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NASA NTRS1972

The entropy rate admissibility criterion for solution of hyperbolic conservation laws

The entropy rate admissibility criterion for solutions of hyperbolic conservation laws is numerically analyzed. The following admissibility criterion for solutions of hyperbolic conservation laws is proposed: a weak solution is admissible if the total entropy decays with the highest possible rate. The equivalence of this criterion and viscosity criterion is established for the single equation and the system of equations of one dimensional nonlinear elasticity.

Dafermos, C. M.↗

NASA NTRS1982

Thermodynamic and transport combustion properties of hydrocarbons with air. Part 1: Properties in SI units

Thermodynamic and transport combustion properties were calculated for a wide range of conditions for the reaction of hydrocarbons with air. Three hydrogen-carbon atom ratios (H/C = 1.7, 2.0, 2.1) were selected to represent the range of aircraft fuels. For each of these H/C ratios, combustion properties were calculated for the following conditions: Equivalence ratio: 0, 0.25, 0.5, 0.75, 1.0, 1.25 Water - dry air mass ratio: 0, 0.03 Pressure, kPa: 1.01325, 10.1325, 101.325, 1013.25, 5066.25 (or in atm: 0.01, 0.1, 1, 10, 50) Temperature, K: every 10 degrees from 200 to 900 K; every 50 degrees from 900 to 3000 K Temperature, R: every 20 degrees from 360 to 1600 R; very 100 degrees from 1600 to 5400 R. The properties presented are composition, density, molecular weight, enthalphy, entropy, specific heat at constant pressure, volume derivatives, isentropic exponent, velocity of sound, viscosity, thermal conductivity, and Prandtl number. Property tables are based on composites that were calculated by assuming both: (1) chemical equilibrium (for both homogeneous and heterogeneous phases) and (2) constant compositions for all temperatures. Properties in SI units are presented in this report for the Kelvin temperature schedules.

Gordon, S.↗

DOE OSTI2023

Dicarbonyl Electrolyte for High-Voltage Lithium Metal Batteries: Importance of the Entropy of Solvation in Bidentate Solvent

An electrolyte system based on dicarbonyl solvents has been proposed and implemented in lithium metal batteries (LMBs). Among several dicarbonyl solvents explored, dimethyl dicarbonate (DMDC) emerged as the most promising electrolyte candidate. Interestingly, despite the structural similarities between DMDC and its monocarbonyl counterpart DMC, the DMDC electrolyte exhibits higher solvent coordination, even at the same lithium-to-carbonyl ratio. Further, this leads to the formation of a more robust solid-electrolyte interphase and enhances the anodic stability of the electrolyte. Notably, in various electrolyte systems, the solvation energy is typically enthalpy-driven. However, the bidentate nature of DMDC introduces a significant role for the entropy of solvation because the Li + -DMDC complexes release fewer free molecules. With the addition of non-solvating co-solvent 1,1,2,2-tetrafluoro-ethyl 2,2,3,3-tetrafluoro-propyl ether (TTE), which reduces the viscosity of the electrolyte, the DMDC-TTE system enables remarkably stable cycling of the lithium anode by manipulating the entropy of solvation. This introduces a new strategy for tailoring functional electrolyte systems.

25 ENERGY STORAGE↗

DOE OSTI2022

Glass length: Workability and meltability of glass as a function of glass melt fragility

Workability and meltability of molten glass are properties important for balancing glass formulation with the design and operations of glass melting and forming facilities. The working and melting “lengths” are the temperature intervals within which glass viscosity allows the melting and forming glass to be performed. They are related to glass melt structure through the glass melt fragility, which, by the augmented Adam-Gibbs equation, is a function of configuration entropy. Both working length and melting length are high for strong glasses and decrease as the melt fragility increases. In this work, analytical formulas are obtained for three-parameter viscosity models VFT, AM, and MYEGA. These models agree with each other and with the Adam-Gibbs equation on the relationship between workability and fragility of glasses but diverge at high-temperatures. The compositional effects on workability and meltability are mediated via the fragility as a function of glass composition expressed in terms of mass and mole component coefficients.

36 MATERIALS SCIENCE↗

NASA NTRS1988

On the convergence of difference approximations to scalar conservation laws

A unified treatment is given for time-explicit, two-level, second-order-resolution (SOR), total-variation-diminishing (TVD) approximations to scalar conservation laws. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced to obtain results in terms of the latter. The existence of a cell entropy inequality is discussed, and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first-order accurate in general. Convergence for TVD-SOR schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Osher, Stanley↗

NASA NTRS1980

An artificial energy method for calculating flows with shocks

The artificial-viscosity method, first proposed by von Neumann and Richtmyer, introduces an artificial viscous pressure term in regions of compression such that an increase in entropy occurs in shock transition zones. The paper describes how dissipative flows can be induced by reducing the total energy available for adiabatic processes in shock zones. A class of inviscid fluid flows, called semiflows, is described in which the flows exhibit thermodynamic differences. Induced dissipative flows modify the pressure in regions of compression in a manner analogous to the artificial-viscosity method and for a gas, the effect is equivalent to suitably modifying the gas constant in the equation of state. By employing MacCormack's method and the usual non-adiabatic equations, numerical solutions of a Riemann problem are compared with the modified artificial energy method, showing that the dissipation effect predicted by the analytical formulation is reflected in the numerical method as well.

Rose, M. E.↗

DOE OSTI2020

Consequences of sp 2 –sp 3 boron isomerization in supercooled liquid borates

In this study, time-resolved high-energy synchrotron x-ray total scattering measurements on supercooled molten lithium metaborate (LiBO 2 ) reveal an isomerization reaction involving conversion of trigonal sp 2 boron to tetrahedral sp 3 boron during quenching and glass formation. Van't Hoff analysis yields an accurate enthalpy change, ΔH = 21(1) kJ mol –1 boron, from which we develop an analytical model for the sp 3 isomer fraction and its contribution to configurational heat capacity (C p conf ) and entropy as a function of temperature and composition. Isomerization constitutes 40% of the total calorimetric C p conf at the glass transition for LiBO 2 and directly contributes to the observed rise in liquid fragility with the lithium content.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1980

Interactive FORTRAN IV computer programs for the thermodynamic and transport properties of selected cryogens (fluids pack)

The thermodynamic and transport properties of selected cryogens had programmed into a series of computer routines. Input variables are any two of P, rho or T in the single phase regions and either P or T for the saturated liquid or vapor state. The output is pressure, density, temperature, entropy, enthalpy for all of the fluids and in most cases specific heat capacity and speed of sound. Viscosity and thermal conductivity are also given for most of the fluids. The programs are designed for access by remote terminal; however, they have been written in a modular form to allow the user to select either specific fluids or specific properties for particular needs. The program includes properties for hydrogen, helium, neon, nitrogen, oxygen, argon, and methane. The programs include properties for gaseous and liquid states usually from the triple point to some upper limit of pressure and temperature which varies from fluid to fluid.

Mccarty, R. D.↗

NASA NTRS1983

Compact finite difference schemes for the Euler and Navier-Stokes equations

Implicit compact finite difference schemes for the Euler equations are described which furnish equivalent treatment of the conservation and nonconservation forms; a simple modification yields an entropy-producing scheme. An extension of the scheme also treats the compressible Navier-Stokes equations; when the viscosity and heat conduction coefficients are negligible only the boundary data appropriate to the Euler equation influence the solution to any significant extent, a result consistent with singular perturbation theory.

Rose, M. E.↗

NASA NTRS1985

On the convergence of difference approximations to scalar conservation laws

A unified treatment of explicit in time, two level, second order resolution, total variation diminishing, approximations to scalar conservation laws are presented. The schemes are assumed only to have conservation form and incremental form. A modified flux and a viscosity coefficient are introduced and results in terms of the latter are obtained. The existence of a cell entropy inequality is discussed and such an equality for all entropies is shown to imply that the scheme is an E scheme on monotone (actually more general) data, hence at most only first order accurate in general. Convergence for total variation diminishing-second order resolution schemes approximating convex or concave conservation laws is shown by enforcing a single discrete entropy inequality.

Osher, S.↗

DOE OSTI2025

Metastability of stratified magnetohydrostatic equilibria and their relaxation

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1982

Design of supercritical swept wings

Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.

Garabedian, P.↗

DOE OSTI2022

Liquid fragility maximum in lithium borate glass‐forming melts related to the local structure

Abstract The structure of liquid lithium pyroborate, Li 4 B 2 O 5 ( J = Li/B = 2), has been measured over a wide temperature range by high‐energy X‐ray diffraction, and compared to that of its glass and borate liquids of other compositions. The results indicate a gradual increase in tetrahedral boron fraction from 3(1)% to 6(1)% during cooling from T = 1271(15) to 721(8) K, consistent with the larger N 4 = 10(1)% found for the glass, and literature 11 B nuclear magnetic resonance measurements. van't Hoff analysis based on a simple boron isomerization reaction BØ 3 O 2 – ⇌ BØO 2 2– yields Δ H = 13(1) kJ mol –1 and Δ S = 40(1) J mol –1 K –1 for the boron coordination change from 4 to 3, which are, respectively, smaller and larger than found for singly charged isomers for J ≤ 1. With these, we extend our model for N 4 ( J , T ), nonbridging oxygen fraction f nbr ( J , T ), configurational heat capacity , and entropy S conf ( J , T ) contributions up to J = 3. A maximum is revealed in at J = 1, and shown semi‐quantitatively to lead to a corresponding maximum in fragility contribution, akin to that observed in the total fragilities by temperature‐modulated differential scanning calorimetry. Lithium is bound to 4.6(2) oxygen in the pyroborate liquid, with 2.7(1) bonds centered around 1.946(8) Å and 1.9(1) around 2.42(1) Å. In the glass, n LiO = 5.4(4), the increase being due to an increase in the number of short Li–O bonds.

36 MATERIALS SCIENCE↗

NASA NTRS1989

Local error estimates for discontinuous solutions of nonlinear hyperbolic equations

Let u(x,t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u sub epsilon(x,t) is the solution of an approximate viscosity regularization, where epsilon greater than 0 is the small viscosity amplitude. It is shown that by post-processing the small viscosity approximation u sub epsilon, pointwise values of u and its derivatives can be recovered with an error as close to epsilon as desired. The analysis relies on the adjoint problem of the forward error equation, which in this case amounts to a backward linear transport with discontinuous coefficients. The novelty of this approach is to use a (generalized) E-condition of the forward problem in order to deduce a W(exp 1,infinity) energy estimate for the discontinuous backward transport equation; this, in turn, leads one to an epsilon-uniform estimate on moments of the error u(sub epsilon) - u. This approach does not follow the characteristics and, therefore, applies mutatis mutandis to other approximate solutions such as E-difference schemes.

Tadmor, Eitan↗

DOE OSTI2020

A general metriplectic framework with application to dissipative extended magnetohydrodynamics

General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that mixes with the usual velocity viscosity. While the Poisson bracket of the ideal version of this model has already been discovered, we determine its metriplectic counterpart that describes the dissipation. This is done using a new and general thermodynamic point of view to derive dissipative brackets, a means of derivation that is natural for understanding and creating dissipative dynamics without appealing to underlying kinetic theory orderings. Finally, the formalism is used to study dissipation in the Lagrangian variable picture where, in the context of extended magnetohydrodynamics, non-local dissipative brackets naturally emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Transverse momentum fluctuations and their correlation with elliptic flow in nuclear collision

In this article, we propose observables v 0 and v 0 (p T ) which quantify the relative fluctuations in the total transverse momentum at fixed multiplicity. We first study the factorization of the fixed multiplicity momentum dependent two particle correlation function into a product of v 0 ($p^{a}_{T}$) and v 0 ($p^{b}_{T}$) within realistic hydrodynamic simulations. Then we present computations of v 0 (p T ) for different particle types. We determine the relation between the integrated v 0 and previously measured observables, and compare results from a hybrid hydrodynamics based model to experimental data. The effects of bulk viscosity and an initial pre-equilibrium stage on the results are quantified. We find that v 0 is strongly correlated with the initial state entropy per elliptic area, S/A. Using this result, we explain how the observed correlations between the elliptic flow and the transverse momentum (both in simulations and experiment) reflect the initial state correlations between 1/A and ellipticity ε 2 at fixed multiplicity. Furthermore, we argue that the systematic experimental study of v 0 , with the same sophistication as used for the other v n , can contribute significantly to our understanding of quark gluon plasma properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1988

Application of a nonisentropic full potential method to AGARD standard airfoils

An entropy-correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Calculated results are presented for the NLR 7301, NACA 0012, and NACA 64A010A airfoils. Comparisons of the present method and solutions of the Euler equations are presented for the NLR 7301 airfoil, and comparisons of the present method and experimental data are presented for all three airfoils. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation. In addition, it is shown that modeling shock-generated entropy extends the range of validity of the full potential method.

Whitlow, Woodrow, Jr.↗

NASA NTRS1988

Application of a nonisentropic full potential method to AGARD standard airfoils

Whitlow, Woodrow, Jr.↗