ALBERT

Description: A 2-D impedance eduction methodology is extended to quasi-3-D sound fields in uniform or shearing mean flow. We introduce a nonlocal, nonreflecting boundary condition to terminate the duct and then educe the impedance by minimizing an objective function. The introduction of a parallel, sparse, equation solver significantly reduces the wall clock time for educing the impedance when compared to that of the sequential band solver used in the 2-D methodology. The accuracy, efficiency, and robustness of the methodology is demonstrated using two examples. In the first example, we show that the method reproduces the known impedance of a ceramic tubular test liner. In the second example, we illustrate that the approach educes the impedance of a four-segment liner where the first, second, and fourth segments consist of a perforated face sheet bonded to honeycomb, and the third segment is a cut from the ceramic tubular test liner. The ability of the method to educe the impedances of multisegmented liners has the potential to significantly reduce the amount of time and cost required to determine the impedance of several uniform liners by allowing them to be placed in series in the test section and to educe the impedance of each segment using a single numerical experiment. Finally, we probe the objective function in great detail and show that it contains a single minimum. Thus, our objective function is ideal for use with local, inexpensive, gradient-based optimizers.

Description: The ability to predict fan noise within complex three-dimensional aircraft engine nacelle geometries is a valuable tool in studying low-noise designs. Recent years have seen the development of aeroacoustic propagation codes using various levels of approximation to obtain such a capability. In light of this, it is beneficial to pursue a design paradigm that incorporates the strengths of the various tools. The development of a quasi-3D methodology (Q3D-FEM) at NASA Langley has brought these ideas to mind in relation to the framework of the CDUCT-LaRC acoustic propagation and radiation tool. As more extensive three dimensional codes become available, it would seem appropriate to incorporate these tools into a framework similar to CDUCT-LaRC and use them in a complementary manner. This work focuses on such an approach in beginning the steps toward a systematic assessment of the errors, and hence the trade-offs, involved in the use of these codes. To illustrate this point, CDUCT-LaRC was used to study benchmark hardwall duct problems to quantify errors caused by wave propagation in directions far removed from that defined by the parabolic approximation. Configurations incorporating acoustic treatment were also studied with CDUCT-LaRC and Q3D-FEM. The cases presented show that acoustic treatment diminishes the effects of CDUCT-LaRC phase error as the solutions are attenuated. The results of the Q3D-FEM were very promising and matched the analytic solution very well. Overall, these tests were meant to serve as a step toward the systematic study of errors inherent in the propagation module of CDUCT-LaRC, as well as an initial test of the higher fidelity Q3D-FEM code.

Description: Determination of acoustic liner impedance for jet engine applications remains a challenge for the designer. Although suitable models have been developed that take account of source amplitude and the local flow environment experienced by the liner, experimental validation of these models has been difficult. This is primarily due to the inability of researchers to faithfully mimic the environment in jet engine nacelles in the laboratory. An in-situ measurement technique, one that can be implemented in an actual engine, is desirable so an accurate impedance can be determined for future modeling and quality control. This paper documents the implementation of such a local acoustic impedance measurement technique that is used under controlled laboratory conditions as well as on full scale turbine engine liner test article. The objective for these series of in-situ measurements is to substantiate treatment design, provide understanding of flow effects on installed liner performance, and provide modeling input for fan noise propagation computations. A series of acoustic liner evaluation tests are performed that includes normal incidence tube, grazing incidence tube, and finally testing on a full scale engine on a static test stand. Lab tests were intended to provide insight and guidance for accurately measuring the impedance of the liner housed in the inlet of a Honeywell Tech7000 turbofan. Results have shown that one can acquire very reasonable liner impedance data for a full scale engine under realistic test conditions. Furthermore, higher fidelity results can be obtained by using a three-microphone coherence technique that can enhance signal-to-noise ratio at high engine power settings. This research has also confirmed the limitations of this particular type of in-situ measurement. This is most evident in the installation of instrumentation and its effect on what is being measured.

Description: As noise constraints become increasingly stringent, there is continued emphasis on the development of improved acoustic liner concepts to reduce the amount of fan noise radiated to communities surrounding airports. As a result, multiple analytical prediction tools and experimental rigs have been developed by industry and academia to support liner evaluation. NASA Langley has also placed considerable effort in this area over the last three decades. More recently, a finite element code (Q3D) based on a quasi-3D implementation of the convected Helmholtz equation has been combined with measured data acquired in the Langley Grazing Incidence Tube (GIT) to reduce liner impedance in the presence of grazing flow. A new Curved Duct Test Rig (CDTR) has also been developed to allow evaluation of liners in the presence of grazing flow and controlled, higher-order modes, with straight and curved waveguides. Upgraded versions of each of these two test rigs are expected to begin operation by early 2008. The Grazing Flow Impedance Tube (GFIT) will replace the GIT, and additional capabilities will be incorporated into the CDTR. The current investigation uses the Q3D finite element code to evaluate some of the key capabilities of these two test rigs. First, the Q3D code is used to evaluate the microphone distribution designed for the GFIT. Liners ranging in length from 51 to 610 mm are investigated to determine whether acceptable impedance eduction can be achieved with microphones placed on the wall opposite the liner. This analysis indicates the best results are achieved for liner lengths of at least 203 mm. Next, the effects of moving this GFIT microphone array to the wall adjacent to the liner are evaluated, and acceptable results are achieved if the microphones are placed off the centerline. Finally, the code is used to investigate potential microphone placements in the CDTR rigid wall adjacent to the wall containing an acoustic liner, to determine if sufficient fidelity can be achieved with 32 microphones available for this purpose. Initial results indicate 32 microphones can provide acceptable measurements to support impedance eduction with this test rig.

Description: This paper presents comparisons of predicted impedance uncertainty limits derived from Monte-Carlo-type simulations with a Two-Parameter (TP) impedance prediction model and measured impedance uncertainty limits based on multiple tests acquired in NASA Langley test rigs. These predicted and measured impedance uncertainty limits are used to evaluate the effects of simultaneous randomization of each input parameter for the impedance prediction and measurement processes. A sensitivity analysis is then used to further evaluate the TP prediction model by varying its input parameters on an individual basis. The variation imposed on the input parameters is based on measurements conducted with multiple tests in the NASA Langley normal incidence and grazing incidence impedance tubes; thus, the input parameters are assigned uncertainties commensurate with those of the measured data. These same measured data are used with the NASA Langley impedance measurement (eduction) processes to determine the corresponding measured impedance uncertainty limits, such that the predicted and measured impedance uncertainty limits (95% confidence intervals) can be compared. The measured reactance 95% confidence intervals encompass the corresponding predicted reactance confidence intervals over the frequency range of interest. The same is true for the confidence intervals of the measured and predicted resistance at near-resonance frequencies, but the predicted resistance confidence intervals are lower than the measured resistance confidence intervals (no overlap) at frequencies away from resonance. A sensitivity analysis indicates the discharge coefficient uncertainty is the major contributor to uncertainty in the predicted impedances for the perforate-over-honeycomb liner used in this study. This insight regarding the relative importance of each input parameter will be used to guide the design of experiments with test rigs currently being brought on-line at NASA Langley.

Description: An intensive investigation into the cause of anomalous behavior commonly observed in impedance eduction techniques is performed. The investigation consists of grid refinement studies, detailed evaluation of results at and near anti-resonance frequencies, comparisons of different model results with synthesized and measured data, assessment or optimization techniques, and evaluation or boundary condition effects. Results show that the root cause of the anomalous behavior is the sensitivity of the educed impedance to small errors in the measured termination resistance at frequencies near anti-resonance or cut-on of a higher-order mode. Evidence is presented to show that the common usage of an anechoic, plane wave termination boundary condition in ducts where the "true" termination is reflective may act as a trigger for these anomalies. Replacing the exit impedance boundary condition by an exit pressure condition is shown to reduce the anomalous results.

Description: This paper presents comparisons of seven propagation codes for predicting liner attenuation in ducts with flow. The selected codes span the spectrum of methods available (finite element, parabolic approximation, and pseudo-time domain) and are collectively representative of the state-of-art in the liner industry. These codes are included because they have two-dimensional and three-dimensional versions and can be exported to NASA's Columbia Supercomputer. The basic assumptions, governing differential equations, boundary conditions, and numerical methods underlying each code are briefly reviewed and an assessment is performed based on two predefined metrics. The two metrics used in the assessment are the accuracy of the predicted attenuation and the amount of wall clock time to predict the attenuation. The assessment is performed over a range of frequencies, mean flow rates, and grazing flow liner impedances commonly used in the liner industry. The primary conclusions of the study are (1) predicted attenuations are in good agreement for rigid wall ducts, (2) the majority of codes compare well to each other and to approximate results from mode theory for soft wall ducts, (3) most codes compare well to measured data on a statistical basis, (4) only the finite element codes with cubic Hermite polynomials capture extremely large attenuations, and (5) wall clock time increases by an order of magnitude or more are observed for a three-dimensional code relative to the corresponding two-dimensional version of the same code.

Description: A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

Description: 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.