SEARCH · Engineering Papers

Results for “Solutions”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20

All sources NASA NTRS DOE OSTI

NASA NTRS1997

Reentry-F Flowfield Solutions at 80,000 ft.

Three equilibrium-air numerical solutions are presented for the Reentry-F flight-test vehicle at Mach 20, 80,000 Ft. conditions, including turbulent flow predictions. The three solutions are from a thin-layer Navier-Stokes code, coupled thin-layer and parabolized Navier-Stokes codes, and an approximate viscous shock-layer code. Boundary-layer and shock-layer profiles are presented and compared between the three solutions, revealing close agreement between the three solution methods. Notable exceptions to the close agreement, with 7-10 percent discrepancies, occur in the density profiles at the boundary-layer edge, in the boundary-layer velocity profiles, and in the shock-layer profiles in regions influenced by the nose bluntness.

Wood, William A.↗

NASA NTRS1997

Some Solutions for the Large Deflections of Uniformly Loaded Circular Membranes

Inconsistent citations in the literature and questions about convergence prompt reexamination of Hencky's classic solution for the large deflections of a clamped, circular isotropic membrane under uniform pressure. This classic solution is observed actually to be for uniform lateral loading because the radial component of the pressure acting on the deformed membrane is neglected. An algebraic error in Hencky's solution is corrected, additional terms are retained in the power series to assess convergence, and results are obtained for two additional values of Poisson's ratio. To evaluate the importance of the neglected radial component of the applied pressure, the problem is reformulated with this component included and is solved, with escalating algebraic complexity, by a similar power-series approach. The two solutions agree quite closely for lightly loaded membranes and diverge slowly as the load intensifies. Differences in maximum stresses and deflections are substantial only when stresses are very high. The more nearly spherical deflection shape of the membrane under true pressure loading suggests that a near-parabolic membrane reflector designed on the basis of the more convenient Hencky theory would not perform as well as expected. In addition, both theories are found to yield closed-form, nonuniform membrane-thickness distributions that produce parabolic middle-surface deflections under loading. Both distributions require that the circular boundary expand radially in amounts that depend on material and loading parameters.

Fichter, W. B.↗

NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗

NASA NTRS1996

High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method

The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.

Wang, Xiao-Yen↗

NASA NTRS1998

Method of Forming a Composite Coating with Particle Materials that are Readily Dispersed in a Sprayable Polyimide Solution

A method for creating a composite form of coating from a sprayable solution of soluble polyimides and particle materials that are uniformly dispersed within the solution is described. The coating is formed by adding a soluble polyimide to a solvent, then stirring particle materials into the solution. The composite solution is sprayed onto a substrate and heated in an oven for a period of time in order to partially remove the solvent. The process may be repeated until the desired thickness or characteristic of the coating is obtained. The polyimide is then heated to at least 495 F, so that it is no longer soluble.

Tran, Sang Q.↗

NASA NTRS1959

Numerical Solution of the Flow of a Perfect Gas Over A Circular Cylinder at Infinite Mach Number

A solution for the two-dimensional flow of an inviscid perfect gas over a circular cylinder at infinite Mach number is obtained by numerical methods of analysis. Nonisentropic conditions of curved shock waves and vorticity are included in the solution. The analysis is divided into two distinct regions, the subsonic region which is analyzed by the relaxation method of Southwell and the supersonic region which was treated by the method of characteristics. Both these methods of analysis are inapplicable on the sonic line which is therefore considered separately. The shapes of the sonic line and the shock wave are obtained by iteration techniques. The striking result of the solution is the strong curvature of the sonic line and of the other lines of constant Mach number. Because of this the influence of the supersonic flow on the sonic line is negligible. On comparison with Newtonian flow methods, it is found that the approximate methods show a larger variation of surface pressure than is given by the present solution.

Hamaker, Frank M.↗

NASA NTRS1959

On Fully Developed Channel Flows: Some Solutions and Limitations, and Effects of Compressibility, Variable Properties, and Body Forces

An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flow has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force (e.g., gravity), an exact fully developed gas flow results. For a liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a Couette flow. In the liquid case two solutions (not a new result) can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations.In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection (due to, say, a wall temperature gradient) and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case (or quasi-incompressible case for free-convection flows) considered by many authors. Finally there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only a such form that independent variables are separable. For the case where the streamwise velocity varies inversely as the square root distance along the channel a solution is given.

Maslen, Stephen H.↗

NASA NTRS1998

Studies of Protein Solution Properties Using Osmotic Pressure Measurements

Examination of the protein crystallization process involves investigation of the liquid and solid state and a protein's properties in these states. Liquid state studies such as protein self association in solution by light scattering methods or other methods have been used to examine a protein Is properties and therefore its crystallization process and conditions. Likewise can osmotic pressure data be used to examine protein properties and various published osmotic pressure studies were examined by us to correlate osmotic pressure to protein solution properties. The solution behavior of serum albumin, alpha - chymotrypsin, beta - lactoglobulin and ovalbumin was examined over a range of temperatures, pH values and different salt types and concentrations. Using virial expansion and a local composition model the non ideal solution behavior in form of the activity coefficients (thermodynamic) was described for the systems. This protein activity coefficient data was related to a protein's solubility behavior and this process and the results will be presented.

Agena, S.↗

NASA NTRS1996

Lack of Evidence for Prenucleation Aggregate Formation in Lysozyme Crystal Growth Solutions

There have been numerous claims of large concentrations of prenucleation aggregates in supersaturated as well as undersaturated lysozyme solutions at high salt concentrations. The presence of these aggregates was derived from measurements of the light or neutron scattering intensity, ultracentrifugation and dialysis behavior, as well as over-simplified crystal growth kinetics considerations. In all these interpretations it has been assumed that lysozyme solutions are either ideal or that protein interactions are independent of salt concentration. Contrary to these presumptions, our static and dynamic light scattering experiments provide evidence that lysozyme forms highly non-ideal, strongly interacting solutions. At low salt concentrations, the scattering intensities fall well below the values expected for an ideal, monomeric solution at the same protein concentration, while diffusivities increase with increasing protein concentration. Upon increase in salt concentration, these trends are eventually reversed. This enhancement in scattering intensity and decrease in diffusivity was widely interpreted as sign of aggregate formation. Yet, a quantitative interpretation of the scattering behavior over the whole salt concentration range can only be given in terms of a transition from net repulsion to net attraction between lysozyme monomers. Increased salt screening of the electrostatic repulsion among the protein macro-ions, together with attractive protein interactions, such as van der Waals, hydrophobic and hydration forces, provide an unambiguous mechanism for the observed transition and a more physical interpretation of the various observations.

Muschol, Martin↗

NASA NTRS1998

Tetragonal Chicken Egg White Lysozyme Solubility in Sodium Chloride Solutions

The solubility of chicken egg white lysozyme, crystallized in the tetragonal form was measured in sodium chloride solutions from 1.6 to 30.7 C, using a miniature column solubility apparatus. Sodium chloride solution concentrations ranged from 1 to 7% (w/v). The solutions were buffered with 0.1 M sodium acetate buffer with the solubility being measured at pH values in 0.2 pH unit increments in the range pH 4.0 to 5.4, with data also included at pH 4.5. Lysozyme solubility was found to increase with increases in temperature and decreasing salt concentration. Solution pH has a varied and unpredictable effect on solubility.

Forsythe, Elizabeth L.↗

NASA NTRS1998

The Effect of Temperature and Solution pH on Tetragonal Lysozyme Nucleation Kinetics

Part of the challenge of macromolecular crystal growth for structure determination is obtaining an appropriate number of crystals with a crystal volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over one week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions, Duplicate experiments indicate the reproducibility of the technique, Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable however, was pH, where crystal numbers changed by two orders of magnitude over the pH range 4.0 to 5.2. Crystal size varied also with solution conditions, with the largest crystals being obtained at pH 5.2. Having optimized the crystallization conditions, a batch of crystals were prepared under exactly the same conditions and fifty of these crystals were analyzed by x-ray techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗

NASA NTRS1999

The Effect of Temperature and Solution pH on the Nucleation of Tetragonal Lysozyme Crystals

Part of the challenge of macromolecular crystal growth for structure determination is obtaining crystals with a volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature, and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over 1 week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable, however, was pH; crystal numbers changed by two orders of magnitude over the pH range 4.0-5.2. Crystal size also varied with solution conditions, with the largest crystals obtained at pH 5.2. Having optimized the crystallization conditions, we prepared a batch of crystals under the same initial conditions, and 50 of these crystals were analyzed by x-ray diffraction techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗

NASA NTRS2000

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

For scattering calculations involving nonspherical particles such as ice crystals, we show that the transverse wave condition is not applicable to the refracted electromagnetic wave in the context of geometric optics when absorption is involved. Either the TM wave condition (i.e., where the magnetic field of the refracted wave is transverse with respect to the wave direction) or the TE wave condition (i.e., where the electric field is transverse with respect to the propagating direction of the wave) may be assumed for the refracted wave in an absorbing medium to locally satisfy the electromagnetic boundary condition in the ray tracing calculation. The wave mode assumed for the refracted wave affects both the reflection and refraction coefficients. As a result, a nonunique solution for these coefficients is derived from the electromagnetic boundary condition. In this study we have identified the appropriate solution for the Fresnel reflection/refraction coefficients in light scattering calculation based on the ray tracing technique. We present the 3 x 2 refraction or transmission matrix that completely accounts for the inhomogeneity of the refracted wave in an absorbing medium. Using the Fresnel coefficients for an absorbing medium, we derive an asymptotic solution in an analytical format for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations. The asymptotic theory can produce reasonable accuracy in the phase function calculations in the infrared window region (wavelengths near 10 micron) if the particle size (in diameter) is on the order of 40 micron or larger. However, since strong absorption is assumed in the computation of the single-scattering albedo in the asymptotic theory, the single scattering albedo does not change with variation of the particle size. As a result, the asymptotic theory can lead to substantial errors in the computation of single-scattering albedo for small and moderate particle sizes. However, from comparison of the asymptotic results with the FDTD solution, it is expected that a convergence between the FDTD results and the asymptotic theory results can be reached when the particle size approaches 200 micron. We show that the phase function at side-scattering and backscattering angles is insensitive to particle shape if the random orientation condition is assumed. However, if preferred orientations are assumed for particles, the phase function has a strong dependence on scattering azimuthal angle. The single-scattering albedo also shows very strong dependence on the inclination angle of incident radiation with respect to the rotating axis for the preferred particle orientations.

Yang, Ping↗

NASA NTRS2000

The Effect of Solution Thermal History on Chicken Egg White Lysozyme Nucleation

Proteins are highly flexible molecules and often exhibit defined conformational changes in response to changes in the ambient temperature. Chicken egg white lysozyme has been previously shown to undergo an apparent structural change when warmed above the tetragonal/orthorhombic phase transition temperature. This is reflected by a change in the habit of the tetragonal and orthorhombic crystals so formed. In this study we show that possible conformational changes induced by heating are stable and apparently non- reversible by simple cooling. Exposure of protein solutions to temperatures above the phase change transition temperature, before combining with precipitant solution to begin crystallization, reduces final crystal numbers. Protein that is briefly warmed to 37 C, then cooled shows no sign of reversal to the unheated nucleation behavior even after storage for 4 weeks at 4 C. The change in nucleation behavior of tetragonal lysozyme crystals, attributed to a structural shift, occurs faster the greater the exposure to temperature above the equi-solubility point for the two phases. Heating for 2 h at 48 C reduces crystal numbers by 20 fold in comparison to the same solution heated for the same time at 30 C. Thermal treatment of solutions is therefore a possible tool to reduce crystal numbers and increase crystal size. The effects of a protein's previous thermal history are now shown to be a potentially critical factor in subsequent macromolecule crystal nucleation and growth studies.

Burke, Michael W.↗

NASA NTRS2000

Lessons Learned During Solutions of Multidisciplinary Design Optimization Problems

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. During solution of the multidisciplinary problems several issues were encountered. This paper lists four issues and discusses the strategies adapted for their resolution: (1) The optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. (2) Optimum solutions obtained were infeasible for aircraft and air-breathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. (3) Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. (4) The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through six problems: (1) design of an engine component, (2) synthesis of a subsonic aircraft, (3) operation optimization of a supersonic engine, (4) design of a wave-rotor-topping device, (5) profile optimization of a cantilever beam, and (6) design of a cvlindrical shell. The combined effort of designers and researchers can bring the optimization method from academia to industry.

Patnaik, Suna N.↗

NASA NTRS2001

Methanol Uptake by Low Temperature Aqueous Sulfuric Acid Solutions

The global methanol budget is currently unbalanced, with source terms significantly larger than the sinks terms. To evaluate possible losses of gaseous methanol to sulfate aerosols, the solubility and reactivity of methanol in aqueous sulfuric acid solutions representative of upper tropospheric and lower stratospheric aerosols is under investigation. Methanol will partition into sulfate aerosols according to its Henry's law solubility. Using standard uptake techniques in a Knudsen cell reactor, we have measured the effective Henry's law coefficient, H*, for cold (196 - 220 K) solutions ranging between 45 and 70 wt % H2SO4. We have found that methanol solubility ranges from approx. 10(exp 5) - 10(exp 7) M/atm for UT/LS conditions. Solubility increases with decreasing temperature and with increasing sulfuric acid content. Although methanol is slightly more soluble than are acetone and formaldehyde, current data indicate that uptake by clean aqueous sulfuric acid particles will not be a significant sink for methanol in the UT/LS. These solubility measurements include uptake due to physical solvation and any rapid equilibria which are established in solution. Reaction between primary alcohols and sulfuric acid does occur, leading to the production of alkyl sulfates. Literature values for the rate of this reaction suggest that formation of CH3OSO3H is not significant over our experimental time scale for solutions below 80 wt % H2SO4. To confirm this directly, results obtained using a complementary equilibrium measurement technique will also be presented.

Iraci, L. T.↗

NASA NTRS2001

The Effect of Solution Thermal History on Chicken Egg White Lysozyme Nucleation

Proteins are highly flexible molecules and often exhibit defined conformational changes in response to changes in the ambient temperature. Chicken egg white lysozyme has been previously shown to undergo an apparent structural change when warmed above the tetragonal/orthorhombic phase transition temperature. This is reflected by a change in the habit of the tetragonal and orthorhombic crystals so formed. In this study, we show that possible conformational changes induced by heating are stable and apparently non-reversible by simple cooling. Exposure of protein solutions to temperatures above the phase change transition temperature, before combining with precipitant solution to begin crystallization, reduces final crystal numbers. Protein that is briefly warmed to 37 C, then cooled shows no sign of reversal to the unheated nucleation behavior even after storage for four weeks at 4 C. The change in nucleation behavior of tetragonal lysozyme crystals, attributed to a structural shift, occurs faster the greater the exposure to temperature above the equi-solubility point for the two phases. Heating for 2 hours at 48 C reduces crystal numbers by 20 fold in comparison to the same solution heated for the same time at 30 C. Thermal treatment of solutions is therefore a possible tool to reduce crystal numbers and increase crystal size. The effects of a protein's previous thermal history are now shown to be a potentially critical factor in subsequent macromolecule crystal nucleation and growth studies.

Burke, Michael W.↗

NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗