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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Excitation of instability waves in a two-dimensional shear layer by sound

The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for abitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach number are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analyzed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80 deg to the flow direction is most effective in exciting instability waves.

Tam, C. K. W.↗
NASA NTRS1980

A simple approximate result for the maximum growth rate of baroclinic instabilities

The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem has precluded extracting simple results of generality. It is shown that there exists very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. The result extends to substantially more general profiles than those in the Charney problem.

Lindzen, R. S.↗
NASA NTRS1983

Simplified Modeling of Tetrahedral Trusses

Tetrahedral-lattice structure exhibits great complexity in mathematical analysis, and complexity quickly increases with number of elements. Solutions for static and dynamic behavior of structure obtained with model consisting of analogous structure with fewer repeating elements. Advantage of continuum models is analytic solutions can be obtained, either in closed form or in relatively-tractable Taylor series.

Leondis, A.↗
NASA NTRS1990

Analysis of the thermal performance of heat pipe radiators

A comprehensive mathematical model and computational methodology are presented to obtain numerical solutions for the transient behavior of a heat pipe radiator in a space environment. The modeling is focused on a typical radiator panel having a long heat pipe at the center and two extended surfaces attached to opposing sides of the heat pipe shell in the condenser section. In the set of governing equations developed for the model, each region of the heat pipe - shell, liquid, and vapor - is thermally lumped to the extent possible, while the fin is lumped only in the direction normal to its surface. Convection is considered to be the only significant heat transfer mode in the vapor, and the evaporation and condensation velocity at the liquid-vapor interface is calculated from kinetic theory. A finite-difference numerical technique is used to predict the transient behavior of the entire radiator in response to changing loads.

Boo, J. H.↗
NASA NTRS1995

Existence of frozen-in coordinate systems

The 'frozen-in' coordinate systems were first introduced in the works on 'reconnection' and 'magnetic barrier' theories (see review by M.l.Pudovkin and V.S.Semenov, Space Sci. Rev. 41,1 1985). The idea was to utilize the mathematical apparatus developed for 'general relativity' theory to simplify obtaining solutions to the ideal MHD equations set. Magnetic field (B), plasma velocity (v), and their vector product were used as coordinate vectors. But there exist no stationary solutions of ideal MHD set that satisfies the required boundary conditions at infinity (A.D.Chertkov, Solar Wind Seven Conf.,Pergamon Press,1992,165) having non-zero vector product of v and B where v and B originate from the same sphere. The existence of a solution is the hidden mine of the mentioned theories. The solution is constructed in the coordinate system, which is unknown and indeterminate before obtaining this solution. A substitution of the final solution must be done directly into the initial MHD set in order to check the method. One can demonstrate that 'solutions' of Petschek's problem, obtained by 'frozen-in' coordinate systems, does not satisfy just the 'frozen-in' equation, i.e. induction equation. It stems from the fact that Petschek's 're-connection' model, treated as a boundary problem, is over determined. This problem was incorrectly formulated.

Chertkov, A. D.↗
NASA NTRS2004

Rotating Reverse Osmosis for Wastewater Reuse

Our previous work established the concept of a low-pressure rotating reverse osmosis membrane system. The rotation of the cylindrical RO filter produces shear and Taylor vortices in the annulus of the device that decrease the concentration polarization and fouling commonly seen with conventional RO filtration techniques. A mathematical model based on the film theory and the solution-diffusion model agrees well with the experimental results obtained using this first generation prototype. However, based on the model, the filtrate flux and contaminant rejection depend strongly on the transmembrane pressure. Therefore, the goal of our current work is to improve the flux of the device by increasing the transmembrane pressure by a factor of 3 to 4. In addition, the rejections for a wider variety of inorganic and organic compounds typically found in space mission wastewater are measured.

Lueptow, Richard M.↗
NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗
NASA NTRS1993

Shielding from space radiations

This Progress Report covering the period of December 1, 1992 to June 1, 1993 presents the development of an analytical solution to the heavy ion transport equation in terms of Green's function formalism. The mathematical development results are recasted into a highly efficient computer code for space applications. The efficiency of this algorithm is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The code may also be applied to accelerator boundary conditions to allow code validation in laboratory experiments. Results from the isotopic version of the code with 59 isotopes present for a single layer target material, for the case of an iron beam projectile at 600 MeV/nucleon in water is presented. A listing of the single layer isotopic version of the code is included.

Chang, C. Ken↗
NASA NTRS1991

Shielding from space radiations

Progress during the period of 1 Jun. - 1 Dec. 1991 is presented. An analytical solution to heavy ion transport equation in terms of Green's function formalism is developed. The mathematical development is recasted into efficient computer code for space applications. The efficiency of this algorithm is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The code is also applied to accelerator boundary conditions to allow code validation in laboratory experiments.

Chang, C. Ken↗
NASA NTRS1983

Mathematical modeling of damage in unidirectional composites

Extending the work of Goree and Gross (1979), solutions are given for a two-dimensional region of unidirectional fibers embedded in an elastic matrix whose initial flaw may take the form of a transverse notch, a rectangular cutout, or a circular hole. Subsequent flaw-induced damage is generated by remote stresses acting parallel to the fibers. For the case of such ductile matrix composites as boron/aluminum, present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Little difference is found for the three types of initial damage considered. In all cases, the presence of additional damage changes the nature of stress distribution through the unbroken fibers.

Goree, J. G.↗
NASA NTRS2017

New Mathematical Functions for Vacuum System Analysis

A new bivariate function has been found that provides solutions of integrals having the form u (sup minus eta) e (sup u) du which arise when developing predictions for the behavior of pressure within a rigid volume under high vacuum conditions in the presence of venting as well as sources characterized by power law transient decay over the range [0,1] for eta and for u greater than or equal to 0. A few properties of the new function are explored in this work. For instance the eta equals 1/2 case reproduces the Dawson function. In addition, a slight variation of the solution technique reproduces the exponential integral for eta equals 1. The technique used to generate these functions leads to an approach for solving a more general class of nonlinear ordinary differential equations, with the potential for identifying other new functions that solve other integrals.

Dawson Function↗
NASA NTRS1976

Solutions to divergence form equations using the method of partial implicitization

Partial implicitization is well suited for use on vector-processing computers since the method is an explicit unconditionally stable numerical technique. So far equations cast in nondivergence form have been used, though equations cast in the divergence form would have inherently greater accuracy. Since the method of partial implicitization is applicable only to relaxing problems to their steady state and is not applicable to true transient problems, a simple mathematical manipulation can be carried out which will produce the desired partial implicitization solution to divergence form equations.

Graves, R. A., Jr.↗
NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗
NASA NTRS1987

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Shankar, Vijaya↗
NASA NTRS1966

New computer system simplifies programming of mathematical equations

Automatic Mathematical Translator /AMSTRAN/ permits scientists or engineers to enter mathematical equations in their natural mathematical format and to obtain an immediate graphical display of the solution. This automatic-programming, on-line, multiterminal computer system allows experienced programmers to solve nonroutine problems.

Reinfelds, J.↗
NASA NTRS1972

On propagation of long waves in curved ducts.

A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.

Rostafinski, W.↗