ALBERT

Description: This paper explores the effects of variable-depth geometry on the amount of noise reduction that can be achieved with acoustic liners. Results for two variable-depth liners tested in the NASA Langley Grazing Flow Impedance Tube demonstrate significant broadband noise reduction. An impedance prediction model is combined with two propagation codes to predict corresponding sound pressure level profiles over the length of the Grazing Flow Impedance Tube. The comparison of measured and predicted sound pressure level profiles is sufficiently favorable to support use of these tools for investigation of a number of proposed variable-depth liner configurations. Predicted sound pressure level profiles for these proposed configurations reveal a number of interesting features. Liner orientation clearly affects the sound pressure level profile over the length of the liner, but the effect on the total attenuation is less pronounced. The axial extent of attenuation at an individual frequency continues well beyond the location where the liner depth is optimally tuned to the quarter-wavelength of that frequency. The sound pressure level profile is significantly affected by the way in which variable-depth segments are distributed over the length of the liner. Given the broadband noise reduction capability for these liner configurations, further development of impedance prediction models and propagation codes specifically tuned for this application is warranted.

Description: A two-dimensional impedance eduction theory is extended to three-dimensional sound fields and peripherally varying duct liners. The approach is to first measure the acoustic pressure field at a series of flush-mounted wall microphones located around the periphery of the flow duct. The numerical solution for the acoustic pressure field at these microphones is also obtained by solving the three-dimensional convected Helmholtz equation using the finite element method. A quadratic objective function based on the difference between the measured and finite element solution is constructed and the unknown impedance function is obtained by minimizing this objective function. Impedance spectra educed for two uniform-structure liners (a wire-mesh and a conventional liner) and a hard-soft-hard peripherally varying liner (for which the soft segment is that of the conventional liner) are presented. Results are presented at three mean flow Mach numbers and fourteen sound source frequencies. The impedance spectra of the uniform-structure liners are also computed using a two-dimensional impedance eduction theory. The primary conclusions of the study are: 1) when measured data is used with the uniform-structure liners, the three-dimensional theory reproduces the same impedance spectra as the two-dimensional theory except for frequencies corresponding to very low or very high liner attenuation; and 2) good agreement between the educed impedance spectra of the uniform structure conventional liner and the soft segment of the peripherally varying liner is obtained.

Description: Two impedance eduction methods are explored for use with data acquired in the NASA Langley Grazing Flow Impedance Tube. The first is an indirect method based on the convected Helmholtz equation, and the second is a direct method based on the Kumaresan and Tufts algorithm. Synthesized no-flow data, with random jitter to represent measurement error, are used to evaluate a number of possible microphone locations. Statistical approaches are used to evaluate the suitability of each set of microphone locations. Given the computational resources required, small sample statistics are employed for the indirect method. Since the direct method is much less computationally intensive, a Monte Carlo approach is employed to gather its statistics. A comparison of results achieved with full and reduced sets of microphone locations is used to determine which sets of microphone locations are acceptable. For the indirect method, each array that includes microphones in all three regions (upstream and downstream hard wall sections, and liner test section) provides acceptable results, even when as few as eight microphones are employed. The best arrays employ microphones well away from the leading and trailing edges of the liner. The direct method is constrained to use microphones opposite the liner. Although a number of arrays are acceptable, the optimum set employs 14 microphones positioned well away from the leading and trailing edges of the liner. The selected sets of microphone locations are also evaluated with data measured for ceramic tubular and perforate-over-honeycomb liners at three flow conditions (Mach 0.0, 0.3, and 0.5). They compare favorably with results attained using all 53 microphone locations. Although different optimum microphone locations are selected for the two impedance eduction methods, there is significant overlap. Thus, the union of these two microphone arrays is preferred, as it supports usage of both methods. This array contains 3 microphones in the upstream hard wall section, 14 microphones opposite the liner, and 3 microphones in the downstream hard wall section.

Description: This paper explores the validity of an indirect method for impedance eduction of multisegment liners. This is accomplished via results obtained with two uniform liners and one two-segment liner, where each segment is constructed to match the geometry of one of the uniform liners. Each uniform liner is evaluated using direct and indirect impedance eduction methods. An indirect impedance eduction method is used to educe the impedance for each segment of the two-segment liner, and the results are compared with those educed for the uniform liners. These impedance spectra are shown to compare favorably for the majority of test conditions. Poorer comparisons are achieved for those test conditions where one segment of the two-segment liner provides little attenuation. Poor attenuation is a wellknown cause for impedance eduction difficulties. Overall, this multisegment impedance eduction method offers the potential to study complicated liners in a more efficient manner (i.e., without the requirement to build and test separate liners to duplicate each unique segment of the multisegment liner). More detailed studies are required to further validate this tool, and are intended to be the focus of future research.

Description: A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.

Description: This study explores the effects of liner length and attenuation on the CHE (convected Helmholtz equation) impedance eduction method, in which the surface impedance of an acoustic liner is inferred through an iterative process based on repeated solutions to the convected Helmholtz equation. Wire mesh-over-honeycomb and perforate-over-honeycomb acoustic liners are tested in the NASA Langley Grazing Flow Impedance Tube, and the resultant data are processed using two impedance eduction methods. The first is the CHE method, and the second is a direct method (labeled the KT method) that uses the Kumaresan and Tufts algorithm to compute the impedance directly. The CHE method has been extensively used for acoustic liner evaluation, but experiences anomalous behavior under some test conditions. It is postulated that the anomalies are related to the liner length and/or attenuation. Since the KT method only employs data measured over the length of the liner, it is expected to be unaffected by liner length. A comparison of results achieved with the two impedance eduction methods is used to explore the interactive effects of liner length and attenuation on the CHE impedance eduction method.

Description: Three perforate-over-honeycomb liner configurations, one uniform and two with spanwise variable impedance, are evaluated based on tests conducted in the NASA Grazing Flow Impedance Tube (GFIT) with a plane-wave source. Although the GFIT is only 2" wide, spanwise impedance variability clearly affects the measured acoustic pressure field, such that three-dimensional (3D) propagation codes are required to properly predict this acoustic pressure field. Three 3D propagation codes (CHE3D, COMSOL, and CDL) are used to predict the sound pressure level and phase at eighty-seven microphones flush-mounted in the GFIT (distributed along all four walls). The CHE3D and COMSOL codes compare favorably with the measured data, regardless of whether an exit acoustic pressure or anechoic boundary condition is employed. Except for those frequencies where the attenuation is large, the CDL code also provides acceptable estimates of the measured acoustic pressure profile. The CHE3D and COMSOL predictions diverge slightly from the measured data for frequencies away from resonance, where the attenuation is noticeably reduced, particularly when an exit acoustic pressure boundary condition is used. For these conditions, the CDL code actually provides slightly more favorable comparison with the measured data. Overall, the comparisons of predicted and measured data suggest that any of these codes can be used to understand data trends associated with spanwise variable-impedance liners.

Description: No abstract available

Description: Four liners are investigated experimentally via tests in the NASA Langley Grazing Flow Impedance Tube. These include an axially-segmented liner and three liners that use reordering of the chambers. Chamber reordering is shown to have a strong effect on the axial sound pressure level profiles, but a limited effect on the overall attenuation. It is also shown that bent chambers can be used to reduce the liner depth with minimal effects on the attenuation. A numerical study is also conducted to explore the effects of a planar and three higher-order mode sources based on the NASA Langley Curved Duct Test Rig geometry. A four-segment liner is designed using the NASA Langley CDL code with a Python-based optimizer. Five additional liner designs, four with rearrangements of the first liner segments and one with a redistribution of the individual chambers, are evaluated for each of the four sources. The liner configuration affects the sound pressure level profile much more than the attenuation spectra for the planar and first two higher-order mode sources, but has a much larger effect on the SPL profiles and attenuation spectra for the last higher-order mode source. Overall, axially variable-depth liners offer the potential to provide improved fan noise reduction, regardless of whether the axially variable depths are achieved via a distributed array of chambers (depths vary from chamber to chamber) or a group of zones (groups of chambers for which the depth is constant).