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At least 685 records · Page 38

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DOE OSTI2020

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy-shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

42 ENGINEERING↗

DOE OSTI2024

Optical second harmonic generation in anisotropic multilayers with complete multireflection of linear and nonlinear waves using ♯SHAARP.ml package

Abstract Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. Closed-form analytical solution of the nonlinear optical responses is essential for evaluating materials whose optical properties are unknown a priori. A recent open-source code, ♯SHAARP. si , can provide such closed form solutions for crystals with arbitrary symmetries, orientations, and anisotropic properties at a single interface. However, optical components are often in the form of slabs, thin films on substrates, and multilayer heterostructures with multiple reflections of both the fundamental and up to ten different SHG waves at each interface, adding significant complexity. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry in Multilayers (♯SHAARP. ml ). The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes using standard and commonly used nonlinear optical materials as well as twisted 2-dimensional heterostructures.

36 MATERIALS SCIENCE↗

NASA NTRS1985

Least squares inversion of Stokes profiles in the presence of velocity gradients

The Auer, Heasley and House Stokes inversion procedure in use at High Altitude Observatory is based on the analytic solution of the equation of transfer for polarized light where the representation of the thermodynamic and magnetic structure of the atmosphere is assumed to have a high degree of invariance, namely, a Milne-Eddington (ME) structure with a constant magnetic field. In the presence of invariance breaking gradients the resultant Stokes profiles are represented only approximately, if at all, by analytic forms. The accuracy of the inversion parameters and their significance as measures of actual structure are explored for the ME and the Landman-Finn sunspot models under the effects of velocity gradients. The resulting field parameters are good to a few percent and prove to be insensitive to the errors committed by the use of a ME-representation, but the resulting ME parameters yield a less precise measure of thermal structure.

Skumanich, A.↗

NASA NTRS1988

I-BIEM, an iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries: A new algorithm. I - Theoretical

A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions, using Green's second identity, is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro- and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1 percent to 0.01 percent of the theoretical values are obtained in a few minutes on a microcomputer.

Cahan, B. D.↗

NASA NTRS1989

Similarity solutions for phase-change problems

A modification of Ivantsov's (1947) similarity solutions is proposed which can describe phase-change processes which are limited by diffusion. The method has application to systems that have n-components and possess cross-diffusion and Soret and Dufour effects, along with convection driven by density discontinuities at the two-phase interface. Local thermal equilibrium is assumed at the interface. It is shown that analytic solutions are possible when the material properties are constant.

Canright, D.↗

NASA NTRS2001

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2002

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2004

Reliability of Complex Nonlinear Numerical Simulations

This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

NASA NTRS2005

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

Yee, H. C.↗

NASA NTRS1983

Viscoelastic study of an adhesively bonded joint

The plane strain problem of two dissimilar orthotropic plates bonded with an isotropic, linearly viscoelastic adhesive is considered. Both the shear and the normal stresses in the adhesive are calculated for various geometries and loading conditions. Transverse shear deformations of the adherends are taken into account, and their effect on the solution is shown in the results. All three inplane strains of the adhesive are included. Attention is given to the effect of temperature, both in the adhesive joint problem and to the heat generation in a viscoelastic material under cyclic loading. This separate study is included because heat generation and or spatially varying temperature are at present too difficult to account for in the analytical solution of the bonded joint, but whose effect can not be ignored in design.

Joseph, P. F.↗

DOE OSTI2020

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology is undoubtedly one of the fields where fractional calculus has become an integral part of cutting-edge research. There exists extensive literature on the theoretical, experimental, and numerical treatment of various fractional viscoelastic flows in constraint geometries. However, the general theoretical approach that unites several most commonly used models is missing. Here we present exact analytical solutions for fractional viscoelastic flow in a circular pipe. We find velocity profiles and shear stresses for fractional Maxwell, Kelvin–Voigt, Zener, Poynting–Thomson, and Burgers models. The dynamics of these quantities are studied with respect to normalized pipe radius, fractional orders, and elastic moduli ratio. Three different types of behavior are identified: monotonic increase, resonant, and aperiodic oscillations. The models developed are applicable in the widest material range and allow for the alteration of the balance between viscous and elastic properties of the materials.

Gritsenko, Dmitry (ORCID:0000000248181512)↗

DOE OSTI2026

Thermo-hydro-mechanical analysis of subsurface ice-based thermal energy storage

Ice-based thermal energy storage systems are widely utilized for cooling and managing peak electrical demand globally, offering daily or weekly storage capabilities for both individual homes and larger office buildings. However, scaling these systems for district-level cooling or integrating them with renewable energy sources presents challenges, especially in accommodating larger volumes and addressing seasonal storage requirements in densely populated urban areas. This paper proposes a novel solution by evaluating subsurface ice-based thermal energy storage, in which the underground is subjected to seasonal freeze/thaw cycles. However, these cycles may influence ground behavior, affecting pore pressure and inducing ground movement. To systematically investigate these challenges, we enhance the TOUGH-FLAC simulator by integrating water/ice phase change capabilities and updating the effective stress–strain constitutive relation. Both modifications are validated against analytical solutions or experimental data. Through numerical simulations spanning a decade with ten seasonal freeze/thaw cycles, we evaluate the performance and long-term stability of a generic subsurface ice-based thermal energy storage system, considering factors such as ground permeability, freezing pipe spacing, freeze/thaw damage, and glycol solution temperature. The simulations indicate that ice formation induces pore pressure variations that drive seasonal surface heave and settlement, controlled by ground permeability, pipe spacing, and glycol solution temperature, along with tensile and localized shear deformation around freeze pipes. This highlights the need for accurate ground property characterization and geomechanical analysis for subsurface ice-based thermal energy storage.

Ground freezing↗

DOE OSTI2024

DECOVALEX-2023: Task C Final Report

The Full-scale Emplacement (FE) heater experiment at the Mont Terri Underground Rock Laboratory (URL) was designed and conducted by Nagra to replicate an emplacement tunnel of Nagra’s reference repository design at 1:1 scale. Alongside testing the technical feasibility of constructing disposal tunnels, emplacing waste containers in the tunnels and then backfilling them, the main goals of the FE experiment are (1) to obtain a better understanding of the coupled effects of induced thermo-hydro-mechanical (THM) processes that may occur and (2) to validate existing coupled THM models (Müller et al., 2017). A key aspect of ensuring safety for repositories located in low-permeability rock involves minimizing any damage to the rock itself, thereby preserving its integrity and promoting a stable environment Amongst a number of processes that could damage the rock is the increase in pore pressure due to thermal loading caused by heat emitted from the waste. To reduce the potential damage of the rock, it is important to analyse the evolution of heat over time due to the heat load of the containers and assess possible consequences by coupled THM models. The aim of Task C of DECOVALEX-2023 was to build 3D numerical models of the FE experiment, focussing in particular on the heating induced pore pressure change in the Opalinus Clay. Data from a large number of sensors were available from the FE experiment for model comparison. These sensors measured temperature and relative humidity in the bentonite around the heaters, and temperature, pressure and displacement/strain in the surrounding Opalinus clay. Data were available from the start of excavation (April 2012) up to August 2020 for most sensors (more than 5 years from the start of heating in December 2014). To fulfil the overall aim of the task, the work was broken down into a number of steps, starting with simpler models to build confidence in each team’s approach and then moving to more complex models that better represent the FE experiment. Step 0 consisted of 2D benchmark models, gradually increasing the number of processes that are represented from thermal (T) only models in Step 0a, to coupled thermal hydraulic (TH) models in Step 0b with a representation of changing porosity, to coupled thermo-hydro-mechanical (THM) models in Step 0c, where porosity changes are calculated by the mechanical model. A detailed specification of processes, parameters, initial and boundary conditions was provided for this step, with the ambition that all teams would work towards close agreement in their model results, thus building confidence in the model implementations. vi It was not straightforward to achieve agreement between the teams, so additional steps (Step 0b2, 0b3, 0c2, 0c3) were added along with derivation of some analytical solutions against which the models could be compared. The reasons for the differences between teams were investigated and found to be caused primarily by different conceptual model assumptions (including temperature dependence of the thermal expansion of water), different model formulations (including porosity evolution) and differences in modelled domain sizes, boundary conditions and grid discretisation. This demonstrates that comparisons between multiple modelling teams and/or comparison with analytical results and experimental data are highly beneficial in providing an indication of uncertainty in model predictions. At the conclusion of Step 0, almost all teams had achieved a close agreement in model results and those that had not achieved an agreement knew the reason for this. Step 1 moved from 2D models to 3D models of the FE experiment without adding technical features like shotcrete or EDZ, and only considering the heating phase. Initially the 3D model was tightly specified to continue to build confidence in the model implementations (Step 1a). The results of Step 1a were compared to the data from the FE-experiment without the teams seeing the data. The teams were then provided with a sub-set of the data from the FE-experiment and invited to consider how best to use the large dataset for model comparison (Step 1b). Teams were then asked to use the data provided to calibrate their models, only changing material property values rather than adding features or processes to their models (Step 1c). In Step 1, teams were asked to only model the heating phase of the experiment, so pressure in the Opalinus Clay was reported as change in pressure since the initial conditions were specified rather than modelled. The change from 2D to 3D models was accompanied by an increase in the dispersion of results between the teams. Some of this was resolved during the task, but some remained and is potentially due to model discretisation. Calibration of parameters was useful in improving the fit of the models to the data but the remaining differences indicated that the models were missing features or processes. In Step 2, the teams were asked to update their models with additional features and processes as well as calibrating parameters to try and improve the fit of the models to the data. Teams were encouraged to represent ventilation of the open FE tunnel prior to backfilling with heaters and bentonite and in Step 2, the absolute pressure in the Opalinus Clay was compared between the teams. Teams took different approaches, but there was consideration of adding shotcrete and an EDZ into the model, representing stress change during excavation and different approaches to modelling ventilation of the FE tunnel. Overall, the documented results showed a very good agreement for temperature. The results for porewater pressure evolution showed a significant improvement for most teams compared to Step 1c with a good agreement to the measurements for several teams whereas some teams overpredicted the pressure increase and others overpredicted the drainage effect especially for the sensors close to the heater. Step 3 was an opportunity for teams to use the models developed in Step 1 and Step 2 to make predictions about the temperature and pressure changes that will be expected at the FE experiment over the next few years in light of the planned changes in thermal output of the heaters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1991

Particle acceleration near X-type magnetic neutral lines

The behavior of charged particles near X-type magnetic neutral lines is investigated. The magnetic field is taken to be hyperbolic and time stationary, with a uniform electric field perpendicular to the magnetic field. The general properties of the orbits of noninteracting particles in that field geometry are examined. Approximate analytic solutions to the orbit equations are derived by considering a magnetic-insulation picture where there is a hole in the magnetic insulation around the neutral line. Scaling laws for the dependence of the energy gain on strengths of the magnetic and electric fields are derived. The kinetic-energy distribution function for accelerated particles is derived for particles flowing past the neutral line. These analytic derivations are supported by computer simulations, in which the relativistic equations of motion for single test particles are numerically solved and the orbits and kinetic-energy gains of the particles are obtained. A number of simulations were performed and one parameter at a time was varied. Applications of the results to magnetic-neutral-line regions in space physics and astrophysics are possible.

Deeg, Hans-Jorg↗

NASA NTRS1990

Numerical solution of the time-dependent kinetic equation for electrons in magnetized plasma

A numerical solution is developed for the time-dependent kinetic equation describing the evolution of arbitrary distributions of electrons injected into a magnetized plasma. Included in the equation are pitch-angle scattering and energy loss because of Coulomb collisions and magnetic mirroring. The numerical code can be easily modified to include other scattering or radiation terms. The numerical results are shown to agree well with known analytic solutions for various simplified configurations such as homogeneous injection in a homogeneous plasma, electron beams moving with small pitch angle with respect to the magnetic field, and injection into a magnetic trap.

Hamilton, Russell J.↗

NASA NTRS2003

Gust Acoustic Response of a Single Airfoil Using the Space-Time CE/SE Method

A 2D parallel Euler code based on the space-time conservation element and solution element (CE/SE) method is validated by solving the benchmark problem I in Category 3 of the Third CAA Workshop. This problem concerns the acoustic field generated by the interaction of a convected harmonic vortical gust with a single airfoil. Three gust frequencies, two gust configurations, and three airfoil geometries are considered. Numerical results at both near and far fields are presented and compared with the analytical solutions, a frequency-domain solver GUST3D solutions, and a time-domain high-order Discontinuous Spectral Element Method (DSEM) solutions. It is shown that the CE/SE solutions agree well with the GUST3D solution for the lowest frequency, while there are discrepancies between CE/SE and GUST3D solutions for higher frequencies. However, the CE/SE solution is in good agreement with the DSEM solution for these higher frequencies. It demonstrates that the CE/SE method can produce accurate results of CAA problems involving complex geometries by using unstructured meshes.

Scott, James↗

NASA NTRS1975

Calculation procedure for transient heat transfer to a cooled plate in a heated stream whose temperature varies arbitrarily with time

Solutions for the surface temperature and surface heat flux are found for laminar, constant property, slug flow over a plate convectively cooled from below, when the temperature of the fluid over the plate varies arbitrarily with time at the plate leading edge. A simple technique is presented for handling arbitrary fluid temperature variation with time by approximating it by a sequence of ramps or steps for which exact analytical solutions are available.

Sucec, J.↗

NASA NTRS1999

A Single-Lap Joint Adhesive Bonding Optimization Method Using Gradient and Genetic Algorithms

A natural process for any engineer, scientist, educator, etc. is to seek the most efficient method for accomplishing a given task. In the case of structural design, an area that has a significant impact on the structural efficiency is joint design. Unless the structure is machined from a solid block of material, the individual components which compose the overall structure must be joined together. The method for joining a structure varies depending on the applied loads, material, assembly and disassembly requirements, service life, environment, etc. Using both metallic and fiber reinforced plastic materials limits the user to two methods or a combination of these methods for joining the components into one structure. The first is mechanical fastening and the second is adhesive bonding. Mechanical fastening is by far the most popular joining technique; however, in terms of structural efficiency, adhesive bonding provides a superior joint since the load is distributed uniformly across the joint. The purpose of this paper is to develop a method for optimizing single-lap joint adhesive bonded structures using both gradient and genetic algorithms and comparing the solution process for each method. The goal of the single-lap joint optimization is to find the most efficient structure that meets the imposed requirements while still remaining as lightweight, economical, and reliable as possible. For the single-lap joint, an optimum joint is determined by minimizing the weight of the overall joint based on constraints from adhesive strengths as well as empirically derived rules. The analytical solution of the sin-le-lap joint is determined using the classical Goland-Reissner technique for case 2 type adhesive joints. Joint weight minimization is achieved using a commercially available routine, Design Optimization Tool (DOT), for the gradient solution while an author developed method is used for the genetic algorithm solution. Results illustrate the critical design variables as a function of adhesive properties and convergences of different joints based on the two optimization methods.

Smeltzer, Stanley S., III↗