Objectives  According to the Lighthill acoustic analogy equation and its development theory, it is feasible to analyze the wavenumber-frequency spectrum of turbulent wall pressure fluctuations, then make it an acoustic source in order to predict flow noise. Moreover, the study of the wavenumber-frequency spectrum is useful for understanding the temporal and spatial characteristics of turbulent structures.

  Methods  Taking the NACA 0012 airfoil, which was studied by Brooks, as an example, we employ the Large Eddy Simulation (LES)method to calculate the flow field and obtain a numerical solution of the wavenumber-frequency spectrum via the Fourier transform. On this basis, we take the wavenumber-frequency spectrum as an input condition for predicting the radiated noise using the acoustic analogue equation of the Goldstein version. At the same time, acoustic software is used to calculate the flow noise. Comparing these two sets of results with Brooks' empirical formula, the sound pressure level is found to be within the same order of magnitude.

  Results  The results show that the spectrum on an airfoil surface with a small curvature change is comparable with the Corcos spectrum model on a flat plate, and their general characteristics are similar. Finally, we conclude that the forecast results of the method in this paper accord better with Brooks' experimental results at low and medium frequencies.

  Conclusions  This shows that it is necessary to carry out the study of wavenumber-frequency spectra, and it is reasonable to make it the main sound source in order to predict flow noise produced at subsonic speed.