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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

A new approach to the solution of large, full matrix equations: A two-dimensional potential flow feasibility study

An approach to the solution of matrix problems resulting from integral equations of mathematical physics is presented. Based on the inherent smoothness in such equations, the problem is reformulated using a set of orthogonal basis vectors, leading to an equivalent coefficient problem which can be of lower order without significantly impairing the accuracy of the solution. This approach was evaluated using a two-dimensional Neumann problem describing the inviscid, incompressible flow over an airfoil. Two different kinds of mode functions were investigated, namely eigenfunction series and Fourier series. The method using Fourier series was found preferable. It uses all of the coefficients from a Fast Fourier Transform algorithm in an approximate method which exploits the known structure of the transformed coefficient matrix and very promising results for the flow over a realistic airfoil are obtained. On the basis of the results presented here, an order of magnitude reduction in this computer time can be expected for such problems as compared with the time for a direct matrix solution.

James, R. M.↗
NASA NTRS1975

Application of Fourier transforms for microwave radiometric inversions

Existing microwave radiometer technology now provides a suitable method for remote determination of the ocean surface's absolute brightness temperature. To extract the brightness temperature of the water from the antenna temperature, an unstable Fredholm integral equation of the first kind is solved. Fourier transform techniques are used to invert the integral after it is placed into a cross correlation form. Application and verification of the methods to a two-dimensional modeling of a laboratory wave tank system are included. The instability of the ill-posed Fredholm equation is examined and a restoration procedure is included which smooths the resulting oscillations. With the recent availability and advances of fast Fourier transform (FFT) techniques, the method presented becomes very attractive in the evaluation of large quantities of data.

Holmes, J. J.↗
NASA NTRS1979

A similarity rule for compressibility and sidewall-boundary-layer effects in two-dimensional wind tunnels

The effect of the sidewall boundary layer on flow in two-dimensional wind tunnels is determined. The small-disturbance and isentropic approximations are made, and the sidewall-boundary-layer dynamics are modeled with the von Karman momentum-integral equation. The effects of the edge-velocity-gradient term in the sidewall momentum integral, which is usually dominant near the model, and the compressibility term are shown to be similar. It is shown that the effect of sidewall suction around the model is not similar to two-dimensional flow. Comparisons with experiment are made to verify the similarity rule.

Barnwell, R. W.↗
NASA NTRS1983

A lifting surface theory in rotational flow

The partial differential equation for small disturbance steady rotational flow in three dimensions is solved through an integral equation approach. The solution is obtained by using the method of weighted residuals. Specific applications are directed to wings in nonuniform subsonic parallel streams with velocity varying in vertical and spanwise directions and to airfoils in nonuniform freestream. Comparison with limited known results indicates that the present method is reasonably accurate. Numerical results for the lifting pressure of airfoil, lift, induced drag, and pitching moments of airfoil, lift, induced drag, and pitching moments of elliptic, rectangular, and delta wings in a jet, wake, or monotonic sheared stream are presented. It is shown that, in addition to the effect of local dynamic pressures, a positive velocity gradient tends to enhance the lift.

Shiau, M. J.↗
NASA NTRS1991

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility being the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements. Recent efforts have focused on reducing run time, improving accuracy and adding more boundary condition choices.

Klang, Eric C.↗
NASA NTRS1990

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility is the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements.

Owen, Vicki L.↗
NASA NTRS1985

Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries

The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.

Aksel, G. N.↗
NASA NTRS1989

Some aspects of transient cooling of a radiating rectangular medium

The emission from a gray radiating medium is analyzed for transient cooling in surroundings at a low temperature. The medium is rectangular with no variations in the direction normal to the cross section. The integral equation for the transient temperature distribution is solved numerically using a two-dimensional Gaussian integration subroutine. The emissive ability for a rectangle at uniform temperature is compared with that for transient cooling where the temperature distribution of the region has reached a fully developed shape, as shown by a separation of variables solution. The two solutions provide the upper and lower bounds for the emittance of a rectangle during transient cooling. The emittances for various aspect ratios are presented as a function of the mean length of the rectangle and are compared with results for a plane layer and a cylinder.

Siegel, Robert↗
NASA NTRS1983

Three-dimensional analysis of chevron-notched specimens by boundary integral method

The chevron-notched short bar and short rod specimens was analyzed by the boundary integral equations method. This method makes use of boundary surface elements in obtaining the solution. The boundary integral models were composed of linear triangular and rectangular surface segments. Results were obtained for two specimens with width to thickness ratios of 1.45 and 2.00 and for different crack length to width ratios ranging from 0.4 to 0.7. Crack opening displacement and stress intensity factors determined from displacement calculations along the crack front and compliance calculations were compared with experimental values and with finite element analysis.

Mendelson, A.↗
NASA NTRS1993

Comprehensive investigation of HgCdTe metalorganic chemical vapor deposition

The principal objective of this experimental and theoretical research program was to explore the possibility of depositing high quality epitaxial CdTe and HgCdTe at very low pressures through metalorganic chemical vapor deposition (MOCVD). We explored two important aspects of this potential process: (1) the interaction of molecular flow transport and deposition in an MOCVD reactor with a commercial configuration, and (2) the kinetics of metal alkyl source gas adsorption, decomposition and desorption from the growing film surface using ultra high vacuum surface science reaction techniques. To explore the transport-reaction issue, we have developed a reaction engineering analysis of a multiple wafer-in-tube ultrahigh vacuum chemical vapor deposition (UHV/CVD) reactor which allows an estimate of wafer or substrate throughput for a reactor of fixed geometry and a given deposition chemistry with specified film thickness uniformity constraints. The model employs a description of ballistic transport and reaction based on the pseudo-steady approximation to the Boltzmann equation in the limit of pure molecular flow. The model representation takes the form of an integral equation for the flux of each reactant or intermediate species to the wafer surfaces. Expressions for the reactive sticking coefficients (RSC) for each species must be incorporated in the term which represents reemission from a wafer surface. The interactions of MOCVD precursors with Si and CdTe were investigated using temperature programmed desorption (TPD) in ultra high vacuum combined with Auger electron spectroscopy (AES). These studies revealed that diethyltellurium (DETe) and dimethylcadmium (DMCd) adsorb weakly on clean Si(100) and desorb upon heating without decomposing. These precursors adsorb both weakly and strongly on CdTe(111)A, with DMCd exhibiting the stronger interaction with the surface than DETe.

Raupp, Gregory B.↗
NASA NTRS1993

Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

A microscopic model for the quasiparticle interaction in neutron matter is presented. Both-particle (pp) and particle-hole (ph) correlations are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for particle-hole interaction and the scattering amplitude of the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules for the scattering amplitude are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the (1)S(sub 0) gap parameter for neutron superfluidity and comment briefly on neutron-star implications.

Wambach, J↗
NASA NTRS1993

Quasiparticle Interactions in Neutron Matter for Applications in Neutron Stars

A microscopic model for the quaisiparticle interaction in neutron matter is presented. Both particle-particle (pp) and particle-hole (ph) correlation are are included. The pp correlations are treated in semi-empirical way, while ph correlations are incorporated by solving coupled two-body equations for the particle hole interaction and the scattering amplitude on the Fermi sphere. The resulting integral equations self-consistently sum the ph reducible diagrams. Antisymmetry is kept at all stages and hence the forward-scattering sum rules are obeyed. Results for Landau parameters and transport coefficients in a density regime representing the crust of a neutron star are presented. We also estimate the S-1 gap parameter for neutron superfluidity and comment briefly on neutron-star implications.

Wambach, J.↗
NASA NTRS1989

High speed propeller acoustics and aerodynamics - A boundary element approach

The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.

Farassat, F.↗
NASA NTRS1985

Aerodynamic properties of turbulent combustion fields

Flow fields involving turbulent flames in premixed gases under a variety of conditions are modeled by the use of a numerical technique based on the random vortex method to solve the Navier-Stokes equations and a flame propagation algorithm to trace the motion of the front and implement the Huygens principle, both due to Chorin. A successive over-relaxation hybrid method is applied to solve the Euler equation for flows in an arbitrarily shaped domain. The method of images, conformal transformation, and the integral-equation technique are also used to treat flows in special cases, according to their particular requirements. Salient features of turbulent flame propagation in premixed gases are interpreted by relating them to the aerodynamic properties of the flow field. Included among them is the well-known cellular structure of flames stabilized by bluff bodies, as well as the formation of the characteristic tulip shape of flames propagating in ducts. In its rudimentary form, the mechanism of propagation of a turbulent flame is shown to consist of: (1) rotary motion of eddies at the flame front, (2) self-advancement of the front at an appropriate normal burning speed, and (3) dynamic effects of expansion due to exothermicity of the combustion reaction. An idealized model is used to illustrate these fundamental mechanisms and to investigate basic aerodynamic features of flames in premixed gases. The case of a confined flame stabilized behind a rearward-facing step is given particular care and attention. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and reattachment length.

Hsiao, C. C.↗