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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.

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NASA NTRS2017

Improvement of Reynolds-Stress and Triple-Product Lag Models

The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.

Fluid dynamics↗
NASA NTRS2017

Improvement of Reynolds-Stress and Triple-Product Lag Models

The Reynolds-stress and triple product Lag models were created with a normal stress distribution which was defined by the accepted 4:3:2 distribution of streamwise, spanwise and wall normal stresses, and a ratio of τ(sub w) = 0.3k in the log layer region of high Reynolds number flat plate flow, which implies R11(+) = 4/(9/2)∗.3 ≈ 2.96. More recent measurements show a more complex picture of the log layer region at high Reynolds numbers. The first cut at improving these models along with the direction for future refinements is described. Comparison with recent high Reynolds number data shows areas where further work is needed, but also shows inclusion of the modeled turbulent transport terms improve the prediction where they influence the solution. Additional work is needed to develop a model that better matches experiments, but there is significant improvement in many of the details of the log layer behavior.

Turbulence↗
NASA NTRS2002

Evaluation of Transport in the Lower Tropical Stratosphere in a Global Chemistry and Transport Model

A general circulation model (GCM) relies on various physical parameterizations and provides a solution to the atmospheric equations of motion. A data assimilation system (DAS) combines information from observations with a GCM forecast and produces analyzed meteorological fields that represent the observed atmospheric state. An off-line chemistry and transport model (CTM) can use winds and temperatures from a either a GCM or a DAS. The latter application is in common usage for interpretation of observations from various platforms under the assumption that the DAS transport represents the actual atmospheric transport. Here we compare the transport produced by a DAS with that produced by the particular GCM that is combined with observations to produce the analyzed fields. We focus on transport in the tropics and middle latitudes by comparing the age-of-air inferred from observations of SF6 and CO2 with the age-of-air calculated using GCM fields and DAS fields. We also compare observations of ozone, total reactive nitrogen, and methane with results from the two simulations. These comparisons show that DAS fields produce rapid upward tropical transport and excessive mixing between the tropics and middle latitudes. The unrealistic transport produced by the DAS fields may be due to implicit forcing that is required by the assimilation process when there is bias between the GCM forecast and observations that are combined to produce the analyzed fields. For example, the GCM does not produce a quasi-biennial oscillation (QBO). The QBO is present in the analyzed fields because it is present in the observations, and systematic implicit forcing is required by the DAS. Any systematic bias between observations and the GCM forecast used to produce the DAS analysis is likely to corrupt the transport produced by the analyzed fields. Evaluation of transport in the lower tropical stratosphere in a global chemistry and transport model.

Douglass, Anne R.↗
NASA NTRS1974

An experimental and analytical study of slip and catalytic boundary conditions applied to spheres in low Reynolds number arc jet flows

Measurements of low-density dissociated arc-heated flows around low and high surface catalycity spheres are compared with numerical solutions to the full Navier-Stokes equations for reacting gas flow fields, taking into account slip and finite surface catalytic boundary conditions. A time-dependent finite difference solution technique developed by Li (1973, 1974) is used in the investigation and a simple transport model is employed for the flows considered. The correctness of the solution approach is demonstrated by the very good agreement obtained between experimental and computational data.

Scott, C. D.↗
NASA NTRS2003

Protoplanetary Nebula Evolution using the Beta Viscosity Model

The evolutionary dynamics of a protoplanetary disk is an important component of the planet formation process. In particular, the dynamic and thermodynamic field plays a critical role in chemical evolution, the migration of dust particles in the nebula, and the radial transport of meteoritic components. The dynamic evolution is investigated using analytical solutions of the surface density transport equations using a turbulence model based on hydrodynamic generation of turbulence. It captures the major properties of the disk including region of separation between radial inflow and-outflow and the evolution of the central plane temperature. The analytical formulas are compared with available numerical solutions based on the alpha viscosity model. The beta viscosity model, heretofore used for steady-state disks, is shown to be a useful approximation for unsteady problems.

Davis, Sanford S.↗
NASA NTRS2023

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗
NASA NTRS2002

Fluid Flow and Solidification Under Combined Action of Magnetic Fields and Microgravity

Mathematical models, both 2-D and 3-D, are developed to represent g-jitter induced fluid flows and their effects on solidification under combined action of magnetic fields and microgravity. The numerical model development is based on the finite element solution of governing equations describing the transient g-jitter driven fluid flows, heat transfer and solutal transport during crystal growth with and without an applied magnetic field in space vehicles. To validate the model predictions, a ground-based g-jitter simulator is developed using the oscillating wall temperatures where timely oscillating fluid flows are measured using a laser PIV system. The measurements are compared well with numerical results obtained from the numerical models. Results show that a combined action derived from magnetic damping and microgravity can be an effective means to control the melt flow and solutal transport in space single crystal growth systems.

Li, B. Q.↗
NASA NTRS2001

Modelling of Trapped Radiation Near Jupiter

Energetic (62 to approx. 130 MeV) proton fluxes measured with the Galileo Probe inside Jupiter's main ring (radii 122,500 to 128,940 km) show a modest increase as Jupiter is approached. Solutions of a reduced (1-d) equatorial diffusion equation with-constant losses described by a lifetime tau match those data for tau greater than or equal to 10(exp 9) s for diffusion coefficient D(sub LL) = 10(exp -9) L(exp 4)/s, 10(exp -9) L(exp -3)/s, or 10(exp -10) L(exp 4)/s (this particle population may be undergoing nearly loss-free inward radial diffusion). Tau would increase as Jupiter is approached if its value were determined by pitch angle scattering due to EM wave-particle interactions. if the absolute amplitudes of the waves' magnetic fluctuations did not vary with radial distance. Exploration of numerical solutions of the diffusive transport equation for Jupiter's magnetospheric ions at die planetary ring and closer to Jupiter has been done. Explicit range-energy relationships for energy loss in ring matter (SiO2), modeled as a continuous disk, are incorporated. A spatial resolution of approx. 1000 km in the radial direction is used in the vicinity of the main ring; off-equatorial ion fluxes have been included (assuming the atmosphere is a perfect absorber). For protons the maximum effect of energy loss in the microscopic size range of ring particles is expected at energies approx. 0.1 Mev. Presumably there could be sufficiently large, unobserved bodies within the ring that would have to be modeled as discrete objects, as planetary satellites would be. Within limitations of the model and computational resources it's planned to characterize solutions for transport of magnetospheric ions past the planetary ring; the procedures that are used are fairly well known and may be applied generally to the simpler magnetospheric models.

Mihalov, John D.↗
NASA NTRS1992

Evolution of solar wind fluctuations and the influence of turbulent 'mixing'

We present various numerical and analytical solutions for the transport of solar wind turbulence. The model used takes into account the effects of convection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) 'mixing' terms. The radial evolution of the fluctuating kinetic energy, magnetic energy, and normalized cross helicity is computed, and, it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In the general case, solutions which differ substantially from those predicted by WKB theory are obtained. The degree of turbulent 'mixing' shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 AU, of the ratio of 'inward' and 'outward' fluctuation energies and the ratio of kinetic to magnetic energies in the fluctuations. The transport properties described here may provide at least a partial explanation for the observed mixing of cross helicities with increasing heliocentric distance in the solar wind.

Oughton, S.↗
NASA NTRS2002

A Simplified Model for an Evolving Protoplanetary Nebula

The dynamical evolution of the protoplanetary nebula is investigated using analytical solutions of the surface density transport equations. Constant and beta viscosity turbulence models are compared with a functional analytical model and the well-known alpha viscosity formulation. The beta viscosity model, heretofore used for steady-state disks, is shown to be a viable tool for separating dynamic and thermodynamic properties of an evolving disk.

Davis, Sanford S.↗
NASA NTRS1987

Real-time operational planning for the U.S. air traffic system

This paper describes an integrated planning model for the U.S. air traffic system. The approach incorporates the dual objectives of monitoring collision risk while minimizing transportation costs. Specialized solution algorithms exploit the underlying structure of the model - especially for large-scale examples. The proposed formulation is tested with real-world data for the Indianapolis control sector. Additional experiments with a CRAY X-MP/24 supercomputer show that a full-scale model can be solved under real time conditions. Despite these advances, additional work is required in developing a practical system. Suggestions are made for combining advances in computer graphics and mathematical modeling.

Mulvey, John M.↗
NASA NTRS2020

On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a welldefined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate (ω) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

Navier–Stokes equations↗
NASA NTRS1986

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.

Amano, R. S.↗
NASA NTRS1980

Updating the limit efficiency of silicon solar cells

The limit efficiency of a silicon solar cell is investigated using an analytical approach. The analytical model is based on the solution of a transport equation for minority carriers derived from the Shockley equations. On the basis of the computations, a 'narrow-region' design approach is suggested for both the front and the back regions of the solar cell. The design relies on low effective surface-recombination velocities, a textured front surface, and an optical internally reflecting back surface. With this approach, the limit efficiency is near 25%, and the optimum cell is 50 to 150 microns thick.

Wolf, M.↗
NASA NTRS2002

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

Yeh, Kao-San↗
NASA NTRS2019

Modeling Mg II During Solar Flares. I. Partial Frequency Redistribution, Opacity, and Coronal Irradiation

The Interface Region Imaging Spectrograph has routinely observed the flaring Mg II near-ultraviolet (NUV) spectrum, offering excellent diagnostic potential and a window into the location of energy deposition. A number of studies have forward-modeled both the general properties of these lines and specific flare observations. Generally these have forward-modeled radiation via post-processing of snapshots from hydrodynamic flare simulations through radiation transfer codes. There has, however, not been a study of how the physics included in these radiation transport codes affects the solution. A baseline setup for forward-modeling Mg II in flares is presented and contrasted with approaches that add or remove complexity. It is shown for Mg II that (1) partial frequency distribution (PRD) is still required during flare simulations despite the increased densities; (2) using full angle-dependent PRD affects the solution but takes significantly longer to process a snapshot; (3) including Mg I in non-LTE (NLTE) results in negligible differences to the Mg II lines but does affect the NUV quasi-continuum; (4) only hydrogen and Mg II need to be included in NLTE; (5) ideally the nonequilibrium hydrogen populations, with nonthermal collisional rates, should be used rather than the statistical equilibrium populations; (6) an atom consisting of only the ground state, h and k upper levels, and continuum level is insufficient to model the resonance lines; and (7) irradiation from a hot, dense flaring transition region can affect the formation of Mg II. We discuss modifications to the RH code allowing straightforward inclusion of the transition region and coronal irradiation in flares.

Kerr, Graham S.↗
NASA NTRS1981

On the origin of the MeV energy nucleon flux associated with CIRs

Measurements of recurrent enhancements of interplanetary nucleon flux in the MeV energy range are presented and interpreted. The features recur at the solar rotation period in association with stream-stream plasma interaction regions corotating with the sun. At distances from the sun less than 1 AU, the maximum intensities of the hydrogen and helium components increase with increasing distance between 300%/AU and 600%/AU. A model is proposed which predicts the acceleration of nuclei from keV plasma energies to MeV energies by means of transit time damping of magnetosonic waves as solar wind plasma flows from the sun. Numerical solutions of the transport equation are derived to demonstrate that the model does not reproduce radial variations of hydrogen and helium fluxes, and estimates are made of the radial diffusive mean free path. Finally, the observations are found to be consistent with nucleon acceleration at the CIR shocks beyond 1 AU with subsequent diffusion toward the sun.

Christon, S. P.↗
NASA NTRSDate not supplied

Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D

The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.

CFD Modeling↗