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Baty, Roy S.

Publications and source records attributed to Baty, Roy S..

18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Ambient melting behavior of stoichiometric uranium oxides

As UO 2 is easily oxidized during the nuclear fuel cycle it is important to have a detailed understanding of the structures and properties of the oxidation products. Experimental work over the years has revealed many stable uranium oxides including UO 2 , U 4 O 9 (UO 2.25 ), U 3 O 7 (UO 2.33 ), U 2 O 5 (UO 2.5 ), U 3 O 8 (UO 2.67 ), and UO 3 , all with a number of different polymorphs. These oxides are broadly split into two categories, fluorite-based structures with stoichiometries in the range of UO 2 to UO 2.5 and less dense layered-type structures with stoichiometries in the range of UO 2.5 to UO 3 . While UO 2 is well characterized, both experimentally and computationally, there is a paucity of data concerning higher stoichiometry oxides in the literature. In this work we determine the ambient melting points of all the six stoichiometric uranium oxides listed above and compare them to the available experimental and/or theoretical data. We demonstrate that a family of the six ambient melting points map out a solid-liquid transition boundary consistent with the high-temperature portion of the phase diagram of uranium-oxygen system suggested by Babelot et al.

Burakovsky, Leonid↗
DOE OSTI2021

On the Symmetry of Blast Waves

This paper presents a brief historical review of G. I. Taylor’s solution of the point blast wave problem which was applied to the Trinity test of the first atomic bomb. Lie group symmetry techniques (also referred to throughout this paper as geometric techniques) are used to derive Taylor’s famous two-fifths law that relates the position of a blast wave to the time after the explosion and the total energy released. The theory of exterior differential systems is combined with the method of characteristics to demonstrate that the solution of the blast wave problem is directly related to the basic relationships that exist between the symmetry (or geometry) and the physics of wave propagation through the equations of motion. The point blast wave model is cast in terms of two exterior differential systems, and both systems are shown to be integrable with local solutions for the velocity, pressure, and density along curves in space and time behind the blast wave. This work is dedicated to the memory of Professor Roy Axford, who introduced many of his students to the topic of symmetry analysis of differential equations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Scale Invariance of the Homentropic Inviscid Euler Equations with Application to the Noh Problem

We investigate the inviscid compressible flow (Euler) equations constrained by an ”isentropic” equation of state (EOS), whose functional form in pressure is an arbitrary function of density alone. Under the aforementioned condition, we interrogate using symmetry methods the scale-invariance of the homentropic inviscid Euler equations. We find that under general conditions, we can reduce the inviscid Euler equations into a system of two coupled ordinary differential equations. To exemplify the utility of these results, we formulate two example scale-invariant, self-similar solutions. The first example includes a shock-free expanding bubble scenario, featuring a modified Tait EOS. The second example features the classical Noh problem, coupled to an arbitrary isentropic EOS. In this case, in order to satisfy the conditions set forth in the classical Noh problem, we find that the solution for the flow is given by a transcendental algebraic equation in the shocked density.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Collapsing Cavities and Converging Shocks in Non-Ideal Materials

As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is unsuited to many real applications, especially those involving high pressure and speed metal deformation. In this work, we consider the collapsing cavity and converging shock test problems, showing to what extent the ideal gas assumption can be removed from their specification. It is found that while most materials simply do not admit simple (that is scaling) solutions in this context, there are infinite-dimensional families of materials which do admit such solutions. We characterize such materials, derive the appropriate ordinary differential equations and analyze the associated nonlinear eigenvalue problem. It is shown that there is an inherent tension between boundedness of the solution, boundedness of its derivatives and the entropy condition. The special case of a constant-speed cavity collapse is considered and found to be heuristically possible, contrary to common intuition. Finally, we give an example of a concrete non-ideal collapsing cavity scaling solution based on a recently proposed pseudo-Mie–Gruneisen equation of state.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Piston driven converging shock waves in a stiffened gas

We present that the problem of a one-dimensional (1D) cylindrically or spherically symmetric shock wave converging into an inviscid, ideal gas was first investigated by Guderley[Starke kugelige und zylinrische verdichtungsstosse in der nahe des kugelmitterpunktes bzw. Der zylinderachse,” Luftfahrtforschung 19, 302 (1942)]. In the time since, many authors have discussed the practical notion of how Guderley-like flows might be generated. One candidate is a constant velocity, converging “cylindrical or spherical piston,” giving rise to a converging shock wave in the spirit of its classical, planar counterpart. A limitation of pre-existing analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is of course necessary for the direct comparison with the classical Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility in describing a wide variety of physical phenomena and, in particular, the shock compression of solid materials. This work is thus intended to provide an extension of previous work to a nonideal EOS. The stiff gas EOS is chosen as a logical starting point due to not only its close resemblance to the ideal gas law but also its relevance to the shock compression of various liquid and solid materials. Using this choice of EOS, the solution of a 1D planar piston problem is constructed and subsequently used as the lowest order term in a quasi-self-similar series expansion intended to capture both curvilinear and nonideal EOS effects. The solution associated with this procedure provides correction terms to the 1D planar solution so that the expected accelerating shock trajectory and nontrivially varying state variable profiles can be obtained. This solution is further examined in the limit as the converging shock wave approaches the 1D curvilinear origin. Lastly, given the stiff gas EOS is not otherwise expected to admit a Guderley-like solution when coupled to the inviscid Euler equations, this work thus provides the semianalytical limiting behavior of a flow that cannot be otherwise captured using self-similar analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Conservation laws in discrete geometry

The small length scales of the dissipative processes of physical viscosity and heat conduction are typically not resolved in the numerical simulation of high Reynolds number flows in the discrete geometry of computational grids. Historically, the simulations of flows with shocks and/or turbulence have relied on solving the Euler equations with dissipative regularization. In this paper, we begin by reviewing the regularization strategies used in shock wave calculations in both a Lagrangian and an Eulerian framework. We exhibit the essential similarities with Large Eddy Simulation models of turbulence, namely that almost all of these depend on the square of the size of the computational cell. In our principal result, we justify that dependence by deriving the evolution equations for a finite-sized volume of fluid. Those evolution equations, termed finite scale Navier-Stokes (FSNS), contain dissipative terms similar to the artificial viscosity first proposed by von Neumann and Richtmyer. Here, we describe the properties of FSNS, provide a physical interpretation of the dissipative terms and show the connection to recent concepts in fluid dynamics, including inviscid dissipation and bi-velocity hydrodynamics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2008

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.

Baty, Roy S.↗
NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗
NASA NTRS1996

Shock-free supersonic elliptic nozzles and method of forming same

A method of forming a shock-free supersonic elliptic nozzle, in which the nozzle to be designed is divided into three sections, a circular-to-elliptic section which begins at a circular nozzle inlet, an elliptic subsonic section downstream from the circular-to-elliptic section and a supersonic section downstream from the elliptic subsonic section. The maximum and minimum radii for each axial point in the circular-to-elliptic section and the elliptic subsonic section are then separately determined, the maximum and minimum radii being the radii for the widest part of an elliptic cross-section and the narrowest part of the elliptic cross-section, respectively. The maximum and minimum radii for each axial point in the supersonic section are determined based on the Method of Characteristics, Then, each of the three sections are based on the maximum and minimum radii for each axial point in the section. The resulting nozzle is acoustically superior.

Seiner, John M.↗
NASA NTRS1993

Shock-free supersonic elliptic nozzles and method of forming same

A method of forming a shock-free supersonic elliptic nozzle, in which the nozzle to be designed is divided into three sections, a circular-to-elliptic section which begins at a circular nozzle inlet, an elliptic subsonic section downstream from the circular-to-elliptic section, and a supersonic section downstream from the elliptic subsonic section is described. The maximum and minimum radii for each axial point in the circular-to-elliptic section and the elliptic subsonic section are then separately determined, the maximum and minimum radii being the radii for the widest part of an elliptic cross-section and the narrowest part of the elliptic cross-section, respectively. The maximum and minimum radii for each axial point in the supersonic section are determined based on the Method of Characteristics. Then, each of the three sections are based on the maximum and minimum radii for each axial point in the section. The resulting nozzle is acoustically superior.

Seiner, John M.↗
NASA NTRS1990

Instability of a supersonic shock-free elliptic jet

A comparison of the measured and the computed spatial stability properties of an aspect ratio 2, supersonic, shock free, elliptic jet is presented. The shock free nature of the elliptic jet furnishes a perfect test of the validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with the linear hydrodynamic stability theory. Aerodynamic and acoustic data are measured to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. The measured mean velocity profiles are employed to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles utilized in the stability analysis. It is shown that the measured frequency associated with peak amplitude noise radiation agrees with that frequency predicted to dominate the large scale structure near the end of the potential core.

Baty, Roy S.↗
NASA NTRS1990

A linear shock cell model for non-circular jets using conformal mapping with a pseudo-spectral hybrid scheme

The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.

Bhat, Thonse R. S.↗
NASA NTRS1990

Instability of a supersonic shock free elliptic jet

This paper presents a comparison of the measured and the computed spatial stability properties of an aspect ratio 2 supersonic shock free elliptic jet. The shock free nature of the elliptic jet provides an ideal test of validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with linear hydrodynamic stability theory. Both aerodynamic and acoustic data were measured. The data are used to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. A hybrid numerical scheme is applied to solve the Rayleigh problem governing the inviscid linear spatial stability of the jet. The measured mean velocity profiles are used to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles used in the stability analysis. Computational results are presented for several modes of instability at two jet cross sections. The acoustic measurements show that a varicose instability is the jet's perferred mode of motion. The stability analysis predicts that the Strouhal number varies linearly as a function of axial distance in the jet's initial mixing region, which is in good qualitative agreement with previous measurements.

Baty, Roy S.↗
NASA NTRS1989

Instability of jets of arbitrary geometry

This paper describes a calculation technique for determining the stability of jets of arbitrary cross section. In particular, elliptic and rectangular jets are considered. The numerical procedure involves both a conformal transformation between the computational domain and the physical plane and a solution of the transformed stability equation in the computational domain. Modern, efficient, conformal mappings are used for both simply and doubly connected domains. The numerical solution is based on a finite difference/pseudospectral discretization of the stability equation. The technique is verified by comparison with previous calculations for circular and elliptic jets. Calculations are performed for the stability of elliptic and rectangular jets of aspect ratio 2. Growth rates, phase velocities, and pressure eigenfunctions are calculated.

Baty, Roy S.↗