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NASA NTRS1972

Automated design and optimization of flexible booster autopilots via linear programming, volume 1

A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory dispersions; and (3) stability with specified tolerances on the vehicle and flight control system parameters. The method is applicable to very high order systems (30th and greater per flight condition). Examples are provided that demonstrate the successful application of the employed algorithm to the design of autopilots for both single and multiple flight conditions.

Hauser, F. D.↗

NASA NTRS1990

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.

Michelassi, V.↗

NASA NTRS2023

Modeling and Simulation for Exercise Vibration Isolation and Stabilization System Design

The microgravity environment that crew members experience on orbit presents a well-known health challenge, particularly when it comes to loss of muscle and bone mass. To counteract these negative effects, exercise countermeasures play a critical role in the daily routine of the crew on the International Space Station (ISS). To help inform requirements for upcoming exploration missions such as the Gateway Program, a new device, called the European Enhanced Exploration Exercise Device (E4D), is being built by the European Space Agency through their contractor, the Danish Aerospace Company. The E4D is being demonstrated on the ISS and is unique from other current exercise devices in that it provides four separate modalities in a single device: resistive, cycle ergometry, seated aerobic rowing, and rope pulling. To support the integration of E4D on ISS, a passive Vibration Isolation and Stabilization (VIS) system was required by NASA, and this responsibility was given to the Johnson Space Center. This paper describes the end-to-end process of modeling, simulation, and analysis used to inform the mechanical design of the VIS system. The process begins with the collection of representative exerciser motion capture (MoCap) through ground-based testing with the developmental E4D in both the Prototype Immersive Technology (PIT) Laboratory and the Active Response Gravity Offload System (ARGOS) facility at the Johnson Space Center. These collected MoCap data are processed through human biomechanics modeling to create forcing functions as input to a multibody dynamics simulation of the combined E4D/VIS system, with numerous resulting outputs. These outputs include microgravity accelerations, overall system displacements, internal and transmitted loads, as well as collisions. Microgravity accelerations are compared for compliance against ISS requirements while displacements are used for sway space determinations on the design and volumetric constraints within the targeted module. Internal loads are supplied to the supporting stress analysis teams and external loads for structural loads and dynamics teams, both at NASA and ESA. Finally, contact and clearance analysis is performed using the simulation to eliminate potential design issues. To ensure that the elements of the multibody simulation were verified and validated, correlation against multiple VIS related ground hardware testbeds was performed and characterized. In addition to the isolation part of the VIS problem, stabilization is also key to the integrated performance and evaluation. Due to the difficulty in defining ISS requirements in this area, the stability of the exerciser was inspected via analysis. Loss of balance was defined analytically as occurring when the resultant force vector acting on the exerciser lies outside the base of support of the feet. Both the VIS and E4D teams have recently gone through their Critical Design Reviews (CDRs) and the iterative model-based approach has been integral to inform mechanical design, particularly in the case of the VIS. This same end-to-end approach is now being applied for the Gateway Program, where an Exploration Exercise Device (EED) derived from the E4D and notional VIS for the device are under concept development.

Countermeasures↗

NASA NTRS2014

Deducing Electronic Unit Internal Response During a Vibration Test Using a Lumped Parameter Modeling Approach

During random vibration testing of electronic boxes there is often a desire to know the dynamic response of certain internal printed wiring boards (PWBs) for the purpose of monitoring the response of sensitive hardware or for post-test forensic analysis in support of anomaly investigation. Due to restrictions on internally mounted accelerometers for most flight hardware there is usually no means to empirically observe the internal dynamics of the unit, so one must resort to crude and highly uncertain approximations. One common practice is to apply Miles Equation, which does not account for the coupled response of the board in the chassis, resulting in significant over- or under-prediction. This paper explores the application of simple multiple-degree-of-freedom lumped parameter modeling to predict the coupled random vibration response of the PWBs in their fundamental modes of vibration. A simple tool using this approach could be used during or following a random vibration test to interpret vibration test data from a single external chassis measurement to deduce internal board dynamics by means of a rapid correlation analysis. Such a tool might also be useful in early design stages as a supplemental analysis to a more detailed finite element analysis to quickly prototype and analyze the dynamics of various design iterations. After developing the theoretical basis, a lumped parameter modeling approach is applied to an electronic unit for which both external and internal test vibration response measurements are available for direct comparison. Reasonable correlation of the results demonstrates the potential viability of such an approach. Further development of the preliminary approach presented in this paper will involve correlation with detailed finite element models and additional relevant test data.

random vibration response↗

NASA NTRS2015

Space Biotech: Hindsight, Insight, Foresight

Over the past forty years, microgravity has inspired and enabled applications in a wide range of sectors including medicine, materials, computers, communications, and national defense. Trends show that demand for high-tech solutions is increasing in these sectors, solutions that require higher resolution, greater precision, novel materials, innovative processes, and more sophisticated tools. These are areas where microgravity can offer unique capabilities for innovation. The Emerging Space Office (ESO) has engaged in multiple studies over the past year that have found that microgravity RD is one of the most promising technology areas for contributing to economic growth and to NASAs mission. The focus of these studies was on terrestrial markets rather than NASA applications, applied research rather than basic research, and commercial rather than academic investigators. There have been more success stories than are generally appreciated and there are significant areas of promising future potential. Many of the problems that have limited commercial microgravity development in the past are being solved. Microgravity research and development (RD) requires iteration and learning, as rapidly as possible. New technologies enable high throughput and rapid data collection in increasingly small payloads. The International Space Station is in orbit and provides a laboratory that is available 247 at least until 2024. Frequent flights by commercial space providers to and from the ISS now enable the fast learning cycles needed by high-tech industries. Launch costs are decreasing and the ability to return payloads to Earth is increasing. New commercial space laboratories, such as those being developed by SpaceX and Bigelow Aerospace, are in the final stages of development and testing. This ecosystem for microgravity RD has never been available before. These are game-changer conditions for attracting high-tech industries to space for terrestrial, as well as NASA, applications. However, few know that these capabilities are available or how to use them. In aggregate, the potential value for new applications from microgravity RD over the next ten years could add billions of dollars per year in terrestrial applications to the future economy, create new jobs, and generate a wide range of public benefits in medical advances, while broadening the customer base for the emerging space industry.

biotech↗

NASA NTRS2024

Automation of the ICME Workflow Incorporating Material Digital Twins at Different Length Scales Within a Robust Information Management System

Recent successes in Integrated Computational Materials Engineering (ICME) have demonstrated the potential in designing ‘fit-for-purpose’ materials for a given application in a cost and time efficient manner. However, the material design process must contain a level of judicious automation in the material decision process; that is implementing some optimization algorithms to truly enable the benefits of ICME, particularly when considering materials at multiple length and time scales. Furthermore, the ability to effectively store developed material models, experimental data used for validation, and link models at multiple length and time scales must be implemented to ensure traceability across the material design process, such that the data gathered can be leveraged towards efficient material design. To enable such an optimization scheme a robust framework must exist: (1) that can capture changes made at a given length scale, (2) automatically propagate changes upstream to the highest scale, and (3) evaluate the material’s performance at the structural level. In this work, a developed framework for tracking material changes, automatically running the necessary simulations to determine the properties at the next highest scale, and saving each iteration of the design process to maintain the application’s digital thread is presented for polymer matrix composites (PMCs). The Automated Information Management Across Organizations and Scales (AIMAOS) program offers users an interactive graphical user interface (GUI) for defining constituent materials, building lamina and laminates, and applying effective laminate properties to finite element and composite optimization third party software. At each length scale, the necessary input files are automatically written, and subsequent analysis tools are called to solve for effective properties at the next scale, which are then read by the AIMAOS tool and displayed to the user. As changes are made to the material at lower length scales, information is automatically propagated upstream to higher length scales, and changes made are automatically tracked and versioned to maintain traceability during the design process. The AIMAOS tools serves as the first step in enabling optimized design of composites from the nano to the macroscale for a given application.

Brandon L Hearley↗

NASA NTRS1984

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Gray, J. L.↗

NASA NTRS1999

Performance and Application of Parallel OVERFLOW Codes on Distributed and Shared Memory Platforms

The presentation discusses recent studies on the performance of the two parallel versions of the aerodynamics CFD code, OVERFLOW_MPI and _MLP. Developed at NASA Ames, the serial version, OVERFLOW, is a multidimensional Navier-Stokes flow solver based on overset (Chimera) grid technology. The code has recently been parallelized in two ways. One is based on the explicit message-passing interface (MPI) across processors and uses the _MPI communication package. This approach is primarily suited for distributed memory systems and workstation clusters. The second, termed the multi-level parallel (MLP) method, is simple and uses shared memory for all communications. The _MLP code is suitable on distributed-shared memory systems. For both methods, the message passing takes place across the processors or processes at the advancement of each time step. This procedure is, in effect, the Chimera boundary conditions update, which is done in an explicit "Jacobi" style. In contrast, the update in the serial code is done in more of the "Gauss-Sidel" fashion. The programming efforts for the _MPI code is more complicated than for the _MLP code; the former requires modification of the outer and some inner shells of the serial code, whereas the latter focuses only on the outer shell of the code. The _MPI version offers a great deal of flexibility in distributing grid zones across a specified number of processors in order to achieve load balancing. The approach is capable of partitioning zones across multiple processors or sending each zone and/or cluster of several zones into a single processor. The message passing across the processors consists of Chimera boundary and/or an overlap of "halo" boundary points for each partitioned zone. The MLP version is a new coarse-grain parallel concept at the zonal and intra-zonal levels. A grouping strategy is used to distribute zones into several groups forming sub-processes which will run in parallel. The total volume of grid points in each group are approximately balanced. A proper number of threads are initially allocated to each group, and in subsequent iterations during the run-time, the number of threads are adjusted to achieve load balancing across the processes. Each process exploits the multitasking directives already established in Overflow.

Djomehri, M. Jahed↗

NASA NTRS1994

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗

NASA NTRS2016

NASA's Space Launch System: A Transformative Capability for Exploration

Currently making rapid progress toward first launch in 2018, NASA's exploration-class Space Launch System (SLS) represents a game-changing new spaceflight capability, enabling mission profiles that are currently impossible. Designed to launch human deep-space missions farther into space than ever before, the initial configuration of SLS will be able to deliver more than 70 metric tons of payload to low Earth orbit (LEO), and will send NASA's new Orion crew vehicle into lunar orbit. Plans call for the rocket to evolve on its second flight, via a new upper stage, to a more powerful configuration capable of lofting 105 t to LEO or comanifesting additional systems with Orion on launches to the lunar vicinity. Ultimately, SLS will evolve to a configuration capable of delivering more than 130 t to LEO. SLS is a foundational asset for NASA's Journey to Mars, and has been recognized by the International Space Exploration Coordination Group as a key element for cooperative missions beyond LEO. In order to enable human deep-space exploration, SLS provides unrivaled mass, volume, and departure energy for payloads, offering numerous benefits for a variety of other missions. For robotic science probes to the outer solar system, for example, SLS can cut transit times to less than half that of currently available vehicles, producing earlier data return, enhancing iterative exploration, and reducing mission cost and risk. In the field of astrophysics, SLS' high payload volume, in the form of payload fairings with a diameter of up to 10 meters, creates the opportunity for launch of large-aperture telescopes providing an unprecedented look at our universe, and offers the ability to conduct crewed servicing missions to observatories stationed at locations beyond low Earth orbit. At the other end of the spectrum, SLS opens access to deep space for low-cost missions in the form of smallsats. The first launch of SLS will deliver beyond LEO 13 6U smallsat payloads, representing multiple disciplines, including three spacecraft competitively chosen through NASA's Centennial Challenges competition. Private organizations have also identified benefits of SLS for unique public-private partnerships. This paper will give an overview of SLS' capabilities and its current status, and discuss the vehicle's potential for human exploration of deep space and other game-changing utilization opportunities.

Robinson, Kimberly F.↗

NASA NTRS2012

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.

Smith, Jeffrey, S.↗

NASA NTRS2016

NASA's Space Launch System: A Transformative Capability for Exploration

Currently making rapid progress toward first launch in 2018, NASA's exploration-class Space Launch System (SLS) represents a game-changing new spaceflight capability, enabling mission profiles that are currently impossible. Designed to launch human deep-space missions farther into space than ever before, the initial configuration of SLS will be able to deliver more than 70 metric tons of payload to low Earth orbit (LEO), and will send NASA's new Orion crew vehicle into lunar orbit. Plans call for the rocket to evolve on its second flight, via a new upper stage, to a more powerful configuration capable of lofting 105 tons to LEO or co-manifesting additional systems with Orion on launches to the lunar vicinity. Ultimately, SLS will evolve to a configuration capable of delivering more than 130 tons to LEO. SLS is a foundational asset for NASA's Journey to Mars, and has been recognized by the International Space Exploration Coordination Group as a key element for cooperative missions beyond LEO. In order to enable human deep-space exploration, SLS provides unrivaled mass, volume, and departure energy for payloads, offering numerous benefits for a variety of other missions. For robotic science probes to the outer solar system, for example, SLS can cut transit times to less than half that of currently available vehicles, producing earlier data return, enhancing iterative exploration, and reducing mission cost and risk. In the field of astrophysics, SLS' high payload volume, in the form of payload fairings with a diameter of up to 10 meters, creates the opportunity for launch of large-aperture telescopes providing an unprecedented look at our universe, and offers the ability to conduct crewed servicing missions to observatories stationed at locations beyond low Earth orbit. At the other end of the spectrum, SLS opens access to deep space for low-cost missions in the form of smallsats. The first launch of SLS will deliver beyond LEO 13 6-unit smallsat payloads, representing multiple disciplines, including three spacecraft competitively chosen through NASA's Centennial Challenges competition. Private organizations have also identified benefits of SLS for unique public-private partnerships. This paper will give an overview of SLS' capabilities and its current status, and discuss the vehicle's potential for human exploration of deep space and other game-changing utilization opportunities.

Robinson, Kimberly F.↗

NASA NTRS2014

A Systems Engineering Approach to Architecture Development

Architecture development is conducted prior to system concept design when there is a need to determine the best-value mix of systems that works collectively in specific scenarios and time frames to accomplish a set of mission area objectives. While multiple architecture frameworks exist, they often require use of unique taxonomies and data structures. In contrast, this presentation characterizes architecture development using terminology widely understood within the systems engineering community. Using a notional civil space architecture example, it employs a multi-tier framework to describe the enterprise level architecture and illustrates how results of lower tier, mission area architectures integrate into the enterprise architecture. It also presents practices for conducting effective mission area architecture studies, including establishing the trade space, developing functions and metrics, evaluating the ability of potential design solutions to meet the required functions, and expediting study execution through the use of iterative design cycles.

Architecture Development↗

NASA NTRS2015

A Systems Engineering Approach to Architecture Development

Architecture development is often conducted prior to system concept design when there is a need to determine the best-value mix of systems that works collectively in specific scenarios and time frames to accomplish a set of mission area objectives. While multiple architecture frameworks exist, they often require use of unique taxonomies and data structures. In contrast, this paper characterizes architecture development using terminology widely understood within the systems engineering community. Using a notional civil space architecture example, it employs a multi-tier framework to describe the enterprise level architecture and illustrates how results of lower tier, mission area architectures integrate into the enterprise architecture. It also presents practices for conducting effective mission area architecture studies, including establishing the trade space, developing functions and metrics, evaluating the ability of potential design solutions to meet the required functions, and expediting study execution through the use of iterative design cycles.

Multi-tier Framework↗

NASA NTRS2015

A Systems Engineering Approach to Architecture Development

Architecture Development↗

NASA NTRS1983

Shock-capturing parabolized Navier-Stokes model /SCIPVIS/ for the analysis of turbulent underexpanded jets

A new computational model, SCIPVIS, has been developed to predict the multiple-cell wave/shock structure in under or over-expanded turbulent jets. SCIPVIS solves the parabolized Navier-Stokes jet mixing equations utilizing a shock-capturing approach in supersonic regions of the jet and a pressure-split approach in subsonic regions. Turbulence processes are represented by the solution of compressibility corrected two-equation turbulence models. The formation of Mach discs in the jet and the interactive turbulent mixing process occurring behind the disc are handled in a detailed fashion. SCIPVIS presently analyzes jets exhausting into a quiescent or supersonic external stream for which a single-pass spatial marching solution can be obtained. The iterative coupling of SCIPVIS with a potential flow solver for the analysis of subsonic/transonic external streams is under development.

Dash, S. M.↗

NASA NTRS1983

Computation of viscous flows over airfoils, including separation, with a coupling approach

Viscous incompressible flows over single or multiple airfoils, with or without separation, were computed using an inviscid flow calculation, with modified boundary conditions, and by a method providing calculation and coupling for boundary layers and wakes, within conditions of strong viscous interaction. The inviscid flow is calculated with a method of singularities, the numerics of which were improved by using both source and vortex distributions over profiles, associated with regularity conditions for the fictitious flows inside of the airfoils. The viscous calculation estimates the difference between viscous flow and inviscid interacting flow, with a direct or inverse integral method, laminar or turbulent, with or without reverse flow. The numerical method for coupling determines iteratively the boundary conditions for the inviscid flow. For attached viscous layers regions, an underrelaxation is locally calculated to insure stability. For separated or separating regions, a special semi-inverse algorithm is used. Comparisons with experiments are presented.

Leballeur, J. C.↗

NASA NTRS2016

Wavenumber-frequency deconvolution of aeroacoustic microphone phased array data of arbitrary coherence

Deconvolution of aeroacoustic data acquired with microphone phased arrays is a computationally-challenging task for distributed sources with arbitrary coherence. A new technique for performing such deconvolution is proposed. This technique relies on analysis of the array data in the wavenumber-frequency domain, allowing for fast convolution and reduced storage requirements when compared to traditional coherent deconvolution. A positive semidefinite constraint for the iterative deconvolution procedure is implemented and shows improved behavior in terms of quantifiable convergence metrics when compared to a standalone covariance inequality constraint. A series of simulations validates the method's ability to resolve coherence and phase angle relationships between partially-coherent sources, as well as determines convergence criteria for deconvolution analysis. Simulations for point sources near the microphone phased array show potential for handling such data in the wavenumber-frequency domain. In particular, a physics-based integration boundary calculation is described, and can successfully isolate sources and track the appropriate integration bounds with and without the presence of flow. Magnitude and phase relationships between multiple sources are successfully extracted. Limitations of the deconvolution technique are determined from the simulations, particularly in the context of a simulated acoustic field in a closed test section wind tunnel with strong boundary layer contamination. A final application to a trailing edge noise experiment conducted in an open-jet wind tunnel matches best estimates of acoustic levels from traditional calculation methods and qualitatively assesses the coherence characteristics of the trailing edge noise source.

phased array↗