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Numerical Experiments and Identification of Areas for Further Consideration (B639388 Subcontract Quarter II Report)

The second quarter of the project was spent carrying out numerical experiments on a variety of test matrices, using a combination of precisions, with the intent to study the numerical properties (namely, accuracy and convergence behavior) of the Conjugate Gradient (CG) method. We summarize our findings in the remainder of the document. Other activities include attending biweekly xSDK meetings. We are also currently collaborating with Steven Thomas (NREL) on the numerical stability analysis of “low-synch” Gram-Schmidt routines, for potential application within high-performance GMRES variants. This work is in progress. The subsequent quarter will be spent delving into the numerical analysis in order to provide theoretical explanation for the behavior observed in our experiments.

97 MATHEMATICS AND COMPUTING↗

Filtering analysis of a direct numerical simulation of the turbulent Rayleigh-Benard problem

A filtering analysis of a turbulent flow was developed which provides details of the path of the kinetic energy of the flow from its creation via thermal production to its dissipation. A low-pass spatial filter is used to split the velocity and the temperature field into a filtered component (composed mainly of scales larger than a specific size, nominally the filter width) and a fluctuation component (scales smaller than a specific size). Variables derived from these fields can fall into one of the above two ranges or be composed of a mixture of scales dominated by scales near the specific size. The filter is used to split the kinetic energy equation into three equations corresponding to the three scale ranges described above. The data from a direct simulation of the Rayleigh-Benard problem for conditions where the flow is turbulent are used to calculate the individual terms in the three kinetic energy equations. This is done for a range of filter widths. These results are used to study the spatial location and the scale range of the thermal energy production, the cascading of kinetic energy, the diffusion of kinetic energy, and the energy dissipation. These results are used to evaluate two subgrid models typically used in large-eddy simulations of turbulence. Subgrid models attempt to model the energy below the filter width that is removed by a low-pass filter.

Eidson, T. M.↗

3D modeling of deep borehole electromagnetic measurements with energized casing source for fracture mapping at the Utah Frontier Observatory for Research in Geothermal Energy

Here, we present a 3D numerical modelling analysis evaluating the deployment of a borehole electromagnetic measurement tool to detect and image a stimulated zone at the Utah Frontier Observatory for Research in Geothermal Energy geothermal site. As the depth to the geothermal reservoir is several kilometres and the size of the stimulated zone is limited to several 100 m, surface-based controlled-source electromagnetic measurements lack the sensitivity for detecting changes in electrical resistivity caused by the stimulation. To overcome the limitation, the study evaluates the feasibility of using a three-component borehole magnetic receiver system at the Frontier Observatory for Research in Geothermal Energy site. To provide sufficient currents inside and around the enhanced geothermal reservoir, we use an injection well as an energized casing source. To efficiently simulate energizing the injection well in a realistic 3D resistivity model, we introduce a novel modelling workflow that leverages the strengths of both 3D cylindrical-mesh-based electromagnetic modelling code and 3D tetrahedral-mesh-based electromagnetic modelling code. The former is particularly well-suited for modelling hollow cylindrical objects like casings, whereas the latter excels at representing more complex 3D geological structures. In this workflow, our initial step involves computing current densities along a vertical steel-cased well using a 3D cylindrical electromagnetic modelling code. Subsequently, we distribute a series of equivalent current sources along the well's trajectory within a complex 3D resistivity model. We then discretize this model using a tetrahedral mesh and simulate the borehole electromagnetic responses excited by the casing source using a 3D finite-element electromagnetic code. This multi-step approach enables us to simulate 3D casing source electromagnetic responses within a complex 3D resistivity model, without the need for explicit discretization of the well using an excessive number of fine cells. We discuss the applicability and limitations of this proposed workflow within an electromagnetic modelling scenario where an energized well is deviated, such as at the Frontier Observatory for Research in Geothermal Energy site. Using the workflow, we demonstrate that the combined use of the energized casing source and the borehole electromagnetic receiver system offer measurable magnetic field amplitudes and sensitivity to the deep localized stimulated zone. The measurements can also distinguish between parallel-fracture anisotropic reservoirs and isotropic cases, providing valuable insights into the fracture system of the stimulated zone. Besides the magnetic field measurements, vertical electric field measurements in the open well sections are also highly sensitive to the stimulated zone and can be used as additional data for detecting and imaging the target. We can also acquire additional multiple-source data by grounding the surface electrode at various locations and repeating borehole electromagnetic measurements. This approach can increase the number of monitoring data by several factors, providing a more comprehensive dataset for analysing the deep-localized stimulated zone. The numerical analysis indicates that it is feasible to use the combination of the energized casing and downhole electromagnetic measurements in monitoring localized stimulated zone at large depths.

58 GEOSCIENCES↗

Superposed Epoch Analysis of Ring Current Geoeffectiveness Related to Solar Wind and Plasma Sheet Drivers

The goal of that proposal was to examine the relationship between solar wind drivers and ring current dynamics through data analysis and numerical simulations. The data analysis study was a statistical examination (via superposed epoch analyses) of a solar cycle's worth of storm data. Solar wind data, geophysical indices, and geosynchronous plasma data were collected for every time period with Dst< -50 nT from 1989 through 2002, and the storm list now exceeds 400 entries. This work was first conducted by a summer undergraduate student, Mr. John Vann (University of Kansas), with funding from the NSF Research Experience for Undergraduates program. It was then continued by a University of Michigan graduate student, Mr. Jichun Zhang. Mr. Zhang is now in his fourth year at U-M and is progressing very well toward a PhD in space science. His dissertation will be based on his data analysis and modeling efforts using this geomagnetic storm database. The results of the data analysis study have been the focus of several conference presentations, and the first manuscript has just been published. Two additional papers are presently being prepared, one on average (superposed) solar wind features for various storm subsets (e.g., intense storms at solar maximum), and another on geosynchronous plasma features for these same storm subsets. The latter result was highlighted by the TR&T program director in his presentation at the COSPAR meeting this summer.

Liemohm, M. W.↗

Identification of combustion mode under MILD conditions using Chemical Explosive Mode Analysis

Direct Numerical Simulations (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed in this paper to identify the contributions of the autoignition and flame modes. This is performed using an extended Chemical Explosive Mode Analysis (CEMA) which accounts for diffusion effects allowing it to discriminate between deflagration and autoignition. This analysis indicates that in premixed MILD combustion conditions, the main combustion mode is ignition for all dilution and turbulence levels and for the two reactant temperature conditions considered. In non-premixed conditions, the preponderance of the ignition mode was observed to depend on the axial location and mixture fraction stratification. With a large mixture fraction lengthscale, ignition is more preponderant in the early part of the domain while the deflagrative mode increases further downstream. On the other hand, when the mixture fraction lengthscale is small, sequential autoignition is observed. Finally, the various combustion modes are observed to correlate strongly with mixture fraction where lean mixtures are more likely to autoignite while stoichiometric and rich mixtures are more likely to react as deflagrative structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales

This the final report for the DE-SC0007096 - Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales - PI: Pavlos Kollias. The final report outline the main findings of the research conducted using the aforementioned award in the area of cloud research from the cloud scale (10-100 m) to the mesoscale (20-50 km).

58 GEOSCIENCES↗

Validation of numerical models for seismic fluid-structure-interaction analysis of nuclear, safety-related equipment

Seismic design, qualification, and risk assessment of nuclear safety-related vessels filled with liquid will have to consider the interaction between the vessel (tank), the contained liquid, and submerged components, if any. Seismic fluid-structure-interaction (FSI) analysis of nuclear vessels will rely on numerical models, which are required to be verified and validated. This study validates previously-verified numerical models using test data generated from earthquake-simulator experiments involving a cylindrical tank. Two solvers in LS-DYNA for FSI simulations are used for the numerical analysis: Arbitrary-Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD). Numerical and test results are compared for responses critical to seismic design of advanced reactor vessels: hydrodynamic pressures on the tank wall, reactions at the support, and wave heights of the contained liquid. Analysis is performed for one-, two-, and three-directional seismic inputs with a range of intensity, and rocking motions. The accuracy of the numerical results and different methods for outputting wave heights are discussed. Recommendations for validation of seismic FSI numerical models of advanced reactors are provided. As a result, the validation exercise presented in this study is broadly applicable to cylindrical tanks, regardless of industry sector.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Sensitivity of Forecast Skill to Different Objective Analysis Schemes

Numerical weather forecasts are characterized by rapidly declining skill in the first 48 to 72 h. Recent estimates of the sources of forecast error indicate that the inaccurate specification of the initial conditions contributes substantially to this error. The sensitivity of the forecast skill to the initial conditions is examined by comparing a set of real-data experiments whose initial data were obtained with two different analysis schemes. Results are presented to emphasize the importance of the objective analysis techniques used in the assimilation of observational data.

Baker, W. E.↗

Evaluation of numerical schemes for the analysis of sound generation by blade-gust interaction

In this investigation three different numerical algorithms have been utilized to compute the flow about a flat plate in the presence of a transverse gust described by a sinusoidal disturbance. The three schemes include the MacCormack explicit finite difference scheme which is second order accurate in both time and space, the Gottlieb and Turkel modification of MacCormack's scheme which is fourth order accurate in space and second order accurate in time, (referred to as the 2-4 scheme), and a two step scheme developed by Bayliss et al. which has second order temporal accuracy and sixth order spatial accuracy (a 2-6 scheme). The flow field results are obtained with these schemes by using the same code with the only difference being the implementation of the respective solution algorithms. The problem is set up so that the sinusoidal disturbance is imposed at the surface of the flat plate as a surface boundary condition. Thus the problem is treated as scattering problem. The computed results include the time average of the acoustic pressure squared along grid lines five points away from the boundaries; distribution throughout the computational domain is monitored at various times. The numerical results are compared with an exact solution obtained by Atassi, Dusey, and Davis.

Scott, J. N.↗

Development of Analysis Methods that Integrate Numeric and Textual Equipment Reliability Data

Within the Light Water Reactor Sustainability (LWRS) program, the Risk-Informed Systems Analysis (RISA) Pathway is performing collaborative research on the development and deployment of technologies designed to assist operating nuclear power plants (NPPs) to reduce operating costs improve plant reliability and availability. One of the RISA research areas is focusing on the development of methods and tools designed to optimize plant operations (e.g., maintenance/replacement schedules, optimal maintenance postures for plant structures, systems, and components [SSCs]) in a manner that is more cost effective than current approaches and makes better use of available SSC health data. The Risk-Informed Asset Management (RIAM) project targets this research area by creating a direct bridge between component equipment reliability (ER) data and system engineer decision making regarding maintenance activity scheduling and component aging management. In this respect, one challenge that NPP system engineers are facing is that the amount of ER data being continuously generated is not only extremely large in size, but it comes in different forms: textual (e.g., condition or maintenance reports) and numeric (e.g., generated by monitoring systems). All these data elements provide them with valuable insights and information regarding: 1) the discovery of anomalous behaviors or degradation trends, 2) the identification of the possible causes behind such behaviors/trends, and 3) the prediction of their direct consequences. However, several challenges have proved to be roadblocks to this process. While some of these challenges are technical in nature (i.e., data are often distributed over several physical servers/databases), others are conceptual in nature: data elements come in different formats (e.g., numeric or textual), and measured values have different scales (e.g., vibration spectra and oil temperature). The activities performed by the RIAM project during FY23 directly tackles the need to simultaneously integrate the analysis of ER data in all its forms, numeric and textual. Note that such task has never been performed before due to the complexity of the systems under consideration but, most importantly, because of the technical challenges behind the harmonization of ER data formats and the lack of adequate computational methods to analyze them. Our approach borrows ideas and concepts from the medical field where integration of several data sources is vital to assist medical practitioners to perform correct diagnosis and indicate optimal treatments. In our view a NPP asset is equivalent to a patient in a medical context. The main difference is the complexity of a human body is a magnitude more complex when compared to typical assets commonly present in NPPs (e.g., centrifugal pumps, or motor operated valves). This simplifies our first requirement when analyzing heterogenous ER data formats: to put data into “context”. Context is here intended as the additional piece of information that is needed by ER data analysis tools to understand what these data elements are referring to, i.e., which king of knowledge they are generating. In our context, this knowledge can be translated into models that capture the form and functional architecture of assets/systems, their dependencies, and how they interact. These models actually emulate the knowledge that that NPP system engineers possess about assets and systems; this is their key of success when analyzing ER data, their challenge is ability to handle large amount of data. Here, we employ model-based system engineering (MBSE) models of systems and assets to represent and capture their architecture and functional, i.e. cause-effect, relations. Then, ER data elements are processed by identifying first of all which elements of the developed MBSE elements they are referring to. For numeric ER data this task is fairly easy since it is possible to precisely pinpoint what MBSE elements the corresponding sensor are observing (e.g., bearing temperature of a centrifugal pump). Task is much harder for textual data since the information contained in issue or maintenance reports needs to “be understood” by a computational tool. Here we called this process as “knowledge extraction”. Once again, we borrow the experience in the medical field where methods to extract knowledge from textual data have been developed in the past decade. The missing element for us is the availability of a complete dictionary of NPP related concepts (in addition to the MBSE models presented earlier) that can put “text into context”. In FY23, such dictionary has been developed along with all the computational elements required for knowledge extraction. Lastly, once numeric and textual ER data elements have been processed and “understood”, then the last step is the discovery of possible cause-effect relations among them. This is performed by observing if a logical connection through the MBSE models exists, and if the

97 MATHEMATICS AND COMPUTING↗

Analysis Of Flow Across Cylinders

Report reviews various experimental, theoretical, and numerical methods of analysis of interactions between fluid and one or more cylinders across which it flows. Begins with discussion of mechanisms inducing vibrations in nests of cylinders. Major portion of review devoted to methods for numerical analysis of flow/cylinder interactions.

Kim, Sang-Wook↗

Mass Transport in Membrane Systems: Flow Regime Identification by Fourier Analysis

The numerical calculation of local mass distributions in membrane systems by computational fluid dynamics (CFD) offers indispensable benefits. However, the concept to calculate such distributions in response to separate variations of operation conditions (OCs) makes it difficult to address overall, flow-physics-related questions, which require the consideration of the collective interaction of OCs. It is shown that such understanding-related relationships can be obtained by the analytical solution of the advection–diffusion equation considered. A Fourier series model (FSM) is presented, which provides exact solutions of an advection–diffusion equation for a wide range of OCs. On this basis, a new zeroth-order model is developed, which is very simple and as accurate as the complete FSM for all conditions of practical relevance. Advection-dominated blocked and diffusion-dominated unblocked flow regimes are identified (depending on a Péclet number which compares the flow geometry with a length scale imposed by the flow), which implies relevant requirements for the use of lab results for pilot- and full-scale applications. Analyses reveal the equivalence of variations of OCs, which offers a variety of options to accomplish desired flow regime changes.

Heinz, Stefan (ORCID:0000000248712416)↗

Computation of unsteady transonic flows through rotating and stationary cascades. 1: Method of analysis

A numerical method of solution of the inviscid, compressible, two-dimensional unsteady flow on a blade-to-blade stream surface through a stage (rotor and stator) or a single blade row of an axial flow compressor or fan is described. A cyclic procedure has been developed for representation of adjacent blade-to-blade passages which asymptotically achieves the correct phase between all passages of a stage. A shock-capturing finite difference method is employed in the interior of the passage, and a method of characteristics technique is used at the boundaries. The blade slipstreams form two of the passage boundaries and are treated as moving contact surfaces capable of supporting jumps in entropy and tangential velocity. The Kutta condition is imposed by requiring the slipstreams to originate at the trailing edges, which are assumed to be sharp. Results are presented for several transonic fan rotors and compared with available experimental data, consisting of holographic observations of shock structure and pressure contour maps. A subcritical stator solution is also compared with results from a relaxation method. Finally, a periodic solution for a stage consisting of 44 rotor blades and 46 stator blades is discussed.

Erdos, J. I.↗

An LU implicity scheme for high speed inlet analysis

A numerical method is developed to analyze the inviscid flowfield of a high speed inlet by the solution of the Euler equations. The lower-upper implicit scheme in conjunction with adaptive dissipation proves to be an efficient and robust nonoscillatory shock capturing technique for high Mach number flows as well as for transonic flows.

Yoon, S.↗

An LU implicit scheme for high speed inlet analysis

A numerical method is developed to analyze the inviscid flowfield of a high speed inlet by the solution of the Euler equations. The LU implicit scheme in conjunction with adaptive dissipation proves to be an efficient and robust nonoscillatory shock capturing technique for high Mach number flows as well as for transonic flows.

Yoon, S.↗

Liquid rocket boosters for the Space Shuttle - An outline of trade issues and analysis techniques

Numerous liquid rocket booster configurations were studied to replace the Solid Rocket Boosters on the current Space Shuttle. While improved safety, reliability, performance and economy of operation were sought, the designs also sought to minimize volumetric growth to reduce aerodynamic loads and structural modifications. Aero loads could be significant as a function of booster diameter if extrapolated directly from solid rocket characteristics. Procedures to meet these goals with analytical booster sizing and simple dynamic simulations are shown. Engine chamber pressure proved to be a good independent variable for implications of pressure-fed and pump-fed engines, fuel and material selection. For some configurations, ascent trajectory modifications were suggested: longer vertical rise, lofting, heads-up orientation, and higher first and second stage target altitudes. Since engine manufacture would dominate booster costs, booster simplification of reuse are discussed based on cost estimates.

Kelly, W. D.↗

Turbine rotor/stator flowfield analysis

A numerical study of the unsteady aerodynamic and thermal environment associated with axial turbine stages is presented. Computations are performed using a modification of the ROTOR1 rotor/stator interaction code. Two different turbine states are analyzed: the first state of the United Technologies Research Center large scale rotating rig and the first state of the Space Shuttle main engine (SSME) high pressure fuel turbopump. Time-averaged blade midspan pressure and heat transfer profiles are calculated using the following different surface boundary conditions: adiabatic wall, prescribed wall temperature, and prescribed heat flux. Numerical solutions for the large scale rotating rig are compared with experimental data. Unsteady pressure envelopes are also presented for each geometry. In addition, instantaneous contours are plotted for the SSME configuration.

Griffin, Lisa↗