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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Improved solution accuracy for TDRSS-based TOPEX/Poseidon orbit determination

Orbit determination results are obtained by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using a batch-least-squares estimator available in the Goddard Trajectory Determination System (GTDS) and an extended Kalman filter estimation system to process Tracking and Data Relay Satellite (TDRS) System (TDRSS) measurements. GTDS is the operational orbit determination system used by the FDD in support of the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft navigation and health and safety operations. The extended Kalman filter was implemented in an orbit determination analysis prototype system, closely related to the Real-Time Orbit Determination System/Enhanced (RTOD/E) system. In addition, the Precision Orbit Determination (POD) team within the GSFC Space Geodesy Branch generated an independent set of high-accuracy trajectories to support the TOPEX/Poseidon scientific data. These latter solutions use the geodynamics (GEODYN) orbit determination system with laser ranging and Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) tracking measurements. The TOPEX/Poseidon trajectories were estimated for November 7 through November 11, 1992, the timeframe under study. Independent assessments were made of the consistencies of solutions produced by the batch and sequential methods. The batch-least-squares solutions were assessed based on the solution residuals, while the sequential solutions were assessed based on primarily the estimated covariances. The batch-least-squares and sequential orbit solutions were compared with the definitive POD orbit solutions. The solution differences were generally less than 2 meters for the batch-least-squares and less than 13 meters for the sequential estimation solutions. After the sequential estimation solutions were processed with a smoother algorithm, position differences with POD orbit solutions of less than 7 meters were obtained. The differences among the POD, GTDS, and filter/smoother solutions can be traced to differences in modeling and tracking data types, which are being analyzed in detail.

Doll, C. E.↗
NASA NTRS2004

Comparisons of the Solutions for the Category 3--Problem 2: Cascade-Gust Interaction

Six different solutions were submitted for this benchmark problem. These were obtained using a variety of methods that can be conveniently categorized in two main groups, a nonlinear time-domain group and a linearized frequency-domain group. The first includes solutions submitted by (1) Hixon, (2) Nallasamy et. al, (3) Shieh et. al, and (4) Wang et. al, and the second includes solutions submitted by (5) Coupland and (6) Serrano et. al. Methods (1) and (2) use sixth order compact differencing schemes and the rest are essentially second order in space. With the exception of the solution submitted by Shieh et. al, all are individually discussed in great detail in the workshop proceedings. Comparisons of the submitted solutions with the benchmark solution are presented below. Due to differences in the level of solution detail provided to the author by the participants, the comparisons do not always include results from all submissions. It should be noted at the outset that, since the benchmark solution itself was numerically computed, the comparisons are somewhat subjective. In order to provide maximum latitude for the participants of the workshop, no restrictions were placed on the type of method that could be used to solve the problem. Neither was there were any stipulations to use a particular grid topology or grid density. Therefore, without a detailed study of the critical features of the computed solutions, it is not possible to make concrete statements about the relative merits of one method over another. Such a study is beyond the scope of the current exercise, especially since complete flowfield details were not provided to the author by all participants. Instead a package, containing the information about the benchmark solution (both the steady and unsteady parts of it), is included on the proceedings CD should the authors who submitted solutions for this problem wish to examine in detail the benchmark solution and compare their results to it.

Envia, Edmane↗
DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evaluation of the Potential for Precipitation of Solids during Storage of Non-Aluminum SNF Solutions

Non-aluminum clad spent nuclear fuels (NASNF) stored in the L-Area basin will be dissolved in H-Canyon using the 6.3D electrolytic dissolver. The solutions will be stored in either the hot or warm canyon until the preparation of a sludge batch for the Defense Waste Processing Facility. Spent nuclear fuel solutions could be stored for 1-2 years before transfer to the H-Area Tank Farm depending on the interval between sludge batches. The solution level in the storage tanks will be maintained; therefore, precipitation of solids due to evaporation is not an issue. However, the precipitation of solids from completely dissolved SNF due to solution instabilities has been observed during intermediate storage of solutions generating hydrated oxides.The presence of fissile material in these solids is generally associated with zirconium molybdate, which is known to act as a host lattice for Pu and can carry the actinides upon precipitation. The formation of zirconium molybdate solids which carry fissile material is a potential concern for the storage of NASNF solutions. To address this concern, the Savannah River National Laboratory performed a literature review to identify knowledge gaps which may require experimental work to determine if the formation of solids is a concern during storage of these solutions. Based on the literature review, the precipitation of zirconium molybdate solids from the Campaign 1 NASNF solutions during intermediatestorage is expected. This conclusion is supported by the identification of zirconium molybdate solids found on the H-Canyon 6.1D Dissolver MK-12 insert spacer. The formation of the zirconium molybdate solids is attributed to hydrolysis and radiolytic processes in the nitric acid solution. As the molybdate solids form, U and Pu can substitute for Zr in the crystal lattice resulting in co-precipitation. Generally, the Pu substitutes directly into the crystal lattice during precipitation while the U associated with the molybdate solids more likely absorbs from the solution. The U in the NASNF solutions is present as uranyl nitrate, a 2+ cation which will not substitute as easily into the molybdate crystal lattice for the Zr 4+ ion.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

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↗
NASA NTRS1995

Supersaturated Electrolyte Solutions: Theory and Experiment

Highly supersaturated electrolyte solutions can be prepared and studied employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the conserved order parameter omega(r,t) associated with fluctuations of the mean solute concentration n(sub 0). Parameters of the corresponding Ginzburg-Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured quantities. A correspondence of 96-99 % between theory and experiment for all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin), and its calculation for various electrolyte solutions at 298 K. The assumption that subcritical solute clusters consist of the electrically neutral Bjerrum pairs has allowed both analytical and numerical investigation of the number-size N(sub c) of nucleation monomers (aggregates of the Bjerrum pairs) which are elementary units of the solute critical clusters. This has also allowed estimations for the surface tension Alpha, and equilibrium bulk energy Beta per solute molecule in the nucleation monomers. The dependence of these properties on the temperature T and on the solute concentration n(sub 0) through the entire metastable zone (from saturation concentration n(sub sat) to spinodal n(sub spin) is examined. It has been demonstrated that there are the following asymptotics: N(sub c), = I at spinodal concentration and N(sub c) = infinity at saturation.

Izmailov, Alexander F.↗
NASA NTRS1999

Gravitational Effects on the Morphology and Kinetics of Photodeposition of Polydiacetylene Thin Films From Monomer Solutions

The goal of this proposed work is to study gravitational effects on the photodeposition of polydiacetylene thin films from monomer solutions onto transparent substrates. Polydiacetylenes have been an extensively studied class of organic polymers because they exhibit many unusual and interesting properties, including electrical conductivity and optical nonlinearity. Their long polymeric chains render polydiacetylenes readily conducive to thin film formation, which is necessary for many applications. These applications require thin polydiacetylene films possessing uniform thicknesses, high purity, minimal inhomogeneities and defects (such as scattering centers), etc. Also, understanding and controlling the microstructure and morphology of the films is important for optimizing their electronic and optical properties. The lack of techniques for processing polydiacetylenes into such films has been the primary limitation to their commercial use. We have recently discovered a novel method for the formation of polydiacetylene thin films using photo-deposition from monomer solutions onto transparent substrates with UV light. This technique is very simple to carry out, and can yield films with superior quality to those produced by conventional methods. Furthermore, these films exhibit good third-order properties and are capable of waveguiding. We have been actively studying the chemistry of diacetylene polymerization in solution and the photo-deposition of polydiacetylene thin films from solution. It is well-known that gravitational factors such as buoyancy-driven convection and sedimentation can affect chemical and mass transport processes in solution. One important aspect of polydiacetylene thin film photodeposition in solution, relevant to microgravity science, is that heat generated by absorption of UV radiation induces thermal density gradients that under the influence of gravity, can cause fluid flows (buoyancy-driven convection). Additionally, changes in the chemical composition of the solution during polymerization may cause solutal convection. These fluid flows affect transport of material to and from the film surface and thereby affect the kinetics of the growth process. This manifests itself in the morphology of the resulting films; films grown under the influence of convection tend to have less uniform thicknesses, and can possess greater inhomogeneities and defects. Specifically, polydiacetylene films photodeposited from solution, when viewed under a microscope, exhibit very small particles of solid polymer which get transported by convection from the bulk solution to the surface of the growing film and become embedded. Even when carried out under conditions designed to minimize unstable density gradients (i.e., irradiating the solution from the top), some fluid flow still takes place (particles remain present in the films). It is also possible that defect nucleation may be occurring within the films or on the surface of the substrate; this, too, can be affected by convection (as is the case with crystal growth). Hence films grown in 1-g will, at best, still possess some defects. The objective of this proposal is to investigate, both in 1-g and in low-g, the effects of gravitational factors (primarily convection) on the dynamics of these processes, and on the quality, morphology, and properties of the films obtained.

Paley, Mark S.↗
NASA NTRS1992

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Felici, Helene Marie↗
DOE OSTI2024

Insights into the Assembly and Conformation of Nanoparticle Organic Hybrid Materials (NOHMs) in Solution with Varying Grafting Type

Recently, nanoparticle organic hybrid materials (NOHMs) have been considered promising electrolytes for energy storage applications due to their unique combination of properties, which include high thermal stability, negligible vapor pressure, and easy synthesis. However, the structural features of NOHMs in electrochemical systems are not well understood. Hence, we investigate the impact of grafting type (ionic vs covalent) on the structure and performance of NOHMs that consist of a silica core and grafted HPE polymer (Jeffamine M2070) in aqueous solution with and without the presence of the supporting electrolyte (0.1 M KHCO 3 ) using small-angle neutron scattering. Careful analyses of the results indicate that even at low grafting density (0.8 chains nm –2 ) and concentration (1–3 wt %), ionic NOHMs solutions contain a free polymer that may interact with the grafted polymer, altering the assembly of NOHMs in solution. Our investigation also elucidates that the covalent NOHM solutions consist of both aggregated and dispersed NOHMs in the solution. Moreover, the addition of the supporting electrolyte affects the assembly and structure of the polymer in the ionic NOHMs solution significantly, whereas only a slight change in the conformation of the grafted polymer is observed for covalent NOHMs. These conformational changes alter the performance of the NOHMs solution, resulting in a dramatic change in viscosity. Careful analysis shows that this significant alteration of solution viscosity in the ionic NOHMs can be traced back to the presence of the free polymer that interacts with the grafted layer and the attenuation of this interaction between the free and grafted polymers with the addition of salt. Furthermore, these studies elucidate the impact of grafting type on the overall structure, assembly, and performance of functionalized NOHMs in aqueous solution and explicitly correlate the structure and assembly of NOHMs to their transport properties and must be considered when designing functional systems that incorporate NOHMs.

25 ENERGY STORAGE↗
DOE OSTI2023

Relationships between Water’s Structure and Solute Affinity at Polypeptoid Brush Surfaces

Excellent antifouling surfaces are generally thought to create a tightly bound layer of water that resists solute adsorption, and highly hydrophilic surfaces such as those with zwitterionic functionalities are of significant current interest as antifoulant strategies. Furthermore, despite significant proofs-of-concept, we still lack a fundamental understanding of how the nanoscopic structure of this hydration layer translates to reduced fouling, how surface chemistry can be tuned to achieve antifouling through hydration water, and why, in particular, zwitterionic surfaces seem so promising. Here, we use molecular dynamics simulations and free energy calculations to investigate the molecular relationships among surface chemistry, hydration water structure, and surface–solute affinity across a variety of surface-decorated chemistries. Specifically, we consider polypeptoid-decorated surfaces that display well-known experimental antifouling capabilities and that can be synthesized sequence specifically, with precise backbone positioning of, e.g., charged groups. Through simulations, we calculate the affinities of a range of small solutes to polypeptoid brush surfaces of varied side-chain chemistries. We then demonstrate that measures of the structure of surface hydration water in response to a particular surface chemistry signal solute–surface affinity; specifically, we find that zwitterionic chemistries produce solute–surface repulsion through highly coordinated hydration water while suppressing tetrahedral structuring around the solute, in contrast to uncharged surfaces that show solute–surface affinity. Based on the relationship of this structural perturbation to the affinity of small-molecule solutes, we propose a molecular mechanism by which zwitterionic surface chemistries enhance solute repulsion, with broader implications for the design of antifouling surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Using high pressure solutions of polyfluoroacrylate and CO 2 to Seal cement cracks for improved wellbore integrity

Polyfluoroacrylate (PFA) is a hydrophobic and oleophobic polymer that is soluble in high pressure carbon dioxide (CO 2 ). In this study, the ability of PFA-CO 2 solutions to greatly reduce the apparent permeability of split or cracked Portland cement cylindrical samples is assessed. The apparent permeability values of confined samples were determined before and after treatment with PFA-CO 2 solutions. In four tests, PFA-CO 2 solutions were continuously displacing pure CO 2 from the cracked cement and the decrease in apparent permeability due to PFA adsorption and wettability alteration was monitored. The lowest apparent permeability cracked cement sample (81 nD) was completely sealed with a very small amount of solution. Samples with initial apparent permeabilities of 89 μD and 29.4 mD exhibited 92% and 99% reductions in permeability, respectively, before the experiments had to be stopped because of the excessively large increase in pressure drop. A 50% reduction in apparent permeability was observed with a 3.80 mD sample. Four other split cement samples (bound together with tape) with an initial apparent permeability in the 9.0–70 mD range were removed from the core holder and immersed in a PFA-CO 2 solution for 24 h to allow for PFA adsorption. Then the PFA-CO 2 solution was depressurized, allowing for the deposition of additional PFA from the solution within the crack as the pressure fell below the cloud point pressure of the PFA-CO 2 solution. These four samples were then confined again in a core holder and apparent permeability reductions of 29–93% were observed. Finally, results from these eight experiments indicates that the more substantial reductions in the nD – mD apparent permeability of the cracked cement correlated to lower initial crack permeability, higher PFA concentration, and slower injection rate of the PFA-CO 2 solution into the crack.

58 GEOSCIENCES↗
DOE OSTI2023

The apparent reversal of the Law of Mass Action in concentrated multicomponent aqueous solutions

Although it is well known that aqueous electrolyte solutions behave non-ideally, few are so non-ideal that adding an electrolyte to a saturated solution with a common ion enhances rather than depresses solubility. Nonetheless, this apparent reversal of the Law of Mass Action (LMA) has been observed in simple nitrate solutions at high concentrations. A leading hypothesis is that ion clusters are formed and stabilized by ions having different charge densities. We report the present study examines this concept, in part by reviewing relevant data from multicomponent aqueous solutions containing sodium nitrate (NaNO 3 ), sodium nitrite (NaNO 2 ), sodium hydroxide (NaOH), and sodium aluminate (NaAl(OH) 4 ) - the major constituents in alkaline nuclear waste. Here, NaOH and NaAl(OH) 4 did not enhance the solubility of NaNO 3 or NaNO 2 , whereas NaNO 2 and NaNO 3 enhanced rather than depressed the solubility of each other despite each having the sodium cation (Na + ) in common. Solutions evaluated in this study have more than 20 molal total Na + concentration, and most have less than one mole of water per mole of ion. Thus, this reversal of the LMA occurs in solutions where there is not enough water to fully hydrate the ions, pointing to the importance of ion cluster formation. Within the composition range of the solutions analyzed here, this reversal of the LMA occurs regardless of NaAl(OH) 4 and NaOH concentrations. Elevated temperatures also result in the reversal of the LMA in the subsystems NaNO 2 -NaNO 3 -H 2 O and NaOH-NaNO 3 -H 2 O, consistent with spectroscopic and computational studies showing enhanced interactions at higher temperatures. Although speciation in these highly concentrated electrolyte solutions is not well understood, the stabilization of ion clusters by: (i) optimizing charge density around the ions through different combinations of mixed cations and anions in solution; and (ii) high temperatures where ions experience prolonged contact, offers important clues for future research into how these species control solubility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks

The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision-support tools for system design and operation. While the nonlinear system is known to have a unique solution (when one exists), the absence of a definite result on the existence of solutions hobbles the development of computational algorithms, for it is not possible to distinguish between algorithm failure and non-existence of a solution. In this letter, we show that for any fluid whose equation of state is a scaled monomial, a unique solution exists for such nonlinear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. However, for gases following the CNGA equation of state, while the question of existence remains open, we construct an alternative system that always has a unique solution and show that the solution to this system is a good approximant of the true solution. Further, the existence result for flow of natural gas in networks also applies to other fluid flow networks such as water distribution networks or networks that transport carbon dioxide in carbon capture and sequestration. Most importantly, our result enables correct diagnosis of algorithmic failure, problem stiffness, and non-convergence in computational algorithms.

42 ENGINEERING↗
DOE OSTI2023

Burst Pressure Solutions of Thin and Thick-Walled Cylindrical Vessels

Pressure vessels (PVs) are widely used in the energy industry. Accurate burst pressure is critical to structural design and safe operation for both thin and thick-walled PVs. The traditional strength theories utilized a single-parameter material property, such as the yield stress or the ultimate tensile stress (UTS) to develop failure models for determining the yield or ultimate pressure carrying capacity in the PV design. The UTS-based Barlow formula is a typical burst pressure model developed from the Tresca strength theory that provides the basis for developing regulation rules and failure models for different industry design codes, such as ASME BPVC, ASME B31.3, and ASME B31G, among others. In order to reduce the conservatism of the Tresca strength model, ASME BPVC recently adapted failure models developed from the von Mises strength theory for the PV design and analysis. It has been commonly accepted that the burst pressure of pipelines depends on the UTS and strain hardening exponent, n, of the pipeline steel. An average shear stress yield theory was thus developed, and the Zhu-Leis solution of burst pressure was obtained as a function of UTS and n for thin-walled line pipes. Experiments showed that the Zhu-Leis solution provides an accurate, reliable prediction of burst pressure for defect-free thin-walled pipes. In order to extend the Zhu–Leis solution to thick-walled cylindrical PVs, this paper defined three new flow stresses, modified the traditional strength theories, and obtained three new burst pressure solutions that are valid for both thin and thick-walled cylindrical vessels. The proposed flow stresses are able to describe the tensile strength and the plastic flow response of PVs for a strain hardening steel. The associated strength theories were then developed in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. From these new strength theories, three burst pressure solutions were obtained for thick-walled cylinders, where the von Mises solution is an upper bound prediction, the Tresca solution is a lower bound prediction, and the Zhu-Leis solution is an intermediate prediction of burst pressure for thick-walled cylinders. Lastly, the proposed burst pressure solutions were evaluated and validated by two large datasets of full-scale burst tests for thick-walled tubes and for thin-walled pipes.

42 ENGINEERING↗
DOE OSTI2022

Effects of Chlorine Capture and a Proposed Density Law on the Reactivity of Plutonium Solution Systems

During fissionable material processing, all normal and credible abnormal conditions must remain safely subcritical. Nuclear Criticality Safety (NCS) uses a number of methods to determine subcriticality, one of which is the use of neutron transport codes such as MCNP6. In order to create models for use with MCNP6, both the geometry and materials in fissionable material processes must be known, or assumptions must be made and quantified for the impact to bias. One of the systems with a significant amount of bias due to material modeling assumptions is in the area of aqueous plutonium processing. These solutions are typically plutonium nitrate solutions or plutonium chloride solutions, which are modeled as fictitious plutonium metal-water mixtures because little is known about the actual density of the solution and there is no current predictive capability approved for use at Los Alamos National Laboratory (LANL) for modeling them. This research is currently underway to fill the gap and develop an algorithm for use with MCNP6 to model the density of plutonium chloride solutions. The method is to be validated with experimental data for density, and also validated with critical experiments using MCNP6. Note that the Chlorine Worth Study (CWS) was performed in December 2021 to help bridge the gap in chlorine data for critical experiments, and is currently awaiting International Criticality Safety Benchmark Evaluation Project (ICSBEP) review. This study was performed by LANL at the National Criticality Experiments Research Center (NCERC) at the Nevada National Security Site (NNSS). Additional information regarding this experiment may currently be found in LA-UR- 22-29180. Additionally, the Chemistry-Actinide Analytical Chemistry (C-AAC) at LANL has performed a number of solution density measurements for PuCl 3 -HC 1 -H 2 O, allowing for such data be used to create a semi-empirical density via the Pitzer method. The published dataset for the measurements is documented in LA-UR-22-25454. This method has already been tested successfully for aqueous plutonium nitrate solutions in SCALE. Current solution density measurements exist of plutonium concentrations of 0-~142g/L, all at 2M HC1, at temperatures 20-40°C. Additional data was taken for HC1-corrected density values, which essentially mimics the data for a pure PuCl x -water solution. The calculations in this report aim to support the current research by demonstrating the difference in system reactivity for the current modeling method when compared to the new proposed modeling with a density law implementation, which is being written as a Python tool to be used with MCNP6.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Lancaster, J. E.↗
NASA NTRS1975

A similarity solution of the Navier-Stokes equations with wall catalysis and slip for hypersonic, low Reynolds number flow over spheres

The slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived. The more realistic multicomponent species slip conditions are shown to be necessary for accurate merged shock layer solutions on a sphere. These slip conditions are used in a first-order similarity solution of the Navier-Stokes equations with nonequilibrium chemistry for the merged shock layer. Results of this quick numerical solution are compared with a time dependent solution around the sphere and with measured arc jet results at low Reynolds numbers. The similarity solution, unlike the time dependent solution, shows smooth radial profiles of the pressure and smooth variations of velocity slip, skin friction, temperature slip and heat transfer around the body. The present first-order similarity solution is valid up to 25 deg from the stagnation point and takes less than 1% of the computer time to run a time dependent scheme. The smaller stand-off distance obtained from the similarity solution is supported by experimental data. The measured heat flux is closer to the similarity solution than the time dependent method at the stagnation point and shows the proper variation with circumferential angle up to at least 40 deg.

Hendricks, W. L.↗
NASA NTRS1976

Solution of the minimum time-to-climb problem by matched asymptotic expansions

Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

Ardema, M. D.↗