TY - JOUR
T1 - An analytical correction to Amiet's solution of airfoil leading-edge noise in non-uniform mean flows
T2 - Journal of Fluid Mechanics
AU - Zhong, S.
AU - Zhang, X.
AU - Peng, B.
AU - Huang, X.
N1 - Export Date: 12 January 2023; Cited By: 5; Correspondence Address: S. Zhong; Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, Hong Kong; email: [email protected]; CODEN: JFLSA
PY - 2020
Y1 - 2020
N2 - Gust/turbulence-leading edge interaction is a significant source of airfoil broadband noise. An approach often used to predict the sound is based on Amiet's flat-plate solution. Analytical studies have been conducted to investigate the influences of airfoil geometries, non-uniform mean flows and turbulence statistics, which, however, were often too convoluted. In this work, the problem is revisited by proposing simple corrections to the standard flat-plate solution to account for the effect of non-uniform mean flows of real airfoils. A key step in the method is to use a new space-time transformation that is analogous to the Prandtl-Glauert transformation to simplify the sound governing equation with spatially varying coefficients to a classical wave equation, which is then solved using the Schwarzschild technique as in Amiet's solution. The impacts of Mach number, wavenumber and airfoil geometry on the prediction accuracy are investigated for both single-frequency and broadband cases, and the results are compared against high-fidelity simulations. It predicts the sound reduction by the airfoil thickness, and reveals that the reduction is caused by the non-uniform streamwise velocity. The limitations of the model are discussed and the approximation errors are estimated. In general, the prediction error increases with the airfoil thickness, the sound frequency and the flow Mach number. Nevertheless, in all cases studied in this work, the proposed correction can effectively improve the prediction accuracy of the flat-plate solution much more efficiently compared to numerical solutions of the Euler equations using computational aeroacoustics. © 2019 Cambridge University Press.
AB - Gust/turbulence-leading edge interaction is a significant source of airfoil broadband noise. An approach often used to predict the sound is based on Amiet's flat-plate solution. Analytical studies have been conducted to investigate the influences of airfoil geometries, non-uniform mean flows and turbulence statistics, which, however, were often too convoluted. In this work, the problem is revisited by proposing simple corrections to the standard flat-plate solution to account for the effect of non-uniform mean flows of real airfoils. A key step in the method is to use a new space-time transformation that is analogous to the Prandtl-Glauert transformation to simplify the sound governing equation with spatially varying coefficients to a classical wave equation, which is then solved using the Schwarzschild technique as in Amiet's solution. The impacts of Mach number, wavenumber and airfoil geometry on the prediction accuracy are investigated for both single-frequency and broadband cases, and the results are compared against high-fidelity simulations. It predicts the sound reduction by the airfoil thickness, and reveals that the reduction is caused by the non-uniform streamwise velocity. The limitations of the model are discussed and the approximation errors are estimated. In general, the prediction error increases with the airfoil thickness, the sound frequency and the flow Mach number. Nevertheless, in all cases studied in this work, the proposed correction can effectively improve the prediction accuracy of the flat-plate solution much more efficiently compared to numerical solutions of the Euler equations using computational aeroacoustics. © 2019 Cambridge University Press.
KW - Aeroacoustics
KW - Aerodynamics
KW - Airfoils
KW - Computational aeroacoustics
KW - Forecasting
KW - Mach number
KW - Approximation errors
KW - Governing equations
KW - High-fidelity simulations
KW - Non-uniform mean flow
KW - Space-time transformations
KW - Spatially varying coefficients
KW - Stream-wise velocities
KW - Turbulence statistics
KW - broadband data
KW - correction
KW - noise
KW - numerical method
KW - sound velocity
KW - spatiotemporal analysis
KW - turbulent flow
KW - Acoustic noise
KW - aeroacoustics
U2 - 10.1017/jfm.2019.839
DO - 10.1017/jfm.2019.839
M3 - Journal article
SN - 0022-1120
VL - 882
SP - A291-A2932
JO - J. Fluid Mech.
JF - J. Fluid Mech.
ER -