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At least 1,063 records · Page 59

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NASA NTRS1981

Numerical solution of transonic stream function equation

The stream function equation, in conservation form, looks similar to the full potential equation and existing methods (e.g. artificial compressibility) can be readily applied. Rotational flows can be calculated once the vorticity (due to shocks or nonuniformity) is evaluated. There are, however, two main difficulties: First, the density is not uniquely determined in terms of the flux (there are two solutions; the subsonic and the supersonic branch with a square root singularity at the sonic point). Methods to overcome this difficulty are studied and results are presented with some remarks on inviscid separation and closed stream lines. Second, the need of two stream functions for three dimensional calculations is briefly discussed.

Hafez, M.↗

NASA NTRS1981

Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades

A linear unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, is being developed to predict the aerodynamic response to blade vibrations in the fan, compressor or turbine stages of modern jet engines. In previous work numerical solutions were restricted to cascades of sharp-edged blades aligned with the mean flow. Under the present effort the solution procedure has been extended to treat blades with rounded or blunt edges. As part of this effort an analytical model-problem study has been conducted to clarify the behavior of first-order perturbation solutions in the vicinity of airfoil edges. Further, a numerical approximation using concepts from singular perturbation theory has been developed to resolve the unsteady boundary value problem for cascades of blunt leading-edged blades. Numerical results for NACA 0012 cascades, including detailed results in the vicinity of a blade leading edge, are presented and evaluated.

Verdon, J. M.↗

NASA NTRS1980

Equilibrium response of flight control systems

The steady-state behavior of an aircraft in response to control and disturbance inputs has a major impact on its performance and flying qualities, and it is, to a large extent, not readily predicted by the aircraft's stability and transient behavior. Singular as well as nonsingular response can result as a consequence of the command vector's definition, i.e., equilibrium in the command vector can imply disequilibrium in the state. The flight control structure can be modified to account for this characteristic, and it is shown that systems with identical eigenvalues and eigenvectors but dissimilar command vectors have markedly different responses.

Stengel, R. F.↗

NASA NTRS1981

On eigensolutions for discontinuous liners in a duct containing uniform mean flow

Sound attenuation in a rectangular acoustically lined duct containing uniform mean flow is analytically investigated using the generalized Wiener-Hopf technique. Uniqueness of the solution is enforced for lined sections of the finite axial extent by imposing edge conditions at the liner interface. Possible edge conditions are considered, including the Kutta condition, and the causal solution corresponding to edge conditions is considered the best choice. Solution methods such as the mode matching and singularity methods imply differing edge conditions, and results show that power attenuation is insensitive to the imposed edge conditions, although significant differences are observed for the reflection coefficient. The amplitude of the exponentially increasing instability mode in the lined section must be set to zero as a first approximation to the nonlinear situation, and results indicate that measurements of the reflection factor can be used to make a more definite decision about physically appropriate edge conditions.

Koch, W.↗

NASA NTRS1982

Higher-Order Panel Method for Aerodynamic Flow Analysis

PANAIR uses high-order panel method to predict inviscid subsonic or supersonic flows about arbitrary configuration. Panel method solves linear partial differential equation numerically by approximating configuration surface with panels on which unknown "singularity strengths" are defined. PANAIR includes advanced software technology as well as advanced aerodynamic technology.

Erickson, L.↗

NASA NTRS1982

Out-of-Core Solutions of Complex Sparse Linear Equations

ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.

Yip, E. L.↗

NASA NTRS1981

Development of an efficient procedure for calculating the aerodynamic effects of planform variation

Numerical procedures to compute gradients in aerodynamic loading due to planform shape changes using panel method codes were studied. Two procedures were investigated: one computed the aerodynamic perturbation directly; the other computed the aerodynamic loading on the perturbed planform and on the base planform and then differenced these values to obtain the perturbation in loading. It is indicated that computing the perturbed values directly can not be done satisfactorily without proper aerodynamic representation of the pressure singularity at the leading edge of a thin wing. For the alternative procedure, a technique was developed which saves most of the time-consuming computations from a panel method calculation for the base planform. Using this procedure the perturbed loading can be calculated in about one-tenth the time of that for the base solution.

Mercer, J. E.↗

NASA NTRS1981

A study of the viscous dissipation and surface loading on a vibrating surface

The energy dissipated by viscosity at the edge of a vibrating flat plate is calculated and compared to the radiated acoustic energy. A correction to the Kirchhoff integral estimate of the noise is derived. For Helmholtz number of order unity and smaller the dissipation can be comparable to or greater than the acoustic energy. A viscous compressible theory of the load distribution on a vibrating two dimensional body is developed. First it is shown that load calculations based on potential theory and the Newmann uniqueness condition (continuity of potential or pressure on the surface) are not in agreement with experiment or the more correct viscous theory. For a flat plate airfoil the eigensolution of potential theory is indeterminant while viscous theory yields a unique solution that has square root singularities at the edges. It is also shown that for compact surfaces the far field acoustics depend only on the magnitude of the eigensolutions of potential theoy and so will be uniquely determined by the viscous theory. It is suggested that the general viscous theory of vibrating surfaces with cross sectional geometry will lead to results in agreement with expermentally measured load distributions.

Yates, J. E.↗

NASA NTRS1981

A development of grid generation procedure for multicomponent aerodynamic configuration

Two approaches for solving the transonic flow in a multi-block grid were explored. The first approach examines a method involving "zonal decomposition" wherein block boundaries are treated as true boundary surfaces separating interfacing grids. The issues investigated involve techniques for matching solutions at a block boundary. A feasibility study was completed and the results are presented. The second approach involves overlapping grids for differencing across a block boundary near an artificially induced coordinate singularity occurring at a fictitious corner. This approach selects a set of neighboring nodes for the fictitious corner such that the resulting physical cells for a node are topologically the same as any other node on the airfoil surface.

Chen, H. C.↗

NASA NTRS1981

The axisymmetric elasticity problem for a laminated plate containing a circular hole

The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.

Delale, F.↗

NASA NTRS1982

Multidisciplinary Research Program in Atmospheric Science

A theoretical analysis of the vertical resolving power of the High resolution Infrared Radiation Sounder (HIRS) and the Advanced Meteorological Temperature Sounder (AMTS) is carried out. The infrared transmittance weighting functions and associated radiative transfer kernels are analyzed through singular value decomposition. The AMTS was found to contain several more pieces of independent information than HIRS when the transmittances were considered, but the two instruments appeared to be much more similar when the temperature sensitive radiative transfer kernels were analyzed. The HIRS and AMTS instruments were also subjected to a thorough analysis. It was found that the two instruments should have very similar vertical resolving power below 500 mb but that AMTS should have superior resolving power above 200 mb. In the layer 200 to 500 mb the AMTS showed badly degraded spread function.

Thompson, O. E.↗

NASA NTRS1981

Determination of wind tunnel constraint effects by a unified pressure signature method. Part 2: Application to jet-in-crossflow

The development of an improved jet-in-crossflow model for estimating wind tunnel blockage and angle-of-attack interference is described. Experiments showed that the simpler existing models fall seriously short of representing far-field flows properly. A new, vortex-source-doublet (VSD) model was therefore developed which employs curved trajectories and experimentally-based singularity strengths. The new model is consistent with existing and new experimental data and it predicts tunnel wall (i.e. far-field) pressures properly. It is implemented as a preprocessor to the wall-pressure-signature-based tunnel interference predictor. The supporting experiments and theoretical studies revealed some new results. Comparative flow field measurements with 1-inch "free-air" and 3-inch impinging jets showed that vortex penetration into the flow, in diameters, was almost unaltered until 'hard' impingement occurred. In modeling impinging cases, a 'plume redirection' term was introduced which is apparently absent in previous models. The effects of this term were found to be very significant.

Hackett, J. E.↗

NASA NTRS1982

Validation of zero-order feedback strategies for medium range air-to-air interception in a horizontal plane

A zero order feedback solution of a variable speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbation (FSP), is compared with the exact open loop solution. The comparison indicates that for initial distances of separation larger than eight turning radii of the evader, the accuracy of the feedback approximation is better than one percent. The result validates the zero order FSP approximation for medium range air combat analysis.

Shinar, J.↗

NASA NTRS1982

The motion of a drop in a rigid surface

The assumptions of a region of slip near a moving contact line (to remove the force singularity) and a constant contact angle are used to obtain the equation for the shape of a thin drop of liquid resting on a rigid plane. Three asymptotic expansions are matched together to obtain an expression for the rate at which the drop spreads. Some cases of sliding motion are also examined. Although the technique is presented here for thin drops only, it can also be applied to drops of arbitrary size.

Hocking, L. M.↗

NASA NTRS1982

Applications of perturbation techniques

Two perturbation techniques were applied to two singular perturbation problems in heat transfer to obtain uniformly valid solutions which can serve as benchmarks for finite difference and finite element techniques. In the first problem, the method of strained parameters coupled with the application of a solvability condition is used to obtain a uniform solution for the problem of unsteady heat conduction in a long nearly circular cylinder. In the second problem, the method of matched asymptotic expansion coupled with Van Dyke's matching principle is used to obtain a uniform solution for the problem of one dimensional conduction-convection heat transfer of a uniform fluid flow.

Kandil, O. A.↗

NASA NTRS1982

Three-dimensional separation and reattachment

The separation of three dimensional turbulent boundary layers from the lee of flight vehicles at high angles of attack is investigated. The separation results in dominant, large scale, coiled vortex motions that pass along the body in the general direction of the free stream. In all cases of three dimensional flow separation and reattachment, the assumption of continuous vector fields of skin friction lines and external flow streamlines, coupled with simple laws of topology, provides a flow grammar whose elemental constituents are the singular points: the nodes, spiral nodes (foci), and saddles. The phenomenon of three dimensional separation may be construed as either a local or a global event, depending on whether the skin friction line that becomes a line of separation originates at a node or a saddle point.

Peake, D. J.↗

NASA NTRS1982

Three-dimensional analysis of 0/90s and 90/0s laminates with a central circular hole

Stress distributions were calculated near a circular hole in laminates, using a three dimensional finite element analysis. These stress distributions were presented three ways: through the thickness at the hole boundary, along radial lines at the 0/90 and 90/0 interfaces, and around the hole at these interfaces. The interlaminar normal stress, and the shear stress, distributions had very steep gradients near the hole boundary, suggesting interlaminar stress singularities. The largest compressive stress occurred at about 60 deg from the load axis. A simple procedure was introduced to calculate interlaminar stresses near the hole boundary. It used stresses calculated by an exact two dimensional analysis of a laminate with a hole as input to a quasi three dimensional model. It produced stresses that agreed closely with those from the three dimensional finite element model.

Raju, I. S.↗

NASA NTRS1982

The elasticity problem for a thick-walled cylinder containing a circumferential crack

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.

Nied, H. F.↗