Wind Tunnel Simulator (2D)

What you are looking at. A low-speed open-circuit (Eiffel-type) wind tunnel: a fan pulls air through a honeycomb and screens, a contraction accelerates it into a glass-walled test section, and the model sits in a smooth stream. The 3D hall, fan, balance, smoke rake and manometer board are a Blender 5.2 model. The airflow itself is computed live by a 2D lattice-Boltzmann solver on the vertical mid-span slice of the test section (1 cell = 1.25 cm, 240 x 96 cells = 3.0 m x 1.2 m); the smoke is a set of tracer particles carried by that field and spread across the span.

Governing equations

Incompressible Navier-Stokes, solved as a kinetic scheme (D2Q9, BGK collision):

fi(x + ci, t + 1) = fi(x, t) - (fi - fieq) / τ,   fieq = wi ρ [1 + 3 ci·u + 4.5 (ci·u)2 - 1.5 u2]

Pressure is p = ρ cs2 with cs2 = 1/3, viscosity ν = (τ - 1/2) / 3. At Reynolds numbers where the grid cannot resolve the smallest eddies a Smagorinsky sub-grid viscosity (C_s = 0.11) is added to τ from the local strain rate, so the flow stays stable and behaves like a large-eddy simulation. The body is a bounce-back wall; the roof and floor are free-slip walls; the inlet has a fixed velocity and the outlet is a zero-gradient boundary.

Forces and coefficients

The force on the model is the momentum exchange on every wall link, F = Σ 2 fi(xf) ci. Coefficients use the model length (chord) L: Cd = Fx / (½ ρ U2 L), Cl = Fy / (½ ρ U2 L). The physical force per metre of span is F' = C · ½ ρ U2 L, drag power P = F'd U. Pressure taps give Cp = (p - p∞) / (½ ρ U2) along the surface; the manometer board on the back wall shows 12 of them as liquid columns.

Reynolds number and the honest limits

The real Reynolds number is Re = U L / ν for the chosen fluid, speed and model size. A 240 x 96 grid cannot resolve Re of several hundred thousand, so the solver runs at Resolver = clamp(Re, 12, 6000) and both numbers are shown. Consequences: laminar-to-turbulent transition, thin boundary layers and the exact stall angle are not predicted for real-world Re; low-Re cases (oil, syrup, small models) are resolved properly, and the vortex street behind a cylinder is quantitatively tested below.

2D slice, 3D look. The model is infinitely long in the span direction as far as the physics goes (an extruded section), so lift and drag are per metre of span and finite-wing effects (tip vortices, induced drag) are absent. Smoke particles are spread over the span for visibility; they follow the mid-span velocity. Real tunnel walls would add boundary layers and blockage corrections; here the roof and floor are free-slip and the blockage ratio (model height / 1.2 m) is large for big models, which raises drag and shedding frequency.

In-page numerical checks

(1) Plane Poiseuille flow with the same D2Q9-BGK collision and streaming against the analytic parabola. (2) Mass-flux conservation: the flux through the tunnel behind the model equals the inlet flux within 3 %. (3) A separate cylinder run at Re = 100 compared with Williamson's relation St = 0.2665 - 1.018 / √Re (the confined domain shifts the measured value by about +10 %, so the tolerance is 20 %). The Strouhal number of the live flow is measured from the lift signal when a clean periodic wake exists.

What to try

• Airfoil at 4 deg, then raise the angle to 15 deg and watch the suction peak grow on the Cp plot and the wake widen; run the angle sweep to record the lift curve.
• Switch to oil, cylinder, 1.6 m/s: a Karman vortex street appears and the lift signal oscillates; compare the measured Strouhal number.
• Sports car: add a rear wing (shape parameter) and see the pressure change on the rear deck; truck: round the cab to lower drag.
• Syrup at 0.3 m/s: Re is about 1, there is no wake at all (creeping flow).

Not affiliated with any tunnel manufacturer; the geometry is generic.