Windtunnel Wall Corrections

Wind Tunnel Wall Corrections (aerodynamics/wind-tunnel/windtunnel-wall-corrections)

Use when the task is correcting measured aerodynamic coefficients for the presence of the walls of a closed solid-wall (slotted or solid) test section, the classical low-speed correction set of Barlow, Rae and Pope (Low-Speed Wind Tunnel Testing, boundary corrections chapter, method set paraphrased here): solid blockage, wake blockage, horizontal buoyancy drag, and the lift interference and streamline curvature corrections. The input is a set of coefficients already reduced from raw balance readings at the measured dynamic pressure; the output is the wall-corrected polar an operator would compare with free-air or CFD data. Raw-run data reduction, tare subtraction, Reynolds and Mach corrections and uncertainty estimation belong to aerodynamics/wind-tunnel/windtunnel-data-reduction, not to this leaf.

Domain quick reference

Closed rectangular test section of cross-sectional area C (m^2) and height h, model of planform area S_model, volume V_model and span b. All corrections below are first order in the small blockage factors.

• Solid blockage: eps_sb = K1 * V_model / C^1.5, with C^1.5 the cubic scale of the section (volume units) and K1 = 0.52 for a closed rectangular section (classical Barlow value, allow override with the tunnel-specific calibration).
• Wake blockage: eps_wb = (S_model / (4 * C)) * CDu, with CDu the uncorrected drag coefficient at the uncorrected dynamic pressure.
• Total blockage: eps = eps_sb + eps_wb.
• Dynamic pressure and speed: q_c = q_u * (1 + eps)^2 and V_c = V_u * (1 + eps). Blockage always raises q and V.
• Buoyancy drag: dCD_buoy = -(dP/dx) * V_model / (q * S_ref), with dP/dx the streamwise static pressure gradient of the empty section in Pa/m. Sign convention: in a closed solid-wall section the core flow accelerates downstream, dP/dx is negative and the increment is positive, drag added; a positive gradient subtracts drag. The buoyancy increment is added to the corrected drag coefficient.
• Lift interference: delta_alpha = delta * (S_model / C) * CLu in radians, delta = pi / 48 for the closed wall (classical value, allow override); corrected alpha = alpha_u + delta_alpha.
• Lift factor: sigma = (pi^2 / 48) * (b / h)^2 for the closed wall (classical value, allow override), valid while b < h.
• Corrected coefficients (first-order form, re-referencing is already inside the factors): CLc = CLu * (1 - sigma - 2 * eps_sb) CDc = CDu * (1 - 3 * eps_sb - 2 * eps_wb) + dCD_buoy
• K1, delta and the sigma coefficient are classical approximations for a closed rectangular section; replace them with the tunnel-specific calibration when one is available (see Compliance).

Workflow

1. Gather the uncorrected measured coefficients CLu, CDu and alpha_u per point, the model planform area S_ref, model volume and span, and the test section area C, height h and uncorrected dynamic pressure q_u.
2. Optionally record the empty-section streamwise pressure gradient dP/dx for the buoyancy term.
3. Compute eps_sb with solid_blockage, eps_wb with wake_blockage and eps with total_blockage (module scripts/windtunnel_wall_corrections_logic.py).
4. Compute sigma with sigma_lift_factor and the angle increment with lift_interference_delta_alpha to get alpha_corrected.
5. Compute CLc with corrected_lift_coefficient and CDc with corrected_drag_coefficient, adding the buoyancy increment from buoyancy_drag_increment when dP/dx is available.
6. Correct the dynamic pressure and speed with corrected_dynamic_pressure and corrected_velocity.
7. For a single point call apply_wall_corrections once; for a whole polar call correct_measured_polar, which returns every corrected point with its correction ledger.
8. Sanity check the fit constraints: model volume below C^1.5, planform area below C, span below h; violations raise ValueError.

Worked example

Model with S_model = 0.16 m^2, volume 0.004 m^3, CDu = 0.03, CLu = 0.5 at alpha_u = 4 deg, span 0.9 m, in a closed test section 1.4 m by 1.0 m (C = 1.4 m^2, h = 1.0 m), q_u = 500 Pa.

• Solid blockage: eps_sb = 0.52 * 0.004 / 1.4^1.5 = 0.0012557.
• Wake blockage: eps_wb = (0.16 / (4 * 1.4)) * 0.03 = 0.0008571.
• Total blockage: eps = 0.0021128.
• Dynamic pressure: q_c = 500 * 1.0021128^2 = 502.12 Pa; velocity ratio V_c / V_u = 1.00211.
• Lift factor: sigma = (pi^2 / 48) * (0.9 / 1.0)^2 = 0.166550.
• Angle increment: delta_alpha = (pi / 48) * (0.16 / 1.4) * 0.5 rad = 0.003740 rad = 0.2143 deg, so alpha_c = 4.2143 deg.
• Corrected lift: CLc = 0.5 * (1 - 0.166550 - 2 * 0.0012557) = 0.41547, below the uncorrected 0.5 as expected for positive blockage.
• Corrected drag: CDc = 0.03 * (1 - 3 * 0.0012557 - 2 * 0.0008571) = 0.0298356, below the uncorrected 0.03.
• Buoyancy with dP/dx = -0.25 Pa/m: dCD_buoy = 0.25 * 0.004 / (500 * 0.16) = 1.25e-5, so CDc = 0.0298356 + 0.0000125 = 0.0298481.

Verification

• eps_sb, eps_wb and eps are non-negative for physical inputs, and every correction shrinks as the model-to-tunnel size ratio shrinks (smaller model volume, planform area or span).
• q_c and V_c exceed their uncorrected values for eps above zero, and collapse to the identity at eps = 0.
• Corrected CL stays below the uncorrected value at positive lift with positive blockage; corrected CD stays below CDu when no buoyancy gradient is applied, and the negative streamwise gradient of a closed section adds drag on top.
• The worked example above reproduces the reference values within 1% (asserted in the contract test).
• ValueError is raised on non-positive inputs and on any model larger than the test section: model volume at or above C^1.5, planform area at or above C, or span at or above the section height.

Related leaves

• aerodynamics/wind-tunnel/windtunnel-data-reduction: reduces raw balance runs (tare, tare shift, Reynolds, Mach, uncertainty) into the uncorrected coefficients this leaf takes as input.
• aerodynamics/drag-polars/drag-polar: the parabolic polar model to compare the corrected points against.
• aerodynamics/drag-polars/lift-curve-slope: the predicted lift slope to check corrected CL against corrected alpha.
• aerodynamics/cfd/cfd-validation: validation culture; wall-corrected wind tunnel data is the experimental anchor for CFD validation, so this correction chain and its constants belong in the validation report next to the error metrics.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 skills/aerodynamics/wind-tunnel/windtunnel-wall-corrections/scripts/test_windtunnel_wall_corrections.py

The test covers the worked example within 1%, internal consistency (monotone shrinkage with model-to-tunnel size, eps non-negative, corrected CL below uncorrected), the q and V identity at zero blockage, the buoyancy sign convention, zero-correction round trips, the full single-point pipeline against the individual calls, a three-point polar against per-point corrections, and ValueError rejection of non-positive inputs and models larger than the test section.

Pitfalls

• Feed uncorrected coefficients: applying this set to coefficients that already carry corrections double-counts the wall effects.
• Do not re-divide the forces by the corrected q: the first-order coefficient factors already contain the dynamic pressure re-referencing.
• Compute the wake blockage from the uncorrected CDu at the uncorrected dynamic pressure, not from an iterated value.
• Take dP/dx from the empty test section, not from a pressure field measured with the model installed.
• Watch the units: dP/dx in Pa/m, q in Pa, volumes in m^3.
• Treat K1 = 0.52, delta = pi/48 and the sigma coefficient pi^2/48 as classical closed-rectangular approximations, not as universal constants; prefer the tunnel-specific calibration when available, and never trust the first-order forms when the model nearly fills the section (span approaching the height, or blockage above a few percent).

Compliance

• STANDARDS-REF, gated: false. NACA Report 824 (public domain) is named as the reference-only anchor for the measured data culture; standard engineering methodology is summarized, not reproduced.
• Honesty note: K1 = 0.52, delta = pi/48 and the sigma coefficient pi^2/48 are classical approximations for a closed rectangular test section as documented in the Barlow, Rae and Pope method set. The operator should replace them with the tunnel-specific calibration when available; the logic functions accept k1, delta and sigma_coefficient overrides for exactly that purpose.