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At least 1,675 records · Page 93
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗
NASA NTRS1976

Finite element solution of turbulent and reacting compressible three-dimensional flows

Results of detailed numerical evaluation of turbulent and reacting three-dimensional compressible flows are presented. These solutions were obtained using a finite element algorithm to solve the system of explicitly non-linear partial differential equations governing three-dimensional, confined unidirectional turbulent flow of a compressible, reacting fluid. Assessments are made of solution accuracy and convergence, including detailed comparisons to experimental data.

Baker, A. J.↗
NASA NTRS1977

Numerical solution of the compressible Navier-Stokes equations using density gradients as additional dependent variables

Numerical solution of two dimensional, time dependent, compressible viscous Navier-Stokes equations about arbitrary bodies was treated using density gradients as additional dependent variables. Thus, six dependent variables were computed with the SOR iteration method. Besides formulation for pressure gradient terms, a formulation for computing the body density was presented. To approximate the governing equations, an implicit finite difference method was employed. In computing the solution for the flow about a circular cylinder, a problem arose near the wall at both stagnation points. Thus, computations with various conditions were tried to examine the problem. Also, computations with and without formulations are compared. The flow variables were computed on 37 by 40 field first, then on an 81 by 40 field.

Kwon, J. H.↗
NASA NTRS1977

A solution to the surface intersection problem

An application-independent geometric model within a data base framework should support the use of Boolean operators which allow the user to construct a complex model by appropriately combining a series of simple models. The use of these operators leads to the concept of implicitly and explicitly defined surfaces. With an explicitly defined model, the surface area may be computed by simply summing the surface areas of the bounding surfaces. For an implicitly defined model, the surface area computation must deal with active and inactive regions. Because the surface intersection problem involves four unknowns and its solution is a space curve, the parametric coordinates of each surface must be determined as a function of the arc length. Various subproblems involved in the general intersection problem are discussed, and the mathematical basis for their solution is presented along with a program written in FORTRAN IV for implementation on the IBM 370 TSO system.

Timer, H. G.↗
NASA NTRS1977

Pressureless sintered beta prime-Si3N4 solid solution: Fabrication, microstructure, and strength

Si3N4, AlN, and Al2O3 were used as basic constituents in a study of the pressureless sintering of beta prime-Si3N4 solid solution as a function of temperature. Y2O3-SiO2 additions were used to promote liquid-phase sintering. The sintered specimens were characterized with respect to density, microstructure, strength, oxidation, and thermal shock resistance. Density greater than 98 percent of theoretical was achieved by pressureless sintering at 1750 C. The microstructure consisted essentially of fine-grained beta prime-Si3N4 solid solution as the major phase. Modulus of rupture strengths up to 483 MPa were achieved at moderate temperature (1000 C), but decreased to 228 MPa at 1380 C. This substantial strength loss was attributed to a glassy grain boundary phase formed during cooling from the sintering temperature. The best oxidation resistance was exhibited by a composition containing 3 mol % Y2O3-SiO2 additives. Water quench thermal shock resistance was equivalent to that of reaction sintered silicon nitride but lower than hot-pressed silicon nitride.

Dutta, S.↗
NASA NTRS1977

A perturbation solution for interlaminar stresses in bidirectional laminates

The paper considers a thin elastic bidirectional symmetric composite laminate subjected to a uniform axial strain. All interlaminar stresses are determined by a zeroth-order perturbation analysis of the governing equations. The method of solution considers the laminate to be composed of an interior region (removed from the free edge) and a boundary layer region. The interior region is analyzed by dropping terms related to powers of the thickness-to-width ratio in the dimensionless elasticity equations. The boundary layer region is studied by introducing a stretching transformation to the governing equations. A uniform solution is then formed by satisfying Prandtl's matching principle of perturbation theory. Results for a four-layer bidirectional graphite-epoxy laminate are compared with existing finite-difference results. It is shown that the perturbation analysis provides more insight into the stress distribution near the free edge.

Hsu, P. W.↗
NASA NTRS1977

Simple analytical solutions for spherically symmetric production and modulation of energetic solar particles

Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.

Gross, M. W.↗
NASA NTRS1978

A combined potential and viscous flow solution for V/STOL engine inlets

A potential flow routine and a viscous boundary layer routine have been combined into a single routine for estimating the flow in and around subsonic inlets. In this combined routine, the viscous flow solution about the inlet body is obtained by adding the viscous displacement thickness to the inlet geometry. Combination of the two flow solutions has resulted in cost savings, both in preparation time and in computer time. This routine is a useful tool in optimizing lip shapes for V/STOL inlets. The method of combining the routine, comparison with NASA test data, and utilization of the routine for V/STOL inlet design are presented.

Ybarra, A. H.↗
NASA NTRS1978

A finite element solution of transonic flow

The use of finite elements is explored in a field in which its use has previously not been deemed very feasible, that of transonic flow. The specific problem chosen is that of steady small-disturbance transonic flow. The nonlinear equations are formulated with an artificial viscosity term added to yield the proper domain of dependence and directional bias in supersonic regions and across imbedded shock waves. Justification is given for the problem and means of solution chosen, and the potential advantages of the finite element procedure over standard finite difference procedures are discussed. Several possible improvements on the method as presently derived are stated. Computational mesh requirements and certain mesh variations are described. Some results equivalent to finite difference calculations are given as a sample solution.

Tatum, K. E.↗
NASA NTRS1978

Numerical solution of a class of integral equations arising in two-dimensional aerodynamics

We consider the numerical solution of a class of integral equations arising in the determination of the compressible flow about a thin airfoil in a ventilated wind tunnel. The integral equations are of the first kind with kernels having a Cauchy singularity. Using appropriately chosen Hilbert spaces, it is shown that the kernel gives rise to a mapping which is the sum of a unitary operator and a compact operator. This allows the problem to be studied in terms of an equivalent integral equation of the second kind. A convergent numerical algorithm for its solution is derived by using Galerkin's method. It is shown that this algorithm is numerically equivalent to Bland's collocation method, which is then used as the method of computation. Extensive numerical calculations are presented establishing the validity of the theory.

Fromme, J.↗
NASA NTRS1978

On a numerical solution of the plastic buckling problem of structures

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic buckling mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.

Gupta, K. K.↗
NASA NTRS1977

Pressureless sintered beta-prime-Si3N4 solid solution - Fabrication, microstructure, and strength

Pressureless sintering of beta-prime-Si3N4 solid solution was studied as a function of temperature using Si3N4, A1N, and Al2O3 as basic constituents. Y2O3-SiO2 additions were used to promote liquid-phase sintering. The sintered specimens were characterized with respect to density, microstructure, strength, oxidation, and thermal shock resistance. Density greater than 98 percent of theoretical was achieved by pressureless sintering at 1750 C. The microstructure consisted essentially of fine-grained beta-prime-Si3N4 solid solution as the major phase. Modulus of rupture strengths up to 483 M Pa were achieved at moderate temperature (1000 C), but decreased to 228 M Pa at 1380 C. This substantial strength loss was attributed to a 'glassy' grain boundary phase formed during cooling from the sintering temperature. The best oxidation resistance was exhibited by a composition containing 3 mol % Y2O3-SiO2 additives. Water quench thermal shock resistance was equivalent to that of reaction sintered silicon nitride but lower than hot-pressed silicon nitride.

Dutta, S.↗
NASA NTRS1978

Navier-Stokes solutions using Stetter's method

Compressible Navier-Stokes equations for quasi-one-dimensional flow in a converging-diverging nozzle have been solved using Stetter's three-step predictor-corrector technique. Particular emphasis is given to the minimum iterative step feature for steady-state solutions. It is found that for the nonviscous-dominated case, Stetter's method attains the steady-state solution in the fewest steps when compared to four other currently used techniques.

Graves, R. A., Jr.↗
NASA NTRS1979

Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Djaferis, T. E.↗
NASA NTRS1979

A study of crystal growth by solution technique

The advantages and mechanisms of crystal growth from solution are discussed as well as the effects of impurity adsorption on the kinetics of crystal growth. Uncertainities regarding crystal growth in a low gravity environment are examined. Single crystals of triglycine sulfate were grown using a low temperature solution technique. Small components were assembled and fabricated for future space flights. A space processing experiment proposal accepted by NASA for the Spacelab-3 mission is included.

Lal, R. B.↗
NASA NTRS1979

Numerical solution of the Navier-Stokes equations for laminar, transonic flows

An implicit finite difference solution of the Navier-Stokes equations yielded time histories of the transonic laminar flow development about a circular cylinder and NACA-0018 airfoil. Reynolds numbers ranged from those corresponding to purely laminar flow to those corresponding to significant turbulence in the boundary layer. Body thermal conditions of an adiabatic wall and a specified body temperature were considered. Versatility in treating arbitrary bodies was incorporated by using numerically generated, body-fitted coordinate transformations. Solution of the simultaneous difference equations for the dependent variables was obtained using an accelerated Gauss-Seidel iterative scheme. Computational results are presented in the form of velocity vector fields, Mach number contours, aerodynamic coefficients, heat transfer rates at the body surface, and body temperature distributions. Truncation analyses of first and second derivative difference approximations resulted in general criteria for numerically generated coordinates so that flow near a body is more accurately represented.

Turner, L., III↗
NASA NTRS1978

A note on obtaining an approximate value for the period of a periodic solution of x-double prime = -V prime /x/

The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.

Lass, H.↗