8.1.2. Nondimensional Inputs#

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

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

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 nondimensional value

Theoretically, the reference values for nondimensionalization 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 nondimensional variables in Flow360.json file:

Table 8.1.2 Reference values for nondimensional inputs in Flow360#

Property

Ref. value for nondim.

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 \(L_\text{gridUnit}\) as defined in case configuration.

8.1.2.1. Compute nondimensional 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 feet, therefore we have:

(8.1.2)#\[\text{timeStepSize} = \frac{2 \ \text{s} \times 340 \ \text{m/s}}{0.3048 \ \text{m}} = 2230.971128608\]

8.1.2.2. Convert RPM to nondimensional rotating speed omega#

The RPM determines the angular speed, and the nondimensional omega can be calculated by using the same equation as the 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 omegaRadians can be written as:

(8.1.3)#\[\text{omegaRadians} = \frac{800 \times 2\pi}{60 \ \text{s}} \times \frac{0.001 \ \text{m}}{340 \ \text{m/s}} = 0.00024639942\]

Alternatively, omegaDegrees is given by:

(8.1.4)#\[\text{omegaDegrees} = \frac{800 \times 360}{60 \ \text{s}} \times \frac{0.001 \ \text{m}}{340 \ \text{m/s}} = 0.01411764706\]