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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Unsteady transonic small-disturbance theory including entropy and vorticity effects

Modifications to unsteady transonic small disturbance theory to include entropy and vorticity effects are presented. The modifications were implemented in the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code. The code permits the aeroelastic analysis of complete aircraft configurations in the flutter critical transonic speed range. Entropy and vorticity effects were incorporated within the solution procedure to more accurately analyze flows with strong shock waves. The modified code includes these effects while retaining the relative simplicity and cost efficiency of the TSD formulation. Detailed descriptions are presented of the entropy and vorticity modifications along with calculated results and comparisons which assess the modified theory. These results are in good agreement with parallel Euler calculations and with experimental data. Therefore, the present method now provides the aeroelastician with an affordable capability to analyze relatively difficult transonic flows without having to solve the computationally more expensive Euler equations.

Batina, John T.↗
NASA NTRS1988

Unsteady transonic small-disturbance theory including entropy and vorticity effects

Modifications to unsteady transonic small-disturbance theory to include entropy and vorticity effects are presented. The modifications have been implemented in the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code developed recently at the NASA Langley Research Center. The code permits the aeroelastic analysis of complete aircraft configurations in the flutter critical transonic speed range. Entropy and vorticity effects have been incorporated within the solution procedure to more accurately analyze flows with strong shock waves. The modified code includes these effects while retaining the relative simplicity and cost efficiency of the TSD formulation. The paper presents detailed descriptions of the entropy and vorticity modifications along with calculated results and comparisons which assess the modified theory. These results are in good agreement with parallel Euler calculations and with experimental data. Therefore, the present method now provides the aeroelastician with an affordable capability to analyze relatively difficult transonic flows without having to solve the computationally more expensive Euler equations.

Batina, John T.↗
NASA NTRS1988

Primordial nucleosynthesis with decaying particles. I - Entropy-producing decays. II - Inert decays

The effect of a nonrelativistic particle X, which decays out of equilibrium, on primordial nucleosynthesis is investigated, including both the energy density of the X particle and the electromagnetic entropy production from its decay. The results are parametrized in terms of the X particle lifetime and the density parameter rm(X), where m(X) is the X particle mass and r is the ratio of X number density to photon number density prior to nucleosynthesis. The results rule out particle lifetimes greater than 1-10 s for large values of rm(X). The question of a decaying particle which produces no electromagnetic entropy in the course of its decay is addressed, and particles which produce both entropy and an inert component in their decay are discussed.

Scherrer, Robert J.↗
NASA NTRS1989

Simple proof of the concavity of the entropy power with respect to Gaussian noise

A very simple proof of M. H. Costa's result that the entropy power of Xt = X + N (O, tI) is concave in t, is derived as an immediate consequence of an inequality concerning Fisher information. This relationship between Fisher information and entropy is found to be useful for proving the central limit theorem. Thus, one who seeks new entropy inequalities should try first to find new inequalities about Fisher information, or at least to exploit the existing ones in new ways.

Dembo, Amir↗
NASA NTRS1990

A kinetic equation with kinetic entropy functions for scalar conservation laws

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

Perthame, Benoit↗
NASA NTRS1992

r-process nucleosynthesis in the high-entropy supernova bubble

We show that the high-temperature, high-entropy evacuated region outside the recent neutron star in a core-collapse supernova may be an ideal r-process site. In this high-entropy environment it is possible that most nucleons are in the form of free neutrons or bound into alpha particles. Thus, there can be many neutrons per seed nucleus even though the material is not particularly neutron rich. The predicted amount of r-process material ejected per event from this environment agrees well with that required by simple galactic evolution arguments. When averaged over regions of different neutron excess in the supernova ejecta, the calculated r-process abundance curve can give a good representation of the solar-system r-process abundances as long as the entropy per baryon is sufficiently high. Neutrino irradiation may aid in smoothing the final abundance distribution.

Meyer, B. S.↗
NASA NTRS1994

Squeezed states and graviton-entropy production in the early universe

Squeezed states are a very useful framework for the quantum treatment of tensor perturbations (i.e. gravitons production) in the early universe. In particular, the non equilibrium entropy growth in a cosmological process of pair production is completely determined by the associated squeezing parameter and is insensitive to the number of particles in the initial state. The total produced entropy may represent a significant fraction of the entropy stored today in the cosmic blackbody radiation, provided pair production originates from a change in the background metric at a curvature scale of the Planck order. Within the formalism of squeezed thermal states it is also possible to discuss the stimulated emission of gravitons from an initial thermal bath, under the action of the cosmic gravitational background field. We find that at low energy the graviton production is enhanced, if compared with spontaneous creation from the vacuum; as a consequence, the inflation scale must be lowered, in order not to exceed the observed CMB quadrupole anisotropy. This effect is important, in particular, for models based on a symmetry-breaking transition which require, as initial condition, a state of thermal equilibrium at temperatures higher than the inflation scale and in which inflation has a minimal duration.

Giovannini, Massimo↗
NASA NTRS1995

Entropy jump across an inviscid shock wave

The shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure are shown to be the same, however density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy, propagation equation cannot be used as a conservation law.

Salas, Manuel D.↗
NASA NTRS1996

Effects of the Stark Shift on the Evolution of the Field Entropy and Entanglement in the Two-Photon Jaynes-Cummings Model

The evolution of the field entropy in the two-photon JCM in the presence of the Stark shift is investigated, and the effects of the dynamic Stark shift on the evolution of the field entropy and entanglement between the atom and field, are examined. The results show that the dynamic Stark shift plays an important role in the evolution of the field entropy in two-photon processes.

Fang, Mao Fa↗
NASA NTRS1999

Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

Shiuhong, Lui↗
NASA NTRS1999

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Yee, H. C.↗
NASA NTRS2013

Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces

Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation methods of arbitrary order. The new methods are closely related to discontinuous Galerkin spectral collocation methods commonly known as DGFEM, but exhibit a more general entropy stability property. Although the new schemes are applicable to a broad class of linear and nonlinear conservation laws, emphasis herein is placed on the entropy stability of the compressible Navier-Stokes equations.

Carpenter, Mark H.↗
NASA NTRS2015

Entropy Stable Staggered Grid Spectral Collocation for the Burgers' and Compressible Navier-Stokes Equations

Staggered grid, entropy stable discontinuous spectral collocation operators of any order are developed for Burgers' and the compressible Navier-Stokes equations on unstructured hexahedral elements. This generalization of previous entropy stable spectral collocation work [1, 2], extends the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to a combination of tensor product Legendre-Gauss (LG) and LGL points. The new semi-discrete operators discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality for both Burgers' and the compressible Navier-Stokes equations in three spatial dimensions. They are valid for smooth as well as discontinuous flows. The staggered LG and conventional LGL point formulations are compared on several challenging test problems. The staggered LG operators are significantly more accurate, although more costly to implement. The LG and LGL operators exhibit similar robustness, as is demonstrated using test problems known to be problematic for operators that lack a nonlinearly stability proof for the compressible Navier-Stokes equations (e.g., discontinuous Galerkin, spectral difference, or flux reconstruction operators).

Carpenter, Mark H.↗
NASA NTRS2016

Towards an Entropy Stable Spectral Element Framework for Computational Fluid Dynamics

Entropy stable (SS) discontinuous spectral collocation formulations of any order are developed for the compressible Navier-Stokes equations on hexahedral elements. Recent progress on two complementary efforts is presented. The first effort is a generalization of previous SS spectral collocation work to extend the applicable set of points from tensor product, Legendre-Gauss-Lobatto (LGL) to tensor product Legendre-Gauss (LG) points. The LG and LGL point formulations are compared on a series of test problems. Although being more costly to implement, it is shown that the LG operators are significantly more accurate on comparable grids. Both the LGL and LG operators are of comparable efficiency and robustness, as is demonstrated using test problems for which conventional FEM techniques suffer instability. The second effort generalizes previous SS work to include the possibility of p-refinement at non-conforming interfaces. A generalization of existing entropy stability machinery is developed to accommodate the nuances of fully multi-dimensional summation-by-parts (SBP) operators. The entropy stability of the compressible Euler equations on non-conforming interfaces is demonstrated using the newly developed LG operators and multi-dimensional interface interpolation operators.

Carpenter, Mark H.↗
DOE OSTI2023

Refractory high entropy alloy compact heat exchanger

Several innovative technologies, including pressure-drop minimization, advanced refractory high entropy alloys, and advanced manufacturing can provide a compact heat exchanger that extends the state-of-the-art heat-exchanger operating range. The compact heat exchanger can reduce pressure drop losses by 100 to 500%, while retaining most of the heat transfer. The compact heat exchanger can be fabricated from refractory high entropy alloys that have favorable corrosion, thermal fatigue, and creep properties at high temperatures and pressures. Therefore, the compact heat exchanger using high entropy alloys can operate at >800° C. and 80 bars.

Kustas, Andrew↗
DOE OSTI2024

Enhancing Mechanical Properties of a Medium-Entropy Alloy by Regulating Mo Addition

Some multi-principal element alloys (MPEAs), including equiatomic, single-phase CrCoNi and CrCoFeMnNi are now widely recognized for their remarkable combinations of pronounced hardening rates, high ductility, and exceptional fracture toughness at room and cryogenic temperatures. To push the limit of hardenability of the medium-entropy alloy, the strategies associated with local lattice distortion or stacking fault energy (SFE) reduction that promote complex heterogeneity and defect dynamics require further investigation. The purposes of this study are to (1) further enhance the mechanical properties of a typical medium-entropy NiCoCr with alloying Mo, and (2) understand the strengthening mechanism of a Mo-added medium-entropy alloys.

Hung, Chang-Yu↗
DOE OSTI2018

Solving the strength-ductility tradeoff in the medium-entropy NiCoCr alloy via interstitial strengthening of carbon

Interstitial solid strengthening is an effective strategy to harden metallic materials, however, it usually deteriorates the ductility. In this work, we report that addition of carbon into the medium-entropy NiCoCr alloy successfully enhances the strength at no expense of ductility. It was found that up to 0.75 at.% carbon was completely solid-solutionized in (NiCoCr )100-x C x (x = 0, 0.10, 0.25, 0.50 and 0.75 at.%) without formation of any carbides. With the increase of carbon content from 0 to 0.75 at.%, the yield and fracture strength were increased from 242 to 347 MPa to 727 and 862 MPa, respectively, whilst the ductility kept as high as about 75%. It is noteworthy that the integral of the stress over strain for the alloy with 0.75 at.% carbon reaches a value of 59 GPa %, surmounting the level of many reported multi-principal elements alloys. Our analysis indicates that carbon addition increases stacking fault energy, thus delaying occurrence of twinning and decreasing the thickness of twin lamellas. At the early deformation stage, carbon decreases the stress localization and stimulates dislocation multiplication. After occurrence of deformation twinning, finer twinning structure in the alloys added with carbon not only can obstacle and trigger more dislocations, but also transfer plastic deformation more efficiently, thus promoting the twinning process, postponing the plastic instability and eventually giving rise to a more pronounced work-hardening. Our conclusions not only have important implications for understanding the solid solution strengthening mechanism in medium-entropy alloys, but also shed lights on developing advanced metallic alloys with a unique combination of strength and ductility.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Effects of transient thermal shock on the microstructures and corrosion properties of a reduced activation high-entropy alloy

The devices would subject transient thermal shocks (TTS) during operation under extremely harsh conditions of nuclear fusion reactors, which inevitably exert significant impact on the microstructure and performance of structural materials. Here, a reduced activation VCrFeTa 0.2 W 0.2 high-entropy alloy (HEA) was developed by vacuum arc melting. The effects of electron beam induced TTS on its microstructure, microhardness, and corrosion properties were investigated. The results indicate that the weight fraction of each phase changes after TTS, showing a significant decrease in the content of BCC1 phase and an increase in the content of BCC2 and Laves phases. The content of BCC1 phase continues to decrease slightly with increasing the power of TTS. Besides, the microhardness of the alloy increases from ~673 HV to ~714 HV after TTS treatments. In the reduced activation HEA, TTS results in a relatively low corrosion current density of ~0.472 μA/cm 2 in 3.5 wt% NaCl solution, around one-third of the current density observed in the as-cast sample. Furthermore, the VCrFeTa 0.2 W 0.2 HEA after TTS exhibits a pitting potential of ~1.165 V SCE , which is much higher than that of the as-cast sample. The refined composite multiscale entropy method is employed to analyze the influence of TTS on current fluctuation behavior during the corrosion process. The reduced activation VCrFeTa 0.2 W 0.2 HEA exhibits excellent properties in harsh environments after TTS, thereby showing advantageous property in the field of nuclear structural materials. Furthermore, TTS is an efficient and controllable strategy for the improvement of the HEAs’ microstructures and performances.

36 MATERIALS SCIENCE↗