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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

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

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.

Alfven Wave Reflection Model of Field-Aligned Currents at Mercury

An Alfven Wave Reflection (AWR) model is proposed that provides closure for strong field-aligned currents (FACs) driven by the magnetopause reconnection in the magnetospheres of planets having no significant ionospheric and surface electrical conductance. The model is based on properties of the Alfven waves, generated at high altitudes and reflected from the low-conductivity surface of the planet. When magnetospheric convection is very slow, the incident and reflected Alfven waves propagate along approximately the same path. In this case, the net field-aligned currents will be small. However, as the convection speed increases. the reflected wave is displaced relatively to the incident wave so that the incident and reflected waves no longer compensate each other. In this case, the net field-aligned current may be large despite the lack of significant ionospheric and surface conductivity. Our estimate shows that for typical solar wind conditions at Mercury, the magnitude of Region 1-type FACs in Mercury's magnetosphere may reach hundreds of kilo-Amperes. This AWR model of field-aligned currents may provide a solution to the long-standing problem of the closure of FACs in the Mercury's magnetosphere. c2009 Elsevier Inc. All rights reserved.

Lyatsky, Wladislaw

Space ecosynthesis: An approach to the design of closed ecosystems for use in space

The use of closed ecological systems for the regeneration of wastes, air, and water is discussed. It is concluded that such systems, if they are to be used for the support of humans in space, will require extensive mechanical and physico-chemical support. The reason for this is that the buffering capacity available in small systems is inadequate, and that natural biological and physical regulatory mechanisms rapidly become inoperative. It is proposed that mathematical models of the dynamics of a closed ecological system may provide the best means of studying the initial problems of ecosystem closure. A conceptual and mathematical model of a closed ecosystem is described which treats the biological components as a farm, calculates the rates of flow of elements through the system by mass-balance techniques and control theory postulates, and can evaluate the requirements for mechanical buffering activities. It is suggested that study of the closure of ecosystems can significantly aid in the establishment of general principles of ecological systems.

Macelroy, R. D.

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

Raju, I. S.

Magnetosphere-Regolith/Exosphere Coupling: Differences and Similarities to the Earth Magnetosphere-Ionosphere Coupling

Of the three Mercury passes made by Mariner 10, the first and third went through the Mercury magnetosphere. The third encounter which occurred during northward IMF (interplanetary magnetic field) showed quiet time magnetic fields. In contrast the third encounter observed clear substorm signatures including dipolarization, field-aligned currents (FACs) and injection of energetic electrons at geosynchronous orbit. However, the determined cross-tail potential drop and the assumed height integrated conductance indicate that the FAC should be 2-50 times weaker than observed. We address this inconsistency and the fundamental problem of FAC closure whether this takes place in the regolith or in the exosphere. The current state of knowledge of the magnetosphere-exosphere/regolith coupling is addressed and similarities and differences to the Earth magnetosphere-ionosphere coupling are discussed.

Gjerleov, J. W.

Quality Interaction Between Mission Assurance and Project Team Members

Mission Assurance independent assessments started during the development cycle and continued through post launch operations. In operations, Health and Safety of the Observatory is of utmost importance. Therefore, Mission Assurance must ensure requirements compliance and focus on process improvements required across the operational systems including new/modified products, tools, and procedures. The deployment of the interactive model involves three objectives: Team member Interaction, Good Root Cause Analysis Practices, and Risk Assessment to avoid reoccurrences. In applying this model, we use a metric based measurement process and was found to have the most significant effect, which points to the importance of focuses on a combination of root cause analysis and risk approaches allowing the engineers the ability to prioritize and quantify their corrective actions based on a well-defined set of root cause definitions (i.e. closure criteria for problem reports), success criteria and risk rating definitions.

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