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NASA NTRS1987

A linear thermal stability analysis for the vertical structure of alpha model accretion disks

The linear equations that describe the thermal stability of the convective and radiative vertical structure of an alpha model accretion disk are derived. For a specific model chosen to be representative of a dwarf nova disk, it is found that the eigenfunction for the temperature shows large excursions in the zone of partial ionization, but that the eigenfunctions for the unstable fundamental mode perturbations of the vertical distance and flux are nearly constant over the vertical extent of the disk. The growth of any instability is thus nearly homologous and the stability criteria derived for vertically averaged structures represent an adequate approximation.

Saio, Hideyuki↗
NASA NTRS1987

Nimbus 7 earth radiation budget wide field of view climate data set improvement. I - The earth albedo from deconvolution of shortwave measurements

A deconvolution method for extracting the top of the atmosphere (TOA) mean, daily albedo field from a set of wide-FOV (WFOV) shortwave radiometer measurements is proposed. The method is based on constructing a synthetic measurement for each satellite observation. The albedo field is represented as a truncated series of spherical harmonic functions, and these linear equations are presented. Simulation studies were conducted to determine the sensitivity of the method. It is observed that a maximum of about 289 pieces of data can be extracted from a set of Nimbus 7 WFOV satellite measurements. The albedos derived using the deconvolution method are compared with albedos derived using the WFOV archival method; the developed albedo field achieved a 20 percent reduction in the global rms regional reflected flux density errors. The deconvolution method is applied to estimate the mean, daily average TOA albedo field for January 1983. A strong and extensive albedo maximum (0.42), which corresponds to the El Nino/Southern Oscillation event of 1982-1983, is detected over the south central Pacific Ocean.

Hucek, Richard R.↗
NASA NTRS1987

Relationship of Thematic Mapper simulator data to leaf area index of temperate coniferous forests

Regional relationships between remote sensing data and the leaf area index (LAI) of coniferous forests were analyzed using data acquired by an Airborne Thematic Mapper. Eighteen coniferous forest stands with a range of projected leaf area index of 0.6-16.1 were sampled from an environmental gradient in moisture and temperature across west-central Oregon. Spectral radiance measurements to account for atmospheric effects were acquired above the canopies from a radiometer mounted on a helicopter. A strong positive relationship was observed between LAI of closed canopy forest stands and the ratio of near-infrared and red spectral bands. A linear regression based on LAI explained 83 percent of the variation in the ratio of the atmospherically corrected bands. A log-linear equation fit the asymptotic characteristic of the relationship better, explaining 91 percent of the variance. The positive relationship is explained by a strong asymptotic inverse relationship between LAI and red radiation and a relatively flat response between LAI and near-infrared radiation.

Peterson, David L.↗
NASA NTRS1987

Circulation control STOL aircraft design aspects

Since Davidson patented Circulation Control Airfoils in 1960, there have been only 2 aircraft designed and flown with circulation control (CC). Designing with CC is complex for the following reasons: the relation between lift increase and blowing momentum is nonlinear; for good cruise performance one must change the wing geometry in flight from a round to a sharp trailing edge. The bleed air from the propulsion engines or an auxiliary compressor, must be used efficiently. In designing with CC, the propulsion and control aspects are just as important as aerodynamics. These design aspects were examined and linearized equations are presented in order to facilitate a preliminary analysis of the performance potential of CC. The thrust and lift requirements for takeoff make the calculated runway length very sensitive to the bleed air ratio. Thrust vectoring improves performance and can offset nose down pitching moments. The choice of blowing jet to free stream velocity ratio determines the efficiency of applying bleed air power.

Loth, John L.↗
NASA NTRS1988

Theoretical study of turbulent channel flow: Bulk properties, pressure fluctuations, and propagation of electromagnetic waves

In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr--Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O--S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend stongly on the structure of the turbulence spectrun at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel.

Canuto, V. M.↗
NASA NTRS1988

On the constrained Chebyshev approximation problem on ellipses

Constrained Chebyshev approximation problems of the type with minimum (p is an element of Pi(sub n):p(c)=1) and maximum (z is an element of E) with /p(z)/ are considered. Here Pi(sub n) denotes the set of all complex polynomials of degree at most n, E is any ellipse in the complex plane, and c is an element of C/E. Such approximation problems arise in the context of optimizing semi-iterative methods for the solution of large, sparse systems of linear equations Ax=b with complex non-Hermitian coefficient matrices A. The problem of obtaining optimal polynomial preconditioners for conjugate gradient type methods for Ax=b also leads to problems of this type. A new family of polynomials -- q(sub n)(z;c), n is an element of N, and c is an element of C/E -- are introduced as the polynomials which are optimal for a modified version of the Chebyshev approximation problem with Pi(sub n) replaced by a certain subfamily. Some simple properties of q(sub n) are also listed. A necessary and sufficient condition for q(sub n) to be the extremal polynomial for the approximation problem is then derived. Finally, it is shown that q(sub n) is indeed optimal for the problem for all fixed n whenever the distance between c and E is sufficiently large. Results of some numerical tests are presented.

Freund, Roland↗
NASA NTRS1989

The role of shock induced trailing-edge separation in limit cycle oscillations

The potential role of shock induced trailing edge separation (SITES) in limit cycle oscillations (LCO) was established. It was shown that the flip-flop characteristics of transition to and from SITES as well as its hysteresis could couple with wing modes with torsional motion and low damping. This connection led to the formulation of a very simple nonlinear math model using the linear equations of motion with a nonlinear step forcing function with hysteresis. A finite difference solution with time was developed and calculations were made for the F-111 TACT were used to determine the step forcing function due to SITES transition. Since no data were available for the hysteresis, a parameter study was conducted allowing the hysteresis effect to vary. Very small hysteresis effects, which were within expected bounds, were required to obtain reasonable response levels that essentially agreed with flight test results. Also in agreement with wind tunnel tests, LCO calculations for the 1/6 scale F-111 model showed that the model should have not experienced LCO.

Cunningham, Atlee M., Jr.↗
NASA NTRS1989

Interaction between Tollmien-Schlichting waves and free-stream disturbances in boundary-layer flows

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small freestream disturbance and a small localized variation of the surface geometry has been carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the freestream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the Tollmien-Schlichting waves.

Bodonyi, R. J.↗
NASA NTRS1989

The FORCE: A portable parallel programming language supporting computational structural mechanics

This project supports the conversion of codes in Computational Structural Mechanics (CSM) to a parallel form which will efficiently exploit the computational power available from multiprocessors. The work is a part of a comprehensive, FORTRAN-based system to form a basis for a parallel version of the NICE/SPAR combination which will form the CSM Testbed. The software is macro-based and rests on the force methodology developed by the principal investigator in connection with an early scientific multiprocessor. Machine independence is an important characteristic of the system so that retargeting it to the Flex/32, or any other multiprocessor on which NICE/SPAR might be imnplemented, is well supported. The principal investigator has experience in producing parallel software for both full and sparse systems of linear equations using the force macros. Other researchers have used the Force in finite element programs. It has been possible to rapidly develop software which performs at maximum efficiency on a multiprocessor. The inherent machine independence of the system also means that the parallelization will not be limited to a specific multiprocessor.

Jordan, Harry F.↗
NASA NTRS1989

Nonmigrating tides

Recently an interesting advancement in the study of nonmigrating tides has occurred. There have been two distinct approaches in works on this subject. One is based on mechanistic models as considering nonuniform global distribution of water vapor or heating only on land, solving a set of linear equations. It is found that insolation absorption of the nonuniformly distributed water vapor produces only weak nonmigrating tides in the lower thermosphere; the planetary boundary layer heating on land can explain the enhanced tides on land and those with short vertical wavelengths in the stratosphere. The other approach is novel and uses simulation on the general circulation model (GCM). This realistic model can reproduce tides globally and in many details. The enhancement of two nonmigrating modes as eastward traveling modes with a wave number 3 and westward traveling modes with a wave number 5 is in surprisingly good agreement with observation at sea level, at 700 mb and even at 300 mb.

Kato, S.↗
NASA NTRS1989

Parallel-vector solution of large-scale structural analysis problems on supercomputers

A direct linear equation solution method based on the Choleski factorization procedure is presented which exploits both parallel and vector features of supercomputers. The new equation solver is described, and its performance is evaluated by solving structural analysis problems on three high-performance computers. The method has been implemented using Force, a generic parallel FORTRAN language.

Storaasli, Olaf O.↗
NASA NTRS1989

Shock structure in non-circular jets

The shock-cell structure of supersonic jets with non-circular exit geometry is modeled using a linearized analysis. The model takes into account the finite thickness of the jet shear layer using realistic velocity and density profiles. The effects of the shear layer turbulence are included by incorporating eddy-viscosity terms. A finite-difference numerical method is used to solve the steady linearized equations of motion. A body-fitted coordinate system is used to describe the shear layer. The variation of the pressure fluctuation with downstream distance is given for circular jets and for an elliptic jet of aspect ratio 2.0. Comparisons with experimental data are made. Difficulties with the numerical technique are also discussed.

Morris, Philip J.↗
NASA NTRS1990

Output model-following control synthesis for an oblique-wing aircraft

Recent interest in oblique-wing aircraft has focused on the potential aerodynamic performance advantage of a variable-skew oblique wing over a conventional or symmetric sweep wing. Unfortunately, the resulting asymmetric configuration has significant aerodynamic and inertial cross-coupling between the aircraft longitudinal and lateral-directional axes. Presented here is a decoupling control law synthesis technique that integrates stability augmentation, decoupling, and the direct incorporation of desired handling qualities into an output feedback controller. The proposed design technique uses linear quadratic regulator concepts in the framework of explicit model following. The output feedback strategy used is a suboptimal projection from the state space to the output space. Dynamics are then introduced into the controller to improve steady-state performance and increase system robustness. Closed-loop performance is shown by application of the control laws to the linearized equations of motion and nonlinear simulation of an oblique-wing aircraft.

Pahle, Joseph W.↗
NASA NTRS1989

Thin-plate spline quadrature of geodetic integrals

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman↗
NASA NTRS1989

Modal identities for multibody elastic spacecraft: An aid to selecting modes for simulation

The question: Which set of modes furnishes a higher fidelity math model of dynamics of a multibody, deformable spacecraft (hinges-free or hinges-locked vehicle modes) is answered. Two sets of general, discretized, linear equations of motion of a spacecraft with an arbitrary number of deformable appendages, each articulated directly to the core body, are obtained using the above two families of modes. By a comparison of these equations, ten sets of modal identities are constructed which involve modal momenta coefficients and frequencies associated with both classes of modes. The sums of infinite series that appear in the identities are obtained in terms of mass, and first and second moments of inertia of the appendages, core body, and vehicle by using certain basic identities concerning appendage modes. Applying the above identities to a four-body spacecraft, the hinges-locked vehicle modes are found to yield a higher fidelity model than hinges-free modes, because the latter modes have nonconverging modal coefficients; a characteristic proved and illustrated.

Hablani, Hari B.↗
NASA NTRS1988

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Bailey, David H.↗
NASA NTRS1989

A numerical study of the interaction between unsteady free-stream disturbances and localized variations in surface geometry

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite-difference and spectral methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves.

Bodonyi, R. J.↗
NASA NTRS1990

Effect of nose bluntness on boundary layer stability and transition

The effect of nose bluntness on boundary layer instability is studied theoretically for a Mach 8 flow past a 7 degree semivertex cone. The basic flow is computed by solving the parabolized Navier-Stokes equations. Linear stability analysis of the basic flow reveals that, with small amount of bluntness, the critical Reynolds number for the onset of instability increases by an order of magnitude compared to the sharp cone value. The computed second mode frequencies are also in reasonable agreement with the experimental results. The results are used to explain the effect of unit Reynolds number on transition present in the quiet aeroballistic range data.

Malik, M. R.↗