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Improvements to the Two-Thickness Method for Deriving Acoustic Properties of Materials

The characteristic impedance and other derivative acoustic properties of a material can be derived from impedance tube data using the specific impedance measured from samples with two different thicknesses. In practice, samples are chosen so that their respective thicknesses differ by a factor of 2. This simplifies the solution of the equations relating the properties of the two samples so that the computation of the characteristic impedance is straightforward. This approach has at least two drawbacks. One is that it is often difficult to acquire or produce samples with precisely a factor of 2 difference in thickness. A second drawback is that the phase information contained in the imaginary part of the propagation constant must be unwrapped before subsequent computations are performed. For well-behaved samples, this is not a problem. For ill behaved samples of unknown properties, the phase unwrapping process can be tedious and difficult to automate. Two alternative approaches have been evaluated which remove the factor-of-2 sample thickness requirement and directly compute unwrapped phase angles. One uses a Newton-Raphson approach to solve for the roots of the samples' simultaneous equations. The other produces a wave number space diagram in which the roots are clearly discernable and easily extracted. Results are presented which illustrate the flexibility of analysis provided by the new approaches and how this can be used to better understand the limitations of the impedance tube data.

Palumbo, Daniel L.↗

Comparing Acoustic Prediction Methods for Additively Manufactured Porous Strutures

While macroscale methods for predicting the acoustic properties of porous structures have been popular in the past, they often require time-consuming manufacturing and testing workflows. Meanwhile, microscale approaches allow the prediction of transport parameters based exclusively on a periodic structure’s unit cell geometry. Here, we compare these methods to predict the characteristic impedance of additively manufactured porous structures. We use the microscale approach to estimate the geometry’s transport parameters, then predict the characteristic properties using the Johnson-Champoux-Allard (JCA) model. We measure the acoustic properties of the printed structures using a normal incidence impedance tube and estimate the transport parameters using an inverse characterization approach. We use the two-thickness method as a macroscale approach to predict the characteristic properties from the measured surface impedances of two sample thicknesses. Finally, we compare these characteristic prediction methods. Our results show that the inverse characterization and two-thickness methods offer the closest match to the measured values at low frequencies.

impedance↗

The Two-Cavity Method for Characterizing Acoustical Materials—an Interlaboratory Study

This study focuses on understanding the sound absorption characteristics of porous acoustic materials, which are determined by two key parameters independent of material thickness: characteristic impedance and propagation constant. These parameters can be characterized by testing a porous sample concept in a normal incidence impedance tube using either the two-thickness or the two-cavity method. In the two-thickness method, two samples of varying thicknesses are required. In contrast, the two-cavity method requires testing one sample at two different air cavity depths behind the porous material. This method is particularly advantageous for materials that are costly or challenging to fabricate. This interlaboratory study evaluates the variability of characteristic properties determined using the two-cavity method. Porous acoustic materials were additively manufactured and tested in the Liner Technology Facility(LTF)at NASA Langley Research Center and the Mechanics, Acoustics and Dynamics Lab (MADLab) at Michigan Technological University. The characteristic properties derived from various cavity depth combinations were used to predict the surface impedance of the sample with a rigid backing. The prediction was then compared the measured impedance spectrum. It was also found that the combinations of cavity depths can significantly influence the accuracy of the deduced properties.

acoustic liners↗

Assessment of Bulk Absorber Properties for Multi-Layer Perforates in Porous Honeycomb Liners

CONTINUING progress in materials technology provides potential for improved acoustic liners for attenuating broadband fan noise emissions from aircraft engine nacelles. Conventional liners (local-reacting perforate-over-honeycomb structures) provide significant narrow-band attenuation, but limited attenuation over wide bandwidths. Two approaches for increasing attenuation bandwidth are to (1) replace the honeycomb structure with bulk material, or (2) cascade multiple layers of perforate/honeycomb structures. Usage of the first approach is limited because of mechanical and maintenance reasons, while multi-layer liners are limited to about three layers because of their additional mechanical complexity, depth and weight. The current research concerns a novel approach reported by the University of Cincinnati, in which a single-layer conventional liner is converted into an extended-reaction, broadband absorber by making the honeycomb core structure porous. This modified single-layer liner requires no increase in depth and weight, and minimal increase in mechanical complexity. Langley has initiated research to identify potential benefits of liner structures with porous cell walls. This research has two complementary goals: (1) develop and validate experimental techniques for treating multi-layer perforates (representative of the internal cells of a liner with porous cell walls) as 1-D bulk materials, and (2) develop analytical approaches to validate this bulk material assumption. If successful, the resultant model can then be used to design optimized porous honeycomb liners. The feasibility of treating an N-layer perforate system (N porous plates separated by uniform air gaps) as a one-dimensional bulk absorber is assessed using the Two-Thickness Method (TTM), which is commonly used to educe bulk material intrinsic acoustic parameters. Tests are conducted with discrete tone and random noise sources, over an SPL range sufficient to determine the nonlinearity of the test specimens, for test specimens consisting of 5, 10 and 15% porous plates. Measured impedances for two liner thicknesses (e.g., 12 and 24 layers) are used as input to the TTM to determine the characteristic impedance and propagation constant that characterize these liners as bulk absorbers. These parameters are then used to calculate the predicted impedance of liners with different thicknesses (e.g., 36 layers), and a comparison of predicted and measured impedances for these other thicknesses is used to determine the efficacy of this approach. Finally, an independent method is used to educe the propagation constant for a single representative sample, and excellent comparison between the results for this method and those for the TTM provides increased confidence in the results achieved with the TTM. In general, the results demonstrate these multi-layer perforates can be acceptably treated as bulk absorbers.

Jones, Michael G.↗

Cascaded Perforates as One-Dimensional, Bulk Absorbers

Porous cell honeycomb liners for aircraft engine nacelles offer the possibility of exploiting extended reaction effects to improve liner attenuation bandwidth as generally attributed to the performance of bulk absorbers. This paper describes an analytical procedure, starting with an impedance prediction model for a single perforated plate, to estimate the bulk-absorber parameters for a cascade of such perforates - a first step to modeling a porous wall honeycomb structure. The objective is to build confidence in a lumped element impedance model, when applied to a uniformly-spaced set of porous plates to predict its .bulk. absorber properties. The model is based upon a modified version of the two-parameter flow resistance model of the form A + BV(sub inc), where A and B are physics-based, semi-empirical parameters that are adjusted to provide an optimum fit to a composite dataset from three plate porosities of 2.5, 5 and 10%. The composite dataset is achieved by reformulating the two-parameter flow resistance model into a .reduced pressure drop coefficient. dependency on perforate hole Reynolds number. The resulting impedance model is employed to calculate surface impedance spectra for N and 2N-layer perforate cascades. The well-known two-thickness method for experimental determination of bulk-absorber parameters is then applied to these .synthesized. data sets to predict the characteristic impedance and propagation constant for the perforate cascades. These results are then compared with experimental results reported in a companion paper.

Parrott, T. L.↗

Evaluation of Novel Liner Concepts for Fan and Airframe Noise Reduction

This paper presents a review of four novel liner concepts: soft vanes, over-the-rotor liners, external liners, and flap side-edge liners. A number of similarities in the design and evaluation of these concepts emerged during these investigations. Since these were the first attempts to study these particular liner concepts, there was limited information to guide the design process. In all cases, the target frequencies (or frequency range) were known, but the optimum acoustic impedance and optimum liner placement were typically not known. For these cases, the maximum available surface was used and a c-impedance was targeted based on the assumption the sound field impinges on the surface at normal incidence. This choice proved fruitful for every application. An impedance prediction model was used to design variable-depth liner configurations, and a graphical design code (ILIAD) was developed to aid in this process. The ability to build increasingly complex liner configurations via additive manufacturing was key, such that multiple designs could quickly be tested in a normal incidence impedance tube. The Two-Thickness Method was used to evaluate available bulk materials, such that bulk liners could also be considered for each application. These novel liner concepts provide sufficient noise reduction to warrant further investigations.

Jones, M. G.↗