3D Wind TunnelBeta

About 3D Wind Tunnel

This wind tunnel switches between two different solvers depending on speed. Below Mach 1.2 it computes the flow around the model directly with a three-dimensional lattice Boltzmann method (D3Q19 lattice, BGK collision plus a Smagorinsky turbulence model) and measures forces from the momentum exchanged at the surface. From Mach 1.2 up it does not compute a flow field at all. Instead it uses local surface inclination methods: each surface triangle gets a pressure coefficient from its angle to the flow (oblique shock, Prandtl–Meyer expansion or modified Newtonian theory), and these are summed. Skin friction is added separately with the reference-temperature method.

The two sides deserve different levels of trust. The supersonic and hypersonic side is closed-form and agrees well with published data (a sphere at Mach 10 gives C_D ≈ 0.92). The subsonic side is bound by the grid a browser can run (at most 128 × 68 × 68): close to textbook values for sharp-edged bodies, well off for smooth curved ones. The sections below explain why.

Real Reynolds number versus grid Reynolds number

At the default conditions (1 m reference length, 68 m/s, sea level) the real Reynolds number is Re = UL/ν = 68 × 1 / 1.46×10⁻⁵ ≈ 4.7×10⁶. Carrying that onto the grid would need a tiny lattice viscosity, and BGK collisions go unstable below about 0.0016. So viscosity stops at that floor, and on the Fine setting (17 cells across the reference length) the grid Re is 0.11 × 17 / 0.0016 ≈ 1,170. The Smagorinsky model makes up part of the difference by mimicking how small eddies drain energy.

Both numbers are shown side by side on purpose. Drag coefficients change with Re, so when the two differ, the measurement can differ from the real object too.

Which shapes you can trust

In the shape duel, the order plate → cube → sphere → teardrop, with C_D falling each time, comes out right. Use the tool to see that the back of a body sets its drag, not to take absolute numbers into a design.

• Sharp-edged bodies such as the flat plate and cube: flow always separates at the edges, so Re hardly matters. The plate gives about 1.26 against a textbook 1.17, within ±10%.
• Bodies where flow follows a curve and then separates (sphere, teardrop, wing): the separation point depends on the boundary layer, which a model 11 to 28 cells across cannot resolve. The sphere comes out near 0.8 instead of 0.47, and the teardrop several times its textbook 0.05.
• Wings: lift grows with angle of attack, but the slope is about half of thin-airfoil theory (2π per radian) and the lift-to-drag ratio is far below a real wing's.

The sphere's drag crisis, which the grid cannot reproduce

A smooth sphere's C_D sits around 0.4–0.5 for Re from 10³ to about 2×10⁵, then drops to roughly 0.1–0.2 near Re 3×10⁵. The boundary layer turns turbulent, hugs the surface longer, separates further back and leaves a narrower wake. Seeing this requires resolving the inside of the boundary layer, so it does not appear on this coarse grid. Golf-ball dimples are a device for triggering that transition at a lower Re.

The fast side: re-entry capsules and shocks

Above about Mach 5, modified Newtonian theory, where pressure coefficient scales with the square of the sine of the impact angle, works well for blunt bodies. The stagnation pressure coefficient approaches about 1.84 for γ = 1.4, and C_D becomes nearly independent of Mach number. The 70° sphere-cone capsule in the re-entry scenario gives about 1.64 with this method, close to the published 1.68. Between Mach 1.2 and 5, compression faces use oblique-shock relations and expansion faces use Prandtl–Meyer.

Between Mach 0.7 and 1.2 neither method holds. Lattice Boltzmann as used here is effectively incompressible and is wrong in principle above Mach 0.3, and surface inclination methods assume supersonic flow. The tool warns you in that range.

Air, water and Mars

Switch the medium to water and the kinematic viscosity drops to about 1/15 of air's (1.0×10⁻⁶ m²/s). The same Re is reached at a much lower speed, which is why water tunnels and towing tanks are used to stand in for airflow. Mars's atmosphere is mostly carbon dioxide (γ ≈ 1.29), so at the same Mach number the pressure behind a shock differs from Earth's.

Worked examples

How to use it

1. Pick a scenario, then set model, attitude, speed and altitude.
2. Wait until the convergence indicator is well filled before reading C_D and C_L.
3. Run an angle-of-attack sweep for wings or a Mach sweep for fast models, and download the CSV.

Frequently asked questions

Related guides

• The Reynolds Number: From a Streak of Dye in 1883 to the Dimples on a Golf Ball