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NASA NTRS1995

Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

Girimaji, Sharath S.↗

NASA NTRS1993

Convective flow effects on protein crystal growth

The experimental setup for the in-situ high resolution optical monitoring of protein crystal growth/dissolution morphologies was substantially improved. By augmenting the observation system with a temperature-controlled enclosure, laser illumination for the interferometric microscope, and software for pixel by pixel light intensity recording, a height resolution of about two unit cells for lysozyme can now be obtained. The repartitioning of Na(+) and Cl(-) ions between lysozyme solutions and crystals was studied. Quite unexpectedly, it was found that the longer crystals were in contact with their solution, the lower was their ion content. The development of a model for diffusive-convective transport and resulting distribution of the growth rate on facets was completed. Results obtained for a realistic growth cell geometry show interesting differences between 'growth runs' at 1g and 0g. The kinematic viscosity of lysozyme solutions of various supersaturations and salt concentrations was monitored over time. In contrast to the preliminary finding of other authors, no changes in viscosity were found over four days. The experimental setup for light scattering investigations of aggregation and nucleation in protein solutions was completed, and a computer program for the evaluation of multi-angle light scattering data was acquired.

Rosenberger, Franz↗

NASA NTRS1984

Turbulent transport models for scramjet flowfields

Turbulence modeling approaches were examined from the standpoint of their capability to predict the complex flowfield features observed in scramjet combustions. Thus, for example, the accuracy of each turbulence model, with respect to the prediction of recirculating flows, was examined. It was observed that for large diameter ratio axisymmetric sudden expansion flows, a choice of turbulence model was not critical because of the domination of their flowfields by pressure forces. For low diameter ratio axisymmetric sudden expansions and planar backward-facing steps flows, where turbulent shear stresses are of greater significance, the algebraic Reynolds stress approach, modified to increase its sensitivity to streamline curvature, was found to provide the best results. Results of the study also showed that strongly swirling flows provide a stringent test of turbulence model assumptions. Thus, although flows with very high swirl are not of great practical interest, they are useful for turbulence model development. Finally, it was also noted that numerical flowfields solution techniques have a strong interrelation with turbulence models, particularly with the turbulent transport models which involve source-dominated transport equations.

Sindir, M. M.↗

NASA NTRS1994

On the prediction of free turbulent jets with swirl using a quadratic pressure-strain model

Data from free turbulent jets both with and without swirl are used to assess the performance of the pressure-strain model of Speziale, Sarkar and Gatski which is quadratic in the Reynolds stresses. Comparative predictions are also obtained with the two versions of the Launder, Reece and Rodi model which are linear in the same terms. All models are used as part of a complete second-order closure based on the solution of differential transport equations for each non-zero component of the Reynolds stress tensor together with an equation for the scalar energy dissipation rate. For non-swirling jets, the quadratic model underestimates the measured spreading rate of the plane jet but yields a better prediction for the axisymmetric case without resolving the plane jet/round jet anomaly. For the swirling axisymmetric jet, the same model accurately reproduces the effects of swirl on both the mean flow and the turbulence structure in sharp contrast with the linear models which yield results that are in serious error. The reasons for these differences are discussed.

Younis, Bassam A.↗

NASA NTRS2005

Numerical Model for Cosmic Rays Species Production and Propagation in the Galaxy

In recent years, considerable progress has been made in studying the propagation and origin of cosmic rays, as new and more accurate data have become available. Many models have been developed to study cosmic ray interactions and propagation showed flexibility in resembling various astrophysical conditions and good agreement with observational data. However, some astrophysical problems cannot be addressed using these models, such as the stochastic nature of the cosmic rays source, small-scale structures and inhomogeneities in the interstellar gas that can affect radioactive secondary abundance in cosmic rays. We have developed a new model and a corresponding computer code that can address some of these limitations. The model depends on the expansion of the backward stochastic solution of the general diffusion transport equation (Zhang 1999) starting from an observer position to solve a group of diffusion transport equations each of which represents a particular element or isotope of cosmic ray nuclei. In this paper we are focusing on key abundance ratios such as B/C, sub-Fe/Fe, (10)Be/(9)Be, (26)Al/(27)Al, (36)Cl/(37)Cl and (54)Mn/(55)Mn, which all have well established cross sections, to evaluate our model. The effect of inhomogeneity in the interstellar medium is investigated. The contribution of certain cosmic ray nuclei to the production of other nuclei is addressed. The contribution of various galactic locations to the production of cosmic ray nuclei observed at solar system is also investigated.

Farahat, Ashraf↗

NASA NTRS2000

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Lin, S.-J.↗

NASA NTRS2014

Numerical Simulations For the F-16XL Aircraft Configuration

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the kε turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Elmiligui, Alaa A.↗

NASA NTRS1994

Coherent pulses in the diffusive transport of charged particles`

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Kota, J.↗

NASA NTRS1991

Response of a confined gas to volumetric heating in the absence of gravity. I - Slow transients

A one-dimensional model for bulk motion induced by a transient volumetric heat source in a confined gas at zero gravity is considered. Rational approximation methods are used to derive a quantitative theory for the gas response to a spatiallly distributed, time-dependent internal power deposition. The resulting low Mach number compressible flow equations are solved by using perturbation methods. Solutions are given for a conduction-free core and thin conductive boundary layers adjacent to the end walls. It is found that may any spatially nonuniform power deposition will cause fluid motion. Net mass transport in the closed container will occur for certain spatially distributed heating. The model mimics the thermal effects of an exothermic gas phase reaction in vapor transport experiments conducted in space. The solutions demonstrate that thermally induced mass transport can be as large as diffusive mass transport in a typical experiment.

Herczynski, A.↗

NASA NTRS1996

Utilization of STRAT Data

One of the goals of the STRAT mission was to improve our understanding of transport in the stratosphere. We have used our coupled 2-D model to analyse transport between the tropics and midlatitudes using aircraft measurements of (CO2) and (N2O) made during the SPADE and ASHOE/MAESA campaigns (Boering et al. 1994) for model validation. We have further used the model to estimate errors in the experimental determination of the age of stratospheric air that arise from nonlinear increases of real tracers such as (CO2) and (SF6). The interpretation of measurements made during STRAT is still in progress. Most of the work performed under this contract has been described in the second year progress report, submitted in April of 1996. In the following, the research is summarized and some additional work that has become relevant in the meantime is described. We have developed an interactive model of the dynamics, chemistry and radiation of the stratosphere with partial support from this contract. The dynamics module integrates the primitive equations on a sphere. Lower boundary zonal winds and eddy geopotential heights are specified from observations. Chemistry and tracer transport are done in two dimensions. The chemistry model is a family model. Long lived species are transported and short lived species are determined in intervals of 5 to 10 days by assuming photochemical steady state. Full diurnal integrations with the fast species are performed periodically and diurnal coefficients, derived from the explicit integration are used to determine the steady state solution. Heating rates in the stratosphere are calculated from model ozone and the model temperatures and circulation fields are used in the chemistry transport module.

Source record↗

NASA NTRS1985

Electrophoretic transport equations - Electrophoretic models based on migration only and their interrelationships

The general equations which describe the electrophoretic transport of components in solution are restated using Newman's general concept of mobilities. A concise derivation of the moving boundary equation and the regulating function from the continuity equation is presented. Various other regulating principles across moving and stationary boundaries are also discussed, which permits a review of the features and interrelationships of the electrophoretic models based on electromigration only. The effect of considering an interactive (dissociating) solvent on the mathematical treatment is discussed.

Thormann, Wolfgang↗

NASA NTRS2008

Neutron Transport Models and Methods for HZETRN and Coupling to Low Energy Light Ion Transport

Exposure estimates inside space vehicles, surface habitats, and high altitude aircraft exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETCHEDS and FLUKA, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light ion (A<4) transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Blattnig, S.R.↗

NASA NTRS2016

Aerodynamic Modeling of Transonic Aircraft Using Vortex Lattice Coupled with Transonic Small Disturbance for Conceptual Design

The need to rapidly scan large design spaces during conceptual design calls for computationally inexpensive tools such as the vortex lattice method (VLM). Although some VLM tools, such as Vorview have been extended to model fully-supersonic flow, VLM solutions are typically limited to inviscid, subcritical flow regimes. Many transport aircraft operate at transonic speeds, which limits the applicability of VLM for such applications. This paper presents a novel approach to correct three-dimensional VLM through coupling of two-dimensional transonic small disturbance (TSD) solutions along the span of an aircraft wing in order to accurately predict transonic aerodynamic loading and wave drag for transport aircraft. The approach is extended to predict flow separation and capture the attenuation of aerodynamic forces due to boundary layer viscosity by coupling the TSD solver with an integral boundary layer (IBL) model. The modeling framework is applied to the NASA General Transport Model (GTM) integrated with a novel control surface known as the Variable Camber Continuous Trailing Edge Flap (VCCTEF).

Transonic Small Disturbance↗

NASA NTRS2009

Coupled Neutron Transport for HZETRN

Exposure estimates inside space vehicles, surface habitats, and high altitude aircrafts exposed to space radiation are highly influenced by secondary neutron production. The deterministic transport code HZETRN has been identified as a reliable and efficient tool for such studies, but improvements to the underlying transport models and numerical methods are still necessary. In this paper, the forward-backward (FB) and directionally coupled forward-backward (DC) neutron transport models are derived, numerical methods for the FB model are reviewed, and a computationally efficient numerical solution is presented for the DC model. Both models are compared to the Monte Carlo codes HETC-HEDS, FLUKA, and MCNPX, and the DC model is shown to agree closely with the Monte Carlo results. Finally, it is found in the development of either model that the decoupling of low energy neutrons from the light particle transport procedure adversely affects low energy light ion fluence spectra and exposure quantities. A first order correction is presented to resolve the problem, and it is shown to be both accurate and efficient.

Slaba, Tony C.↗

NASA NTRS1987

A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables.

Amano, R. S.↗

NASA NTRS1977

Analysis of the theory of high energy ion transport

Procedures for the approximation of the transport of high-energy ions are discussed on the basis of available data on ion nuclear reactions. A straightahead approximation appears appropriate for space applications. The assumption that the secondary-ion-fragment velocity is equal to that of the fragmenting nucleus is inferior to straightahead theory but is of sufficient accuracy if the primary ions display a broad energy spectrum. An iterative scheme for the solution of the inhomogenous integral transport equations holds promise for practical calculation. A model calculation shows that multiple charged ion fragments penetrate to greater depths in comparison with the free path of a primary heavy ion.

Wilson, J. W.↗

NASA NTRS1984

The small ice cap instability in diffusive climate models

Simple climate models which invoke diffusive heat transport and ice cap albedo feedback have equilibrium solutions with no stable ice cap smaller than a radius of about 20 deg on a great circle. Attention is presently given to a solution of this phenomenon which is physically appealing. The ice-free solution has a thermal minimum, and if the minimum temperature is just above the critical value for ice formation, then the artificial addition of a patch of ice leads to a widespread depression of the temperature below the critical freezing temperature. A second stable solution will then exist whose spatial extent is determined by the range of the influence function of a point sink of heat, due to the albedo shift in the patch.

North, G. R.↗

NASA NTRS1980

The vagaries of variable viscosity convection

The wavelength dependence of convection with a temperature-dependent viscosity is studied using two-dimensional finite difference models. A steady-state solution with a horizontal wavelength of eight times the depth is found to transport heat more efficiently than a solution with exactly the same parameters but with a wavelength of twice the depth. Only at the longer wavelengths is it possible for the top high viscosity boundary layer to participate more fully in the flow. Using models with a constant heat flux resulted in a decrease in the interior temperature of approximately 30% for the longer wavelength. It is also demonstrated that a parameterization using only a constant viscosity thermal structure and an interior viscosity is inadequate to parameterize the variable viscosity calculations described. This suggests that parameterized convection schemes may not accurately resolve the thermal evolution of planetary interior unless they can correctly include the effects of vertical viscosity structure.

Daly, S. F.↗