TRACE User Guide  TRACE Version 9.6.1
Variable Names for I/O

This gives an overview of the variable names used by TRACE using the Nomenclature and Subscripts. Definitions and some explanations are given in Details.

Name Symbol Unit Description
AeroDamping \(\delta\) - Aerodynamic damping for a structural mode.
AeroExcitation \(\epsilon\) - Aerodynamic excitation (in the context of forced response analysis).
AeroExcitationScaled \(\epsilon_{scaled}\) - Aerodynamic excitation (in the context of forced response analysis) scaled by the AmplificationFactor used during the mapping process of the eigenmode displacements. The scaled excitation is the aerodynamic excitation with respect to the unscaled eigenmode displacements.
AeroStiffness \(\kappa\) - Aerodynamic stiffness for a structural mode.
AeroStimulus \(S\) - Aerodynamic stimulus.
AeroStimulusSigned \(S_{\mathrm{signed}}\) - Aerodynamic stimulus with respect to the signed mean aerodynamic forces.
AeroWork \(W_\mathrm{cyc}\) \(\N\m\) Work per cycle exerted by the aerodynamic forces for an eigenmode \(\Psi\).
AeroWorkL1Norm \(\left\|dW_\mathrm{cyc}/dS \right\|_{L^1}\) \(\N\m\) \(L^1\)-norm of the work per cycle and area.
AeroWorkModulus \(\left\|W_\mathrm{cyc}\right\|\) \(\N\m\) Absolute value of (complex) work per cycle exerted by the aerodynamic forces for an eigenmode \(\Psi\).
AeroWorkMeanPressurePart \(W_\mathrm{cyc,mp}\) \(\N\m\) Part of the modal work per cycle which is due to the mean pressure.
AeroWorkPerArea \(dW_\mathrm{cyc}/dS\) \(\kg/\s^{2}\) Work per cycle and area exerted by the aerodynamic forces for an eigenmode \(\Psi\).
AngularMomentumFlux - \(\kg \, \m^2 \, \s^{-2}\) -
AreaRatio - - Relation between outflow and inflow throughflow surface area.
Chord \(c\) \(\m\) -
ChordAxial \(c_x\) \(\m\) -
CoefAreaRotationSpeedSquare \(C_\mathrm{ars}\) \(\m^2/\s^2\) -
CoefDiffusion \(DF\) - Diffusion coefficient - loading criterion for compressors. \(s/c\) is the mean pitch/chord ratio (hub, tip) of the current blade row.
CoefEntropyRise \(C_{\Delta s}\) - -
CoefFlowAxial \(\Phi_x\) - Axial component of flow coefficient.
CoefLossScholzV1 \(\omega_{\Scholz 1}\) - Loss coefficient after Scholz (1).
CoefLossScholzV2 \(\omega_{\Scholz 2}\) - Loss coefficient after Scholz (2). \(h_{\outflow,\is}\) is computed from the absolute total pressure and enthalpy at inlet and the static pressure at outlet.
CoefPressure \(c_p\) - -
CoefPressureStagDiffDyn \(\omega\) - Total pressure loss coefficient in relative frame of reference based on dynamic pressure. Compressors: reference is inlet, turbines: reference is outlet
CoefPressureStagDiffDynAbs \(\omega_{\abs}\) - Total pressure loss coefficient in absolute frame of reference based on dynamic pressure. Compressors: reference is inlet, turbines: reference is outlet
CoefPressureStagDiffDynTh \(\omega_{\mathrm{theoretic}}\) - Total pressure loss coefficient in relative frame of reference normalized using the theoretic dynamic pressure.
CoefPressureStagDiffStag \(\omega_{\tot}\) - Total pressure loss coefficient in relative frame of reference based on dynamic pressure. Compressors: reference is outlet, turbines: reference is inlet
CoefPressureStagDiffStagAbs \(\omega_{\tot, \abs}\) - Total pressure loss coefficient in absolute frame of reference based on total pressure. Compressors: reference is outlet, turbines: reference is inlet
CoefPressureStagIsLossDyn \(\zeta_{\tot, \is}\) - Isentropic total pressure loss coefficient in relative frame of reference based on dynamic pressure. Compressors: Reference is inlet, turbines: Reference is outlet
CoefPressureStagIsLossDynAbs \(\zeta_{\tot, \abs, \is}\) - Isentropic total pressure loss coefficient in absolute frame of reference based on dynamic pressure. Compressors: reference is inlet, turbines: reference is outlet
CoefPressureStagLossDyn \(\zeta_{\tot}\) - Total pressure loss coefficient in relative frame of reference based on dynamic pressure. Compressors: Reference is inlet, turbines: Reference is outlet
CoefPressureStagLossDynAbs \(\zeta_{\tot, \abs}\) - Total pressure loss coefficient in absolute frame of reference based on dynamic pressure. Compressors: reference is inlet, turbines: reference is outlet
CoefSkinFriction \(c_f\) - Wall skin friction coefficient.
CoefVelocityMean \(c_{v,\mean}\) - -
CoefVelocityRatio \(c_{v,\mathrm{ratio}}\) - -
CoefWork \(\psi\) - Work coefficient or enthalpy rise coefficient. \(r_{\mean}\) is the arithmetic mean of the mass averaged radius at in- and outlet.
CoefWork2 \(\psi_2\) - Alternative definition for work coefficient.
CoefWorkIsentropic \(\psi_{\is}\) - Isentropic work coefficient or isentropic enthalpy rise coefficient.
CoefWorkIsentropic2 \(\psi_{\is,2}\) - Alternative definition for isentropic work coefficient.
CoefZweifel \(C_{\Zweifel}\) \(\m^2\) Blade loading criterion for turbines.
CoordinateMeanRTheta \(r_{mean}\Theta\) \(\m\) Turbomachinary coordinate which consists of the mean radius and local theta coordinate.
CoordinateR \(r\) \(\m\) Radial, normally spanwise, coordinate.
CoordinateTheta \(\theta\) - Pitchwise coordinate.
CoordinateX \(x\) \(\m\) Cartesian coordinate x. Turbomachines: axial direction.
CoordinateY \(y\) \(\m\) Cartesian coordinate y.
CoordinateZ \(z\) \(\m\) Cartesian coordinate z.
CoordinateXi \(\xi\) - Normalised coordinate in streamwise direction.
CoordinateEta \(\eta\) - Normalised coordinate in spanwise direction.
DeHaller \(DH\) - Simple blade loading criterion for compressors.
Density \(\rho\) \(\kg/\m^3\) Density of fluid.
DiffusorExitPressureStagAbs \(p_{\tot, \abs, \Diff, \outflow}\) \(Pa\) If the diffusor is not part of the computational mesh the absolute total pressure at the exit of the diffusor has to be given to determine the efficiency of the turbine-diffusor combination.
DisplacementX \(\delta x\) \(\m\) \(x\) component of grid point displacement (difference of coordinates)
DisplacementY \(\delta y\) \(\m\) \(y\) component of grid point displacement (difference of coordinates)
DisplacementZ \(\delta z\) \(\m\) \(z\) component of grid point displacement (difference of coordinates)
DisplacementMagnitude \(\delta xyz\) \(\m\) Magnitude of grid point displacement (difference of coordinates)
DistanceWallCoordinate \(y^+\) - Dimensionless wall distance computed from the distance \(d\) to the nearest viscous wall. The friction velocity is given by \(u_\tau = \sqrt{\tau_w / \rho}\) with the wall shear stress \(\tau_w\).
EfficiencyIsentropicH \(\eta_{\is}\) - Isentropic efficiency defined for rotors, stages, groups, turbomachines.
EfficiencyIsentropicHLeak \(\eta_{\is,\leak}\) - Isentropic efficiency defined for rotors, stages, groups, turbomachines.
EfficiencyIsentropicHMLeak \(\eta_{\is,\mleak}\) - -
EfficiencyIsentropicHWoLeak \(\eta_{\is,\noleak}\) - Isentropic efficiency defined for rotors, stages, groups, turbomachines.
EfficiencyIsentropicSwirl \(\eta_{\is,\swirl}\) - Isentropic efficiency based on swirl (rotors, stages, groups, turbomachines).
EfficiencyIsInclDiffusor \(\eta_{\is,\noleak,\Diff}\) - Isentropic efficiency including the total pressure loss in the diffusor.
EfficiencyIsLeaksDiffusor \(\eta_{\is,\leak,\Diff}\) - Isentropic efficiency including the total pressure loss in the diffusor.
EfficiencyPolytropic \(\eta_{\pol}\) - Polytropic efficiency.
EfficiencyPolyInclDiffusor \(\eta_{\pol,\Diff}\) - Polytropic efficiency computed from inlet stagnation values, exit stagnation temperature and a user defined exit stagnation pressure, to account for the additional losses of a diffusor which is not part of the configuration.
EnergyDensityStagnation - \(\N \m^{-2}\) -
EnergyDensityStagnationAbs - \(\N \m^{-2}\) -
Enthalpy \(h\) \(\m^2/\s^2\) -
EnthalpyStagnation \(h_{\tot}\) \(\m^2/\s^2\) Relative stagnation enthalpy.
EnthalpyStagnationAbs \(h_{\tot,\abs}\) \(\m^2/\s^2\) Absolute stagnation enthalpy.
EnthalpyStagnationRot \(h_\tot\) \(\m^2/\s^2\) Relative total enthalpy.
Entropy \(s\) \(\m^2/(\K\s^2)\) Entropy of fluid.
FactorSwirl - - -
FlowDirectionR - - Radial component of velocity direction vector in cylindrical coordinates.
FlowDirectionTheta - - Circumferential component of velocity direction vector in cylindrical coordinates.
FlowDirectionThetaAbs - - Circumferential component of absolute velocity direction vector in cylindrical coordinates.
FlowDirectionX - - Axial ( \(x\)) component of velocity direction vector.
FlowDirectionY - - \(y\) component of velocity direction vector in cartesian coordinates.
FlowDirectionYAbs - - \(y\) component of absolute velocity direction vector in cartesian coordinates.
FlowDirectionZ - - \(z\) component of velocity direction vector in cartesian coordinates.
FlowTurningAlpha - \(\degree\) Relative pitchwise flow turning based on \(\alpha_{\Theta,\MTU}\). Turbine: no absolute value !
FlowTurningAlphaAbs - \(\degree\) Absolute pitchwise flow turning based on \(\alpha_{\Theta,\MTU,\abs}\). Turbine: no absolute value !
FlowTurningAlphaZ - \(\degree\) Relative pitchwise flow turning based on \(\alpha_{\z}\). Turbine: no absolute value !
FlowTurningAlphaZAbsOK - \(\degree\) Absolute pitchwise flow turning based on \(\alpha_{\z,\abs}\). Turbine: no absolute value !
FlowTurningMeridional - \(\degree\) Radial flow turning based on \(\alpha_r\).
FlowTurningTheta - \(\degree\) Pitchwise flow turning in relative frame of reference. Turbine: no absolute value !
FlowTurningThetaAbs - \(\degree\) Pitchwise flow turning in absolute frame of reference. Turbine: no absolute value !
FractionSpecificWork - - Specific work of a rotor divided by the specific work of a contol volume (stage, component, volume)
FrameVelocityTheta - \(\m/\s\) Velocity of rotating frame of reference at the reference radius, e.g., the mass averaged radius.
FrequencyShift \(\delta f\) \(1/\s\) Frequency shift of an eigenmode due to aerodynamic stiffness \(\kappa\).
FrequencyUpdate \(f\) \(1/\s\) Updated (guessed) frequency from a coupled FSI flutter simulation in the frequency domain.
Gamma \(\gamma\) - Transported variable in \(\gamma\)- \(Re_\theta\) transition model.
IdealGasConstant \(R\) \(\J \cdot \kg^{-1} \cdot \K^{-1}\) Specific gas constant.
Mach \(M\) - Mach number in relative frame of reference.
MachAbs \(M_{\abs}\) - Mach number in absolute frame of reference.
MachIsentropic \(M_{\is}\) - Isentropic Mach number.
MachMeridional \(M_{\mer}\) - Meridional Mach number.
MachRot \(M_{\rot}\) - Relative Mach number computed from the absolute velocities, the rotational speed, and the reference radius.
MassFlow \(\dot{m}\) \(\kg/\s\) -
MassFlowCorrected \(\dot{m}_\mathrm{ISA}\) \(\kg/\s\) Mass flow corrected via ISA conditions: \(p_{\Reference}\) = 101325 Pa, \(T_{\Reference}\) = 288.15 K.
MassFlowDefect \(\zeta\) - Mass flow defect.
MassFlowReduced \(\dot{m}_{\red}\) \(\m\s\K^{\frac{1}{2}}\) Reduced mass flow rate.
MassFlowUnsigned \(\left\|\dot{m}\right\|\) \(\kg/\s\) -
MixingLossPressureStagnation \(\omega_{mix}\) - Mixing loss computed as total pressure loss. \(p_\tot\) and \(p\) refer to the average reference value under consideration (e.g. flux average), \(\overline{p}_\tot^W\) is the so-called work average, cf. [8].
MomentumDensityMeridRatio - - Meridional velocity density ratio.
MomentumDensityR - \(\kg \cdot \m^{-2}\cdot \s^{-1}\) Radial component of the momentum density.
MomentumDensityTheta - \(\kg \cdot \m^{-2}\cdot \s^{-1}\) Circumferential component of the relative momentum density.
MomentumDensityThetaAbs - \(\kg \cdot \m^{-2}\cdot \s^{-1}\) Circumferential component of the absolute momentum density.
MomentumDensityX - \(\kg \cdot \m^{-2}\cdot \s^{-1}\) Axial component of the momentum density.
NormalX \(n_x\) - \(x\) component of face normal vector
NormalY \(n_y\) - \(y\) component of face normal vector
NormalZ \(n_z\) - \(z\) component of face normal vector
NumberOfAirfoils \(n_{\blades}\) - Number of blades across annulus.
NumberOfSegments \(n_{\segments}\) - Number of segments across annulus.
Pitch \(s\) \(\m\) Blade pitch for turbomachines and linear cascades.
PitchChordRatio - - Pitch to chord ratio for turbomachines and linear cascades.
PowerHLeak \(P_{\htot,\leak}\) \(\W\) Overall power output accounting for all bleeds and leaks.
PowerHMLeak \(P_{\htot,\mleak}\) \(\W\) Overall power output accounting for all main bleeds and leaks.
PowerHWoLeak \(P_{\htot,\noleak}\) \(\W\) Overall power output based on main inlets and outlets only.
PowerIsentropicHLeak \(P_{\htot,\is,\leak}\) \(\W\) Overall {isentropic} power output accounting for all bleeds and leaks.
PowerIsentropicHMLeak \(P_{\htot,\is,\mleak}\) \(\W\) Overall {isentropic} power output accounting for all main bleeds and main leaks.
PowerIsentropicHWoLeak \(P_{\htot,\is,\noleak}\) \(\W\) Overall isentropic power output {without} accounting for bleeds and leaks.
PowerReducedHLeak \(P_{\red,\leak}\) \(\W/(\Pa \sqrt{\K})\) -
PowerSwirl \(P_{\swirl}\) \(\W\) -
Pressure \(p\) \(\Pa\) Static pressure.
PressureNormalized \(p^*\) - Normalized pressure.
PressureRatio \(\pi\) - Static pressure ratio.
PressureStagnation \(p_{\tot}\) \(\Pa\) Stagnation or total pressure in {relative} frame of reference.
PressureStagnationAbs \(p_{\tot,\abs}\) \(\Pa\) Stagnation or total pressure in {absolute} frame of reference.
PressureStagnationAbsRatio \(\pi_{\tot,\abs}\) - Stagnation or total pressure ratio in {absolute} frame of reference.
PressureStagnationRatio \(\pi_{\tot}\) - Stagnation or total pressure ratio in {relative} frame of reference.
PressureStagnationRot \(p_{\tot,\rot}\) \(\Pa\) Relative total pressure.
PressureStaticStagAbsRatio \(\pi_{\mathrm{s},\tot,\abs}\) - Static to total pressure ratio in absolute frame of reference.
ReactionEnthalpy \(\rho_h\) - -
ReactionPressure \(\rho_p\) - -
ReactionVelocity \(\rho_v\) - -
RelativeArcLength \(s_{\rel}\) - Relative arc length of a point on a spatial curve.
RelativeChannelHeight \(H_{\rel}\) - Relative channel height in S3 direction.
RelativeChord \(c^*\) - Coordinate \(x_c\) in chordwise direction.
RelativeChordAxial \(c_{\x}^*\) - Coordinate \(x - x_{\LE}\) in axial direction normalised with axial chord length \(c_{x}\).
RelativeChordRadial \(c_{r}^*\) - Relative chord in terms of radial coordinate \(r\).
RelativeCoordinateR \(r_{\rel}\) - Relative radial coordinate.
RelativeMassFlow \(\dot{m}_{\rel}\) - Relative mass flow rate across blade span - h=0: hub, h=H: shroud
RelativeMeridionalLength \(s_{\mer}^*\) - With \(\Delta s_{\mer} = \sum_\LE\sqrt{\Delta x^2 + \Delta r^2} = \sum_\LE\sqrt{(x - x_{\LE})^2 + (r - r_{\LE})^2}\) and \(S_{\mer} = \sum_\LE^\TE \Delta s_{\mer}\)
RelativePressure \(p_{\rel}\) - Relative pressure \(p/p_{\steady}\) in terms of the pressure field from the steady solution \(p_{\steady}\).
RelativeTemperature \(T_{\rel}\) - Relative temperature \(T/T_{\steady}\) in terms of the temperature field from the steady solution \(T_{\steady}\).
RelativeVelocityMeridMag \(v_{\mer,\rel}\) - Relative meridional velocity \(v_{\mer}/v_{\mer,\steady}\) in terms of the meridional velocity field from the steady solution \(v_{\mer,\steady}\).
ReTheta \(Re_\theta\) - Transported variable in \(\gamma\)- \(Re_\theta\) transition model.
ReynoldsInflow \(Re\) or \(Re_\inflow\) - Reynolds number based on inflow conditions, used primarily in compressors.
ReynoldsOutflow \(Re\) or \(Re_\outflow\) - Reynolds number based on outflow conditions, used primarily in turbines.
RotatingFrameVelocityTheta - \(\m/\s\) Frame velocity of rotating system.
RotationSpeed - \(1/\s\) Rotational speed of relative system in rounds per second.
RotationSpeedReduced - \(1/(s \sqrt{\K})\) Reduced wheel speed of rotor.
ShapeFactor12 \(H_{\12}\) - Boundary layer shape factor: displacement thickness / momentum thickness.
ShapeFactor32 \(H_{\32}\) - Boundary layer shape factor: energy thickness / momentum thickness.
ShearStressWall \(\tau_w\) \(Pa\) In POST and in the 2D-TRACE.cgns of the unstructured solver of TRACE, the absolute value of the shear stress will be used. In structured TRACE, the direction is determined from the x-component of the tangential velocity.
SpatialAverageType - - Averaging type: \(0=\)flux, \(1=\)mass, \(2=\)area
SpecificHeatPressure \(c_p\) \(\m^2/(\s^2 \K)\) Specific heat capacity at constant pressure.
SpecificHeatRatio \(\kappa\) - Ratio of specific heats or heat capacity ratio.
SpecificWorkH \(w\) \(\J/\kg\) Specific work of turbomachine or turbomachine component.
SpecificWorkSwirl \(w_{\swirl}\) \(\J/\kg\) Specific work based on swirl.
SwirlAbs \(K_{\abs}\) \(\m^2/\s\) Flow swirl in absolute frame of reference.
Temperature \(T\) \(\K\) Static temperature of flow.
TemperatureRothalpy \(T_{\rot}\) \(\K\) -
TemperatureStagAbsRatio \(\tau_{\abs}\) - Total temperature ratio in absolute frame of reference.
TemperatureStagnation \(T_{\tot}\) \(\K\) Total temperature in relative frame of reference.
TemperatureStagnationAbs \(T_{\tot, \abs}\) \(\K\) Total temperature in absolute frame of reference.
TemperatureStagnationAbsDiff \(\Delta T_{\tot, \abs}\) \(\K\) Difference in total temperature in absolute frame of reference.
TemperatureStagnationRot \(T_{\tot,\rot}\) \(\K\) Relative total temperature.
TemperatureStagRatio \(\tau\) - Total temperature ratio in relative frame of reference.
ThicknessBoundaryLayer \(\delta\) \(\m\) Boundary layer thickness based on \(p_t\)-criterion. Edge is defined as point where \(p_t = 0.995 p_{t, \mathrm{max}}.\)
ThicknessDisplacement \(\delta_1\) \(\m\) Boundary layer displacement thickness.
ThicknessDisplacementInc \(\delta_{1, \mathrm{inc}}\) \(\m\) Boundary layer displacement thickness incompressible formulation.
ThicknessEnergy \(\delta_3\) \(\m\) Boundary layer energy thickness.
ThicknessMomentum \(\delta_2\) \(\m\) Boundary layer momentum thickness.
ThicknessMomentumInc \(\delta_2\) \(\m\) Boundary layer momentum thickness incompressible formulation.
TurbulentDissipationRate \(\omega\) \(1/\s\) Turbulent dissipation rate.
TurbulentDistance \(d\) \(\m\) Distance to nearest viscous wall.
TurbulentEnergyKinetic \(k\) \(\m^2 / \s^2\) Turbulent kinetic energy.
TurbulenceIntensity \(Tu\) - Turbulence level or turbulence intensity of fluid with turbulent kinetic energy \(k\) and velocity magnitude \(v\).
TurbulenceIntensityAbs \(Tu_{abs}\) - Turbulence level or turbulence intensity of fluid with turbulent kinetic energy \(k\) and velocity magnitude \(v_\abs\) in absolute frame of reference.
TurbulentLengthScale \(L_T\) \(\m\) Turbulent length scale corresponding to turbulent kinetic energy \(k\) and specific turbulent dissipation rate \(\omega\) (as used in Wilcox and Menter \(\omega\)-equation).
VelocityAngleAlpha \(\alpha^*_{\Theta}\) \(\degree\) Azimuthal or pitchwise flow angle.
VelocityAngleAlphaAbs \(\alpha^*_{\Theta,\abs}\) \(\degree\) Absolute azimuthal or pitchwise flow angle.
VelocityAngleAlphaZ \(\alpha_{z}\) \(\degree\) Azimuthal or pitchwise flow angle with respect to the axial velocity.
VelocityAngleAlphaZAbs \(\alpha_{\z,\abs}\) \(\degree\) Absolute azimuthal or pitchwise flow angle with respect to the axial velocity.
VelocityAngleEpsilon \(\epsilon\) \(\degree\) Radial flow angle.
VelocityAngleEpsilonCylAbs \(\epsilon_{\cyl,\abs}\) \(\degree\) Radial flow angle.
VelocityAngleR \(\alpha_r\) \(\degree\) Radial flow angle.
VelocityAngleTheta \(\alpha_{\theta}\) \(\degree\) Azimuthal or pitchwise angle defined as angle between the velocity and the meridional velocity.
VelocityAngleThetaAbs \(\alpha_{\theta,\abs}\) \(\degree\) Absolute azimuthal or pitchwise flow angle defined as angle between the absolute velocity and the meridional velocity.
VelocityAngleY \(\alpha_{y}\) \(\degree\) Angle between y- and x-component of velocity vector in relative frame of reference.
VelocityAngleYAbs \(\alpha_{y,\abs}\) \(\degree\) Angle between y- and x-component of velocity vector in absolute frame of reference.
VelocityAngleZ \(\alpha_{z}\) \(\degree\) Angle between z- and x-component of velocity vector.
VelocityMeridionalMagnitude \(\left\|{v_{mer}}\right\|\) \(\m/\s\) Norm of the vector of the meridional velocity \(v_{\mer}\).
VelocityMagnitude \(v\) \(\m/\s\) Magnitude of relative velocity vector.
VelocityMagnitudeAbs \(v_\abs\) \(\m/\s\) Magnitude of absolute velocity vector.
VelocityMagnitudeRot \(v_{\rot}\) \(\m/\s\) Relative velocity magnitude
VelocityR \(v_r\) \(\m/\s\) Velocity component in \(r\)-wise (radial) direction.
VelocityRatio \(\frac{v_{\outflow}} {v_{\inflow}}\) - Deceleration ratio - loading criterion for compressors.
VelocitySound \(a\) \(\m/\s\) Speed of sound.
VelocityTheta \(v_{\theta}\) \(\m/\s\) Velocity component in pitchwise direction
VelocityThetaAbs \(v_{\theta, \abs}\) \(\m/\s\) Velocity component in pitchwise direction for absolute frame of reference.
VelocityThetaRot \(v_{\theta, rot}\) \(\m/\s\) Wheel velocity component in pitchwise direction
VelocityX \(v_x\) \(\m/\s\) Velocity component in \(x\)-wise direction.
VelocityXAbs \(v_{x, \abs}\) \(\m/\s\) Velocity component in \(x\)-wise direction for absolute frame of reference.
VelocityY \(v_y\) \(\m/\s\) Velocity component in \(y\)-wise direction.
VelocityYAbs \(v_{y, \abs}\) \(\m/\s\) Velocity component in \(y\)-wise direction for absolute frame of reference.
VelocityZ \(v_z\) \(\m/\s\) Velocity component in \(z\)-wise direction.
VelocityZAbs \(v_{z, \abs}\) \(\m/\s\) Velocity component in \(z\)-wise direction for absolute frame of reference.
ViscosityEddy \(\mu_{T}\) \(\kg/(\m\s)\) Eddy viscosity as returned by active turbulence model.
ViscosityEddyRatio - - Eddy viscosity normalised by local molecular viscosity.
ViscosityKinematic \(\nu\) \(\m^2/\s\) Kinematic fluid viscosity.
ViscosityMolecular \(\mu\) \(\kg/(\m\s)\) Molecular fluid viscosity.
VorticityNorm \(W_{norm}\) \(1/\s\) Vorticity vector and its norm
WaveNumberTheta \(m\) - Circumferential wave number.
WaveNumberY \(k_y\) \(1 / \m\) Wave number in \(y\) direction.
WorkReduced \(W_{\red}\) \(\J/(\kg\K)\) Reduced work.
Zweifel \(\Zweifel\) \(\m\) Loading criterion for turbines.

Nomenclature

Name Description Unit
\(A\) Area \(\m^2\)
\(C\) Coefficient \(-\)
\(DF\) Diffusion factor \(-\)
\(DH\) De Haller number \(-\)
\(E\) Modal energy \(\N\m\)
\(H\) Enthalpy \(\mathrm{J}\)
Blade span, channel height \(\m\)
Boundary layer parameter \(-\)
\(K\) Swirl of fluid \(\m^2/\s\)
\(L\) Length \(\m\)
\(M\) Mach number \(-\)
\(MVDR\) Meridional velocity density ratio \(-\)
\(Nu\) Nusselt number \(-\)
\(P\) Power \(\W\)
\(R\) Gas constant \(\m^2/\s^2\)
\(Re\) Reynolds number \(-\)
\(S\) Entropy \(\N\m/\K\)
Overall arc length \(\m\)
\(T\) Temperature \(\K\)
\(Tu\) Turbulence level \(-\)
\(W\) Work \(\N\m\)
\(\Zweifel\) Zweifel number \(-\)
\(a\) Speed of sound \(\m/\s\)
\(c\) Blade chord length \(\m\)
\(c_{f}\) Skin friction coefficient \(-\)
\(c_{p}\) Specific heat at constant pressure \(\m^2/(\K\s^2)\)
Pressure coefficient \(-\)
\(c_{v}\) Specific heat at constant volume \(\m^2/(\K\s^2)\)
\(d\) Distance \(\m\)
\(e\) Specific internal energy \(\m^2/\s^2\)
\(h\) Specific enthalpy \(\m^2/\s^2\)
Blade height counting from hub \(\m\)
\(k\) Turbulent kinetic energy \(\m^2/\s^2\)
\(\dot{m}\) Mass flux \(\kg/\s\)
\(n_{\blades}\) Number of blades \(-\)
\(\vec n\) Outward pointing unit normal \(-\)
\(p\) Pressure \(\Pa\)
\(q\) Dynamic Pressure \(\Pa\)
\(r\) Radius, radial coordinate \(r\) (cylindrical coordinates) \(\m\)
\(s\) Specific entropy \(\m^2/(\K\s^2)\)
Blade pitch \(\m\)
Arc length \(\m\)
\(\mathbf{v}\) Velocity (vector) \(\m/\s\)
\(v\) Velocity (magnitude) \(\m/\s\)
\(v_\abs\) Absolute velocity (magnitude) \(\m/\s\)
\(v_\mer\) Meridional velocity component \(\m/\s\)
\(v_x, v_r, v_\theta\) Cylindrical velocity components \(\m/\s\)
\(w\) Specific work \(\J/\kg\)
\(x\) Cartesian coordinate \(x\) \(\m\)
\(y\) Cartesian coordinate \(y\) \(\m\)
\(z\) Cartesian coordinate \(z\) \(\m\)
\(\theta\) Angular coordinate (Cylindrical coordinates) \(-\)
\(y^+\) Dimensionless wall distance \(-\)
\(\alpha_{\theta}, \alpha_{z}, \alpha^*_{\theta}\) Circumferential (azimuthal, pitchwise) flow angles \(\degree\)
\(\alpha_r\) Radial or spanwise flow angle \(\degree\)
\(\epsilon, \epsilon_{\cyl,\abs}\) Radial or spanwise flow angle \(\degree\)
\(\delta\) Boundary layer thickness \(\m\)
\(\delta_1\) Boundary layer displacement thickness \(\m\)
\(\delta_2\) Boundary layer momentum thickness \(\m\)
\(\delta_3\) Boundary layer energy thickness \(\m\)
\(\Gamma\) Blade surface \(\m^2\)
\(\kappa\) Ratio of specific heats \(-\)
\(\epsilon\) Radial or spanwise flow angle \(\degree\)
\(\omega\) Total pressure loss coefficient \(-\)
\(\Omega\) Angular frequency \(\s^{-1}\)
Rotational speed (radian per time) \(\s^{-1}\)
\(\Phi\) Flow coefficient \(-\)
\(\Psi\) Work coefficient \(-\)
Eigenmode \(\m\)
\(\zeta\) Mass flow defect \(-\)
Loss coefficient \(-\)
\(\mu\) Dynamic viscosity of fluid \(\kg/(\m\s)\)
\(\nu\) Molecular viscosity \(\m^2/\s\)
\(\xi\) Normalised streamwise coordinate \(-\)
\(\eta\) Normalised spanwise coordinate \(-\)
Efficiency \(-\)
\(\pi\) Pressure ratio \(-\)
\(\rho\) Fluid density \(\kg/\m^3\)
\(\tau\) Temperature ratio \(-\)
Shear stress \(\Pa\)
\(\tau_w\) Shear stress wall \(\Pa\)

Subscripts

Name Description
\(\LE\) Blade leading edge
\(\TE\) Blade trailing edge
\(\T\) Turbulent
\(\Zweifel\) Zweifel
\(\abs\) Absolute frame of reference
\(\ax\) Axial component of the corresponding quantity
\(\blades\) Blade
c Chordwise oriented coordinate system
\(\cool\) Cooling flows
\(\Diff\) Diffuser
\(\htot\) Defined via total enthalpy
\(\inflow\) Inflow location
\(\is\) Isentropic property
\(\leak\) Leakage flow
\(\mbleed\) Main bleeds
\(\mcool\) Main cooling flows
\(\mleak\) Main leaks
\(\mean\) Mean value
\(\mer\) Meridional
\(\noleak\) Without leakage flow
\(\outflow\) Outflow location
\(\pol\) Polytropic property
r Radial direction
\(\red\) Reduced value
\(\Ref\) Reference value
\(\rel\) Quantity related to a reference value
\(\rot\) Defined via rothalpy of fluid
\(\rotor\) Value for the rotor (of a domain)
s Static property
\(\steady\) Value of steady flow field
\(\swirl\) Based on swirl
\(\tan\) Tangential to solid body
\(\tot\) Total property
\(\wall\) Wall location
\(\theta\) Pitchwise
12 Boundary layer relation - \(\delta_1 : \delta_2\)
32 Boundary layer relation - \(\delta_3 : \delta_2\)
* Normalised quantity