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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Dynamic Retrieval Augmented Generation of Ontologies using Artificial Intelligence (DRAGON-AI)

Ontologies are fundamental components of informatics infrastructure in domains such as biomedical, environmental, and food sciences, representing consensus knowledge in an accurate and computable form. However, their construction and maintenance demand substantial resources and necessitate substantial collaboration between domain experts, curators, and ontology experts. We present Dynamic Retrieval Augmented Generation of Ontologies using AI (DRAGON-AI), an ontology generation method employing Large Language Models (LLMs) and Retrieval Augmented Generation (RAG). DRAGON-AI can generate textual and logical ontology components, drawing from existing knowledge in multiple ontologies and unstructured text sources.We assessed performance of DRAGON-AI on de novo term construction across ten diverse ontologies, making use of extensive manual evaluation of results. Our method has high precision for relationship generation, but has slightly lower precision than from logic-based reasoning. Our method is also able to generate definitions deemed acceptable by expert evaluators, but these scored worse than human-authored definitions. Notably, evaluators with the highest level of confidence in a domain were better able to discern flaws in AI-generated definitions. We also demonstrated the ability of DRAGON-AI to incorporate natural language instructions in the form of GitHub issues.These findings suggest DRAGON-AI's potential to substantially aid the manual ontology construction process. However, our results also underscore the importance of having expert curators and ontology editors drive the ontology generation process.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2025

ELM 1016706669-AA B581 GDE01 Generator Summary pg 4-5 only

The table below shows the general load breakdown for 581GDE01. Although the total connected load exceeds the generator’s 150kW nameplate capacity, the normal configured load during standby power mode is less, which was measured at 81kW, or 54%, during preventive maintenance activities on 12/12/24. The generator’s available spare capacity must account for dynamically changing loads that can increase the total power demand at any time. If the two online VFD’s are operated at full speed the actual standby mode load is estimated to increase by 38kW, which would bring the total configured load during standby power mode to 119kW, or 79%, still within 581GDE01’s acceptable capacity. Per the LLNL Site 200 Generator Consolidation Final Study 2022, “Standby Emergency Generator nameplate ratings are based upon operation with varying load averaging 70% of the nameplate for 200 hours per year. Continuous loading between 70% and 100% will reduce a generator’s expected lifetime before a major overhaul. This is never a problem with Laboratory machines because of conservative application of generators and the reliability of the normal power system combines to keeps the load and hours down”. To achieve optimal performance and prolong generator life, the recommended generator loading is between 40% and 70%, optimally at 70%, which 581GDE01 appropriately falls within.

42 ENGINEERING↗
NASA NTRS1982

An investigation of the uniform random number generator

Most random number generators that are in use today are of the congruential form X(i+1) + AX(i) + C mod M where A, C, and M are nonnegative integers. If C=O, the generator is called the multiplicative type and those for which C/O are called mixed congruential generators. It is easy to see that congruential generators will repeat a sequence of numbers after a maximum of M values have been generated. The number of numbers that a procedure generates before restarting the sequence is called the length or the period of the generator. Generally, it is desirable to make the period as long as possible. A detailed discussion of congruential generators is given. Also, several promising procedures that differ from the multiplicative and mixed procedure are discussed.

Temple, E. C.↗
NASA NTRS1983

Effects of voltage control in utility interactive dispersed storage and generation systems

When a small generator is connected to the distribution system, the voltage at the point of interconnection is determined largely by the system and not the generator. The effect on the generator, on the load voltage and on the distribution system of a number of different voltage control strategies in the generator is examined. Synchronous generators with three kinds of exciter control are considered, as well as induction generators and dc/ac inverters, with and without capacitor compensation. The effect of varying input power during operation (which may be experienced by generators based on renewable resources) is explored, as well as the effect of connecting and disconnecting the generator at ten percent of its rated power. Operation with a constant slightly lagging factor is shown to have some advantages.

Kirkham, H.↗
NASA NTRS1992

Interactive solution-adaptive grid generation

TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.

Choo, Yung K.↗
NASA NTRS1993

An experimental investigation of S-duct flow control using arrays of low-profile vortex generators

An experimental investigation was undertaken to measure the effect of various configurations of low-profile vortex generator arrays on the flow in a diffusing S-duct. Three parameters that characterize the vortex generator array were systematically varied to determine their effect: (1) the vortex generator height, (2) the streamwise location of the vortex generator array, and (3) the vortex generator spacing. Each array of vortex generators tested improved total pressure recovery. The configuration employing the largest vortex generators was the most effective in reducing total pressure distortion but did not produce the greatest total pressure recovery. No configuration of vortex generators completely eliminated the flow separation that naturally occurs in the S-duct; however the extent of the separated flow region was reduced.

Reichert, B. A.↗
NASA NTRS1993

Next generation initiation techniques

Four-dimensional data assimilation strategies can generally be classified as either current or next generation, depending upon whether they are used operationally or not. Current-generation data-assimilation techniques are those that are presently used routinely in operational-forecasting or research applications. They can be classified into the following categories: intermittent assimilation, Newtonian relaxation, and physical initialization. It should be noted that these techniques are the subject of continued research, and their improvement will parallel the development of next generation techniques described by the other speakers. Next generation assimilation techniques are those that are under development but are not yet used operationally. Most of these procedures are derived from control theory or variational methods and primarily represent continuous assimilation approaches, in which the data and model dynamics are 'fitted' to each other in an optimal way. Another 'next generation' category is the initialization of convective-scale models. Intermittent assimilation systems use an objective analysis to combine all observations within a time window that is centered on the analysis time. Continuous first-generation assimilation systems are usually based on the Newtonian-relaxation or 'nudging' techniques. Physical initialization procedures generally involve the use of standard or nonstandard data to force some physical process in the model during an assimilation period. Under the topic of next-generation assimilation techniques, variational approaches are currently being actively developed. Variational approaches seek to minimize a cost or penalty function which measures a model's fit to observations, background fields and other imposed constraints. Alternatively, the Kalman filter technique, which is also under investigation as a data assimilation procedure for numerical weather prediction, can yield acceptable initial conditions for mesoscale models. The third kind of next-generation technique involves strategies to initialize convective scale (non-hydrostatic) models.

Warner, Tom↗
NASA NTRS1994

Experimental investigations of on-demand vortex generators

Conventional vortex generators as found on many civil aircrafts are mainly for off-design conditions - e.g. suppression of separation or loss of aileron power when the Mach number accidentally rises above the design (cruise) value. In normal conditions they perform no useful function and exert a significant drag penalty. Recently there have been advances in new designs for passive vortex generators and boundary layer control. While traditionally the generators heights were of the order of the boundary layer thickness (delta), recent advances have been made where generators of the order of delta/4 have been shown to be effective. The advancement of MIcro-Electro-Mechanical (MEM) devices has prompted several efforts in exploring the possibility of using such devices in turbulence control. These new devices offer the possibility of boundary layer manipulation through the production of vortices, momentum jets, or other features in the flow. However, the energy output of each device is low in general, but they can be used in large numbers. Therefore, the possibility of moving from passive vortex generators to active (on-demand) devices becomes of interest. Replacement of fixed rectangular or delta-wing generators by devices that could be activated when needed would produce substantial economies. Our proposed application is not strictly 'active' control: the vortex generators would simply be switched on, all together, when needed (e.g. when the aircraft Mach number exceeded a certain limit). To this extent our scheme is simpler; however, to promote mixing and suppress separation we desire to deposit longitudinal vortices into the outer layer of the boundary layer as in conventional vortex generators. This requires a larger device although an alternative might be an array of smaller devices, for example, a longitudinal row with phase differences in the modulation signals so that the periodic vortices join up. The vortex pair with common flow up has the advantage that it will naturally drift away from the surface, but the disadvantage is that the net vorticity is zero so that the pair is eventually obliterated by turbulent mixing, rather than simply being diffused as in the case of a single vortex. It should be possible to devise alternative shapes of cavity wall so that the jet emerges obliquely and produces net longitudinal vorticity.

Saddoughi, Seyed G.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parmetrized surfaces

An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

Spekreijse, S. P.↗
NASA NTRS1995

Preliminary results of the on-demand vortex-generator experiments

This is a report on the continuation of our experimental investigations (Saddoughi 1994) of 'on-demand' vortex generators. Conventional vortex generators as found on aircraft wings are mainly for suppression of separation during the off-design conditions. In cruise they perform no useful function and exert a significant drag penalty. Therefore, replacement of fixed rectangular or delta-wing generators by devices that could be activated when needed would be of interest. Also in our previous report, we described one example of an 'on-demand' device, which was developed by Jacobson & Reynolds (1995) at Stanford University, suitable for manufacture by micro-electro-mechanical technology. This device consists of a surface cavity elongated in the stream direction and covered with a lid cantilevered at the upstream end. The lid, which is a metal sheet with a sheet of piezoelectric ceramic bonded to it, lies flush with the boundary. On application of a voltage the ceramic expands or contracts; however, adequate amplitude can be obtained only by running at the cantilever resonance frequency and applying amplitude modulation: for 2.5 mm x 20 mm cantilevered lids, they obtained maximum tip displacements of the order of 100 pm. Thus fluid is expelled from the cavity through the gap around the lid on the downstroke. They used an asymmetrical gap configuration and found that periodic emerging jets on the narrow side induced periodic longitudinal vorticity into the boundary layer. Their device was used to modify the inner layer of the boundary layer for skin-friction reduction. The same method could be implemented for the replacement of the conventional vortex generators; however, to promote mixing and suppress separation we needed to deposit longitudinal vortices into the outer layer of the boundary layer, which required a larger vortex generator than the device built by Jacobson & Reynolds. Our vortex generator was built with a mechanically-driven cantilevered lid with an adjustable frequency. The device was made about ten times the size of Jacobson & Reynolds', the shape or size of the cavity and lid (28 mm x 250 mm) could be easily changed. The cavity depth, the cantilever-tip displacement, and the maximum lid frequency were 20 mm, 10 mm, and 60 Hz respectively. Our vortex generator was mounted on a turntable so that its yaw angle could be changed. Finally, tests over a range of ratios of vortex generator size to boundary-layer thickness could be carried out simply by changing the streamwise location of the device.

Saddoughi, Seyed G.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parametrized surfaces

An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.

Spekreijse, S. P.↗
NASA NTRS1998

Development and Testing of Automatically Generated ACS Flight Software for the MAP Spacecraft

By integrating the attitude determination and control system (ACS) analysis and design, flight software development, and flight software testing processes, it is possible to improve the overall spacecraft development cycle, as well as allow for more thorough software testing. One of the ways to achieve this integration is to use code-generation tools to automatically generate components of the ACS flight software directly from a high-fidelity (HiFi) simulation. In the development of the Microwave Anisotropy Probe (MAP) spacecraft, currently underway at the NASA Goddard Space Flight Center, approximately 1/3 of the ACS flight software was automatically generated. In this paper, we will examine each phase of the ACS subsystem and flight software design life cycle: analysis, design, and testing. In the analysis phase, we scoped how much software we would automatically generate and created the initial interface. The design phase included parallel development of the HiFi simulation and the hand-coded flight software components. Everything came together in the test phase, in which the flight software was tested, using results from the HiFi simulation as one of the bases of comparison for testing. Because parts of the spacecraft HiFi simulation were converted into flight software, more care needed to be put into its development and configuration control to support both the HiFi simulation and flight software. The components of the HiFi simulation from which code was generated needed to be designed based on the fact that they would become flight software. This process involved such considerations as protecting against mathematical exceptions, using acceptable module and parameter naming conventions, and using an input/output interface compatible with the rest of the flight software. Maintaining good configuration control was an issue for the HiFi simulation and the flight software, and a way to track the two systems was devised. Finally, an integrated test approach was devised to support flight software testing at both the unit- and build-test levels using the HiFi simulation to generate data for performance verification. Another benefit of the simulation and code-generation application used on the MAP project is that it supported bringing flight software and test data into the HiFi simulation environment. It was possible to integrate parts of the hand-coded flight software into the HiFi simulation, and also possible to import flight software test data for comparison and performance verification. This capability was used to incorporate the flight software Kalman filter into the HiFi simulation. This enabled us to greatly increase the amount of testing that could be done on the filter, because we could exert a greater degree of control over the software-only simulation than over the flight software test environment. Also, since the simulation could be used to run the Kalman filter faster than real time, our testing efficiency was greatly increased. We will conclude our discussion with a summary of the lessons learned thus far using automatically- generated code for the MAP project, and the spacecraft status as we work towards our scheduled launch in the year 2000.

ODonnell, James R., Jr.↗
NASA NTRS2004

Source Term Model for Vortex Generator Vanes in a Navier-Stokes Computer Code

A source term model for an array of vortex generators was implemented into a non-proprietary Navier-Stokes computer code, OVERFLOW. The source term models the side force created by a vortex generator vane. The model is obtained by introducing a side force to the momentum and energy equations that can adjust its strength automatically based on the local flow. The model was tested and calibrated by comparing data from numerical simulations and experiments of a single low profile vortex generator vane on a flat plate. In addition, the model was compared to experimental data of an S-duct with 22 co-rotating, low profile vortex generators. The source term model allowed a grid reduction of about seventy percent when compared with the numerical simulations performed on a fully gridded vortex generator on a flat plate without adversely affecting the development and capture of the vortex created. The source term model was able to predict the shape and size of the stream-wise vorticity and velocity contours very well when compared with both numerical simulations and experimental data. The peak vorticity and its location were also predicted very well when compared to numerical simulations and experimental data. The circulation predicted by the source term model matches the prediction of the numerical simulation. The source term model predicted the engine fan face distortion and total pressure recovery of the S-duct with 22 co-rotating vortex generators very well. The source term model allows a researcher to quickly investigate different locations of individual or a row of vortex generators. The researcher is able to conduct a preliminary investigation with minimal grid generation and computational time.

Waithe, Kenrick A.↗
NASA NTRS1997

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

Melcher, Kevin J.↗
NASA NTRS2004

Epoxy Adhesives for Stator Magnet Assembly in Stirling Radioisotope Generators (SRG)

As NASA seeks to fulfill its goals of exploration and understanding through missions planned to visit the moons of Saturn and beyond, a number of challenges arise from the idea of deep space flight. One of the first problems associated with deep space travel is electrical power production for systems on the spacecraft. Conventional methods such as solar power are not practical because efficiency decreases substantially as the craft moves away from the Sun. The criterion for power generation during deep space missions are very specific, the main points requiring high reliability, low mass, minimal vibration and a long lifespan. A Stirling generator, although fairly old in concept, is considered to be a potential solution for electrical power generation for deep space flight. A Stirling generator works on the same electromagnetic principles of a standard generator, using the linear motion of the alternator through the stationary stator which produces electric induction. The motion of the alternator, however, is produced by the heating and cooling dynamics of pressurized gases. Essentially heating one end and cooling another of a contained gas will cause a periodic expansion and compression of the gas from one side to the other, which a displacer translates into linear mechanical motion. NASA needs to confirm that the materials used in the generator will be able to withstand the rigors of space and the life expectancy of the mission. I am working on the verification of the epoxy adhesives used to bond magnets to the steel lamination stack to complete the stator; in terms of in-service performance and durability under various space environments. Understanding the proper curing conditions, high temperature properties, and degassing problems as well as production difficulties are crucial to the long term success of the generator. system and steel substrate used in the stator. To optimize the curing conditions of the epoxies, modulated differential scanning calorimetry analysis was done as a function of cure time and temperatures. Adhesion bond strength was tested at various temperatures with lap shear samples using Hiperco 50 substrate to ensure that the proper adhesive is being used. To try and solve the problem of bondline thickness, micro glass beads of 0.0017" in diameter were investigated to see if any other physical properties of the epoxy were affected. Efforts will be made to develop a standard, optimized, fabrication process/procedure of sub-scale magnet-stator assemblies for various adhesive performance evaluation studies under simulated generator conditions. Also, accelerated aging testing will be done in a pressurized canister with stator assembly samples for three years to verify if any degassing or thermal degradation of the epoxy occurs. The necessity of verifying the correct epoxy adhesive system for the stator magnet in the SRG is crucial because failure of the stator assembly would jeopardize the electrical system, and thereby the entire mission itself. My work involves specimen fabrications, testing, and data analyses of the epoxy adhesive system for the stator magnet in the SRG is crucial because failure of the stator assembly would jeopardize the electrical system, and thereby the entire mission itself.

Cater, George M.↗
NASA NTRS2006

Flexible Generation of Kalman Filter Code

Domain-specific program synthesis can automatically generate high quality code in complex domains from succinct specifications, but the range of programs which can be generated by a given synthesis system is typically narrow. Obtaining code which falls outside this narrow scope necessitates either 1) extension of the code generator, which is usually very expensive, or 2) manual modification of the generated code, which is often difficult and which must be redone whenever changes are made to the program specification. In this paper, we describe adaptations and extensions of the AUTOFILTER Kalman filter synthesis system which greatly extend the range of programs which can be generated. Users augment the input specification with a specification of code fragments and how those fragments should interleave with or replace parts of the synthesized filter. This allows users to generate a much wider range of programs without their needing to modify the synthesis system or edit generated code. We demonstrate the usefulness of the approach by applying it to the synthesis of a complex state estimator which combines code from several Kalman filters with user-specified code. The work described in this paper allows the complex design decisions necessary for real-world applications to be reflected in the synthesized code. When executed on simulated input data, the generated state estimator was found to produce comparable estimates to those produced by a handcoded estimator

Richardson, Julian↗
NASA NTRS2007

Automatic Command Sequence Generation

Automatic Sequence Generator (Autogen) Version 3.0 software automatically generates command sequences for the Mars Reconnaissance Orbiter (MRO) and several other JPL spacecraft operated by the multi-mission support team. Autogen uses standard JPL sequencing tools like APGEN, ASP, SEQGEN, and the DOM database to automate the generation of uplink command products, Spacecraft Command Message Format (SCMF) files, and the corresponding ground command products, DSN Keywords Files (DKF). Autogen supports all the major multi-mission mission phases including the cruise, aerobraking, mapping/science, and relay mission phases. Autogen is a Perl script, which functions within the mission operations UNIX environment. It consists of two parts: a set of model files and the autogen Perl script. Autogen encodes the behaviors of the system into a model and encodes algorithms for context sensitive customizations of the modeled behaviors. The model includes knowledge of different mission phases and how the resultant command products must differ for these phases. The executable software portion of Autogen, automates the setup and use of APGEN for constructing a spacecraft activity sequence file (SASF). The setup includes file retrieval through the DOM (Distributed Object Manager), an object database used to store project files. This step retrieves all the needed input files for generating the command products. Depending on the mission phase, Autogen also uses the ASP (Automated Sequence Processor) and SEQGEN to generate the command product sent to the spacecraft. Autogen also provides the means for customizing sequences through the use of configuration files. By automating the majority of the sequencing generation process, Autogen eliminates many sequence generation errors commonly introduced by manually constructing spacecraft command sequences. Through the layering of commands into the sequence by a series of scheduling algorithms, users are able to rapidly and reliably construct the desired uplink command products. With the aid of Autogen, sequences may be produced in a matter of hours instead of weeks, with a significant reduction in the number of people on the sequence team. As a result, the uplink product generation process is significantly streamlined and mission risk is significantly reduced. Autogen is used for operations of MRO, Mars Global Surveyor (MGS), Mars Exploration Rover (MER), Mars Odyssey, and will be used for operations of Phoenix. Autogen Version 3.0 is the operational version of Autogen including the MRO adaptation for the cruise mission phase, and was also used for development of the aerobraking and mapping mission phases for MRO.

Fisher, Forest↗
NASA NTRS2010

Modeling Vortex Generators in the Wind-US Code

A source term model which simulates the effects of vortex generators was implemented into the Wind-US Navier Stokes code. The source term added to the Navier-Stokes equations simulates the lift force which would result from a vane-type vortex generator in the flowfield. The implementation is user-friendly, requiring the user to specify only three quantities for each desired vortex generator: the range of grid points over which the force is to be applied and the planform area and angle of incidence of the physical vane. The model behavior was evaluated for subsonic flow in a rectangular duct with a single vane vortex generator, supersonic flow in a rectangular duct with a counterrotating vortex generator pair, and subsonic flow in an S-duct with 22 co-rotating vortex generators. The validation results indicate that the source term vortex generator model provides a useful tool for screening vortex generator configurations and gives comparable results to solutions computed using a gridded vane.

Dudek, Julianne C.↗