Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “entropy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

The numerical viscosity of entropy stable schemes for systems of conservation laws. I

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

Tadmor, Eitan↗
NASA NTRS1992

Discrete-time entropy formulation of optimal and adaptive control problems

The discrete-time version of the entropy formulation of optimal control of problems developed by G. N. Saridis (1988) is discussed. Given a dynamical system, the uncertainty in the selection of the control is characterized by the probability distribution (density) function which maximizes the total entropy. The equivalence between the optimal control problem and the optimal entropy problem is established, and the total entropy is decomposed into a term associated with the certainty equivalent control law, the entropy of estimation, and the so-called equivocation of the active transmission of information from the controller to the estimator. This provides a useful framework for studying the certainty equivalent and adaptive control laws.

Tsai, Yweting A.↗
NASA NTRS1993

Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states

We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.

Aragone, C.↗
NASA NTRS1996

Conditional Entropy-Constrained Residual VQ with Application to Image Coding

This paper introduces an extension of entropy-constrained residual vector quantization (VQ) where intervector dependencies are exploited. The method, which we call conditional entropy-constrained residual VQ, employs a high-order entropy conditioning strategy that captures local information in the neighboring vectors. When applied to coding images, the proposed method is shown to achieve better rate-distortion performance than that of entropy-constrained residual vector quantization with less computational complexity and lower memory requirements. Moreover, it can be designed to support progressive transmission in a natural way. It is also shown to outperform some of the best predictive and finite-state VQ techniques reported in the literature. This is due partly to the joint optimization between the residual vector quantizer and a high-order conditional entropy coder as well as the efficiency of the multistage residual VQ structure and the dynamic nature of the prediction.

Kossentini, Faouzi↗
NASA NTRS2014

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Parsani, Matteo↗
NASA NTRS2015

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Parsani, Matteo↗
NASA NTRS1972

Calculation of heat transfer on shuttle type configurations including the effects of variable entropy at boundary layer edge

A relatively simple method is presented for including the effect of variable entropy at the boundary-layer edge in a heat transfer method developed previously. For each inviscid surface streamline an approximate shockwave shape is calculated using a modified form of Maslen's method for inviscid axisymmetric flows. The entropy for the streamline at the edge of the boundary layer is determined by equating the mass flux through the shock wave to that inside the boundary layer. Approximations used in this technique allow the heating rates along each inviscid surface streamline to be calculated independent of the other streamlines. The shock standoff distances computed by the present method are found to compare well with those computed by Maslen's asymmetric method. Heating rates are presented for blunted circular and elliptical cones and a typical space shuttle orbiter at angles of attack. Variable entropy effects are found to increase heating rates downstream of the nose significantly higher than those computed using normal-shock entropy, and turbulent heating rates increased more than laminar rates. Effects of Reynolds number and angles of attack are also shown.

Dejarnette, F. R.↗
NASA NTRS1986

A minimum entropy principle in the gas dynamics equations

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Tadmor, E.↗
NASA NTRS1992

Investigations on entropy layer along hypersonic hyperboloids using a defect boundary layer

A defect approach coupled with matched asymptotic expansions is used to derive a new set of boundary layer equations. This method ensures a smooth matching of the boundary layer with the inviscid solution. These equations are solved to calculate boundary layers over hypersonic blunt bodies involving the entropy gradient effect. Systematic comparisons are made for both axisymmetric and plane flows in several cases with different Mach and Reynolds numbers. After a brief survey of the entropy layer characteristics, the defect boundary layer results are compared with standard boundary layer and full Navier-Stokes solutions. The entropy gradient effects are found to be more important in the axisymmetric case than in the plane one. The wall temperature has a great influence on the results through the displacement effect. Good predictions can be obtained with the defect approach over a cold wall in the nose region, with a first order solution. However, the defect approach gives less accurate results far from the nose on axisymmetric bodies because of the thinning of the entropy layer.

Brazier, J. P.↗
NASA NTRS1996

Monitoring of Time-Dependent System Profiles by Multiplex Gas Chromatography with Maximum Entropy Demodulation

The maximum entropy technique was successfully applied to the deconvolution of overlapped chromatographic peaks. An algorithm was written in which the chromatogram was represented as a vector of sample concentrations multiplied by a peak shape matrix. Simulation results demonstrated that there is a trade off between the detector noise and peak resolution in the sense that an increase of the noise level reduced the peak separation that could be recovered by the maximum entropy method. Real data originated from a sample storage column was also deconvoluted using maximum entropy. Deconvolution is useful in this type of system because the conservation of time dependent profiles depends on the band spreading processes in the chromatographic column, which might smooth out the finer details in the concentration profile. The method was also applied to the deconvolution of previously interpretted Pioneer Venus chromatograms. It was found in this case that the correct choice of peak shape function was critical to the sensitivity of maximum entropy in the reconstruction of these chromatograms.

Becker, Joseph F.↗
NASA NTRS1995

Entropy Generation in Regenerative Systems

Heat exchange to the oscillating flows in regenerative coolers generates entropy. These flows are characterized by oscillating mass flows and oscillating temperatures. Heat is transferred between the flow and heat exchangers and regenerators. In the former case, there is a steady temperature difference between the flow and the heat exchangers. In the latter case, there is no mean temperature difference. In this paper a mathematical model of the entropy generated is developed for both cases. Estimates of the entropy generated by this process are given for oscillating flows in heat exchangers and in regenerators. The practical significance of this entropy is also discussed.

Kittel, Peter↗
NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗
NASA NTRS1997

Absolute Equilibrium Entropy

The entropy associated with absolute equilibrium ensemble theories of ideal, homogeneous, fluid and magneto-fluid turbulence is discussed and the three-dimensional fluid case is examined in detail. A sigma-function is defined, whose minimum value with respect to global parameters is the entropy. A comparison is made between the use of global functions sigma and phase functions H (associated with the development of various H-theorems of ideal turbulence). It is shown that the two approaches are complimentary though conceptually different: H-theorems show that an isolated system tends to equilibrium while sigma-functions allow the demonstration that entropy never decreases when two previously isolated systems are combined. This provides a more complete picture of entropy in the statistical mechanics of ideal fluids.

Shebalin, John V.↗
NASA NTRS2006

Entropy Generation/Availability Energy Loss Analysis Inside MIT Gas Spring and "Two Space" Test Rigs

The results of the entropy generation and availability energy loss analysis under conditions of oscillating pressure and oscillating helium gas flow in two Massachusetts Institute of Technology (MIT) test rigs piston-cylinder and piston-cylinder-heat exchanger are presented. Two solution domains, the gas spring (single-space) in the piston-cylinder test rig and the gas spring + heat exchanger (two-space) in the piston-cylinder-heat exchanger test rig are of interest. Sage and CFD-ACE+ commercial numerical codes are used to obtain 1-D and 2-D computer models, respectively, of each of the two solution domains and to simulate the oscillating gas flow and heat transfer effects in these domains. Second law analysis is used to characterize the entropy generation and availability energy losses inside the two solution domains. Internal and external entropy generation and availability energy loss results predicted by Sage and CFD-ACE+ are compared. Thermodynamic loss analysis of simple systems such as the MIT test rigs are often useful to understand some important features of complex pattern forming processes in more complex systems like the Stirling engine. This study is aimed at improving numerical codes for the prediction of thermodynamic losses via the development of a loss post-processor. The incorporation of loss post-processors in Stirling engine numerical codes will facilitate Stirling engine performance optimization. Loss analysis using entropy-generation rates due to heat and fluid flow is a relatively new technique for assessing component performance. It offers a deep insight into the flow phenomena, allows a more exact calculation of losses than is possible with traditional means involving the application of loss correlations and provides an effective tool for improving component and overall system performance.

Ebiana, Asuquo B.↗
NASA NTRS2013

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Fisher, Travis C.↗
NASA NTRS2013

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Carpenter, Mark H.↗
NASA NTRS1972

Entropy and chemical change. 1: Characterization of product (and reactant) energy distributions in reactive molecular collisions: Information and enthropy deficiency

Optimal means of characterizing the distribution of product energy states resulting from reactive collisions of molecules with restricted distributions of initial states are considered, along with those for characterizing the particular reactant state distribution which yields a given set of product states at a specified total energy. It is suggested to represent the energy-dependence of global-type results in the form of square-faced bar plots, and of data for specific-type experiments as triangular-faced prismatic plots. The essential parameters defining the internal state distribution are isolated, and the information content of such a distribution is put on a quantitative basis. The relationship between the information content, the surprisal, and the entropy of the continuous distribution is established. The concept of an entropy deficiency, which characterizes the specificity of product state formation, is suggested as a useful measure of the deviance from statistical behavior. The degradation of information by experimental averaging is considered, leading to bounds on the entropy deficiency.

Bernstein, R. B.↗
NASA NTRS1974

Magnetization and magnetic entropy of Dy2Ti2O7

Isothermal measurements of the magnetic entropy, magnetization, and differential susceptibility of Dy2Ti2O7 have been made. Absolute values of magnetic entropy have been determined as a function of applied magnetic field for several temperatures in the range 2-20 K, and several isofield lines in the magnetic entropy-temperature plane have been determined. Magnetization measurements, which extended into the saturation region, yield a powder-average magnetic moment of about 4.7 Bohr magnetons per ion. A van Vleck contribution to M was also observed. The results are consistent with the assumption of a nearly pure Jz equals + or - 15/2 ground-state Kramers doublet for the Dy(+++) ion. Comments on the suitability of Dy2Ti2O7 for use in a magnetic refrigerator cycling between 4.2 and 20 K are included.

Flood, D. J.↗