Can OpenMDAO unit conversion handle nonstandard-power scalings?

Question

In tokamak plasma physics, scaling laws are often used to estimate plasma performance. These often require non-standard units, in particular, plasma density n in units of 10^19 or 10^20 particles per cubic meter, often called n₁₉ and n₂₀, respectively. (Nobody calls these 10 or 100 exa-particles-per-cubic-meter.) At the same time, many physics formulae call for these values in the "standard" m^-3.

I can imagine an OpenMDAO ScalingLaw component taking in an input with units=m**-3 (and probably ref=1e19 for numerical ease), and then manually dividing by 1e19 to get an n19.

Is there a 'better' way to handle this scale conversion automatically?

Answer 1

It sounds like the appropriate approach here might just be to add new units to OpenMDAO's unit library. This would make the conversion automatic as the data is passed around.

For instance, in astrodynamics we sometimes invent "canonical" units in which the distance unit is set to some specified value (like the Earth's radius), the gravitational parameter GM is assumed to be 1, and time units fall out of this. In OpenMDAO, the Distance Units (DU) can be set using the following code somewhere in your script before you start defining inputs and outputs:

import openmdao.utils.units as units

# Add canonical units to OpenMDAO
MU_earth = 3.986592936294783e14
R_earth = 6378137.0

period = 2 * np.pi * np.sqrt(R_earth**3 / MU_earth)

units.add_unit('TU', f'{period}*s')
units.add_unit('DU', f'{R_earth}*m')

You can verify the functionality by adding the units and then using the OpenMDAO convert_units function to test them:

import openmdao.utils.units as units
from openmdao.api import convert_units

units.add_unit('n19', '10**19/m**3')
units.add_unit('n20', '10**20/m**3')

print(convert_units(1, 'n19', 'm**-3'))

which outputs

1e+19

Once those units are added to the system, you can specify units='n19' or units='n20' when you add inputs or outputs.