Acoustic scaling of an axial fan with non-uniform inlet flows

An experimental study was carried out to vary circumferential and radial components of incoming disturbances for a propeller-type axial fan connected to an anechoically terminated inlet duct. It was suggested that the acoustic pressure from rotating blades encountering a low-frequent gust have the scaling parameter of\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\rho _0 c_0 |\underline a |$$ \end{document} Ma, while the one for a high-frequent gust be properly scaled by\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\rho _0 c_0 |\underline a |$$ \end{document} . Here\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\rho _0 c_0 |\underline a |$$ \end{document} , Ma are the characteristic impedance of medium, the amplitude of disturbed velocity, and Mach number, respectively. These scalings were applied to identify both compact and non-compact noise sources from low-frequent gusts using the spectral decomposition method. The method of acoustic scaling proposed in this study turned out to be more effective for the sound radiated into a duct by the interaction of low-frequent incoming gusts with the propeller fan than previous approaches.