On balance equations for heterogeneous continua.
Balance equations for heterogeneous continua - substances consisting of many distinct, possibly interacting constituents derived from classical continuum physics viewpoint
BALANCE EQUATION↗
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An efficient algorithm using matrix methods to solve wind tunnel force-balance equations
An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.
Smith, D. L.↗
Thermodynamic energy balance equations for Space Shuttle Orbiter gas compartment during ascent and re-entry
Thermodynamic energy balance equations are derived and applied to midsection Orbiter-payload atmospheric thermal math models (TMMs) to predict Orbiter component, element, compartment, internal insolation and structure temperatures in support of NASA/JSC mission planning, postflight thermal analysis and payload thermal integration planning. The equations are extended and applied to the forward section, midsection, and aft section of the TMMs for five Orbiter mission phases: prelaunch on pad with purge, lift-off to ascent, re-entry to touchdown, post landing without purge, and post-landing with purge. Predicted results from the 390 node/DFI atmospheric TMM are in good agreement with STS-1 flight measurement data.
Ting, P. C.↗
Solving the Linear Balance Equation on the Globe as a Generalized Inverse Problem
A generalized (pseudo) inverse technique was developed to facilitate a better understanding of the numerical effects of tropical singularities inherent in the spectral linear balance equation (LBE). Depending upon the truncation, various levels of determinancy are manifest. The traditional fully-determined (FD) systems give rise to a strong response, while the under-determined (UD) systems yield a weak response to the tropical singularities. The over-determined (OD) systems result in a modest response and a large residual in the tropics. The FD and OD systems can be alternatively solved by the iterative method. Differences in the solutions of an UD system exist between the inverse technique and the iterative method owing to the non- uniqueness of the problem. A realistic balanced wind was obtained by solving the principal components of the spectral LBE in terms of vorticity in an intermediate resolution. Improved solutions were achieved by including the singular-component solutions which best fit the observed wind data.
Lu, Huei-Iin↗
Retrieving the Balanced Winds on the Globe as a Generalized Inverse Problem
A generalized inverse technique is applied to retrieve two types of balanced winds that characterize the large-scale dynamics of the atmosphere: rotational winds based upon the linear balance equation, and divergent winds based upon the vorticity budget equation. Both balance equations are singular at or near the equator. The balance equations are transformed in spherical harmonic function space to an under-determined system, for which the scale-weighed least-squares solution consists of a sum of principal and singular components. The principal components represent the response to the source function for the regular eigenmodes, while the singular components are determined by the projection of an independent measurement on the singular eigenmodes. The method was tested with the NCEP/NCAR reanalysis data in which a quasi-balance condition exists. A realistic balanced wind field is retrievable when the singular components are computed based upon the reanalyzed wind data.
Lu, Huei-Iin↗
Construction of surface pressure field from scatterometer wind field
An account of the construction of surface pressure fields from Seasat-A satellite scatterometer (SASS) winds as carried out by different methods, and the comparison of these pressure fields with those derived from in situ ship observations is presented. On the assumption that the pressure adjusts itself instantaneously to the motion field, it may be computed by various methods. One of these makes use of planetary boundary theory, and of the possible techniques in this category a two-layer iterative scheme admitting of the parametrization of diabatic and baroclinic effects and of secondary flow was chosen. A second method involves the assumption of zero two-dimensional divergence, leading to a Laplace's equation (the balance equation) in pressure, with the wind field serving as a forcing function. This method does not accommodate adiabatic or baroclinic effects, and requires a knowledge of the pressure at all boundary points. Two comparison fields are used for validation: the conventional operational analyses of the US National Meteorological Center (NMC), and the special analyses of the Gulf of Alaska Experiment (GOASEX), which were done by hand. The results of the computations were as follows: (1) The pressure fields, as computed from the SASS winds alone, closely approximated the NMC fields in regions where reasonable in situ coverage was available (typically, one or two mb differences over most of the chart, three to four mb in extreme cases); (2) In some cases the SASS-derived pressure fields displayed high-resolution phenomena not detected by the NMC fields, but evident in the GOASEX data; and, (3) As expected, the pressure fields derived from the balance equation were much smoother and less well resolved than the SASS-derived or NMC fields. The divergence as measured from the SASS winds is smaller than, but of the same order of magnitude as, the vorticity.
Wurtele, Morton G.↗
On surface energy and the continuum thermodynamics of brittle fracture
When a separating body is viewed as a nonequilibrium thermodynamic process, the full thermodynamic nature of the surface energy induced by crack propagation becomes apparent. Within such a general framework it is no longer possible to view the surface energy as a material constant. For the self-propagating crack the induced surface energy is shown to depend explicitly on the square of the crack propagation speed. It is also shown that a separating body produces entropy even though the mechanical response of the solid may be elastic. The introduction of surface quantities such as surface energy into the continuum description of the fracture process forces a major departure from the mechanics appropriate to the nonseparating body. Local equations of balance are no longer obtainable as derived consequences of postulated global balance equations. They must instead be imposed as separate additional postulates.
Eftis, J.↗
Alterations of the climate of a primitive equation model produced by filtering approximations and subsequent tuning and stochastic forcing
A comparison is made of the simulated climates of nonlinear models based on the primitive equations (PE), balance equations (BE), and quasi-geostrophic (QG) equations. The models and numerical procedures are identical in all possible respects. The models are highly truncated spectral forms of Lorenz's (1960) energy preserving two-layer model. Two means of making use of the information contained in the (presumed known) short-term prediction error statistics are investigated. An unrealistically high level of thermal forcing is used so that the model climates are sufficiently different to allow any improvements due to the empirical methods to be observed. The general tuning problem is outlined and the QG model is tuned, using data obtained from a PE model run, to minimize the mean squared short term prediction error.
Hoffman, R. N.↗
Principles of the radiosity method versus radiative transfer for canopy reflectance modeling
The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.
Gerstl, Siegfried A. W.↗
Sensitivity analysis for the dynamic response of thermoviscoplastic shells of revolution
A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric, fully-coupled, thermoviscoplastic response of shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of large-strain, transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be viscoplasticity with strain hardening and thermal hardening, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used for the shell equations with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. The energy-balance equation is solved using a Galerkin procedure, with the temperature as the fundamental unknown. Spatial discretization is performed in one dimension (meridional direction) for the momentum and constitutive equations of the shell, and in two dimensions (meridional and thickness directions) for the energy-balance equation. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) for the momentum equation; a predictor-corrector version of the trapezoidal rule is used for the energy-balance equation; and an explicit scheme consistent with the central difference method is used to integrate the constitutive equations. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading.
Kulkarni, Makarand↗
Mapping the Limitations of Breakthrough Analysis in Fixed-Bed Adsorption
The separation of gases through adsorption plays an important role in the chemical processing industry, where the separation step is often the costliest part of a chemical process and thus worthy of careful study and optimization. This work developed a number of new, archival aspects on the computer simulations used for the refinement and design of these gas adsorption processes: 1. Presented a new approach to fit the undetermined heat and mass transfer coefficients in the axially dispersed plug flow equation and associated balance equations 2. Examined and described the conditions where non-physical simulation results can arise 3. Presented an approach to determine the limits of the axial dispersion and LDF mass transfer terms above which non-physical simulation results occur.
Knox, James Clinton↗
Ion-neutral coupling in the high-latitude F region Evaluation of ion heating terms from Dynamics Explorer 2
Ion and neutral motions in the high latitude F layer were studied simultaneously during six passes of the Dynamics Explorer 2 spacecraft. The passes were made over the south polar cap in October 1981. An ion energy balance equation was defined to express the exchange of energy between the F layer and other atmospheric constituents. A momentum equation expressed the momentum exchange between the species. An approximate form of the energy balance equation was also formulated. The time constant for ion-neutral collisional momentum transfer significantly affected Joule heating in the F layer. Regions of large velocity disparities and ion temperature enhancements were detected as hot spots. The results indicate that a feedback mechanism may arise in terms of neutral compositional changes and enhanced ionospheric recombination. The approximate equation furnished values for ion heating rates which matched the data.
Killeen, T. L.↗
Mass balance approaches for estimating the intestinal absorption and metabolism of peptides and analogues: theoretical development and applications
A theoretical analysis for estimating the extent of intestinal peptide and peptide analogue absorption was developed on the basis of a mass balance approach that incorporates convection, permeability, and reaction. The macroscopic mass balance analysis (MMBA) was extended to include chemical and enzymatic degradation. A microscopic mass balance analysis, a numerical approach, was also developed and the results compared to the MMBA. The mass balance equations for the fraction of a drug absorbed and reacted in the tube were derived from the general steady state mass balance in a tube: [formula: see text] where M is mass, z is the length of the tube, R is the tube radius, Pw is the intestinal wall permeability, kr is the reaction rate constant, C is the concentration of drug in the volume element over which the mass balance is taken, VL is the volume of the tube, and vz is the axial velocity of drug. The theory was first applied to the oral absorption of two tripeptide analogues, cefaclor (CCL) and cefatrizine (CZN), which degrade and dimerize in the intestine. Simulations using the mass balance equations, the experimental absorption parameters, and the literature stability rate constants yielded a mean estimated extent of CCL (250-mg dose) and CZN (1000-mg dose) absorption of 89 and 51%, respectively, which was similar to the mean extent of absorption reported in humans (90 and 50%). It was proposed previously that 15% of the CCL dose spontaneously degraded systematically; however, our simulations suggest that significant CCL degradation occurs (8 to 17%) presystemically in the intestinal lumen.(ABSTRACT TRUNCATED AT 250 WORDS).
Non-NASA Center↗
HCMM satellite follow-on investigation no. 25. Soil moisture and heat budget evalution in selected European zones of agricultural and environmental interest (TELLUS project)
A simple procedure to evaluate actual evaporation was derived by linearizing the surface energy balance equation, using Taylor's expansion. The original multidimensional hypersurface could be reduced to a linear relationship between evaporation and surface temperature or to a surface relationship involving evaporation, surface temperature and albedo. This procedure permits a rapid sensitivity analysis of the surface energy balance equation as well as a speedy mapping of evaporation from remotely sensed surface temperatures and albedo. Comparison with experimental data yielded promising results. The validity of evapotranspiration and soil moisture models in semiarid conditions was tested. Wheat was the crop chosen for a continuous measurement campaign made in the south of Italy. Radiometric, micrometeorologic, agronomic and soil data were collected for processing and interpretation.
Source record↗
A Realistic Accretion Disk Model for AGNs
We present a new relativistic accretion disk model of AGNs, based on alpha modified accretion disk theory, where alpha is a parameter that characterizes the efficiency of the mechanism of angular momentum transport. In this model we have considered a geometrically-thin, high-luminosity (alpha-accretion disk, around a supermassive black hole. The geometrically thin limit assumes a local energy balance within the accretion disk, which has been used to derive the plasma temperature of the disk. The energy balance equation has three solutions: low, medium and high temperature, depending on the heating rate of the accretion disk. We predict that the inner part of a high luminosity accretion disk is in the high- temperature (10(exp 7) to 10(exp 9) K) state and for this we obtain the high temperature solution of the energy balance equation using a Comptonization process. We find the local spectrum of each ring of the disk (we have divided the high temperature region of the disk into 50 rings) to be a diluted Wien spectrum. However, the emergent integral spectrum of the high temperature region is a power-law with a high-energy cutoff that depends on the basic parameters of AGNs (the accretion rate, the incidence angle, and the mass and the angular momentum of the central black hole). We have fitted the observed spectra of 28 AGNs using the present model and have derived the values of the basic parameters of these AGNs. Results of these spectral fittings have been discussed in the framework of the unification model of AGNs.
Suleimanov, V.↗
Theoretical study of the ionospheric G factor
A derivation from kinetic theory of the energy balance equation used in wave interaction work is reviewed. Then G is defined and two models for G are presented: one, a model based on Gerjuoy-Stein cross sections for both O2 and N2; the other based on a more recent model for O2 cross sections. The two models differ considerably in their temperature dependence. The limits of applicability of the useful energy balance equation (hence of the concept of G) are discussed and it is found that no difficulty arises unless the transmitter power is more than 1000 times that now employed at the present operating frequency.
Hagenbuch, K. M.↗
Direct numerical simulation of curved turbulent channel flow
Low Reynolds number, mildly curved, turbulent channel flow has been simulated numerically without subgrid scale models. A new spectral numerical method developed for this problem was used, and the computations were performed with 2 million degrees of freedom. A variety of statistical and structural information has been extracted from the computed flow fields. These include mean velocity, turbulence stresses, velocity skewness, and flatness factors, space time correlations and spectra, all the terms in the Reynolds stress balance equations, and contour and vector plots of instantaneous velocity fields. The effects of curvature on this flow were determined by comparing the concave and convex sides of the channel. The observed effects are consistent with experimental observations for mild curvature. The most significant difference in the turbulence statistics between the concave and convex sides was in the Reynolds shear stress. This was accompanied by significant differences in the terms of the Reynolds shear stress balance equations. In addition, it was found that stationary Taylor-Gortler vortices were present and that they had a significant effect on the flow by contributing to the mean Reynolds shear stress, and by affecting the underlying turbulence.
Moser, R. D.↗
A comparative analysis of two land surface heterogeneity representations
Two contrasting representations of land surface variability used in general circulation models (GCMs) are compared through an analysis of their corresponding surface energy balance equations. In one representation (the 'mixture' approach), different vegetation types are assumed to be homogeneously mixed over a grid square, so that the GCM atmosphere sees near-surface conditions pertaining to the mixture only. In the second representation (the 'mosaic' approach), different vegetation types are viewed as separate 'tiles' of a grid-square 'mosaic', and each tile interacts with the atmosphere independently. The mosaic approach is computationally simpler and in many ways more flexible than the mixture approach. Analytical solutions to the linearized energy balance equations and numerical solutions to the nonlinear equations both demonstrate that the mixture strategy, when applied to two coexisting vegetation types that differ only in canopy transpiration resistance, promotes both total turbulent flux and latent heat flux relative to the mosaic strategy. The effective differences between the strategies, however, are small over a wide range of conditions. In particular, the strategies are effectively equivalent when the transpiration resistances of the different vegetation types are of the same order of magnitude.
Koster, Randal D.↗