Application of synthetic array techniques for improved simulations of hot supersonic jet noise

Abstract

The synthetic array technique has previously been used to provide insight for developing improved microphone array data processing techniques. In recent work, however, it has also been successfully applied to diagnose the source of unexpected (and nonphysical) tones which arose in unsteady computational fluid dynamics (CFD) simulations of hot supersonic jets. The insight obtained from this method has allowed the authors to rapidly arrive at a strategy that greatly improves the results. This success opens up additional areas where the synthetic array technique can find application.

Keywords

Computational fluid dynamics computational aeroacoustics synthetic array technique jet noise

Introduction

Noise generated by low bypass ratio turbofan engines represents one of the most acute noise sources faced by Navy personnel. Currently, the Jet Noise Reduction project of the Office of Naval Research (ONR) is maturing known noise reduction approaches that could each provide limited but still significant reduction in the peak-directivity jet noise. The authors worked on an ONR-funded effort aimed at improving both the tools for investigating noise in hot supersonic jets and the fundamental understanding of that noise.

The approach taken for the ONR-funded effort centered on the use of the “synthetic array technique.”¹ This approach involved the use of large eddy simulation (LES) to generate unsteady near-field data in jet flows. The near-field noise was then numerically propagated to the far-field phased array microphone locations using a Ffowcs Williams–Hawkings (FW-H) solver. Different microphone array analysis methods were then used to predict noise source locations and strengths. The synthetic array technique allows beamforming predictions to be compared with the original LES near-field results and corresponding FW-H far-field predictions. In the ONR-funded effort, discrepancies between the results from the different methods were used to guide development of new and improved phased array source models and analysis techniques.

The ONR-funded effort, like our previous synthetic array applications, was focused on ultimately improving the data analysis techniques used for microphone array experiments (as well as improving overall understanding of the acoustics of hot supersonic jets). It was discovered, however, that the same methodology can provide important insights for diagnosing problems in CFD solutions. The current paper discusses this novel application for the synthetic array approach.

Numerical methods

The synthetic array technique combines the abilities of three different numerical tools to predict the unsteady flow from a high speed jet, the resulting acoustics, and an analysis of the noise sources. The Navier–Stokes equations are solved using the “Compressible High Order Parallel Acoustics” (CHOPA) computational aeroacoustics solver² to obtain an unsteady flow field in the vicinity of the jet. Data from this solution are then fed into the PSU-WOPWOP³ FW-H⁴ solver to predict the far-field acoustics. This prediction is used to record sound levels (and phase) at virtual microphone locations, and this information is fed into the Beamform Interactive software package, which is used to analyze the data using a variety of microphone array data processing methods.

This methodology is referred to as the “synthetic array technique” as it uses numerical methods to perform an analysis identical to those used for experimental data from microphone arrays. A similar technique was used successfully in previous joint efforts by Innovative Technology Applications Company, LLC, Dr Dougherty, and Profs. Brentner and Morris for the acoustics of an airfoil with a blunt trailing edge and also to study the acoustics of wind turbines.¹

The following is an overview of the numerical tools used for this work.

The CHOPA flow solver

The CFD code used for this work is the CHOPA solver. CHOPA was originally developed for aeroacoustic studies of airfoil gust response⁵ and cavity acoustics.⁶ It has been adapted for jet noise simulations,^7,8 and that is the primary application for which it has been used more recently, though it is capable of much more general applications.

CHOPA uses the fourth-order dispersion relation preserving (DRP) scheme of Tam and Webb⁹ for spatial discretization. The blended second- and sixth-order filtering approach of Lockard and Morris⁵ is used to prevent the spurious buildup of unresolved scales in the solution. The sixth-order filter prevents the nonphysical buildup of energy in the highest resolvable scales, while the second-order dissipation keeps CHOPA stable near strong gradients. There are three options for controlling the activation of the second-order dissipation: a pressure-based switch, a density-based switch, and a combination of the two. The pressure-based switch is preferred, but in especially challenging regions, the other options may be used (usually the combined switch based on pressure and density).

Earlier versions of CHOPA typically used an explicit Runge–Kutta method in conjunction with a dual-time marching scheme in order to maintain temporal accuracy. More recently, an implicit scheme with dual-time stepping has been used. This provides a significant speed improvement over previous versions. Additional speedup is obtained through the use of the message passing interface (MPI) to run in parallel. CHOPA has been found to be particularly sensitive to the choice of MPI library on some systems, with some versions exhibiting much slower performance than others. In addition, some variants were found to produce random slowdowns of the code which reduced a previously well-performing run to such a slow pace as to be unworkable. These effects are highly system dependent (e.g. OpenMPI works well on some systems, but not on others), and thus no simple solution can be recommended. Instead, when porting the code to a new system, one must compare the performance of multiple MPI libraries to find the one that yields the best performance, both in speed and stability. By selecting the best (for CHOPA) available MPI library, appropriate compiler options, and using the implicit scheme, it is possible to obtain an order of magnitude better performance with CHOPA than was available just a few years ago with earlier versions of the code.

CHOPA solves the Navier–Stokes equations in conservative form on structured, multiblock grids with abutting boundaries. Block boundaries can be either point matched or nonpoint matching. While structured grids allow for relatively easy implementation of higher order schemes (in this case, the fourth-order DRP scheme), they do require additional effort for complex geometries or small geometric features. In CHOPA, this is mitigated through the use of the immersed boundary method (IBM).^10,11 This technique allows the incorporation of small geometric features (such as chevrons) without requiring the expense of a fully body conformal mesh. Instead, a small region of finer grid is typically placed in the vicinity of the desired geometric features, and points that fall inside those features are treated as “immersed,” and the solution is modified appropriately for those points. A simple example of this is shown in Figure 1.

Turbulence effects are modeled using variations of the Spalart–Allmaras one equation turbulence model.¹² The original detached eddy simulation (DES) model¹³ is available for use, but more commonly, an implicit large eddy simulation (ILES)¹⁴ version of the DES model is used (since DES has often been found to be too dissipative for the jet cases of interest here^15,16). The ILES version uses a conventional Reynolds-averaged Navier–Stokes Spalart turbulence model in near-wall regions. However, away from the walls the turbulence model is turned off, and the code relies on the inherent dissipation of the numerics (specifically the sixth-order filter) to cascade resolved turbulent kinetic energy to unresolved scales.

The PSU-WOPWOP noise prediction code

PSU-WOPWOP is a FW-H solver developed at The Pennsylvania State University (PSU) by Dr Brentner and his research team.^3,17–19 The code was originally developed to compute the noise of rotorcraft in maneuvering flight but was developed using an object-oriented design in the Fortran 95 language in a very general manner. Both the impermeable and permeable surface solutions of the FW-H equation,²⁰ as expressed by Farassat’s Formulation 1A,^21,22 have been implemented in the code.

In the current work, flow properties were recorded on permeable acoustic data surfaces (ADS) by CHOPA. PSU-WOPWOP requires the location of the surfaces (which can be time dependent, although only rigid and stationary surfaces are used here) along with the time-dependent specification of density, momentum, and pressure at each of the surface mesh points. The ADS data are used to predict the acoustic pressure at arbitrary observer locations, corresponding, for example, to microphone locations in a phased array.

PSU-WOPWOP’s ability to efficiently process different observer locations in parallel using MPI enables the simultaneous computation of a large number of positions, as might be used, for example, in an extensive microphone array.

The Beamform Interactive microphone array data analysis software

Beamform Interactive is a commercial product of OptiNav, Inc. which is designed for processing microphone array data. There are numerous modules in Beamform Interactive, which allow the user to apply various array processing methods. They can be classified as generalized inverse processing, beamforming, and deconvolution methods.

Generalized inverse methods produce an extended, coherent, source model to attempt to account for the array data. They differ in the basis functions for the model, the error norm, the regularization technique, and the solver. They are low frequency methods. The near-field acoustic holography of Earl Williams²³ is an example of a generalized inverse method. The generalized inverse module in Beamform Interactive, GINV,²⁴ can use monopole or plane wave basis functions. It minimizes the L² norm of the error, applies Gaussian smoothing for regularization, and uses a matrix formulation to account for partial coherence between sources.

Beamforming methods assume an incoherent source distribution which is usually taken as monopoles, but can also be multipoles or wave patterns that imply sources with extended support, such as duct modes or wavepackets. Beamforming is not limited to low frequency. One hallmark of beamforming is that a source strength estimate for a single point or mode is independent of the results for the other points or modes. The beamforming options in Beamform Interactive include:

Frequency domain beamforming (FDBF): This is the conventional beamforming technique.²⁵ The diagonal elements of the cross spectral matrix (CSM) can be included normally, replaced by 0 values (diagonal deletion or diagonal removal), or replaced by optimized values to minimize the trace while keeping the CSM nonnegative definite.

Default mode: If no options are selected, then Beamform Interactive performs cross correlation beamforming, which is similar to FDBF, but not limited to narrow frequency bands.

Functional beamforming:^26,27 This is the currently recommended method. It is a nonlinear generalization of FDBF that gives substantially higher dynamic range and improved resolution. For the current jet noise work, a wavepacket-based source model has been developed and implemented which provides improved results over all previous approaches when combined with functional beamforming.²⁸ It should be noted that functional beamforming works better with synthetic data than real data. This is because, depending on the specific settings, functional beamforming can be very sensitive to errors in the computed steering vector. This sensitivity is what gives it good resolution and dynamic range, but in real tests, experimental vagaries such as imperfectly known microphone locations and variability of microphone sensitivity cause steering vector errors that can degrade the functional beamforming results. In synthetic data, however, microphone errors are not present, with the result that the sort of peak suppression that often plagues functional beamforming is not seen. If it still occurs, it may be attributable to limitations of the physical modeling used to compute the steering vectors, such as failing to account for the source directivity.

Deconvolution methods algebraically combine beamforming results for multiple points in the source map to improve the scaling, resolution, dynamic range of the complete map. Deconvolution is best suited to low-medium frequency because it is typically slow at high frequency. The deconvolution methods in Beamform Interactive include:

CLEAN-SC: This method is an implementation of Sijtsma’s²⁹ algorithm.

TIDY: This is an OptiNav method, related to CLEAN-SC but formulated using the cross correlation matrix, allowing analysis with unlimited bandwidth.

DAMAS2: This is OptiNav’s modification of the DAMAS³⁰ algorithm that uses FFTs, and is faster, but assumes that the point spread function is translationally invariant. Beamform Interactive uses a special nonuniform grid for its analysis which makes this assumption nearly true.

Linear programming: This is also related to DAMAS but solves a modified problem to produce similar results in much less time.³¹

Orthogonal beamforming: This is an extension of a method by Sarradj.³² The original method beamforms using each eigenvector of the CSM and puts a dot at the peak location for each eigenvector in which the strength of the dot is the eigenvalue. Dougherty’s extension uses the eigenvector again as a basis for a projection algorithm. For each source point and each far-field observation point, a ray is drawn from the source point, through the array, and on to the far-field point. The eigenvector expresses the phase and amplitude of that orthogonal component over the array. That pattern is interpolated at the place where the ray crosses the array plane to get a contribution for the far field. For each far-field point, the contributions are summed incoherently to give the projected sound pressure level (SPL). Unlike the GINV approach, this method is not limited to low frequency.

Problem identification

The current work examines a military-style faceted nozzle geometry which can be fitted with chevrons. The design is modeled after configurations used for experimental tests at NASA Glenn Research Center³³ and the PSU.³⁴ The baseline geometry is shown in Figure 2. The design Mach number for the baseline nozzle is 1.5. The dimensions of the PSU model have been employed for the current work, with a throat diameter of 0.631 in.

An exterior view of the nozzle with chevrons attached is shown in Figure 3. In this configuration, 12 chevrons are attached at the nozzle exit to match the inner contours of the facets. Each chevron has a width of 80% of the nozzle facets, extends downstream for 25.8% of the throat diameter, and penetrates 9.3% D into the flow.

Experimental data are available for three different operating conditions, summarized in Table 1. All three operating conditions have been examined for both the baseline configuration and with chevrons installed. The simulations thus addressed overexpanded, nearly perfectly expanded, and underexpanded conditions.

Table 1.

Nozzle operating conditions.

NPR	TTR	M_j	$T_{j} / T_{\infty}$	M_a
3.0	3.0	1.36	2.190	2.013
3.5	3.0	1.47	2.095	2.135
4.0	3.0	1.56	2.018	2.223

The original baseline geometry cases were solved using a 14 block mesh with 22.4 million points. This mesh used point-matched boundaries between all blocks. Sample cross-sections are shown in Figure 4. Using this computational grid, the CHOPA solver was able to obtain acceptable results (consistent with prior work) for both the overexpanded and the nearly perfectly expanded conditions.

When IBM was applied to this baseline mesh to account for the chevrons, however, it was found that the chevrons were not adequately resolved. As a result, modifications were made to increase the resolution in the chevron region, at the cost of introducing nonmatching block boundaries, similar to the block highlighted in Figure 5. Flow in this image is from left to right, and a portion of the nozzle lip is visible on the left side. The top of Figure 5 is exterior to the nozzle. After a number of revisions, a chevron configuration mesh was developed which contains 25.3M points in 22 blocks. The approximation of the chevrons for this mesh is shown in Figure 6. Some “stair stepping” is apparent in this view, which is an unavoidable aspect of IBM.

A set of locations for the virtual microphones that make up a synthetic array, along with a far-field arc has been selected. A total of 127 “microphones” are positioned to observe the flow. The first 100 make up the array, and the remaining 27 are the “far-field” microphones. The microphone locations are plotted relative to the nozzle and computational mesh in Figure 7.

The initial ADS on which solution properties were recorded is shown in Figure 8. The design is based on a configuration used for previous simulations of the same jets.³⁵ The ADS was constructed from portions of selected planes in the computational mesh. One effect of this (which will be addressed further below) is that the ADS initially contracts in radius immediately downstream of the jet exit, because it follows the contours of the mesh which was modified to better resolve the chevrons (for the IBM). Once past this initial contraction, the surface is approximately conical in shape and extends roughly 30 jet exit diameters downstream from the exit. At the jet exit plane, the ADS is positioned slightly beyond the outer wall of the nozzle—about 1.33 jet exit diameters across. At the downstream end, the ADS widens to 5.4 jet exit diameters. The ADS is closed everywhere except at the jet exit itself.

Results

As mentioned above, acceptable results for the baseline geometry were obtained for both the nearly perfectly expanded conditions and the overexpanded conditions. A number of challenges were encountered in obtaining acceptable CFD results for chevron nozzle cases. In analyzing our initial results, the presence of unexpected (nonphysical) tones in the predicted SPL spectra was noted. Using the acoustic pressure signal predicted by PSU-WOPWOP from the ADS data recorded by the CHOPA solver, a representative plot for the nearly perfectly expanded case is shown in Figure 9 for the SPL predicted at a distance of 100 nozzle radii along a vector 110° from the downstream jet axis. The tones are clearly visible for the chevron nozzle case. The experimental results plotted in Figure 9 (and subsequent figures) are taken from the tests at NASA Glenn Research Center³³ and the PSU.³⁴ Both experimental configurations measured far-field noise directly using microphones positioned in an arc similar to the 27 far-field “microphones” shown in Figure 7. Because strong tones had not been observed in previous simulations of the same chevron nozzle (such as those of Du and Morris³⁵), the working assumption was that these tones were numerical artifacts of some source.

To investigate these tones, the synthetic array technique was employed. Looking at the beamformed results, the same peaks in the above spectra (Figure 9) are also easily seen (Figure 10).

A functional beamforming sweep through this frequency range is shown in Figure 11 (frequency increases from left to right and top to bottom). The top left image represents frequencies centered at 53,850 Hz, which is near the minimum frequency of the highlighted range in Figure 10, while the bottom right (centered at 60,450 Hz) represents the maximum. The specific center frequency in each image is noted at the top left of each image (in Hertz, preceded by “CF”). The bin width for each plot is a constant 347.4 Hz. In the first seven images in Figure 11, a hot spot is visible near the lower lip of the cartoon representation of the nozzle (shown on the left side of each image). This location corresponds to the tip of one of the chevrons. A similar, if somewhat less obvious hot spot is visible on the upper side of the nozzle in the last six images. It thus appears that these spurious tones are associated with the presence of the chevrons in this calculation. This is consistent with the lack of similar tones in the baseline geometry run.

In considering how to adjust the simulation to avoid these tones, it was noted that, as discussed above, the chevrons are being modeled using IBM. In this approach, the computational mesh in the chevron region, while refined compared to the rest of the jet plume, is (by design) not what it would be if a body-fitted mesh were employed. This is exacerbated by the penetration of the chevrons into the jet plume (away from the region of greatest mesh clustering). The grid resolution may therefore be inadequate, leading to instability. In addition, the nature of IBM is such that the computational stencils used for spatial discretization will use points inside the chevrons. From a discrete numerics perspective, this looks like a modified stencil, but not a properly consistent upwind-biased or one-sided method.

In either case, decreased stability may be accompanied by an increased sensitivity to the time step being taken. Accordingly, the nearly perfectly expanded chevron jet case was rerun with a 20% smaller time step. The effect of this small change on the SPL spectra is illustrated in Figure 12. The dominant tones that were so prominent before are significantly reduced.

For the next test, the computational mesh was also modified to increase the grid resolution in the vicinity of the chevrons. This modification was made without changing the mesh topography or the overall number of points; the grid lines were merely shifted to better follow the contours of the chevrons. Figure 13 shows a result from the new grid, run with an even smaller time step than before (nondimensional time of 0.002). As the figure shows, the spurious tones have been eliminated in the new run.

Further refinements

While the results shown above represented a clear improvement over what came before, there were still anomalies present which required further investigation. Specifically, at low angles, the OASPL was significantly overpredicted, as shown in Figure 14 for the underexpanded baseline case.

These excessive levels were found to be associated with overprediction of noise in the middle to upper range of frequencies, as illustrated in Figure 15. This figure, which represents in some ways the worst results obtained from the CFD simulations, shows the nonphysical “hump” in the spectrum and displacement of the peak Strouhal number to higher frequencies.

Several possible sources for this problem were considered. First, it was noted that the permeable surface formulation of the FWH equation which is being used in PSU-WOPWOP was not intended for configurations where strong unsteady flow features pass through the ADS. This has been observed by many (including the authors in work dealing with landing gear noise) to result in spurious noise sources appearing at the ADS. Previous work has found that the downstream cap of the ADS is a particular source of nonphysical noise, and that this can be mitigated through the averaging of the results from a series of surfaces placed near each other at the downstream end of the ADS.^15,36 The initial tests of this hypothesis did not indicate that it was a major factor in what was observed, but it remained a candidate explanation to be explored.

A second, related possibility that was considered was that the radial extent of the ADS was not sufficient to avoid interference from flow structures convecting downstream. This situation, if the hypothesis was correct, was made more severe when the mesh was modified to better follow the contours of the chevrons. Visualization of the ADS with a flow solution snapshot confirmed that unsteady flow features were indeed penetrating the ADS, as shown in Figure 16. In the figure, vertical lines are placed every 10 nozzle diameters downstream, while the horizontal lines are a single nozzle diameter apart. The vortical structures (visualized in the form of an iso-surface and centerline cross-section contours) can clearly be seen penetrating the surface within the first 10 diameters from the nozzle exit, and the pressure footprints of other flow structures (plotted on the approximately conical ADS itself) can be observed for a considerable distance further downstream.

A third possible contributor to this issue was considered: the large jumps in mesh spacing between the central core blocks and the surrounding neighbors (see Figure 4). Signals that are resolved on the outer meshes but could not be accurately propagated on the core mesh might result in the appearance of spurious signals and dispersion errors.

To begin to address these three issues, a further set of runs was made (the seventh such set—denoted “v7 mesh” in the following plots). For this last set of runs, the resolution in the core meshes was doubled in the transverse directions (kept the same in the streamwise direction), which brought the total mesh size to about 28 million points. In addition, the number of ADS patches on which data were saved was vastly increased (from 17 to more than 400) in order to allow construction of surfaces at any of three different radial locations and up to 15 downstream end-cap locations.

Results were obtained using the new mesh and ADS patch locations for all six cases. PSU-WOPWOP was used to obtain an initial far-field acoustic prediction for an ADS definition that used the third possible downstream end-cap location and the outermost (third) radial surface (denoted “ADS 3,3” in the following plots). The ADS surface is shown in Figure 17. In contrast to the original surface (in Figure 8), this one is significantly wider, especially in the vicinity of the nozzle exit, in order to reduce the interactions between the ADS and the strong vortical structures noted in Figure 16. However, the downstream extent of the new ADS is decreased compared to the earlier version. The possibility of using a shorter ADS was considered because all of our prior jet beamforming results pointed to the vast majority of noise being generated within 10 diameters of the jet exit.

As shown in Figure 18 (for the baseline nearly perfectly expanded case), the new directivity results are greatly improved at the lower observer angles, while maintaining a similar quality at higher angles.

Looking at specific spectra, a similar trend is observed, as illustrated in Figure 19. This figure shows the SPL at a 30° observer angle in the baseline nearly perfectly expanded nozzle flow. Compared to the previous CFD results, the latest results are greatly improved, with the peak location and magnitude now correct, and the overshoot at higher frequencies significantly reduced.

Similar results were observed for all three baseline cases (for which experimental data are available), and the chevron cases appeared qualitatively better as well (though no specific data were available to compare against for those cases). A representative result is shown in Figure 20. The curves have the expected shapes, and the relationship between them is as expected, in that increasing Mach number increases noise levels and adding chevrons reduces noise.

A final set of tests was performed to determine how much of the differences in the above v7 results was due to the new ADS location and how much due to the core mesh refinement. To do this, a second ADS case was constructed which closely matched that used for the v6 runs, and PSU-WOPWOP was rerun. This surface consists of the 15th downstream end-cap position and the innermost radial position; these results are designated “ADS 15,1” in the following plots.

Figure 21 shows the OASPL directivity for the nearly perfectly expanded baseline jet case. Clearly, the v7 simulation data, when analyzed using a similar ADS as used for the v6 analysis, produce almost identical results as the earlier data. Similar behavior is shown in Figure 22 which shows results for the 30° observer angle in the underexpanded baseline jet case. The same behavior was seen for every quantity and location examined for all the cases simulated in the current effort. Taken together with earlier tests (not shown here) that indicated little impact to changing the downstream extent of the ADS or even whether or not it is closed, the results clearly indicate that the radial position of the ADS is the dominant contributor to the errors seen earlier at low observer angles.

The issue of spurious noise related to the ADS position suggests a further application of the synthetic array technique: looking for apparent noise sources on the ADS itself. Properly handled, the ADS should not have any significant noise sources directly on it. Some preliminary investigations were performed using the synthetic microphone data to examine the ADS to ensure that this is in fact the case. As shown in Figure 23, there are indications that, while it is not a dominant noise source, there is some spurious noise being generated at the end cap of the ADS. As in this case, if issues are discovered, this technique automatically gives us the problematic locations, which can save significant time in the search for the solution.

Summary

As discussed above, the synthetic array technique has been used to successfully diagnose the source of spurious tones observed in simulations of the nearly perfectly expanded hot supersonic chevron jet case. The functional beamforming method was able to pinpoint the source of the noise, and this suggested both the underlying numerical cause and a possible solution. As far as the authors are aware this is the first use of a synthetic array to diagnose problems with CFD solutions. The nonphysical noise that resulted from the excessive time step primarily affected the higher observer angles. It showed up in the OASPL as an overshoot at the affected angles. The spectra at these angles showed one or more very strong tones in the mid-range frequencies.

It was also discovered that the ADS configuration used for the earlier simulations was too close to the jet plume. Because of this, significant flow structures were penetrating the surface, and this led to spurious noise sources which contaminated our analysis. Unlike the time step-related errors, this other spurious noise primarily impacted the lower observer angles and shows up as a broadband excess of noise at higher frequencies.

Conclusions and recommendations

The synthetic array technique has been found to be an effective method for diagnosing spurious noise sources in CFD solutions. Knowing where the problems originate in space allowed a solution to be developed quickly.

The current work benefited greatly from the availability of both experimental datasets and also prior computations of the same configurations (e.g. the work of Du and Morris³⁵). This allowed rapid assessment of whether or not anomalies were present in the solutions. In cases where comparison data are not available, such assessment becomes more challenging, but the current work points to some strategies which may be beneficial. First, recall that the spurious tones initially observed in the chevron jet results (e.g. in Figure 12) were extremely sensitive to the time step used in the simulation, whereas an actual tonal response should be present for any time step which can adequately resolve its acoustic frequency. Thus, one test to assess whether or not a predicted acoustic field is being corrupted by spurious results is to vary the time step and observe its effect, if any, on the predicted spectra. In addition, the results presented above clearly show the impact of an improperly placed ADS on sound predictions. For the jet simulations discussed here, the radial position of the ADS was particularly important. Therefore, an assessment of the extent to which the ADS is or is not penetrated by strong unsteady flow features should be performed. If possible, collecting data on multiple ADS configurations (with varying radial locations) is also recommended. If any of these tests indicate a problem, then the same synthetic array techniques used above to identify the specific problem areas can be used to speed the development of solutions.

Thus, in the current work, the synthetic array technique has been found to provide benefits not only for the development of improved array processing methods used for jet noise (such as a new wavepacket-based source model that has been implemented in Beamform Interactive) but also helps to resolve problematic features of the CFD. Taking advantage of this synergy allows researchers to both obtain better data from both simulation and experiment.

Footnotes

Acknowledgements

Computer resources for this work were provided by the DoD High Performance Computing Modernization Program; the support of the Navy DoD Supercomputing Resource Center and the US Army Engineer Research and Development Center is noted in particular. The opinions expressed here are those of the authors and do not necessarily reflect any opinions of the government sponsors.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was sponsored by the United State Navy Office of Naval Research under ONR award N00014-12-C-0011.

References

Nelson CC, Cain AB, Raman G, et al. Numerical studies of wind turbine acoustics. In: 50th AIAA aerospace sciences meeting, Nashville, Tennessee, 9–12 January 2012, AIAA paper 2012-0006.

Kuo

C-W

Morris

. Simulations and measurements of the flow and noise in hot supersonic jets. Noise Control Eng J 2012; 60: 577–594.

Hennes

Lopes

Shirey

. PSUWOPWOP user’s manual, University Park: The Pennsylvania State University, 2009.

Ffowcs Williams

Hawkings

. Sound generation by turbulence and surfaces in arbitrary motion. Phil Trans R Soc A 1969; 264: 321–342.

Lockard

Morris

. Radiated noise from airfoils in realistic mean flows. AIAA J 1998; 36: 907–914.

Shieh CM and Morris PJ. Comparison of two- and three-dimensional turbulent cavity flows. In: 39th AIAA aerospace sciences meeting, Reno, Nevada, 8–11 January 2001, AIAA paper 2001-0511.

Paliath U and Morris PJ. Prediction of jet noise from circular beveled nozzles. In: 11th AIAA/CEAS aeroacoustics conference, Monterey, California, 23–25 May 2005, AIAA paper 2005-3096.

Paliath U and Morris PJ. Prediction of jet noise from rectangular nozzles. In: 44th AIAA aerospace sciences meeting, Reno, Nevada, 9–12 January 2006, AIAA paper 2006-0618.

Tam

CKW

Webb

. Dispersion-relation-preserving finite difference schemes for computational acoustics. J Comput Phys 1993; 107: 262–281.

10.

Mittal

Iaccarino

. Immersed boundary methods. Annu Rev Fluid Mech 2005; 37: 239–261.

11.

Mohd-Yusof J. Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries. In: CTR Annual Research Briefs, Center for Turbulence Research, Stanford Univ., 1997, pp.317–327.

12.

Spalart PR and Allmaras SR. A one-equation turbulence model for aerodynamic flows. In: 30th AIAA aerospace sciences meeting, Reno, Nevada, 6–9 January 1992, AIAA paper 92-0439.

13.

Spalart PR, Jou WH, Strelets M, et al. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: Proceedings of the advances in DNS/LES: 1st AFOSR international conference on DNS/LES, Arlington, TX, 4–8 August 1997. Columbus, OH: Greyden Press.

14.

Grinstein

. Recent progress on monotone integrated large eddy simulation of free jets. JSME Int J 2006; 49: 890–898.

15.

Shur

Spalart

Strelets

MKh

. Noise prediction for increasingly complex jets. Part I: methods and tests. Int J Aeroacoust 2005; 4: 213–246.

16.

Shur

Spalart

Strelets

MKh

. Noise prediction for increasingly complex jets. Part II: applications. Int J Aeroacoust 2005; 4: 247–266.

17.

Brès GA. Modeling the noise of arbitrary maneuvering rotorcraft: analysis and implementation of the PSU-WOPWOP noise prediction code. M.S. thesis. University Park, PA: Department of Aerospace Engineering, The Pennsylvania State University, 2002.

18.

Perez G. Investigation of the influence of maneuver on rotorcraft noise. M.S. thesis. University Park, PA: Department of Aerospace Engineering, The Pennsylvania State University, 2002.

19.

Brès

Brentner

Perez

. Maneuvering rotorcraft noise prediction. J Sound Vib 2004; 275: 719–738.

20.

Brentner

Farassat

. Modeling aerodynamically generated sound of helicopter rotors. Prog Aerosp Sci 2003; 39: 83–120.

21.

Farassat

Succi

. The prediction of helicopter discrete frequency noise. Vertica 1983; 7: 309–320.

22.

Farassat F. Derivation of formulations 1 and 1A of Farassat. NASA TM 2007-214853, 2007.

23.

Williams

. Fourier acoustics: sound radiation and near-field acoustical holography, London: Academic Press, 1999.

24.

Dougherty

. Improved generalized inverse beamforming for jet noise. Int JAeroacoust 2012; 11: 259–289.

25.

Blllingsley

Kinns

. The acoustic telescope. J Sound Vib 1976; 48: 485–510.

26.

Dougherty RP. Functional beamforming. In: 5th Berlin beamforming conference, BeBeC 2014-1, Berlin, Germany, 19–20 Febuary 2014.

27.

Dougherty RP. Functional beamforming for aeroacoustic source distributions. In: 20th AIAA/CEAS aeroacoustics conference, Atlanta, Georgia, 16–20 June 2014, AIAA paper 2014-3066.

28.

Dougherty RP, Brentner K, Cain AB, et al. Improved phased array measurement techniques for jet noise understanding. In: Proceeding of the 16th international conference on fluid flow technologies conference on modelling fluid flow (CMFF'15), Budapest, Hungary, 1–4 September 2015.

29.

Sijtsma

. CLEAN based on spatial source coherence. Int J Aeroacoustics 2007; 6: 357–374.

30.

Brooks TF and Humphreys WM Jr. A deconvolution approach for the mapping of acoustic sources (DAMAS) determined from phased microphone arrays. In: 10th AIAA/CEAS aeroacoustics conference, Manchester, Great Britain, 10–12 May 2004, AIAA paper 2004-2954.

31.

Dougherty RP, Ramachandran RC and Raman G. Deconvolution of sources in aeroacoustic images from phased microphone arrays using linear programming. In: 19th AIAA/CEAS aeroacoustics conference, Berlin, Germany, 27–29 May 2013, AIAA paper 2013-2210.

32.

Sarradj

. A fast signal subspace approach for the determination of absolute levels from phased microphone array measurements. J Sound Vib 2010; 329: 1553–1569.

33.

Bridges J, Wernet MP and Frate FC. PIV measurements of chevrons on F400-series tactical aircraft nozzle model. In: 49th AIAA aerospace sciences meeting, Orlando, Florida, 4–7 January 2011, AIAA paper 2011-1157.

34.

McLaughlin

Bridges

Kuo

. On the scaling of small, heat simulated jet noise measurements to moderate size exhaust jets. Int J Aeroacoust 2010; 9: 627–654.

35.

Du Y and Morris PJ. Noise simulations of supersonic hot jets for chevron nozzles. In: 17th AIAA/CEAS aeroacoustics conference, Portland, Oregon, 5–8 June 2011, AIAA paper 2011-2787.

36.

Mendez S, Shoeybi M, Sharma A, et al. Post-processing of large-eddy simulations for jet noise predictions. In: CTR Annual Research Briefs, Center for Turbulence Research, Stanford Univ., 2009, pp.17–31.