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NASA NTRS2001

Vibroacoustic Model Validation for a Curved Honeycomb Composite Panel

Finite element and boundary element models are developed to investigate the vibroacoustic response of a curved honeycomb composite sidewall panel. Results from vibroacoustic tests conducted in the NASA Langley Structural Acoustic Loads and Transmission facility are used to validate the numerical predictions. The sidewall panel is constructed from a flexible honeycomb core sandwiched between carbon fiber reinforced composite laminate face sheets. This type of construction is being used in the development of an all-composite aircraft fuselage. In contrast to conventional rib-stiffened aircraft fuselage structures, the composite panel has nominally uniform thickness resulting in a uniform distribution of mass and stiffness. Due to differences in the mass and stiffness distribution, the noise transmission mechanisms for the composite panel are expected to be substantially different from those of a conventional rib-stiffened structure. The development of accurate vibroacoustic models will aide in the understanding of the dominant noise transmission mechanisms and enable optimization studies to be performed that will determine the most beneficial noise control treatments. Finite element and boundary element models of the sidewall panel are described. Vibroacoustic response predictions are presented for forced vibration input and the results are compared with experimental data.

Buehrle, Ralph D.↗

NASA NTRS2002

Advanced Nacelle Acoustic Lining Concepts Development

The work reported in this document consisted of six distinct liner technology development subtasks: 1) Analysis of Model Scale ADP Fan Duct Lining Data (Boeing): An evaluation of an AST Milestone experiment to demonstrate 1995 liner technology superiority relative to that of 1992 was performed on 1:5.9 scale model fan rig (Advanced Ducted Propeller) test data acquired in the NASA Glenn 9 x 15 foot wind tunnel. The goal of 50% improvement was deemed satisfied. 2) Bias Flow Liner Investigation (Boeing, VCES): The ability to control liner impedance by low velocity bias flow through liner was demonstrated. An impedance prediction model to include bias flow was developed. 3) Grazing Flow Impedance Testing (Boeing): Grazing flow impedance tests were conducted for comparison with results achieved at four different laboratories. 4) Micro-Perforate Acoustic Liner Technology (BFG, HAE, NG): Proof of concept testing of a "linear liner." 5) Extended Reaction Liners (Boeing, NG): Bandwidth improvements for non-locally reacting liner were investigated with porous honeycomb core test liners. 6) Development of a Hybrid Active/Passive Lining Concept (HAE): Synergism between active and passive attenuation of noise radiated by a model inlet was demonstrated.

Bielak, G.↗

NASA NTRS2003

Effects of Impact Damage in Midplane Asymmetric Sandwich Composites

Several structural sandwich composites arc in service on military and commercial aerospace vehicles, however, these components have been limited to secondary structures partly because the impact damage and damage tolerance of these composites have not been extensively characterized. To improve durability, safety, and life cycle performance of PMCs while reducing maintenance costs, combined analysis, and test methods that provide a means of predicting critical engineering properties after impact damage of the structure, must be developed. A key enabling technology here is the establishment of the correlation between the impact test results conducted in the laboratory and the mechanics-based phenomenological solutions. This research was undertaken to investigate the compression and flexural properties following low velocity impact of a nomex/phenolic honeycomb core, fiberglass/epoxy facesheet, midplane asymmetric sandwich composite. One facesheet (thin side) was composed of two plies of the fiberglass/epoxy (0/90), while the other facesheet (thick side) was composed of four plies (0/90/0/90) of fiberglass/epoxy. Due to the differences in facesheet thickness, impact damage was separately induced on the thick side as well as the thin side. The compression and flexural strength properties for each damage arrangement were compared using different levels of impact energy ranging from 0 to 452 Joules. In all cases, higher impact energy resulted in decreased compression and flexural strength. Impact on the thin side showed slightly more retention of compression strength at low impact levels, whereas higher residual compressive strength was observed from impact on the thick side at higher impact levels. Different facesheet thicknesses or midplane asymmetry, played an important role in the flexural strength, however, low velocity impact on the both the thick and thin fiberglass/epoxy facesheet side showed an almost linear loss of flexural strength to saturation.

Meador, Michael↗

NASA NTRS2003

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 samples were then tested in the grazing flow ducts of each of the four laboratories. Perhaps the most significant result of these comparisons is that the educed acoustic resistances for the liners used in this study increase as the mean flow profile is modified from uniform to 3-D shear. This realization has demonstrated the need for an frequency-dependent impedance eduction technique that incorporates 3-D shear flow and is efficient.

Jones, M. G.↗

NASA NTRS2003

Radiated Sound Power from a Curved Honeycomb Panel

The validation of finite element and boundary element model for the vibro-acoustic response of a curved honeycomb core composite aircraft panel is completed. The finite element and boundary element models were previously validated separately. This validation process was hampered significantly by the method in which the panel was installed in the test facility. The fixture used was made primarily of fiberboard and the panel was held in a groove in the fiberboard by a compression fitting made of plastic tubing. The validated model is intended to be used to evaluate noise reduction concepts from both an experimental and analytic basis simultaneously. An initial parametric study of the influence of core thickness on the radiated sound power from this panel, using this numerical model was subsequently conducted. This study was significantly influenced by the presence of strong boundary condition effects but indicated that the radiated sound power from this panel was insensitive to core thickness primarily due to the offsetting effects of added mass and added stiffness in the frequency range investigated.

Robinson, Jay H.↗

NASA NTRS2003

Hypervelocity Impact Test Results for a Metallic Thermal Protection System

Hypervelocity impact tests have been performed on specimens representing metallic thermal protection systems (TPS) developed at NASA Langley Research Center for use on next-generation reusable launch vehicles (RLV). The majority of the specimens tested consists of a foil gauge exterior honeycomb panel, composed of either Inconel 617 or Ti-6Al-4V, backed with 2.0 in. of fibrous insulation and a final Ti-6Al-4V foil layer. Other tested specimens include titanium multi-wall sandwich coupons as well as TPS using a second honeycomb sandwich in place of the foil backing. Hypervelocity impact tests were performed at the NASA Marshall Space Flight Center Orbital Debris Simulation Facility. An improved test fixture was designed and fabricated to hold specimens firmly in place during impact. Projectile diameter, honeycomb sandwich material, honeycomb sandwich facesheet thickness, and honeycomb core cell size were examined to determine the influence of TPS configuration on the level of protection provided to the substructure (crew, cabin, fuel tank, etc.) against micrometeoroid or orbit debris impacts. Pictures and descriptions of the damage to each specimen are included.

Karr, Katherine L.↗

NASA NTRS2003

Nonlinear Thermal Analyses of a Liquid Hydrogen Tank Wall

A thermal evaluation of a composite tank wall design for a liquid hydrogen tank was performed in the present study. The primary focus of the current effort was to perform one-dimensional, temperature nonlinear, transient thermal analyses to determine the through-the-thickness temperature profiles. These profiles were used to identify critical points within the flight envelope that could have detrimental effects on the adhesive bondlines used in the construction of the tank wall. Additionally, this paper presents the finite element models, analysis strategies, and thermal analysis results that were determined for several vehicle flight conditions. The basic tank wall configuration used to perform the thermal analyses consisted of carbon-epoxy facesheets and a Korex honeycomb core sandwich that was insulated with an Airex cryogenic foam and an Alumina Enhanced Thermal Barrier (AETB-12). Nonlinear, transient thermal analyses were conducted using the ABAQUS finite element code. Tank wall models at a windward side location on the fuel tank were analyzed for three basic flight conditions: cold-soak (ground-hold), ascent, and re-entry. Additionally, three ambient temperature boundary conditions were applied to the tank wall for the cold-soak condition, which simulated the launch pad cooldown process. Time-dependent heating rates were used in the analyses of the ascent and reentry segments of the flight history along with temperature dependent material properties. The steady-state through-the-thickness temperature profile from the cold-soak condition was used as the initial condition for the ascent analyses. Results from the nonlinear thermal analyses demonstrated very good correlation with results from similar models evaluated by Northrop- Grumman using a different analysis tool. Wall through-the-thickness temperature gradients as a function of flight time were obtained for future incorporation into a full-scale thermostructural analysis to evaluate the adhesive bondlines. As a result of the thermal analyses conducted, a sufficient level of confidence was demonstrated in the thermal modeling and analysis capabilities of ABAQUS to warrant future use as a thermo-structural analysis tool to evaluate cryogenic tank wall designs.

Smeltzer, Stanley S., III↗

NASA NTRS2001

Hybrid Composites for LH2 Fuel Tank Structure

The application of lightweight carbon fiber reinforced plastics (CFRP) as structure for cryogenic fuel tanks is critical to the success of the next generation of Reusable Launch Vehicles (RLV). The recent failure of the X-33 composite fuel tank occurred in part due to microcracking of the polymer matrix, which allowed cryogen to permeate through the inner skin to the honeycomb core. As part of an approach to solve these problems, NASA Langley Research Center (LaRC) and Marshall Space Flight Center (MSFC) are working to develop and investigate polymer films that will act as a barrier to the permeation of LH2 through the composite laminate. In this study two commercially available films and eleven novel LaRC films were tested in an existing cryogenics laboratory at MSFC to determine the permeance of argon at room temperature. Several of these films were introduced as a layer in the composite to form an interleaved, or hybrid, composite to determine the effects on permeability. In addition, the effects of the interleaved layer thickness, number, and location on the mechanical properties of the composite laminate were investigated. In this initial screening process, several of the films were found to exhibit lower permeability to argon than the composite panels tested.

Grimsley, Brian W.↗

NASA NTRS1999

Shape Optimization of Cylindrical Shell for Interior Noise

In this paper an analytic method is used to solve for the cross spectral density of the interior acoustic response of a cylinder with nonuniform thickness subjected to turbulent boundary layer excitation. The cylinder is of honeycomb core construction with the thickness of the core material expressed as a cosine series in the circumferential direction. The coefficients of this series are used as the design variable in the optimization study. The objective function is the space and frequency averaged acoustic response. Results confirm the presence of multiple local minima as previously reported and demonstrate the potential for modest noise reduction.

Robinson, Jay H.↗

NASA NTRS2003

The Evaluation of High Temperature Adhesive Bonding Processes for Rocket Engine Combustion Chamber Applications

NASA Glenn Research Center is currently evaluating the possibility of using high- temperature polymer matrix composites to reinforce the combustion chamber of a rocket engine. One potential design utilizes a honeycomb structure composed of a PMR-II- 50/M40J 4HS composite facesheet and titanium honeycomb core to reinforce a stainless steel shell. In order to properly fabricate this structure, adhesive bond PMR-II-50 composite. Proper prebond surface preparation is critical in order to obtain an acceptable adhesive bond. Improperly treated surfaces will exhibit decreased bond strength and durability, especially in metallic bonds where interface are susceptible to degradation due to heat and moisture. Most treatments for titanium and stainless steel alloys require the use of strong chemicals to etch and clean the surface. This processes are difficult to perform due to limited processing facilities as well as safety and environmental risks and they do not consistently yield optimum bond durability. Boeing Phantom Works previously developed sol-gel surface preparations for titanium alloys using a PETI-5 based polyimide adhesive. In support of part of NASA Glenn Research Center, UDRI and Boeing Phantom Works evaluated variations of this high temperature sol-gel surface preparation, primer type, and primer cure conditions on the adhesion performance of titanium and stainless steel using Cytec FM 680-1 polyimide adhesive. It was also found that a modified cure cycle of the FM 680-1 adhesive, i.e., 4 hrs at 370 F in vacuum + post cure, significantly increased the adhesion strength compared to the manufacturer's suggested cure cycle. In addition, the surface preparation of the PMR-II-50 composite was evaluated in terms of surface cleanness and roughness. This presentation will discuss the results of strength and durability testing conducted on titanium, stainless steel, and PMR-II-50 composite adherends to evaluate possible bonding processes.

McCray, Daniel↗

NASA NTRS2003

Effects of Fiber Reinforcement Architecture on the Hygrothermal-Mechanical Performance of Polyimide Matrix Composites for Aeropropulsion Applications

A lightweight sandwich support structure, for the combustor chamber of a new generation liquid propellant rocket engine, was designed and fabricated using a polymer matrix composite (PMC) facesheet on a Ti honeycomb core. The PMC facesheet consisted of high stiffness carbon fiber, M40JB, and high temperature Polyimides, such as PMR-II-50 and HFPE-II-52. Six different fiber architectures; four harness satin (4HS) woven fabric, uni-tape, woven-uni hybrid, stitched woven fabric, stitched uni-tape and triaxial braided structures have been investigated for optimum stiffness-thickness-weight-hygrothermal performance design criteria for the hygrothermal-mechanical propulsion service exposure conditions including rapid heating up to 200 F/sec, maximum operating temperature of 600 F, internal pressure up to 100 psi. One of the specific objectives in this study is to improve composite blistering resistance in z-direction at minimum expense of in-plane mechanical properties. An extensive property-performance database including dry-wet mechanical properties at various temperatures, thermal-physical properties, such as blistering onset condition was generated for fiber architecture down-selection and design guidelines. Various optimized process methods such as vacuum bag compression molding, solvent assistant resin transfer molding (SaRTM), resin film infusion (RFI) and autoclaving were utilized for PMC panel fabrication depending on the architecture type. In the case of stitched woven fabric architecture, the stitch pattern in terms of stitch density and yarn size was optimized based on both in-plane mechanical properties and blistering performance. Potential reduction of the in-plane properties transverse to the line of stitching was also evaluated. Efforts have been made to correlate the experimental results with theoretical micro-mechanics predictions. Changes in deformation mechanism and failure sequences in terms of fiber architecture will be discussed.

Shin, E. Eugene↗

NASA NTRS2006

Using the Climbing Drum Peel (CDP) Test to Obtain a G(sub IC) value for Core/Facesheet Bonds

A method of measuring the Mode I fracture toughness of core/facesheet bonds in sandwich Structures is desired, particularly with the widespread use of models that need this data as input. This study examined if a critical strain energy release rate, G(sub IC), can be obtained from the climbing drum peel (CDP) test. The CDP test is relatively simple to perform and does not rely on measuring small crack lengths such as required by the double cantilever beam (DCB) test. Simple energy methods were used to calculate G(sub IC) from CDP test data on composite facesheets bonded to a honeycomb core. Facesheet thicknesses from 2 to 5 plies were tested to examine the upper and lower bounds on facesheet thickness requirements. Results from the study suggest that the CDP test, with certain provisions, can be used to find the GIG value of a core/facesheet bond.

Nettles, A. T.↗

NASA NTRS2008

Configuration Effects on Acoustic Performance of a Duct Liner

Continued success in aircraft engine noise reduction necessitates ever more complete understanding of the effect that flow path geometry has on sound propagation in the engine. The Curved Duct Test Rig (CDTR) has been developed at NASA Langley Research Center to investigate sound propagation through a duct of comparable size (approximately the gap of GE90) and physical characteristics to the aft bypass duct of typical aircraft engines. The liner test section is designed to mimic the outer/inner walls of an engine exhaust bypass duct that has been unrolled circumferentially. Experiments to investigate the effect of curvature along the flow path on the acoustic performance of a test liner are performed in the CDTR and reported in this paper. Flow paths investigated include both straight and curved with offsets from the inlet to the discharge plane of and 1 duct width, respectively. The test liners are installed on the side walls of the liner test section. The liner samples are perforate over honeycomb core, which design is typical of liners installed in aircraft nacelles. In addition to fully treated side walls, combinations of treated and acoustically rigid walls are investigated. While curvature in the hard wall duct is found not to reduce the incident sound significantly, it does cause mode scattering. It is found that asymmetry of liner treatment causes scattering of the incident mode into less attenuated modes, which degrades the overall liner attenuation. It is also found that symmetry of liner treatment enhances liner performance by eliminating scattering into less attenuated modes. Comparisons of measured liner attenuation with numerical results predicted by an analytic model based on the parabolic approximation (CDUCT-LaRC) have also been made and are reported in this paper. The effect of curvature in the rigid wall configuration estimated by CDUCT-LaRC is similar to the observed results, and the mode scattering seen in the measurements also occurs in the analytic model results. The analytic model and experiment show similar differences of overall attenuation between one wall treated and both walls treated.

Gerhold, Carl H.↗

NASA NTRS2008

Electromagnetically Clean Solar Arrays

The term 'electromagnetically clean solar array' ('EMCSA') refers to a panel that contains a planar array of solar photovoltaic cells and that, in comparison with a functionally equivalent solar-array panel of a type heretofore used on spacecraft, (1) exhibits less electromagnetic interferences to and from other nearby electrical and electronic equipment and (2) can be manufactured at lower cost. The reduction of electromagnetic interferences is effected through a combination of (1) electrically conductive, electrically grounded shielding and (2) reduction of areas of current loops (in order to reduce magnetic moments). The reduction of cost is effected by designing the array to be fabricated as a more nearly unitary structure, using fewer components and fewer process steps. Although EMCSAs were conceived primarily for use on spacecraft they are also potentially advantageous for terrestrial applications in which there are requirements to limit electromagnetic interference. In a conventional solar panel of the type meant to be supplanted by an EMCSA panel, the wiring is normally located on the back side, separated from the cells, thereby giving rise to current loops having significant areas and, consequently, significant magnetic moments. Current-loop geometries are chosen in an effort to balance opposing magnetic moments to limit far-0field magnetic interactions, but the relatively large distances separating current loops makes full cancellation of magnetic fields problematic. The panel is assembled from bare photovoltaic cells by means of multiple sensitive process steps that contribute significantly to cost, especially if electomagnetic cleanliness is desired. The steps include applying a cover glass and electrical-interconnect-cell (CIC) sub-assemble, connecting the CIC subassemblies into strings of series-connected cells, laying down and adhesively bonding the strings onto a panel structure that has been made in a separate multi-step process, and mounting the wiring on the back of the panel. Each step increases the potential for occurrence of latent defects, loss of process control, and attrition of components. An EMCSA panel includes an integral cover made from a transparent material. The silicone cover supplants the individual cover glasses on the cells and serves as an additional unitary structural support that offers the advantage, relative to glass, of the robust, forgiving nature of the silcone material. The cover contains pockets that hold the solar cells in place during the lamination process. The cover is coated with indium tin oxide to make its surface electrically conductive, so that it serves as a contiguous, electrically grounded shield over the entire panel surface. The cells are mounted in proximity to metallic printed wiring. The painted-wiring layer comprises metal-film traces on a sheet of Kapton (or equivalent) polyimide. The traces include contact pads on one side of the sheet for interconnecting the cells. Return leads are on the opposite side of the sheet, positioned to form the return currents substantially as mirror images of, and in proximity to, the cell sheet currents, thereby minimizing magnetic moments. The printed-wiring arrangement mimics the back-wiring arrangement of conventional solar arrays, but the current-loop areas and the resulting magnetic moments are much smaller because the return-current paths are much closer to the solar-cell sheet currents. The contact pads are prepared with solder fo electrical and mechanical bonding to the cells. The pocketed cover/shield, the solar cells, the printed-wiring layer, an electrical bonding agent, a mechanical-bonding agent, a composite structural front-side face sheet, an aluminum honeycomb core, and a composite back-side face sheet are all assembled, then contact pads are soldered to the cells and the agents are cured in a single lamination process.

Stem, Theodore G.↗

NASA NTRS2008

Probability of Detection Study on Impact Damage to Honeycomb Composite Structure using Thermographic Inspection

A probability of detection study was performed for the detection of impact damage using flash heating infrared thermography on a full scale honeycomb composite structure. The honeycomb structure was an intertank structure from a previous NASA technology demonstration program. The intertank was fabricated from IM7/8552 carbon fiber/epoxy facesheets and aluminum honeycomb core. The intertank was impacted in multiple locations with a range of impact energies utilizing a spherical indenter. In a single blind study, the intertank was inspected with thermography before and after impact damage was incurred. Following thermographic inspection several impact sites were sectioned from the intertank and cross-sectioned for microscopic comparisons of NDE detection and actual damage incurred. The study concluded that thermographic inspection was a good method of detecting delamination damage incurred by impact. The 90/95 confidence level on the probability of detection was close to the impact energy that delaminations were first observed through cross-sectional analysis.

Hodge, Andrew J.↗

NASA NTRS2007

Heat Rejection Systems Utilizing Composites and Heat Pipes: Design and Performance Testing

Polymer matrix composites offer the promise of reducing the mass and increasing the performance of future heat rejection systems. With lifetimes for heat rejection systems reaching a decade or more in a micrometeoroid environment, use of multiple heat pipes for fault tolerant design is compelling. The combination of polymer matrix composites and heat pipes is of particular interest for heat rejection systems operating on the lunar surface. A technology development effort is under way to study the performance of two radiator demonstration units manufactured with different polymer matrix composite face sheet resin and bonding adhesives, along with different titanium-water heat pipe designs. Common to the two radiator demonstration units is the use of high thermal conductivity fibers in the face sheets and high thermal conductivity graphite saddles within a light weight aluminum honeycomb core. Testing of the radiator demonstration units included thermal vacuum exposure and thermal vacuum exposure with a simulated heat pipe failure. Steady state performance data were obtained at different operating temperatures to identify heat transfer and thermal resistance characteristics. Heat pipe failure was simulated by removing the input power from an individual heat pipe in order to identify the diminished performance characteristics of the entire panel after a micrometeoroid strike. Freeze-thaw performance was also of interest. This paper presents a summary of the two radiator demonstration units manufactured to support this technology development effort along with the thermal performance characteristics obtained to date. Future work will also be discussed.

Jaworske, Donald A.↗

NASA NTRS2008

NDE for the ARES I Upper Stage Common Bulkhead

The current design of the ARES 1 Upper Stage uses a common bulkhead to separate the liquid hydrogen and liquid oxygen tanks. The bulkhead consists of aluminum face sheets bonded to a Phenolic honeycomb core. The face sheets, or domes, are friction stir welded to Y-rings that connect the bulkhead to the barrel sections of the liquid hydrogen and liquid oxygen tanks. Load between the Y-rings is carried by an externally attached bolting ring. The development of nondestructive evaluation methods for the ARES I Upper Stage Common Bulkhead are outlined in this presentation. Methods for inspecting the various components of the bulkhead are covered focusing in on the dome skins, core-to-dome bond lines and friction stir welds as well as structural details like the fastener holes. Thermography, shearography and ultrasonic methods are discussed for the bond lines. Eddy current methods are discussed for the fastener holes and dome skins. A combination of phased array ultrasound, liquid penetrant and radiography are to being investigated for use on the friction stir welds. Keywords: Composite materials, NDE, Cryogenic structures

Walker, James↗

NASA NTRS2009

Impedance Eduction in Ducts with Higher-Order Modes and Flow

An impedance eduction technique, previously validated for ducts with plane waves at the source and duct termination planes, has been extended to support higher-order modes at these locations. Inputs for this method are the acoustic pressures along the source and duct termination planes, and along a microphone array located in a wall either adjacent or opposite to the test liner. A second impedance eduction technique is then presented that eliminates the need for the microphone array. The integrity of both methods is tested using three sound sources, six Mach numbers, and six selected frequencies. Results are presented for both a hardwall and a test liner (with known impedance) consisting of a perforated plate bonded to a honeycomb core. The primary conclusion of the study is that the second method performs well in the presence of higher-order modes and flow. However, the first method performs poorly when most of the microphones are located near acoustic pressure nulls. The negative effects of the acoustic pressure nulls can be mitigated by a judicious choice of the mode structure in the sound source. The paper closes by using the first impedance eduction method to design a rectangular array of 32 microphones for accurate impedance eduction in the NASA LaRC Curved Duct Test Rig in the presence of expected measurement uncertainties, higher order modes, and mean flow.

Watson, Willie R.↗