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NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

NASA NTRS1992

Systematic study of Reynolds stress closure models in the computations of plane channel flows

The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.

Demuren, A. O.↗

NASA NTRS1992

Predicting equilibrium states with Reynolds stress closures in channel flow and homogeneous shear flow

Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. A direct theoretical connection is made between homogeneous shear flow in equilibrium and the log-layer of fully-developed turbulent channel flow. It is shown that if a second-order closure model is calibrated to yield good equilibrium values for homogeneous shear flow it will also yield good results for the log-layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the log-layer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.

Abid, R.↗

NASA NTRS1990

Through-the-thickness fatigue crack closure behavior in an aluminum alloy

The variation in fatigue crack closure behavior across the thickness of aluminum alloy specimens was investigated. The specimen geometries examined were the middle crack tension M(T) and compact tension C(T). The fatigue crack closure behavior was determined using remote displacement and strain gages, near tip strain gages, and fatigue striations. A hybrid experimental/numerical method was also used to infer the crack opening loads. The results indicate a variation in crack opening load, of 0.2 in the specimen interior to 0.4 to 0.5 at the surface.

Dawicke, D. S.↗

NASA NTRS1992

A PDF closure model for compressible turbulent chemically reacting flows

The objective of the proposed research project was the analysis of single point closures based on probability density function (pdf) and characteristic functions and the development of a prediction method for the joint velocity-scalar pdf in turbulent reacting flows. Turbulent flows of boundary layer type and stagnation point flows with and without chemical reactions were be calculated as principal applications. Pdf methods for compressible reacting flows were developed and tested in comparison with available experimental data. The research work carried in this project was concentrated on the closure of pdf equations for incompressible and compressible turbulent flows with and without chemical reactions.

Kollmann, W.↗

NASA NTRS1992

Second order closure modeling of turbulent buoyant wall plumes

Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

Zhu, Gang↗

NASA NTRS1992

Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem

Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.

Deissler, Robert G.↗

NASA NTRS1993

Fast parallel algorithms that compute transitive closure of a fuzzy relation

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. The original algorithm proposed by L. Zadeh (1971) requires the computation time O(n(sup 4)), where n is the number of elements in the relation. In 1974, J. C. Dunn proposed a O(n(sup 2)) algorithm. Since we must compute n(n-1)/2 different values s(a, b) (a not equal to b) that represent the fuzzy relation, and we need at least one computational step to compute each of these values, we cannot compute all of them in less than O(n(sup 2)) steps. So, Dunn's algorithm is in this sense optimal. For small n, it is ok. However, for big n (e.g., for big databases), it is still a lot, so it would be desirable to decrease the computation time (this problem was formulated by J. Bezdek). Since this decrease cannot be done on a sequential computer, the only way to do it is to use a computer with several processors working in parallel. We show that on a parallel computer, transitive closure can be computed in time O((log(sub 2)(n))2).

Kreinovich, Vladik YA.↗

NASA NTRS1993

Perspective - Systematic study of Reynolds stress closure models in the computations of plane channel flows

Demuren, A. O.↗

NASA NTRS1993

Predicting equilibrium states with Reynolds stress closures in channel flow and homogeneous shear flow

Abid, R.↗

NASA NTRS1994

An alternative assessment of second-order closure models in turbulent shear flows

The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.

Speziale, Charles G.↗

NASA NTRS1995

On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory

The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.

Speziale, Charles G.↗

NASA NTRS1995

Characterization of the Minimum Energy Paths for the Ring Closure Reactions of C4H3 with Acetylene

The ring closure reaction of C4H3 with acetylene to give phenyl radical is one proposed mechanism for the formation of the first aromatic ring in hydrocarbon combustion. There are two low-lying isomers of C4H3; 1-dehydro-buta-l-ene-3-yne (n-C4H3) and 2-dehydro-buta-l-ene-3-yne (iso-C4H3). It has been proposed that only n-C4H3 reacts with acetylene to give phenyl radical, and since iso-C4H3 is more stable than n-C4H3, formation of phenyl radical by this mechanism is unlikely. We report restricted Hartree-Fock (RHF) plus singles and doubles configuration interaction calculations with a Davidson's correction (RHF+1+2+Q) using the Dunning correlation consistent polarized valence double zeta basis set (cc-pVDZ) for stationary point structures along the reaction pathway for the reactions of n-C4H3 and iso-C4H3 with acetylene. n-C4H3 plus acetylene (9.4) has a small entrance channel barrier (17.7) (all energetics in parentheses are in kcal/mol with respect to iso-C4H3 plus acetylene) and the subsequent closure steps leading to phenyl radical (-91.9) are downhill with respect to the entrance channel barrier. Iso-C4H3 Plus acetylene also has an entrance channel barrier (14.9) and there is a downhill pathway to 1-dehydro-fulvene (-55.0). 1-dehydro-fulvene can rearrange to 6-dehydro-fulvene (-60.3) by a 1,3-hydrogen shift over a barrier (4.0), which is still below the entrance channel barrier, from which rearrangement to phenyl radical can occur by a downhill pathway. Thus, both n-C4H3 and iso-C4H3 can react with acetylene to give phenyl radical with small barriers.

Walch, Stephen P.↗

NASA NTRS1997

An Analysis of Closure Mechanisms in the Plasma Wake of the TSS-1R Satellite

Collisionless Plasma Expansion (CPE), also known as "plasma expansion into a vacuum," in its most fundamental form, is the process by which a plasma expands into a void, or region highly depleted of particles. In CPE, the expansion is driven by the highly mobile electron constituent of the plasma as it moves across the density gradient and into the void region. A bi-polar electric field is set up between this rapidly expanding electron front and the massive ions, which have a low thermal speed and lag behind in the region of the plasma-void interface. These ions are quickly accelerated by the expansion electric field and can, theoretically, approach the thermal speed of the electrons. CPE is a fundamental and a very robust process in that it only requires that a sharp density gradient exist in a plasma. It has already been observed to exist in various plasmas ranging over five orders of magnitude in density. The range of phenomena in which CPE has been observed includes the closure of plasma wakes created in simulated space plasmas in the laboratory; it was found to be the process controlling the refilling of the wake created by the Space Shuttle in the ionospheric plasma; and recent in situ data, obtained by the WIND spacecraft as it passed through the wake of the earth's moon last year, have shown CPE to be involved in the closure of the Lunar wake. CPE is also expected to influence the morphology and physics of the solar wind interactions with Mercury and Mars, and has been suggested as a potential factor in such wide ranging phenomena as the acceleration of plasma away from the coma of comets and the energization of ions that underlies the upward expansion of the polar wind into the earth's magnetosphere. The Tethered Satellite System (TSS)-1R data provides an opportunity to test this process in situ under semi-controlled conditions. The available data shows the intensity, drift energy and angle of inclination to the wake of the converging ion streams at a down stream distance of one satellite radius (80 CM).

Stone, N. H.↗

NASA NTRS1999

Supersonic Aftbody Closure Wind-Tunnel Testing, Data Analysis, and Computational Results

This paper reports on the model, test, and results from the Langley Supersonic Aftbody Closure wind tunnel test. This project is an experimental evaluation of the 1.5% Technology Concept Aircraft (TCA) aftbody closure model (Model 23) in the Langley Unitary Plan Wind Tunnel. The baseline TCA design is the result of a multidisciplinary, multipoint optimization process and was developed using linear design and analysis methods, supplemented with Euler and Navier-Stokes numerical methods. After a thorough design review, it was decided to use an upswept blade attached to the forebody as the mounting system. Structural concerns dictated that a wingtip support system would not be feasible. Only the aftbody part of the model is metric. The metric break was chosen to be at the fuselage station where prior aft-sting supported models had been truncated. Model 23 is thus a modified version of Model 20. The wing strongback, flap parts, and nacelles from Model 20 were used, whereas new aftbodies, a common forebody, and some new tails were fabricated. In summary, significant differences in longitudinal and direction stability and control characteristics between the ABF and ABB aftbody geometries were measured. Correcting the experimental data obtained for the TCA configuration with the flared aftbody to the representative of the baseline TCA closed aftbody will result in a significant reduction in longitudinal stability, a moderate reduction in stabilizer effectiveness and directional stability, and a moderate to significant reduction in rudder effectiveness. These reductions in the stability and control effectiveness levels of the baseline TCA closed aftbody are attributed to the reduction in carry-over area.

Allen, Jerry↗

NASA NTRS2000

In Situ Aerosol Size Distributions and Clear Column Radiative Closure During ACE-2

As part of the second Aerosol Characterization Experiment (ACE-2) during June and July of 1997, aerosol size distributions were measured on board the CIRPAS Pelican aircraft through the use of a DMA and two OPCS. During the campaign, the boundary layer aerosol typically possessed characteristics representative of a background marine aerosol or a continentally influenced aerosol, while the free tropospheric aerosol was characterized by the presence or absence of a Saharan dust layer. A range of radiative closure comparisons were made using the data obtained during vertical profiles flown on four missions. Of particular interest here are the comparisons made between the optical properties as determined through the use of measured aerosol size distributions and those measured directly by an airborne 14-wavelength sunphotometer and three nephelometers. Variations in the relative humidity associated with each of the direct measurements required consideration of the hygroscopic properties of the aerosol for size distribution based calculations. Simultaneous comparison with such a wide range of directly measured optical parameters not only offers evidence of the validity of the physicochemical description of the aerosol when closure is achieved, but also provides insight into potential sources of error when some or all of the comparisons result in disagreement. Agreement between the derived and directly measured optical properties varied for different measurements and for different cases. Averaged over the four case studies, the derived extinction coefficient at 525 nm exceeded that measured by the sunphotomoter by 2.5% in the clean boundary later, but underestimated measurements by 13% during pollution events. For measurements within the free troposphere, the mean derived extinction coefficient was 3.3% and 17% less than that measured by the sunphotometer during dusty and nondusty conditions, respectively. Likewise, averaged discrepancies between the derived and measured scattering coefficient were -9.6%, +4.7%, +17%, and -41% for measurements within the clean boundary layer, polluted boundary layer, free troposphere with a dust layer, and free troposphere without a dust layer, respectively. Each of these quantities, as well as the majority of the > 100 individual comparisons from which they were averaged, were within estimated uncertainties.

Collins, D. R.↗

NASA NTRS2000

Clear-Sky Closure Studies of Lower Tropospheric Aerosol and Water Vapor During ACE-2 Using Airborne Sunphotometer, Airborne In-Situ, Space-Borne, and Ground-Based Measurements

We report on clear-sky column closure experiments (CLEARCOLUMN) performed in the Canary Islands during the second Aerosol Characterization Experiment (ACE-2) in June/July 1997. We present CLEARCOLUMN results obtained by combining airborne sunphotometer and in-situ (optical particle counter, nephelometer, and absorption photometer) measurements taken aboard the Pelican aircraft, space-borne NOAA/AVHRR data and ground-based lidar and sunphotometer measurements. During both days discussed here, vertical profiles flown in cloud-free air masses revealed 3 distinctly different layers: a marine boundary layer (MBL) with varying pollution levels, an elevated dust layer, and a very clean layer between the MBL and the dust layer. A key result of this study is the achievement of closure between extinction or layer aerosol optical depth (AOD) computed from continuous in-situ aerosol size-distributions and composition and those measured with the airborne sunphotometer. In the dust, the agreement in layer AOD (lambda = 380-1060 nm) is 3-8%. In the MBL there is a tendency for the in-situ results to be slightly lower than the sunphotometer measurements (10-17% at lambda = 525 nm), but these differences are within the combined error bars of the measurements and computations.

Schmid, Beat↗

NASA NTRS2000

Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing

A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.

He, Gouwei↗