A theoretical and experimental study of the influence of shear flow on the attenuation of sound in a lined duct is presented. Both upstream and downstream propagation are considered. Solutions of the linearized equations for acoustic-wave propagation in flow, based upon both uniform and power-law models of the mean-flow profile, are compared with attenuation measurements in a duct having two opposite side walls lined with a porous fiberglas® blanket for a frequency-geometry range kδ⩽1 and midstream Mach numbers Ml<0.2. Here, k is the plane wavenumber and δ is the aerodynamic boundary-layer thickness. Both profile models yield results in close agreement with experiments at low frequencies, kδ<0.1. For intermediate and high frequencies, 0.1 <kδ<1, the uniform-flow model fails, as expected, since it can only account for the convective effects of the flow upon attenuation of sound. It was not expected that the power-law model, which seemingly accounts for the effects of both convection and refraction within the shear layer upon the sound wave, would yield results much the same as those obtained for the uniform-flow profile, and thus fail in various degrees for this frequency range. Also, scattering of sound by turbulent flow does not appear to be strong enough to account for discrepancies between theory and experiment. As a result, the problem of accurately predicting the effects of refraction upon sound attenuation in the range 0.1 <kδ <1 remains unsolved. The uniform-flow model, for which solutions are easily obtained, proves useful from an acoustical-engineering point of view.
The correlation properties of turbulent wall pressure fluctuations are investigated experimentally with a view toward developing an adequate phenomenological model of the pressure correlation function for use in engineering calculations. It was found that both mean eddy sizes and mean eddy lifetimes determined by averaging over broad frequency bands did not contain sufficient information to accurately describe the high frequency end of the turbulent power spectrum. Thus, such gross quantities are of somewhat limited utility in detailed analysis, for instance, in predicting response of multimodal mechanical systems driven by flowing turbulence. However, by measuring eddy sizes and lifetimes over narrow frequency bands it appears possible to construct mathematical models for the turbulent pressure correlations which are successful in predicting the turbulent power spectrum over the frequency band of interest which could include the entire spectrum. In addition, measurements of rms pressure and space-time correlations are presented which supplement the data obtained by W. W. Willmarth [-NASA Memo. 3-17-59 W (1959)-] for a somewhat higher mach range.
Response characteristics of the random motion of a bar forced by bounda^-layer turbulence are investigated experimentally for flow speeds up to a Mach number of 0.3. The experimental results are found to be in reasonably good agreement with theoretical calculations of response obtained by using a phenomenological convecting and decaying pressure correlation function for the turbulence, having parameters which are measurable and relatively easy to interpret. However, a new interpretation is placed upon statistical parameters such is the mean eddy lifetimes and sizes which specify the correlation field. Experimental and theoretical results are viewed in terms of a pole-zero diagram in the complex-frequency plane, which portrays graphically the interaction between the convecting and decaying properties of the turbulence and the bar. Because of an observed velocity and frequency dependence of the turbulent correlation lifetimes, it is found that random motion of a bar due to boundary-la}^ turbulence is controlled essentially by its transient response, independent of mode number and convection velocity. The theoretical results obtained for the bar are readily extended to a plate. Extension of the anatysis to a higher Mach-number range also is considered. Symbolsa m , a,mr = Fourier coefficient of displacement response of the bar (plate) 0?n, Omr = Fourier coefficient of the forcing function for the bar (plate) c m , Cmr = bending wave velocity of the rath (rarth) mode of the bar (plate) f(x,t) = force function whose space-time correlations are specified h = thickness of the bar (plate) k m , kmr = eigenvalue of the rath mode of the bar (plate) l x = length of the bar (plate) l y = width of the bar (plate) m,n,r,s = positive integers p{x,y,t) = pressure / = time v = mean eddy drift velocity w(x,y,t) = displacement of the neutral plane of the bar (plate) x,y = rectangular space coordinates B = flexural rigidity of the bar (plate) E -Young's modulus for a bar F T (x,oo)= Fourier transform of the force /r(ff,0 L x = longitudinal eddy size L y = lateral eddy size M = mass per unit length of the bar (per unit area of the plate) Py(x,v,co) = Fourier transform of the pressure, PT(x,y,t)
The displacement response of a simple panel (bar) to turbulent boundary layer pressure fluctuations has been investigated experimentally and the results compared with theoretical predictions based upon a decaying and convecting correlation field as proposed by R. H. Lyon [J. Acoust. Soc. Am. 28, 391–398 (1956)]. The response is interpreted in terms of a locus of natural frequencies of the turbulence and the panel in the complex frequency domain with special attention focused on hydrodynamic considerations. The importance and interpretation of parameters such as eddy decay frequencies and eddy convection frequencies as obtained from correlation studies will be emphasized. (This work was sponsored by the U. S. Air Force.)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.