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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Generalization and extension of the law of acoustic energy conservation in a nonuniform flow

An exact conservation equation is derived which generalizes the familiar acoustic energy equations. The new relation is valid for arbitrary disturbances to a viscous, compressible flow. It is suggested by a development of the acoustic energy equation by means of a regular perturbation expansion of the general energy equation of fluid mechanics. A perturbation energy density and flux are defined and identified as the exact physical quantities whose leading order perturbation representations are the usual acoustic energy density and flux. The conservation equation governing the perturbation energy quantities is shown to yield previously known results for several special cases.

Myers, M. K.↗
NASA NTRS1986

A generalized theory for eccentric and misalignment effects in high-pressure annular seals

High-pressure annular seal leakage and dynamic coefficients vary with eccentricity and misalignment. Recent seal leakage data with both concentric and fully eccentric alignments support the seal leakage model with surface roughness and eccentricity effects included. In this paper, the seal dynamic coefficient calculation has been generalized and allows direct calculation of the seal dynamic coefficients at any circumferential location. The generalized solution agrees with the results obtained by using the calculated values of an earlier paper and performing a coordinate transformation. The analysis results coincide with the measured data in showing that the stiffness and damping matrices of seal coefficients are not skew symmetric, and the main diagonal seal coefficients are not equal. The measured direct stiffnesses were found higher than predicted by the concentric seal theory, but this may be explained by the presence of eccentricity in the test operating mode.

Chen, W. C.↗
NASA NTRS1984

Application of the generalized reduced gradient method to conceptual aircraft design

The complete aircraft design process can be broken into three phases of increasing depth: conceptual design, preliminary design, and detail design. Conceptual design consists primarily of developing general arrangements and selecting the configuration that optimally satisfies all mission requirements. The result of the conceptual phase is a conceptual baseline configuration that serves as the starting point for the preliminary design phase. The conceptual design of an aircraft involves a complex trade-off of many independent variables that must be investigated before deciding upon the basic configuration. Some of these variables are discrete (number of engines), some represent different configurations (canard vs conventional tail) and some may represent incorporation of new technologies (aluminum vs composite materials). At Lockheed-Georgia, the sizing program is known as GASP (Generalized Aircraft Sizing Program). GASP is a large program containing analysis modules covering the many different disciplines involved fin defining the aricraft, such as aerodynamics, structures, stability and control, mission performance, and cost. These analysis modules provide first-level estimates the aircraft properties that are derived from handbook, experimental, and historical sources.

Gabriele, G. A.↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described, allow modeling of wing cross sections having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗
NASA NTRS1987

On the eigenvalue and eigenvector derivatives of a general matrix

The existence of differentiable eigenvalues and eigenvectors for a general matrix is addressed. The eigenspace which contains differentiable eigenvectors is determined and computed by using the concept of subspace intersection in conjunction with the singular value decomposition algorithm. The differentiable eigenvectors associated with repeated eigenvalues should be simultaneously the eigenvectors of the general matrix and its corresponding sensitivity matrix. Furthermore, the derivatives for differentiable eigenvectors associated with repeated eigenvalues can be computed using higher order derivatives of the matrix, whereas the corresponding eigenvalue derivatives are the eigenvalues of the sensitivity matrix.

Juang, Jer-Nan↗
NASA NTRS1986

General object-oriented software development

Object-oriented design techniques are gaining increasing popularity for use with the Ada programming language. A general approach to object-oriented design which synthesizes the principles of previous object-oriented methods into the overall software life-cycle, providing transitions from specification to design and from design to code. It therefore provides the basis for a general object-oriented development methodology.

Seidewitz, Edwin V.↗
NASA NTRS1987

A generalized procedure for constructing an upwind based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some linear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to scalar nonlinear equations and a constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance in numerical experiments. The formulation is extended to the nonlinear system. It is demonstrated that the present procedure can easily convert existing central or upwind, and second- or higher-order differencing schemes to preserve monotonicity and yield physically admissible solutions. The formulation is simple mathematically as well as numerically; both matrix-vector multiplication and Riemann solver are avoided. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made.

Liou, Meng-Sing↗
NASA NTRS1987

Flight duration, airspeed practices and altitude management of airplanes involved in the NASA VGH General Aviation Program

Flight duration, airspeed, and altitude information obtained from NASA velocity gravity height (VGH) recorders is presented for each of 95 general aviation airplanes flown in twin- and single-engine executive, personal, instructional, commercial survey, aerial application, aerobatic, commuter, and float operations. These data complement normal acceleration data obtained from the same airplanes and reported in NASA-TM-84660, and together they provide a data base for the design and analysis of general aviation airplane operations.

Jewel, Joseph W., Jr.↗
NASA NTRS1986

Teleparallelism as a universal connection on null hypersurfaces in general relativity

It is shown that a close relationship between the inner geometry of a null hypersurface N3 and the Newman-Penrose (NP) (1962, 1963) spin coefficient formalism exists. Projecting the null complex NP tetrad onto N3, two triads of basis vectors in N3 are obtained. The inner geometry of N3 is based on the assumption that these vectors are parallelly transported along the surface; this gives rise to the teleparallel connection as a metric nonsymmetric affine connection. The gauge freedom for the choice of the basis triads is given by the isotropy subgroup of the local Lorentz group leaving invariant the direction of the null generators of N3, and teleparallelism is determined by the equivalence class of the basis triads with respect to the global gauge group. Nine of the twelve NP coefficients are identified as the triad components of the torsion and the second fundamental form of N3. The resulting generalized Gauss-Codazzi equations are identical to nine of the NP equations, i.e., to the half of the Ricci identities. This result gives a geometrical meaning to the entire formalism. Finally a general proof of Penrose's theorem that the shear of the null generators of N3 is the only initial null datum for a gravitational field on N3 is presented.

Mazur, P. O.↗
NASA NTRS1986

Application of propfan propulsion to general aviation

Recent studies of advanced propfan propulsion systems have shown significant reductions in fuel consumption of 15-30 percent for transport class aircraft. This paper presents the results of a study which examined applying propfan propulsion to General Aviation class aircraft to determine if similar improvements could be achieved for business aircraft. In addition to the potential performance gains, this paper also addresses the cost aspects of propfan propulsion on General Aviation aircraft emphasizing the significant impact that the cost of capital and tax aspects have on determining the total cost of operation for business aircraft.

Awker, R. W.↗
NASA NTRS1986

Energetics analysis of the observed and simulated general circulation using three-dimensional normal mode expansions

The energetics characteristics of the observed and simulated general circulation are analyzed using three-dimensional normal mode expansions. The data sets involved are the Goddard Laboratory for Atmospheres (GLA) analysis and simulation data and the Geophysical Fluid Dynamics Laboratory (GFDL) analysis data. The spectral energy properties of the Rossby and gravity modes and energy transformations are presented. Significant influences of model characteristics and the assimilation techniques are observed in the barotropic energy spectrum, particularly for the gravity mode. Energy transformations of the zonal mean field in the GLA analysis and simulation are similar, but distinctly different from that in the GFDL analysis. However, overall, the energy generation in the baroclinic mode is largely balanced by the sink in the barotropic mode. The present study may demonstrate utilities of the three-dimensional normal mode energetics in the analysis of the general circulation.

Tanaka, Hiroshi↗
NASA NTRS1987

A generalized procedure for constructing an upwind-based TVD scheme

A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.

Liou, Meng-Sing↗
NASA NTRS1987

General surface equations for glancing incidence telescopes

A generalized set of equations are derived for two mirror glancing incidence telescopes using Fermat's principle, a differential form of the law of reflection, the generalized sine condition, and a ray propagation equation described in vector form as a theoretical basis. The resulting formulation groups the possible telescope configurations into three distinct classes which are the Wolter, Wolter-Schwarzschild, and higher-order telescopes in which the Hettrick-Bowyer types are a subset. Eight configurations are possible within each class depending on the sign and magnitude of the parameters.

Saha, Timo T.↗
NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described in this paper, allow modeling of wing cross section having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗
NASA NTRS1987

New test of general relativity - Measurement of de Sitter geodetic precession rate for lunar perigee

According to general relativity, the calculated rate of motion of lunar perigee should include a contribution of 19.2 msec/yr from geodetic precession. It is shown that existing analyses of lunar-laser-ranging data confirm the general-relativistic rate for geodetic precession with respect to the planetary dynamical frame. In addition, the comparison of earth-rotation results from lunar laser ranging and from VLBI shows that the relative drift of the planetary dynamical frame and the extragalactic VLBI reference frame is small. The estimated accuracy is about 10 percent.

Bertotti, Bruno↗
NASA NTRS1987

The role of earth radiation budget studies in climate and general circulation research

The use of earth radiation budget (ERB) data for climate and general circulation research is studied. ERB measurements obtained in the 1960's and 1970's have provided data on planetary brightness, planetary global energy balances, the greenhouse effect, solar insolation, meridional heat transport by oceans and atmospheres, regional forcing, climate feedback processes, and the computation of albedo values in low latitudes. The role of clouds in governing climate, in influencing the general circulation, and in determining the sensitivity of climate to external perturbations needs to be researched; a procedure for analyzing the ERB data, which will address these problems, is described. The approach involves estimating the clear-sky fluxes from the high spatial resolution scanner measurement and defining a cloud radiative forcing; the global average of the sum of the solar and long-wave cloud forcing yields the net radiative effect of clouds on the climate.

Ramanathan, V.↗
NASA NTRS1987

Downdrafts within High Plains cumulonimbi. I - General kinematic structure

Results from a comprehensive investigation in which observations from several case studies are integrated with three-dimensional cloud model results to examine the general kinematic structure of downdrafts associated with High Plains precipitating convection are presented. One particular downdraft type, the low-level precipitation-associated downdraft, is the focus of this paper. General airflow and trajectory patterns within low-level downdrafts are convergent from 0.8 km upwards to downdraft top, typically less than 5 km AGL. Observed mass flux profiles often increase rapidly with height as a result of strong buoyancy forcing below the melting level. Inflow to the low-level downdraft, although vertically continuous can be separated into two branches. The up-down branch originating within the planetary boundary layer initially rises up to 4 km and then descends within the main precipitation-associated downdraft. The midlevel branch, usually more pronounced during early downdraft stages, originates from above the PBL and transports low-valued theta sub e air to low levels. The depth of the low-level downdraft can be approximated by the environmental sounding transition level, defined as the vertical height interval separating conditionally unstable to neutral air below from roughly stable air above. The low-level downdraft is most frequently located along the upshear storm flank relative to the updraft, although a downshear downdraft may become common under higher environmental wind shear.

Knupp, Kevin R.↗