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At least 55 records · Page 3

Recent developments in transonic Euler flow over a circular cylinder

Numerical solutions to the Euler equations for transonic flow over a circular cylinder suggest that the inviscid flow separates ahead of the rear stagnation point. The present understanding of this phenomenon and various solutions presented at a workshop on this subject are discussed. All the evidence suggests that inviscid separation is a feature of the Euler equations induced by vorticity and/or stagnation pressure loss in the flow. The possibility of multiple solutions suggested by Hafez (1981) and the oscillatory behavior for the full circle observed by Steger (1977) are seen as needing further investigation.

Salas, M. D.↗

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗

HLPW-4/GMGW-3: Mesh Adaptation for RANS Technology Focus Group Workshop Summary

The AIAA workshop series helps guide the Computational Fluid Dynamics (CFD) community through publicly available test cases and impartial evaluation to establish the state-of-the-art in applied CFD. A summary of the Mesh Adaptation Technical Focus Group submissions for the joint Fourth CFD High Lift Prediction and Third Geometry & Mesh Generation Workshop is provided. The Common Research Model High-Lift variant (CRM-HL) is the target of this investigation. A 2D high-lift airfoil solution verification case was extracted from the 3D CRM-HL. Low variation is shown between 2D solutions with mesh adaptation to control estimated solution interpolation and output errors. As expected, variation for these mesh adaptation techniques is larger for the 3D CRM-HL than the 2D airfoil. More importantly, the 3D mesh adapted results have a lower variation than expert-crafted meshes of equal or larger size. Suspected multiple solutions to Reynolds-averaged Navier-Stokes with the Spalart-Allmaras turbulence model appear to resolve into a common solution with mesh resolution.

HLPW-4↗

Final Technical Report: Transport of Complex Mixtures in Ion-Containing Polymer Membranes

Permselective ion-containing membranes are an integral component for many applications from water treatment, fuel cells, and solar fuels devices where the selective transport of molecules and ions is desired. In solar fuels devices, ion-containing polymer membranes are responsible for permitting selective transport of ions between electrodes to maintain overall charge neutrality yet limit transport of reaction products produced at the electrodes. While the transport of single solutes through such membranes has been fairly well described, binary and multicomponent transport is poorly understood due to the myriad of interactions that occur in these systems (i.e. between co-permeants and between permeants and the membrane). Solar fuels devices are just one example of an application where understanding the transport of multiple simultaneous species is critically important to improving device performance as product crossover leads to reductions in overall device performance. The objectives of this research was to improve our understanding of the complex array of factors that influence transport behavior of multiple solutes within ion-containing polymer membranes. This experimental project addressed the lack of fundamental understanding of multicomponent transport behavior by synthesizing ion exchange membranes with varied incorporation of comonomers (ionic and neutral moieties) to investigate fundamental relationships between membrane structure, membrane physiochemical properties, and transport behavior of solutes and complex solute mixtures through dense, hydrated membranes.

25 ENERGY STORAGE↗

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗

Review of linear compressible stability theory

Aspects of the linear compressible stability theory are considered, with special attention given to the inviscid theory and the additional solutions that arise when there is a region of supersonic flow relative to the phase velocity. For the case of highly cooled flat-plate boundary layers at Mach number 5.8, the unstable region is found to include supersonic outgoing waves. A previously unknown neutral incoming wave has also been identified. An example of viscous multiple solutions is provided, and calculations of higher viscous discrete modes and the compressible counterpart of the Squire mode are presented. It is noted that compressible stability theory is missing a firm connection with boundary-layer transition.

Mack, Leslie M.↗

Slicing Solutions for Wire Arc Additive Manufacturing

Both commercial and research applications of wire arc additive manufacturing (WAAM) have seen considerable growth in the additive manufacturing of metallic components. However, there remains a clear lack of a unified paradigm for toolpath generation when slicing parts for WAAM deposition. Existing toolpath generation options typically lack the appropriate features to account for all complexities of the WAAM process. This manuscript explores the key slicing challenges specific to toolpaths for WAAM geometry and pairs each consideration with multiple solutions to mitigate most negative effects on completed components. These challenges must be addressed to minimize voids, prevent bead collapse, and ensure deposited components accurately approximate the desired geometry. Slicing considerations are grouped into four general categories: geometric, process, thermal, and productivity. Geometric considerations are addressed with overhang compensation, corner-sharpening, and toolpath-smoothing features. Process considerations are addressed with start point configuration and controls for the bead lengths and end points. Thermal and productivity considerations are addressed with island optimization, multi-material printing, and connected insets. Finally, tools for the post-processing of generated G-code are explored. Overall, these solutions represent a critical set of slicing features used to improve generated toolpaths and the quality of the components deposited with those toolpaths.

36 MATERIALS SCIENCE↗

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗

Check-Cases for Verification of 6-Degree-of-Freedom Flight Vehicle Simulations

The rise of innovative unmanned aeronautical systems and the emergence of commercial space activities have resulted in a number of relatively new aerospace organizations that are designing innovative systems and solutions. These organizations use a variety of commercial off-the-shelf and in-house-developed simulation and analysis tools including 6-degree-of-freedom (6-DOF) flight simulation tools. The increased affordability of computing capability has made highfidelity flight simulation practical for all participants. Verification of the tools' equations-of-motion and environment models (e.g., atmosphere, gravitation, and geodesy) is desirable to assure accuracy of results. However, aside from simple textbook examples, minimal verification data exists in open literature for 6-DOF flight simulation problems. This assessment compared multiple solution trajectories to a set of verification check-cases that covered atmospheric and exo-atmospheric (i.e., orbital) flight. Each scenario consisted of predefined flight vehicles, initial conditions, and maneuvers. These scenarios were implemented and executed in a variety of analytical and real-time simulation tools. This tool-set included simulation tools in a variety of programming languages based on modified flat-Earth, round- Earth, and rotating oblate spheroidal Earth geodesy and gravitation models, and independently derived equations-of-motion and propagation techniques. The resulting simulated parameter trajectories were compared by over-plotting and difference-plotting to yield a family of solutions. In total, seven simulation tools were exercised.

Murri, Daniel G.↗

Qualitative Headspace GCMS Analysis of Lunar Regolith and Volatile Simulant Mixtures

Introduction: Future Artemis missions aim to return the volatile-bearing samples collected near lunar polar craters. We, as advanced curation scientists, are responsible for developing techniques and methodologies for preserving the integrity of returned samples and the science value those samples contain. The extent to which that preservation is possible, and the trade-offs preservation requires (e.g. monetary costs, sample volume limitations) all must be considered. Even less-than pristine volatile-bearing samples will be of tremendous value to the scientific community seeking to unravel the history of lunar surface volatiles and, more broadly, volatiles in the solar system. A sample collected on the lunar surface will experience at least five distinctive periods during which any changes here referred to as “alteration” will certainly occur at some scale: collection on the lunar surface; transportation back to Earth; long-term storage; curatorial processing; and allocation/distribution. The Planetary Exploration and Astromaterials Research Lab (PEARL) seeks to understand temperature and pressure effects on returned volatile samples by working with high-fidelity volatile-containing regolith simulants, setting the foundation for the future of cold curation. This abstract is focused on gas-surface interactions between LCROSS volatiles and readily available lunar regolith simulants. Experiments involved analyzing differences in headspace gas composition for various combinations of volatile and regolith simulants using gas chromatography/mass spectrometry (GC/MS). Experimental Procedure: The volatile simulants were chosen based on the molecules detected during the LCROSS mission.1 Stock solutions of condensed lunar volatile analytes were: methanol, 7 N ammonia in methanol, and 0.4% hydrogen sulfide in water. The regolith simulants used were primarily JSC-1A and NU-LHT-4M. Additional regolith simulant control studies were conducted with <150 μm sieved sand and KBr. A nested vial sample preparation approach separated the liquid stock solutions from the regolith, eliminating potential matrix effects between liquid and solid phases. Fifteen microliter aliquots of liquid volatile simulants were added to a 2 mL liquid GC vial and capped in atmosphere. An 18G needle punctured the 2 mL GC vial immediately before being transferred and sealed in a 20 mL GC vial containing 0-0.3 g of regolith simulant, see Figure 1. Separating the analytes ensures any changes observed in the total headspace gases is a result of gas-surface and/or gas-gas interactions. Equipment and Method: Initial GC/MS method development for the separation and identification of relevant headspace gases can be found in Amick, et al. 2023.2 The only hardware change is a different column: a TG-1701MS 30 m × 0.25 mm × 1.00 μm column. The vials were sampled at 10°C, room temperature (~25°C) and 50°C. Low temperature samples were kept in a chilled autosampler stage for at least 1 hour prior to sampling. High temperature samples were agitated at 50°C for 5 minutes immediately prior to injection onto the column. Headspace chromatograms were collected for each combination of temperature, regolith, and volatile simulant, including controls without one or both types of analytes, in triplicate. The chromatogram elution window for each analyte or significant atmospheric gas was identified using the peak mass spectrum cross-referenced with Figure 1.Picture of the nested vial set-up. a NIST MS library search. Each analyte peak was integrated after filtering the mass spectrum trace for the parent or most unique mass-to-charge ratio. For example, the mass-to-charge ratio used to identify, filter for, and integrate the carbon dioxide peak was centered around 44 m/z. Results: Figure 2 shows the integrated peak area for hydrogen sulfide in all combinations of regolith simulants, temperatures, and the addition of ammonia in methanol solution. Multiple repeat experiments with H2S and regolith simulants have confirmed hydrogen sulfide is removed from the headspace within 1 hour when exposed to JSC-1A, NU-LHT-4M and sand (not pictured). The consumption of H2S by lunar regolith simulants at different temperatures indicates surface chemistry will be an integral component in sample integrity and preservation. It is important to note that while the effect of surface chemistry on gaseous hydrogen sulfide is intriguing, further investigation into more chemically accurate regolith simulants is necessary and ongoing. The sulfur in hydrogen sulfide is in its most reduced state while off-the-shelf, terrestrially sourced JSC-1A and NU-LHT-4M are more oxidized than most lunar materials,3which likely leads to different oxidation-reduction reactions than would be expected in lunar regolith. Figure 3 shows the integrated peak area of carbon dioxide for each sample combination that contained ammonia in methanol solution. The addition of ammonia to the GC vials results in a consistent and reproducible decrease in carbon dioxide gas, even at 50°C. The effect became more pronounced when JSC-1A or NU-LHT-4M were present. This set of experiments demonstrated that the sample composition will affect the chemical and physical state of each component present. Future spectroscopic and microscopy experiments will be geared towards identifying the cause for the CO2(g) concentration decrease and the consumption of hydrogen sulfide. As cold and volatile curation scientists, this information provides necessary insight on how to appropriately handle and analyze volatile bearing returned samples, as well as predict the effect chemical composition has on the various sample phases we will analyze upon return to Earth. Unlike traditional curation of geologic materials, the molecules in a sample cannot be identified or processed using the naked eye or even an optical microscope. Volatile curation will require a combination of analytical techniques, including but not limited to highly sensitive gas and solid/condensed phase spectroscopy. This set of experiments has demonstrated the need for more detailed studies of volatile mixtures with mineralogically and geochemically analogous lunar regolith simulants to prepare for the curation of volatile-rich lunar samples from the south polar region of the Moon. References: [1] Colaprete, A., et al. (2010) Science, 330, (463-468). [2] Amick, C. L., et al.(2023) Houston, Texas, [3] Heiken, G. H., et al.(1991) (778-778)

Cecilia L Amick↗

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗

Stability of absorption phenomena in laser-thermal propulsion

The mean flow and stability characteristics of laser absorption phenomena in a choked converging-diverging nozzle are considered. Calculations are presented for a given nozzle geometry and a series of laser intensities. Gas absorptivities corresponding to a hydrogen-cesium mixture are used with different initial temperatures being selected to investigate the effects of changes in the shape of the k-T curve. Both stability and mean flow calculations are limited to the one-dimensional case. The mean flow results show a decrease in mass flow as laser power is increased, along with increasingly steep temperature profiles. Calculations span regions of partial and complete absorption. One region is found where multiple solutions exist. Local stability results indicate the u-c characteristic is the only unstable mode in the unheated case. Laser heat addition makes this mode more unstable and also destabilizes the u-characteristic. Numerical calculations of disturbance propagation show that the instability of the u-c disturbances is counteracted by their reflection to u + c disturbances at the upstream end. The growth of the u-disturbances is localized in regions where the temperature profile is steep and they are damped in other regions. The increasing destabilization that is observed with increased laser power is probably the reason for difficulty in obtaining converged mean flow solutions at high laser intensities.

Merkle, C. L.↗

Squeeze-film dampers for turbomachinery stabilization

A technique for investigating the stability and damping present in centrally preloaded radially symmetric multi-mass flexible rotor bearing systems is presented. In general, one needs to find the eigenvalues of the linearized perturbation equations, though zero frequency stability maps may be found by solving as many simultaneous non-linear equations as there are dampers; and in the case of a single damper, such maps may be found directly, regardless of the number of degrees of freedom. The technique is illustrated for a simple symmetric four degree of freedom flexible rotor with an unpressurized damper. This example shows that whereas zero frequency stability maps are likely to prove to be a simple way to delineate multiple solution possibilities, they do not provide full stability information. Further, particularly for low bearing parameters, the introduction of an unpressurized squeeze film damper may promote instability in an otherwise stable system.

Mclean, L. J.↗

Breakdown of the conservative potential equation

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock waves are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Salas, M. D.↗

Breakdown of the conservative potential equation

The conservative full-potential equation is used to study transonic flow over five airfoil sections. The results of the study indicate that once shock are present in the flow, the qualitative approximation is different from that observed with the Euler equations. The difference in behavior of the potential eventually leads to multiple solutions.

Salas, M. D.↗