The present state of RNG and its impact on one-point closure
The use of renormalization group methods in one-point closure problems is discussed. This material is directly relevant to the production of K-epsilon turbulence models.
Orszag, S.↗
SEARCH · Search NASA
Results for “Closure problem”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
PDF methods for turbulent reactive flows
Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.
Hsu, Andrew T.↗
Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models
Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.
Avissar, Roni↗
A new approach to the formulation of scalar flux closure
This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.
Shabany, Y.↗
LES, DNS, and RANS for the Analysis of High-Speed Turbulent Reacting Flows
A filtered density function (FDF) method suitable for chemically reactive flows is developed in the context of large eddy simulation. The advantage of the FDF methodology is its inherent ability to resolve subgrid scales (SGS) scalar correlations that otherwise have to be modeled. Because of the lack of robust models to accurately predict these correlations in turbulent reactive flows, simulations involving turbulent combustion are often met with a degree of skepticism. The FDF methodology avoids the closure problem associated with these terms and treats the reaction in an exact manner. The scalar FDF approach is particularly attractive since it can be coupled with existing hydrodynamic computational fluid dynamics (CFD) codes.
Colucci, P. J.↗
Model equations for simulating flows in multistage turbomachinery
A steady, three dimensional average-passage equation system was derived. The purpose was to simulate multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. Moreover, these equations have a closure problem that is similar to that of the Reynolds-average Navier-Stokes equations. A scaled form of the average-passage equation system could provide an improved mathematical model for simulating the flow in the design and in the off-design conditions of a multistage machine.
Adamczyk, John J.↗
Investigation of EM Emissions by the Electrodynamic Tether, Inclusive of an Observational Program (EMET)
Our TSS-1/R investigation, which we shall refer to as EMET in this report, was an integral part of the effort by the TSS-1/R Investigators' Working Group (IWG) to come to an understanding of the complex interaction between the tethered satellite system and the ionosphere. All of the space-borne experiments were designed to collect data relevant to the local interaction. Only the ground- based experiments, EMET and its Italian counterpart Observations on the Earth's Surface of Electromagnetic Emissions (OESEE), held out any hope of characterizing the long range effects of the interaction. This was to be done by detecting electromagnetic waves generated by the system in the ionosphere, assuming the signal reached the Earth's surface with sufficient amplitude. As the type of plasma waves excited to carry charge away from the charge-exchange regions of the system at each end of the tether is one of the theoretical points about which there is greatest disagreement, a definitive identification of tether-generated waves could mark significant progress in the so-called current closure problem of electrodynamic tethers. Dr. Mario Grossi of the Smithsonian Astrophysical Observatory (SAO) initiated the investigation, and his experience in the field of ULF-ELF waves and their detection was invaluable throughout its course. Rice University had the responsibility of setting up the EMET ULF-VLF ground stations under a subcontract from SAO. Principal Investigator (PI) for the Rice effort was Prof. William E. Gordon, who was primary observer at the Arecibo Observatory during TSS-LR. Dr. Steve Noble handled major day-to-day operations, training, and planning for the ground-based measurements. Dr. James McCoy of NASA JSC, a member of the Mona/Arecibo team, was pilot for the numerous flights ferrying personnel and equipment between Puerto Rico and Mona Island. Final responsibility for the measurements rested with SAO, and the activities of field personnel and SAO investigators were closely co-ordinated during the mission. Dr. Enrico Lorenzini of SAO served as the eyes, ears, and brain of EMET in the Science Operations Area and PI table during the mission, whenever the PI was absent during the round-the-clock mission operations. The Rice University final report to SAO, which is included as an Appendix, contains details of the remote sites, means of communication, sensors, etc., as well as the affiliations of personnel involved in the data-gathering effort.
Estes, Robert D.↗
Toward a Unified Parameterization of the Boundary Layer and Moist Convection: A New Type of Mass-Flux Model - Part 1
Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.
Lappen, Cara-Lyn↗
On the necessity of a certain convexity condition for lower closure of control problems.
Existence problem of optimal controls analyzed for necessity of convexity condition for lower closure
Brunovsky, P.↗
Remarks on the construction of a second-order closure description of turbulent reacting flows
In this paper an attempt is made to illustrate how second-order closure techniques might be used to make detailed calculations of turbulent diffusion flames. Two of the problems of closure that are peculiar to turbulent chemically reacting flows are discussed in some detail. These are the problem of computing in a consistent way all the correlations of fluctuations in scalar quantities needed for closure and the problem of the generation of turbulence by chemical reactions. Tentative closure models are put forward for both of these problems. Although the closure model for fluctuations in scalar quantities can, to a certain extent, be checked against idealized numerical examples for which exact solutions are known, the validity of both the closure models proposed here must, in the end, be determined by detailed comparison of computed results with experimental data.
DONALDSON C. DUP.↗
The generalized drift flux approach: Identification of the void-drift closure law
The main characteristics and the potential advantages of generalized drift flux models are presented. In particular it is stressed that the issue on the propagation properties and on the mathematical nature (hyperbolic or not) of the model and the problem of closure are easier to tackle than in two fluid models. The problem of identifying the differential void-drift closure law inherent to generalized drift flux models is then addressed. Such a void-drift closure, based on wave properties, is proposed for bubbly flows. It involves a drift relaxation time which is of the order of 0.25 s. It is observed that, although wave properties provide essential closure validity tests, they do not represent an easily usable source of quantitative information on the closure laws.
Boure, J. A.↗
Application of a substructuring technique to the problem of crack extension and closure
A substructuring technique, originally developed for the efficient reanalysis of structures, is incorporated into the methodology associated with the plastic analysis of structures. An existing finite-element computer program that accounts for elastic-plastic material behavior under cyclic loading was modified to account for changing kinematic constraint conditions - crack growth and intermittent contact of crack surfaces in two dimensional regions. Application of the analysis is presented for a problem of a centercrack panel to demonstrate the efficiency and accuracy of the technique.
Armen, H., Jr.↗
Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation
Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.
Le Roux, J. A.↗
Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows
The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.
Schaefer, John↗
Eddy Covariance Theory: A Review
Eddy covariance (EC), the gold standard for measuring ecosystem scale gas and heat exchanges, has transformed our understanding of the breathing of the biosphere, and thus global change biology. Despite numerous methodological improvements and insights gained from the technique, the community faces persistent challenges that have been present since the first EC measurements. Here, we review the theoretical developments underpinning EC. We present theoretical developments in four important areas that have relevance to EC measurements of the net ecosystem exchanges (NEE) of gases and heat from a single tower: (i) measuring the total vertical flux density, (ii) flux attenuation, (iii) coordinate rotations, and (iv) energy balance closure. Persistent problems with EC measurements, such as the inability to close the energy budget, led us to identify two priorities for revisiting the theory underlying: (i) sensible heat flux calculations, and (ii) constraining the mean vertical wind velocity. We present a framework for improved calculation of sensible heat flux derived from first principles of fluid mechanics and thermodynamics that considers coupled heat and mass transfer so that conservation of both is obeyed. These refinements are motivated by the need for unbiased measurements of energy and mass transfer between the land surface and atmosphere for ecosystem research and to validate satellite observations and land surface models.
ecosystem fluxes↗
Closure assumptions in the cumulus parameterization problem
While concentrating on the thermodynamical aspects of parameterizing deep cumulus clouds, some of the existing schemes are reviewed with an emphasis on their closure assumptions. It is shown that the closure assumptions in these schemes are some combination of four types. It is emphasized that observations should be used more extensively than in the past to directly verify and improve closure assumptions and to assess the limit of parameterizability. As an example, results from an analysis of the macroscopic behavior of moist convection are presented. The results suggest that cumulus clouds are basically parameterizable, in spite of the existence of mesoscale organization.
Arakawa, Akio↗
Galaxy luminosity functions, M/L ratios, and closure of the Universe - Numbers and problems
Data on the luminosity function (LF) of galaxies are reviewed and compared, and the result of Kirshner et al. (1983) giving a 'standard LF' is chosen as a best guess. Departures from the 'standard LF' for specific galaxy types and environments (clusters, groups, field) are discussed briefly. A luminosity density of about 1.4 x 10 to the -2nd h 'galaxies' per cubic megaparsec is obtained. The mean M/L ratio needed to give critical cosmological density (Omega sub 0 = 1) is then 920 h in solar units on the face-on magnitude system. Comparison with measured M/L ratios for galaxies and clusters, and with constraints imposed by inflation and nucleosynthesis, poses two problems of 'invisible mass'.
Felten, J. E.↗
System development and early biological tests in NASA's biomass production chamber
The Biomass Production Chamber at Kennedy Space Center was constructed to conduct large scale plant growth studies for NASA's CELSS program. Over the past four years, physical systems and computer control software have been continually upgraded and the degree of atmospheric leakage from the chamber has decreased from about 40 to 5 percent of the total volume per day. Early tests conducted with a limited degree of closure showed that total crop (wheat) growth from the best trays was within 80 percent of reported optimal yields for similar light levels. Yields from subsequent tests under more tightly closed conditions have not been as good--up to only 65 percent of optimal yields. Yields appear to have decreased with increasing closure, yet potential problems exist in cultural techniques and further studies are warranted. With the ability to tightly seal the chamber, quantitative data were gathered on CO2 and water exchange rates. Results showed that stand photosynthesis and transpiration reached a peak near 25 days after planting, soon after full vegetative ground cover was established. In the final phase of testing when atmospheric closure was the highest, ethylene gas levels in the chamber rose from about 10 to nearly 120 ppb. Evidence suggests that the ethylene originated from the wheat plants themselves and may have caused an epinastic rolling of the leaves, but no apparent detrimental effects on whole plant function.
Wheeler, R. M.↗