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Physical-Definition.md

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Physical Definition
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The physical definition of a case includes the definition of the free-stream, the reference values and the non-dimensionalization. SU2 offers different ways of setting and computing this definition. This document gives a short overview on the config options and their physical relation.

Reference Values

Solver Version
EULER, NAVIER_STOKES, RANS, INC_EULER, INC_NAVIER_STOKES, INC_RANS, FEM_EULER, FEM_NAVIER_STOKES 7.0.0

The following table depicts the reference values used by most of the solvers in SU2. The highlighted variables vary depending on the actual solver and the user input.

Variable Unit Reference
Length $$m$$ $$l_{ref} = 1$$
Density $$\frac{kg}{m^3}$$ $$\rho_{ref}$$ (based on user input)
Velocity $$\frac{m}{s}$$ $$v_{ref}$$ (based on user input)
Temperature $$K$$ $$T_{ref}$$ (based on user input)
Pressure $$Pa$$ $$p_{ref}$$ (based on user input)
Viscosity $$\frac{kg}{ms}$$ $$\mu_{ref} = \rho_{ref}v_{ref}l_{ref}$$
Time $$s$$ $$t_{ref} = \frac{l_{ref}}{v_{ref}}$$
Heatflux $$\frac{W}{m^2}$$ $$Q_{ref} = \rho_{ref}v^3_{ref} $$
Gas Constant $$\frac{m^2}{s^2 K}$$ $$R_{ref} = \frac{v^2_{ref}}{T_{ref}}$$
Conductivity $$\frac{W}{mK}$$ $$k_{ref} = \mu_{ref}R_{ref}$$
Force $$N$$ $$ F_{ref} = \rho_{ref}v^2_{ref}l^2_{ref} $$

Free-Stream Definition (Compressible)

Solver Version
EULER, NAVIER_STOKES, RANS,FEM_EULER, FEM_NAVIER_STOKES 7.0.0

The physical definition for the compressible solvers in SU2 based around the definition of the free-stream. The free-stream values are not only used as boundary conditions for the MARKER_FAR option, but also for initialization and non-dimensionalization. That means even if you don't have any farfield BCs in your problem, it might be important to prescribe physically meaningful values for the options.

Thermodynamic State

The thermodynamic state of the free-stream is defined by the pressure $$p_{\infty}$$, the density $$\rho_{\infty}$$ and the temperature $$T_{\infty}$$. Since these quantities are not independent, only two of these values have to be described and the third one can be computed by an equation of state, depending on the fluid model used. There are two possible ways implemented that can be set using FREESTREAM_OPTION:

  • TEMPERATURE_FS (default): Density $$\rho_{\infty}$$ is computed using the specified pressure $$p_{\infty}$$ (FREESTREAM_PRESSURE) and temperature $$T_{\infty}$$ (FREESTREAM_TEMPERATURE).
  • DENSITY_FS: Temperature $$T_{\infty}$$ is computed using the specified pressure $$p_{\infty}$$ (FREESTREAM_PRESSURE) and density $$\rho_{\infty}$$ (FREESTREAM_DENSITY).

Mach Number and Velocity

The free-stream velocity $$v_{\infty}$$ is always computed from the specified Mach number $$Ma_{\infty}$$ (MACH_NUMBER) and the computed thermodynamic state. The flow direction is based on the angle of attack (AOA) and the side-slip angle (SIDESLIP_ANGLE, for 3D).

Reynolds Number and Viscosity

If it is a viscous computation, by default the pressure $$p_{\infty}$$ will be recomputed from a density $$\rho_{\infty}$$ that is found from the specified Reynolds number $$Re$$ (REYNOLDS_NUMBER). Note that for an ideal gas this does not change the Mach number $$Ma_{\infty}$$ as it is only a function of the temperature $$T_{\infty}$$. If you still want to use the thermodynamic state for the free-stream definition, set the option INIT_OPTION to TD_CONDITIONS (default: REYNOLDS). In both cases, the viscosity is computed from the dimensional version of Sutherland's law or the constant viscosity (FREESTREAM_VISCOSITY), depending on the VISCOSITY_MODEL option.

Non-Dimensionalization

For all schemes, as reference values for the density and temperature the free-stream values are used, i.e. $$ \rho_{ref} = \rho_{\infty}, T_{ref} = T_{\infty}$$. The reference velocity is based on the speed of sound defined by the reference state: $$v_{ref} = \sqrt{\frac{p_{ref}}{\rho_{ref}}}$$. The dimensionalization scheme can be set using the option REF_DIMENSIONALIZATION and defines how the reference pressure $$p_{ref}$$ is computed:

  • DIMENSIONAL: All reference values are set to 1.0, i.e. the computation is dimensional.
  • FREESTREAM_PRESS_EQ_ONE: Reference pressure equals free-stream pressure, $$p_{ref} = p_{\infty}$$.
  • FREESTREAM_VEL_EQ_MACH: Reference pressure is chosen such that the non-dimensional free-stream velocity equals the Mach number: $$p_{ref} = \gamma p_{\infty}$$.
  • FREESTREAM_VEL_EQ_ONE: Reference pressure is chosen such that the non-dimensional free-stream velocity equals 1.0: $$p_{ref} = Ma^2_{\infty} \gamma p_{\infty}$$.

Flow Condition (Incompressible)

Solver Version
INC_EULER, INC_NAVIER_STOKES, INC_RANS 7.0.0

The physical definition of the incompressible solvers is accomplished by setting an appropriate flow condition for initialization and non-dimensionalization. SU2 solves the incompressible Navier-Stokes equations in a general form allowing for variable density due to heat transfer through the low-Mach approximation (or incompressible ideal gas formulation).

Thermodynamic and Gauge Pressure

In the incompressible problem the thermodynamic pressure is decoupled from the governing equations and density is therefore only a function of temperature variations. The absolute value of the pressure is not important and any reference to the pressure $$p$$ is considered as the gauge value, i.e. it is zero-referenced against ambient air pressure, so it is equal to absolute pressure minus (an arbitrary) atmospheric pressure.

Initial State and Non-Dimensionalization

The initial state, i.e. the initial values of density $$\rho_0$$, velocity vector $$\bar{v}_{0}$$ and temperature $$T_0$$ are set with INC_DENSITY_INIT, INC_VELOCITY_INIT and INC_TEMPERATURE_INIT, respectively. The initial pressure $$p_0$$ is always set to 0.0.

The reference values $$\rho_{ref}, T_{ref}, v_{ref}$$ equal the initial state values by default (or if INC_NONDIM= INITIAL_VALUES). If INC_NONDIM is set to REFERENCE_VALUES you can define different values for them using the options INC_DENSITY_REF, INC_VELOCITY_REF and INC_TEMPERATURE_REF. The reference pressure is always computed by $$p_{ref} = \rho_{ref}v^2_{ref}$$.

Note: The initial state is also used as boundary conditions for MARKER_FAR.

Turbulence Models

Solver Version
*_RANS 7.4.0

This section describes how to setup turbulence models for RANS simulations. Turbulence is activated using the option KIND_SOLVER= RANS, or KIND_SOLVER= INC_RANS A turbulence model can then be selected via the option KIND_TURB_MODEL Different submodels and parameters are specified via the different options listed below. The turbulent Prandtl number can be modified with the option PRANDTL_TURB (the default is 0.9).

Spalart-Allmaras (SA)

SU2 implements several versions and corrections of the SA model. The model is selected using KIND_TURB_MODEL= SA and the modifications via the SA_OPTIONS list. If this list is empty, then SU2 defaults to SA-noft2. The freestream and inlet conditions are specified via the option FREESTREAM_NU_FACTOR= 3 (ratio of SA variable to freestream kinematic viscosity).

The following modifications are allowed (refer to NASA's TMR for further info):

  • Versions:
    • NEGATIVE - Negative SA model.
    • EDWARDS - Edwards modification.
    • BCM - BCM transitional model.
    • WITHFT2 - SA model with ft2 term, note that by default we omit this term.
  • Corrections:
    • QCR2000 - Quadratic contitutive relation used in the stress tensor.
    • COMPRESSIBILITY - Mixing layer compressibility correction.
    • ROTATION - Dacles-Mariani et al. rotation correction.

All the modifications can be combined with each other expect NEGATIVE and EDWARDS. For example, to specify SA-neg-R-comp-QCR2000 use SA_OPTIONS= NEGATIVE, WITHFT2, ROTATION, COMPRESSIBILITY, QCR2000. However, some combinations are not considered standard, e.g. SA-neg should have the ft2 term, whereas SA-noft2-Edwards and SA-noft2-BCM should not have the ft2 term, and they are usually not combined with other corrections (see TMR for more details). To use non-standard combinations it is necessary to add EXPERIMENTAL to the option list, e.g. SA_OPTIONS= NEGATIVE, BCM, EXPERIMENTAL.

The rough wall correction is implicitly turned on by specifying roughness values for wall markers via the WALL_ROUGHNESS option.

Shear Stress Transport (SST)

SU2 implements the "Standard" (1994) and 2003 versions of the SST model along with several modifications.

Note: Currently all versions are "modified" i.e. the turbulence kinetic energy (TKE) is not included in the viscous stress tensor.

The main model is selected using KIND_TURB_MODEL= SST and the version and modifications via the SST_OPTIONS list. If this list is empty SU2 defaults to the baseline 1994 model, V1994m (see warning below). The options allow for a version and a set of modifiers to the version. The freestream and inlet conditions are specified via the options FREESTREAM_TURBULENCEINTENSITY= 0.05 (5%) and FREESTREAM_TURB2LAMVISCRATIO= 10 (ratio of turbulent to laminar viscosity).

Note: The default values for these options are suitable for internal flows but may be too high for external aerodynamics problems.

The following modifications are allowed:

  • Versions:
    • V1994m - SSTm WARNING: Our implementation has a small inconsistency with the literature, which will be resolved in the next major SU2 update (i.e. version 8).
    • V2003m - SST-2003m (no known inconsistencies).
  • Production modifications:
    • VORTICITY - Uses vorticity to compute the source term instead of strain-rate magnitude.
    • KATO_LAUNDER - Uses the Kato-Launder modification (vorticity times strain-rate).
    • UQ - Production is computed using a modified stress tensor for uncertainty quantification. Note with this modification TKE is always included in the stress tensor.
  • Corrections:
    • SUSTAINING - SST with controlled decay.
    • Curvature corrections are currently not implemented.

Modifications from each of these three groups can be combined, for example SST_OPTIONS= V2003m, VORTICITY, SUSTAINING

Transition Models

Solver Version
*_RANS 7.5.0

This section describes how to setup transition models for RANS simulations. Transition is activated using the option KIND_SOLVER= RANS, or KIND_SOLVER= INC_RANS together with a choice of KIND_TRANS_MODEL (different from NONE). Currently, the only valid option for KIND_TRANS_MODEL is LM, for Langtry-Menter transition models. Different submodels and correlations are then specified via LM_OPTIONS (for example LM_OPTIONS= LM2015, MENTER_LANGTRY).

The following modifications are allowed:

  • Versions:
    • LM2015 - Correction to include stationary crossflow instabilities. It has to be used only in 3D problems. The RMS of roughness used in this model has to be set through the separate option HROUGHNESS.
  • Correlations (only one can be specified):
    • MALAN - This is the default correlation when the LM model is coupled with the SA turbulence model.
    • SULUKSNA - This should be used only if the SST model is used. It should require a formulation of the Re_theta_t correlation that omits the pressure gradient parameter, however it is not clear.
    • KRAUSE - This correlation should be used for hypersonic flows. Its implementation at the moment is unclear due to inconsistencies in the literature.
    • KRAUSE_HYPER - This correlation should be used for hypersonic flows. Its implementation at the moment is unclear due to inconsistencies in the literature.
    • MEDIDA - Designed for SA turbulence model. Has problems when dealing with separation induced transition.
    • MEDIDA_BAEDER - Designed for SA turbulence model. Has problems when dealing with separation induced transition.
    • MENTER_LANGTRY - This is the default correlation when the LM model is coupled with the SST turbulence model.