Search NASA⌕ Search

SEARCH · Search NASA

Results for “Closed form solution”

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 829 records · Page 46

Apparatus for diffusion controlled dialysis under microgravity conditions

Apparatus for implementing crystal growth by allowing mixing of solutions under microgravity conditions includes a housing within which a number of pairs of chambers are formed. The chambers of each pair are aligned and a rotary valve is positioned between the chambers of each pair. When the valve is in a first position one chamber of each pair may communicate with the other chamber. A separate valve is provided for each pair of chambers so that each pair of chambers may be activated independently of the others and sequentially at selected intervals. Protein solution may be located within a small cavity in a cap which closes one of the chambers of a pair, and the cavity in the cap is closed by a dialysis membrane. The length of certain pairs of chambers may differ from the length of other pairs of chambers to optimize conditions for various dialysis productions, and wicking material may be incorporated into selected chambers for controlling the critical approach to supersaturation.

Carter, Daniel C.↗

A New Spin for Understanding the Peculiar Horizontal Branch Morphology of the Galactic Globular Clusters NGC 6388 and NGC 6441

In this paper we present multiband optical and UV Hubble Space Telescope photometry of the two Galactic globular clusters NGC 6388 and NGC 6441 Aims. We investigate the properties of their anomalous horizontal branches (HB) in different photometric planes in order to shed light on the nature of the physical mechanism(s) responsible for the existence of an extended HB blue tail, and of a slope in the HB, visible in all the color-magnitude diagrams. Methods. New photometric data have been collected and carefully reduced. Empirical data have been compared with updated stellar models of low-mass, metal-rich, He-burning structures, transformed to the observational plane with appropriate atmosphere models. Results. We have obtained the first UV color-magnitude diagrams for NGC 6388 and NGC 6441. These diagrams confirm previous results, obtained in optical bands, about the presence of a sizeable stellar population of extremely hot Horizontal Branch stars. At least in NGC 6388, we find a clear indication that at the hot end of the horizontal branch the distribution of stars forms a hook-like feature, closely resembling those observed in NGC 2808 and w Centauri. We briefly review the theoretical scenarios which have been suggested for interpreting this observational feature. We investigate also on the tilt in the horizontal branch morphology, and provide further evidence that supports early suggestions according to which this feature cannot be interpreted as an effect of differential reddening or radiative levitation, though these effects contribute to create the anomaly. We demonstrate that a possible solution of the puzzle is to assume that a small fraction (approx. 13% in NGC 6388 and approx. 8% NGC 6441) of the stellar population in the two clusters is strongly helium enriched (Y approx. 0.40 in NGC6388 and Y approx. 0.35 in NGC 6441). This solution necessarily implies the presence of a double generation of stars in the two clusters.

Busso, G.↗

A form-factor method for determining the structure of distorted stars

The equilibrium equations of a uniformly rotating and tidally distorted star are reduced to the same form as for a spherical star except for the inclusion of two form factors. One factor, expressing the buoyancy effects of centrifugal force, is determined directly from the integrated structure variables. The other factor, expressing the deviation from spherical shape, is shown to be relatively insensitive to errors in the assumed shape, so that accurate solutions are obtained in spite of the use of an a priori shape. The method is employed by adding computations for the factors to an existing spherical model program. Upper Main Sequence models determined by this method compare closely with results from the double approximation method even for critical rotation and tidal distortion.

Wolfe, R. H., Jr.↗

A High Frequency Model of Cascade Noise

Closed form asymptotic expressions for computing high frequency noise generated by an annular cascade in an infinite duct containing a uniform flow are presented. There are two new elements in this work. First, the annular duct mode representation does not rely on the often-used Bessel function expansion resulting in simpler expressions for both the radial eigenvalues and eigenfunctions of the duct. In particular, the new representation provides an explicit approximate formula for the radial eigenvalues obviating the need for solutions of the transcendental annular duct eigenvalue equation. Also, the radial eigenfunctions are represented in terms of exponentials eliminating the numerical problems associated with generating the Bessel functions on a computer. The second new element is the construction of an unsteady response model for an annular cascade. The new construction satisfies the boundary conditions on both the cascade and duct walls simultaneously adding a new level of realism to the noise calculations. Preliminary results which demonstrate the effectiveness of the new elements are presented. A discussion of the utility of the asymptotic formulas for calculating cascade discrete tone as well as broadband noise is also included.

Envia, Edmane↗

Influence of Turbulence on the Restraint of Liquid Jets by Surface Tension in Microgravity Investigated

Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, surface tension forces must contain jets. To model this phenomenon, a numerical method that tracks the fluid motion and the surface tension forces is required. Jacqmin has developed a phase model that converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly away. Previous attempts at this formulation were criticized for smearing the interface. This can be overcome by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function. The solution of this equation can be rewritten as two coupled Poisson equations that also include the velocity. After the code was implemented in axisymmetric form and verified by several test cases at the NASA Glenn Research Center, the drop tower runs of Aydelott were modeled. Work last year with a laminar model was found to overpredict Aydelott's results, except at the lowest Reynolds number conditions of 400. This year, a simple turbulence model was implemented by adding a turbulent viscosity based on the mixing-length hypothesis and empirical measurements of previous works. Predictions made after this change was implemented have been much closer to experimentally observed flow patterns and geyser heights. Two model runs is shown. The first, without any turbulence correction, breaks through the free surface and strikes the far end of the tank. In the second, the turbulence spreads the jet momentum over more of the free surface, enabling the surface tension forces to turn the jet back into the bulk liquid. The model geyser height with the second model is 1.1 cm. This is quite close to the 1.5-cm geyser height measured by Aydelott.

Chato, David J.↗

The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields

Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas.

Lerche, I.↗

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I. P.↗

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I-P.↗

Inertial currents in isotropic plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasmas, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MHD plasma. Solutions are developed by taking the MHD limit ot two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗

Inertial Currents in Isotropic Plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasma, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MED plasma. Solutions are developed by taking the MHD limit of two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗

Fabrication of strain-isolated ceramic coated combustor components

The use of strain-isolated ceramic coated material to produce an AGT1500 combustor scroll-shaped transition duct which requires no air for film cooling is investigated. The scroll receives the exhaust of the can-style combustor liner and turns it into the annular inlet of the high pressure gas producer turbine nozzle. Strain-isolation of plasma sprayed thermal barrier coating is achieved by placing a compliant pad between the structural base metal and the ceramic coating. The compliant pad is brazed to the metal structure. In order to achieve a good braze bond, the strain-isolating compliant pad and base metal must be closely matched in shape and tightly fixtured for joining. The complex geometry of the AGT1500 scroll makes it impractical to attack pads to the supporting structure in its finished shape. Instead the pads are brazed to flat stock and post-formed into scroll sections. While test samples were successfully post-formed, plasma sprayed, and subjected to cyclic heating, the forming of full scale parts by normal methods resulted in tearing of the Hastelloy-X base metal because of embrittlement by the braze material. Several solutions were explored which finally resulted in the successful forming of full scale scroll parts.

Rutter, S.↗

Theoretical and experimental characterization of coplanar waveguide discontinuities for filter applications

A full-wave analysis of shielded coplanar waveguide two-port discontinuities based on the solution of an appropriate surface integral equation in the space domain is presented. Frequency-dependent scattering parameters for open-end and short-end coplanar waveguide (CPW) stubs are computed using this method. The numerically derived results are compared with measurements performed in the frequency range 5-25 GHz and show very good agreement. From the scattering parameters, lumped-element equivalent circuits have been derived to model the discontinuities. The inductors and capacitors of these models have been represented by closed-form equations, as functions of the stub length, to compute the circuit element values for these discontinuities.

Dib, Nihad I.↗

Inertial currents in isotropic plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasma, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, magnetohyrodynamic (MHD) plasma. Solutions are developed by taking the MHD limit of two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗

Dataset for: Rooftop solar and energy storage programs can remediate energy-limiting behaviors of energy insecure households

Energy insecurity affects most low-income households in the United States. Energy insecurity, which is characterized by a household’s inability to afford their energy needs, often leads to risky choices, causing other forms of insecurity including food and health. Although there are government programs designed to provide relief to low-income households that face energy insecurity, eligibility for these programs is usually determined by household income, and those with incomes close to the threshold face uncertainty or may be left out. In many cases, these households turn to energy-limiting behaviors as a strategy to lower their electric utility bills. This paper explores the relationship between energy insecurity and energy-limiting behaviors to investigate alternative solutions that target the households that may fall out of available energy assistance programs. We explore the role of battery energy storage systems and rooftop solar photovoltaics in improving energy affordability. The results show that residential rooftop solar and behind-the-meter energy storage can offset two-thirds of the bill savings that households attain through energy-limiting behavior. Household renewable energy systems could complement existing energy assistance programs to provide long-term bill relief, enabling occupants to live in their homes with comfort and dignity. This dataset is intended to allow readers to reproduce and customize the analysis performed in this work to their benefit.

Kerby, Jessica [Pacific Northwest National Laborat↗

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.↗

Fluid Physics and Macromolecular Crystal Growth in Microgravity

The molecular structure of biological macromolecules is important in understanding how these molecules work and has direct application to rational drug design for new medicines and for the improvement and development of industrial enzymes. In order to obtain the molecular structure, large, well formed, single macromolecule crystals are required. The growth of macromolecule crystals is a difficult task and is often hampered on the ground by fluid flows that result from the interaction of gravity with the crystal growth process. One such effect is the bulk movement of the crystal through the fluid due to sedimentation. A second is buoyancy driven convection close to the crystal surface. On the ground the crystallization process itself induces both of these flows. Buoyancy driven convection results from density differences between the bulk solution and fluid close to the crystal surface which has been depleted of macromolecules due to crystal growth. Schlieren photograph of a growing lysozyme crystal illustrating a 'growth plume' resulting from buoyancy driven convection. Both sedimentation and buoyancy driven convection have a negative effect on crystal growth and microgravity is seen as a way to both greatly reduce sedimentation and provide greater stability for 'depletion zones' around growing crystals. Some current crystal growth hardware however such as those based on a vapor diffusion techniques, may also be introducing unwanted Marangoni convection which becomes more pronounced in microgravity. Negative effects of g-jitter on crystal growth have also been observed. To study the magnitude of fluid flows around growing crystals we have attached a number of different fluorescent probes to lysozyme molecules. At low concentrations, less than 40% of the total protein, the probes do not appear to effect the crystal growth process. By using these probes we expect to determine not only the effect of induced flows due to crystal growth hardware design but also hope to optimize crystallization hardware so that destructive flows are minimized both on the ground and in microgravity.

Pusey, M.↗

Goes-16 On-Station Custom Maneuver Generation with Focussuite

This paper discusses the process of the NOAA GOES Mission Operations Support Team (MOST) in mitigating the effects of inconsistently performing ArcJet Thrusters (AJTs) aboard the GOES-16 spacecraft in geostationary orbit. These AJTs are hot-gas thrusters which augment the gas flow using an electric arc to increase the exit velocity of the gases. Fuel flow problems have led to GOES-16 being unable to safely use its AJTs for maneuvers at times. This primarily affects North/South Station-Keeping (NSSK) maneuvers, which control inclination and use a majority of the station-keeping fuel budget. As a result, GOES-16 has had to occasionally resort to using non-AJT hot-gas thrusters. These thrusters are not placed as close to GOES-16's centerline, have lower thrust, and have lower specific impulse when compared to AJTs. In addition, MOST’s ground systems do not officially support using these non-AJT thrusters for NSSK maneuvers. MOST had to quickly develop workaround solutions using the FocusSuite Autofocus programming environment to compute the maneuvers. This paper outlines the mixture of commercial off-the-shelf (COTS) and MOST-developed products which have allowed GOES-16 to continue station-keeping even with inconsistently-per-forming AJTs, showing that script-based automation systems like Autofocus can simplify complex solutions to a few scripted user inputs.

Henry Heim↗

Coordination Chemistry and Photoluminescence of Sm(II) Dibenzo-24-crown-8 Complexes

Three Sm(II) dibenzo-24-crown-8 (db24c8) complexes were synthesized in anhydrous, air-free conditions via the reaction of SmI 2 with db24c8 and tetrabutylammonium tetraphenylborate ([TBA][BPh 4 ]; where needed) in acetonitrile (CH 3 CN), dimethoxyethane (DME), and tetrahydrofuran (THF) to yield [Sm(db24c8)(CH 3 CN) 2 ][BPh 4 ][I]·CH 3 CN, [Sm(db24c8)(DME)]I 2 , and [Sm(db24c8)(THF) 2 ]I 2 , respectively. In each case, a 10-coordinate, staggered dodecahedral (2:6:2) environment is formed around the Sm 2+ center that is completed by either two solvent molecules (CH 3 CN or THF) or one bidentate solvent molecule (DME). Inner-sphere solvent molecules can be excluded by reacting SmI 2 with db24c8 in 1:3 THF:toluene to yield Sm(db24c8)I 2 . Here, this molecule features a distorted, eight-coordinate, hexagonal pyramidal Sm 2+ metal center, where the coordinated db24c8 molecule shows a torsion angle unexpectedly close to the 180° antiperiplanar arrangement and two uncoordinated db24c8 oxygen atoms. Solution UV–vis–NIR measurements demonstrate that Sm 2+ is a good size match for the cavity of various db24c8 conformations and that Eu 2+ and Yb 2+ exhibit competition between acetonitrile solvation and the Eu 2+ and Yb 2+ /db24c8 complexes in solution. During excitation by 546 nm light, both [Sm(db24c8)(DME)]I 2 and [Sm(db24c8)(THF) 2 ]I 2 exhibit mixed 5d → 4f and 4f → 4f emission at 20 °C and exclusively 4f → 4f at −180 °C, whereas Sm(db24c8)I 2 only shows 5d → 4f emission regardless of temperature. Photoluminescence from [Sm(db24c8)(CH 3 CN) 2 ][BPh 4 ][I]·CH 3 CN is quenched.

Cations↗