Willie R. Watson

VALIDATION OF AN IMPEDANCE EDUCTION METHOD IN FLOW

Results are reported for validating a method for educing the normal incidence impedance of a locally reacting liner in a grazing incidence, nonprogressive acoustic wave environment with flow. The results demonstrate the ability of the method to reproduce the normal incidence admittance of a solid steel plate and normal incidence impedance of two soft test liners in a uniform flow. The selected test liners are known to be locally reacting and exhibit no amplitude-dependent impedance nonlinearities and only minimal flow effects. Baseline results for these liners are, therefore, established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewarts adaptation (Stewart, G. W., III, A Modification of Davidons Minimization Method to Accept Difference Approximations of Derivatives, Journal of ACM, Vol. 14, No. 1, 1967, pp. 72-83) of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method very Marly reproduces the normal incidence impedance spectrum for each of the test liners; thus, its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers is demonstrated.

Benchmark Data for Evaluation of Aeroacoustic Propagation Codes With Grazing Flow

Increased understanding of the effects of acoustic treatment on the propagation of sound through commercial aircraft engine nacelles is a requirement for more efficient liner design. To this end, one of NASA s goals is to further the development of duct propagation and impedance reduction codes. A number of these codes have been developed over the last three decades. These codes are typically divided into two categories: (1) codes that use the measured complex acoustic pressure field to reduce the acoustic impedance of treatment that is positioned along the wall of the duct, and (2) codes that use the acoustic impedance of the treatment as input and compute the sound field throughout the duct. Clearly, the value of these codes is dependent upon the quality of the data used for their validation. Over the past two decades, data acquired in the NASA Langley Research Center Grazing Incidence Tube have been used by a number of researchers for comparison with their propagation codes. Many of these comparisons have been based upon Grazing Incidence Tube tests that were conducted to study specific liner technology components, and were incomplete for general propagation code validation. Thus, the objective of the current investigation is to provide a quality data set that can be used as a benchmark for evaluation of duct propagation and impedance reduction codes. In order to achieve this objective, two parallel efforts have been undertaken. The first of these is the development of an enhanced impedance eduction code that uses data acquired in the Grazing Incidence Tube. This enhancement is intended to place the benchmark data on as firm a foundation as possible. The second key effort is the acquisition of a comprehensive set of data selected to allow propagation code evaluations over a range of test conditions.

Comparison of Acoustic Impedance Eduction Techniques for Locally-Reacting Liners

Typical acoustic liners used in current aircraft inlets and aft-fan ducts consist of some type of perforated facesheet bonded to a honeycomb core. A number of techniques for determining the acoustic impedance of these locallyreacting liners have been developed over the last five decades. In addition, a number of models have been developed to predict the acoustic impedance of locallyreacting liners in the presence of grazing flow, and to use that information together with aeroacoustic propagation codes to assess the noise absorption provided by these liners. These prediction models have incorporated the results from databases acquired with specific impedance eduction techniques. Thus, while these prediction models are acceptable for liners that are similar to those tested in these databases, their application to new liner configurations must be viewed with caution. The primary purpose of this paper is to provide a comparison of impedance eduction techniques that have been implemented at various aerospace research laboratories in the United States (NASA Langley Research Center, General Electric Aircraft Engines, B. F. Goodrich and Boeing). A secondary purpose is to provide data for liner configurations that extend the porosity range beyond that which has been previously used in common aircraft engine nacelles. Two sets of liners were designed to study the effects of three parameters: perforate hole diameter, facesheet thickness and porosity. These two sets of liners were constructed for testing in each of the laboratories listed above. The first set of liners was designed to fit into the NASA Langley and Boeing test facilities. The second set was designed to fit into the General Electric Aircraft Engines and B. F. Goodrich test facilities. By using the same parent material, both sets of liners were identical to within the limits of material and fabrication variability. Baseline data were obtained in the normal incidence impedance tubes at NASA Langley and B. F. Goodrich. The results were found to compare extremely well. The

Comparison of Two Waveguide Methods for Educing Liner Impedance in Grazing Flow

Acoustic measurements taken with several liners in a flow impedance tube are used to assess two waveguide methods, the single mode method (SMM) and the finite element method (FEM), for impedance eduction in the presence of uniform grazing flow. Both methods use complex acoustic pressure data acquired over the liner length to educe the liner impedance. The SMM is based on the assumption that the sound pressure level and phase decay rates of a single progressive mode can be extracted from the measured complex acoustic pressures. No a priori assumptions are made in the FEM regarding the measured data. For no-flow conditions, the accuracy of each method is demonstrated by the excellent agreement between no-flow impedances educed in a grazing incidence tube and those acquired in a normal incidence tube. For grazing flow conditions (Mach numbers up to 0.5), the relative accuracy of the two waveguide methods is demonstrated by comparing the impedances educed with the FEM to the corresponding results for the SMM. Significant discrepancies occur for both methods for tests conducted at 0.5 kHz. Possible explanations for these discrepancies are explored with, as yet, no clear answer. Above 0.5 kHz, the results indicate the SMM can be used when the acoustic pressure profile is dominated by a single progressive mode, whereas the FEM can be used for all cases.

Comparison of a Convected Helmholtz and Euler Model for Impedance Eduction in Flow

Impedances educed from a well-tested convected Helmholtz model are compared to that of a recently developed linearized Euler model using two ceramic test liners under the assumed conditions or uniform flow and a plane wave source. The convected Helmholtz model is restricted to uniform mean flow whereas the linearized Euler model can account for the effect or the shear layer. Test data to educe the impedance is acquired from measurements obtained in the NASA Langley Research Center Grazing Incidence Tube for mean flow Mach numbers ranging from 0.0 to 0.5 and source frequencies ranging from 0.5 kHz to 3.0 kHz. The unknown impedance of the liner b educed by judiciously choo~ingth e impedance via an optimization method to match the measured acoustic pressure on the wall opposite the test liner. Results are presented on four spatial grids using three different optimization methods (contour deformation, Davidon-Fletcher Powell, and the Genetic Algorithm). All three optimization methods converge to the same impedance when used with the same model and to nearly identical impedances when used on different models. h anomaly was observed only at 0.5 kHz for high mean flow speeds. The anomaly is likely due to the use of measured data in a flow regime where shear layer effects are important but are neglected in the math models. Consistency between the impedances educed using the two models provides confidence that the linearized Euler model is ready For application to more realistic flows, such as those containing shear layers.

Design and Evaluation of Modifications to the NASA Langley Flow Impedance Tube

The need to minimize fan noise radiation from commercial aircraft engine nacelles continues to provide an impetus for developing new acoustic liner concepts. If the full value of such concepts is to be attained, an understanding of grazing flow effects is crucial. Because of this need for improved understanding of grazing flow effects, the NASA Langley Research Center Liner Physics Group has invested a large effort over the past decade into the development of a 2-D finite element method that characterizes wave propagation through a lined duct. The original test section in the Langley Grazing IncidenceTube was used to acquire data needed for implementation of this finite element method. This test section employed a stepper motor-driven axial-traversing bar, embedded in the wall opposite the test liner, to position a flush-mounted microphone at pre-selected locations. Complex acoustic pressure data acquired with this traversing microphone were used to educe the acoustic impedance of test liners using this 2-D finite element method and a local optimization technique. Results acquired in this facility have been extensively reported, and were compared with corresponding results from various U.S. aeroacoustics laboratories in the late 1990 s. Impedance data comparisons acquired from this multi-laboratory study suggested that it would be valuable to incorporate more realistic 3-D aeroacoustic effects into the impedance eduction methodology. This paper provides a description of modifications that have been implemented to facilitate studies of 3-D effects. The two key features of the modified test section are (1) the replacement of the traversing bar and its flush-mounted microphone with an array of 95 fixed-location microphones that are flush-mounted in all four walls of the duct, and (2) the inclusion of a suction device to modify the boundary layer upstream of the lined portion of the duct. The initial results achieved with the modified test section are provided in this report, and a comparison of these results with those achieved using the original test section is used to demonstrate that the data acquisition and analysis with the new test section can be confidently used for impedance eduction.

Effects of Flow Profile on Educed Acoustic Liner Impedance

This paper presents results of an investigation of the effects of shear flow profile on impedance eduction processes employed at NASA Langley. Uniform and 1-D shear-flow propagation models are used to educe the acoustic impedance of three test liners based on aeroacoustic data acquired in the Langley Grazing Flow Impedance Tube, at source levels of 130, 140 and 150 dB, and at centerline Mach numbers of 0.0, 0.3 and 0.5. A ceramic tubular, calibration liner is used to evaluate the propagation models, as this liner is expected to be insensitive to SPL, grazing flow Mach number, and flow profile effects. The propagation models are then used to investigate the effects of shear flow profile on acoustic impedances educed for two conventional perforate-over-honeycomb liners. Results achieved with the uniform-flow models follow expected trends, but those educed with the 1-D shear-flow model do not, even for the calibration liner. However, when the flow profile used with the shear-flow model is varied to increase the Mach number gradient near the wall, results computed with the shear-flow model are well matched to those achieved with the uniform-flow model. This indicates the effects of flow profile on educed acoustic liner impedance are small, but more detailed investigations of the flow field throughout the duct are needed to better understand these effects.

A Comparative Study of Four Impedance Eduction Methodologies Using Several Test Liners

A comparative study of four commonly used impedance eduction methods is presented for a range of liner structures and test conditions. Two of the methods are restricted to uniform flow while the other two accommodate both uniform and boundary layer flows. Measurements on five liner structures (a rigid-wall insert, a ceramic tubular liner, a wire mesh liner, a low porosity conventional liner, and a high porosity conventional liner) are obtained using the NASA Langley Grazing Flow Impedance Tube. The educed impedance of each liner is presented for forty-two test conditions (three Mach numbers and fourteen frequencies). In addition, the effects of moving the acoustic source from upstream to downstream and the refractive effects of the mean boundary layer on the wire mesh liner are investigated. The primary conclusions of the study are that: (1) more accurate results are obtained for the upstream source, (2) the uniform flow methods produce nearly identical impedance spectra at and below Mach 0.3 but significant scatter in the educed impedance occurs at the higher Mach number, (3) there is better agreement in educed impedance among the methods for the conventional liners than for the rigid-wall insert, ceramic, or wire mesh liner, and (4) the refractive effects of the mean boundary layer on the educed impedance of the wire mesh liner are generally small except at Mach 0.5.

Optimization Method for Educing Variable-Impedance Liner Properties

A new approach to educing normal incidence acoustic impedance of nonuniform test specimens in grazing incidence and grazing-flow environments is described. An optimization algorithm is shown to provide an efficient means for searching out an impedance distribution to match the measured acoustic field along the upper wall of a duct opposite the test specimen. The flow duct is allowed to transmit multimodal, nonprogressive acoustic waves in a flow environment; however, only a no-flow environment is discussed. A key feature of the method is the expansion of the impedance function as a plecewise continuous polynomial with undetermined coefficients. The upper wall acoustic pressure is computed numerically as a function of these coefficients by using a finite element method. The Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance by determining the values of the undetermined coefficients that minimize the difference between the measured and the numerically computed upper wall pressure. Results show that this more robust method reduces by a factor of 30 the time required to make impedance determinations as compared with the contour deformation method and is better suited for liners with spatially varying impedance.

Design curves for rectangular splitter silencers

Abstract Passive silencers with acoustic fill such as glass fiber, rock wool or foam are commonly used in conventional heating, ventilation and air conditioning systems. Acoustic performance can be estimated for a few basic silencers through the use of design curves available in the literature. Recently, a large microcomputer data base using design curves generated to cover the entire range of manufactured rectangular silencers was made available. Details of the design curves and the mathematical model are presented. Insertion loss of the silencers is estimated from attenuation rates calculated from a finite element method. Unlike existing models, the present method considers multimodal acoustic propagation and can be extended to account for the effects of shearing airflows in the airway. The sound-absorbing material is considered to be bulk reacting. Wave propagation in the material is thus included. Design curves are grouped by using three nondimensional parameters, thereby covering the entire line of conventional rectangular duct silencers. Results from the model are compared to least attenuated mode predictions and to actual test data. The results show that the present model gives better predictions than least attenuated mode models. Good comparison between the current model and the test data was also observed. Development of a computer program for a quick estimation of the insertion loss is also described.