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At least 541 records · Page 30

Ceramic Heat Pipe for Thermal Management of a High Frequency Inductor

As the power density of electric machines and power electronics continues to increase to meet the demands of more electric aircraft, the thermal management of these devices becomes increasingly important. Ideally, the thermal management solution of the device should have high thermal conductivity and be electrically insulating so that it can be directly integrated with the device in question. Technical ceramics are a class of materials that meet these two requirements. Direct liquid cooling by submerging electric components in a dielectric fluid is an alternate option, but adds system complexity and may incur pumping loss. In this work, the thermal management solution for a high frequency inductor is presented. A conventional wicked heat pipe is designed that is made from a solid ceramic case with a sintered ceramic wick. This heat pipe can provide structural support for the core and windings and is electrically insulating, so it does not incur any additional eddy current losses from the high frequency magnetic fields. It does not require additional pumping power, because conventional wicked heat pipes are passive devices. In this paper, the manufacturing process of the ceramic heat pipe is also presented. It is shown that the sintering of large diameter spherical ceramic particles is difficult due to their high specific surface area and low surface free energy. To overcome this difficulty, a flux material was used to initiate liquid phase sintering. The results of the sintering trials show that for the 120 μm diameter α-Al2O3 powder selected for the wick, the combination of 1650°C sintering temperature and the addition of 5 wt% talc sintered the porous matrix together sufficiently for use as a heat pipe wick.

High frequency inductor↗

Flow Boiling and Condensation Experiment (FBCE): Summary of Findings for Flow Boiling based on Completed ISS Experiments

Since 2011, researchers from Purdue University and NASA Glenn Research Center (GRC) have been collaborating to investigate the effects of gravity on several aspects of flow boiling and flow condensation. This massive research endeavor, termed the Flow Boiling and Condensation Experiment (FBCE), has culminated in development of NASA’s largest and most complex facility for investigation of two-phase fluid physics onboard the ISS. FBCE consists of two separate studies: flow boiling, using the Flow Boiling Module (FBM), and flow condensation, using the Condensation Module for Heat Transfer Measurements (CM-HT); this presentation concerns the FBM portion of FBCE. Fitted with FBM, FBCE was launched to the ISS in August 2021 and experiments were successfully performed starting in February 2022 to amass a large microgravity-flow-boiling database supported by extensive visualization of interfacial behavior using high-speed video. Based on FBCE experiments performed previously in Earth gravity and parabolic flight, along with the new ISS data, several empirical correlations, theoretical models, and CFD models have been developed, enabling the prediction of crucial flow boiling parameters, including heat transfer coefficient and critical heat flux (CHF). These predictive tools, which will be summarized in this presentation, are expected to serve as foundation for design of future space systems involving flow boiling.

Two-phase flow and phase transition↗

Flow Boiling and Condensation Experiment (FBCE): Latest Findings from the Summary ISS Experiments

Since 2011, researchers from Purdue University and NASA Glenn Research Center (GRC) have been collaborating to investigate the effects of gravity on several aspects of flow boiling and flow condensation. This massive research endeavor, termed the Flow Boiling and Condensation Experiment (FBCE), has culminated in development of NASA’s largest and most complex facility for investigation of two-phase fluid physics onboard the ISS. FBCE consists of two separate studies: flow boiling, using the Flow Boiling Module (FBM), and flow condensation, using the Condensation Module for Heat Transfer Measurements (CM-HT); the FBM experiments have already been completed while the condensation experiments began in 2024. This presentation will summarize mostly new results from the flow boiling experiments, with a focus on analysis of pressure drop and two-phase flow instabilities in microgravity using both experimental data and video records from the ISS experiments, as well as development of machine learning models. These new predictive tools are part of the arsenal of predictive methods developed by the Purdue-Glenn team for design of future space systems.

Microgravity↗

Simulation study of chemo-mechanical impacts of CO 2 injection in morrow b sandstone reservoir

Here, this study investigates the impacts of geomechanical and geochemical changes on carbon storage in a partially depleted oil reservoir, using results from four different coupled simulation models. Models were used to examine the relative importance of storage mechanisms, and how changing reservoir parameters might affect these mechanisms through time. The study uses data from a Morrowan sandstone reservoir in the Farnsworth Unit (FWU), Ochiltree County, Texas which is currently undergoing CO 2 enhanced oil recovery (EOR). Partially depleted oil reservoirs such as the FWU offer attractive carbon utilization and/or storage targets because of existing infrastructure and economic benefits from incremental oil recovery as well as tax credits. However, prediction of storage capacity or long-term fluid migration in these fields can be difficult because of the wide variation in formation fluids and operational histories that may have undergone. CO 2 injection can cause complex geomechanical and geochemical responses in a reservoir as a result of interplay between dynamic changes in pore pressure, reservoir temperature, fluid composition, and interactions between formation fluids, CO 2 , and reservoir rock. Thus, multiple coupled numerical simulation models must be developed and used to more precisely understand what CO 2 storage mechanisms are most significant, as well as the long-term fate of the stored CO 2 . Our study used results from hydrodynamic, coupled hydro-geomechanical, coupled hydro-geochemical, and coupled hydro-geomechanical-geochemical models to examine how changes in geomechanical and geochemical properties can impact the injectivity or storage capacity of CO 2 . Models simulated historical field operations and then forward-modeled a water-alternate-gas (WAG) operation for 20 years, followed by a 1000-year post-injection monitoring. The work demonstrates that in this specific reservoir, geomechanical impacts appear to be more significant than any geochemical processes, which showed minimal impact on reservoir properties. Furthermore, these simulation scenarios corroborated other studies showing more than 90% of CO 2 injected are being stored and will remain stored in the reservoir. The study was able to draw on a rich set of data from this currently operational project for the work. Because the Morrow is a widespread oil-bearing reservoir in the midcontinent of the United States and is fairly typical of many sandstone reservoirs elsewhere, the study has significance beyond the boundaries of our field area.

58 GEOSCIENCES↗

The Geology of The Mt. Simon Sandstone Storage Complex at the Wabash #1 Well, Vigo Co., Indiana (Subtask 7.2, Technical Report)

The Wabash CarbonSAFE project drilled the Wabash #1 stratigraphic test well (ID# 168045) at the Wabash Valley Resources (WVR) IGCC facility in Vigo County, Indiana, to characterize and evaluate the basal Cambrian Mt. Simon Sandstone for commercial-scale CO 2 storage near the site. This report presents an extensive geologic characterization of the Mt. Simon storage complex and relevant data collected from the Wabash #1 well, such as lithologic data collected from cuttings and core, geophysical logging, geomechanical analysis of core samples, and well testing and fluid sampling within the Mt. Simon Sandstone. The Mt. Simon storage complex comprises two major sections: the Mt. Simon Sandstone as the potential reservoir and the overlying Eau Claire Formation as its primary seal. Within the report, an extensive depositional, sedimentological, and geochronologic characterization of the Mt. Simon is included with supportive chapters on the regional geology and the geophysical, petrophysical, and petrologic data collected during the project. An overview of 2D seismic reflection data collected from and around the test well is presented. Also presented are chapters on the characterization of the sealing Eau Claire Formation, including a chapter on the capacity of the primary and secondary seals to the Mt. Simon as well as a chapter on geomechanical testing results of the Eau Claire Formation and Mt. Simon Sandstone. Some of the information discussed in this report was used in the development of static and dynamic geologic models of the Mt. Simon Sandstone storage complex. The static and dynamic modeling of CO 2 injection in the Mt. Simon Sandstone are discussed in a separate report (Dessenberger et al., 2022) under the Wabash CarbonSAFE project.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

TOUGH-RFPA: Coupled thermal-hydraulic-mechanical Rock Failure Process Analysis with application to deep geothermal wells

This paper presents a coupled thermal-hydraulic-mechanical (THM) model for simulating failure processes in geological media. The coupling between stress/strain and heat transfer describing how thermal expansion affects stress is based on the theory of thermo-elasticity. Additionally, the coupling between stress/strain and fluid flow describing how pore-pressure affects stress is governed by Biot's consolidation theory. Stress/strain-dependent porosity/permeability/capillary-pressure defines the influence of stress on fluid flow and thermal fields. The THM model is implemented in the solver module that links the multiphase, multicomponent fluid flow simulator TOUGH2 with the geomechanical simulator RFPA (Rock Failure Process Analysis), which is based on the concept that heterogeneity leads to non-linearity and progressive failure behavior. Capability of TOUGH-RFPA simulator was verified by two benchmark problems related to hydraulic-mechanical and thermal-mechanical response in a hollow cylinder. Then the applicability of TOUGH-RFPA was demonstrated for modeling cooling-induced damage around a very deep geothermal well with mesoscopic heterogeneous properties, which showed complex damage evolution and fracturing during well cooling and fluid pressurization.

42 ENGINEERING↗

Probing multiscale dissolution dynamics in natural rocks through microfluidics and compositional analysis

Mineral dissolution significantly impacts many geological systems. Carbon released by diagenesis, carbon sequestration, and acid injection are examples where geochemical reactions, fluid flow, and solute transport are strongly coupled. The complexity in these systems involves interplay between various mechanisms that operate at timescales ranging from microseconds to years. Current experimental techniques characterize dissolution processes using static images that are acquired with long measurement times and/or low spatial resolution. These limitations prevent direct observation of how dissolution reactions progress within an intact rock with spatially heterogeneous mineralogy and morphology. We utilize microfluidic cells embedded with thin rock samples to visualize dissolution with significant temporal resolution (100 ms) in a large observation window (3 × 3 mm). Here we injected acidic fluid into eight shale samples ranging from 8 to 86 wt % carbonate. The pre- and postreaction microstructures are characterized at the scale of pores (0.1 to 1 µm) and fractures (1 to 1,000 µm). We observe that nonreactive particle exposure, fracture morphology, and loss of rock strength are strongly dependent on both the relative volume of reactive grains and their distribution. Time-resolved images of the rock unveil the spatiotemporal dynamics of dissolution, including two-phase flow effects in real time and illustrate the changes in the fracture interface across the range of compositions. Moreover, the dynamical data provide an approach for characterizing reactivity parameters of natural heterogeneous samples when porous media effects are not negligible. The platform and workflow provide real-time characterization of geochemical reactions and inform various subsurface engineering processes.

58 GEOSCIENCES↗

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics. The focus here is on those methods particularly well- suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid computational fluid dynamics algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid computational fluid dynamics in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, Perry A.↗

Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.

58 GEOSCIENCES↗

Unsteady Three-Dimensional Simulation of a Shear Coaxial GO2/GH2 Rocket Injector with RANS and Hybrid-RAN-LES/DES Using Flamelet Models

Historically, the analysis and design of liquid rocket engines (LREs) has relied on full‐scale testing and one‐dimensional empirical tools. The testing is extremely expensive and the one‐dimensional tools are not designed to capture the highly complex, and multi‐dimensional features that are inherent to LREs. Recent advances in computational fluid dynamics (CFD) tools have made it possible to predict liquid rocket engine performance, stability, to assess the effect of complex flow features, and to evaluate injector‐driven thermal environments, to mitigate the cost of testing. Extensive efforts to verify and validate these CFD tools have been conducted, to provide confidence for using them during the design cycle. Previous validation efforts have documented comparisons of predicted heat flux thermal environments with test data for a single element gaseous oxygen (GO2) and gaseous hydrogen (GH2) injector. The most notable validation effort was a comprehensive validation effort conducted by Tucker et al. [1], in which a number of different groups modeled a GO2/GH2 single element configuration by Pal et al [2]. The tools used for this validation comparison employed a range of algorithms, from both steady and unsteady Reynolds Averaged Navier‐Stokes (U/RANS) calculations, large‐eddy simulations (LES), detached eddy simulations (DES), and various combinations. A more recent effort by Thakur et al. [3] focused on using a state‐of‐the‐art CFD simulation tool, Loci/STREAM, on a two‐dimensional grid. Loci/STREAM was chosen because it has a unique, very efficient flamelet parameterization of combustion reactions that are too computationally expensive to simulate with conventional finite‐rate chemistry calculations. The current effort focuses on further advancement of validation efforts, again using the Loci/STREAM tool with the flamelet parameterization, but this time with a three‐dimensional grid. Comparisons to the Pal et al. heat flux data will be made for both RANS and Hybrid RANSLES/ Detached Eddy simulations (DES). Computation costs will be reported, along with comparison of accuracy and cost to much less expensive two‐dimensional RANS simulations of the same geometry.

Westra, Doug G.↗

Intermediate Temperature Proton‐Conducting Solid Oxide Electrolysis Cells with Improved Performance and Durability

Technical understanding: A high-performance and stable intermediate temperature proton-conducting solid oxide electrolysis cell (PCEC) will add significantly to the hydrogen roadmap of EERE. However, the low electrocatalytic activity of the air electrode and the instability of the electrolyte are technical barriers. In this research, we utilized computational fluid dynamic modeling and materials/microstructure engineering to investigate the complex reaction chain and to improve the performance and reliability of the protonic ceramic electrochemical cells. An active and stable Pr 1.8 Ba 0.2 NiO 4+δ -BaZr 0.1 Ce 0.7 Y 0.1 Yb 0.1 O 3-δ (BZCYYb) scaffold conformal coating electrode was rationally designed where the robust Pr 1.8 Ba 0.2 NiO 4+δ functions both as a catalytic active and a protective layer. The PCECs with porosity-optimized scaffold conformal coating electrodes demonstrate 1.46 Acm -2 under 1.3 V at 600°C, which is among the highest in recent years. The final optimization by computational fluid dynamic modeling and conformal coating technique was applied to evolve the PCEC air electrode from Pr 2 NiO 4+δ to Pr 1.8 Ba 0.2 NiO 4+δ -BaZr 0.1 Ce 0.7 Y 0.1 Yb 0.1 O 3-δ scaffold conformal coating. The electrolysis current was boosted from 0.445A/cm 2 to 1.46A/cm 2 at 600°C and 1.3V. A superior low degradation rate of 1mV/kh was achieved in a 5000-hour of operation. Technical effectiveness and economic feasibility: The effectiveness of this TCO conformal coating on electrolyte backbone as air electrode has been proven by long-term demonstration. Based on the highly conductive BZCYYb electrolyte and the TCO steam electrode PNO, this project rationally took advantage of the existent materials to structure a PCEC device with high TRL and low risk. The solution infiltration method used to structure the conformal coating is a standard method used by the solid oxide cell community. Very minimal adoption is needed in the current SOC fabrication process. It is a cost-effective, scalable method for manufacturing, and brings up remarkable impact on the current technical status of PCEC. Benefit to the public: The findings in the research showed the industry that the severe challenge in PCEC can be overcome in a practical way. A various energy-hydrogen ecosystem is not beyond reach. The success of this technology provides sustainable and affordable H 2 to society. It will stimulate investment from the governmental and private sectors in response to the device manufacture and deployment, and the related infrastructure construction. It will generate high-pay domestic jobs and environmental benefits to the general public in the United States.

08 HYDROGEN↗

Wind Farm Simulation and Layout Optimization in Complex Terrain: Preprint

This work reports on incorporating complex terrain into wind farm simulations for the purpose of layout optimization. Adding complex terrain boundary conditions to NREL's medium fidelity computational fluid dynamics model, WindSE, produces significant separation, flow curvature, and speedup effects that would otherwise be difficult to capture with lower-fidelity models or a flat-terrain assumption. These flow features, in turn, can significantly impact the optimal turbine array layout. We demonstrate the impact of complex terrain on flow in both an idealized and real-world setting, and discuss modifications to the code that enable gradient-based optimization using terrain-aware adjoint gradients. Through several optimization case studies, we show that the layout optimization process takes advantage of speedup effects on terrain high points, and leverages flow curvature effects that modify wake trajectories. This yields substantial power improvements over gridded layouts, and hints at future research directions in simulation and optimization for wake trajectories in complex terrain.

17 WIND ENERGY↗

Analysis and representation of complex structures in separated flows

We discuss our recent work on extraction and visualization of topological information in separated fluid flow data sets. As with scene analysis, an abstract representation of a large data set can greatly facilitate the understanding of complex, high-level structures. When studying flow topology, such a representation can be produced by locating and characterizing critical points in the velocity field and generating the associated stream surfaces. In 3D flows, the surface topology serves as the starting point. The 2D tangential velocity field near the surface of the body is examined for critical points. The tangential velocity field is integrated out along the principal directions of certain classes of critical points to produce curves depicting the topology of the flow near the body. The points and curves are linked to form a skeleton representing the 2D vector field topology. This skeleton provides a basis for analyzing the 3D structures associated with the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations. Integration origins are successively refined to produce stream surfaces. The map of the global topology is completed by generating those stream surfaces associated with 3D critical points.

Helman, James↗

Continued Verification of MOOSE Structural Mechanics Tools for Modeling Core Bowing Phenomena in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY22, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21. Several benchmark verification examples were selected from the IAEA verification and validation report. These examples involve clusters of ducts representative of a sector of a hexagonal reactor core which bow into each other and cause contact and load pad elevations, as well as single ducts subjected to irradiation fields undergoing swelling and subsequent bowing. The MOOSE-based results were compared to both IAEA benchmark participants’ results, analytic equations as available, and NUBOW-3D, a beam model code developed by Argonne National Laboratory. In every case, the MOOSE results agreed with other simulations results, providing additional verification basis of the tools for this particular physics application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FY23 Status Report on MOOSE-Based Approaches to Modeling Core Bowing in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY23, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21 and FY22. Several benchmark verification examples were selected from the IAEA verification and validation report with increased number of ducts and more complex contact interaction behavior. These examples involve a full symmetric sector with restraint rings at multiple load pad locations to simulate a limited free-bow restraint system concept, as well as irradiation induced swelling and creep effects in a sector. In addition, improvements to the contact module sideset assignment were assessed and compared with previous MOOSE results to verify the contact behavior. The MOOSE-based results were compared to IAEA benchmark participants’ results. In every case, the MOOSE results agreed with other simulations results for estimating bowing behavior, providing additional verification basis of the tools for this particular physics application. Estimation of contact forces were mostly in agreement, with a few outlier results. A plan was suggested for dealing with the discrepancies with estimating contact force values. In addition, a 1-way coupling demonstration was performed using subchannel analysis code Pronghorn-SC and MOOSE on an ABR-1000-design sodium-cooled fast reactor assembly to evaluate coolant and duct wall temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Extrusion of Complex Surface Meshes Utilizing Face Offsetting and Mean Curvature Smoothing

Grids for three-dimensional Computational Fluid Dynamics problems frequently require a prismatic layer of cells, typically extruded in the off-body direction from a two-dimensional surface mesh to properly resolve boundary layers. When the surface geometry is complex, the extrusion process can fail, resulting in the physical boundary layer being thicker than the prismatic layer, leading to under-resolved boundary layers. To address the shortcomings of existing grid generation tools, a new tool has been developed as part of the Mesh Tools suite, that is capable of extruding complex surface meshes. The new tool uses a face offsetting method to preserve surface curvature and a mean curvature smoothing algorithm to prevent the cells from self-intersecting in concave regions. Testing of the new tool found that not only were complex surface meshes able to be extruded to the desired thickness, but extrusion of simple surface meshes was also improved, due to the face offsetting method.

mesh extrusion↗

Catalytic resonance theory: Circumfluence of programmable catalytic loops

Chemical reactions on heterogeneous catalyst surfaces exhibit complex networks of elementary reactions with multiple pathways to fluid phase products, sometimes leading to surface reaction loops consisting of a closed cycle reaction pathway. While conventional catalysts at steady state exhibit zero net flux in either direction around a catalytic loop, the loop turnover frequency of three-species surface loops was evaluated in this work via microkinetic modeling to assess the reaction loop behavior resulting from a catalytic surface oscillating between two or more surface energy states. For dynamic heterogeneous catalysts undergoing applied oscillations of surface energy (i.e., programs), surface reaction loops of three species were shown to exhibit non-zero net flow of molecules around the loop, with the extent of loop turnover frequency varying with the applied frequency and amplitude of a sinusoidal or square wave oscillation. Alternatively, some dynamic surface reactions exhibited oscillations only between two surface species or resulted in surfaces covered by a single species at all times. Here, more complex behavior was observed for dynamic surface programs of three distinct electronic states, with the temporal order of applied states controlling the direction of flow of molecules within a three-molecule surface loop. Catalytic loops have the potential to limit overall catalytic reaction rates and use energy in programmable catalysts, while some applications could purposely impose non-zero loop turnover frequency for improved surface reaction control.

Catalysis↗

B-spline Method in Fluid Dynamics

B-spline functions are bases for piecewise polynomials that possess attractive properties for complex flow simulations : they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, and yield numerical schemes with high resolving power, where the order of accuracy is a mere input parameter. This paper reviews the progress made on the development and application of B-spline numerical methods to computational fluid dynamics problems. Basic B-spline approximation properties is investigated, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards efficient complex geometry spline methods are covered, such as local interpolation methods, fast solution algorithms on cartesian grid, non-conformal block-structured discretization, formulation of spline bases of higher continuity over triangulation, and treatment of pressure oscillations in Navier-Stokes equations. Application of some of these techniques to the computation of viscous incompressible flows is presented.

Botella, Olivier↗