Calculate Data from Expressions

Use the Calculate tool to create new field quantities using a python expression. The new fields can be derived from existing fields or be completely independent of other results in the dataset.

There are some important characteristics of the Calculate tool that need to be understood to use it effectively. When a new function is created, it is not immediately evaluated. Rather, the expression syntax is parsed and checked for validity. If an expression contains invalid functions or variables it will not be accepted by the calculate context and the text will revert back to the previous state. Once the expression is validated, it is added to the global variable list within the session of HyperMesh CFD. It is not until that expression is selected to use for contouring, streamline tracing, or generating an iso-surface that it is evaluated. When the expression is evaluated, it is evaluated on a local basis. For example, you create an expression for total pressure:

pTot = 0.5*density*velocity**2 + pressure

If you then choose to color a slice plane by pTot, it is calculated based on the local coordinates and results variables available on that slice plane. No information from the parent volume dataset is accessed. This is done to minimize memory overhead of the derived variables and to improve performance. However, if your expression includes gradients of quantities, it is important to note that the gradients will not be calculated on a global level. Rather, they will be evaluated using the data on the surface. In the case of a slice plane, this means that the gradients will not be accurate in the plane normal direction. This “calculate on demand” approach also has some implications for querying the fields prior to use. A number of features in the user interface rely on the ability to query the function range. One example is the range setting of the colormap. For pre-existing variables, the range is populated based on a query of the range of the scalar. Since derived fields are not computed a priori, the range inputs will not be populated with proper values.

  1. From the Post ribbon, click the Calculate tool.
    Figure 1.


    The Derived Data Calculator dialog opens.
    Figure 2.
  2. Click to add a variable.
  3. Define the name and expression.
    • Define the name without spaces so that it can be utilized in further expression definitions.
    • If using an existing variable with a space in its names, like “wall shear stress”, replace the spaces with “_”.
    • Expressions are defined in python syntax.
    Tip: Click / to import or export defined expressions. CFD_Formulas.zip contains an example CSV file with a list of standard functions you can utilize.
    Tip: Click to automatically load predefined expressions for common aerodynamic coefficients and other derived fields. A complete list of the fields in given in the table below.

    The output of each expression produces new results at each node of the geometry that it is operating on. Results fields are stored as numpy arrays and can be operated on using standard numpy operations. For example, the x-component of the velocity array can be accessed with slicing by using the following syntax:

    XVel = velocity[:,0]

    Alternatively, the pre-defined field for the x component of the velocity could be directly referred to in an expression as follows:

    XVelSquared = (x velocity)*(x velocity)

    The expression shown above is not acceptable python syntax due to the space in the “x velocity” string. To overcome this, each expression is parsed prior to evaluation to convert the variable names to a valid python expression.

A number of internal functions are available for use in the Calculate context. The following table lists the variables and functions:
Function/Variable Description Example
Name Expression
gradient() Calculates the gradient of a field gradVel gradient(velocity)
mag() Calculates the magnitude of an array velMag mag(velocity)
strain() Calculates the strain of a vector velStrain strain(velocity)
eigenvalue() Calculates the eigenvalue of an array lambda2 eigenvalue(velStrain**2.0 + (gradVel-velStrain)**2.0)
cross() Calculates the cross product of two vectors powellParameter cross(vorticity,velocity)
curl() Calculates the curl of a vector vorticity curl(velocity)
divergence() Calculates the divergence of an array divVel divergence(velocity)
make_vector() Creates a vector from three scalar fields velocity_xy make_vector(velocity[:,0],velocity[:,1],velocity[:,2]*0.0)

Some functions above return vector and tensor quantities. At the current time, HyperMesh CFD has no way to know a priori what the return dimension of a given function will be. As such, results may be unpredictable for complex expressions. The expression validation also becomes more complex as nested functions are used. It is best to use multiple fields to build up complex expressions. For example, to compute the Q-criterion, first compute the gradient of the velocity, then sum the gradients in a separate expression to evaluate Q:

Name Expression
gradVel gradient(velocity)
Q_criterion -0.5*( gradVel[:,0,0]*gradVel[:,0,0] + gradVel[:,1,0]*gradVel[:,0,1] + gradVel[:,2,0]*gradVel[:,0,2] + gradVel[:,0,1]*gradVel[:,1,0] + gradVel[:,1,1]*gradVel[:,1,1] + gradVel[:,2,1]*gradVel[:,1,2] + gradVel[:,0,2]*gradVel[:,2,0] + gradVel[:,1,2]*gradVel[:,2,1] + gradVel[:,2,2]*gradVel[:,2,2] )
Field SI Units
pressure_inf Pa
velocity_magnitude_inf m/s
density_inf kg/m^3
velocity_magnitude m/s
pressure_static Pa
pressure_dynamic Pa
pressure_dynamic_inf Pa
pressure_coefficient Non-dimensional
total_pressure Pa
total_pressure_coefficient Non-dimensional
total_pressure_inf Pa
velocity_magnitude_coefficient Non-dimensional
shear_stress_magnitude N/m^2
skin_friction_coefficient Non-dimensional
velocity_xy m/s (Vector)
velocity_xz m/s (Vector)
velocity_yz m/s (Vector)
velocity_gradient 1/sec (Tensor)
velocity_strain Non-dimensional (Vector)
Q_criterion 1/sec^2
lambda2 1/sec^2
lambda2_magnitude 1/sec^2
lambda2_x 1/sec^2
lambda2_y 1/sec^2
lambda2_z 1/sec^2
vorticity 1/sec (Vector)
vorticity_magnitude 1/sec
vorticity_x 1/sec
vorticity_y 1/sec
vorticity_z 1/sec
powell m/sec^2 (Vector)
powell_magnitude m/sec^2
powell_x m/sec^2
powell_y m/sec^2
powell_z m/sec^2
xCrd m
yCrd m
zCrd m
surface_normal_x Non-dimensional
surface_normal_y Non-dimensional
surface_normal_z Non-dimensional
pressure_stress_x N/m^2
pressure_stress_y N/m^2
pressure_stress_z N/m^2
x_total N/m^2
y_total N/m^2
z_total N/m^2