AIAA Sonic Boom Prediction Workshop Research Articles

Introduction to the Special Section on the Third AIAA Sonic Boom Prediction Workshop

Introduction to the Special Section on the Third AIAA Sonic Boom Prediction Workshop

Sonic boom focus modeling of benchmark cases using the PCBoom suite

Focusing of sonic booms is a phenomenon that can arise from particular atmospheric conditions or aircraft trajectories including acceleration, turns, or other variations from steady level flight. Because such maneuvers are unavoidable, development of regulations for civil supersonic flight will depend on the capability to understand and predict the scenarios in which focus booms can lead to ground overpressures several times higher than typical carpet booms. Models for predicting sonic boom focal zones and focus boom signatures have been developed by several organizations, and a recent AIAA Sonic Boom Prediction Workshop provided an opportunity to compare results among such models. Rallabhandi et al. developed benchmark cases to further extend verification of focus boom models. The PCBoom suite of tools, including the lossy nonlinear Tricomi equation (LNTE) module, was used to predict caustic geometry and pressure signatures near the caustic arising from a constant acceleration level trajectory and also from an accelerating climb trajectory. A recently developed methodto streamline the focus boom modeling process within PCBoom was exercised as part of this benchmark case evaluation. [Work supported by the National Aeronautics and Space Administration under project VXAHA321.]

Shock–Plume Interaction Near-Field Summary for the Third AIAA Sonic Boom Prediction Workshop

The Third AIAA Sonic Boom Prediction Workshop was held during January 2020, on the weekend before the AIAA SciTech conference. The workshop consisted of two days: the first day focused on near-field computational fluid dynamics (CFD), and the second day on propagation techniques. The near-field CFD study included two configurations: one simplified shock–plume interaction case and one more complex configuration based on a design for the NASA low-boom flight demonstrator. The motivation for the workshop stems from the goal of obtaining supersonic commercial overland flight. In order to replace the current prohibition with a certification standard, an international effort is required to quantify the accuracy and reliability of prediction methods. The workshops also identify deficiencies in existing methods where further research should be focused such as issues with extrema, shock position, and grid coarseness. This paper provided a summary and comparison of the results for the shock–plume interaction case, also known as the biconvex case. Overall agreement between the participants was very good, with the largest local standard deviations due to a slight shift of the shock location, not the predicted strength of the shocks. Variation in the submission ensemble sample deviation was comparable to the experimental ensemble sample deviation, and they overlapped for most of the forward portion of the signature.

USM3D Simulations for the Third AIAA Sonic Boom Prediction Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases included a near-field biconvex shock–plume interaction wind tunnel model and the C608 low boom flight demonstrator. Numerical simulations were conducted on the mixed-element and tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach known as BoomGrid. The near-field pressure signatures were extracted and propagated to the ground, and the perceived loudness levels on the ground were computed. The USM3D near-field pressure signatures, corresponding ground signatures, and loudness levels on the ground were compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of near-field pressure signature prediction was investigated and results were compared with that of mean values from other workshop participants. The effect of using wall-function models for predicting near-field pressure signatures was also evaluated. Results showed that the overpressure signatures extracted from the wall-modeled simulations and the wall-resolved simulations are in good agreement. The use of wall functions (wall-modeled simulations) allowed for approximately 23% savings in the time to solution and yielded comparable perceived loudness levels on the ground to the wall-resolved Reynolds-averaged Navier–Stokes simulations.

Structured and Unstructured Simulations for the Third AIAA Sonic Boom Prediction Workshop

Predictions using the launch ascent and vehicle aerodynamics (LAVA) solver framework for the NASA shock–plume interaction biconvex model and C608 supersonic aircraft prototype geometries are compared in support of the Third AIAA Sonic Boom Prediction workshop. Descriptions of the mesh generation techniques and numerical methods are provided along with a comparison of near-field and far-field predictions with available experimental data as well as other workshop submissions. Strong agreement was observed between the LAVA structured curvilinear and unstructured solver near-field predictions for the biconvex model and the C608 aircraft: predictions that were also compared against validation and verification data. Additionally, near-field and far-field ground signature results using the combination of a truncated computational fluid dynamics (CFD) domain coupled to a midfield space marching method and propagated to the ground using sBOOM will be discussed. This approach is shown to provide an efficient way to propagate near-field pressure signatures to the ground with the same accuracy as the near-field CFD coupled to sBOOM but at less computational cost.

Low-Boom Demonstrator Near-Field Summary for the Third AIAA Sonic Boom Prediction Workshop

A summary and statistical analysis of the near-field computational fluid dynamics (CFD) submissions for the Third AIAA Sonic Boom Prediction Workshop is provided with a focus on the C608 Low Boom Flight Test Demonstrator. The C608 is more complex in terms of geometry and propulsion boundary conditions than previous workshop cases and is more representative of vehicles with lower ground loudness and the potential for lower annoyance. The near-field signatures submitted by the participants are propagated to the ground to compute statistics of loudness measures over the vehicle sonic boom carpet. Principle component analysis is used to extract the primary variation modes. Context from previous sonic boom workshops indicates that this workshop has the lowest variation even though the case is more challenging because it is quieter and more complex. The results documented in this summary indicate that the international state-of-the-art for near-field CFD has a variation that is small enough for meaningful low-boom design and analysis. Low-boom configuration analysis methods with low variation are important tools to develop certification processes for addressing the prohibition on overland supersonic commercial flight.

Summary of Propagation Cases of the Third AIAA Sonic Boom Prediction Workshop

A summary is provided for the propagation portion of the Third AIAA Sonic Boom Prediction Workshop held on January 4–5, 2020, in conjunction with the AIAA SciTech 2020 conference. Near-field pressure waveforms for two cases were supplied at multiple azimuthal angles. Ground signatures across the breadth of the sonic boom primary carpet and their corresponding loudness metrics were requested. Each case had some required, as well as some optional, runs. The required cases included atmospheric profiles with measured data including winds. Optional cases included a level-acceleration sonic boom focusing case and prediction under standard atmospheric conditions. Participants provided ground signatures along with several loudness metrics using their best sonic boom prediction practices. All the participants’ submissions are compared and discussed for each case. Noise or loudness measures are calculated, and detailed comparisons and statistical analyses are performed and presented. Compared with previous workshops, the selected cases in the current workshop have much lower boom loudness levels. As was observed in the past workshops, the variation in the loudness measures and spread between participants’ submissions increased as the computation proceeded from undertrack locations toward the lateral cutoff. Lessons learned during this workshop are discussed, and recommendations are made for potential improvements and possible subsequent workshops as we collectively attempt to refine our analysis methods.

UNS3D Near-Field Predictions for the Third AIAA Sonic Boom Prediction Workshop

This paper presents the results of turbulent flow simulations prepared for the Third AIAA Sonic Boom Prediction Workshop. Solutions were prepared for two geometries that exhibited shock–plume interaction features: the NASA biconvex shock–plume interaction wind-tunnel model, and the NASA C608 low-boom concept aircraft. The unstructured, finite volume Navier–Stokes solver UNS3D was used to predict the turbulent near-field flow with Menter’s shear stress transport turbulence model. Four solver setups with different combinations of the flux function, gradient reconstruction, and slope limiter were applied to each geometry. UNS3D predictions were compared against a grid-specific ensemble dataset created using workshop participant submissions and experimental data when available. Predictions of the biconvex geometry were found to be in good agreement with both the experimental and ensemble datasets. The weighted least-squares with QR decomposition (LSQR) gradient reconstruction approach was only successful for the biconvex geometry, with no converged cases being achieved on C608 grids. The Dervieux limiter, used only to aid simulations on the C608 using weighted LSQR, was observed to be too dissipative to be of practical use. Near-field predictions of the C608 geometry using Green–Gauss gradient reconstruction and a modified Venkatakrishnan limiter were found to correlate well with the ensemble data. The perceived level of the resulting sonic boom carpet was 1.5 dB quieter along the first 20 deg of the carpet than the ensemble mean, and it peaked at an azimuth angle of 30 deg with a value of 76.1 dB. A study of the undertrack near-field pressure signature revealed the components of the predicted signatures responsible for the variances observed in the sonic boom carpet.

Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all cases from the Third AIAA Sonic Boom Prediction Workshop. An inviscid, embedded-boundary Cartesian-mesh flow solver is used in conjunction with adjoint-based mesh adaptation to compute near-field pressure signatures. Specialized techniques are applied to maximize accuracy and minimize cost on Cartesian meshes. Regions of the flow most sensitive to discretization error are identified using Richardson extrapolation. Timing results and mesh sizes for near-field cases demonstrate that decomposition into multiple off-track simulations is efficient in both computational time and wall-clock time, with results among the least computationally expensive of those presented at the workshop. Pressure signals are propagated to the ground using an augmented Burgers equation solver to predict boom carpets. Ground signatures and loudness metrics are presented for a standard atmosphere as well as an atmosphere with wind profiles that affect overall noise levels and can significantly widen the boom carpet. Mesh convergence studies show that high sampling frequencies, around 500 kHz, are required for on-track propagation; the sampling frequency increases at large off-track angles due to longer acoustic ray paths. Overall, the approach presented here yields accurate results for predicting low-sonic-boom signatures.

Unstructured/Structured Overset Grid Simulation for the Third AIAA Sonic Boom Prediction Workshop

The Third AIAA Sonic Boom Prediction Workshop was held in January 2020, and in the near-field section of the workshop, several simulated near-field pressure signatures of the C608 airplane, an early version of the NASA X-59, were compared. The authors have applied the unstructured/structured overset grid method to the C608 airplane case. In this method, an unstructured grid is used in the vicinity of the airplane, and the flowfield at several body lengths away from the airplane is simulated by oversetting a structured Mach cone aligned grid with the unstructured grid. It is found that the near-field pressure signatures can be obtained accurately with sharp pressure jumps in the signature by using a fine structured grid in the midfield even when a relatively coarse unstructured grid is used in the near-field of the airplane. The results show that the unstructured/structured overset grid method is a way to obtain accurate near-field pressure signatures for sonic boom estimation efficiently.

DLR TAU Near-Field Simulations for the Third AIAA Sonic Boom Prediction Workshop

The accurate prediction of the sonic boom is essential for the development of a future low-boom supersonic aircraft. In this paper, the best practice for predicting near-field pressure signatures with the German Aerospace Center (DLR) TAU code is applied for geometries and grids provided by the third AIAA Sonic Boom Prediction Workshop. The near-field part of the workshop provided two cases, the biconvex case and the NASA C608 case. Both geometries were analyzed by DLR. The biconvex case is used to study shock–plume interactions and the NASA C608 case is used to assess the status of near-field simulations for a realistic low- boom flight demonstrator. Results for the DLR TAU simulations on the workshop-provided grids are presented for different grid refinement levels using Reynolds-averaged Navier–Stokes simulations. In addition to the provided grids, a setup for mixed-element grids with varying setups is described. The predicted near-field signatures agree very well with other workshop participants’ results and wind-tunnel data.

PCBoom Propagation Modeling for the Third AIAA Sonic Boom Prediction Workshop

The PCBoom suite of tools was used to model atmospheric propagation cases and the optional focus case as part of the Third AIAA Sonic Boom Prediction Workshop. The Focused Boom module FOBoom version 7.1.0 was used to complete ray tracing calculations using computational fluid dynamics pressure data as the source. Lossy propagation was modeled using PCBoom’s interactive Burgers equation solver, PCBurg, and final results were obtained with the batch analysis tool HeadlessBurgers. The effects of sampling rate, time-step factor, and other factors on model results were investigated. Lateral cutoff angles were refined by finely incrementing azimuth angles and examining propagation paths and ground metrics. The optional focus case, in which the vehicle trajectory included acceleration, was also modeled using PCBoom. An interactive program (RayCau) was used to generate ray diagrams showing the caustic and the delta-tangent ray to confirm the focus condition and to facilitate identification of the ray and signature for input to the lossy nonlinear Tricomi equation (LNTE) solver. PCBurg was used to obtain the lossy signature at the delta tangent position. Finally, the LNTE module was used to compute signatures in the vicinity of the focal zone.

Introduction to the Special Section on Second AIAA Sonic Boom Prediction Workshop

Introduction to the Special Section on Second AIAA Sonic Boom Prediction Workshop

Application of Exactly Linearized Error Transport Equations to Sonic Boom Prediction Workshop

The computational fluid dynamics (CFD) prediction workshops sponsored by the AIAA have created invaluable opportunities to discuss the predictive capabilities of CFD in areas in which it has struggled, for example, sonic boom prediction. While there are many factors that contribute to disagreement between simulated and experimental results, such as modeling or discretization errors, quantifying the errors contained in a simulation is important for those who make decisions based on the computational results. The linearized error transport equations (ETE) combined with a truncation error estimate is a method to quantify one source of error. The ETE are implemented with a complex-step method to provide an exact linearization with minimal source code modifications to CFD and multidisciplinary analysis methods including atmospheric propagation of sonic boom signatures. Uniformly refined grids from the 2nd AIAA Sonic Boom Prediction Workshop demonstrate the utility of the linearized ETE for multidisciplinary analysis, capturing the general trends of the discretization error when flow features are resolved while also demonstrating issues related to error prediction near strong shocks or when under-resolved flow features are present.

USM3D Simulations for Second Sonic Boom Workshop

The NASA Tetrahedral Unstructured Software System with the USM3D flow solver was used to compute the test cases for the Second AIAA Sonic Boom Prediction Workshop (SBPW2). The intent of this paper is to document the USM3D results for SBPW2 test cases. The test cases included an axisymmetric equivalent area body, a Japan Aerospace Exploration Agency wing–body, and a NASA low-boom supersonic configuration modeled with flow-through nacelles and engine boundary conditions. All simulations were conducted for a freestream Mach number of 1.6, 0 deg angle of attack, and a Reynolds number of 5.7 million per meter. Simulations were conducted on the tetrahedral grids provided by the workshop committee as well as a family of grids generated by an in-house approach for sonic-boom analyses known as BoomGrid using current best practices. The near-field pressure signatures were extracted and propagated to the ground with the atmospheric propagation code sBOOM. The USM3D near-field pressure signatures, corresponding sBOOM ground signatures, and loudness levels on the ground are compared with mean values from other workshop participants.

Nearfield Summary and Statistical Analysis of the Second AIAA Sonic Boom Prediction Workshop

A summary is provided for the Second AIAA Sonic Boom Workshop held on January 8–9, 2017, in conjunction with AIAA SciTech 2017. The workshop used four models of increasing complexity: an axisymmetric body, a wing-body, and a wing-body with tail configuration with either flow-through nacelles or propulsion boundary conditions. The last configuration was optional. The models were designed with similar nearfield signatures to isolate geometry and shock/expansion interaction effects. These cases are more relevant to vehicles with lower ground loudness and have the potential for lower annoyance than those in previous workshops. Eleven international participant groups submitted nearfield signatures. In addition, noise levels were computed by propagating the nearfield signatures to the ground. This allowed the evaluation of grid convergence and statistical distribution with respect to the noise metric. Prediction dramatically improved for the wing-body with tail and flow-through nacelle case between the first and second workshops. The models for the second workshop with quieter ground noise levels than those in the first workshop exposed weaknesses in analysis, particularly in convective discretization. While progress is documented since the first workshop, improvement to the analysis methods for a possible subsequent workshop is also provided.

Comparing Anisotropic Adaptive Strategies on the Second AIAA Sonic Boom Workshop Geometry

The recent release of the second AIAA sonic boom geometry offers the opportunity to review the classical anisotropic adaptive strategies for complex geometries. The design of Mach-aligned tailored grids is also a great challenge to see how adaptivity can compete with user-defined tailored grids. Two classical adaptive strategies, multiscale and goal-oriented, are compared with the results obtained on tailored grids. For the flow solver, several low-dissipation numerical schemes of order 4 and 6 are discussed with respect to regular second-order scheme both on inviscid and Reynolds-averaged Navier–Stokes flow models. Finally, a nonlinear error analysis is performed to assess the convergence of the sequence of adaptive meshes with respect to tailored grids. All results and discussions are based on the C25D baseline geometry provided for the Second AIAA Sonic Boom Prediction Workshop.

Summary of Propagation Cases of the Second AIAA Sonic Boom Prediction Workshop

A summary is provided for the propagation portion of the second AIAA Sonic Boom Prediction Workshop, held 8 January 2017 in conjunction with the AIAA SciTech 2017 Conference. Near-field pressure waveforms for two cases were supplied, and ground signatures at multiple azimuthal angles as well as their corresponding loudness metrics were requested from 10 participants, representing three countries. Each case had some required as well as some optional runs. The required cases included atmospheric profiles with measured data including winds, using radiosonde balloon data at multiple geographically spread locations. The humidity profiles provided for the optional cases were taken from American National Standards Institute guidance. Participants provided ground signatures along with the requested data, including some loudness metrics using their best practices, which included lossy as well as lossless atmospheric propagation schemes. All the participants’ submissions, for each case, are compared and discussed. Noise or loudness measures are calculated, and detailed comparisons and statistical analyses are performed and presented. It has been observed that the variation in the loudness measures and spread between participants’ submissions increased as the computation proceeded from undertrack locations toward the lateral cutoff. Lessons learned during this workshop are discussed, and recommendations are made for potential improvements and possible subsequent workshops.

DLR TAU Simulations for the Second AIAA Sonic Boom Prediction Workshop

The accurate prediction of the sonic boom is essential for the development of a future low-boom supersonic aircraft. In this paper, geometries and grids provided by the Second AIAA Sonic Boom Prediction Workshop are used to improve a best practice for predicting near-field pressure signatures with the DLR TAU code. The workshop-provided low-boom geometries with different complexities, such as an axisymmetric body, a delta-wing body, and a full aircraft configuration with a cruciform tail and an engine. Results for the DLR TAU simulations on the workshop-provided grids are presented for different grid refinement levels using both Euler and Reynolds-averaged Navier–Stokes simulations. In addition to the provided grids, mixed-element grids with varying setups are generated. The positions of the shocks and expansions are essentially identical for all medium to fine grids but vary for very coarse grids due to the surface triangulation. The pressure magnitude at shocks and expansions is higher for simulations on fine grids compared to coarse grids. It is shown that the influence of the viscosity on the pressure signatures is more significant than the influence of the grid resolution. The agreement between TAU solutions and other participants’ solutions is good.

Cart3D Simulations for the Second AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all test cases prescribed in the Second AIAA Sonic Boom Prediction Workshop. An inviscid, embedded-boundary Cartesian-mesh flow solver is used to compute “boom carpets”—pressure signatures at a range of specified distances and off-track angles. To accelerate the process, each boom carpet is automatically decomposed into several independent meshes, computed in parallel. Each mesh uses output-based mesh adaptation to affordably obtain credible results. This paper discusses improved Cartesian meshing strategies for boom prediction, including Mach alignment, azimuthal alignment, high-aspect-ratio cells, and adaptation functional weighting. The resulting nearfield signatures generally exhibit good convergence with mesh refinement. For an independent evaluation of our results, this study introduces a local error estimation procedure that highlights regions of the signatures most sensitive to mesh refinement. Results are also presented for the two atmospheric propagation test cases, which investigate the effects of atmospheric profiles on ground noise. Propagation is handled with an augmented Burgers’ equation method (NASA’s sBOOM), and ground noise metrics are compared.