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NASA NTRS2014

Nuclear Thermal Rocket Element Environmental Simulator (NTREES) Upgrade Activities

Over the past year the Nuclear Thermal Rocket Element Environmental Simulator (NTREES) has been undergoing a significant upgrade beyond its initial configuration. The NTREES facility is designed to perform realistic non-nuclear testing of nuclear thermal rocket (NTR) fuel elements and fuel materials. Although the NTREES facility cannot mimic the neutron and gamma environment of an operating NTR, it can simulate the thermal hydraulic environment within an NTR fuel element to provide critical information on material performance and compatibility. The first phase of the upgrade activities which was completed in 2012 in part consisted of an extensive modification to the hydrogen system to permit computer controlled operations outside the building through the use of pneumatically operated variable position valves. This setup also allows the hydrogen flow rate to be increased to over 200 g/sec and reduced the operation complexity of the system. The second stage of modifications to NTREES which has just been completed expands the capabilities of the facility significantly. In particular, the previous 50 kW induction power supply has been replaced with a 1.2 MW unit which should allow more prototypical fuel element temperatures to be reached. The water cooling system was also upgraded to so as to be capable of removing 100% of the heat generated during. This new setup required that the NTREES vessel be raised onto a platform along with most of its associated gas and vent lines. In this arrangement, the induction heater and water systems are now located underneath the platform. In this new configuration, the 1.2 MW NTREES induction heater will be capable of testing fuel elements and fuel materials in flowing hydrogen at pressures up to 1000 psi at temperatures up to and beyond 3000 K and at near-prototypic reactor channel power densities. NTREES is also capable of testing potential fuel elements with a variety of propellants, including hydrogen with additives to inhibit corrosion of certain potential NTR fuel forms. Additional diagnostic upgrades included in the present NTREES set up include the addition of a gamma ray spectrometer located near the vent filter to detect uranium fuel particles exiting the fuel element in the propellant exhaust stream to provide additional information any material loss occurring during testing. Other aspects of the upgrade included reworking NTREES to reduce the operational complexity of the system despite the increased complexity of the induction heating system. To this end, many of the controls were consolidated on fewer panels. As part of this upgrade activity, the Safety Assessment (SA) and the Standard Operating Procedures (SOPs) for NTREES were extensively rewritten. The new 1.2 MW induction heater consists of three physical units consisting of a transformer, rectifier, and inverter. This multiunit arrangement facilitated increasing the flexibility of the induction heater by more easily allowing variable frequency operation. Frequency ranges between 20 and 60 kHz can be accommodated in the new induction heater allowing more representative power distributions to be generated within the test elements.

Emrich, William J., Jr.↗
NASA NTRS2017

Measuring Surface Bulk Elemental Composition on Venus

The extreme surface environment (462 C, 93 bars pressure) of Venus makes subsurface measurements of its bulk elemental composition extremely challenging. Instruments landed on the surface of Venus must be enclosed in a pressure vessel. The high surface temperatures also require a thermal control system to keep the instrumentation temperatures within their operational range for as long as possible. Since Venus surface probes can currently operate for only a few hours, it is crucial that the lander instrumentation be able to make statistically significant measurements in a short time. An instrument is described that can achieve such a measurement over a volume of thousands of cubic centimeters of material by using high energy penetrating neutron and gamma radiation. The instrument consists of a Pulsed Neutron Generator (PNG) and a Gamma-Ray Spectrometer (GRS). The PNG emits isotropic pulses of 14.1 MeV neutrons that penetrate the pressure vessel walls, the dense atmosphere and the surface rock. The neutrons induce nuclear reactions in the rock to produce gamma rays with energies specific to the element and nuclear process involved. Thus the energies of the detected gamma rays identify the elements present and their intensities provide the abundance of each element. The GRS spectra are analyzed to determine the Venus elemental composition from the spectral signature of individual major, minor, and trace radioactive elements. As a test of such an instrument, a Schlumberger Litho Scanner oil well logging tool was used in a series of experiments at NASA's Goddard Space Flight Center. The Litho Scanner tool was mounted above large (1.8 m x 1.8 m x.9 m) granite and basalt monuments and made a series of one-hour elemental composition measurements in a planar geometry more similar to a planetary lander measurement. Initial analysis of the results shows good agreement with target elemental assays

Venus↗
NASA NTRS2019

Elemental Variation and Petrogenesis of Pyroxenes in HED Meteorites by Multivariable Discriminant Analysis Method

HED (Howardite, Eucrite and Diogenite) are meteorites with mafic and ultramafic igneous composition. Previous studies suggested HED came from asteroid (4) Vesta and they were generated by magmatic melting followed by differentiation crystallization, metamorphic, and impact. Uniform oxygen isotopic composition of HED samples favors global magma ocean for (4) Vesta. However, the petrological diversity of HED may indicate more complex magma processes in the meteorites. In general, most of the geochemical studies are using traditional methods (e.g. element to element or ratio to ratio plots) to classify the different rock type and groups. With the traditional methods, only limited elements can be shown in a figure. As such, some meteorites may have been identified as HED by a traditional method but found different either in isotopic composition or other elemental characteristic. These anomalous HED meteorites may or may not come from asteroid (4) Vesta. In fact, magma is a unit system where any elemental change should affect to all other elements as a whole, it would be reasonable to consider all elements together to look for the systematical changes. Using multivariable discriminant analysis (MDA) method is one of such testing for their geochemical variation. The method may be able to help us to better understand the petrologic processes and the relationship among elements. This study is to test the MDA method by focus mainly on pyroxene composition of eucrite and diogenite.

Peng, Z. X.↗
NASA NTRS2017

Computationally Efficient Beam Elements for Accurate Stresses in Sandwich Laminates and Laminated Composites with Delaminations

Laminated composites are prone to delamination failure due to the lack of reinforcement through the thickness. Therefore, during the design process the initiation and propagation of delaminations should be accounted for as early as possible. This paper presents computationally efficient nine degree-of-freedom (dof) and eight-dof shear locking-free beam elements using the mixed form of the refined zigzag theory (RZT(sup(m))). The corresponding nine-dof and eight-dof elements use the anisoparametric and constrained anisoparametric interpolation schemes, respectively, to eliminate shear locking in slender beams. The advantage of the present element over previous RZT beam elements is that no post-processing is required to accurately model the transverse shear stress while maintaining the computational efficiency of a low-order beam element. Comparisons with high-fidelity finite element models and three-dimensional elasticity solutions show that the elements can robustly and accurately predict the displacement field, axial stress and transverse shear stress through the thickness of a sandwich beam or a composite laminate with an embedded delamination. In fact, the accuracy and computational efficiency of predicting stresses in laminates with embedded delaminations make the present elements attractive choices for RZT-based delamination initiation and propagation methodologies available in the literature.

R. M. J. Groh↗
NASA NTRSDate not supplied

Trace Elemental Abundances in Calcium-Aluminum-Rich Inclusions in CV Chondrites

Introduction: Calcium-aluminum-rich inclusions (CAIs), are the first formed solids that define the age of the Solar System [1,2]. CAIs are thought to have condensed from nebular gas [3,4] within the first <1 Ma of Solar System formation [5,6]. CAIs have experienced numerous early Solar System processes including condensation, evaporation, melting, recrystallization, and aqueous alteration [e.g., 7]. The chemical, mineralogical, and textural diversity among CAIs results from a range of chemical and physical processes recorded during nebular and parent body epoch. This study aims to explore the mineralogical, textural, and chemical compositions of CAIs including the trace elemental abundances in CAI phases to determine the early Solar System processes recorded in them. Samples and Analytical Methods: We analyzed one CAI each from CV3 chondrites Northwest Africa (NWA) 5508 designated as ‘Saguaro’, and Northwest Africa (NWA) 12772 designated as ‘Hoopoe’. Back-scatter electron (BSE) images were collected using a Phenom XL scanning electron microscope (SEM) at the Lunar and Planetary Institute (LPI) and the JEOL JXA-8530F electron probe microanalyzer (EPMA) at Johnson Space Center (JSC)-NASA. Additionally, energy dispersive X-ray spectrometry (EDS) elemental maps of select areas for these samples were collected using a 15.0kV beam energy and a 40µA emission current. Using the EPMA, wavelength-dispersive X-ray spectroscopy (WDS) quantitative data were collected. In-situ trace element measurements for both CAIs were determined at JSC-NASA using a Photon Machines 193nm laser ablation system and a Thermo-Scientific Element-XR inductively coupled plasma mass spectrometer (ICP-MS). Analyses consisted of 30s ablations at 10Hz, spot sizes of 20-25µm, and a fluence of 6.0 J/cm2 for anorthite and melilite, and a 3.5 J/cm2 fluence for all other phases. NIST612 was used to correct for instrument drift, while BHVO-2g was used as a primary calibration standard. BCR-2g and in-house mineral standards were regularly measured as unknowns to ensure accuracy. Results: Saguaro is a coarse-grained CAI, ~11 x 6 mm in dimensions. Saguaro contains spinel, Al-rich pyroxene, anorthite, Mg-rich melilite, and minor perovskite in its interior and is therefore classified as a Type B CAI. Individual melilite grains shows normal compositional zoning with an Ak content ranging from ~24 to 54 with no apparent trend from the core to the edge of the CAI. The spinel appears euhedral and occurs both as clusters and as spinel palisades [8]. Two rim sequences surround most of the sample: the inner rim being a Wark-Lovering (WL) rim (~10-35 µm) containing pyroxene, spinel, and melilite (or anorthite), and the outer rim is a finer-grained, thicker (~100 µm), accretionary rim (Fig. 1). The mineral phases in Saguaro record an overall flat REE pattern with an average negative Eu anomaly in pyroxene, and an average positive Eu anomaly in anorthite and melilite respectively. Anorthite, melilite, and pyroxene have a minor depletion in Tm (Fig. 2). The Hoopoe CAI is a compact, coarse-grained ~6 × 4 mm in size. The major mineralogy includes hibonite, spinel, melilite, anorthite, and perovskite. Therefore, it is classified as a compact transitional type A and B. (?)zoning was observed in some hibonites. Individual melilite grains show both reverse and normal zoning, where the Ak content ranges from ~6- to 28. Melilite shows two distinct textures. One texture consisted of smooth melilite that appeared homogenous, while the second appeared to consist of many fine fractures. The spinel also often appears clustered. The WL-rim sequence surrounding Hoopoe is ~25 µm thick and composed of spinel, perovskite, hibonite, and melilite/anorthite. It is then partially surrounded by an outer accretionary rim (~75µm). Like before, refractory metal nuggets appeared concentrated near the WL rims. Other metal assemblages rich in Fe and Ni were also observed. All major mineral phases in Hoopoe display relatively flat REE patterns, except for varying Eu and Tm between phases (Fig. 2). There is a prominent negative Eu anomaly in perovskite and an average positive Eu anomaly in spinel, anorthite, and hibonite respectively (Fig. 2, 3). The mixed phases along the rim of the CAI also display a negative Eu anomaly, and all phases the CAI were depleted in Pb. Discussion: The CV3 CAIs analyzed in this study were classified based on their mineralogy and textures into Type A versus Type B CAIs [10]. Hibonite appears to be pseudomorphically replacing the spinel, (i.e., is hibonite in composition, but appears in the shape of spinel). Spinel palisades. The presence of spinel palisades present in Saguaro are consistent with the melting and recrystallization experienced by this CAI. Trace elemental analyses. Saguaro and Hoopoe display similar trace element patterns to each other, with both appearing generally flat, with anomalies in Eu, and Tm. Melilite and anorthite display positive Eu anomalies in both CAIs, in addition to the hibonite in Hoopoe (Fig. 2). The phases that are depleted in Eu are pyroxene and perovskite in both Saguaro and Hoopoe, respectively (Fig. 3). Given that Eu is volatile in reducing environments [11], this could possibly indicate reducing conditions at the time anorthite and melilite crystallized, with the gas they formed from containing Eu. As these CAIs continued to form, this gas as a result would become depleted in Eu. This also could be supported by the propensity of anorthite and melilite to take up Eu from its surroundings and incorporate it into their structure [12]. In addition, analyzing the assemblage of the phases in the Saguaro, melilite and anorthite (Eu enriched) often surround the pyroxene (Eu depleted) as they are crystallized. This intergrowth of phases and the proximity of the phases would support that the Eu is being incorporated into some phases, preventing it from incorporating into other. Trace elemental analyses of the CAI rims will be evaluated in more detail, as they are complicated by the transient signal being composed of a mixture of mineral phases. Broadly, however, the patterns in the rims of both CAIs are comparable to each other, and for Hoopoe, to the mixed phase patterns in the core (Fig. 3). Other studies have found that CAI rims can be depleted in Ce and Yb [13], however we did not observe these anomalies in the two CAIs discussed here. Given their similarity, the trace elemental analyses of the mixed interior (i.e. core) and rim phases could be interpreted as forming from similar, if not the same, reservoirs. The REE abundance between the rim and core of Hoopoe are also similar, indicating they may have formed from a gas of the same or similar composition. Acknowledgments: We thank the ASU Center for Meteorite Studies for loaning the samples used in this work and Tabb Prissel for his assistance with the analysis. Mouti Al-Hashimi thanks Sam Crossley and Cyrena Goodrich for their help with the LPI SEM training. This work was supported by the LPI Summer Intern Program in Planetary Science and the LPI Cooperative Agreement. References: [1] Connelly J.N. (2012) Science, 338, 651-655. [2] MacPherson G. J. (2014) Treatise on Geochem., 2, 139-179. [3] Grossman L. (1972) GCA, 36, 597-619. [4] Ebel, D.S. (2006) Meteorites and the Early Solar System II (D. S. Lauretta & H. Y. McSween, Eds.) 253-277. [5] MacPherson G. J. (2012) Earth Planet. Sci. Lett., 331-332, 43-54. [6] MacPherson G.J. (2017) GCA, 201, 65-82. [7] Krot A.N. (1995) Meteoritics & Planet. Sci., 30, 748-775. [8] Wark and Lovering (1982) GCA, 46, 2595-2607. [9] Palme H. and Jones A. (2003) Treatise on Geochemistry (H. D. Holland and K. K. Turekian Eds.), 1, 41-61. [10] Grossman L. (1980) Ann. Rev. Earth Planet. Sci., 8, 559-608. [11] Floss C. et al. (1996) GCA, 60, 1975-1997. [12] Mason B. and Martin P. M. (1974) Earth Planet. Sci. Lett., 22, 141-144. [13] Wark B. and Boynton W. V. (2001) Meteoritics & Planet. Sci., 36, 1135-1166.

X Mouti↗
NASA NTRS2024

Bulk Major and Trace Elemental Composition of an Aggregate Sample From Asteroid Bennu

On September 24, 2023, NASA’s OSIRIS-REx mission returned a capsule to Earth carrying material from asteroid Bennu. This event was the first time a U.S. mission delivered pristine samples from an asteroid and is the largest asteroid sample return to date. As these samples represent some of the oldest, most primitive, and pristine materials available to us, and which originate from a known and well-studied asteroid, they allow us a rare opportunity to gain a better understanding of the formation and evolution of our solar system. Key to understanding the material returned from asteroid Bennu is establishing its bulk chemical composition. Previous studies have shown that each chondrite group has a distinct elemental composition. For the carbonaceous chondrites specifically, each group exhibits a distinct pattern of moderately and highly volatile elemental depletions, relative to CI chondrites. CI chondrites are considered the most primitive chondrite group and broadly represent the solar photosphere composition. The two most striking features of these depletion patterns is that the moderately volatile element depletions increase with decreasing 50% condensation temperature and then plateau out at abundances that roughly correlate with matrix abundance. Due to these distinctive patterns, bulk elemental composition has become an important classification tool for establishing the different chondrite groups and the connections between them. As such, determining the bulk chemical composition of the Bennu aggregates will help to test two mission hypothesis: “Bennu’s bulk elemental composition reflects that of its main parent asteroid and is similar to the composition of the Sun, with depletions in moderately to highly volatile elements” and “Bennu’s dominant lithologies are comparable in bulk mineralogy, petrology, and composition to the most aqueously altered carbonaceous chondrites” . Furthermore as the carbonaceous and non-carbonaceous chondrites are thought to have likely formed in the inner and outer protoplanetary disk, respectively (e.g., [8]), determining the bulk chemical compositions of the Bennu aggregates will also help test the major mission hypothesis that “Bennu's parent body formed beyond the snow line by accretion of material in the pro-toplanetary disk” . Regarding chondrite formation, observed elemental patterns have been successfully used to model how the mixing of volatile-rich and volatile-poor chondritic components can produce the observed carbonaceous chondrites groups. They have also been significant in investigating how volatilization processes influenced chondrite formation. As such, establishing bulk chemical compositions of the pristine Bennu samples is vital for understanding the asteroid, and solar system formation. To begin this processes, we analyzed the bulk major and trace elemental compositions of Bennu aggregates.

P Koefoed↗
NASA NTRS1972

Application of finite-element method in the computation of temperature with emphasis on radiative exchanges.

Analyses pertaining to the solution of heat transfer problems in combined modes based on the finite-element method are presented. Two elements - a triangular element employing two spatial variables and a multi-faceted bar element employing one spatial variable - with nonlinear radiation on the boundaries are detailed. The radiative effects considered on the diffuse-gray surface elements include: (1) directional radiant fluxes from distant sources, (2) radiative exchanges including surfaces of prescribed temperatures, and (3) radiative exchanges including elements whose temperatures are not known a priori. The nonlinear part of the boundary condition is treated in two different ways: (1) a consistent linearization method, and (2) a direct energy distribution method. Applications of these elements together with solution algorithms to three sample problems exhibit solution capability and obtainable accuracy.

Lee, H.-P.↗
NASA NTRS1973

Atmophilic elements in lunar soils

Ten volatile elements are more abundant in soil 14163 than in 14259 by factors of 1.4 or greater, too high to be explained by the 15% higher KREEP content of 14163. The enrichments suggest that these elements are easily volatilized by energetic events generated by solar particles or micrometeorites and as a result move from site to site through the lunar atmosphere. The elements Zn, C, and Cd are correlated with excess Ar-40 in Apollo 15 soils. Since concentrations also increase in the direction of the Apennine Front, the correlation chiefly indicates that the Front regolith is enriched in these elements relative to the Apollo 15 regolith away from the Front. The absence of known lunar rock types showing Zn and Cd concentrations as high as those in the Apollo 15 Front regolith or the Apollo 14 or 16 highlands regoliths and the relatively uniform concentrations of both elements in these soils despite differences in major element composition suggest that large amounts of these elements were released as volatiles during early lunar magmatic activity.

Chou, C.-L.↗
NASA NTRS1974

A correlation study of finite-element modeling for vibrations of composite material panels

A correlation study has been made to evaluate the effectiveness of finite-element modeling for vibrations of composite material panels. The three types of composite material panels studied were: (1) symmetrically laminated cross-ply panels, (2) unsymmetrically laminated cross-ply panels, and (3) a 1/6-scale sandwich wing model. Correlations of finite-element predictions for frequencies and vibration modes were made with Rayleigh-Ritz analyses and experimental data. For the symmetrically laminated panels, the finite-element representation predicted vibration modes very accurately. For the unsymmetrically laminated panels it was found that predictions using uncoupled finite-element plate bending elements did not give good agreement with experimental data. The constant-chord, swept-wing model was effectively analyzed by finite-element presentations using either sandwich elements or ribs and spars.

Thornton, E. A.↗
NASA NTRS1976

TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures

The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗
NASA NTRS1977

Finite-element methodology for thermal analysis of convectively cooled structures

A finite-element method for steady-state thermal analysis of convectively cooled structures is presented. The method is based on representing the coolant passages by finite elements with fluid bulk temperature nodes and fluid/structure interface modes. Four finite elements are described: two basic elements (mass transport and surface convection) and two integrated elements for applications to discrete tube and plate-fin convectively cooled structural configurations. Comparative finite-element and lumped-parameter thermal analyses of several convectively cooled structures demonstrate the practicality of utilizing finite-element methodology for thermal analysis of realistic convectively cooled structures.

Source record↗
NASA NTRS1978

A direct element resequencing procedure

Element by element frontal solution algorithms are utilized in many of the existing finite element codes. The overall computational efficiency of this type of procedure is directly related to the element data input sequence. Thus, it is important to have a pre-processor which will resequence these data so as to reduce the element wavefronts to be encountered in the solution algorithm. A direct element resequencing algorithm is detailed for reducing element wavefronts. It also generates computational by products that can be utilized in pre-front calculations and in various post-processors. Sample problems are presented and compared with other algorithms.

Akin, J. E.↗
NASA NTRS1980

TAP 2: A finite element program for thermal analysis of convectively cooled structures

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Thornton, E. A.↗
NASA NTRS1982

A finite element approach for shells of revolution with a local deviation

A finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of elements: rotational, general, and transitional shell elements. The rotational shell elements are used in the region where the shell is axisymmetric. The general shell element are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis. The form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated. The coupling of harmonic degrees of freedom due to the locally nonaxisymmetric geometry was studied. The use of a substructuring technique and separate partial harmonic analysis is recommended.

Han, K. J.↗
NASA NTRS1984

STARS: A general-purpose finite element computer program for analysis of engineering structures

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Gupta, K. K.↗
NASA NTRS1985

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Karlovitz, L. A.↗
NASA NTRS1986

Prediction of sound fields in cavities using boundary element methods

Two boundary element formulations of acoustical behavior exist; the Direct Boundary Element Methods (DBEM) based on the Helmholtz Integral Equations and the Indirect Boundary Element Methods (IBEM) based on Huygen's Principle. In this investigation, both methods are implemented utilizing a simple linear superparametric element. In addition the IBEM is studied using a quadratic isoparametric element. The accuracy and relative efficiency of the various techniques are examined. In order to properly model aircraft interior cavities the additional capability to model wall treatments and internal point sources is added to the methods. The procedures are verified for several well-understood cavity problems. The relative merits of each boundary element method and the finite element method are examined.

Bernhard, R. J.↗
NASA NTRS1987

A finite element computational method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.

Kim, Sang-Wook↗