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At least 19 records

Mechanics of fatigue crack closure

Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.

Newman, J. C., Jr.↗

Study of one-dimensional spectral dynamic equations of the Reynolds stresses in homogeneous anisotropic turbulence: Application to split-spectrum modeling

The CTR numerical data base generated by direct simulation of homogeneous anisotropic turbulence was used to calculate all of the terms in the spectral balance equations for the turbulent Reynolds stresses. The aim in not only to test the main closure assumptions used in the split-spectrum models, but also to try to devise improved hypotheses deduced from the statistical information. Numerical simulations of turbulent flows provide a large amount of data, a thought provoking wealth of information. The main advantage of this type of comparison is that a great variety of flows can be considered, and this is necessary to test closure hypotheses. Moreover various initial conditions can be introduced in the calculation, even if they are not experimentally feasible. All the terms in the spectral equations can be calculated. The limited Reynolds numbers of the simulations and the statistical noise caused by a small sample, particularly at the large scales, causes some difficulty in the interpretation of the results, but the method of approach proved to be a powerful tool for testing and improving spectral closures.

Schiestel, R.↗

Subgrid Combustion Modeling for the Next Generation National Combustion Code

In the first year of this research, a subgrid turbulent mixing and combustion methodology developed earlier at Georgia Tech has been provided to researchers at NASA/GRC for incorporation into the next generation National Combustion Code (called NCCLES hereafter). A key feature of this approach is that scalar mixing and combustion processes are simulated within the LES grid using a stochastic 1D model. The subgrid simulation approach recovers locally molecular diffusion and reaction kinetics exactly without requiring closure and thus, provides an attractive feature to simulate complex, highly turbulent reacting flows of interest. Data acquisition algorithms and statistical analysis strategies and routines to analyze NCCLES results have also been provided to NASA/GRC. The overall goal of this research is to systematically develop and implement LES capability into the current NCC. For this purpose, issues regarding initialization and running LES are also addressed in the collaborative effort. In parallel to this technology transfer effort (that is continuously on going), research has also been underway at Georgia Tech to enhance the LES capability to tackle more complex flows. In particular, subgrid scalar mixing and combustion method has been evaluated in three distinctly different flow field in order to demonstrate its generality: (a) Flame-Turbulence Interactions using premixed combustion, (b) Spatially evolving supersonic mixing layers, and (c) Temporal single and two-phase mixing layers. The configurations chosen are such that they can be implemented in NCCLES and used to evaluate the ability of the new code. Future development and validation will be in spray combustion in gas turbine engine and supersonic scalar mixing.

Menon, Suresh↗

The Role of Margin in Link Design and Optimization

Link analysis is a system engineering process in the design, development, and operation of communication systems and networks. Link models that are mathematical abstractions representing the useful signal power and the undesirable noise and attenuation effects (including weather effects if the signal path transverses through the atmosphere) that are integrated into the link budget calculation that provides the estimates of signal power and noise power at the receiver. Then the link margin is applied which attempts to counteract the fluctuations of the signal and noise power to ensure reliable data delivery from transmitter to receiver. (Link margin is dictated by the link margin policy or requirements.) A simple link budgeting approach assumes link parameters to be deterministic values typically adopted a rule-of-thumb policy of 3 dB link margin. This policy works for most S- and X-band links due to their insensitivity to weather effects. But for higher frequency links like Ka-band, Ku-band, and optical communication links, it is unclear if a 3 dB link margin would guarantee link closure. Statistical link analysis that adopted the 2-sigma or 3-sigma link margin incorporates link uncertainties in the sigma calculation. (The Deep Space Network (DSN) link margin policies are 2-sigma for downlink and 3-sigma for uplink.) The link reliability can therefore be quantified statistically even for higher frequency links. However in the current statistical link analysis approach, link reliability is only expressed as the likelihood of exceeding the signal-to-noise ratio (SNR) threshold that corresponds to a given bit-error-rate (BER) or frame-error-rate (FER) requirement. The method does not provide the true BER or FER estimate of the link with margin, or the required signalto-noise ratio (SNR) that would meet the BER or FER requirement in the statistical sense. In this paper, we perform in-depth analysis on the relationship between BER/FER requirement, operating SNR, and coding performance curve, in the case when the channel coherence time of link fluctuation is comparable or larger than the time duration of a codeword. We compute the "true" SNR design point that would meet the BER/FER requirement by taking into account the fluctuation of signal power and noise power at the receiver, and the shape of the coding performance curve. This analysis yields a number of valuable insights on the design choices of coding scheme and link margin for the reliable data delivery of a communication system - space and ground. We illustrate the aforementioned analysis using a number of standard NASA error-correcting codes.

Cheung, K.↗

A statistical investigation of the single-point pdf of velocity and vorticity based on direct numerical simulations

Vorticity plays a fundamental role in turbulent flows. The dynamics of vorticity in turbulent flows and the effect on single-point closure models were investigated. The approach was to use direct numerical simulations of turbulent flows to investigate the pdf of velocity and vorticity. The preliminary study of homogeneous shear flow has shown that the expectation of the fluctuating pressure gradient, conditioned with a velocity component, is linear in the velocity component, and that the coefficient is independent of velocity and vorticity. In addition, the work shows that the expectation of the pressure gradient, conditioned with a vorticity component, is essentially zero.

Mortazavi, M.↗

A new stochastic systems approach to structural integrity

This paper develops improved stochastic models for the description of a large variety of fatigue crack growth phenomena that occur in components of considerable importance to the functionality and reliability of complex engineering structures. In essence, the models are based on the McGill-Markov and Closure-Lognormal stochastic processes. Not only do these models have the capability of predicting the statistical dispersion of crack growth rates, they also, by incorporating the concept of crack closure, have the capability of transferring stochastic crack growth properties measured under ideal laboratory conditions to situations of industrial significance, such as those occurring under adverse loading and/or environmental conditions. The primary data required in order to be in a position to estimate the pertinent parameters of these stochastic models are obtained from a statistically significant number of replicate tests. In this paper, both the theory and the experimental technique are illustrated using a Ti-6Al-4V alloy. Finally, important structural integrity, reliability, availability and maintainability concepts are developed and illustrated.

Provan, James W.↗

Dynamics and structure of turbulent premixed flames

In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the opportunity to work close at hand with the (in this case numerical) experimental data. Not only can one spot patterns and relationships in the data which could be important, but one can also get to know the limitations of the technique being used, so that when the next experiment is being designed it will address resolvable questions. A three-year grant from the Australian Research Council has enabled us to develop a small capability at the University of Sydney to work on DNS of turbulent reacting flow, and to analyze data bases generated at CTR. Collaboration between the University of Sydney and CTR is essential to this project and finding a workable modus operandum for this collaboration, given the constraints involved, has been a major objective of the past year's effort. The overall objectives of the project are: (1) to obtain a quantitative understanding of the dynamics of turbulent premixed flames at high turbulence levels with a view to developing improved second order closure models; and (2) to carry out new DNS experiments on turbulent premixed flames using a carefully chosen multistep reduced mechanism for the chemical kinetics, with a view to elucidating the laser diagnostic findings that are contrary to the findings for DNS using one-step kinetics. In this first year the objectives have been to make the existing CTR data base more accessible to coworkers at the University of Sydney, to make progress on understanding the dynamics of the flame in this existing CTR data base, and to carefully construct a suitable multistep reduced mechanism for use in a new set of DNS experiments on turbulent premixed flames.

Bilger, R. W.↗

A Combined Al-Mg/Pb-Pb Age of the Solar System

Astrophysical models of planet formation and protoplanetary disk evolution demand precise and accurate timing of the sequence of events in the solar nebula, relative to a time t=0, usually taken to be during the short epoch of CAI (Ca-rich, Al-rich inclusion) formation. Most CAIs formed withlive26Al (mean-life τ26= 1.034 Myr [1]), with an abundance 26Al/27Al ≈ (26Al/27Al)SS= 5.23 × 10-5[2]. We adopt this as the widespread level of 26Al in the solar nebula at t=0. Assuming spatial homogeneity of 26Al, an inclusion that had less 26Al, (26Al/27Al)0, formed a time Δt26= τ26ln[(26Al/27Al)SS/ (26Al/27Al)0] after t=0.These ages are typical precise to within ±0.1 Myr. Igneous bulk meteorites and inclusions can be relatively dated by the Al-Mg chronometer, but only ifΔt26<6 Myr. The Pb-Pb system is useful as a longer relative chronometer. It yields absolute ages tPb using 207Pb/206Pb, 206Pb/204Pb, and 238U/235U ratios measured indifferent portions of a sample, assuming certain half-lives [4]. These absolute ages are uncertain to within ±9 Myr due to uncertainties in the 235U half-life[3], but times of formation ΔtPb= tCAI–tPb relative to t=0, are more precise(±0.5Myr),iftCAI can be found. Here, tCAI means the Pb-Pb age that would be measured in CAIs using the half-lives the community typically uses, if they achieved isotopic closure at t=0. Unfortunately, direct Pb-Pb dating of CAIs has not definitively determined tCAI. Based on four CAIs with canonical (26Al/27Al)0,[5,6] found tPb= 4567.30 ± 0.16 Myr. No other CAI ages with measured 238U/235U have been reported in the refereed literature, but there are hints of other CAIs with ages tPb= 4568.0 ± 0.2 Myr [7] and tPb= 4568.3 ± 0.2 Myr [8].It is unclear whether anyof these igneous type B CAIs isotopically closed at t=0 or represents tCAI. Instead of measurements, we advocate finding tCAI by minimizing the discrepancies between the Al-Mg and Pb-Pb chronometers. Assuming Δt26=ΔtPb, we find the implied t’CAI= tPb+Δt26, then define t*CAIas the weighted mean of the t’CAI. t*CAIis the best guess for the Pb-Pb age of t=0; the assumption of homogeneity is justified if the t’CAI cluster within errors around t*CAI. This statistical approach is similar to, but improves on, that of[9]. We find t*CAI= 4568.73 ± 0.16 Myr. Below we discuss our methodology and the implications of this age for CAIs, 1.4 Myr older than the reported and typically used age 4567.30±0.16 Myr. Methods: We base our estimate of t*CAIon five achondrites for which published (26Al/27Al)0and Pb-Pb ages exist: the quenched angrites D’Orbigny, Sahara 99555 (SAH 99555), and Northwest Africa (NWA) 1670; the pseudo-eucrite Asuka 881394; and the inner disk achondrite. All are “NC” (non-carbonaceous) achondrites that likely cooled quickly enough that the Al-Mg and Pb-Pb systems achieved isotopic closure simultaneously. We also considered the “CC” (carbonaceous chondrite-like) achondrites NWA 2796 and NWA 6704, butdo not include them in our fit. Al-Mg and Pb-Pb seem not to have closed simultaneously, possibly because formation in the outer disk from volatile-rich composition led to slower cooling. Of the 8 chondrules from NWA 5697 measured by [20,21], we also consider the 4 for which 238U/235U was measured: 2-C1, 5-C2, 3-C5, 11-C1.Depending on their post-formation thermal histories, the Al-Mg and Pb-Pb systems in chondrules may or may not have closed simultaneously. Table 1: (26Al/27Al)0, Pb-Pb ages of selected samplesSample(26Al/27Al)0/ 10-6RefPb-PbRefD’Orbigny3.98±0.15104563.43±0.19♮10-12SAH 995553.64±0.18104563.88±0.2712NWA16705.92±0.59104564.39±0.24*10Asuka 88139413.1±0.5613-154564.98±0.1715NWA 73253.03±0.14164563.4±2.616NWA 27963.94±0.16174562.89±0.5917NWA 67043.03±0.14184562.76±0.26192-C17.56±1.53204567.57±0.56*215-C27.04±1.51204567.54±0.52*213-C58.85±1.83204566.20±0.63*2111-C15.55±1.84204565.84±0.72*21*regression based on one subset of data points ♮weighted mean of two datasets Pb-Pb ages are proportional to the intercept of the line formed by linear regression of 207Pb/206Pb vs. 206Pb/204Pb data from various washes, leachates and residues of acid dissolution of a sample. Because contamination by terrestrial or primordial Pb is pervasive, some fractions must be excluded from regressions to ensure a fit with acceptable mean squares weighted deviation (MSWD). Usually points are excluded based on low [Pb], or low 206Pb/204Pb ratio(low radiogenic component), with single outliers identified [11,12,15,16,17]. In the starred examples (Table 1)and the case of 3 CAI Pb-Pb ages [5], up to half the points were excluded solely because did not fit a pre-determined line. This approach is vulnerable to confirmation bias and produces fits with low MSWD and too-low Pb-Pb age uncertainty. Regressing the same data points as [10], were produce the Pb-Pb age of NWA 1670 of 4564.39±0.24 Myr. But selecting other combinations of data points, other, equally valid, isochrons yield ages from 4563.77±0.21 Myr to 4564.64±0.23 Myr. Similar arguments apply to the Pb-Pb isochrons built by [21] for chondrules 2-C1 (we find 4567.33±0.44 to 4567.85±0.46 Myr), 5-C2 (4566.84±0.53 to 4567.70±0.44 Myr), 3-C5 (4565.84±0.54to 4567.04±0.54)and 11-C1 (4565.36±0.51 to 4565.74±0.45 Myr). Our adopted ages for these and NWA 1670 are listed in Table 2.Table 2. tCAI estimated from various components, using our regressions for the chondrules & NWA 1670.SampleΔt26(Myr)tPb(Myr)t’CAI(Myr)D’Orbigny5.05±0.044563.43±0.194568.48±0.19SAH 995555.14±0.054563.88±0.274569.02±0.27NWA16704.64±0.104564.21±0.634568.85±0.67Asuka 8813943.81±0.044564.98±0.174568.79±0.17NWA 73255.33±0.054563.4±2.64568.7±2.6NWA 27965.06±0.044562.89±0.594567.95±0.59NWA 67045.29±0.134562.76±0.264568.05±0.292-C12.00±0.214567.59±0.704569.59±0.725-C22.07±0.224567.23±0.914569.30±0.933-C51.84±0.214566.44±1.124568.28±1.1411-C12.32±0.344565.52±0.664567.84±0.73achondrite4568.72±0.16chondrules4568.76±0.58combined4568.73±0.16A weighted average of the five NC achondrites(or just D’Orbigny, SAH 99555 and Asuka 881394)yields t*CAI= 4568.72 ± 0.16Myr. All are consistent with this value to within 1.8σ, and MSWD=1.5. Including the 4 U-corrected chondrules, t*CAI= 4568.73± 0.16Myrwith MSWD=1.66, which is statistically significant. All chondrules and NC achondrites are consistent with this to within 1.8σ, (Figure 1).Figure 1. Al-Mg formation times after t=0 vs. Pb-Pb ages. The five NC achondrites and four chondrules are consistent with a Pb-Pb age of t=0 of 4568.7 Myr. Discussion: The data from achondrites and chondrules are consistent with a single Pb-Pb age at t=0, justifying the assumption of 26Al homogeneity. The age, 4568.7 Myr, is ≈1.4 Myr older than the commonly accepted Pb-Pb age of CAIs that formed with canonical 26Al/27Al at t=0 [3]. Others have interpreted the discrepancy to signify 26Al heterogeneity in the CAI-forming region[5,21]. We suggest instead that CAIs were exposed to transient heating events that reset the Pb-Pb system without disturbing the Al-Mg system. Notably, chondrules typically experienced transient heating at these times in the nebula [22]. If so, direct measurements of CAIs will not yield as reliable a Pb-Pb age of t=0 as statistical approaches like this and that of [9].References:[1] Auer et al. 2009. [2] Jacobsen, B et al. 2008, EPSL 272, 353-364. [3] Tissot, Fet al. 2017, GCA 213, 593-617.[4] Villa, I et al. 2016, GCA 172, 387-392.[5] Amelin, Y et al. 2010, EPSL 300, 343-350.[6] Connelly, Jet al. 2012, Science 338, 651.[7] Bouvier, Aet al. 2011, LPICo 1639, 9054. [8] Bouvier, Aand Wadhwa, M2010, Nat Geosci 3, 637-641.[9] Nyquist, Let al. 2009, GCA 73, 5115-5136.[10] Schiller et al. 2015. [11] Wadhwa & Brennecka 2012. [12] Tissot et al. 2017. [13] Nyquist et al. 2003. [14] Wadhwa et al. 2009. [15] Wimpenny et al. 2019, GCA 244, 478-501.[16] Koefoed et al. 2016, GCA 183, 31-45. [17] Bouvier, A et al. 2011, GCA 75, 5310-5323. [18] Sanborn, Met al. 2019, GCA 245, 577-596. [19] Amelin, Yet al. 2019, GCA 245, 628-642.[20] Bollard, Jet al. 2017, Sci Adv 3 ,e1700407. [21] Bollard, Jet al. 2019, GCA 260, 62-83.[22] Villeneuve, J et al. 2009, Science 325, 985

S. J. Desch↗

On near-wall turbulent flow modelling

The behavior of various terms in the Reynolds-stress transport equations is evaluated in view results of near-wall turbulence characterizations which show that all components of the velocity-pressure gradient correlation vanish at the wall. A methodology for deriving an asymptotically correct model of the velocity-pressure gradient correlation is proposed, and a model capable of approaching the high-Reynolds number model for pressure distribution far from the wall is derived. A parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds number-dependent; with this modification, excellent agreement is obtained with measured and simulated near-wall turbulence statistics.

Lai, Y. G.↗

Scale resolving simulations of the NASA Juncture Flow Model using the LAVA solver

Two distinct simulation methodologies: Delayed Detached Eddy Simulation (DDES) and stress based Wall-modelled Large Eddy Simulation (WMLES) are evaluated using structured overset curvilinear grids for the NASA juncture flow model. While both methodologies are shown to mitigate the primary shortcomings of steady state Reynolds Averaged Navier Stokes(RANS) simulations, several unresolved aspects are identified. Strong sensitivity to RANS-typegrid refinement is observed in the DDES with a substantial deterioration of the solution quality with increasing spatial resolution associated with deficiencies in the shielding function. Mean profiles for attached boundary layers on the fuselage show spurious inflections suggesting modelled stress depletion on finer grids. Lower numerical dissipation in terms of spatial discretization and time step size is seen to improve the solution quality, and the advantage of using RC and QCR2000 corrections in the underlying RANS closure is demonstrated for DDES on RANS-type meshes. Equilibrium Wall-Modelled LES used grids that resolved the tripping dots over the fuselage nose and the wing leading edge, consistent with the experiment setup. These simulations resulted in a cost-competitive approach compared to DDES on RANS-type grids. Although the agreement between WMLES predictions of first and second order single point statistics with experimental measurements is promising, a fundamental shortcoming is noted in terms of an overshoot in streamwise momentum in corner regions of the wing-fuselage juncture. This excess momentum subsequently delays the onset of separation,thereby resulting in an underprediction in length of the separation bubble. Some quantitative sensitivity to numerical discretization is observed; lowering of numerical dissipation shows better agreement with the experiment.

T^3↗

Non-Gaussian approach for parametric random vibration of non-linear structures

The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

Ibrahim, R. A.↗

PDF approach for turbulent scalar field: Some recent developments

The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.

Gao, Feng↗

Space vehicle approach velocity judgments under simulated visual space conditions

There were 35 volunteers who responded when they first perceived an increase in apparent size of a collimated, two-dimensional perspective image of an Orbiter vehicle. The variables of interest included the presence (or absence) of a fixed reticle within the field of view (FOV), background starfield velocity, initial range to the vehicle and vehicle closure velocity. It was found that: 1) increasing vehicle approach velocity yielded a very small (but significant) effect of faster detection of vehicle movement, nevertheless, response variability was relatively large; 2) including the fixed reticle in the FOV produced significantly slower detection of vehicle radial movement, however this occurred only at the largest range and the magnitude of the effect was only about 15% of the one sigma value; and 3) increasing background star velocity during this judgment led to slower detection of vehicle movement. While statistically significant, this effect was small and occurred primarily at the largest range. A possible explanation for the last two findings is that other static and dynamic objects within the visual field may compete for available attention which otherwise would be available for judging image expansion; thus, the target's retinal image has to expand more than otherwise for its movement to be detected. This study also showed that the Proximity Operations Research Mockup at NASA/Ames can be used effectively to investigate a variety of visual judgment questions related to future space operations. These findings are discussed in relation to previous research and possible underlying mechanisms.

Space Flight↗

The pdf approach to turbulent flow

This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.

Kollmann, W.↗

Toward a Turbulence Constitutive Relation for Rotating Flows

In rapidly rotating turbulent flows the largest scales of the motion are in approximate geostrophic balance. Single-point turbulence closures, in general, cannot attain a geostrophic balance. This article addresses and resolves the possibility of constitutive relation procedures for single-point second order closures for a specific class of rotating or stratified flows. Physical situations in which the geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal nondivergence, Taylor-Proudman theorem and two-dimensionality are, in the context of both the instantaneous and averaged equations, discussed. It is shown, in the absence of vortex stretching along the axis of rotation, that turbulence is frame-indifferent. A derivation and discussion of a geostrophic constraint which the prognostic equations for second-order statistics must satisfy for turbulence approaching a frame-indifferent limit is given. These flow situations, which include rotating and nonrotating stratified flows, are slowly evolving flows in which the constitutive relation procedures are useful. A nonlinear non-constant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations consistent with the geostrophic balance is described. The rapid-pressure strain model coefficients are not constants determined by numerical optimization but are functions of the state of the turbulence as parameterized by the Reynolds stresses and the turbulent heat fluxes. The functions are valid for all states of the turbulence attaining their limiting values only when a limit state is achieved. These issues are relevant to strongly vortical flows as well as flows such as the planetary boundary layers, in which there is a transition from a three-dimensional shear driven turbulence to a geostrophic or horizontal turbulence.

Ristorcelli, J. R.↗

Alternative Representations of Convective Processes in the NASA GEOS-5 AGCM

The gap in explicit resolution of phenomena between global climate models and cloud resolving models is shrinking at a steady pace with global integrations of several km in resolution now practical for at least some time scales. In moving toward finer resolution the long standing problem of convective parameterization is being examined along with the assumption of convective quasi-equilibrium and how this can be reconciled with the stochastic and intermittent nature of convection. In this context we examine the nature of parameterized convection in the NASA Goddard Earth Observing System (GEOS-5) Atmospheric General Circulation Model. Our analysis uses both coarse (2.5 degree) and fine scale 0.25 degree spatial resolution integrations. Two basic formulations are compared: the default option is the Relaxed Arakawa-Schubert (RAS) scheme which invokes a sequence of linearly entraining plumes and quasi-equilibrium closure. An optional modification of this method (the "Stochastic Tokioka" constraint) places a random lower limit on plume entrainment. An alternative representation is the Kain-Fritsch parameterization which was originally developed for mesoscale numerical modeling strategies. Here entrainment is determined by a crude buoyancy sorting approach that allows the plume spectrum to be more responsive to ambient vertical stratification of moisture. Diagnostics of the model behavior are referenced to recent observational evidence of continuous phase transition behavior. In particular we examine the relationship between column water vapor and probablility of convective presence and intensity. Sensitivity of the statistics of convective behavior to parcel mixing/entrainment formulations and parcel initial thermodynamics are considered. Observational statistics from A-Train and TRMM sensors provide validation of the model integrations.

Robertson, Franklin↗

Jet Noise Diagnostics Supporting Statistical Noise Prediction Methods

The primary focus of my presentation is the development of the jet noise prediction code JeNo with most examples coming from the experimental work that drove the theoretical development and validation. JeNo is a statistical jet noise prediction code, based upon the Lilley acoustic analogy. Our approach uses time-average 2-D or 3-D mean and turbulent statistics of the flow as input. The output is source distributions and spectral directivity. NASA has been investing in development of statistical jet noise prediction tools because these seem to fit the middle ground that allows enough flexibility and fidelity for jet noise source diagnostics while having reasonable computational requirements. These tools rely on Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solutions as input for computing far-field spectral directivity using an acoustic analogy. There are many ways acoustic analogies can be created, each with a series of assumptions and models, many often taken unknowingly. And the resulting prediction can be easily reverse-engineered by altering the models contained within. However, only an approach which is mathematically sound, with assumptions validated and modeled quantities checked against direct measurement will give consistently correct answers. Many quantities are modeled in acoustic analogies precisely because they have been impossible to measure or calculate, making this requirement a difficult task. The NASA team has spent considerable effort identifying all the assumptions and models used to take the Navier-Stokes equations to the point of a statistical calculation via an acoustic analogy very similar to that proposed by Lilley. Assumptions have been identified and experiments have been developed to test these assumptions. In some cases this has resulted in assumptions being changed. Beginning with the CFD used as input to the acoustic analogy, models for turbulence closure used in RANS CFD codes have been explored and compared against measurements of mean and rms velocity statistics over a range of jet speeds and temperatures. Models for flow parameters used in the acoustic analogy, most notably the space-time correlations of velocity, have been compared against direct measurements, and modified to better fit the observed data. These measurements have been extremely challenging for hot, high speed jets, and represent a sizeable investment in instrumentation development. As an intermediate check that the analysis is predicting the physics intended, phased arrays have been employed to measure source distributions for a wide range of jet cases. And finally, careful far-field spectral directivity measurements have been taken for final validation of the prediction code. Examples of each of these experimental efforts will be presented. The main result of these efforts is a noise prediction code, named JeNo, which is in middevelopment. JeNo is able to consistently predict spectral directivity, including aft angle directivity, for subsonic cold jets of most geometries. Current development on JeNo is focused on extending its capability to hot jets, requiring inclusion of a previously neglected second source associated with thermal fluctuations. A secondary result of the intensive experimentation is the archiving of various flow statistics applicable to other acoustic analogies and to development of time-resolved prediction methods. These will be of lasting value as we look ahead at future challenges to the aeroacoustic experimentalist.

Bridges, James E.↗

NASA Lewis Launch Collision Probability Model Developed and Analyzed

There are nearly 10,000 tracked objects orbiting the earth. These objects encompass manned objects, active and decommissioned satellites, spent rocket bodies, and debris. They range from a few centimeters across to the size of the MIR space station. Anytime a new satellite is launched, the launch vehicle with its payload attached passes through an area of space in which these objects orbit. Although the population density of these objects is low, there always is a small but finite probability of collision between the launch vehicle and one or more of these space objects. Even though the probability of collision is very low, for some payloads even this small risk is unacceptable. To mitigate the small risk of collision associated with launching at an arbitrary time within the daily launch window, NASA performs a prelaunch mission assurance Collision Avoidance Analysis (or COLA). For the COLA of the Cassini spacecraft, the NASA Lewis Research Center conducted an in-house development and analysis of a model for launch collision probability. The model allows a minimum clearance criteria to be used with the COLA analysis to ensure an acceptably low probability of collision. If, for any given liftoff time, the nominal launch vehicle trajectory would pass a space object with less than the minimum required clearance, launch would not be attempted at that time. The model assumes that the nominal positions of the orbiting objects and of the launch vehicle can be predicted as a function of time, and therefore, that any tracked object that comes within close proximity of the launch vehicle can be identified. For any such pair, these nominal positions can be used to calculate a nominal miss distance. The actual miss distances may differ substantially from the nominal miss distance, due, in part, to the statistical uncertainty of the knowledge of the objects positions. The model further assumes that these position uncertainties can be described with position covariance matrices. With these, and some additional simplifying assumptions, a closed-form solution for the probability of collision is obtained. This solution provides clear insights into how each of the independent parameters affects the probability of collision. It shows that for a given maximum probability of collision and prior knowledge of the objects position uncertainties and sizes, only knowledge of the nominal closest approach distance is required to make the launch/no launch decision. The model was completed and used for the mission assurance COLA analysis for the Cassini spacecraft, which was launched on a Titan IV/Centaur rocket on October 15, 1997. Although the model was specifically developed for the Cassini mission, it is clearly applicable for other launches as well. The effect of COLA closures on the launch window is shown. The bar represents the entire 140-min launch window on October 15, 1997; the blackened areas represent the loss of launch opportunities due to the potential for a collision with an orbiting object.

Bollenbacher, Gary↗