Wind Tunnel Loss Budget

What is modelled

Air in a wind tunnel is drawn through flow-straightening honeycomb and screens, speeded up in a contraction, passes the model in the test section, slows down in a diffuser and leaves. Each part wastes some of the flow energy as turbulence and friction, and the fan has to make up the total. The energy ratio, the kinetic power of the test-section flow divided by the fan shaft power, measures how efficient the tunnel is.

Equations

• Loss coefficients referred to the test-section dynamic pressure K = Klocal (Ats/A)² since the dynamic pressure scales as 1/A².
• Screen K = 1.3 (1 − β) + ((1 − β)/β)²; test section K = f L/D with f = 0.316 Re−1/4.
• Diffuser K = f (1 − 1/AR²) / (8 sin(θ/2)) + 3.2 tan(θ/2)1.25 (1 − 1/AR)² and exit loss 1/AR².
• Fan power P = ΣK · ½ρV² V A / η and energy ratio ER = ½ρV³A / P.

Checks run in the page

• The static pressure drop through a smooth contraction by numerical integration against Bernoulli.
• The diffuser angle with least loss from two independent searches.
• Total-pressure bookkeeping with local dynamic pressures against the referred sum.
• The fan power scaling with the cube of speed (a little less because of the friction factor).

Honest simplifications

The diffuser and screen loss correlations are textbook engineering forms and are approximate, the tunnel is open-circuit and has no corners or turning vanes, the test section is empty (the model adds blockage and drag that are not included), the contraction loss is a fixed small number, and the fan curve is replaced by a constant efficiency.

• Press Short, steep diffuser and see the diffuser become the largest loss.
• Press Many fine screens and read how the screens and honeycomb cost energy.
• Press Weak contraction and Fast and large to see how the energy ratio changes with the contraction ratio and speed.