - SpecificHeatRatio_Pressure Specific heat at constant pressure (cp) L2/(T2Θ) SpecificHeatRatio_Volume Specific heat at constant volume (cv) L2/(T2Θ) CoefPressure cp - CoefSkinFrictionX cf ⋅ ex - CoefSkinFrictionY cf ⋅ ey - CoefSkinFrictionZ cf ⋅ ez - Coef_PressureDynamic ρrefq2ref / 2 M/(LT2) Coef_PressureReference pref M/(LT2)

A.5 Characteristics and Riemann Invariants Based on 1-D Flow

Boundary condition specification for inflow/outflow or farfield boundaries often involves Riemann invariants or characteristics of the linearized inviscid flow equations. For an ideal compressible gas, these are typically defined as follows: Riemann invariants for an isentropic 1-D flow are,

[∂/∂t + (u ± c) ∂/∂x] [u ± 2c / (γ − 1)] = 0

Characteristic variables for the 3-D Euler equations linearized about a constant mean flow are,

[∂/∂t + Λn ∂/∂x] W′n(x,t) = 0     n = 1, 2, ..., 5

where the characteristics and corresponding characteristic variables are

Characteristic Λn W'n Entropy u p′ − ρ′c2 Vorticity u v′ Vorticity u w′ Acoustic u ± c p′ ± u′ρc

Primed quantities are linearized perturbations, and the remainder are evaluated at the mean flow. The only non-zero mean-flow velocity component is u. The data-name identifiers defined for Riemann invariants and characteristic variables are listed in the following table.

Data-Name Identifier Description Units RiemannInvariantPlus u + 2c / (γ − 1) L/T RiemannInvariantMinus u − 2c / (γ − 1) L/T CharacteristicEntropy p′ − ρ′c2 M/(LT2) CharacteristicVorticity1 v′ L/T CharacteristicVorticity2 w′ L/T CharacteristicAcousticPlus p′ + u′ρc M/(LT2) CharacteristicAcousticMinus p′ − u′ρc M/(LT2)

A.6 Forces and Moments

Conventions for data-name identifiers for forces and moments are defined in this section. Ideally, forces and moments should be attached to geometric components or less ideally to surface grids. Currently, the standard mechanism for storing forces and moments is generally through the ConvergenceHistory_t node, either attached to the entire configuration (under CGNSBase_t) or attached to a zone (under Zone_t).

Given a differential force f (i.e., a force per unit area), the force integrated over a surface is,

F = Fxex + Fyey + Fzez = f dA

where ex, ey and ez are the unit vectors in the x, y and z directions, respectively. The moment about a point r0 integrated over a surface is,

M = Mxex + Myey + Mzez = (rr0) × f dA

Lift and drag components of the integrated force are,

L = FL      D = FD

where L and D are the unit vectors in the positive lift and drag directions, respectively.

Lift, drag and moment are often computed in auxiliary coordinate frames (e.g., wind axes or stability axes). We introduce the convention that lift, drag and moment are computed in the (ξ, η, ζ) coordinate system. Positive drag is assumed parallel to the ξ-direction (i.e., D = eξ); and positive lift is assumed parallel to the η-direction (i.e., L = eη). Thus, forces and moments defined in this auxiliary coordinate system are,

L = Feη      D = Feξ

M = Mξeξ + Mηeη + Mζeζ = (rr0) × f dA

Lift, drag and moment coefficients in 3-D are defined as,

CL = L / (ρrefq2refSref / 2)      CD = D / (ρrefq2refSref / 2)      CM = M / (ρrefq2refcrefSref / 2)

where ρrefq2ref / 2 is a reference dynamic pressure, Sref is a reference area, and cref is a reference length. For a wing, Sref is typically the wing area and cref is the mean aerodynamic chord. In 2-D, the sectional force coefficients are,

cl = L′ / (ρrefq2refcref / 2)      cd = D′ / (ρrefq2refcref / 2)      cm = M′ / (ρrefq2refc2ref / 2)

where the forces are integrated along a contour (e.g., an airfoil cross-section) rather than a surface.

The data-name identifiers and definitions provided for forces and moments and their associated coefficients are listed in the table below. For coefficients, the dynamic pressure and length scales used in the normalization are provided.

Data-Name Identifier Description Units ForceX Fx = F ⋅ ex ML/T2 ForceY Fy = F ⋅ ey ML/T2 ForceZ Fz = F ⋅ ez ML/T2 ForceR Fr = F ⋅ er ML/T2 ForceTheta Fθ = F ⋅ eθ ML/T2 ForcePhi Fφ = F ⋅ eφ ML/T2 Lift L or L' ML/T2 Drag D or D' ML/T2 MomentX Mx = M ⋅ ex ML2/T2 MomentY My = M ⋅ ey ML2/T2 MomentZ Mz = M ⋅ ez ML2/T2 MomentR Mr = M ⋅ er ML2/T2 MomentTheta Mθ = M ⋅ eθ ML2/T2 MomentPhi Mφ = M ⋅ eφ ML2/T2 MomentXi Mξ = M ⋅ eξ ML2/T2 MomentEta Mη = M ⋅ eη ML2/T2 MomentZeta Mζ = r ⋅ eζ ML2/T2 Moment_CenterX x0 = r0 ⋅ ex L Moment_CenterY y0 = r0 ⋅ ey L Moment_CenterZ z0 = r0 ⋅ ez L CoefLift CL or cl - CoefDrag CD or cd - CoefMomentX CM ⋅ ex or cm ⋅ ex - CoefMomentY CM ⋅ ey or cm ⋅ ey - CoefMomentZ CM ⋅ ez or cm ⋅ ez - CoefMomentR CM ⋅ er or cm ⋅ er - CoefMomentTheta CM ⋅ eθ or cm ⋅ eθ - CoefMomentPhi CM ⋅ eφ or cm ⋅ eφ - CoefMomentXi CM ⋅ eξ or cm ⋅ eξ - CoefMomentEta CM ⋅ eη or cm ⋅ eη - CoefMomentZeta CM ⋅ eζ or cm ⋅ eζ - Coef_PressureDynamic ρrefq2ref / 2 M/(LT2) Coef_Area Sref L2 Coef_Length cref L

A.7 Time-Dependent Flow

Data-name identifiers related to time-dependent flow include those associated with the storage of grid coordinates and flow solutions as a function of time level or iteration. Also included are identifiers for storing information defining both rigid and arbitrary (i.e., deforming) grid motion.

Data-Name Identifier Data Type Description Units TimeValues real Time values T IterationValues int Iteration values - NumberOfZones int Number of zones used for each recorded step - NumberOfFamilies int Number of families used for each recorded step - ZonePointers char Names of zones used for each recorded step - FamilyPointers char Names of families used for each recorded step - RigidGridMotionPointers char Names of RigidGridMotion structures used for each recorded step for a zone - ArbitraryGridMotionPointers char Names of ArbitraryGridMotion structures used for each recorded step for a zone - GridCoordinatesPointers char Names of GridCoordinates structures used for each recorded step for a zone - FlowSolutionPointers char Names of FlowSolution structures used for each recorded step for a zone - OriginLocation real Physical coordinates of the origin before and after a rigid grid motion L RigidRotationAngle real Rotation angles about each axis of the translated coordinate system for rigid grid motion α RigidVelocity real Grid velocity vector of the origin translation for rigid grid motion L/T RigidRotationRate real Rotation rate vector about the axis of the translated coordinate system for rigid grid motion α/T GridVelocityX real x-component of grid velocity L/T GridVelocityY real y-component of grid velocity L/T GridVelocityZ real z-component of grid velocity L/T GridVelocityR real r-component of grid velocity L/T GridVelocityTheta real θ-component of grid velocity α/T GridVelocityPhi real φ-component of grid velocity α/T GridVelocityXi real ξ-component of grid velocity L/T GridVelocityEta real η-component of grid velocity L/T GridVelocityZeta real ζ-component of grid velocity L/T