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DOE OSTI2017

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

Coronal heating has been a long-standing conundrum in solar physics. Parker's conjecture that spontaneous current singularities lead to nanoflares that heat the corona has been controversial. In ideal magnetohydrodynamics (MHD), can genuine current singularities emerge from a smooth 3D line-tied magnetic field? To numerically resolve this issue, the schemes employed must preserve magnetic topology exactly to avoid artificial reconnection in the presence of (nearly) singular current densities. Structure-preserving numerical methods are favorable for mitigating numerical dissipation, and variational integration is a powerful machinery for deriving them. However, successful applications of variational integration to ideal MHD have been scarce. In this thesis, we develop variational integrators for ideal MHD in Lagrangian labeling by discretizing Newcomb's Lagrangian on a moving mesh using discretized exterior calculus. With the built-in frozen-in equation, the schemes are free of artificial reconnection, hence optimal for studying current singularity formation. Using this method, we first study a fundamental prototype problem in 2D, the Hahm-Kulsrud-Taylor (HKT) problem. It considers the effect of boundary perturbations on a 2D plasma magnetized by a sheared field, and its linear solution is singular. We find that with increasing resolution, the nonlinear solution converges to one with a current singularity. The same signature of current singularity is also identified in other 2D cases with more complex magnetic topologies, such as the coalescence instability of magnetic islands. We then extend the HKT problem to 3D line-tied geometry, which models the solar corona by anchoring the field lines in the boundaries. The effect of such geometry is crucial in the controversy over Parker's conjecture. The linear solution, which is singular in 2D, is found to be smooth. However, with finite amplitude, it can become pathological above a critical system length. The nonlinear solution turns out smooth for short systems. Nonetheless, the scaling of peak current density vs. system length suggests that the nonlinear solution may become singular at a finite length. With the results in hand, we cannot confirm or rule out this possibility conclusively, since we cannot obtain solutions with system lengths near the extrapolated critical value.

solar corona↗

DOE OSTI2019

Radiation Leakage and the Precision of Characterizing Nuclear Material Using Calorimetric Assay - 19233

For measuring a waste drum containing multi-nuclide radioactive material calorimetric assay is often combined with gamma ray and neutron measurements. To reduce the methodological uncertainties of the inventory determination in a multi-nuclide matrix, the escaping radiation must be quantized as much as the encapsulated gamma-rays and α-, β-, n- particles depositing radiological heat inside the drum. To differentiate the possible variety of heat sources in a radioactive waste drum, Monte Carlo simulations are utilized resembling the waste drum and the calorimeter in both, their geometries as well as the material compositions. MCNP6-based numerical imaging of the Large Volume Calorimeter (LVC) designed by KEP Nuclear(France) allows simulating various scenarios for different particles types, energies and source locations to accompany and support the interpretation of calorimetric KEP-LVC measurements anticipated within the CHANCE project. For the analyses, the particle flux and energy deposition in each layer of the calorimeter are displayed. The results yield that a significant part of the emitted radiation leaves the system and does not contribute to the heat deposited inside the drum. As an example, the particle flux study of a 200 L mock-up drum placed inside the KEP-LVC calorimeter is discussed. A tally 4 with mesh option for both gamma and neutrons up to 5 MeV simulates the mean flux in each cell and for various source location and source distribution patterns. The expected energy deposition is cumulated for each layer, and over the whole energy range it reveals that actually a small but well known fraction of particles escapes the LVC calorimeter. This makes it a very suitable apparatus for the anticipated experiments on large and heterogeneous waste drums. The results suggest that the most interesting cases would be polyethylene, bitumen and concrete matrices [3, 5]. However, it must be kept in mind that the high-energy part of the gamma and neutron radiation flux can reach the reference chamber of the calorimeter and deposit some energy there, which may compromise the calibration and cause double-bias. The simulations showed that, depending on source location and power, neutron and high-energy gamma radiation leakage can influence the heat measurements differently. In general, part of the simulation results suggest that for waste drums with a high emission rate the accuracy of calorimetric assay can be decreased due to radiation escape. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Triaxial Shear Tests on Simulated Sierra White Fault Gouge & Borehole Simulation in Sierra White Gouge

Laboratory shear tests were conducted on pulverized Sierra White granite (SWG) to investigate slip mechanisms in naturally occurring faults. Synthetic fault geometries were constructed by sandwiching fine grained SWG powder in between steel forcing blocks. For dry experiments, ~3.5 g of SWG powder was poured onto the face of the lower steel forcing block and leveled. For saturated experiments, enough fluid was added to the ~3.5 g of Sierra White granite powder to form a slurry. This slurry was applied to the lower forcing block and leveled. Inclined forcing blocks with 25.4 mm diameter and 35° faces, which were machined from ground steel rods with fine teeth on the faces, help to hold the gouge in place and prevent delamination at the interface. The top forcing block had a 2.03 mm centered hole to allow pore fluid access to the gouge. A fine steel mesh prevented back flow of the gouge into pore fluid lines. Samples were isolated from the confining medium using three layers of heat shrink polyolefin, as shown in Figure 1. The outer layer was shrunk over the o-rings on the end caps to form an impermeable seal, which was reinforced with steel tie wires on both sides of the o-rings. Hardened steel spacers and copper shim stock was placed between the steel forcing blocks and the end caps to preserve the parallelism of the Hastelloy wetted parts. For dry samples, the end caps were plugged, while the end caps for the saturated samples were connected to pore lines.

58 GEOSCIENCES↗

NASA NTRS1980

Comparison of finite element analysis of a piping tee using NASTRAN and CORTES/SA

A comparison of finite element analyses of a piping tee was made using NASTRAN and CORTES/SA, a modified version of SAP3 having a special purpose input processor for generating geometries for a wide variety of tee joints. Four finite element models were subjected in force, moment, and pressure loadings. Flexibility factors and principal stresses were computed for each model and compared with results obtained experimentally by Combustion Engineering, Inc. Results from the NASTRAN analyses were in good agreement with experimental results for all loadings except internal pressure. The CORTES/SA analyses gave good results for the internal pressure loading, but poorer results for out of plane bending moments or forces resulting in out of plane bending. Two of the basic load cases in CORTES/SA were found to contain errors that could not be easily corrected. COST COMPARison of NASTRAN and CORTES/SA showed NASTRAN to be less expensive to two than CORTES/SA for identical meshes.

Quezon, A. J.↗

DOE OSTI2022

Quasi-Helmholtz decomposition, Gauss' laws and charge conservation for finite element particle-in-cell

Development of particle-in-cell (PIC) methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better understanding of function spaces that are necessary to represent all Maxwell quantities, and (c) more recently, the fundamental rubrics that should be obeyed in space and time so as to satisfy Gauss' laws and the equation of continuity. In that vein, methods have been developed recently that satisfy these equations and are agnostic to time stepping methods. While this development is indeed a significant advance, it should be noted that implicit FEM transient solvers support an underlying null space that corresponds to a gradient of a scalar potential ∇Φ(r) (or t∇Φ(r) in the case of wave equation solvers). While explicit schemes do not suffer from this drawback, they are only conditionally stable with time step sizes that are mesh dependent and very small. Furthermore, the null space produces spurious charge that can corrupt the desired physics of a PIC simulation. The way to overcome this bottleneck, and indeed, satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on a tessellation. In the re-formulation presented, we strictly satisfy the equation of continuity and Gauss' laws for both the electric and magnetic flux densities. Results illustrating the efficacy of this scheme will be demonstrated by analyzing non-neutral beams with space-charge and the adiabatic expansion of a neutral plasma with realistic parameters (Debye length and real mass ratios).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Electron beam simulation from gun to collector: Towards a complete solution

An electron-beam simulation technique for high-resolution complete EBIS/T modelling is presented. The technique was benchmarked on the high compression HEC{sup 2} test-stand with an electron beam current, current density and energy of 10 A, 10 kA/cm{sup 2} and 49.2 keV, and on the immersed electron beam at REXEBIS for electron beam characteristics of 0.4 A, 200 A/cm{sup 2} and 4.5 keV. In both Brillouin-like and immersed beams the electron-beam radius varies from several millimeters at the gun, through some hundreds of micrometers in the ionization region to a few centimeters at the collector over a total length of several meters. We report on our approach for finding optimal meshing parameters, based on the local beam properties such as magnetic field-strength, electron energy and beam radius. This approach combined with dividing the problem domain into sub-domains, and subsequent splicing of the local solutions allowed us to simulate the beam propagation in EBISes from the gun to the collector using a conventional PC in about 24–36 h. Brillouin-like electron beams propagated through the complete EBIS were used to analyze the beam behavior within the collector region. We checked whether elastically reflected paraxial electrons from a Brillouin-like beam will escape from the collector region and add to the loss current. We have also studied the power deposition profiles as function of applied potentials using two electrode geometries for a Brillouin-like beam including the effects of backscattered electrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2010

Assessment of Hybrid RANS/LES Turbulence Models for Aeroacoustics Applications

Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroacoustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex configurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Although the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the experimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in unresolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging.

Vatsa, Veer N.↗

DOE OSTI2020

Fresnel zone plate development for x-ray radiography of hydrodynamic instabilities at the National Ignition Facility

The study of Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities in a planar geometry at high energy densities at the National Ignition Facility (NIF) requires high spatial resolution imaging. We demonstrate the potential of Fresnel zone plates (FZPs) to achieve resolution that would unlock such studies. FZPs are circular aperiodic gratings that use diffraction to focus x rays and produce an image with high spatial resolution. Taking into account the NIF’s challenging environment, we have designed a specific array of five FZPs for a zinc backlighter to take a radiograph of a target with 9 keV x rays. We measured a mean resolution for the FZP of 1.9µm±0.5µm and a ±1mm depth of focus at an x-ray calibration facility as well as a 2.3µm±0.4µm resolution on a resolution wire mesh shot on the NIF. We also performed an in-depth analysis of the image quality to assess the capability to resolve the small features present in RT and RM instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Application of SPH Factors to PHWR Lattice Homogenization

Pressurized Heavy-Water Reactors (PHWRs) are heavy-water moderated and cooled. They consist of a horizontal, cylindrical, non-pressurized calandria vessel which contains the heavy-water moderator and is penetrated axially by fuel channels. Fuel channels consist of two concentric tubes separated by a gas gap: an inner tube called the pressure tube, and an outer tube called the calandria tube. The pressure tubes hold the fuel bundles, which are cooled by the flow of coolant at high temperature and pressure. The coolant flows in opposite directions in adjacent channels. The gap between the pressure and calandria tubes ensures that the temperature of the moderator remains relatively low, below 80 deg. C. For a CANDU 6 reactor, there are 380 fuel channels, each holding 12 37-element fuel bundles, approximately 10-cm in diameter and 50-cm long each. The fuel pins are arranged in three concentric rings (consisting of 6, 12 and 18 pins respectively), plus a central pin. The distance between channels (lattice pitch) is approximately 28.6 cm. Production core-level neutronics calculations are usually performed in a Cartesian geometry using few group diffusion and a simplified core model, whereby neutronics properties are homogenized over large regions called nodes. For Light Water reactors (LWRs), the two-dimensional axial (x-y) projection of a node corresponds to one fuel assembly. For PHWRs, a node usually consists of one fuel bundle and its associated moderator. For LWRs, advanced core-level calculations based on advanced node-level homogenization methods, such as Generalized Equivalence Theory (GET) or Super-homogenisation (SPH), improve the accuracy of full-core calculations compared to - standard homogenization. For rectangular fuel-pin arrangements, SPH can be used to perform pin-cell level homogenization which allows subsequent core-level diffusion calculations to be performed using fine Cartesian meshes. For PHWRs, the distribution of fuel pins in concentric rings makes the use of Cartesian mesh refinement impractical. However, SPH can still be applied, albeit using a coarser node subdivision, by dividing the heterogeneous node into 3x3 sub-regions in such a way that the central sub-region includes the entire fuel channel. This work investigates the use of SPH homogenization using a 3x3 subdivision of the PHWR node. Preliminary results show that the use of SPH factors does not yield more accurate results than standard homogenization when applied to PHWR nodes using a 3x3 subdivision. The explanation appears to lie in the fact that SPH factors are dependent on node-boundary leakage. Future investigations to confirm the leakage-dependence of SPH factors are recommended. Accuracy improvements may also be achievable by using smaller SPH regions at the periphery of the PHWR node, in an attempt to reduce the SPH factors' dependence on node-boundary leakage. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Sci-Sat AM: Radiation Dosimetry and Practical Therapy Solutions - 08: A Low-Cost Optical Scanner and Gantry for use with 3D Printing of Radiation Therapy Accessories

Purpose: Three-dimensional printing has been implemented at our institution to create customized treatment accessories including shielding and bolus. In order to effectively use 3D printing, the topography of the patient must first be acquired. To this end, we have evaluated a low-cost structured-light 3D scanner in order to assess the clinical viability of this technology. Methods: For ease of use, the scanner (3D Systems, Sense 3D Scanner) was mounted in a simple gantry that guided its motion and maintained an optimum distance between the scanner and the object. To characterise the spatial accuracy of the scanner, we used a geometric phantom and an anthropomorphic head phantom. The geometric phantom was machined from plastic and had overall dimensions of 24 cm by 15 cm and included a hemispherical and a tetrahedron protrusion roughly the dimensions of an average forehead and nose respectively. Meshes acquired by the optical scanner were compared to meshes generated from high-resolution CT images. Results: Scans were acquired in under one minute. Most of the optical scans contained noticeable artefacts although in most instances these were considered minor. Using an algorithm that calculated distances between the two meshes, we found most of the optical scanner measurements agreed with those from CT to within about 1 mm for the geometric phantom and to within about 2 mm for the head phantom. Conclusion: In summary, we deemed this scanner to be clinically acceptable and it has been used to design treatment accessories for several skin cancer patients.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2002

Multi-Zone Liquid Thrust Chamber Performance Code with Domain Decomposition for Parallel Processing

Computational Fluid Dynamics (CFD) has considerably evolved in the last decade. There are many computer programs that can perform computations on viscous internal or external flows with chemical reactions. CFD has become a commonly used tool in the design and analysis of gas turbines, ramjet combustors, turbo-machinery, inlet ducts, rocket engines, jet interaction, missile, and ramjet nozzles. One of the problems of interest to NASA has always been the performance prediction for rocket and air-breathing engines. Due to the complexity of flow in these engines it is necessary to resolve the flowfield into a fine mesh to capture quantities like turbulence and heat transfer. However, calculation on a high-resolution grid is associated with a prohibitively increasing computational time that can downgrade the value of the CFD for practical engineering calculations. The Liquid Thrust Chamber Performance (LTCP) code was developed for NASA/MSFC (Marshall Space Flight Center) to perform liquid rocket engine performance calculations. This code is a 2D/axisymmetric full Navier-Stokes (NS) solver with fully coupled finite rate chemistry and Eulerian treatment of liquid fuel and/or oxidizer droplets. One of the advantages of this code has been the resemblance of its input file to the JANNAF (Joint Army Navy NASA Air Force Interagency Propulsion Committee) standard TDK code, and its automatic grid generation for JANNAF defined combustion chamber wall geometry. These options minimize the learning effort for TDK users, and make the code a good candidate for performing engineering calculations. Although the LTCP code was developed for liquid rocket engines, it is a general-purpose code and has been used for solving many engineering problems. However, the single zone formulation of the LTCP has limited the code to be applicable to problems with complex geometry. Furthermore, the computational time becomes prohibitively large for high-resolution problems with chemistry, two-equation turbulence model, and two-phase flow. To overcome these limitations, the LTCP code is rewritten to include the multi-zone capability with domain decomposition that makes it suitable for parallel processing, i.e., enabling the code to run every zone or sub-domain on a separate processor. This can reduce the run time by a factor of 6 to 8, depending on the problem.

Homayun K. Navaz↗

NASA NTRS2003

Modified Involute Helical Gears: Computerized Design, Simulation of Meshing, and Stress Analysis

The computerized design, methods for generation, simulation of meshing, and enhanced stress analysis of modified involute helical gears is presented. The approaches proposed for modification of conventional involute helical gears are based on conjugation of double-crowned pinion with a conventional helical involute gear. Double-crowning of the pinion means deviation of cross-profile from an involute one and deviation in longitudinal direction from a helicoid surface. Using the method developed, the pinion-gear tooth surfaces are in point-contact, the bearing contact is localized and oriented longitudinally, and edge contact is avoided. Also, the influence of errors of aligment on the shift of bearing contact, vibration, and noise are reduced substantially. The theory developed is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry in comparison with conventional helical involute gears.

Handschuh, Robert↗

NASA NTRS2003

Modified Involute Helical Gears: Computerized Design, Simulation of Meshing and Stress Analysis

The computerized design, methods for generation, simulation of meshing, and enhanced stress analysis of modified involute helical gears is presented. The approaches proposed for modification of conventional involute helical gears are based on conjugation of double-crowned pinion with a conventional helical involute gear. Double-crowning of the pinion means deviation of cross-profile from an involute one and deviation in longitudinal direction from a helicoid surface. Using the method developed, the pinion-gear tooth surfaces are in point-contact, the bearing contact is localized and oriented longitudinally, and edge contact is avoided. Also, the influence of errors of alignment on the shift of bearing contact, vibration, and noise are reduced substantially. The theory developed is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry in comparison with conventional helical involute gears.

COMPUTER AIDED DESIGN↗

NASA NTRSDate not supplied

Simulation of Dynamic Crushing Behavior of Simulated Carbon/Epoxy Stanchions Using MAT58 and MAT213 in LS-DYNA

Carbon fiber-reinforced polymer (CFRP) composites have shown promise as a material for structures designed to absorb energy in crush-style impact loading. In complementing the lightweight and tailorable characteristics of CFRP structures, the benefits of impact energy absorption are particularly interesting in aerospace vehicles that require excellent crashworthiness performance. However, simulating the behavior of CFRP structures in dynamic, crushing-style impact loading is challenging because of the many damage and failure modes that are essential to capture in the model. For the present investigation, CFRP stanchions were tested using a crash sled experimental test rig. The stanchions were designed by the Composite Materials Handbook-17 (CMH-17) Crashworthiness Working Group for the purpose of comparing experimental crash sled tests to corresponding simulations of the tests. The stanchions are C-channel shaped and represent a geometry common in the interior of aerospace vehicle structures. Explicit simulations in LSDYNA were performed using a well-established composite material model (MAT58) and a next-generation material model (MAT213). Fully integrated shell elements were utilized instead of 3D solid elements to limit computation time. In all models, each of the sixteen plies were represented with individual layers of shell elements with tiebreak contact between each adjacent ply pair to simulate interlaminar fracture. Simulating the crushing of the stanchions occurred in two phases. First, the material models were calibrated using flat specimens that were manufactured with the same layup as the stanchions. While the original goal was calibration of material-related properties, meshdependent behavior was observed in simulations with either material model, and an unstructured mesh was selected to remediate undesirable mesh-dependent failure modes. Additionally, for both the MAT58 and MAT213 models, it was found that either the crush force or the failure mode could be modeled accurately, but no set of parameters could be identified to attain both results in the same model. Once satisfactory calibration was achieved, the same material parameters were applied to the stanchion crush simulations. The stanchion simulations showed that MAT213 more accurately predicted the experimentally determined crush force, and both material models predicted key aspects of the experimentally observed failure modes.

Composite Materials↗

DOE OSTI2016

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1988

Grid generation for general 2-D regions using hyperbolic equations

A method for applying a hyperbolic grid generation scheme to the construction of meshes in general 2-D regions has been developed. This approach, which follows the theory developed by Steger and Chaussee (1980) and the algorithm outlined by Kinsey and Barth (1984), is based on improving local grid control. This is accomplished by adding an angle control source term to the equations and using a new algorithm for computing the volume source term. These modifications lead to superior methods for fixing the 'local' problems of hyperbolic grid generation, namely, propagation of initial discontinuities and formation of grid shocks (crossing grid lines). More importantly, a method for solving the global problem of constraining the grid with more than one boundary (internal grid generation) has been developed. These algorithms have been implemented in an interactive grid generation program and the results for several geometries are presented and discussed.

Cordova, Jeffrey Q.↗

NASA NTRSDate not supplied

Mixed-element USM3D Contributions to the 4th AIAA High-Lift Prediction Workshop

This paper discusses results of the mixed-element USM3D (USM3D-ME) simulations performed for the 4th AIAA High-Lift Prediction Workshop. The workshop was separated into six Technical Focus Groups to investigate the impact of geometry modeling, grid, and computational methods for predicting high lift flows. This work was performed under the Fixed Grid RANS Technical Focus Group. The primary geometry selected for the workshop was the High-Lift Common Research Model. The performed simulations included a flap deflection study and both a grid refinement study and pitch sweep for the nominal flap deflection configuration. The results show that USM3D-ME RANS solutions, generally, tends to underpredict the lift coefficient and to predict a less negative pitching moment relative to the experimental data. The predicted drag coefficient values agree better with experiment for smaller angles of attack but were observed to be larger than experiment for the largest angle of attack simulated. The results of the grid refinement study demonstrated a lack of grid convergence for the provided grid family. The results of the grid refinement study are consistent with the submissions to the Fixed Grid and Mesh Adaptation Technical Focus Groups. Grid convergence for the provided grid family remains elusive for the international community. A 2D Multielement Airfoil configuration was included to enable a turbulence model verification study, which illustrated favorable agreement between USM3D-ME and the solutions provided by other flow solvers.

CFD↗

NASA NTRSDate not supplied

Mixed-Element USM3D Contributions to the 4th AIAA High-Lift Prediction Workshop

CFD↗