This paper reports measurements of the cross-spectral density of the wall-pressure fluctuations beneath a turbulent boundary layer for three different surface-roughness conditions. The roughness consisted of sparsely populated, uniformly distributed sand particles—each roughness being distinguished by the sand-particle size. Separate studies of the spectral density and of the lateral and longitudinal narrow-band normalized space-time correlations were made in order to determine the cross-spectral density of the wall-pressure fluctuations. The results indicate that only the spectral density is strongly dependent on roughness size, for the roughnesses examined. To relate quantitatively the spectral densities measured on each surface, the roughness was characterized in terms of Nikuradse's equivalent sand-roughness parameter. The spectral density was then normalized, using this roughness parameter, the shear velocity, and the local coefficient of skin friction. Also, for the roughest surface, the pressure fluctuations in the vicinity of a particle and the correlation of these fluctuations with pressure fluctuations at some distance from the particle were examined in order to determine any observable effects of the local flow about the particles. The results indicate that the local flow can be ignored, provided that the roughness size is not too large. The measurements do not reveal any direct relation between the cross-spectral densities measured on rough surfaces with those measured on smooth.
A linear rigid frame, cylindrical capillary theory of sound propagation in porous media is extended to include nonlinear effects of the Forchheimer type, by making a particle velocity-dependent correction to the complex density. This type of nonlinearity becomes important at incident sound-pressure levels above approximately 120 dB re: 20 μPa for highly porous fibrous materials. Data from three experiments on air-saturated porous media and foams, at levels up to 170 dB, are compared to the rigid frame theory with Forchheimer-type extension. One of the experiments measured a low-frequency approximation for the complex density directly; the others measured internal attenuation and surface admittance (inverse impedance). The generally good agreement found between predictions based on the Forchheimer-type nonlinear theory and each of the experiments suggests that this type of nonlinearity is the dominant one for propagation in many types of air-saturated fibrous porous media. Some interesting surface absorption characteristics are predicted at incident sound-pressure levels above 140 dB, especially at lower frequencies.
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.
It is well known that the flow resistance, as defined by Darcy's law, becomes a function of the fluid velocity when the fluid velocity becomes sufficiently large. For porous materials in air, there appears to be two separate nonlinear flow regimes: For low velocities, the resistance coefficient increases with the square of the fluid velocity; and, for high velocities, the resistance coefficient increases linearly with the magnitude of the fluid velocity. Similar regimes also exist for the mass coefficient; however, the mass coefficient is observed to decrease with increasing fluid velocity. (For pure-tone excitation, it is shown that these relationships then hold for the complex magnitude of the particle velocity. ) In this paper, the two nonlinear flow regimes are parametrized for several porous materials. Nonlinear corrections are made to linear wave theory, and numerical solutions for pure tones are obtained that are then used to predict surface admittance and internal pressures of finite length sample. A simple surface pressure criterion is put fourth based upon the materials nonlinear parameters that gives an approximate maximum surface pressure that a porous material could be exposed to before nonlinear phenomena become important in describing the material's characteristics. PACS numbers: 43.25.Ba, 43.25.Ed, 43.55.Ev
This work concerns both the theoretical prediction and measurement of structural parameters in open-cell highly porous polyurethane foams. Of particular interest are the dynamic flow resistance, thermal time constant, and mass structure factor and their dependence on frequency and geometry of the cellular structure. The predictions of cell size parameters, static flow resistance, and heat transfer as accounted for by a Nusselt number are compared with measurement. Since the static flow resistance and inverse thermal time constant are interrelated via the ’’mean’’ pore size parameter of Biot, only two independent measurements such as volume porosity and mean filament diameter are required to make the predictions for a given fluid condition. The agreements between this theory and nonacoustical experiments are excellent.
A standing wave apparatus employing multiple microphones for measuring fundamental properties of acoustic materials is analyzed. The apparatus is basically a tube with a compression driver at one end with a rigid plug at the other and a finite length sample of acoustic material strategically located in between. A microphone array is then used in obtaining the pressure and velocity boundary conditions of the sample from which basic acoustic properties can be calculated. Such properties as internal propagation constant, characteristic admittance (inverse impedance), and bulk modulus are measured and data for a 100-pore-per-inch (ppi) open-cell acoustic foam is presented. A relatively new parameter called the complex flow impedance is measured under low-and high-intensity levels and is shown to exhibit finite amplitude properties. Of particular concern is how finite sample lengths effect the accuracy of the measurements. It is shown that in general a long sample length (on the order of a wavelength or more) is required for the accurate measurement of propagation constant, characteristic admittance, and bulk modulus measurements while a short length (much less than a wavelength) is required for good finite amplitude flow impedance measurements. Previous studies of flow impedance have been carried out using a similar but not identical apparatus [W. E. Zorumski and T. L. Parrott, "Nonlinear AcousticTheory for Rigid Porous Materials," U.S. NASA TN-6196, 1971; K. U. Ingard and T. A. Dear, "Measurements of the Acoustic Flow Resistance," J. Sound Vib. 103, 567-572 (1985) ]. However, the previous studies have lacked an analysis of the possible errors in the measurement methods that can be very significant for these types of flow impedance measurements. PACS numbers' 43.25.Ed, 43.25.Zx, 43.85.Bh LIST OF SYMBOLS a• effective pore radius in rigid frame model Zz. d sample thickness Zs, , kb complex propagation constant of wave in porous material ]•b K complex bulk modulus of fluid in porous material M mass loading part of flow impedance, = I'm(Zr)/cø Po static pressure of fluid Pb P complex excess (acoustic) pressure amplitude (taken to be the peak value, not rms) Po Npr Prandtl number of fluid rrø R resistive part of flow impedance, = Re(Z•.) v U complex particle velocity (the peak value, co not rms) COT
This work is concerned primarily with the acoustic structure and propagation of sound in highly porous, layered, fine fiber materials. Of particular interest is the utilization of the Kozeny number for determining the static flow resistance and the static structure factor based on flow permeability measurements. In this formulation the Kozeny number is a numerical constant independent of volume porosity at high porosities. The other essential parameters are then evaluated employing techniques developed earlier for open-cell foams. [J. Acoust. Soc. Am. 72, 879–887 (1982)]. The attenuation and progressive phase characteristics in bulk samples were measured and compared with predicted values. The agreements on the whole were very satisfactory.
This paper is concerned with predicting the acoustic behavior of highly porous, layered, flexible, fine fiber materials at low frequencies. A theoretical model of fiber behavior is developed that consists of two independent modes of vibration that exhibit resonance at zero frequency and a finite frequency. This model also incorporates a fiber parameter g that governs the fraction of fibers that can resonate which is now hypothesized to be frequency dependent and was found to range between a comparatively low value g0 near zero frequency and a high value g∞ at higher frequencies. These asymptotic values and the location of the transition region were found empirically. There is good agreement between this model and experiments designed to measure the effective resistivity φe and the effective density ρe of the fluid in the pores of the fibers over a wide range of frequencies.
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