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At least 919 records · Page 51

Predicting Transonic Flutter Using Nonlinear Computational Simulations

This paper builds on the computational aeroelastic results published previously and generated in support of the second Aeroelastic Prediction Workshop for the NASA Benchmark Supercritical Wing configuration. The computational results are obtained using FUN3D, an unstructured flow solver developed at the NASA Langley Research Center. Flutter analyses are performed using various aerodynamic models including linear doublet lattice, Euler solutions, Reynolds averaged Navier-Stokes and Delayed Detached Eddy Simulations. The analyses are performed across the transonic Mach range for a range in angle of attack from 0° to 5°, with focus on identifying the transonic dips in the flutter onset boundaries.

Heeg, Jennifer↗

Wind Tunnel Investigation of the Supersonic Stage Separation Aerodynamics of a Generic 0.0175-Scale Bimese Two-Stage-to-Orbit Reusable Launch Vehicle Configuration

A wind tunnel investigation was conducted of the supersonic stage separation aerodynamics of a generic two-stage-to-orbit bimese wingbody configuration in the NASA Langley Research Center Unitary Plan Wind Tunnel. Proximity and isolated model testing was conducted at Mach numbers of 2.3, 3.0, and 4.5 and a unit Reynolds number of 2.0 million per foot using 0.0175-scale models of the Langley Glide-Back Booster concept designated as the orbiter and booster in belly-to-belly and back-to-belly configurations. Longitudinal forces and moments were obtained on both models and surface static pressure measurements were obtained on the orbiter model at 328 relative proximity locations and at relative angles of attack of 0 degrees and 5 degrees. The test results supported a larger effort to develop and validate experimental and computational tools applicable to the design and simulation of stage separation and abort procedures for reusable launch vehicles composed of multiple bodies, including winged bodies. An initial proof-of-concept experiment featuring low-cost uninstrumented models was conducted to verify an emerging automated model control system and new support system hardware, and to identify potential model and support system blockage and unsteady aerodynamics/model dynamics prior to committing to higher-fidelity instrumented models. This investigation led to upgrades in the facility stage separation hardware, calibration and testing techniques and capabilities, and data analysis and documentation methodologies that have been extended to the more recent NASA Constellation and Space Launch System crew and cargo launch vehicle programs. A virtual diagnostics interface methodology was used to facilitate the design of the stage separation support hardware, to position the models in the test section, and to define the experimental test space. Advances in the facility automated model positioning system established a foundation for the development of a continuous-sweep data acquisition technique that is responsible for significant productivity improvements to the current NASA Space Launch System test program. The automated model positioning capability was leveraged to conduct a companion statistically-designed stage separation experiment requiring randomization of the relative proximity positions of the orbiter and booster models. The respective zones of influence and interference effects of the orbiter and booster were identified from three-dimensional scatter plots, contour and influence maps, and two-dimensional plotting methods. The highly-nonlinear, shock-dominated aerodynamic characteristics of the orbiter and booster in the Unitary Plan Wind Tunnel exhibited good agreement with independent test data obtained in a NASA Marshall Space Flight Center wind tunnel and with computational fluid dynamics predictions using a compressible, three-dimensional flow solver and an inviscid, unstructured Cartesian method.

Erickson, Gary E.↗

Recent Progress in OVERFLOW Convergence Improvements

Improvements have been made to the implicit symmetric successive overrelaxation algorithm in the OVERFLOW 2.3 structured, overset grid, computational fluid dynamics flow solver. These improvements, consisting of implicit boundary conditions, improved flux Jacobian linearizations, and CFL number ramping, are a series of evolutionary changes to the linear solver that have resulted in increased nonlinear convergence rates and faster time to solution. A series of test cases are presented that demonstrate the effect of the changes through comparison with the original SSOR path and other linear solver implementations within OVERFLOW.

Joseph M Derlaga↗

Simulations of a Turbulent Flow Subjected to Favorable and Adverse Pressure Gradients

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted “speed bump” geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proven to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest-fidelity simulation techniques. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation, and development of internal layers where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units, which is found to provide a significant speedup compared to an earlier solver optimized for central processing unit architectures.

Ali Uzun↗

USM3D Simulations for Third Sonic Boom Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include an axisymmetric equivalent area body, 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 grids and 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 Boom Grid. The near-field pressure signatures were extracted, propagated to the ground and the perceived loudness levels on the ground was computed. The USM3D near-field pressure signatures,corresponding ground signatures, and loudness levels on the ground are compared with mean values from other workshop participants.

Supersonics↗

FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

The 1st AIAA Stability and Control Prediction Workshop was created to establish best practices for the prediction of stability & control derivatives using computational fluid dynamics and assess the limitations of these computational methods when those best practices are applied. The inaugural workshop considers the ONERA version of the NASA/Boeing Common Research Model(CRM), which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel tests have been conducted for this configuration with longitudinal tests having been previously published, in addition to unpublished data at small sideslip angles that will serve as ‘blind’ data for workshop data comparisons. Participants were provided a ‘family’ of unstructured grids for the full-span ONERA CRM model with the wind-tunnel sting included. This family of mixed-element grids consists of 5 levels of refinement (tiny, coarse, medium, fine, and extra fine) with surface and volume mesh scaling, resulting in a size range of 14.6 to 53.4 million nodes. In addition, a medium refinement mesh has been provided for the ONERA CRM configuration without a sting to evaluate the sting’s impact on static longitudinal stability characteristics. In addition to these workshop-provided grids, the present work also considers an equivalent ‘family’ of computational grids generated using Heldenmesh™, a rapid grid generation software by Helden Aerospace Corporation for creating high-quality, three-dimensional, mixed-element unstructured meshes. Because of the authors’ familiarity with this software, these additional grids were generated as a comparison to the workshop-provided grids and to better understand the implications of using volume-mirrored grids for stability and control predictions. The present work will contribute to the workshop with test case data generated using the NASA FUN3D code, a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Numerical simulations will be conducted using the Quadratic Constitutive Relationship (QCR) version of the Spalart-Allmaras (SA) turbulence model with negative turbulence variable provisions. Both steady and2nd-order, time-accurate simulation results are to be generated and compared for select test cases, as time permits, to investigate their impact on FUN3D predictions. The present work will consider the three primary workshop test cases: (1) grid convergence study, (2) Mach number effect on static stability, and (3) wind tunnel sting increments. Additionally, data will be provided for the two optional test cases, which include:(1) static stability derivative calculations and (2)sideslip angle sweeps. In each of the test cases, the vehicle is stationary, and the body is assumed to be rigid, where vehicle deformation has been accounted for in the model configuration geometry. For all test cases, longitudinal and lateral force and moment aerodynamic coefficients will be provided for the total configuration, in addition to a component-level breakdown that includes the port wing, starboard wing, fuselage, and tail.

CFD↗

Comparison of Computational Predictions of the Mach 0.80 Transonic Truss-Braced Wing Configuration with Experimental Data

The NASA Langley and Ames Research Centers have teamed together for comparisons of computational predictions of the Boeing Mach 0.80Transonic Truss-Braced Wing (TTBW) configuration with a high-speed experimental dataset. The Mach 0.80 TTBW vehicle is a high wing, high aspect ratio configuration, designed for a high lift-to-drag ratio. System studies have predicted significant fuel burn and emissions benefits with the TTBW technology moving toward meeting NASA Subsonic Transport Systems-Level-Metrics. A 4.5% scale Mach 0.80 design TTBW model was recently tested at the NASA Ames Research Center 11-by 11-Foot Transonic Wind Tunnel(11-Ft TWT),providing a valuable dataset to validate computational tools and investigate best practices as risk reduction efforts continue for the development of the advanced TTBW vehicle. The NASA Computational Fluid Dynamics (CFD) team has computed free-air flow solutions on the Mach 0.80 design flight configuration and two wind tunnel configuration variants using the USM3D and LAVA flow solvers. Accurate modeling of the configuration tested in the wind tunnel environment is critical to validating the CFD tools, thus the team has included the internal cavity region and sting in their modeling of the configuration, similar to that tested in the 11-Ft TWT. Overall, the CFD simulations compared well and show similar trends as the corrected experimental data for lift and drag polars. The CFD predicted lift curve is shifted in angle of attack from what was observed in the experiment. The shift in lift also was seen in the pitching moment comparison plots. CFD solutions were computed at constant CL test point values and showed overall very good agreement when comparing constant spanwise cuts of pressure coefficient data on the wing and strut with experimental data. CFD cavity corrections were also investigated using the 11-Ft TWT cavity correction method, similar to that used to correct the wind tunnel data. Results showed some improvement in pitching moment coefficient predictions, and an increase in drag, shifting the data to the right in drag polars, further from the experimental data at lower lift conditions, good agreement near the design CL, and slight improvement at the higher lift conditions.

Transonic Truss-Braced Wing↗

USM3D Simulations for Third Sonic Boom Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include a nearfield 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 for sonic boom analyses known as BoomGrid. The near-field pressure signatures were extracted, 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 are compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of near-field pressure signatures prediction was investigated and results are compared with that of mean values from other workshop participants. The effect of using wall function grids in accurately predicting near-field pressure signatures was also evaluated.

Supersonics↗

The Influence of Computer Architecture on Performance and Scaling for Hypersonic Flow Simulations

It is critical to understand how hypersonic simulation tools perform on a range of computational platforms. This information will aid in the acquisition of appropriate hardware and the potential refactoring of hypersonic codes to run on different systems. In this paper, we consider two representative high-speed reacting flow cases: a model Mach 8 hypersonic waverider glide vehicle and a model hydrocarbon-fueled hypersonic ramjet propulsion system. In both scenarios, the flow fields are in chemical non-equilibrium and are modeled by the multi-species reacting Navier-Stokes equations. For these simulations we use several hypersonic simulation tools, including US3D, Kestrel, FUN3D, and the JENRER© flow solver. We explore several high performance computing systems containing IntelR© XeonR© Platinum processors, AMD EPYCTM7702 processors, and NVIDIAR© Tesla V100 devices. We compare performance and strong scaling between the different systems.

CPU↗

LA-8 Computational Analysis and Validation Studies Using FlightStream

With the emerging market of Urban Air Mobility and the associated unique new flight vehicles with the capability of vertical takeoff and landing, design tools need to be calibrated to assist in the development of these new flight vehicle concepts. Distributed electric propulsion (DEP) covers these vehicles with high-energy flow from the array of motors, which leads to extensive propulsion/airframe interaction effects. With limited experimental data of vehicles using DEP and vehicle operation across a large range of angles of attack, including post-stall conditions, there is a lack of validated design tools to advance new vehicle concepts that have blown wings and operate in multiple flight modes. Although some CFD tools can handle the integration of multiple propulsors and unique geometries, the computational time with a full vehicle is extraordinary. FlightStream, a surface vorticity flow solver that can run in a fraction of the time of other CFD methods, has been evaluated using the Langley Aerodrome No. 8 (LA-8) vehicle as a test case. The LA-8 vehicle is a DEP tandem tilt-wing research vehicle that was designed, built, and tested at NASA Langley Research Center. The LA-8 design features both high-performance and high-technical risks aspects. The vehicle has gone through extensive design of experiments wind tunnel testing in the NASA Langley 12-Foot Low-Speed Wind Tunnel in order to capture all modes of operation. In addition, the LA-8 vehicle has undergone wind tunnel testing with and without propellers, which contributes to the validation of FlightStream for aerodynamic performance in blown and unblown wing cases. This study shows that FlightStream can produce trends and magnitudes of the lift and drag coefficients similar to the data collected from the wind tunnel testing of LA-8. The test cases were both blown and unblown wing cases and with and without high lift control surface deflections.

Steven Curtis Geuther↗

USM3D Simulations for the Third Sonic Boom Prediction Workshop (SBPW-3)

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include a nearfield 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 for sonic boom analyses known as BoomGrid. The near-field pressure signatures were extracted, 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 are compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of near-field pressure signatures prediction was investigated and results are compared with that of mean values from other workshop participants. The effect of using wall function grids in accurately predicting near-field pressure signatures was also evaluated.

Supersonics↗

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 nearfield pressure signatures. Specialized techniques are applied to maximize accuracy and minimize cost on Cartesian meshes. The Richardson-based error estimate highlights regions of the signatures most sensitive to mesh refinement. Timing results and coarse, medium, and fine mesh sizes for nearfield cases demonstrate that the parallel decomposition approach is efficient in both computational time and wall-clock. 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 more realistic atmospheric profiles, which 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 propagation, and the sampling frequency increases at large off-track angles with longer acoustic ray paths and propagation times. The numerical methods yield accurate results for predicting low sonic boom signatures while being among the least computationally expensive of the workshop.

ARMD↗

Nonlinear Unsteady Aerodynamic Modeling Using Empirical Orthogonal Functions

Empirical orthogonal function modeling is explained and applied to identify compact discrete-time nonlinear unsteady aerodynamic models from data generated by an unsteady three-dimensional compressible Navier-Stokes flow solver for an airfoil undergoing various pitching motions. Model structures, model parameter estimates, and model parameter uncertainty estimates for nondimensional lift, drag, and pitching moment coefficient models were determined autonomously and directly from the data. Prediction tests using data that were not used in the modeling process showed that the identified models exhibited excellent prediction capability, which is a strong indicator of an accurate model.

empirical↗

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no or some addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4 rocket engine fired on 1m2 area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon. The resulting computed values of plume impingement surface temperature, stagnation pressure, gas velocity, shear stress and heat flux were then matched as closely as possible in the Earth’s atmosphere in a sub-scale rocket engine GO2/CH4 test which was provided by Masten Space Systems in Mojave, California. The rocket engine was mounted on a test stand with vertical translation capabilities so that the landing operations of a lander could be simulated (Figure 1).The pad materials test coupons were placed at the surface of a large bin containing simulated lunar basalt regolith and subjected to a test firing as shown in Figure 2. The results of this testing will be presented with related findings, analysis and discussion.

Plume Surface Interaction↗

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no, or some, addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4rocket engine fired on a 1m2area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon.

Lunar↗

NASA Langley FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

This work summarizes the results of FUN3D analyses conducted for the 1st AIAA Stability and Control Workshop on behalf of participants from the NASA Langley Research Center. The workshop was created to establish best practices for the prediction of stability and control derivatives using computational fluid dynamics and assess the limitations of these methods when those best practices are applied. The inaugural workshop considered the ONERA version of the NASA/Boeing Common Research Model, which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel data at small sideslip angles remain unpublished and served as ‘blind’ data for computational comparisons. The present research generated workshop test case data using the NASA FUN3D code, which is a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Steady- state numerical simulations were conducted for workshop test cases investigating the following: grid convergence, Mach number effect on static stability, wind tunnel sting increments, static stability-derivative calculations, and a sideslip angle sweep. Results were generated for two series of unstructured, mixed-element grids, one set provided by the workshop and another set created using the HeldenMesh grid generation software. The results provided include total- and component-level breakdowns of the force and moment coefficients, in addition to sectional pressure distributions for the wing and tail components for comparisons to wind tunnel data.

CFD↗

Investigation of a Smooth Local Correlation-based Transition Model in a Discrete-Adjoint Aerodynamic Shape Optimization Algorithm

A smooth local correlation-based transition model is fully coupled to a RANS-based Newton-Krylov flow solver and discrete-adjoint gradient-based optimization algorithm. The free-transition optimization framework is evaluated using lift-constrained drag minimizations of airfoils at design conditions ranging from light to single-aisle aircraft and an infinite swept wing at design conditions representative of a transonic strut-braced wing aircraft. The impact of the streamwise grid resolution on the ability of the optimization algorithm to delay boundary-layer transition is investigated, with the results demonstrating that streamwise grid resolution requirements increase as the transition length decreases with increasing Reynolds number. The optimization problem at the light aircraft design conditions is demonstrated to be multi-modal, with the optimization algorithm producing two distinct designs: one with a thin, reflexed trailing edge and steep pressure recovery regions, the other with increased aft loading, with the latter design outperforming the former. A drag minimization of an airfoil at transonic design conditions demonstrates that the optimization algorithm successfully trades a decrease in viscous drag by delaying boundary-layer transition with an increase in wave drag, while the drag minimization of an infinite swept wing demonstrates the capability of the optimizational gorithm to delay both Tollmien-Schlichting and stationary crossflow instabilities.

AATT↗