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At least 1,765 records · Page 98
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NASA NTRS1978

Creation of lumped parameter thermal model by the use of finite elements

In the finite difference technique, the thermal network is represented by an analogous electrical network. The development of this network model, which is used to describe a physical system, often requires tedious and mental data preparation and checkout by the analyst which can be greatly reduced through the use of the computer programs to develop automatically the mathematical model and associated input data and graphically display the analytical model to facilitate model verification. Three separate programs are involved which are linked through common mass storage files and data card formats. These programs are SPAR, CINGEN and GEOMPLT, and are used to (1) develop thermal models for the MITAS II thermal analyzer program; (2) produce geometry plots of the thermal network; and (3) produce temperature distribution and time history plots.

Source record↗
NASA NTRS1977

Computational design of the basic dynamical processes of the UCLA general circulation model

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Arakawa, A.↗
NASA NTRS1977

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

Williams, S. D.↗
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1977

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented which optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗
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

Calculation of transonic potential flowfields about complex, three-dimensional configurations

Methods for extending iterative, finite-difference calculations of transonic potential flowfields to complex three-dimensional configurations are discussed. One particularly attractive approach is to use relatively simple conformal mappings in combination with shearing transformations to generate computational domains that are nearly-conformally mapped from the physical space in one family of coordinate surfaces, and which map the complex boundaries to grid surfaces. The application of such a method to a general wing-body combination or to a multi-bladed fan is discussed. A transformation to map the wing-fuselage or fan-hub combination to a convenient computational domain is proposed. The transformation is useful in its own right for treating the two-dimensional problems of flow past a profile in a wind tunnel or through a cascade. Some results of preliminary calculations are presented.

Caughey, D. A.↗
NASA NTRS1977

Displacement thickness distributions in transonic flows about 3-D wings

The transonic 3-D inviscid small-perturbation solution of Bailey and Ballhaus is combined with a finite-difference solution for Prandtl's boundary-layer equations in order to include viscous effects. The inviscid-viscous interaction is modeled by means of the displacement surface, which can be thought of as the effective body surface seen by the inviscid flow. Displacement thickness, lift, and pressure distributions resulting from the combined solution are presented for transonic flows about the RAE 101 A wing and a Lockheed transport wing, both at small angles of attack. The influence of changing arbitrarily the start of transition on the displacement surface and lift is discussed for the RAE wing flow.

Kordulla, W.↗
NASA NTRS1977

Meteorite impact ejecta - Dependence of mass and energy lost on planetary escape velocity

The amounts of material and energy which escape a planet in a meteorite impact event is calculated as functions of impact and escape velocities. Results are obtained from the computed flow induced by the impact of iron and gabbroic anorthosite spheres onto a half-space of anorthosite at impact velocities of 5 to 45 km/sec. The impact-induced flows were determined by a numerical method using the mass, momentum, and energy conservation relations in finite-difference approximation, within an Eulerian computational grid. The impact velocities at which ejecta losses equal meteorite mass gains are found to be approximately 20, 35, and 45 km/sec for anorthosite objects and approximately 25, 35, and 40 km/sec for iron objects striking anorthosite surfaces for the gravity fields of the moon, Mercury and Mars.

Okeefe, J. D.↗
NASA NTRS1977

Comparison of numerical and experimental 'conical' flow fields in supersonic corners with compression and/or expansion

The flow field produced by the intersection of two plane solid surfaces in a supersonic stream is a complex interference flow. These flows can be fully compressive, fully expansive, or of mixed compression-expansion nature. This paper presents a comparison of the experimentally obtained flow-field structure in an axial corner with that predicted numerically by using a shock-capturing finite-difference method. The effect of sweep and surface deflection are evaluated, and the general influence of each is presented for the three classes of corner flow. The results show that the numerical method is a valuable aid in understanding the flow structure for simple configurations. In addition, confidence in the numerical method is gained for use in solving more general three-dimensional configurations where the flow is nonconical and several wave interaction may be presented.

Anderson, D. A.↗
NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗
NASA NTRS1978

Computational fluid dynamics applied to flows in an internal combustion engine

The reported investigation is a continuation of studies conducted by Diwakar et al. (1976) and Griffin et al. (1976), who reported the first computational fluid dynamic results for the two-dimensional flowfield for all four strokes of a reciprocating internal combustion (IC) engine cycle. An analysis of rectangular and cylindrical three-dimensional engine models is performed. The working fluid is assumed to be inviscid air of constant specific heats. Calculations are carried out of a four-stroke IC engine flowfield wherein detailed finite-rate chemical combustion of a gasoline-air mixture is included. The calculations remain basically inviscid, except that in some instances thermal conduction is included to allow a more realistic model of the localized sparking of the mixture. All the results of the investigation are obtained by means of an explicity time-dependent finite-difference technique, using a high-speed digital computer.

Griffin, M. D.↗
NASA NTRS1978

Computational studies of turbulent merger of corotational vortices

A computational study has been conducted to gain a better understanding of the criteria governing the merger of corotating vortices. The zero-equation and one-equation turbulent-flow models are used to model the interaction of two rolled-up, corotational vortices. A model appropriate for the swirling flow under consideration has been proposed to prescribe the algebraic variation of mixing-length in the flow field. The unsteady, two-dimensional equations in a cross-plane are solved for primitive variables using an implicit finite-difference code. The computed downstream merging distances are in good agreement with available wind tunnel data.

Raj, P.↗
NASA NTRS1978

Turbulent viscous shock layer solutions for Jovian entry at small angles of attack

The equations governing the laminar and turbulent flows of reacting gas mixtures in chemical equilibrium over axially symmetric blunt bodies at small angles of attack are developed and presented in the unsteady conservative form. Solutions are obtained in the planes of symmetry of the flow field for the typical conditions encountered by a probe entering the Jovian atmosphere at small angles of attack. The eddy-viscosity is approximated by a two-layer model. The shock wave is treated as a discontinuity across which the shock relations are used to compute the flow conditions behind the shock. A time-asymptotic finite-difference method is used to solve the equations. The zero angle of attack results for a hyperboloid are compared with the existing results but neither experimental nor computational results are available for comparison with the present results at angle of attack.

Jumar, A.↗
NASA NTRS1978

A procedure for calculating laminar, transitional and/or turbulent three-dimensional boundary layers including surface curvature effects about arbitrary blunt-nosed bodies

The governing equations for laminar, transitional and/or turbulent, incompressible, three-dimensional boundary layers are solved numerically. The equations are developed in terms of an orthogonal surface coordinate system and include surface curvature effects. The coordinates are generated numerically, while the inviscid flow is obtained from a general potential flow procedure. The only restrictions on body geometry are that it possess a blunt nose and a plane of symmetry. The boundary-layer equations, after being transformed into similarity type variables, are solved using the implicit finite-difference Krause scheme. Various test cases are presented to establish the accuracy of the resulting computer program.

Dwoyer, D. L.↗
NASA NTRS1978

A split-recoupled-semidirect computational technique applied to transonic flow over lifting airfoils

A new version of the semidirect iterative method eliminates significant restrictions of previous versions of the method. A semidirect method solves finite-difference equations by a rapid globally implicit iterative process driven by a fast direct elliptic solver. The new approach can treat complex systems of equations in an efficient 'correction form', and allows the use of general, nonorthogonal, boundary-fitted coordinate transformations. These features are expected to lead to significant practical applications with conservation-equation systems in either two or three dimensions. The present application to the full potential equations for steady transonic flow over an airfoil at angle of attack illustrates the utility of the technique.

Martin, E. D.↗
NASA NTRS1978

Computational transonic flow about realistic aircraft configurations

A numerical method has been developed to compute transonic flows about realistic wing-fuselage configurations. The finite difference scheme employs an improved small disturbance flow equation. A unique grid embedding technique, which was heretofore applied to airfoils and wings, has been extended to include the treatment of both body and wing-body shapes. The resulting high-density mesh is shown to be a valuable asset in resolving details of the three-dimensional flow. A mathematical modeling system is used to process arbitrary fuselage geometries for body boundary conditions. Correlations with experimental data for simple isolated bodies, an isolated fuselage, and wing-fuselage combinations are included.

Boppe, C. W.↗
NASA NTRS1978

Influence of precursor heating on viscous flow around a Jovian entry body

The influence of changes in precursor region flow properties (resulting from the absorption of radiation from the shock layer) on the entire shock layer flow phenomena is investigated. Axially symmetric case is considered for both the preheating zone (precursor region) and shock layer. The flow in the shock layer is considered to be viscous with chemical equilibrium but radiative nonequilibrium. Realistic thermo-physical and spectral models are employed and results are obtained by implicit finite difference and iterative procedures. The results indicate that precursor heating increases the radiative heating of the body by a maximum of 7.5% for a 116 KM entry conditions.

Tiwari, S. N.↗