8.1. Pre-Processing#

8.1.1. Non-Dimensional Inputs#

In Flow360, most variables are non-dimensional. The non-dimensionalization reduces the number of free parameters and helps to provide better understanding of the underlying physics. A non-dimensional variable is obtained by dividing its dimensional counterpart by an appropriately selected constant like Eq.(8.1.1)

(8.1.1)#\[\text{non-dimensional variable} = \frac{\text{dimensional variable}}{\text{reference value}}\]

Note

Any value presented here in symbolic format (for example \(A_\text{ref}\)) refers to a dimensional value, whereas any value written in text format (for example “geometry/refArea”) refers to a non-dimensional value

Theoretically, the reference values for non-dimensionalization can be arbitrary as long as the resulting equations are identical to the original ones, but in practice, the reference values are usually selected based on some typical parameters of problems and flow characteristics to avoid confusion. The following list shows some commonly used non-dimensional variables in Flow360.json file:

Table 8.1.1 Reference values for non-dimensional inputs in Flow360#

Property

Ref. value for non-dim.

Examples in Flow360.json

Length

\(L_\text{gridUnit}\)

geometry->{momentCenter, momentLength}, actuatorDisks->thickness, BETDisks->{radius, chordRef, thickness, bladeLineChord, chords, sectionalRadiuses}

Area

\(L_\text{gridUnit}^2\)

geometry->refArea

Dynamic viscosity

\(\rho_\infty C_\infty L_\text{gridUnit}\)

freestream->muRef

Angular speed

\(C_\infty/L_\text{gridUnit}\)

slidingInterfaces->omegaRadians, BETDisks->omega

Time

\(L_\text{gridUnit}/C_\infty\)

TimeStepping->timeStepSize

Note

  • The freestream/Reynolds is based on the given reference velocity \(U_\text{ref}\) and \(L_\text{gridUnit}\).

  • The definition on \(L_\text{gridUnit}\) can be found in case configuration.

8.1.1.1. Compute non-dimensional time step timeStepSize#

The definition of “timeStepSize” can be found at timeStepping. Assume the physical time step size is 2 seconds, speed of sound of freestream is 340 m/s and grid unit is 1 feet, so the \(\text{timeStepSize} = \frac{2 \text{ s} \times 340\text{ m/s}}{0.3048 \text{ m}}=2230.971128608\).

8.1.1.2. Convert RPM to non-dimensional rotating speed omegaRadians#

The RPM determines the angular speed, and the non-dimensional “omegaRadians” can be calculated by dimensional angular speed from slidingInterfaces (list). Assume the RPM = 800, speed of sound of freestream is 340 m/s and grid unit is 1 millimeter, so \(\text{omegaRadians}=\Omega\times L_\text{gridUnit}/C_\infty=\frac{800\times 2\pi}{60\text{ s}}\times\frac{0.001 \text{ m}}{340\text{ m/s}}=0.00024639942\).