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Unstructured CFD Aerodynamic Analysis of a Generic UCAV Configuration

Three independent studies from the United States (NASA), Sweden (FOI), and Australia (DSTO) are analyzed to assess the state of current unstructured-grid computational fluid dynamic tools and practices for predicting the complex static and dynamic aerodynamic and stability characteristics of a generic 53-degree swept, round-leading-edge uninhabited combat air vehicle configuration, called SACCON. NASA exercised the USM3D tetrahedral cell-centered flow solver, while FOI and DSTO applied the FOI/EDGE general-cell vertex-based solver. The authors primarily employ the Reynolds Averaged Navier-Stokes (RANS) assumption, with a limited assessment of the EDGE Detached Eddy Simulation (DES) extension, to explore sensitivities to grids and turbulence models. Correlations with experimental data are provided for force and moments, surface pressure, and off-body flow measurements. The vortical flow field over SACCON proved extremely difficult to model adequately. As a general rule, the prospect of obtaining reasonable correlations of SACCON pitching moment characteristics with the RANS formulation is not promising, even for static cases. Yet, dynamic pitch oscillation results seem to produce a promising characterization of shapes for the lift and pitching moment hysteresis curves. Future studies of this configuration should include more investigation with higher-fidelity turbulence models, such as DES.

Frink, Neal T.↗

Airborne and Shipborne Polarimetric Measurements over Open Ocean and Coastal Waters: Intercomparisons and Implications for Spaceborne Observations

Comprehensive polarimetric closure is demonstrated using observations from two in-situ polarimeters and Vector Radiative Transfer (VRT) modeling. During the Ship-Aircraft Bio-Optical Research (SABOR) campaign, the novel CCNY HyperSAS-POL polarimeter was mounted on the bow of the R/V Endeavor and acquired hyperspectral measurements from just above the surface of the ocean, while the NASA GISS Research Scanning Polarimeter was deployed onboard the NASA LaRC's King Air UC-12B aircraft. State-of-the-art, ancillary measurements were used to characterize the atmospheric and marine contributions in the VRT model, including those of the High Spectral Resolution Lidar (HSRL), the AErosol RObotic NETwork for Ocean Color (AERONET-OC), a profiling WETLabs ac-9 spectrometer and the Multi-spectral Volume Scattering Meter (MVSM). An open-ocean and a coastal scene are analyzed, both affected by complex aerosol conditions. In each of the two cases, it is found that the model is able to accurately reproduce the Stokes components measured simultaneously by each polarimeter at different geometries and viewing altitudes. These results are mostly encouraging, considering the different deployment strategies of RSP and HyperSAS-POL, which imply very different sensitivities to the atmospheric and ocean contributions, and open new opportunities in above-water polarimetric measurements. Furthermore, the signal originating from each scene was propagated to the top of the atmosphere to explore the sensitivity of polarimetric spaceborne observations to changes in the water type. As expected, adding polarization as a measurement capability benefits the detection of such changes, reinforcing the merits of the full-Stokes treatment in modeling the impact of atmospheric and oceanic constituents on remote sensing observations.

Matteo Ottaviani↗

Assessment of the Mars Helicopter Thermal Design Sensitivities Using the Veritrek Software

The Mars Helicopter will be a technology demonstration conducted during the Mars 2020 mission. The primary mission objective is to achieve several 90-second flights and capture visible light images via forward and nadir mounted cameras. These flights could possibly provide reconnaissance data for sampling site selection for other Mars surface missions. The helicopter is powered by a solar array, which stores energy in secondary batteries for flight operations, imaging, communications, and survival heating. The helicopter thermal design is driven by minimizing survival heater energy while maintaining compliance with allowable flight temperatures in a variable thermal environment. Due to the small size of the helicopter and its complex geometries, along with the fact that it operates with very low power and small margins, additional care had to be paid while planning thermal tests and designing the thermal system. A Thermal Desktop® model has been developed to predict the thermal system’s performance. A reduced-order model (ROM) created with the Veritrek software has been utilized to explore the sensitivities of the thermal system’s drivers, such as electronics dissipations, gas gaps, heat transfer coefficients, etc., as well as to assess and verify the final thermal design. This paper presents the performance of the Veritrek software products and the details of the ROM creation process. The results produced by Veritrek were utilized to study the effect of the major thermal design drivers and Mars environment on the Mars Helicopter in as little as 10 days, an effort that would have taken over 4 months using traditional thermal analysis techniques.

Hengeveld, Derek W.↗

Geophysical aspects of remote sensing

Results obtained through the NASA Earth Resources Aircraft Program at Mill Creek, Oklahoma, provide a case history example of the application of remote sensing to the identification of geologic rock units. Thermal infrared images are interpreted by means of a sequence of models of increasing complexity. The roles of various parameters are examined: rock properties (thermal inertia, albedo, emissivity), site location (latitude), season (sun's declination), atmospheric effects (cloud cover, transmission, air temperature), and topographic orientation (slope, azimuth). The results obtained at this site also illustrate the development of an important application of remote sensing in geologic identification. Relatively pure limestones and dolomites of the Mill Creek test area can be differentiated in nighttime infrared images, and facies changes between them can be detected along and across strike. The predominance on the earth's surface of sedimentary rocks, of which limestone and dolomite are major members, indicates the importance of this discrimination.

Watson, K.↗

Ascent and eruption of basaltic magma on the earth and moon

The ascent and emplacement of basaltic magma on the earth and moon is modeled by the application of geological and physical observations and constraints. Relatively simple mathematical models of the motion of gas/liquid mixtures are shown to be adequate in the treatment of basaltic eruptions, provided that allowance is made for the coalescence of gas bubbles and that realistic geological and petrochemical constraints are applied to the numerical values of variables. Because gas exsolution from magmas on the earth and moon commonly occur at depths of less than 2 km, it is generally convenient to consider separately the rise of bubble-free magmatic liquid at depth in a planetary crust and the more complex motions occurring near the surface with gas exsolution.

Wilson, L.↗

Numerical study of external burning flowfields

This paper demonstrates the successful application of CFD to modeling an external burning flowfield. The study used the 2D, 3D, and PNS versions of the SPARK code. Various grids, boundary conditions, and ignition methodologies have been employed. Flameholding was achieved through the use of a subsonic outflow condition and a hot block located behind the step to ignite the fuel. Since the resulting burning produces a large subsonic region downstream of the cowl, this entire surface can be pressurized to the level of the back pressure. An evaluation of interactions between the ramjet exhaust and the external burning products demonstrate the complexity of this design issue. Ths code is now capable of evaluating the external burning effectiveness for flight vehicles using simple injector schemes, and the methodology can be readily applied to other external burning designs.

Bittner, Robert D.↗

Isolated Nozzle Analysis Using OVERFLOW

LaRC conducted a code validation study for the OVERFLOW code to ascertain its accuracy for boattail drag prediction. The OVERFLOW results compared favorably with the LaRC 16-ft. Transonic Wind Tunnel (TWT) data, and prior CFD solutions from PAB3D and CFL3D. The ultimate goal is to investigate the installation drag of the nacelle boattails with powered nozzles at transonic mach numbers. The OVERFLOW solver was chosen because of its ability to accept volume overlapping structured grid for very complex airframe configurations. Structured grid components for representing the transonic nozzle boattail can be added to the BCAG grid for a TCA airframe with 2D bifurcated inlet and flow through nacelle without alteration. The focus of this research was to determine the suitability of the OVERFLOW solver for accomplishing this ultimate goal. This presentation will first introduce the transonic nozzle boattail wind-tunnel model geometry, followed by an examination of aerodynamic features based on the current OVERFLOW solutions and the solutions obtained previously using PAB3D, comparisons of Cp on the flap surface between the OVERFLOW solutions, wind tunnel data, and solutions from other CFD codes, an assessment of boattail drag count prediction, and a work plan for FY99.

Wong, Tin-Chee↗

An Overview of Regional Experiments on Biomass Burning Aerosols and Related Pollutants in Southeast Asia: From BASE-ASIA and the Dongsha Experiment to 7-SEAS

By modulating the Earth-atmosphere energy, hydrological and biogeochemical cycles, and affecting regional-to-global weather and climate, biomass burning is recognized as one of the major factors affecting the global carbon cycle. However, few comprehensive and wide-ranging experiments have been conducted to characterize biomass-burning pollutants in Southeast Asia (SEA) or assess their regional impact on meteorology, the hydrological cycle, the radiative budget, or climate change. Recently, BASEASIA (Biomass-burning Aerosols in South-East Asia: Smoke Impact Assessment) and the 7-SEAS (7- South-East Asian Studies) Dongsha Experiment were conducted during the spring seasons of 2006 and 2010 in northern SEA, respectively, to characterize the chemical, physical, and radiative properties of biomass-burning emissions near the source regions, and assess their effects. This paper provides an overview of results from these two campaigns and related studies collected in this special issue, entitled Observation, modeling and impact studies of biomass burning and pollution in the SE Asian Environment. This volume includes 28 papers, which provide a synopsis of the experiments, regional weatherclimate, chemical characterization of biomass-burning aerosols and related pollutants in source and sink regions, the spatial distribution of air toxics (atmospheric mercury and dioxins) in source and remote areas, a characterization of aerosol physical, optical, and radiative properties, as well as modeling and impact studies. These studies, taken together, provide the first relatively complete dataset of aerosol chemistry and physical observations conducted in the sourcesink region in the northern SEA, with particular emphasis on the marine boundary layer and lower free troposphere (LFT). The data, analysis and modeling included in these papers advance our present knowledge of source characterization of biomass-burning pollutants near the source regions as well as the physical and chemical processes along transport pathways. In addition, we raise key questions to be addressed by a coming deployment during springtime 2013 in northern SEA, named 7-SEASBASELInE (Biomass-burning Aerosols Stratocumulus Environment: Lifecycles and Interactions Experiment). This campaign will include a synergistic approach for further exploring many key atmospheric processes (e.g., complex aerosol-cloud interactions) and impacts of biomass burning on the surface-atmosphere energy budgets during the lifecycles of biomass burning emissions.

aerosol/biomass burning↗

An Evolving Broad Iron Line from the First Galactic Ultraluminous X-Ray Pulsar Swift J0243.6+6124

We present a spectral study of the ultraluminous Be/X-ray transient pulsar Swift J0243.6+6124 using Neutron Star Interior Composition Explorer (NICER) observations during the system's 2017–2018 giant outburst. The 1.2–10 keV energy spectrum of the source can be approximated with an absorbed cutoff power-law model. We detect strong, luminosity-dependent emission lines in the 6–7 keV energy range. A narrow 6.42 keV line, observed in the sub-Eddington regime, is seen to evolve into a broad Fe-line profile in the super-Eddington regime. Other features are found at 6.67 and 6.97 keV in the Fe-line complex. An asymmetric broad-line profile, peaking at 6.67 keV, is possibly due to Doppler effects and gravitational redshift. The 1.2–79 keV broadband spectrum from Nuclear Spectroscopic Telescope Array (NuSTAR) and NICER observations at the outburst peak is well described by an absorbed cutoff power law plus multiple Gaussian lines and a blackbody component. Physical reflection models are also tested to probe the broad iron-line feature. Depending on the mass accretion rate, we found emission sites that are evolving from ~5000 km to a range closer to the surface of the neutron star. Our findings are discussed in the framework of the accretion disk and its implication on the magnetic field, the presence of optically thick accretion curtain in the magnetosphere, jet emission, and the massive, ultrafast outflow expected at super-Eddington accretion rates. We do not detect any signatures of a cyclotron absorption line in the NICER or NuSTAR data.

Gaurava K. Jaisawal↗

Immersive Technologies for Human-in-the-Loop Lunar Surface Simulations

NASA, the National Aeronautics and Space Administration, continually seeks innovative solutions to enhance its operations, particularly in the realms of testing, evaluation, and training for future missions. Immersive technologies, such as virtual, augmented, and mixed reality have proven to be powerful tools for immersing users in realistic, interactive, and engaging environments. This paper explores how the Simulation and Graphics Branch at NASA’s Johnson Space Center (JSC) leverages immersive technology, modern commercial rendering engines, and physics-based systems simulations to develop human-in-the-loop systems for humanity’s return to the Moon through the Artemis program. When NASA returns to the Moon, astronauts will travel to the Moon’s South Pole where lighting conditions will cause a more complex operational environment. Human-in-the-loop simulations play a crucial role in NASA’s mission planning, spacecraft and space systems development, and evaluation of operational scenarios. The development of immersive environments such as a lunar rover mockup at a video wall enables engineers and astronauts to simulate and experience mission scenarios, integrated spacecraft systems, and operational procedures in a relevant environment before deployment. By integrating realistic virtual environments, immersive technology allows for the visualization and interaction with virtual spacecraft models, mission landscapes, and complex operational tasks. This approach helps identify potential design flaws, operational challenges, and safety considerations. It also provides valuable insights for risk reduction and helps improve mission efficiency and effectiveness. With advanced motion tracking systems and custom virtual environments, data can be gathered and evaluated to help NASA refine training protocols, develop specialized training procedures, and optimize human-robotic interactions for future space missions. Furthermore, immersive technology offers opportunities for future training initiatives at NASA. The Virtual Reality Laboratory at JSC has pioneered training with Virtual Reality (VR) since the Hubble Space Telescope repair missions in the early 1990’s. Extended Reality (XR) simulations enable astronauts to rehearse complex spacewalks, spacecraft maneuvers, and extravehicular activities in a safe and controlled environment. By replicating the physical and cognitive challenges of space missions, immersive training experiences enhance astronauts’ situational awareness, decision-making abilities, and adaptability to unexpected scenarios. Additionally, immersive technology facilitates collaborative training, allowing geographically dispersed crew and mission control personnel to engage in synchronized simulations, fostering teamwork and effective communication. The adoption of immersive technology in NASA’s testing, evaluation, and future training programs has yielded significant benefits. By incorporating human-in-the-loop simulations for studies involving Extra Vehicular Activities (EVA), surface mobility and landing systems, NASA can identify and mitigate risks, optimize operational procedures, and enhance mission success. Ultimately, immersive simulation experiences can empower astronauts to better navigate the complexities of space missions, ensuring their safety, productivity, and success in the dynamic and challenging environments they will experience at the Lunar South Pole.

HITL↗

The Global Water Monitor: Lake, Wetland, and River Reach Monitoring for Resource Management and Hazard Observation

The Global Water Monitor is a monitoring program offering surface water-related products for lakes, reservoirs, river reaches, and wetlands, https://blueice.gsfc.nasa.gov/gwm. These products are derived from multiple satellite-based altimetry and multispectral imaging platforms. The primary measurements are water level, slope, and extent, derived from a series of NASA and other agency instruments (Sentinel-3,-6, ICESat-2, SWOT, MODIS). The system serves stakeholders, the US Department of Agriculture Foreign Agricultural Service and the US Geological Survey, as well as various international, national, state, and intelligence agencies, engineers, ecologists, and hydrological researchers. Considering the sensitivity of ground-based data and the remote accessibility of many basins, the satellites offer global coverage, accuracy, and continuity of measurements. Observation of storage fluctuations in lakes and reservoirs provides users with knowledge of short and long-term drought conditions that can affect both water and energy resources. Emphasis is on changing climatic conditions, water sharing between nations, and regional stability. Measurements across a wetland complex can assist with efforts to assess hydrological dynamics with a focus on conservation efforts that aid both natural ecology and the sharing of precious water resources – the latter potentially being required in a basin across the municipal, crop irrigation, aquaculture, livestock, and power station spectrum. Observations of river reaches assists in the collection of basic hydraulic information, particularly in gauge-poor regions, for modelling efforts and the estimation of discharge, and at high-latitudes satellite-based river observations serve projects that warn of spring melts and flood hazards. We look at how recent improvements in instrument technology and mission operations are assisting with acquiring true global coverage and cross-validation efforts, and how stakeholders interact with the project in terms of setting requirements, product format, and accessibility methods. Examples show the application of the products across a range of programs, and in addition to meeting operational requirements, how the multi-decadal surface water levels are creating a high-quality timeline of Earth Data Records.

Lakes↗

Science Archives in the 21st Century: A NASA LAMBDA Report

Lambda is a thematic data center that focuses on serving the cosmic microwave background (CMB) research community. LAMBDA is an active archive for NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) mission data sets. In addition, LAMBDA provides analysis software, on-line tools, relevant ancillary data and important web links. LAMBDA also tries to preserve the most important ground-based and suborbital CMB data sets. CMB data is unlike other astrophysical data, consisting of intrinsically diffuse surface brightness photometry with a signal contrast of the order 1 part in 100,000 relative to the uniform background. Because of the extremely faint signal levels, the signal-to-noise ratio is relatively low and detailed instrument-specific knowledge of the data is essential. While the number of data sets being produced is not especially large, those data sets are becoming large and complex. That tendency will increase when the many polarization experiments currently being deployed begin producing data. The LAMBDA experience supports many aspects of the NASA data archive model developed informally over the last ten years-that small focused data centers are often more effective than larger more ambitious collections, for example; that data centers are usually best run by active scientists; that it can be particularly advantageous if those scientists are leaders in the use of the archived data sets; etc. LAMBDA has done some things so well that they might provide lessons for other archives. A lot of effort has been devoted to developing a simple and consistent interface to data sets, for example; and serving all the documentation required via simple 'more' pages and longer explanatory supplements. Many of the problems faced by LAMBDA will also not surprise anyone trying to manage other space science data. These range from persuading mission scientists to provide their data as quickly as possible, to dealing with a high volume of nuisance (spam) messages. Because so many data center problems and solutions are common across individual data centers and disciplines it would be very valuable to establish some new systems of communication - such as informal email lists for administrators and developers. But resources are very limited, so new timeconsuming and inefficient mechanisms - like too-frequent and too-structured meetingsshould be avoided. Although there are great advantages to being small, agile and independent, there are also some areas where science data centers within and without NASA could be better coordinated - for the assignment of persistent identifiers; to encourage the early adoption of useful standards and technologies; etc. Some super-structure to facilitate such coordination might be beneficial as long as it doesn't begin to control the other work of the archives, and become a "methodology police". In this respect the CCSDS "Reference Model for an Open Archive Information System" is a little worrying. It may be that the closer a data center gets to following such a detailed prescription, the less effective it will become. It is much better to have an informal coordination process than a bureaucratic straight-jacket.

Butterworth, P.↗

Vesta Evolution from Surface Mineralogy: Mafic and Ultramafic Mineral Distribution

Vesta is the only intact, differentiated, rocky protoplanet and it is the parent body of HED meterorites. Howardite, eucrite and diogenite (HED) meteorites represent regolith, basaltic-crust, lower-crust and possibly ultramafic-mantle samples of asteroid Vesta. Only a few of these meteorites, the orthopyroxene-rich diogenites, contain olivine, a mineral that is a major component of the mantles of differentiated bodies, including Vesta. The HED parent body experienced complex igneous processes that are not yet fully understood and olivine and diogenite distribution is a key measurement to understand Vesta evolution. Here we report on the distribution of olivine and its constraints on vestan evolution models.

DeSanctis, M. C.↗

Space Weather Products and Tools Used in Auroral Monitoring and Forecasting at CCMC/SWRC

Key points discussed in this chapter are (1) the importance of aurora research to scientific advances and space weather applications, (2) space weather products at CCMC that are relevant to aurora monitoring and forecasting, and (3) the need for more effort from the whole community to achieve a better and long‐lead‐time forecast of auroral activity. Aurora, as manifestations of solar wind−magnetosphere−ionosphere coupling that occurs in a region of space that is relatively easy to access for sounding rockets, satellites, and other types of observational platforms, serves as a natural laboratory for studying the underlying physics of the complex system. From a space weather application perspective, auroras can cause surface charging of technological assets passing through the region, result in scintillation effects affecting communication and navigation, and cause radar cluttering that hinders military and civilian applications. Indirectly, an aurora and its currents can induce geomagnetically induced currents (GIC) on the ground, which poses major concerns for the wellbeing and operation of power grids, particularly during periods of intense geomagnetic activity. In addition, accurate auroral forecasting is desired for auroral tourism. In this chapter, we first review some of the existing auroral models and discuss past validation efforts. Such efforts are crucial in transitioning a model(s) from research to operations and for further model improvement and development that also benefits scientific endeavors. Then we will focus on products and tools that are used for auroral monitoring and forecasting at the Space Weather Research Center (SWRC). As part of the CCMC (Community Coordinated Modeling Center), SWRC has been providing space weather services since 2010.

Zheng, Yihua↗

Space Weather Products and Tools Used in Auroral Monitoring and Forecasting at CCMC/SWRC

Key points discussed in this chapter are (1) the importance of aurora research to scientific advances and space weather applications, (2) space weather products at CCMC that are relevant to aurora monitoring and forecasting, and (3) the need for more effort from the whole community to achieve a better and long-lead- time forecast of auroral activity. Aurora, as manifestations of solar wind-magnetosphere-ionosphere coupling that occurs in a region of space that is relatively easy to access for sounding rockets, satellites, and other types of observational platforms, serves as a natural laboratory for studying the underlying physics of the complex system. From a space weather application perspective, auroras can cause surface charging of technological assets passing through the region, result in scintillation effects affecting communication and navigation, and cause radar cluttering that hinders military and civilian applications. Indirectly, an aurora and its currents can induce geomagnetically induced currents (GIC) on the ground, which poses major concerns for the wellbeing and operation of power grids, particularly during periods of intense geomagnetic activity. In addition, accurate auroral forecasting is desired for auroral tourism. In this chapter, we first review some of the existing auroral models and discuss past validation efforts. Such efforts are crucial in transitioning a model(s) from research to operations and for further model improvement and development that also benefits scientific endeavors. Then we will focus on products and tools that are used for auroral monitoring and forecasting at the Space Weather Research Center (SWRC). As part of the CCMC (Community Coordinated Modeling Center), SWRC has been providing space weather services since 2010.

Zheng, Yihua↗

The measurement of boundary layers on a compressor blade in cascade. Volume 1: Experimental technique, analysis and results

Measurements were made of the boundary layers and wakes about a highly loaded, double-circular-arc compressor blade in cascade. These laser Doppler velocimetry measurements have yielded a very detailed and precise data base with which to test the application of viscous computational codes to turbomachinery. In order to test the computational codes at off-design conditions, the data were acquired at a chord Reynolds number of 500,000 and at three incidence angles. Moreover, these measurements have supplied some physical insight into these very complex flows. Although some natural transition is evident, laminar boundary layers usually detach and subsequently reattach as either fully or intermittently turbulent boundary layers. These transitional separation bubbles play an important role in the development of most of the boundary layers and wakes measured in this cascade and the modeling or computing of these bubbles should prove to be the key aspect in computing the entire cascade flow field. In addition, the nonequilibrium turbulent boundary layers on these highly loaded blades always have some region of separation near the trailing edge of the suction surface. These separated flows, as well as the subsequent near wakes, show no similarity and should prove to be a challenging test for the viscous computational codes.

Zierke, William C.↗

Radar transponder antenna pattern analysis for the space shuttle

In order to improve tracking capability, radar transponder antennas will soon be mounted on the Shuttle solid rocket boosters (SRB). These four antennas, each being identical cavity-backed helices operating at 5.765 GHz, will be mounted near the top of the SRB's, adjacent to the intertank portion of the external tank. The purpose is to calculate the roll-plane pattern (the plane perpendicular to the SRB axes and containing the antennas) in the presence of this complex electromagnetic environment. The large electrical size of this problem mandates an optical (asymptotic) approach. Development of a specific code for this application is beyond the scope of a summer fellowship; thus a general purpose code, the Numerical Electromagnetics Code - Basic Scattering Code, was chosen as the computational tool. This code is based on the modern Geometrical Theory of Diffraction, and allows computation of scattering of bodies composed of canonical problems such as plates and elliptic cylinders. Apertures mounted on a curved surface (the SRB) cannot be accomplished by the code, so an antenna model consisting of wires excited by a method of moments current input was devised that approximated the actual performance of the antennas. The improvised antenna model matched well with measurements taken at the MSFC range. The SRB's, the external tank, and the shuttle nose were modeled as circular cylinders, and the code was able to produce what is thought to be a reasonable roll-plane pattern.

Radcliff, Roger↗

Active control of wake/blade-row interaction noise through the use of blade surface actuators

A combined analytical/computational approach for controlling of the noise generated by wake/blade-row interaction through the use of anti-sound actuators on the blade surfaces is described. A representative two-dimensional section of a fan stage, composed of an upstream fan rotor and a downstream fan exit guide vane (FEGV), is examined. An existing model for the wakes generated by the rotor is analyzed to provide realistic magnitudes for the vortical excitations imposed at the inlet to the FEGV. The acoustic response of the FEGV is determined at multiples of the blade passing frequency (BPF) by using the linearized unsteady flow analysis, LINFLO. Acoustic field contours are presented at each multiple of BPF illustrating the generated acoustic response disturbances. Anti-sound is then provided by placing oscillating control surfaces, whose lengths and locations are specified arbitrarily, on the blades. An analysis is then conducted to determine the complex amplitudes required for the control surface motions to best reduce the noise. It is demonstrated that if the number of acoustic response modes to be controlled is equal to the number of available independent control surfaces, complete noise cancellation can be achieved. A weighted least squares minimization procedure for the control equations is given for cases in which the number of acoustic modes exceeds the number of available control surfaces. The effectiveness of the control is measured by the magnitude of a propagating acoustic response vector, which is related to the circumferentially averaged sound pressure level (SPL), and is minimized by a standard least-squares minimization procedure.

Kousen, Kenneth A.↗