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DOE OSTI2023

Analytical solution and parameter estimation for heat of wetting and vapor adsorption during spontaneous imbibition in tuff

An analytical expression is derived for the thermal response observed during spontaneous imbibition of water into a dry core of zeolitic tuff. Sample tortuosity, thermal conductivity, and thermal source strength are estimated from fitting an analytical solution to temperature observations during a single laboratory test. Here, the closed-form analytical solution is derived using Green's functions for heat conduction in the limit of “slow” water movement; that is, when advection of thermal energy with the wetting front is negligible. The solution has four free fitting parameters and is efficient for parameter estimation. Laboratory imbibition data used to constrain the model include a time series of the mass of water imbibed, visual location of the wetting front through time, and temperature time series at six locations. The thermal front reached the end of the core hours before the visible wetting front. Thus, the predominant form of heating during imbibition in this zeolitic tuff is due to vapor adsorption in dry zeolitic rock ahead of the wetting front. The separation of the wetting front and thermal front in this zeolitic tuff is significant, compared to wetting front behavior of most materials reported in the literature. This work is the first interpretation of a thermal imbibition response to estimate transport (tortuosity) and thermal properties (including thermal conductivity) from a single laboratory test.

36 MATERIALS SCIENCE↗

NASA NTRS1986

Local equilibrium assumption for round jet calculations

The similarity solutions of So and Hwang (1986) for self-preserving incompressible turbulent round jets are used to derive closed-form similarity solutions to the k and epsilon equations, and the effect of the local-equilibrium assumption (LEA) on round-jet computations is evaluated. Numerical results are presented graphically and compared with the experimental data of Wygnanski and Fiedler (1969) and the computational results of Launder et al. (1972) and Vollmers and Rotta (1977). It is found that when the LEA is accounted for, the jet-centerline turbulent kinetic energy k0 decays as 1/x (where x is the axial coordinate), whereas without accounting for LEA it decays as 1/(x squared); 1/x decay is shown to be in better agreement with observations.

So, R. M. C.↗

NASA NTRS2006

General Solution for Theoretical Packet Data Loss Rate

Communications systems which transfer blocks ("frames") of data must use a marker ("frame synchronization pattern") for identifying where a block begins. A technique ("frame synchronization strategy") is used to locate the start of each frame and maintain synchronization as additional blocks are processed. A device which strips out the frame synchronization pattern [FSP] and provides an "end of frame" pulse is called a frame synchronizer. As clock and data errors are introduced into the system, the start-of-block marker becomes displaced and/or corrupted. The capability of the frame synchronizer to stay locked to the pattern under these conditions is a figure of merit for the frame synchronization strategy. It is important to select a strategy which will stay locked nearly all the time at bit error rates where the data is usable. ("Bit error rate" [BER] is the fraction of binary bits which are inverted by passage through a communication system.) The fraction of frames that are discarded because the frame synchronizer is not locked is called "Percent Data Loss" or "Packet Data Loss rate" [PDL]. A general approach for accurately predicting PDL given BER was developed in Theoretical Percent Data Loss Calculation and Measurement Accuracy, T. P. Kelly, LESC-30554, December 1992. Kelly gave a solution in terms of matrix equations, and only addressed "level" channel encoding. This paper goes on to give a closed-form polynomial solution for the most common class of frame synchronizer strategies, and will also address "mark" and "space" (differential) channel encoding, and burst error environments. The paper is divided into four sections and follows a logically ordered presentation, with results developed before they are evaluated. However, most readers will derive the greatest benefit from this paper by treating the results as reference material. The result developed for differential encoding can be extended to other applications (like block codes) where the probability is needed that a block contains only a certain number of errors.

Lansdowne, Chatwin↗

NASA NTRS2015

Fairing Separation Analysis Using SepTOOL

This document describes the relevant equations programmed in spreadsheet software, SepTOOL, developed by ZIN Technologies, Inc. (ZIN) to determine the separation clearance between a launch vehicle payload fairing and remaining stages. The software uses closed form rigid body dynamic solutions of the vehicle in combination with flexible body dynamics of the fairing, which is obtained from flexible body dynamic analysis or from test data, and superimposes the two results to obtain minimum separation clearance for any given set of flight trajectory conditions. Using closed form solutions allows SepTOOL to perform separation calculations several orders of magnitude faster compared to numerical methods which allows users to perform real time parameter studies. Moreover, SepTOOL can optimize vehicle performance to minimize separation clearance. This tool can evaluate various shapes and sizes of fairings along with different vehicle configurations and trajectories. These geometries and parameters are inputted in a user friendly interface. Although the software was specifically developed for evaluating the separation clearance of launch vehicle payload fairings, separation dynamics of other launch vehicle components can be evaluated provided that aerodynamic loads acting on the vehicle during the separation event are negligible. This document describes the development of SepTOOL providing analytical procedure and theoretical equations whose implementation of these equations is not disclosed. Realistic examples are presented, and the results are verified with ADAMS (MSC Software Corporation) simulations. It should be noted that SepTOOL is a preliminary separation clearance assessment software for payload fairings and should not be used for final clearance analysis.

fairings↗

NASA NTRS1993

An extended laser flash technique for thermal diffusivity measurement of high-temperature materials

Knowledge of thermal diffusivity data for high-temperature materials (solids and liquids) is very important in analyzing a number of processes, among them solidification, crystal growth, and welding. However, reliable thermal diffusivity versus temperature data, particularly those for high-temperature liquids, are still far from complete. The main measurement difficulties are due to the presence of convection and the requirement for a container. Fortunately, the availability of levitation techniques has made it possible to solve the containment problem. Based on the feasibility of the levitation technology, a new laser flash technique which is applicable to both levitated liquid and solid samples is being developed. At this point, the analysis for solid samples is near completion and highlights of the technique are presented here. The levitated solid sample which is assumed to be a sphere is subjected to a very short burst of high power radiant energy. The temperature of the irradiated surface area is elevated and a transient heat transfer process takes place within the sample. This containerless process is a two-dimensional unsteady heat conduction problem. Due to the nonlinearity of the radiative plus convective boundary condition, an analytic solution cannot be obtained. Two options are available at this point. Firstly, the radiation boundary condition can be linearized, which then accommodates a closed-form analytic solution. Comparison of the analytic curves for the temperature rise at different points to the experimentally-measured values will then provide the thermal diffusivity values. Secondly, one may set up an inverse conduction problem whereby experimentally obtained surface temperature history is used as the boundary conditions. The thermal diffusivity can then be elevated by minimizing the difference between the real heat flux boundary condition (radiation plus convection) and the measurements. Status of an experimental study directed at measuring the thermal diffusivity of high-temperature solid samples of pure Nickel and Inconel 718 superalloys are presented. Preliminary measurements showing surface temperature histories are discussed.

Shen, F.↗

NASA NTRS1987

Solutions of some problems in applied mathematics using MACSYMA

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Punjabi, Alkesh↗

NASA NTRS1974

Diagnostics of seeded RF plasmas: An experimental study related to the gaseous core reactor

Measurements of the temperature profiles in an RF argon plasma were made over magnetic field intensities ranging from 20 amp turns/cm to 80 amp turns/cm. The results were compared with a one-dimensional numerical treatment of the governing equations and with an approximate closed form analytical solution that neglected radiation losses. The average measured temperatures in the plasma compared well with the numerical treatment, though the experimental profile showed less of an off center temperature peak than predicted by theory. This may be a result of the complex turbulent flow pattern present in the experimental torch and not modeled in the numerical treatment. The radiation term cannot be neglected for argon at the power levels investigated. The closed form analytical approximation that neglected radiation led to temperature predictions on the order of 1000 K to 2000 K higher than measured or predicted by the numerical treatment which considered radiation losses.

Thompson, S. D.↗

DOE OSTI2022

Putting multipoint kinetics to the test: preliminary analysis of the MUSE-4 experiment with APOLLO3

Modeling neutron kinetics is a challenging task and over the years, several approaches have been developed offering different tradeoffs between precision and cost. Probably the most popular one is point kinetics (PK), which, despite being very cheap, provides good results for many applications. One of the limitations of PK is that it is not able to model effects that happen before the prompt jump time scale. In practice, applications, where those time scales are interesting, are rare and those for which experimental data are available are even rarer. One of those cases is the MUSE-4 experiment for which the focus is on the very fast behavior and where we have no thermal feedback. As we have shown in a recent paper, a simple extension of PK, known as multipoint kinetics (MPK), can overcome this limitation. In this paper, which is intended as a preliminary study, we show how a simple MPK model can qualitatively reproduce the fast behavior that we cannot model with PK. Moreover, we will show how to exploit its low cost and compact form to model also slow effects as the precursors built up, behaviours that are not affordable to model with more expensive techniques, such as kinetic Monte Carlo simulations. For the periodic pulse transients with no feedbacks we will also provide an analytical solution in closed form. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2002

Analysis of Tank PMD Rewetting Following Thrust Resettling

Recent investigations have successfully demonstrated closed-form analytical solutions of spontaneous capillary flows in idealized cylindrical containers with interior corners. In this report, the theory is extended and applied to complex containers modeling spacecraft fuel tanks employing propellant management devices (PMDs). The specific problem investigated is one of spontaneous rewetting of a typical partially filled liquid fuel/cryogen tank with PMD after thrust resettling. The transients of this flow impact the logistics of orbital maneuvers and potentially tank thermal control. The general procedure to compute the initial condition (mean radius of curvature for the interface) for the closed-form transient flows is first outlined then solved for several 'complex' cylindrical tanks exhibiting symmetry. The utility and limitations of the technique as a design tool are discussed in a summary, which also highlights comparisons with NASA flight data of a model propellant tank with PMD.

Weislogel, M. M.↗

NASA NTRS2001

A {1,2}-Order Plate Theory Accounting for Three-Dimensional Thermoelastic Deformations in Thick Composite and Sandwich Laminates

A {1,2}-order theory for laminated composite and sandwich plates is extended to include thermoelastic effects. The theory incorporates all three-dimensional strains and stresses. Mixed-field assumptions are introduced which include linear in-plane displacements, parabolic transverse displacement and shear strains, and a cubic distribution of the transverse normal stress. Least squares strain compatibility conditions and exact traction boundary conditions are enforced to yield higher polynomial degree distributions for the transverse shear strains and transverse normal stress through the plate thickness. The principle of virtual work is used to derive a 10th-order system of equilibrium equations and associated Poisson boundary conditions. The predictive capability of the theory is demonstrated using a closed-form analytic solution for a simply-supported rectangular plate subjected to a linearly varying temperature field across the thickness. Several thin and moderately thick laminated composite and sandwich plates are analyzed. Numerical comparisons are made with corresponding solutions of the first-order shear deformation theory and three-dimensional elasticity theory. These results, which closely approximate the three-dimensional elasticity solutions, demonstrate that through - the - thickness deformations even in relatively thin and, especially in thick. composite and sandwich laminates can be significant under severe thermal gradients. The {1,2}-order kinematic assumptions insure an overall accurate theory that is in general superior and, in some cases, equivalent to the first-order theory.

Tessler, A.↗

NASA NTRS1988

Benchmark solutions for the galactic ion transport equations with spatial and energy coupling

In order to anticipate future space shielding requirements, NASA has initiated an effort to formulate computational methods to simulate radiation effects in space. As part of the program, numerical transport algorithms have been developed for the deterministic Boltzman equation describing galactic cosmic ray (GCR) interactions with matter. It thus becomes necessary to assess the accuracy of proposed deterministic algorithms. For this reason, analytical benchmark solutions to mathematically tractable galactic cosmic ray equations have recently been obtained. Even though these problems involve simplifying assumptions of the associated physics, they still contain the essential features of the basic transport processes. The solutions obtained are features of the basic transport processes. The solutions obtained are compared to results from numerical algorithms in order to ensure proper coding and to provide a measure of the accuracy of the numerical methods used in the algorithm. For the first time, mathematical methods have been applied to the galactic ion transport (GIT) equations in the straight ahead approximation with constant nuclear properties. The approach utilizes a Laplace transforms inversion yielding a closed form benchmark solution which is also computationally efficient.

Ganapol, Barry D.↗

NASA NTRS2005

Rover mast calibration, exact camera pointing, and camara handoff for visual target tracking

This paper presents three technical elements that we have developed to improve the accuracy of the visual target tracking for single-sol approach-and-instrument placement in future Mars rover missions. An accurate, straightforward method of rover mast calibration is achieved by using a total station, a camera calibration target, and four prism targets mounted on the rover. The method was applied to Rocky8 rover mast calibration and yielded a 1.1-pixel rms residual error. Camera pointing requires inverse kinematic solutions for mast pan and tilt angles such that the target image appears right at the center of the camera image. Two issues were raised. Mast camera frames are in general not parallel to the masthead base frame. Further, the optical axis of the camera model in general does not pass through the center of the image. Despite these issues, we managed to derive non-iterative closed-form exact solutions, which were verified with Matlab routines. Actual camera pointing experiments aver 50 random target image paints yielded less than 1.3-pixel rms pointing error. Finally, a purely geometric method for camera handoff using stereo views of the target has been developed. Experimental test runs show less than 2.5 pixels error on high-resolution Navcam for Pancam-to-Navcam handoff, and less than 4 pixels error on lower-resolution Hazcam for Navcam-to-Hazcam handoff.

camera handoff↗

DOE OSTI2021

Analytic phase solutions of three-wave interactions

Closed-form analytic phase solutions of three-wave interactions are presented for the first time. The cases from simple second harmonic generation to most general three wave interactions without any constraints are considered. The phase amplification or deamplification behavior in the phase-sensitive parametric process is illustrated using the results obtained here. The analytic solutions agree with the results from direct numerical integration. The validity range of an approximate phase solution is discussed.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A phased workflow to define permit‐ready locations for large volume CO 2 injection and storage

Abstract To‐date, only two UIC Class VI permits have been issued by the US Environmental Protection Agency. We illustrate a four‐phase workflow to first identify regional storage resources and then down‐select sites to yield permit‐ready locations that can accept and store large volumes of CO 2 . Specific permit requirements should guide objectives and define deliverables of respective workflow phases. In the first phase we used available regional data and screened structure and injection zones to locate resources that match CO 2 volumes planned to be captured. Available data were also used to assess presence and depth of usable groundwater, the key resource being protected via permitting. We then used advanced, closed‐form, analytical solutions (EASiTool) to estimate CO 2 injectivity into each hydrologically connected injection compartment. In the second phase we acquired and conditioned additional wireline logs and leased available seismic datasets. We interpreted the depositional systems from wireline well‐log character and mapped sandbody geometry to interpolate injection and confining‐zone distribution. Using available data, we mapped faults and locations of freshwater and overpressure (or other capacity‐limiting geologic parameters) in more detail. In the third phase, we used the augmented geologic data to develop a static model for the selected area, extracted the areas of highest interest, and generated and ran dynamic (flow) models. In a fourth phase, we reduced major uncertainties identified in earlier phases. Our case study indicates that to complete preparation of a permit application requires (1) improved lithologic characterization information (thicknesses and horizontal and vertical connectivity) and (2) better definition of poorly defined local faults. © 2023 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

58 GEOSCIENCES↗

DOE OSTI2022

Multiscale plasticity of geomaterials predicted via constrained optimization‐based granular micromechanics

Abstract A general framework to derive nonlinear elastic and elastoplastic material models from granular micromechanics is proposed, where a constraint‐based variational structure is introduced to classical grain contact‐based homogenization methods of hyperelasticity. Like the classical hyperelastic methods, reference solutions for closed‐form hyperelastic material models are analytically derived from the grain‐scale contact mechanics. However, unlike prior methods, the proposed homogenization framework defines closed‐form hyperelastoplastic material models that extend multiscale variational methods to granular plasticity. The proposed framework is used to develop novel granular micromechanics‐based macroscopic models for a Mises type solid, Drucker–Prager type plasticity, and grain‐contact cohesive‐debonding with a deviatorically and volumetrically coupled nonlinearly elastic response. Macroscopic plastic parameters and yield criteria are explicitly related to their microscale counterparts, for example, the friction coefficient governing intergranular slip. Numerical examples and comparison to measurements from the literature, including triaxial compaction of concrete, are provided to investigate model predictions and demonstrate calibration to experimental data.

Bryant, E. C.↗

DOE OSTI2023

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Engineering↗