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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A Finite-Element Formulation for Subsonic Flows Around Complex Configurations

The problem of potential steady subsonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗
NASA NTRS1969

On the auto and cross correlation of PN sequences

The autocorrelation and crosscorrelation properties of pseudorandom (PN) sequences are analyzed by using some important properties of PN sequences. These properties make this discussion understandable without the need of linear algebraic approach. The analysis is followed by some experimental results.

Morakis, J. C.↗
NASA NTRS1974

A finite element method for potential aerodynamics around complex configurations

A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flow around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of the flow field around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with a hyperboloidal surface. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, intrinsically general and flexible, is also fast, accurate and in excellent agreement with existing results.

Chen, L.-T.↗
NASA NTRS1974

A finite-element method for lifting surfaces in steady incompressible subsonic flow

The problem of potential steady subsonic flow for lifting surfaces is considered. This problem requires the solution of an integral equation relating the value of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface is divided into small (quadrilateral hyperboloidal) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each element and equal to their values at the centroids of the elements. This yields a set of linear algebraic equations. Numerical results are in good agreement with existing ones.

Morino, L.↗
NASA NTRS1974

A finite element formulation for supersonic flows around complex configurations

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element are assumed to be constant and equal to its value at the centroid of the element. This yields a set of linear algebraic equations whose coefficients are given by source and doublet integrals over the surface elements. Closed form evaluations of the integrals are presented.

Morino, L.↗
NASA NTRS1975

Temperature fields of an absorptive medium in a radiating system of arbitrary configuration (the spatial problem)

A generalized zonal method based on systems of linear algebraic equations is used to determine the temperature fields in an absorptive grey medium filling a closed radiation system that consists of three boundary zones, of which one is adiabatic and the other two are isothermal. The example calculation considers the case of a solenoidal radiation field of local radiative equilibrium.

Surinov, Y. A.↗
NASA NTRS1975

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

Chen, L. T.↗
NASA NTRS1974

A finite-element analysis for steady and oscillatory supersonic flows around complex configurations

The problem of small perturbation potential supersonic flow around complex configurations is considered. This problem requires the solution of an integral equation relating the values of the potential on the surface of the body to the values of the normal derivative, which is known from the small perturbation boundary conditions. The surface of the body is divided into small (hyperboloidal quadrilateral) surface elements, sigma sub i, which are described in terms of the Cartesian components of the four corner points. The values of the potential (and its normal derivative) within each element is assumed to be constant and equal to its value at the centroid of the element, and this yields a set of linear algebraic equations. The coefficients of the equation are given by source and doublet integrals over the surface elements, sigma sub i. The results obtained using the above formulation are compared with existing analytical and experimental results.

Morino, L.↗
NASA NTRS1974

HAL/S - The programming language for Shuttle

HAL/S is a higher order language and system, now operational, adopted by NASA for programming Space Shuttle on-board software. Program reliability is enhanced through language clarity and readability, modularity through program structure, and protection of code and data. Salient features of HAL/S include output orientation, automatic checking (with strictly enforced compiler rules), the availability of linear algebra, real-time control, a statement-level simulator, and compiler transferability (for applying HAL/S to additional object and host computers). The compiler is described briefly.

Martin, F. H.↗
NASA NTRS1975

A finite element analysis of the exact nonlinear formulation of a lifting surface in steady incompressible flow, with the evaluation of the correct wake geometry

The problem of steady incompressible flow for lifting surfaces is considered. An integral equation is solved relating the values of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface and the wake are divided into small quadrilateral surface elements. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each lifting surface element and equal to their values at the centroids of the lifting surface elements. This yields a set of linear algebraic equations. An iteration procedure is used to obtain the wake geometry: the velocities at the corner points of the wake elements are calculated and the wake streamlines are aligned to be parallel to the velocity vector. The procedure is repeated until convergence is attained.

Suciu, E. O.↗
NASA NTRS1976

The effect of adhesive layer on crack propagation in laminates

The effect of the adhesive layer on crack propagation in composite materials is investigated. The composite medium consists of parallel load carrying laminates and buffer strips arranged periodically and bonded with thin adhesive layers. The strips, assumed to be isotropic and linearly elastic, contain symmetric cracks of arbitrary lengths located normal to the interfaces. Two problems are considered: (1) thin adhesive layers are approximated by uncoupled tension and shear springs distributed along the interfaces of the strips for which only the case of internal cracks can be treated rigorously; (2) broken laminates and the true singular behavior in the presence of the adhesive layer are studied. The adhesive is then treated as an isotropic, linearly elastic continuum. General expressions for field quantities are obtained in terms of infinite Fourier integrals. These expressions give a system of singular integral equations in terms of the crack surface displacement derivatives. By using appropriate quadrature formulas, the integral equations reduce to a system of linear algebraic equations which are solved numerically.

Gecit, M. R.↗
NASA NTRS1976

NASA-Ames three-dimensional potential flow analysis system (POTFAN) equation solver code (SOLN) version 1

A computer program known as SOLN was developed as an independent segment of the NASA-Ames three-dimensional potential flow analysis systems of linear algebraic equations. Methods used include: LU decomposition, Householder's method, a partitioning scheme, and a block successive relaxation method. Due to the independent modular nature of the program, it may be used by itself and not necessarily in conjunction with other segments of the POTFAN system.

Davis, J. E.↗
NASA NTRS1976

A nonlinear finite-element analysis of wings in steady incompressible flows with wake roll-up

The problem of lifting surfaces and complex aircraft configurations in steady incompressible flow is considered. For lifting surfaces the problem is formulated in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential on the lifting surface. For complex configurations the problem is formulated in terms of an integral equation relating the potential to its normal derivative on the surface of the aircraft. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential (or the potential discontinuity) and its normal derivative to be constant within each element. The wake geometry is obtained by iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines.

Suciu, E. O.↗
NASA NTRS1976

Finite difference procedure for boundary layers including effects of longitudinal and transverse curvatures

A second order viscous layer solution procedure has been developed that does in a consistent way include curvature effects and the corresponding normal pressure gradients. In the present system, the normal momentum equation is retained. The parabolic system of nonlinear partial differential equations is converted by linear finite differencing procedures to a system of linear algebraic equations and solved in primitive coordinates. The solutions have been shown to give smooth stable distributions for all the variables, most particularly the normal velocity which plays an important role in the interaction procedure. An algorithm for matching the viscous layer solution with a rotational characteristics outer solution has been developed.

Tassa, Y.↗
NASA NTRS1977

Nonlinear steady incompressible lifting-surface analysis with wake roll-up

The problem of lifting surfaces in steady incompressible flow is considered in terms of an integral equation relating the potential discontinuity on wing and wake to the normal derivative of the potential (normal wash) on the lifting surface. The integral equation is approximated by a system of linear algebraic equations obtained by dividing the surfaces into small quadrilateral elements and by assuming the potential discontinuity and the normal wash to be constant within each element. The wake geometry is obtained through iteration by satisfying the condition that the velocity be tangent to the surface of the wake and that the potential discontinuity be constant along the streamlines. Numerical results are in good agreement with existing ones

Suciu, E. O.↗
NASA NTRS1977

Unsteady flow in a supersonic cascade with strong in-passage shocks

Linearized theory is used to study the unsteady flow in a supersonic cascade with in-passage shock waves. We use the Wiener-Hopf technique to obtain a closed-form analytical solution for the supersonic region. To obtain a solution for the rotational flow in the subsonic region we must solve an infinite set of linear algebraic equations. The analysis shows that it is possible to correlate quantitatively the oscillatory shock motion with the Kutta condition at the trailing edges of the blades. This feature allows us to account for the effect of shock motion on the stability of the cascade. Unlike the theory for a completely supersonic flow, the present study predicts the occurrence of supersonic bending flutter. It therefore provides a possible explanation for the bending flutter that has recently been detected in aircraft-engine compressors at higher blade loadings.

Goldstein, M. E.↗
NASA NTRS1978

Calculation of unsteady transonic flows using the integral equation method

The basic integral equations for a harmonically oscillating airfoil in a transonic flow with shock waves are derived; the reduced frequency is assumed to be small. The problems associated with shock wave motion are treated using a strained coordinate system. The integral equation is linear and consists of both line integrals and surface integrals over the flow field which are evaluated by quadrature. This leads to a set of linear algebraic equations that can be solved directly. The shock motion is obtained explicitly by enforcing the condition that the flow is continuous except at a shock wave. Results obtained for both lifting and nonlifting oscillatory flows agree satisfactorily with other accurate results.

Nixon, D.↗
NASA NTRS1980

Image-analysis library

MATHPAC image-analysis library is collection of general-purpose mathematical and statistical routines and special-purpose data-analysis and pattern-recognition routines for image analysis. MATHPAC library consists of Linear Algebra, Optimization, Statistical-Summary, Densities and Distribution, Regression, and Statistical-Test packages.

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