The effect of frequency dependence and anisotropy on the aerofoil turbulent boundary layer wall pressure spectrum

Several versions of the TNO model have been implemented to compute the surface pressure spectrum beneath the turbulent boundary layer in the vicinity of the trailing edge of an aerofoil. These models provide essential input for widely used Amiet-method-type trailing edge noise prediction schemes. However, the accuracy of these reduced order models remains limited, particularly under varying pressure gradient conditions. To address this, we introduce modifications to the original model formulations, including the incorporation of frequency-dependent correlation scales in the turbulent velocity spectrum and a kinematic shape factor accounting for boundary layer pressure gradient effects in the definition of the correlation length scale. The methodology is implemented using fast-turnaround Reynolds-Averaged Navier–Stokes solutions together with XFOIL panel-method boundary-layer inputs for NACA0012 and NACA0015 aerofoils. The test cases include tripped turbulent boundary layers at zero angle of attack with free-stream velocities of 20–80 m/s ( R e c = 2.6 × 10 5 –1.0 × 10 6 ), and naturally transitioned boundary layers at angles of attack up to 12 ∘ with velocities of 30–50 m/s ( R e c = 1.7 × 10 6 –2.9 × 10 6 ). The proposed model predicts surface pressure spectra within 1–2 dB of experimental data in the low- to mid-frequency range, representing an improvement over previous TNO variants. Moreover, the anisotropy stretching coefficients also show good agreement with boundary-layer measurements.