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At least 1,549 records · Page 86

Lessons Learned from Numerical Simulations of the F-16XL Aircraft at Flight Conditions

Nine groups participating in the Cranked Arrow Wing Aerodynamics Project International (CAWAPI) project have contributed steady and unsteady viscous simulations of a full-scale, semi-span model of the F-16XL aircraft. Three different categories of flight Reynolds/Mach number combinations were computed and compared with flight-test measurements for the purpose of code validation and improved understanding of the flight physics. Steady-state simulations are done with several turbulence models of different complexity with no topology information required and which overcome Boussinesq-assumption problems in vortical flows. Detached-eddy simulation (DES) and its successor delayed detached-eddy simulation (DDES) have been used to compute the time accurate flow development. Common structured and unstructured grids as well as individually-adapted unstructured grids were used. Although discrepancies are observed in the comparisons, overall reasonable agreement is demonstrated for surface pressure distribution, local skin friction and boundary velocity profiles at subsonic speeds. The physical modeling, steady or unsteady, and the grid resolution both contribute to the discrepancies observed in the comparisons with flight data, but at this time it cannot be determined how much each part contributes to the whole. Overall it can be said that the technology readiness of CFD-simulation technology for the study of vehicle performance has matured since 2001 such that it can be used today with a reasonable level of confidence for complex configurations.

Rizzi, Arthur↗

Multijunction Solar Cell Development and Production at Spectrolab

Development of multijunction space solar cells is much like that for any high technology product. New products face two major pressures from the market: improving performance while maintaining heritage. This duality of purpose is not new and has been represented since ancient times by the Roman god Janus.[1] This deity was typically represented as two faces on a single head: one facing forward and the other to the rear. The image of Janus has been used as symbolism for many combined forces of dual purpose, such as the balance in life between beginnings and endings, or between art and science. For our purposes, Janus represents our design philosophy balance between looking to the future for improvement while simultaneously blending past heritage. In the space photovoltaics industry there are good reasons for both purposes. Looking to the past, a product must have a space flight heritage to gain widespread use. The main reason being that this is an unforgiving business. Spacecraft are expensive to build, launch and operate. Typically once a satellite is launched, in-field service for a power systems problem is near impossible.[2Balanced with this is looking forward. New missions typically require more power than previous programs or attempt new objectives such as a new orbit. And there is always the cost pressure for both the satellite itself as well as the launch costs. Both of which push solar technology to improve power density at a lower cost. The consequence of this balance in a high-risk environment is that space PV develops as a series of infrequent large technology steps or generational changes interspersed with more frequent small technology steps or evolutionary changes. Figure 1 gives a bit of clarification on this point. It depicts the historical progress in space solar cells tracked by efficiency against first launch date for most major products introduced by Spectrolab. The first generation is the Si-based technology reaching a peak values near 15% AM0 (herein denoted for max. power, AM0, 1.353 W/cm2, 28 C). The GaAs single junction device generation supplanted this technology with first flight of GaAs on GaAs substrate in 1982.[3] More recently this generation has been supplanted by the multijunction solar cell GaInP/GaAs/Ge generation. The first launch of a commercial satellite powered by multijunction technology was in 1997 (Hughes HS 601HP) using solar arrays based on Spectrolab s dual junction (DJ) cells. The cells at that time were an impressive 21.5% efficient at beginning-of-life (BOL).[4] Eight years later, the multijunction device has evolved through several versions. The incorporation of an active Ge subcell formed the Triple Junction (TJ) product line at 25.1% efficient, on orbit since November 2001. The evolution of the TJ into the Improved Triple Junction (ITJ) at 26.8% efficient has been on orbit since June of 2002.[5]

Fetzer, Chris↗

Graphical User Interface for Simulink Integrated Performance Analysis Model

The J-2X Engine (built by Pratt & Whitney Rocketdyne,) in the Upper Stage of the Ares I Crew Launch Vehicle, will only start within a certain range of temperature and pressure for Liquid Hydrogen and Liquid Oxygen propellants. The purpose of the Simulink Integrated Performance Analysis Model is to verify that in all reasonable conditions the temperature and pressure of the propellants are within the required J-2X engine start boxes. In order to run the simulation, test variables must be entered at all reasonable values of parameters such as heat leak and mass flow rate. To make this testing process as efficient as possible in order to save the maximum amount of time and money, and to show that the J-2X engine will start when it is required to do so, a graphical user interface (GUI) was created to allow the input of values to be used as parameters in the Simulink Model, without opening or altering the contents of the model. The GUI must allow for test data to come from Microsoft Excel files, allow those values to be edited before testing, place those values into the Simulink Model, and get the output from the Simulink Model. The GUI was built using MATLAB, and will run the Simulink simulation when the Simulate option is activated. After running the simulation, the GUI will construct a new Microsoft Excel file, as well as a MATLAB matrix file, using the output values for each test of the simulation so that they may graphed and compared to other values.

Durham, R. Caitlyn↗

Fission Surface Power Technology Development Testing at NASA's Early Flight Fission Test Facility

Fission surface power (FSP) systems could be used to provide power anytime, anywhere on the surface of the Moon or Mars. FSP systems could be used at polar locations, at locations away from the poles, or in permanently shaded regions, with excellent performance at all sites. A potential reference 40 kWe option has been devised that is cost-competitive with alternatives while providing more power for less mass anywhere on the lunar surface. The reference FSP system (FSPS) is also readily extensible for use on Mars. At Mars the system would be capable of operating through global dust storms and providing year-round power at any Martian latitude. Under the NASA Exploration Technology Development Program (ETDP), NASA and the Department of Energy (DOE) have begun technology development on Fission Surface Power (FSP). The primary customer for this technology is the NASA Constellation Program which is responsible for the development of surface systems to support human exploration on the moon and Mars. The objectives of the FSP technology project are: 1) Develop FSP concepts that meet expected surface power requirements at reasonable cost with added benefits over other options. 2) Establish a hardware-based technical foundation for FSP design concepts and reduce overall development risk. 3) Reduce the cost uncertainties for FSP and establish greater credibility for flight system cost estimates. 4) Generate the key products to allow Agency decision-makers to consider FSP as a viable option for flight development. To be mass efficient, FSP systems must operate at higher coolant temperatures and use different types of power conversion than typical terrestrial systems. The primary reason is the difficulty in rejecting excess heat to space. Although many options exist, NASA s current reference FSP system uses a fast spectrum, pumped-NaK cooled reactor coupled to a Stirling power conversion subsystem. The reference system uses technology with significant terrestrial heritage while still providing excellent performance on the surface of the moon or Mars. Recent testing at NASA s Early Flight Fission Test Facility (EFF-TF) has helped assess the viability of the reference FSP system, and has helped evaluate methods for system integration. In June, 2009, a representative pumped NaK loop (provided by Marshall Space Flight Center) was coupled to a Stirling power converter (provided by Glenn Research Center) and tested at various conditions representative of those that would be seen during actual FSP system operation. In all areas, performance of the integrated system exceeded project goals. High-temperature NaK pump testing has also been performed at the EFF-TF, as has testing of methods for providing long-duration NaK purity.

Houts. Michael G.↗

Deliberate Satellite Fragmentations and their Effects on the Long-Term Space Environment

Since 1964 at least 56 spacecraft and two launch vehicle upper stages have been deliberately fragmented while in Earth orbit. Many of these events have had no long-lasting effects on the near-Earth space environment, but one represents the most devastating satellite breakup in history that will pose hazards to operational spacecraft in low Earth orbit for decades to come. International space debris mitigation guidelines now call for avoiding the creation of long-lived debris from intentional satellite fragmentations. This paper summarizes the reasons for and environmental consequences of deliberate satellite fragmentations. Contrary to popular belief, only one in five deliberate fragmentations have been related to the testing of anti-satellite weapon systems, for which only one such test has occurred during the past 25 years. Other reasons for deliberate satellite fragmentations range from engineering tests to protecting national security information. Whereas the majority of deliberate satellite fragmentations have occurred in low Earth orbits, some have involved spacecraft in highly elliptical orbits. The former Soviet Union and the current Russian Federation have been responsible for 90% of all identified deliberate on-orbit satellite fragmentations.

Johnson, N. L.↗

Hybrid Automated Diagnosis of Discrete/Continuous Systems

A recently conceived method of automated diagnosis of a complex electromechanical system affords a complete set of capabilities for hybrid diagnosis in the case in which the state of the electromechanical system is characterized by both continuous and discrete values (as represented by analog and digital signals, respectively). The method is an integration of two complementary diagnostic systems: (1) beacon-based exception analysis for multi-missions (BEAM), which is primarily useful in the continuous domain and easily performs diagnoses in the presence of transients; and (2) Livingstone, which is primarily useful in the discrete domain and is typically restricted to quasi-steady conditions. BEAM has been described in several prior NASA Tech Briefs articles: "Software for Autonomous Diagnosis of Complex Systems" (NPO-20803), Vol. 26, No. 3 (March 2002), page 33; "Beacon-Based Exception Analysis for Multimissions" (NPO-20827), Vol. 26, No. 9 (September 2002), page 32; "Wavelet-Based Real-Time Diagnosis of Complex Systems" (NPO-20830), Vol. 27, No. 1 (January 2003), page 67; and "Integrated Formulation of Beacon-Based Exception Analysis for Multimissions" (NPO-21126), Vol. 27, No. 3 (March 2003), page 74. Briefly, BEAM is a complete data-analysis method, implemented in software, for real-time or off-line detection and characterization of faults. The basic premise of BEAM is to characterize a system from all available observations and train the characterization with respect to normal phases of operation. The observations are primarily continuous in nature. BEAM isolates anomalies by analyzing the deviations from nominal for each phase of operation. Livingstone is a model-based reasoner that uses a model of a system, controller commands, and sensor observations to track the system s state, and detect and diagnose faults. Livingstone models a system within the discrete domain. Therefore, continuous sensor readings, as well as time, must be discretized. To reason about continuous systems, Livingstone uses monitors that discretize the sensor readings using trending and thresholding techniques. In development of the a hybrid method, BEAM results were sent to Livingstone to serve as an independent source of evidence that is in addition to the evidence gathered by Livingstone standard monitors. The figure depicts the flow of data in an early version of a hybrid system dedicated to diagnosing a simulated electromechanical system. In effect, BEAM served as a "smart" monitor for Livingstone. BEAM read the simulation data, processed the data to form observations, and stored the observations in a file. A monitor stub synchronized the events recorded by BEAM with the output of the Livingstone standard monitors according to time tags. This information was fed to a real-time interface, which buffered and fed the information to Livingstone, and requested diagnoses at the appropriate times. In a test, the hybrid system was found to correctly identify a failed component in an electromechanical system for which neither BEAM nor Livingstone alone yielded the correct diagnosis.

Park, Han↗

What was Learned from Numerical Simulations of F-16XL (CAWAPI) at Flight Conditions

Nine groups participating in the CAWAPI project have contributed steady and unsteady viscous simulations of a full-scale, semi-span model of the F-16XL aircraft. Three different categories of flight Reynolds/Mach number combinations were computed and compared with flight-test measurements for the purpose of code validation and improved understanding of the flight physics. Steady-state simulations are done with several turbulence models of different complexity with no topology information required and which overcome Boussinesq-assumption problems in vortical flows. Detached-eddy simulation (DES) and its successor delayed detached-eddy simulation (DDES) have been used to compute the time accurate flow development. Common structured and unstructured grids as well as individually-adapted unstructured grids were used. Although discrepancies are observed in the comparisons, overall reasonable agreement is demonstrated for surface pressure distribution, local skin friction and boundary velocity profiles at subsonic speeds. The physical modeling, be it steady or unsteady flow, and the grid resolution both contribute to the discrepancies observed in the comparisons with flight data, but at this time it cannot be determined how much each part contributes to the whole. Overall it can be said that the technology readiness of CFD-simulation technology for the study of vehicle performance has matured since 2001 such that it can be used today with a reasonable level of confidence for complex configurations.

Rizzi, Arthur↗

Focusing Light Beams To Improve Atomic-Vapor Optical Buffers

Specially designed focusing of light beams has been proposed as a means of improving the performances of optical buffers based on cells containing hot atomic vapors (e.g., rubidium vapor). There is also a companion proposal to improve performance by use of incoherent optical pumping under suitable conditions. Regarding the proposal to use focusing: The utility of atomic-vapor optical buffers as optical storage and processing devices has been severely limited by nonuniform spatial distributions of intensity in optical beams, arising from absorption of the beams as they propagate in atomic-vapor cells. Such nonuniformity makes it impossible to optimize the physical conditions throughout a cell, thereby making it impossible to optimize the performance of the cell as an optical buffer. In practical terms simplified for the sake of brevity, "to optimize" as used here means to design the cell so as to maximize the group delay of an optical pulse while keeping the absorption and distortion of the pulse reasonably small. Regarding the proposal to use incoherent optical pumping: For reasons too complex to describe here, residual absorption of light is one of the main impediments to achievement of desirably long group delays in hot atomic vapors. The present proposal is directed toward suppressing residual absorption of light. The idea of improving the performance of slow-light optical buffers by use of incoherent pumping overlaps somewhat with the basic idea of Raman-based slow-light systems. However, prior studies of those systems did not quantitatively answer the question of whether the performance of an atomic vapor or other medium that exhibits electromagnetically induced transparency (EIT) with Raman gain is superior to that of a medium that exhibits EIT without Raman gain.

Strekalov, Dmitry↗

Buckling Imperfection Sensitivity of Axially Compressed Orthotropic Cylinders

Structural stability is a major consideration in the design of lightweight shell structures. However, the theoretical predictions of geometrically perfect structures often considerably over predict the buckling loads of inherently imperfect real structures. It is reasonably well understood how the shell geometry affects the imperfection sensitivity of axially compressed cylindrical shells; however, the effects of shell anisotropy on the imperfection sensitivity is less well understood. In the present paper, the development of an analytical model for assessing the imperfection sensitivity of axially compressed orthotropic cylinders is discussed. Results from the analytical model for four shell designs are compared with those from a general-purpose finite-element code, and good qualitative agreement is found. Reasons for discrepancies are discussed, and potential design implications of this line of research are discussed.

Schultz, Marc R.↗

Aeroelasticity Benchmark Assessment: Subsonic Fixed Wing Program

The fundamental technical challenge in computational aeroelasticity is the accurate prediction of unsteady aerodynamic phenomena and the effect on the aeroelastic response of a vehicle. Currently, a benchmarking standard for use in validating the accuracy of computational aeroelasticity codes does not exist. Many aeroelastic data sets have been obtained in wind-tunnel and flight testing throughout the world; however, none have been globally presented or accepted as an ideal data set. There are numerous reasons for this. One reason is that often, such aeroelastic data sets focus on the aeroelastic phenomena alone (flutter, for example) and do not contain associated information such as unsteady pressures and time-correlated structural dynamic deflections. Other available data sets focus solely on the unsteady pressures and do not address the aeroelastic phenomena. Other discrepancies can include omission of relevant data, such as flutter frequency and / or the acquisition of only qualitative deflection data. In addition to these content deficiencies, all of the available data sets present both experimental and computational technical challenges. Experimental issues include facility influences, nonlinearities beyond those being modeled, and data processing. From the computational perspective, technical challenges include modeling geometric complexities, coupling between the flow and the structure, grid issues, and boundary conditions. The Aeroelasticity Benchmark Assessment task seeks to examine the existing potential experimental data sets and ultimately choose the one that is viewed as the most suitable for computational benchmarking. An initial computational evaluation of that configuration will then be performed using the Langley-developed computational fluid dynamics (CFD) software FUN3D1 as part of its code validation process. In addition to the benchmarking activity, this task also includes an examination of future research directions. Researchers within the Aeroelasticity Branch will examine other experimental efforts within the Subsonic Fixed Wing (SFW) program (such as testing of the NASA Common Research Model (CRM)) and other NASA programs and assess aeroelasticity issues and research topics.

Florance, Jennifer P.↗

Aviation Fueling: A Cleaner, Greener Approach

Projected growth of aviation depends on fueling where specific needs must be met. Safety is paramount, and along with political, social, environmental and legacy transport systems requirements, alternate aviation fueling becomes an opportunity of enormous proportions. Biofuels sourced from halophytes, algae, cyanobacteria, and weeds using wastelands, waste water, and seawater have the capacity to be drop-in fuel replacements for petroleum fuels. Biojet fuels from such sources solves the aviation CO2 emissions issue and do not compete with food or freshwater needs. They are not detrimental to the social or environmental fabric and use the existing fuels infrastructure. Cost and sustainable supply remains the major impediments to alternate fuels. Halophytes are the near-term solution to biomass/biofuels capacity at reasonable costs; they simply involve more farming, at usual farming costs. Biofuels represent a win-win approach, proffering as they do at least the ones we are studying massive capacity, climate neutral-to-some sequestration, and ultimately, reasonable costs.

Hendricks, Robert C.↗

A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover

Bluespec SystemVerilog (BSV) is a Hardware Description Language based on the guarded action model of concurrency. It has an elegant semantics, which makes it well suited for formal reasoning. To date, a number of BSV designs have been verified with hand proofs, but little work has been conducted on the application of automated reasoning. We present a prototype shallow embedding of BSV in the PVS theorem prover. Our embedding is compatible with the PVS model checker, which can automatically prove an important class of theorems, and can also be used in conjunction with the powerful proof strategies of PVS to verify a broader class of properties than can be achieved with model checking alone.

Richards, Dominic↗

Low Speed and High Speed Correlation of SMART Active Flap Rotor Loads

Measured, open loop and closed loop data from the SMART rotor test in the NASA Ames 40- by 80- Foot Wind Tunnel are compared with CAMRAD II calculations. One open loop high-speed case and four closed loop cases are considered. The closed loop cases include three high-speed cases and one low-speed case. Two of these high-speed cases include a 2 deg flap deflection at 5P case and a test maximum-airspeed case. This study follows a recent, open loop correlation effort that used a simple correction factor for the airfoil pitching moment Mach number. Compared to the earlier effort, the current open loop study considers more fundamental corrections based on advancing blade aerodynamic conditions. The airfoil tables themselves have been studied. Selected modifications to the HH-06 section flap airfoil pitching moment table are implemented. For the closed loop condition, the effect of the flap actuator is modeled by increased flap hinge stiffness. Overall, the open loop correlation is reasonable, thus confirming the basic correctness of the current semi-empirical modifications; the closed loop correlation is also reasonable considering that the current flap model is a first generation model. Detailed correlation results are given in the paper.

Kottapalli, Sesi B. R.↗

Development of a User Interface for a Regression Analysis Software Tool

An easy-to -use user interface was implemented in a highly automated regression analysis tool. The user interface was developed from the start to run on computers that use the Windows, Macintosh, Linux, or UNIX operating system. Many user interface features were specifically designed such that a novice or inexperienced user can apply the regression analysis tool with confidence. Therefore, the user interface s design minimizes interactive input from the user. In addition, reasonable default combinations are assigned to those analysis settings that influence the outcome of the regression analysis. These default combinations will lead to a successful regression analysis result for most experimental data sets. The user interface comes in two versions. The text user interface version is used for the ongoing development of the regression analysis tool. The official release of the regression analysis tool, on the other hand, has a graphical user interface that is more efficient to use. This graphical user interface displays all input file names, output file names, and analysis settings for a specific software application mode on a single screen which makes it easier to generate reliable analysis results and to perform input parameter studies. An object-oriented approach was used for the development of the graphical user interface. This choice keeps future software maintenance costs to a reasonable limit. Examples of both the text user interface and graphical user interface are discussed in order to illustrate the user interface s overall design approach.

Ulbrich, Norbert Manfred↗

Proposal for a Joint NASA/KSAT Ka-band RF Propagation Terminal at Svalbard, Norway

This slide presentation discusses the placement of a Ka-band RF Propagation Terminal at Svalbard, Norway. The Near Earth Network (NEN) station would be managed by Kongsberg Satellite Services (KSAT) and would benefit NASA and KSAT. There are details of the proposed NASA/KSAT campaign, and the responsibilities each would agree to. There are several reasons for the placement, a primary reason is comparison with the Alaska site, Based on climatological similarities/differences with Alaska, Svalbard site expected to have good radiometer/beacon agreement approximately 99% of time.

Volosin, Jeffrey↗

Template Matching Approach to Signal Prediction

A new approach to signal prediction and prognostic assessment of spacecraft health resolves an inherent difficulty in fusing sensor data with simulated data. This technique builds upon previous work that demonstrated the importance of physics-based transient models to accurate prediction of signal dynamics and system performance. While models can greatly improve predictive accuracy, they are difficult to apply in general because of variations in model type, accuracy, or intended purpose. However, virtually any flight project will have at least some modeling capability at its disposal, whether a full-blown simulation, partial physics models, dynamic look-up tables, a brassboard analogue system, or simple hand-driven calculation by a team of experts. Many models can be used to develop a predict, or an estimate of the next day s or next cycle s behavior, which is typically used for planning purposes. The fidelity of a predict varies from one project to another, depending on the complexity of the simulation (i.e. linearized or full differential equations) and the level of detail in anticipated system operation, but typically any predict cannot be adapted to changing conditions or adjusted spacecraft command execution. Applying a predict blindly, without adapting the predict to current conditions, produces mixed results at best, primarily due to mismatches between assumed execution of spacecraft activities and actual times of execution. This results in the predict becoming useless during periods of complicated behavior, exactly when the predict would be most valuable. Each spacecraft operation tends to show up as a transient in the data, and if the transients are misaligned, using the predict can actually harm forecasting performance. To address this problem, the approach here expresses the predict in terms of a baseline function superposed with one or more transient functions. These transients serve as signal templates, which can be relocated in time and space against the signal background. One then has the ability to reconstruct a signal regardless of the precise timing of the transients. During operation, one applies the actual start times of spacecraft activities as they occur, and produces a reconstructed, accurate predict in real-time. This general approach is valid under two important conditions. First, the transients themselves must be time-invariant. Second, the transients must be reasonably consistent with respect to different operating points. Both of these assumptions are generally valid, but in the case of a complicated system with numerous types of overlapping transients, this approach may not be effective. Fortunately, there tend to be few transients in spacecraft telemetry of sensor quantities or low-level health and status information because these signals rarely reflect multiple different types of operation. Furthermore, if the predict is at least reasonably close to actual operation, the shift either in time, or in the operating point when the transient occurs - is likely to be small. The proposed approach considers three ways to recognize a transient. The first and most reliable is to use a different signal that identifies operating mode - often the transient will be correlated to a change in operating mode, and this change can usually be detected positively from discrete signals in spacecraft telemetry. If there is no useful mode signal, the second option is to identify the transient template by hand, and detect the onset of the transient using a curve-fitting approach. Finally, if one elects not to choose by hand, there is an option for automatic selection. This technique has been applied to sensor data from several JPL missions and industrial applications, demonstrating an improvement in accurate prediction of future behavior and early detection of system problems. This technique is applicable to practically any time-varying, quantitative sensor measurement.

Mackey, Ryan↗

The Roles of Beneficiation in Lunar Work

Natural feedstocks used for any process are intrinsically variable. They may also contain deleterious components or low concentrations of desired fractions. For these three reasons it is standard industrial practice to beneficiate feedstocks. This is true across all industries which trans-form raw materials into standardized units. On the Moon there are three natural resources: vacuum, radiation and regolith. To utilize in situ resources on the Moon it is reasonable to presume some beneficiation of the regolith (ground rock) resource will be desirable if not essential. As on Earth, this will require fundamental understanding of the physics and chemistry of the relevant processes, which are exceeding complex in detail. Further, simulants are essential test articles for evaluation of components and systems planned for lunar deployment. Simulants are of course made from geologic feedstocks. Therefore, there is variation, deleterious components and incorrect concentrations of desired fractions in the feedstocks used for simulants. Thus, simulant production can benefit from beneficiation of the input feedstocks. Beneficiation of geologic feedstocks is the subject of extractive metallurgy. Clearly, NASA has two discrete interests pertaining to the science and technology of extractive metallurgy.

Rickman, Doug L.↗

Numerical Study Comparing RANS and LES Approaches on a Circulation Control Airfoil

A numerical study over a nominally two-dimensional circulation control airfoil is performed using a large-eddy simulation code and two Reynolds-averaged Navier-Stokes codes. Different Coanda jet blowing conditions are investigated. In addition to investigating the influence of grid density, a comparison is made between incompressible and compressible flow solvers. The incompressible equations are found to yield negligible differences from the compressible equations up to at least a jet exit Mach number of 0.64. The effects of different turbulence models are also studied. Models that do not account for streamline curvature effects tend to predict jet separation from the Coanda surface too late, and can produce non-physical solutions at high blowing rates. Three different turbulence models that account for streamline curvature are compared with each other and with large eddy simulation solutions. All three models are found to predict the Coanda jet separation location reasonably well, but one of the models predicts specific flow field details near the Coanda surface prior to separation much better than the other two. All Reynolds-averaged Navier-Stokes computations produce higher circulation than large eddy simulation computations, with different stagnation point location and greater flow acceleration around the nose onto the upper surface. The precise reasons for the higher circulation are not clear, although it is not solely a function of predicting the jet separation location correctly.

Rumsey, Christopher L.↗