Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient calculation”

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.

At least 1,225 records · Page 68

Comparison of three-dimensional turbulent boundary-layer calculations with experiment

A numerical simulation is carried out of the incompressible three-dimensional turbulent boundary-layer experiments of van den Berg and Elsenaar (1972), Dechow (1977), and Muller (1982). The simulation is effected by integrating the boundary-layer equations together with an algebraic eddy-viscosity turbulence model. With this computational method, the downstream portion of the flow treated by van den Berg and Elsenaar, where the crossflow is large, cannot be predicted. It is believed that this flow is significantly influenced by elliptic flow-field effects. Even though Dechow's experiment also indicated departures from the boundary-layer concept, the calculations made here agree reasonably well with the mean-flow development up to separation. The normal pressure gradients in Muller's experiment are found to be negligible in regions with large skewing, making it possible to test turbulence models using the boundary-layer equations. The simulation of this flow compares favorably with the experimental data throughout the flow field.

Muller, U. R.↗

The Goertler vortex instability mechanism in three-dimensional boundary layers

The two-dimensional boundary layer on a concave wall is centrifugally unstable with respect to vortices aligned with the basic flow for sufficiently high values of the Goertler number. However, in most situations of practical interest the basic flow is three-dimensional and previous theoretical investigations do not apply. The linear stability of the flow over an infinitely long swept wall of variable curvature is considered. If there is no pressure gradient in the boundary layer the instability problem can always be related to an equivalent two-dimensional calculation. However, in general, this is not the case and even for small values of the crossflow velocity field dramatic differences between the two and three-dimensional problems emerge. When the size of the crossflow is further increased, the vortices in the neutral location have their axes locally perpendicular to the vortex lines of the basic flow.

Hall, P.↗

Chromospheric structure of cool carbon stars

A semiempirical chromospheric model is proposed for TX Psc which is a prototype for the N-type carbon stars. Observational data imply that the chromospheric temperature rise must begin at a low density, that the temperature gradient in the lower chromosphere must be steep, that partial redistribution must be employed in the Mg II calculation, and that the lower chromosphere is expanding away from the photosphere with a velocity of close to 50 km/s. The present model also shows that the microturbulent velocity is about 7 km/s at the temperature minimum region, dropping to 5 km/s in the chromosphere, and that the Lyman lines are optically thick in the chromosphere.

Luttermoser, Donald G.↗

An Analytical Study of Dilution Jet Mixing in a Cylindrical Duct

The mixing performance in a mixing section of a rich burn/quick mix/lean burn (RQL) combustor was calculated using a 3-D numerical model in a non-reacting environment. The numerically calculated results were compared with the measured data reported by Hatch, Sowa, Samuelsen, and Holdeman, 1992. The numerical 3-D temperature fields qualitatively agree with the experimental data. Also, the development of the mixing flow and temperature non-uniformity trends throughout the mixing section for the numerically calculated results quantitatively agree with the measured data. The numerical model predicts less mixing and enhances the temperature gradients as compared to the measured data for the cases reported by Hatch et al. (1992) which include circular and slot orifice shapes (with different slant angles and aspect ratios). The predicted and measured results generally agree in the selection of the slanted slot orifice configuration yielding the best overall mixing performance (based on temperature uniformity) of all the configurations analyzed.

Oechsle, V. L.↗

Enhancement of diffusive transport in oscillatory flows

The theory of transport of passive scalars in oscillatory flows is reexamined. The differences between transport in standing and traveling waves are emphasized. Both Lagrangian and Eulerian diffusivities are calculated, and the conditions for their applicability are discussed. Numerical simulations are conducted to understand the expulsion of gradients from time-dependent eddies and the resulting transport. The results indicate that it is the Eulerian diffusivity that is of primary relevance for describing enhanced transport on spatial scales larger than that of the eddies.

Knobloch, E.↗

An analytical study of dilution jet mixing in a cylindrical duct

The mixing performance in a mixing section of a rich burn/quick mix/lean burn (RQL) combustor was calculated using a 3-D numerical model in a non-reacting environment. The numerically calculated results were compared with the measured data reported by Hatch, Sowa, Samuelsen, and Holdeman, 1992. The numerical 3-D temperature fields qualitatively agree with the experimental data. Also, the development of the mixing flow and temperature non-uniformity trends throughout the mixing section for the numerically calculated results quantitatively agree with the measured data. The numerical model predicts less mixing and enhances the temperature gradients as compared to the measured data for the cases reported by Hatch et al. (1992) which include circular and slot orifice shapes (with different slant angles and aspect ratios). The predicted and measured results generally agree in the selection of the slanted slot orifice configuration yielding the best overall mixing performance (based on temperature uniformity) of all the configurations analyzed.

Oechsle, V. L.↗

An Investigation of the Compatibility of Radiation and Convection Heat Flux Measurements

A method for determining time-resolved absorbed surface heat flux and surface temperature in radiation and convection environments is described. The method is useful for verification of aerodynamic, heat transfer and durability models. A practical heat flux gage fabrication procedure and a simple one-dimensional inverse heat conduction model and calculation procedure are incorporated in this method. The model provides an estimate of the temperature and heat flux gradient in the direction of heat transfer through the gage. This paper discusses several successful time-resolved tests of this method in hostile convective heating and cooling environments.

Liebert, Curt H.↗

Improved Stratospheric Temperature Retrievals for Climate Reanalysis

The Data Assimilation Office (DAO) is embarking on plans to generate a twenty year reanalysis data set of climatic atmospheric variables. One of the focus points will be in the evaluation of the dynamics of the stratosphere. The Stratospheric Sounding Unit (SSU), flown as part of the TIROS Operational Vertical Sounder (TOVS), is one of the primary stratospheric temperature sensors flown consistently throughout the reanalysis period. Seven unique sensors made the measurements over time, with individual instrument characteristics that need to be addressed. The stratospheric temperatures being assimilated across satellite platforms will profoundly impact the reanalysis dynamical fields. To attempt to quantify aspects of instrument and retrieval bias we are carefully collecting and analyzing all available information on the sensors, their instrument anomalies, forward model errors and retrieval biases. For the retrieval of stratospheric temperatures, we adapted the minimum variance approach of Jazwinski (1970) and Rodgers (1976) and applied it to the SSU soundings. In our algorithm, the state vector contains an initial guess of temperature from a model six hour forecast provided by the Goddard EOS Data Assimilation System (GEOS/DAS). This is combined with an a priori covariance matrix, a forward model parameterization, and specifications of instrument noise characteristics. A quasi-Newtonian iteration is used to obtain convergence of the retrieved state to the measurement vector. This algorithm also enables us to analyze and address the systematic errors associated with the unique characteristics of the cell pressures on the individual SSU instruments and the resolving power of the instruments to vertical gradients in the stratosphere. The preliminary results of the improved retrievals and their assimilation as well as baseline calculations of bias and rms error between the NESDIS operational product and col-located ground measurements will be presented.

Rokke, L.↗

Review of Skin Friction Measurements Including Recent High-Reynolds Number Results from NASA Langley NTF

This paper reviews flat plate skin friction data from early correlations of drag on plates in water to measurements in the cryogenic environment of The NASA Langley National Transonic Facility (NTF) in late 1996. The flat plate (zero pressure gradient with negligible surface curvature) incompressible skin friction at high Reynolds numbers is emphasized in this paper, due to its importance in assessing the accuracy of measurements, and as being important to the aerodynamics of large scale vehicles. A correlation of zero pressure gradient skin friction data minimizing extraneous effects between tests is often used as the first step in the calculation of skin friction in complex flows. Early data compiled by Schoenherr for a range of momentum thickness Reynolds numbers, R(sub Theta) from 860 to 370,000 contained large scatter, but has proved surprisingly accurate in its correlated form. Subsequent measurements in wind tunnels under more carefully controlled conditions have provided inputs to this database, usually to a maximum R(sub Theta) of about 40,000. Data on a large axisymmetric model in the NASA Langley National Transonic Facility extends the upper limit in incompressible R(sub Theta) to 619,800 using the van Driest transformation. Previous data, test techniques, and error sources ar discussed, and the NTF data will be discussed in detail. The NTF Preston tube and Clauser inferred data accuracy is estimated to be within -2 percent of a power-law curve fit, and falls above the Spalding theory by 1 percent at R(sub Theta) of about 600,000.

Watson, Ralph D.↗

Thermoelastic Formulation of Stiffened, Unsymmetric Composite Panels for Finite Element Analysis of High Speed Aircraft

An emerging technology need for capturing 3-D panel thermoelastic response with 2-D planar finite element models (FEMs) is aided with an equivalent plate stiffness and thermal coefficient formulation. The formulation is general and applies to all panel concepts. Included with the formulation is the ability to provide membrane-bending coupling of unsymmetric sections and calculation of all thermal expansion and bending responses from in-plane and through-the-thickness temperature gradients. Thermal residual strains for both the laminates and plies are included. The general formulation is defined and then applied to a hat-shaped, corrugated stiffened panel. Additional formulations are presented where required to include all of the hat's unique characteristics. Each formulation is validated independently with 3-D FEA.

Collier, Craig S.↗

Heat Transfer Through Turbulent Friction Layers

The "general Prandtl number" Pr(exp 1) - A(sub q)/A Pr, aside from the Reynolds number determines the ratio of turbulent to molecular heat transfer, and the temperature distribution in turbulent friction layers. A(sub q) = exchange coefficient for heat; A = exchange coefficient for momentum transfer. A formula is derived from the equation defining the general Prandtl number which describes the temperature as a function of the velocity. For fully developed thermal boundary layers all questions relating to heat transfer to and from incompressible fluids can be treated in a simple manner if the ratio of the turbulent shear stress to the total stress T(sub t)/T in the layers near the wall is known, and if the A(sub q)/A can be regarded as independent of the distance from the wall. The velocity distribution across a flat smooth channel and deep into the laminar sublayer was measured for isothermal flow to establish the shear stress ratio T(sub t)/T and to extend the universal wall friction law. The values of T(sub t)/T which resulted from these measurements can be approximately represented by a linear function of the velocity in the laminar-turbulent transition zone. The effect of the temperature relationship of the material values on the flow near the wall is briefly analyzed. It was found that the velocity at the laminar boundary (in contrast to the thickness of the laminar layer) is approximately independent of the temperature distribution. The temperature gradient at the wall and the distribution of temperature and heat flow in the turbulent friction layers were calculated on the basis of the data under two equations. The derived formulas and the figures reveal the effects of the Prandtl number, the Reynolds number, the exchange quantities and the temperature relationship of the material values.

Reichardt, H.↗

Formation of thin sulfide rinds on the CM parent body

Many of the textures that are observed in CM chondrites have been alternately assigned nebular, parent-body, or combined nebular-parent body origins. Since it is very difficult to substantiate the production of complex textures in the nebula, an alternate approach to this problem is to rigorously determine which of the observable textures could have been produced by reasonable aqueous alteration processes on the CM parent body. Potential parent body reactions involving S deserve special attention because S-bearing phase define many important CM textures, such as rims. We have examined the possibility that the thin (about 5 microns) rinds of sulfides observed around some partially dissolved olivines within the chondrules and matrixes of CM chondrites were formed by the preferential precipitation of sulfides at or near dissolving olivine boundaries during parent-body alteration. Our model defines two infinite and parallel planes of olivine that are separated by pure water. Average separation distances between olivine grains in CM chondrites at the time of accretion (about 100-200 microns) were estimated by assuming a closed system fluid/rock ratio of 45% and varying the bimodal grain-size distribution. We restrict our calculations to the case of an isochemical system with sufficient bisulfide in solution to account for precipitation of pyrrhotite at STP. Our model examines the possibility that dissolving olivines with compositions between Fo(sub 0.9) and Fo(sub 0.4) can produce a strong gradient of Fe(2+) at pHs from 7 to 12 such that the precipitation of pyrrhotite will be initiated at the olivine-fluid boundary. Since CM phase equilibria is consistent with highly reducing conditions, Fe released by olivines would largely remain in solution as Fe(2+) until the solubility product of a Fe(2+) bearing phase was exceeded. Our calculations indicate that all examined combinations of olivine composition and pH yield a strong Fe(2+) gradient at the time the pyrrhotite solubility is exceeded near the olivine-fluid boundary. This favors the initiation of sulfide precipitation around dissolving olivines. However, sulfide rinds are not observed around all partially dissolved olivine grains in CM chondrites, which suggests that the availability of aqueous sulfide species limits the production of the thin sulfide rinds.

Browning, L. B.↗

Influence of plasma pedestal profiles on access to ELM-free regimes in ITER

The influence of current density and pressure gradient profiles in the pedestal on the access to the regimes free from edge localized modes (ELMs) like quiescent H-mode in ITER is investigated. Using the simulator of MHD modes localized near plasma boundary based on the KINX code, calculations of the ELM stability were performed for the ITER plasma in scenarios 2 and 4 under variations of density and temperature profiles with the self-consistent bootstrap current in the pedestal. Low pressure gradient values at the separatrix, the same position of the density and temperature pedestals and high poloidal beta values facilitate reaching high current density in the pedestal and a potential transition into the regime with saturated large scale kink modes. New version of the localized MHD mode simulator allows one to compute the growth rates of ideal peeling-ballooning modes with different toroidal mode numbers and to determine the stability region taking into account diamagnetic stabilization. The edge stability diagrams computations and sensitivity studies of the stability limits to the value of diamagnetic frequency show that diamagnetic stabilization of the modes with high toroidal mode numbers can help to access the quiescent H-mode even with high plasma density but only with low pressure gradient values at the separatrix. The limiting pressure at the top of the pedestal increases for higher plasma density. With flat density profile the access to the quiescent H-mode is closed even with diamagnetic stabilization taken into account, while toroidal mode numbers of the most unstable peeling-ballooning mode decrease from n = 10−40 to n = 3−20.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Saturated ideal kink/peeling formations described as three-dimensional magnetohydrodynamic tokamak equilibrium states

Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schlüter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The Derivation of the Gradient of the Acoustic Pressure on a Moving Surface for Application to the Fast Scattering Code (FSC)

In this paper we develop an analytic expression for calculation of the the acoustic pressure from a rotating blade on a moving surface for application to the Fast Scattering Code (FSC). The analytic result is intended to be used in the helicopter noise prediction code PSU-WOPWOP. One of the goals of the derivation is obtaining a result that will not use any more information than are needed for the prediction of the thickness and loading noise. The result derived here achieves this goal and its incorporation in PSU-WOPWOP is straight forward and attainable.

Farassat, F.↗

Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098

Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.

J S Gorce↗

The temperature gradient between 100 and 120 km

Oxygen density profiles inferred from Ogo 6 green nightglow emission vary too sharply between 100 and 120 km to be consistent with temperature gradients in standard model atmospheres, and the eddy diffusion coefficient K determined from these observations reaches its maximum below 115 km. For three atomic oxygen profiles obtained at geographic latitudes of -27.69, +48.89, and +59.10 the temperature profiles required to create a downward flux that varies with altitude as the integrated photolytic production rate above that altitude are calculated, assuming K to be invariant with altitude and latitude. The oxygen distribution can be reconciled with a constant eddy coefficient above 100 km if the temperature gradient reaches a value between 10 and 20 deg K/km for low values of the eddy coefficient (about 500,000 sq cm/sec) or between 30 and 50 deg K/km for a higher eddy coefficient (about 1.6 million sq cm/sec). The maximum gradient for the Jacchia (1971) model is about 10 deg K/km. These temperature profiles predict Ar/N ratios consistent with those measured by sounding rockets. The low K profiles are large enough to remove a large part of the solar energy deposited below 120 km by thermal conduction.

Donahue, T. M.↗

Uncovering the linear boron environment in Na 3 BP 2 through solid-state 11 B NMR spectroscopy

Boron-based compounds exhibit a wide range of structural diversity, with potential applications spanning organic and inorganic chemistry. Herein, we focus on the characterization of the linear boron-phosphorus unit P═B═P in Na 3 BP 2 using solid-state nuclear magnetic resonance (ssNMR) spectroscopy and density functional theory (DFT) calculations. High-resolution 11 B ssNMR spectra were recorded at two fields, and key parameters such as chemical shift anisotropy (CSA), quadrupolar coupling constants (C Q ), and electric field gradient (EFG) tensors were extracted. The 11 B NMR results revealed a distinct chemical environment for the two-coordinate boron atom, with a CSA span (Ω) of 280 ppm and a C Q of 3.0 MHz. These values were further validated through periodic plane-wave DFT calculations, which showed good agreement with experimental results. The obtained spectral parameters are compared to other linear boron units, such as the BO 2 motif, providing a broader context for understanding boron coordination in inorganic compounds. This work expands the body of NMR knowledge on boron-containing materials, particularly for linear boron motifs. The findings contribute to the growing field of boron chemistry and its potential applications in advanced materials.

Porter, Andrew P. [Ames Laboratory (AMES), Ames, I↗