Windtunnel Data Reduction

Wind Tunnel Data Reduction (aerodynamics/wind-tunnel/windtunnel-data-reduction)

Use when the task is experimental wind tunnel test data reduction: converting raw balance forces and pressure tap readings into corrected aerodynamic coefficients. The leaf covers tare and tareshift subtraction, solid and wake blockage, wall interference, streamline curvature, Reynolds number and Mach corrections, coefficient reduction referenced to planform area and reference length, and uncertainty estimation from repeated runs. It is the experimental counterpart to the computational leaves (cfd/panel-method, airfoil/xfoil-analysis): those compute aerodynamics, this one reduces measured data.

Domain quick reference

• Tare: the support system (sting, strut, brackets) carries load even with the model unloaded. Record a tare run with the model removed or at zero lift and subtract it from every balance reading. A model at zero angle of attack whose raw drag equals its tare reads zero net drag after subtraction.
• Tareshift: the tare itself changes with angle of attack because the support loads the balance differently as the model pitches. Bracket the polar with tare runs at a low and a high angle and interpolate the tare linearly at each measurement angle.
• Solid blockage: the model volume displaces air in the closed test section, accelerating the flow around the model. The solid blockage increment is eps_sb = K1 * (model volume / test section volume), with K1 = 0.96 for a closed rectangular section (0.34 for an open one).
• Wake blockage: the model wake fills the test section and slows the flow, raising the effective dynamic pressure. The wake blockage increment is eps_wb = 0.25 * (S / C) * CDu, with S the planform area, C the test section area, CDu the uncorrected drag coefficient.
• Blockage correction: the corrected dynamic pressure is q_corr = q_u * (1 + eps)^2 and the corrected speed is V_corr = V_u * (1 + eps), with eps = eps_sb + eps_wb. Blockage always raises the dynamic pressure.
• Wall interference: the tunnel walls constrain the streamlines around a lifting model like an image vortex system, adding an angle of attack increment delta_alpha = delta * (S / C) * CL, with delta = 0.82 for a closed section and 0.125 for an open one.
• Streamline curvature: the curved streamlines act like added camber, shifting the angle of attack and the pitching moment. The increments scale with (S / C) * CL * (chord / height) and reduce the moment magnitude for a positive CL.
• Reynolds number: measured coefficients are only valid at the test Reynolds number. Scale a reference drag with the flat plate skin friction law CD(Re) = CD_ref * (Re_ref / Re)^n, n = 0.2 turbulent, n = 0.5 laminar.
• Mach corrections: above M = 0.3 use the compressible dynamic pressure q = 0.5 * gamma * p * M^2 and correct pressure coefficients with the Prandtl Glauert factor Cp = Cp_inc / sqrt(1 - M^2).
• Coefficient reduction: CL = L / (q S), CD = D / (q S), Cm = M / (q S c_ref) referenced to planform area S and reference length c_ref; local Cp = (p_local - p_ref) / q.
• Uncertainty: repeated runs of the same condition give a sample mean, a sample standard deviation (n - 1 denominator), a standard error of the mean std / sqrt(n), and an expanded uncertainty at a coverage factor (typically 2 for about 95% confidence).
• Correction ledger: record every applied correction with its numeric value so the final coefficients are auditable and reproducible.

Workflow

1. Record the tare runs: balance readings with the model removed or unloaded at the low and high angles of the polar.
2. For each measurement point, interpolate the tare at the measurement angle and subtract it from the raw lift, drag, and moment.
3. Compute the uncorrected coefficients at the measured dynamic pressure (use the compressible form when M >= 0.3).
4. Compute the solid and wake blockage increments, sum them, and correct the dynamic pressure and speed.
5. Apply the wall interference and streamline curvature corrections to the angle of attack and the pitching moment.
6. Re-reduce the forces at the corrected dynamic pressure to get the final CL, CD, and Cm; compute Cp distributions from the pressure taps with the corrected q.
7. Apply Reynolds number scaling if the reference data come from a different Reynolds number.
8. Repeat the measurement condition several times and report the mean coefficients with the expanded uncertainty from the repeat runs.
9. Write the correction ledger alongside the coefficients.

Correction formulas

Tare at angle alpha between two tare runs (tareshift):

tare(alpha) = tare_low + (tare_high - tare_low)
               * (alpha - alpha_low) / (alpha_high - alpha_low)

Blockage:

eps_sb = K1 * V_model / V_test_section
eps_wb = 0.25 * (S / C) * CDu
eps = eps_sb + eps_wb
q_corr = q_u * (1 + eps)^2
V_corr = V_u * (1 + eps)

Wall interference and streamline curvature:

delta_alpha_wall = delta * (S / C) * CL          (radians)
delta_alpha_curv = (S / C) * CL * (chord / (4 h)) (radians)
delta_cm = -(S / C) * CL * (chord / (8 h))

Reynolds and Mach:

CD(Re_test) = CD_ref * (Re_ref / Re_test)^n
q = 0.5 * gamma * p * M^2
Cp = Cp_inc / sqrt(1 - M^2)

Coefficients:

CL = L / (q S)          CD = D / (q S)
Cm = M / (q S c_ref)    Cp = (p_local - p_ref) / q

Uncertainty from n repeat runs:

mean = sum(x_i) / n
s = sqrt(sum((x_i - mean)^2) / (n - 1))
SE = s / sqrt(n)        U = k * SE    (k = 2 default)

Worked example

Model: wing with planform area S = 0.4 m^2, reference chord c_ref = 0.25 m in a closed rectangular test section of area 8.0 m^2, height 1.5 m, volume 6.0 m^3. Model volume 0.004 m^3.

Raw readings at alpha = 4 deg: L = 510.0 N, D = 32.0 N, M = 12.5 N m. Tare runs bracket the polar: at 0 deg tare drag 2.0 N, at 10 deg 2.2 N (lift and moment tare zero). Measured dynamic pressure q = 980 Pa.

1. Tare at 4 deg: 2.0 + 0.2 * (4 / 10) = 2.08 N of drag. Corrected forces: L = 510 N, D = 29.92 N, M = 12.5 N m.
2. Uncorrected coefficients at q = 980 Pa: CL = 510 / 392 = 1.30102, CD = 29.92 / 392 = 0.07633, Cm = 12.5 / 98 = 0.12755.
3. Blockage: eps_sb = 0.96 * 0.004 / 6 = 0.00064, eps_wb = 0.25 * (0.4 / 8) * 0.07633 = 0.000954, eps = 0.001594, q_corr = 980 * 1.001594^2 = 983.13 Pa.
4. Wall interference: delta_alpha = 0.82 * 0.05 * 1.30102 rad = 3.056 deg. Streamline curvature: 0.155 deg, delta_cm = -0.001355. Corrected angle alpha = 4 + 3.056 + 0.155 = 7.21 deg.
5. Final coefficients on q_corr: CL = 510 / (983.13 * 0.4) = 1.29688, CD = 29.92 / (983.13 * 0.4) = 0.07608, Cm = 12.5 / (983.13 * 0.4 * 0.25) - 0.001355 = 0.12579.

Repeated runs of the same condition gave drag coefficient values 0.0300, 0.0305, 0.0298, 0.0302, 0.0301: mean 0.03012, sample std 0.000259, standard error 0.000116, expanded uncertainty at coverage 2 U = 0.000232, so the reported CD is 0.03012 +/- 0.00023.

Behavior contract (gate 3)

python3 skills/aerodynamics/wind-tunnel/windtunnel-data-reduction/scripts/test_windtunnel_data_reduction.py

Stdlib unittest only, offline, deterministic. Covers tare subtraction removing the drag offset, tareshift interpolation, blockage raising the dynamic pressure, wall interference and streamline curvature values, Reynolds and Mach corrections, the coefficient formulas on the known case above, the full pipeline with ledger, and the uncertainty bounds.

Pitfalls

• Keep the reference area and length consistent everywhere: CL, CD, and Cm all use the same planform area and reference chord.
• Apply the tare before computing any coefficient; a forgotten tare leaves a drag offset that inflates CD at every angle.
• Compute the wake blockage from the uncorrected drag coefficient; iterating with the corrected value changes nothing of consequence.
• Do not apply the Prandtl Glauert factor at or above M = 1; it is a subsonic correction only.
• Report the standard error of the mean, not the per-run scatter, as the uncertainty of the reported mean; the expanded uncertainty is the coverage factor times the standard error.
• Use at least three repeat runs for a meaningful sample standard deviation.