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NASA NTRS1994

Improved solution accuracy for Landsat-4 (TDRSS-user) orbit determination

This paper presents the results of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft, Landsat-4, obtained using a Prototype Filter Smoother (PFS), with the accuracy of an established batch-least-squares system, the Goddard Trajectory Determination System (GTDS). The results of Landsat-4 orbit determination will provide useful experience for the Earth Observing System (EOS) series of satellites. The Landsat-4 ephemerides were estimated for the January 17-23, 1991, timeframe, during which intensive TDRSS tracking data for Landsat-4 were available. Independent assessments were made of the consistencies (overlap comparisons for the batch case and convariances for the sequential case) of solutions produced by the batch and sequential methods. The filtered and smoothed PFS orbit solutions were compared with the definitive GTDS orbit solutions for Landsat-4; the solution differences were generally less than 15 meters.

Oza, D. H.↗
NASA NTRS1994

Open solutions to distributed control in ground tracking stations

The advent of high speed local area networks has made it possible to interconnect small, powerful computers to function together as a single large computer. Today, distributed computer systems are the new paradigm for large scale computing systems. However, the communications provided by the local area network is only one part of the solution. The services and protocols used by the application programs to communicate across the network are as indispensable as the local area network. And the selection of services and protocols that do not match the system requirements will limit the capabilities, performance, and expansion of the system. Proprietary solutions are available but are usually limited to a select set of equipment. However, there are two solutions based on 'open' standards. The question that must be answered is 'which one is the best one for my job?' This paper examines a model for tracking stations and their requirements for interprocessor communications in the next century. The model and requirements are matched with the model and services provided by the five different software architectures and supporting protocol solutions. Several key services are examined in detail to determine which services and protocols most closely match the requirements for the tracking station environment. The study reveals that the protocols are tailored to the problem domains for which they were originally designed. Further, the study reveals that the process control model is the closest match to the tracking station model.

Heuser, William Randy↗
NASA NTRS1995

Validation of the SINDA/FLUINT code using several analytical solutions

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

Keller, John R.↗
NASA NTRS1995

Developmental problems and their solution for the Space Shuttle main engine alternate liquid oxygen high-pressure turbopump: Anomaly or failure investigation the key

The Space Shuttle main engine (SSME) alternate high-pressure liquid oxygen pump experienced synchronous vibration and ball bearing life problems that were program threatening. The success of the program hinged on the ability to solve these development problems. The design and solutions to these problems are engirded in the lessons learned and experiences from prior programs, technology programs, and the ability to properly conduct failure or anomaly investigations. The failure investigation determines the problem cause and is the basis for recommending design solutions. For a complex problem, a comprehensive solution requires that formal investigation procedures be used, including fault trees, resolution logic, and action items worked through a concurrent engineering-multidiscipline team. The normal tendency to use an intuitive, cut-and-try approach will usually prove to be costly, both in money and time and will reach a less than optimum, poorly understood answer. The SSME alternate high-pressure oxidizer turbopump development has had two complex problems critical to program success: (1) high synchronous vibrations and (2) excessive ball bearing wear. This paper will use these two problems as examples of this formal failure investigation approach. The results of the team's investigation provides insight into the complexity of the turbomachinery technical discipline interacting/sensitivities and the fine balance of competing investigations required to solve problems and guarantee program success. It is very important to the solution process that maximum use be made of the resources that both the contractor and Government can bring to the problem in a supporting and noncompeting way. There is no place for the not-invented-here attitude. The resources include, but are not limited to: (1) specially skilled professionals; (2) supporting technologies; (3) computational codes and capabilities; and (4) test and manufacturing facilities.

Ryan, R.↗
NASA NTRS1995

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

Hodge, Steve L.↗
NASA NTRS1994

Unique determination of solutions to the Burnett equations

Recent success in applying the Burnett equations to the one-dimensional shock-structure problem has raised the issue of whether the full Burnett equations can be used replace the Navier-Stokes equations for solving boundary-value problems in rarefied gasdynamics. As is familiar from the classical rarefied gasdynamics literature, the Burnett equations, if not solved as a successive approximation to the Navier-Stokes equations for a small Knudsen number, would require more boundary conditions than those in the Navier-Stokes system, owing to the presence of the higher-order derivatives. In this paper, this issue is examined with concrete solution examples for the steady Couette flows, addressing specifically whether solutions to the full Burnett equations can be uniquely determined without adding more boundary conditions than those in the Navier-Stokes system. The analysis, supported by detailed numerical solutions, confirms that additional boundary conditions are needed as long as the Knudsen number is not identically zero, lest the solution to the Burnett equations is not unique.

Lee, C. J.↗
NASA NTRS1995

Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

Goossens, Marcel↗
NASA NTRS1995

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

The global asymptotic nonlinear behavior of 1 1 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

Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity

The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.

Higuera, F. J.↗
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↗