8.1.6. User Defined Expressions

Note

This is currently a beta feature and may be subject to change during the lifetime of the release.

User Defined Expressions are a powerful tool to interact with solver variables in order to expand the realm of what can be achieved. The major use of user defined expression falls into the following catagories:

• Simulate custom dynamics.

• Monitor and analyze custom variables.

• Initializing complex flow field.

• Specifying flow condition on boundaries.

8.1.6.1. Guidance on how to write User Defined Expressions

The expression follows syntax that is very similar to the C language. Although it should be mentioned that, for safety reasons, not all C language features are supported. Statements are separated by semicolon. Examples are available here and here in our tutorials.

The following operators and functions are allowed to define an expression:

8.1.6.2. Scalar function and operators

Symbol	Mathematical operator / function
+	Scalar addition
-	Scalar subtraction
*	Scalar multiplication
/	Scalar division
pow(a,b)	Base scalar a raised to the power scalar b
sqrt()	Square-root of scalar
log()	Natural Logarithm
exp()	Base-e exponential
sin(), cos(), tan()	Trigonometric Functions
min(), max()	Minimum/Maximum value of the two
ceil(), floor()	Smallest/largest integer that is greater/smaller than the input
pi	Constant pi = 3.14158…

Caution

Please note that in all instances of User Defined Expressions integer divisions (i.e. "18/12") will discard the fraction part (which results in 1 in this case) consistent with the C language. Please consider explicitly using at least one float number in division (i.e. "18.0/12") if such behavior is not desired.

8.1.6.3. Functions that operate on vectors

Note that the vector being used in the following functions must have 3 components.

Function	Mathematical function
subtract(C, A, B)	\(\vec{C} = \vec{A} - \vec{B}\)
cross(C, A, B)	\(\vec{C} = \vec{A} \times \vec{B}\) where \(\times\) is the vector cross product
dot(A, B)	returns \(\vec{A} \cdot \vec{B}\) where \(\cdot\) is the vector dot product
magnitude(A)	returns the length/magnitude of \(\vec{A}\)

8.1.6.4. Solver variables

In an expression, users can use solution variables as well as custom variables. There are three categories of solver variables:

• Variables that are defined on all grid nodes and is not bound to a specific “source” (like zone or patch).

• Variables that are unique to the entire grid/simulation and are not bound to a specific “source” (like zone or patch). Unlike the first category, values of these variables are not related to particular grid nodes.

• Variables that are associated with a certain “source”. For example the CL has to be associated with a surface patch; theta has to be associated with certain volume zone(s). See examples in user defined post processing and user defined dynamics.

Note

All variables are non-dimensional. More information on nondimensionalization in Flow360 can be found at Nondimensional Inputs and Nondimensional Outputs.

8.1.6.4.1. Variables that are defined on all grid nodes

For the variables that are defined on all grid nodes, the following solver variables can be used. These variables are listed as arrays since their values depends on the grid nodes.

Name	Type[component]	Note
mut	Array[1]	Turbulent viscosity
mu	Array[1]	Laminar viscosity
solutionNavierStokes	Array[5]	Solution for the N-S equation in conservative form in non-inertial reference frame
residualNavierStokes	Array[5]	Residual for the N-S equation in conservative form in non-inertial reference frame
solutionTurbulence	Array[2/1]	Solution for the turbulence model. Number of component depends on underlying turbulence model
residualTurbulence	Array[2/1]	Residual for the turbulence model. Number of component depends on underlying turbulence model
kOmega	Array[2]	Effectively solutionTurbulence when using SST model
nuHat	Array[1]	Effectively solutionTurbulence when using SA model
solutionTransition	Array[2]	Solution for the transition model
residualTransition	Array[2]	Residual for the transition model
solutionHeatSolver	Array[1]	Solution for the heat equation
residualHeatSolver	Array[1]	Residual for the heat equation
coordinate	Array[3]	Nodal coordinates in earth system
primitiveVars	Array[5]	rho, u, v, w, p (density, 3 velocities and pressure)

8.1.6.4.2. Simulation wide variables

For this second category, the following solver variables can be used. These variables are listed as scalars since they have a unique value across the entire grid/simulation.

Name	Type[component]	Note
MachRef	Scalar	MachRef specified by the user in freestream
muRef	Scalar	muRef specified by the user in freestream
Tref	Scalar	Temperature specified by the user in freestream
t	Scalar	Physical time
physicalStep	Scalar	Physical time step, starting from 0
pseudoStep	Scalar	Pseudo time step within the physical time step, starting from 0
timeStepSize	Scalar	Physical time step size
alphaAngle	Scalar	alphaAngle specified by the user in freestream
betaAngle	Scalar	betaAngle specified by the user in freestream
pressureFreestream	Scalar	Freestream reference pressure. Has a constant value of 1.0 / 1.4
momentLengthX	Scalar	X component of momentLength specified by the user in geometry
momentLengthY	Scalar	Y component of momentLength specified by the user in geometry
momentLengthZ	Scalar	Z component of momentLength specified by the user in geometry
momentCenterX	Scalar	X component of momentCenter specified by the user in geometry
momentCenterY	Scalar	Y component of momentCenter specified by the user in geometry
momentCenterZ	Scalar	Z component of momentCenter specified by the user in geometry

8.1.6.4.3. Zone or patch associated variables

For variables that are associated with a certain zone or patch, the following solver variables can be used. For bet_thrust, bet_torque and bet_omega user can add the index of the bet disk into the variable name such as bet_0_thrust which indicates the thrust of the first bet disk.

Note

The forces (forceX/Y/Z) and moments (momentX/Y/Z) should be distinguished from the force/moment coefficients (e.g. CL, CMy). The forces and moments are the numerators of the force/moment coefficients as shown in Table 8.3.2.

All variables that are also listed in universal variables have the same definitions here. Some variables will not be available if the corresponding feature is not enabled. For example solutionTransition is not available if the case does not use transition model.

Name	Type[component]	Source type	Note
bet_thrust	Scalar	BET Disk ID	Thrust force for the BET disk
bet_torque	Scalar	BET Disk ID	Torque for the BET disk
bet_omega	Scalar	BET Disk ID	Rotation speed for the BET disk
CD	Scalar	Patch name	Drag coefficient on the patch
CL	Scalar	Patch name	Lift coefficient on the patch
forceX	Scalar	Patch name	Total force on the patch in X direction
forceY	Scalar	Patch name	Total force on the patch in Y direction
forceZ	Scalar	Patch name	Total force on the patch in Z direction
momentX	Scalar	Patch name	Total moment with respect to momentCenter on the patch in X direction
momentY	Scalar	Patch name	Total moment with respect to momentCenter on the patch in Y direction
momentZ	Scalar	Patch name	Total moment with respect to momentCenter on the patch in Z direction
nodeNormals	Array[3]	Patch name	Normal vector of the patch. Its magnitude is the area associated with the node
theta	Scalar	Zone name	Rotation angle (in radians) of the volume zone
omega	Scalar	Zone name	Rotation speed of the volume zone
omegaDot	Scalar	Zone name	Rotation acceleration of the volume zone
wallFunctionMetric	Array[1]	Patch name	(beta feature) : This metric is a local indicator of the quality of the wall model. A value less than 1.25 indicates a good estimation of the wall shear stress. Between 1.25 and 10 indicates lower confidence, and values greater than 10 are not reliable for wall shear stress estimation.
wallShearStress	Array[3]	Patch name	Wall viscous shear stress on the patch in X, Y and Z
yPlus	Array[1]	Patch name	Non-dimensional wall distance, \(y^+\) on the patch

Explanation on the source type:

• BET Disk ID: this is the index/position of the BET disk as they appear in the case JSON. Starting from 0.

• Patch name: name of the patch defined in the mesh file.

• Zone name: name of the volume zone defined in the mesh file.