## Abstract

Two-point velocity statistics near the trailing edge of a controlled diffusion airfoil are obtained, both experimentally and analytically, by decomposing Poisson's equation for pressure into the mean-shear (MS) and turbulence-turbulence (TT) interaction terms. The study focuses on the modeling of each interaction term, in order to allow for the reconstruction of the wall-pressure spectra from tomographic velocimetry data, without numerically solving for pressure. The two-point correlation of the wall-normal velocity that describes the magnitude of the MS source term is found to be influenced by various competing factors such as blocking, mean-shear, and the adverse mean pressure gradient. The blocking term is found to supersede the other interaction terms close to the wall, making the two-point velocity correlation self-similar. The most dominant TT term that contributes to far-field noise for an observer located perpendicular to the airfoil chord at the mid-span is shown to be the one that quantifies the variation of the wall-normal velocity fluctuations in the longitudinal direction because of the statistical homogeneity of turbulence in planes parallel to the wall. A model to determine the contribution of the TT interaction term is proposed where the fourth-order two-point correlation can be modeled using Lighthill's approximation. However, its contribution toward wall-pressure spectra is found to be substantially lower than the MS term in the present case.

Original language | English |
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Article number | 105105 |

Number of pages | 27 |

Journal | Physics of Fluids |

Volume | 32 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2020 |