SEARCH · Engineering Papers

Results for “entropy functional”

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.

SourceResearch connectionFrom yearThrough year

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

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRS1991

Image construction from the IRAS survey

IRAS survey data can be used successfully to produce images of extended objects. The major difficulties, i.e., nonuniform sampling, different response functions for each detector, and varying signal-to-noise levels for each detector for each scan, have been resolved. The results of three different image construction techniques are compared: coaddition, constrained least-squares, and maximum entropy. The maximum entropy result is superior. An image of the galaxy M51 with an average spatial resolution of 45 arcsecods, using 60 microns survey data is presented. This exceeds the telescope diffraction limit of about 1 minute of arc at this wavelength.

Bontekoe, T. R.↗

NASA NTRS1990

Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions

A method for predicting the unsteady aerodynamic response of a cascade of airfoils to entropic, vortical, and acoustic gust excitations is being developed. Here, the unsteady flow is regarded as a small perturbation of a nonuniform isentropic and irrotational steady background flow. A splitting technique is used to decompose the linearized unsteady velocity into rotational and irrotational parts leading to equations for the complex amplitudes of the linearized unsteady entropy, rotational velocity, and velocity potential that are coupled only sequentially. The entropic and rotational velocity fluctuations are described by transport equations for which closed-form solutions in terms of the mean-flow drift and stream functions can be determined. The potential fluctuation is described by an inhomogeneous convected wave equation in which the source term depends on the rotational velocity field, and is determined using finite-difference procedures. The analytical and numerical techniques used to determine the linearized unsteady flow are outlined. Results are presented to indicate the status of the solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described herein leads to very efficient predictions of cascade unsteady aerodynamic response phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Verdon, Joseph M.↗

NASA NTRS2004

On Bayesian Inductive Inference & Predictive Estimation

We investigate Bayesian inference and the Principle of Maximum Entropy (PME) as methods for doing inference under uncertainty. This investigation is primarily through concrete examples that have been previously investigated in the literature. We find that it is possible to do Bayesian inference and PME inference using the same information, despite claims to the contrary, but that the results are not directly comparable. This is because Bayesian inference yields a probability density function (pdf) over the unknown model parameters, whereas PME yields point estimates. If mean estimates are extracted from the Bayesian pdfs, the resulting parameter estimates can differ radically from the PME values and also from the Maximum Likelihood values. We conclude that these differences are due to the Bayesian inference not assuming anything beyond the given prior probabilities and the data, whereas PME implicitly assumes that the given constraints are the only constraints that are operating. Since this assumption can be wrong, PME values may have to be revised when subsequent data shows evidence for more constraints. The entropy concentration previously "proved" by E. T. Jaynes is shown to be in error. Further, we show that PME is a generalized form of independence assumption, and so can be a very powerful method of inference when the variables being investigated are largely independent of each other.

Cheeseman, Peter↗

NASA NTRS2000

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

NASA NTRS1993

An estimate of the second law thermodynamic efficiency of the various units comprising an Environmental Control and Life Support System (ECLSS)

The objective of this paper is to present an estimate of the second law thermodynamic efficiency of the various units comprising an Environmental Control and Life Support System (ECLSS). The technique adopted here is based on an evaluation of the 'lost work' within each functional unit of the subsystem. Pertinent information for our analysis is obtained from a user interactive integrated model of an ECLSS. The model was developed using ASPEN. A potential benefit of this analysis is the identification of subsystems with high entropy generation as the most likely candidates for engineering improvements. This work has been motivated by the fact that the design objective for a long term mission should be the evaluation of existing ECLSS technologies not only the basis of the quantity of work needed for or obtained from each subsystem but also on the quality of work. In a previous study Brandhorst showed that the power consumption for partially closed and completely closed regenerable life support systems was estimated as 3.5 kw/individual and 10-12 kw/individual respectively. With the increasing cost and scarcity of energy resources, our attention is drawn to evaluate the existing ECLSS technologies on the basis of their energy efficiency. In general the first law efficiency of a system is usually greater than 50 percent. From literature, the second law efficiency is usually about 10 percent. The estimation of second law efficiency of the system indicates the percentage of energy degraded as irreversibilities within the process. This estimate offers more room for improvement in the design of equipment. From another perspective, our objective is to keep the total entropy production of a life support system as low as possible and still ensure a positive entropy gradient between the system and the surroundings. The reason for doing so is as the entropy production of the system increases, the entropy gradient between the system and the surroundings decreases, and the system will gradually approach equilibrium with the surroundings until it reaches the point where the entropy gradient is zero. At this point no work can be extracted from the system. This is called the 'dead state' of the system.

Chatterjee, Sharmista↗

NASA NTRS2023

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy Data Fusion to Map Global Surface Ozone Concentration and Associated Uncertainty

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R 2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m −3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Ozone↗

NASA NTRS1975

Normal- and oblique-shock flow parameters in equilibrium air including attached-shock solutions for surfaces at angles of attack, sweep, and dihedral

Normal- and oblique-shock flow parameters for air in thermochemical equilibrium are tabulated as a function of shock angle for altitudes ranging from 15.24 km to 91.44 km in increments of 7.62 km at selected hypersonic speeds. Post-shock parameters tabulated include flow-deflection angle, velocity, Mach number, compressibility factor, isentropic exponent, viscosity, Reynolds number, entropy difference, and static pressure, temperature, density, and enthalpy ratios across the shock. A procedure is presented for obtaining oblique-shock flow properties in equilibrium air on surfaces at various angles of attack, sweep, and dihedral by use of the two-dimensional tabulations. Plots of the flow parameters against flow-deflection angle are presented at altitudes of 30.48, 60.96, and 91.44 km for various stream velocities.

Hunt, J. L.↗

NASA NTRS1991

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗

NASA NTRS1994

Equilibrium, stability, and orbital evolution of close binary systems

We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We consider both synchronized and nonsynchronized systems, constructing the compressible generalizations of the classical Darwin and Darwin-Riemann configurations. Our method can be applied to a wide variety of binary models where the stellar masses, radii, spins, entropies, and polytropic indices are all allowed to vary over wide ranges and independently for each component. We find that both secular and dynamical instabilities can develop before a Roche limit or contact is reached along a sequence of models with decreasing binary separation. High incompressibility always makes a given binary system more susceptible to these instabilities, but the dependence on the mass ratio is more complicated. As simple applications, we construct models of double degenerate systems and of low-mass main-sequence star binaries. We also discuss the orbital evoltuion of close binary systems under the combined influence of fluid viscosity and secular angular momentum losses from processes like gravitational radiation. We show that the existence of global fluid instabilities can have a profound effect on the terminal evolution of coalescing binaries. The validity of our analytic solutions is examined by means of detailed comparisons with the results of recent numerical fluid calculations in three dimensions.

Lai, Dong↗

NASA NTRS1972

Melting of iron by significant structure theory

From Eyring's method of significant structures, a partition function is derived for liquid iron. The solid at high temperature is described in the Einstein approximation. Magnetic and electronic contributions to the thermodynamic properties of both the liquid and solid phases are considered. The model is compatible with properties (thermal expansion, compressibility, heat capacity, entropy of melting, and volume change on melting) at one atm. The melting temperature at high pressure is found by satisfying the requirement that the Gibbs free energies of the liquid and solid phases are equal at the melting temperature. Under conditions at the earth's core-mantle boundary, the melting temperature of iron is greater than approximately 5000 K, and under inner-outer core conditions the melting temperature is greater than approximately 7000 K. These estimates are consistent with the Lindemann melting law, but not with the Kraut-Kennedy melting law.

Leppaluoto, D. A.↗

NASA NTRS1975

Computational procedure for three-dimensional boundary layers on aircraft and aerospace vehicles

An implicit numerical procedure is developed to solve the full three-dimensional laminar, boundary layer equations over realistic aircraft and spacecraft configurations. This procedure utilizes splined functions in the direction normal to the surface and finite differences in the cross flow direction. Calculation of off-pitch plane attachment and detachment lines can be calculated. The solution procedure permits the incorporation of a wide variety of turbulent models and boundary conditions including; entropy layer procedures, specified surface temperatures or heat flux distributions, surface catalysis, mass addition, and the coupling to both three-dimensional inviscid codes and surface ablation codes. In addition, reasonable computing times are obtained.

Kendall, R. M.↗

NASA NTRS1984

Dynamic compression and volatile release of carbonates

Particle velocity profiles upon shock compression and isentropic releases were measured for polycrystalline calcite. The Solenhofen limestone release paths lie, close to the Hugoniot. Calcite 3 to 2 transition, upon release, was observed, but rarefaction shocks were not detected. The equation of state is used to predict the fraction of material devolatilized upon isentropic release as a function of shock pressure. The effect of ambient partial pressure of CO2 on the calculations is demonstrated and considered in models of atmospheric evolution by impact induced mineral devolatilization. The radiative characteristics of shocked calcite indicate that localization of thermal energy occurs under shock compression. Shock entropy calculations result in a minimum estimate of 90% devolatilization upon complete release from 10 GPa. Isentropic release paths from calculated continuum Hugoniot temperatures cross into the CaO (solid) + CO2 (vapor) field at improbably low pressures. It is found that release paths from measured shock temperatures cross into the melt plus vapor field at pressures greater than .5 GPa, which suggests that devolatilization is initiated at the shear banding sites.

Tyburczy, J. A.↗

NASA NTRS1986

Dynamic compression and volatile release of carbonates

Particle velocity profiles upon shock compression and isentropic releases were measured for polycrystalline calcite. The Solenhofen limestone release paths lie close to the Hugoniot. Calcite 3 to 2 transition, upon release was observed, but rarefaction shocks were not detected. The equation of state is used to predict the fraction of material devolatilized upon isentropic release as a function of shock pressure. The effect of ambient partial pressure of CO2 on the calculations is demonstrated and considered in models of atmospheric evolution by impact induced mineral devolatilization. The radiative characteristics of shocked calcite indicate that localization of thermal energy occurs under shock compression. Shock entropy calculations result in a minimum estimate of 90 percent devolatilization upon complete release from 10 GPa. Isentropic release paths from calculated continuum Hugoniot temperatures cross into the CaO (solid) + CO2 (vapor) field at improbably low pressures. It is found that release paths from measured shock temperatures cross into the melt plus vapor field at pressures greater than .5 GPa, which suggests that devolatilization is initiated at the shear banding sites.

Tyburczy, J. A.↗

NASA NTRS1992

Algorithmic information theory and the hidden variable question

The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.

Fuchs, Christopher↗

NASA NTRS1965

Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave, phase 1 final report, 29 jun. 1964 - 29 jul. 1965

The contribution of high entropy production regions to the generation and propagation characteristics of a finite amplitude pressure is considered. Preliminary analysis indicates that, for nozzles where pressure rations are above critical, the predominant contribution may come from the shock layer formation in the exhaust region. Temperature effects indicate high dependence of the forcing function upon the initial temperature of the media.

WAVE PROPAGATION↗

NASA NTRS1977

Identification and measurement of combustion noise from a turbofan engine using correlation and coherence techniques

Fluctuating pressure measurements within the combustor and tailpipe of a turbofan engine are made simultaneously with far field acoustic measurements. The pressure measurements within the engine are accomplished with cooled semi-infinite waveguide probes utilizing conventional condenser microphones as the transducers. The measurements are taken over a broad range of engine operating conditions and for 16 far field microphone positions between 10 deg and 160 deg relative to the engine inlet axis. Correlation and coherence techniques are used to determine the relative phase and amplitude relationships between the internal pressures and far field acoustic pressures. The results indicate that the combustor is a low frequency source region for acoustic propagation through the tailpipe and out to the far field. Specifically, it is found that the relation between source pressure and the resulting sound pressure involves a 180 deg phase shift. The latter result is obtained by Fourier transforming the cross correlation function between the source pressure and acoustic pressure after removing the propagation delay time. Further, it is found that the transfer function between the source pressure and acoustic pressure has a magnitude approximately proportional to frequency squared. These results are shown to be consistent with a model using a modified source term in Lighthill's turbulence stress tensor, wherein the fluctuating Reynolds stresses are replaced with the pressure fluctuations due to fluctuating entropy.

Karchmer, A. M.↗

NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗

NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗