Question: SI unit conversion and scaling

[djObsidian]

Greetings!

I am trying to wrap my head around the unit conversion system in this project. While I have reviewed previous issues regarding units (#27, #55, and #265), I still have some specific questions about how to correctly define the SI mapping.

The conversion coefficients are set using:
units.set_m_kg_s(lbm_length, lbm_velocity, lbm_density, si_length, si_velocity, si_density);

I am struggling to understand what exactly si_length and si_velocity represent in a physical context. Specifically, "length and velocity of WHAT?"

1. Length Scaling

Taking the Electric Ducted Fan (EDF) example: the STL files are dimensioned in millimeters. If I want to simulate this in meters, should si_length be set to 0.001 (representing 1 mm in meters)? Or something else?

2. Velocity Scaling

In the example, the flow velocity is initialized as lbm.u.y[n] = 0.3f * lbm_u;.

• If I assume my free-stream velocity is 1 m/s (or 10 m/s), do I simply pass that value as si_velocity?
• What if I want to run a static simulation where the initial velocity in all cells is zero (e.g., to measure the output flow generated by the EDF itself)? What value should be assigned to si_velocity in this "zero-start" scenario?

3. Time and Resolution

I am also unclear about the time step resolution.

• What determines the temporal resolution of a single step?
• I see that units.t() can be used to convert physical time into the number of steps. Is there a straightforward way to perform the inverse conversion?
• For instance, in the EDF example, how would I calculate the exact RPM in physical units?

I would provide greatly appreciate any clarification on these points. Thank you in advance for your help!

[ProjectPhysX]

Hi @djObsidian,

for the unit conversion you set 3 pairs of values with orthogonal units - usually some length, some velocity, and the density, in IS units and LBM units. From these 3 pais the 3 base units [m], [kg], [s] are calculated and then any other quantity can be converted between unit systems - usually you know the viscosity in SI units and then convert it to LBM units. This makes the Reynolds number match between SI units and LBM units, so the physics are equivalent.

Let's look at the example of the EDF setup:

• length: Select the length of any suitable geometry feature. You can use for example the diameter of the rotor, say you know in SI units it's 0.1m, and in LBM units (depending on how much memory you have available, you set it to 200 grid cells. The box then will be a bit bigger to dit it, say 300 grid cells.
• velocity: Here you should use the expected largest velocity in the system - the bladetip velocity of the rotor. Say you know the RPM and rotor diameter, and from that you calculate bladetip velicity in SI units to be 10m/s. In LBM units you can in theory freely set any velocity, you want to choose it as large as possible to keep simulation runtime fast, but due to numerical stability reasons don't go above 0.1. Say you choose 0.075 to be on the safe side.
• density: You run it in air at sea level, that means a density of 1kg/m³ in SI units. In LBM units, the mean density always is 1.

These 3 pairs you feed into

void set_m_kg_s(const float x, const float u, const float rho/*=1.0f*/, const float si_x, const float si_u, const float si_rho) { // length x, velocity u, density rho in both simulation and SI units
	unit_m = si_x/x; // length si_x = x*[m]
	unit_kg = si_rho/rho*cb(unit_m); // density si_rho = rho*[kg/m^3]
	unit_s = u/si_u*unit_m; // velocity si_u = u*[m/s]
	print_info("Unit Conversion: 1 cell = "+to_string(1000.0f*this->si_x(1.0f), 3u)+" mm, 1 s = "+to_string(this->t(1.0f))+" time steps");
}

With these 3 base units, convert the viscosity of air from SI units to LBM units via units.nu(si_nu);. You can now also convert the time interval of 1 LBM time step back to SI units via units.si_t(1ull);, that gives you the length of each LBM time step in SI units.

What happens if you make the box larger in LBM units, say 600 grid cells? Then the rotor dimaeter becomes 400 grid cells, and the resulting unit_m will be reduced to half, so viscosity gets adjusted accordingly during units.nu(si_nu); and Reynolds number still matches between SI and LBM units.

There's a full catalogue of conversion functions in src/units.hpp so you don't have to deal with figuring out SI units of quantities.

It is also possible to manually set the 3 base units in set_m_kg_s(const float m, const float kg, const float s) - from any other 3 pairs of orthogonal quantities. The default way via length+velocity+density is just more convenient and prevents you from ending up with unstable LBM unit velocity, or LBM unit density other than 1 that will also be unstable. The viscosity - what you convert last - has the largest wiggleroom in stability.

Kind regards,
Moritz