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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1979

Numerical solution of compressible viscous flows

The presented review is concerned with the problem of calculating compressible viscous flows. Basic numerical considerations and problems associated with calculating viscous flows are examined and current numerical approaches toward the solution of the Navier-Stokes equations are discussed. It is pointed out that the numerical solution of the full time-dependent equations for turbulent flow is not practical with present computers. Therefore, turbulence effects must be accounted for by modeling. Developments related to turbulence modeling are described. In connection with a discussion of numerical methods for solving viscous flow equations, attention is given to numerical domains of dependence of typical explicit and implicit methods, the diffusion problem, the convection-diffusion problem, and the split-hybrid method.

Maccormack, R. W.↗
NASA NTRS1979

Energy conserving norms for the solution of hyperbolic systems of partial differential equations

The hyperbolic system of partial differential equations with a real constant square coefficient matrix A is considered. The problem of finding an energy conserving norm for the solution of the system is reduced to the problem of characterizing those matrices appearing in the boundary conditions which satisfy two specific matrix equations. Necessary and sufficient conditions on the coefficient matrix A and the matrices appearing in boundary conditions are derived for an energy conserving norm. The conditions serve as criteria on a given system which determine whether or not the solution will have its energy conserved in some norm. Examples of specific systems and boundary conditions are also provided.

Gunzburger, M. D.↗
NASA NTRS1978

Numerical solution of the Navier-Stokes equations for arbitrary blunt bodies in supersonic flows

A time-dependent, two-dimensional Navier-Stokes code employing the body-fitted coordinate technique has been developed for supersonic flows past blunt bodies of arbitrary shape. The computer program is based on the finite-difference approximation of the compressible Navier-Stokes equations transformed to nonorthogonal curvilinear coordinates with the contravariant components of the velocity vector as dependent variables. The bow shock ahead of the body is obtained as part of the solution, by 'shock capturing'. Numerical solutions of the complete equations are presented in detail for free-stream Mach number 4.6, Reynolds number 10,000, and an isothermal wall temperature of 556 K for a circular cylinder with the free-stream outer boundaries forming a hyperbola in the front and a circular arc in the back.

Warsi, Z. U. A.↗
NASA NTRS1979

The classical solution of a definite integral occurring in the satellite theory in the extended phase space

A method of integrating the functions defined by Scheifele and Graf (1974), arising in the elimination of time from the arguments of satellite theory using Delaunay elements in the extended phase space, is proposed. By repeated applications of an identity of Stiefel and Scheifele (1971), neglecting certain terms, and assuming a solution in the form of a product of Bessel functions, a solution expanded in the eccentricity is obtained.

Bond, V. R.↗
NASA NTRS1978

Numerical solution for supersonic flow near the trailing edge of a flat plate

In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates that the asymptotic triple deck theory for supersonic trailing edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.

Degani, D.↗
NASA NTRS1980

Chemical-milling solution for invar alloy

Excellent surface finishes and tolerances are achieved using two formulations. Solution A gives finish of 3.17 micrometers after milling at 57 to 63 deg C. Constituents of A are: Hydrofluoric acid (70%), 5,8 oz/gal; nitric acid (40-42) degrees Baume), 40 oz/gal. Alternative solution gives 2.16 micrometer finish, and differs from A by addition of 7% phosphoric acid. Formulations eliminate channeling at root fillets, dishing, island formation, and overhangs.

Batiuk, W.↗
NASA NTRS1980

Steady state solutions to dynamically loaded periodic structures

The general problem of solving for the steady state (time domain) dynamic response (i.e., NASTRAN rigid format-8) of a general elastic periodic structure subject to a phase difference loading of the type encountered in traveling wave propagation problems was studied. Two types of structural configurations were considered; in the first type, the structure has a repeating pattern over a span that is long enough to be considered, for all practical purposes, as infinite; in the second type, the structure has structural rotational symmetry in the circumferential direction. The theory and a corresponding set of DMAP instructions which permits the NASTRAN user to automatically alter the rigid format-8 sequence to solve the intended class of problems are presented. Final results are recovered as with any ordinary rigid format-8 solution, except that the results are only printed for the typical periodic segment of the structure. A simple demonstration problem having a known exact solution is used to illustrate the implementation of the procedure.

Kalinowski, A. J.↗
NASA NTRS1980

Experimental techniques for determination of the role of diffusion and convection in crystal growth from solution

Various studies of the concentration of the solution around a growing crystal using interferometric techniques are reviewed. A holographic interferometric technique used in laboratory experiments shows that a simple description of the solution based on the assumption of a purely diffusive mechanism appears inadequate since the convection, effective even in reduced columns, always affects the growth.

Zefiro, L.↗