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Sensitivity analysis of a layered piezoelectric system using ZFEM
The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .
Verification of a Viscous Computational Aeroacoustics Code Using External Verification Analysis
The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.
Verification of a Viscous Computational Aeroacoustics Code using External Verification Analysis
The External Verification Analysis approach to code verification is extended to solve the three-dimensional Navier-Stokes equations with constant properties, and is used to verify a high-order computational aeroacoustics (CAA) code. After a brief review of the relevant literature, the details of the EVA approach are presented and compared to the similar Method of Manufactured Solutions (MMS). Pseudocode representations of EVA's algorithms are included, along with the recurrence relations needed to construct the EVA solution. The code verification results show that EVA was able to convincingly verify a high-order, viscous CAA code without the addition of MMS-style source terms, or any other modifications to the code.
Supporting Crew Autonomy in Deep Space Exploration: Preliminary Onboard Capability Requirements and Proposed Research Questions. Technical Report of the Autonomous Crew Operations Technical Interchange Meeting
Communication delays are a critical challenge posed by long duration deep space exploration. Space missions historically have relied on an ever-present Mission Control Center (MCC) to direct operations in near real-time. As unanticipated anomalies that defeat fault detection and resolution systems do arise, the lack of real-time communication will significantly weaken what the MCC support represents: a reliable safety net for the flight crew through its deep and diverse areas of expertise and investigative resources. As a consequence, future space vehicles and habitats need to be equipped with capabilities to support the flight crew to operate with little or no ground support. Considerations must be given to vehicle and mission designs that will fortify the traditionally ground-centered safety net and forge new support systems, when communication delays exist. In August 2018, NASA’s Human Research Program, through its Human Factors and Behavioral Performance Element, convened a Technical Interchange Meeting (TIM) on Autonomous Crew Operations at NASA Ames Research Center. The goal of the meeting was to gather input from NASA centers, industry, academia, and branches of the Department of Defense (DoD) to address how intelligent technologies can be applied to augment onboard capabilities to support crew anomaly response. The TIM featured 24 presentations by 29 speakers and hosted a total of 59 attendees, including 43 from 5 NASA centers (Ames, Johnson, Langley, Marshall, and Jet Propulsion Lab) and 4 from the DoD (3 from Army Research Lab and 1 from Naval Postgraduate School), with remaining attendees from academia (e.g., UC Davis, CMU) and industry (e.g., IBM, Siemens). Discussions were centered around three themes: standards and guidelines, lessons learned in analog environments, and technologies. To help provide a framework for discussion, a concept matrix describing anomaly response processes was created prior to the TIM (Figure 1, page 6). The matrix captures the steps involved (monitoring and detection, diagnosis, solution development and evaluation, solution implementation and verification, resolution documentation) as well as the resources and capabilities required to support these steps (data, knowledge, analysis, synthesis, resource management). A wallpaper size printout of the matrix was utilized at the TIM to solicit attendee inputs along the three themes; the activity garnered 108 submissions of ideas. Overall, what emerged from TIM discussions was a picture of mismatch between crew anomaly response needs and support that can be provided by existing intelligent technologies. The needs are broad, spanning multiple steps and processes/resources, with many of which lacking support from existing technologies, such as knowledge management throughout the steps of problem solving (especially in resolution documentation) and manpower management. The solutions provided by existing intelligent technologies are specific to the steps/processes that they are designed to support and constrained to solving only problems similar to those that have occurred before. What is lacking from technologies is typically made up by humans, specifically their complex critical thinking, creative problem solving, and domain expertise. In the end, the TIM highlighted the pressing need to support responses to onboard anomalies during autonomous crew operations, particularly those that have eluded the system tests, inspection, and other assurance processes. Such anomalies can potentially threaten crew and vehicle safety, as well as significantly impact overall operations with additional workload. These fairly rare events are difficult to anticipate and prepare for, given the state-of-the-art in intelligent technologies. This is true even for anomalies that stem from “unknown knowns”—cases in which there is sufficient external information to characterize the problem but the overall pattern fails to be recognized by the problem solver, or in which the internal knowledge needed to solve a problem is held tacitly and potentially accessible by the problem solver but not articulated. It follows that the ability to tackle anomalies lies not only with the availability of relevant information and knowledge but also their accessibility in times of need. To that end, we propose research questions along the following three broad themes: • How intelligent technologies can help make relevant knowledge and information available? • How intelligent technologies can help make relevant knowledge and information accessible? • How intelligent technologies can help support the crew operating as a team in anomaly response processes?
Semi-analytic solutions to the Noh problem with a black box EoS
The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.
Verification of the REBUS Software
Ongoing design activities at Argonne National Laboratory are requiring a thorough verification of the Argonne Reactor Computation codes be performed. REBUS is central to this system. The driver for this effort requires the Triangular-Z and hexagonal-Z core geometry options of REBUS to be verified. Previous work identified the REBUS features required to be verified to support current design activities, features of which are generally applicable to hexagonal-Z fast reactor designs. The scope of this verification effort includes verifying REBUS’s ability to correctly intepret the user input model, verifying that the features identified yield the intended results, and verifying the correctness of the REBUS output tables. The REBUS software verification relies heavily upon the accuracy of the embedded DIF3D software, the verification of which was completed and documented elsewhere. Given that DIF3D produces an accurate solution, the primary focus of the verification in the REBUS software is to ensure that it properly uses the DIF3D solution and that the depletion system (Bateman equations) are correctly implemented. This manuscript reiterates the verification tasks and displays results with respect to the features needed for current design activities. Analytic solutions of the Batemen equations are displayed and the results calculated with REBUS are displayed demonstrating the accuracy. Since coupled Bateman and neutron diffusion/transport solutions are extremely difficult to obtain, much of the focus is placed on how REBUS uses a given DIF3D solution assuming the accuracy of the DIF3D solution. The verification effort identified no issues that are debilitating or otherwise impactful to the design usage of REBUS, and thus REBUS version 11.0, release 3012 is considered verified. It is important to note that several outputs of REBUS are identified to be inaccurate, such as burnup in MWD/MT. Most of the relevant ones for VTR are generally accurate with 10-20% errors which is not impactful as all regular REBUS users are aware of this issue and know how to hand calculate the results. The REBUS manual further makes it clear that these values are consistent with the methodology being used by REBUS and thus the “errors” are more of an inconsistent definition with respect to what a user would expect given a definition in literature. Other issues that were identified included unclear documentation and software bugs all of which were inconsequential to the final results.
Quantum protocol for decision making and verifying truthfulness among N ‐quantum parties: Solution and extension of the quantum coin flipping game
Abstract The authors devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has particular relevance in a modified version of the quantum coin flipping game. The key innovation of the authors’ work includes the new design of a quantum coin that excludes any advantage of cheating, by which the long‐standing problem of the fair design of the game is, affirmatively, solved. Furthermore, the analysis is extended to N ‐parties communicating with each other, where multiple solutions for the verification of each player's measurement is proposed. The results in the N ‐party scenario could have particular relevance for the implementation of future quantum networks, where verification of quantum information is a necessity.
Space station MSFC-DPD-235/DR no. CM-03 specification, modular space station project, Part 1 CEI
Contract engineering item specifications for the modular space station are presented. These specifications resulted from the development and allocations of requirements which are concise statements of performance or constraints on performance. Specifications contain requirements for functional performance and for the verification of design solutions.
Transonic flow over wing/fuselage configurations
Wing Body Code (WIBCO) program simulates flow-field configurations for reduction of design cost and improvement of aircraft performance. Inputs to WIBCO consist of ambient flow conditions and geometric configuration data; grid control and relaxation parameters are internally set. Outputs include input data echo, grid system verification, relaxation-solution convergence history, and computed velocities, pressures, forces, moments, reference lengths, and areas. Program is written in FORTRAN IV for batch execution.
Verifying performance requirements
Today, it is impossible to verify performance requirements on Ada software, except in a very approximate sense. There are several reasons for this difficulty, of which the main reason is the lack of use of information on the mapping of the program onto the target machine. An approach to a partial solution to the verification of performance requirements on Ada software is proposed, called the rule based verification approach. This approach is suitable when the target machine is well defined and when additional effort and expense are justified in order to guarantee that the performance requirements will be met by the final system.
Inspection and Verification of Domain Models with PlanWorks and Aver
When developing a domain model, it seems natural to bring the traditional informal tools of inspection and verification, debuggers and automated test suites, to bear upon the problems that will inevitably arise. Debuggers that allow inspection of registers and memory and stepwise execution have been a staple of software development of all sorts from the very beginning. Automated testing has repeatedly proven its considerable worth, to the extent that an entire design philosophy (Test Driven Development) has been developed around the writing of tests. Unfortunately, while not entirely without their uses, the limitations of these tools and the nature of the complexity of models and the underlying planning systems make the diagnosis of certain classes of problems and the verification of their solutions difficult or impossible. Debuggers provide a good local view of executing code, allowing a fine-grained look at algorithms and data. This view is, however, usually only at the level of the current scope in the implementation language, and the data-inspection capabilities of most debuggers usually consist of on-line print statements. More modem graphical debuggers offer a sort of tree view of data structures, but even this is too low-level and is often inappropriate for the kinds of structures created by planning systems. For instance, god or constraint networks are at best awkward when visualized as trees. Any any non-structural link between data structures, as through a lookup table, isn't captured at all. Further, while debuggers have powerful breakpointing facilities that are suitable for finding specific algorithmic errors, they have little use in the diagnosis of modeling errors.
A Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors
A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.
Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors
Flexible inhibitors are generally used in solid rocket motors (SRMs) as a means to control the burning of propellant. Vortices generated by the flow of propellant around the flexible inhibitors have been identified as a driving source of instabilities that can lead to thrust oscillations in launch vehicles. Potential coupling between the SRM thrust oscillations and structural vibration modes is an important risk factor in launch vehicle design. As a means to predict and better understand these phenomena, a multidisciplinary simulation capability that couples the NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This capability is crucial to the development of NASA's new space launch system (SLS). This paper summarizes the efforts in applying the coupled software to demonstrate and investigate fluid-structure interaction (FSI) phenomena between pressure waves and flexible inhibitors inside reusable solid rocket motors (RSRMs). The features of the fluid and structural solvers are described in detail, and the coupling methodology and interfacial continuity requirements are then presented in a general Eulerian-Lagrangian framework. The simulations presented herein utilize production level CFD with hybrid RANS/LES turbulence modeling and grid resolution in excess of 80 million cells. The fluid domain in the SRM is discretized using a general mixed polyhedral unstructured mesh, while full 3D shell elements are utilized in the structural domain for the flexible inhibitors. Verifications against analytical solutions for a structural model under a steady uniform pressure condition and under dynamic modal analysis show excellent agreement in terms of displacement distribution and eigenmode frequencies. The preliminary coupled results indicate that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor. This insight could have profound implications for SRM and flexible inhibitor designs for current and future launch vehicles including SLS.
A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation
Here, the present work describes a new approach to evaluation and root finding for the kinetic dispersion relation of Langmuir waves, which is central to the analytical understanding of collisionless damping in plasmas. The plasma dispersion function is solved to machine precision using direct integration in the complex plane in combination with an analytic evaluation of the residue to account for the deformation along the Landau contour. To efficiently attain machine precision, the contour is displaced in the complex plane prior to integration, and numerical subtleties related to the placement of the contour are discussed. The approach is generic in that it applies to arbitrary distribution functions, with the present manuscript focused on relativistic cases. Detailed verification of results via direct kinetic simulation in a variety of configuration space dimensions is also presented. Finally, the technique is applied to the challenging case of highly relativistic (i.e. extremely hot) plasmas. Here we show both qualitative agreement with prior work, as well as the disappearance of the Landau root which would have significant implication for real-life observation or experiment.
Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis
Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.
Application of FUN3D and CFL3D to the Third Workshop on CFD Uncertainty Analysis
Two Reynolds-averaged Navier-Stokes computer codes - one unstructured and one structured - are applied to two workshop cases (for the 3rd Workshop on CFD Uncertainty Analysis, held at Instituto Superior Tecnico, Lisbon, in October 2008) for the purpose of uncertainty analysis. The Spalart-Allmaras turbulence model is employed. The first case uses the method of manufactured solution and is intended as a verification case. In other words, the CFD solution is expected to approach the exact solution as the grid is refined. The second case is a validation case (comparison against experiment), for which modeling errors inherent in the turbulence model and errors/uncertainty in the experiment may prevent close agreement. The results from the two computer codes are also compared. This exercise verifies that the codes are consistent both with the exact manufactured solution and with each other. In terms of order property, both codes behave as expected for the manufactured solution. For the backward facing step, CFD uncertainty on the finest grid is computed and is generally very low for both codes (whose results are nearly identical). Agreement with experiment is good at some locations for particular variables, but there are also many areas where the CFD and experimental uncertainties do not overlap.
Numerical Modeling of Ablation Heat Transfer
A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.