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At least 1,405 records · Page 78

High-performance finite elements with MFEM

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. Furthermore, this paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED).

97 MATHEMATICS AND COMPUTING↗

Mathematical nuances of Gaussian process-driven autonomous experimentation

Abstract The fields of machine learning (ML) and artificial intelligence (AI) have transformed almost every aspect of science and engineering. The excitement for AI/ML methods is in large part due to their perceived novelty, as compared to traditional methods of statistics, computation, and applied mathematics. But clearly, all methods in ML have their foundations in mathematical theories, such as function approximation, uncertainty quantification, and function optimization. Autonomous experimentation is no exception; it is often formulated as a chain of off-the-shelf tools, organized in a closed loop, without emphasis on the intricacies of each algorithm involved. The uncomfortable truth is that the success of any ML endeavor, and this includes autonomous experimentation, strongly depends on the sophistication of the underlying mathematical methods and software that have to allow for enough flexibility to consider functions that are in agreement with particular physical theories. We have observed that standard off-the-shelf tools, used by many in the applied ML community, often hide the underlying complexities and therefore perform poorly. In this paper, we want to give a perspective on the intricate connections between mathematics and ML, with a focus on Gaussian process-driven autonomous experimentation. Although the Gaussian process is a powerful mathematical concept, it has to be implemented and customized correctly for optimal performance. We present several simple toy problems to explore these nuances and highlight the importance of mathematical and statistical rigor in autonomous experimentation and ML. One key takeaway is that ML is not, as many had hoped, a set of agnostic plug-and-play solvers for everyday scientific problems, but instead needs expertise and mastery to be applied successfully. Graphical abstract

97 MATHEMATICS AND COMPUTING↗

Predicting Critical Transitions in Multiscale Data

Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.

97 MATHEMATICS AND COMPUTING↗

Enabling Low-Temperature (LTP) Ignition Technologies for Multi-Mode Engines through the Development of a Validated High-Fidelity LTP Model for Predicative Simulations Tools

The goal of multi-mode engine architectures is to extend current lean-burn dilution limits with renewable fuels, which requires spark plugs to deposit high energies (hundreds of mJ) in order to initiate ignition and complete combustion. At elevated energy deposition rates, spark plugs experience increased electrode erosion and thermal losses, which ultimately shortens the spark-plug lifetime and lowers ignition efficiency. As such, in order to safeguard the efficiency gains of multi-mode concepts, new and improved ignition technologies are required. Recently, non-equilibrium low-temperature plasmas (LTP) have been shown to promote energy-efficient ignition via quenching and transport of electronically excited atoms and molecules, selective radical production and fast heating of hydrocarbon/air mixtures [1-2]. Thus, LTP is seen as a technology that can potentially improve the energy extraction efficiency of fuels, while enabling kinetically controlled combustion modes towards fuel leaner conditions to realize current DOE VTO goals of improving the sustainability of future mobility [3]. Although many previous studies have demonstrated the efficacy of plasma-assisted ignition to enhance combustion, the detailed enhancement mechanisms remain largely unknown, especially for oxygenated fuels and at elevated pressures that are most relevant to practical engine conditions. These barriers hinder the development of accurate and comprehensive numerical models that seek to describe LTP-based ignition in existing engine design software tools and methods. Current state-of-the-art simulation capabilities for LTP ignition systems are in need of improvements since they deliver qualitative results only due to important limitations of existing approaches. Firstly, validated kinetic models with elementary steps for plasma discharges in oxygenated fuel/air mixtures of relevance to the transportation sector are required. Such kinetic models do not exist at present and will be developed and validated within this project. Secondly, plasma discharges and reactive mixture ignition are multi-scale, unsteady processes requiring high-performance numerical methods and software that execute efficiently on DOE supercomputers. Such software does not exist at present and will be developed and applied to practical LTP ignition scenarios as part of this project. Thirdly, experimental databases that are tailored to serve as benchmark in support of the development of predictive computational models of LTP ignition do not exist and will be part of this project.

33 ADVANCED PROPULSION SYSTEMS↗

Ab Initio Design of High-Entropy Thermal/ Environmental Barrier Coatings

Next generation thermal/environmental barrier coatings (TEBC) require carefully balancing various properties including phase stability, thermal conductivity, coefficient of thermal expansion (CTE), mechanical properties, and resistance against hot corrosion and water vapor recession. This work mainly focuses on rapid design of cost-effective high entropy rare-earth disilicates and aluminum garnets to protect SiC-based ceramic matrix composites and nickel-based superalloys in the hot section of gas turbine engines using density functional theory methods. Our calculations identify several low-cost high entropy TEBC exhibiting ultralow thermal conductivity at 1500 K and desirable CTE while maintaining good mechanical properties, including Er1/2Y3/4Yb3/4Si2O7, Gd1/4Er1/4Y3/4Yb3/4Si2O7, Eu1/4Er1/4Y3/4Yb3/4Si2O7, and (Y1/4Gd1/4Er1/4Yb1/4)3Al5O12. This work also aims to gain fundamental understanding of oxygen diffusion in model disilicates. Minimizing oxidizer (such as water vapor and oxygen) permeability through the EBC layer can significantly decrease the growth rate of thermally grown oxide and extend the service life of the coating system. Oxygen diffusion mechanisms including formation energy of defects under varying oxygen conditions and defect migration energy barriers will be presented.

coefficient of thermal expansion↗

Scramjet nozzle design and analysis as applied to a highly integrated hypersonic research airplane

The configuration and performance of the propulsion system for the hypersonic research vehicle are discussed. A study of the interactions between propulsion and aerodynamics of the highly integrated vehicle was conducted. The hypersonic research vehicle is configured to test the technology of structural and thermal protection systems concepts and the operation of the propulsion system under true flight conditions for most of the hypersonic flight regime. The subjects considered are: (1) research vehicle and scramjet engine configurations to determine fundamental engine sizing constraints, (2) analytical methods for computing airframe and propulsion system components, and (3) characteristics of a candidate nozzle to investigate vehicle stability and acceleration performance.

Small, W. J.↗

Flight effects on exhaust noise for turbojet and turbofan engines: Comparison of experimental data with prediction

It was demonstrated that static and in flight jet engine exhaust noise can be predicted with reasonable accuracy when the multiple source nature of the problem is taken into account. Jet mixing noise was predicted from the interim prediction method. Provisional methods of estimating internally generated noise and shock noise flight effects were used, based partly on existing prediction methods and partly on recent reported engine data.

Stone, J. R.↗

Investigation of refracting flows for acoustic suppression

An experimental investigation to determine the possibility of using refracting flows for the suppression of aircraft inlet noise is described. Observations of wave refraction in duct flows and measurements of the increase in effectiveness of acoustic linings due to refraction have suggested methods for the design of engine inlet ducts which can either suppress noise internally or direct it to where it causes less annoyance.

Sloan, D.↗

Predicting lifetime of cast parts

Life expectancy of cast aluminum machine parts can be predicted accurately from fatigue tests at 78 K on notched specimens of aluminum alloy. Method was developed for rocket engine turbopump parts made of high strength, heat treatable alloy with high silicon content; however, technique is applicable to other aluminum casting alloys.

Cooper, R. A.↗

Integrated analysis of large space systems

Based on the belief that actual flight hardware development of large space systems will necessitate a formalized method of integrating the various engineering discipline analyses, an efficient highly user oriented software system capable of performing interdisciplinary design analyses with tolerable solution turnaround time is planned Specific analysis capability goals were set forth with initial emphasis given to sequential and quasi-static thermal/structural analysis and fully coupled structural/control system analysis. Subsequently, the IAC would be expanded to include a fully coupled thermal/structural/control system, electromagnetic radiation, and optical performance analyses.

Young, J. P.↗

Rapid approximate determination of nonlinear solutions - Application to aerodynamic flows and design/optimization problems

Stahara et al. (1978) have considered the use of an approximation technique which employs two or more nonlinear base solutions determined by the full computational method to predict entire families of related nonlinear solutions. The present investigation provides results for several applications of that method which demonstrate both its accuracy and its utility for engineering applications. Attention is given to the perturbation concept and methods, aspects of coordinate straining, aspects of analytical formulation, and an application to surface properties. In a discussion of the results, single and multiple parameter perturbations are considered along with a combination of the approximation method with optimization procedures. The results show that it is possible to combine in certain cases large savings in computational cost with improved optimization.

Stahara, S. S.↗

Mechanics of conducting a task analysis

Task analysis (TA) which is a set of analytical procedures used to describe human work in terms of tasks is discussed. The method of TA was derived from various techniques of methods analysis of the industrial engineers. The topic of TA is organized around the following main areas: (1) a detailed discussion of what a TA is; (2) the uses of TA; (3) evaluation of the TA procedure and an assessment of the procedure's worth.

Rappold, V.↗

Windmilling of the rotor of a turbojet engine with an axial-flow compressor under flight conditions

The concept of rotor windmilling is understood to mean rotation of the rotor caused solely by the energy of the air (not gas) streaming through the apertures between the blades (under conditions of power shut-off) under the action of dynamic pressure. The concept of windmilling is analyzed for an engine with an axial-flow compressor, showing that windmilling must be taken into account in such cases as in-flight reignition of the engine. A graph-analytic method for determining the range of windmilling is proposed.

Borgon, J.↗

Lewis Research Center spin rig and its use in vibration analysis of rotating systems

The Lewis Research Center spin rig was constructed to provide experimental evaluation of analysis methods developed under the NASA Engine Structural Dynamics Program. Rotors up to 51 cm (20 in.) in diameter can be spun to 16,000 rpm in vacuum by an air motor. Vibration forcing functions are provided by shakers that apply oscillatory axial forces or transverse moments to the shaft, by a natural whirling of the shaft, and by an air jet. Blade vibration is detected by strain gages and optical blade-tip motion sensors. A variety of analogy and digital processing equipment is used to display and analyze the signals. Results obtained from two rotors are discussed. A 56-blade compressor disk was used to check proper operation of the entire spin rig system. A special two-blade rotor was designed and used to hold flat and twisted plates at various setting and sweep angles. Accurate Southwell coefficients have been obtained for several modes of a flat plate oriented parallel to the plane of rotation.

Brown, G. V.↗

Geometrically nonlinear analysis of laminated elastic structures

Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.

Reddy, J. N.↗