Wind Turbine Aerodynamics - 10 - Predicting Noise
23 August 2026, Pascal Weihing
BPM model for trailing edge noise prediction
Total sound pressure level is modeled by contributions from the suchtion $s$ and pressure $p$ sides and the effect of the angle of attack $\alpha$
$$ L_{p, TBLTE} = 10log_{10}\left(10^{L_{p, \alpha} / 10}+10^{L_{p, s} / 10} + 10^{L_{p, p} / 10} \right) $$
How do the contributions of the suction and pressure sides differ in the spectrum?
- when airfoil creates lift, $\delta^_p$ is typically smaller than $\delta^_s$
- level scales with $10 log_{10} \delta^*$
- for a given logal mach number, $\frac{St_p}{St_{peak}} = 1$ is reached at higher frequencies
level is lower on the pressure side
peak frequency is higher on the pressure side
The Empirical BPM Model
| pros | cons |
|---|---|
| simple implementation | model does not take into account the airfoil shape (derived for NACA0012) |
| very few input quantities required ($\alpha, \delta^*, Re$) | model contains explicit angle of attack ranges |
| very fast when using XFOIL boundary layer data | model typically overpreducts high frequencies |
| shape of spectra and peak region predicted reasonably well | -- |
The TNO model for trailing edge noise prediction
- wall-bounded turbulence is anisotropic ($\approx u_1^2:u_2^2:u_3^2 = 4:2:3$)
- pressure gradient or streamline curvature increases the effect of anisotropy
- only wall-normal component $u_2^2$ relevant for TE noise
- linear eddy viscosity turbulence models assume isotropic turbulence ($u_1^2=u_2^2=u_3^2= \frac{2}{3}k_T$)
| pros | cons |
|---|---|
| derived from physics | turbulence statistics are needed as input - flow simulation based on RANS required |
| depends on turbulence statistics | trailing edge serrations cannot be taken into account, since farfield model is derived for flow perpendicular to edge |
| works independent of airfoil shape | -- |
| applicable to angles of attack close to flow separation | -- |
| computationally relatively cheap | -- |
The Moving Axis Spectrum
- takes into account change of the turbulence spectrum of propagating in streamwise direction
- change of propagation velocity of the different eddy sizes during propagation
- original TNO model uses gaussian function
- "the higher the wave number, the less this approach matters"
Hornung Model for the Moving Axis Space
- new model should consider the decay in wavenumber space
- combination of two time scales as basis for new model + further small modifications:
- timescale of the turbulent eddies
- onsager-scale: describes decay of turbulence structures
Validation example in last lecture video