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Results for “Variational formulation”

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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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Solar luminosity variations and the climate of Mars

Attempts to resolve the solar neutrino flux problem have led to suggestions of large scale oscillations in the solar luminosity on a geological time scale. A simple climatological model of Mars indicates that its climate may be much more sensitive to luminosity changes than the earth's because of strong positive feedback mechanisms at work on Mars. Mariner-9 photographs of Mars show an abundance of large sinuous channels that point to an epoch of higher atmospheric pressures and abundant liquid water. Such an epoch could have been the result of large-scale, solar luminosity variations. However, our climatological model suggests that other less controversial mechanisms, such as obliquity or polar albedo changes, also could have led to such an epoch. As more becomes known about Mars, it may prove possible to formulate a history of Martian climate. By discovering effects that cannot be due to other mechanisms one may be able to form a chronology of solar luminosity variations to compare with data from the earth.

Toon, O. B.↗
NASA NTRS1976

Design of efficient stiffened shells of revolution

A method to produce efficient piecewise uniform stiffened shells of revolution is presented. The approach uses a first order differential equation formulation for the shell prebuckling and buckling analyses and the necessary conditions for an optimum design are derived by a variational approach. A variety of local yielding and buckling constraints and the general buckling constraint are included in the design process. The local constraints are treated by means of an interior penalty function and the general buckling load is treated by means of an exterior penalty function. This allows the general buckling constraint to be included in the design process only when it is violated. The self-adjoint nature of the prebuckling and buckling formulations is used to reduce the computational effort. Results for four conical shells and one spherical shell are given.

Majumder, D. K.↗
NASA NTRS1994

Controllability of Free-piston Stirling Engine/linear Alternator Driving a Dynamic Load

This paper presents the dynamic behavior of a Free-Piston Stirling Engine/linear alternator (FPSE/LA) driving a single-phase fractional horse-power induction motor. The controllability and dynamic stability of the system are discussed by means of sensitivity effects of variations in system parameters, engine controller, operating conditions, and mechanical loading on the induction motor. The approach used expands on a combined mechanical and thermodynamic formulation employed in a previous paper. The application of state-space technique and frequency domain analysis enhances understanding of the dynamic interactions. Engine-alternator parametric sensitivity studies, similar to those of the previous paper, are summarized. Detailed discussions are provided for parametric variations which relate to the engine controller and system operating conditions. The results suggest that the controllability of a FPSE-based power system is enhanced by proper operating conditions and built-in controls.

Kankam, M. David↗
NASA NTRS1972

Information extraction techniques for multi-spectral scanner data

Multispectral data recognition and information extraction problems considered are: (1) signature extension for improved recognition processing over large areas; (2) choice of density functions for recognition decision rules; (3) channel selection for cost reduction; and (4) radiation balance mapping for interpretation of wide spectrum scanner data. The formulation of a simulation model and reprocessing of both aircraft and space data reduces scan angle variations and extends signatures from one altitude to another. Comparison of the usefulness of empirical density functions and that of Gaussian density functions for recognition processing establishes the advantages of normal assumption for individual fields in processing of multispectral scanner data. Also reported is a procedure for producing radiation balance maps from wide spectra by analyzing energy budgets of vegetation and other surface materials through partitioning net absorbed radiant energy and estimating incoming power density at both short and long wavelengths.

Malila, W. A.↗
NASA NTRS1981

Green's function for cracks of equal length from a circular hole in an infinite sheet

Stress-intensity factors are obtained for twin collinear cracks emanating from a hole in an infinite plate. Point forces that tend to make the crack surfaces separate and slide are applied to one of the cracks. A conformal mapping and the Muskelishvili formulation involving series representation of the Kolosov stress functions are used to derive the solutions. The variation of stress-intensity factor with crack length and with point of application of the loads is presented for both crack tips.

Shivakumar, V.↗
NASA NTRS1989

Aerodynamics of engine-airframe interaction

The development of the variational approach for the solution of inviscid aerodynamic problems using solution adaptive grids is discussed. The formulation of a new, directional weighting, functional has been shown to have desirable properties. The scheme has been applied to compute the transonic flow past two-dimensional airfoils using the Euler equations of inviscid, compressible flow. Transonic flows in quasi-one-dimensional nozzles and over the two dimensional airfoils are solved on the various solution-adaptive-grids to demonstrate the applicability of the proposed directional-concentration functional and the grid adaptation process from the stand point of improving the solution accuracy and demonstrating the overall convergence.

Caughey, David A.↗
NASA NTRS1990

Structural concept studies for a horizontal cylindrical lunar habitat and a lunar guyed tower

A conceptual structural design of a horizontal cylindrical lunar habitat is presented. The design includes the interior floor framing, the exterior support structure, the foundation mat, and the radiation shielding. Particular attention was given on its efficiency in shipping and field erection, and on selection of structural materials. Presented also is a conceptual design of a 2000-foot lunar guyed tower. A special field erection scheme is implemented in the design. In order to analyze the over-all column buckling of the mast, where its axial compression includes its own body weight, a simple numerical procedure is formulated in a form ready for coding in FORTRAN. Selection of structural materials, effect of temperature variations, dynamic response of the tower to moonquake, and guy anchoring system are discussed. Proposed field erection concepts for the habitat and for the guyed tower are described.

Yin, Paul K.↗
NASA NTRS1992

H-infinity synthesis using a bilinear pole shifting transform

An H-inifinity control law design is presented for a benchmark problem consisting of an undamped pair of spring-coupled masses with a sensor and actuator that are not collocated. This simple mechanical system captures many of the salient features of more complex aircraft and space structure vibration control problems. The H-infinity problem formulation enables the issue of stability robustness in the face of large mass and spring constant variation to be directly addressed. Constraints on closed-loop dominant pole locations and settling time are accommodated via a simple s-plane bilinear transform. The transform parameter can give direct control of closed-loop disturbance settling time and controller open-loop pole-zero locations. A four-state H-infinity minimum phase controller was found to meet the given specifications of each design. Detailed analysis on the tradeoffs of sensor noise vs control energy are also presented.

Chiang, R. Y.↗
NASA NTRS1960

Heat Transfer to Longitudinal Laminar Flow Between Cylinders

Consideration is given to the fully developed heat transfer characteristics for longitudinal laminar flow between cylinders arranged in an equilateral triangular array. The analysis is carried out for the condition of uniform heat transfer per unit length. Solutions are obtained for the temperature distribution, and from these, Nusselt numbers are derived for a wide range of spacing-to-diameter ratios. It is found that as the spacing ratio increases, so also does the wall-to-bulk temperature difference for a fixed heat transfer per unit length. Corresponding to a uniform surface temperature around the circumference of a cylinder, the circumferential variation of the local heat flux is computed. For spacing ratios of 1.5 - 2.0 and greater, uniform peripheral wall temperature and uniform peripheral heat flux are simultaneously achieved. A simplified analysis which neglects circumferential variations is also carried out, and the results are compared with those from the more exact formulation.

Sparrow, Ephraim M.↗
NASA NTRS1987

Variational approach to probabilistic finite elements

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
NASA NTRS1991

Variational approach to probabilistic finite elements

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Belytschko, T.↗
NASA NTRS1973

Comparison of finite-difference schemes for analysis of shells of revolution

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Noor, A. K.↗
NASA NTRS1986

Gust response of hingeless rotors

The gust response of a coupled hingeless rotor-fuselage system is studied in both hover and forward flight. Each rotor blade undergoes flap bending, lag bending, and torsional deflections. The blades are discretized into beam elements, each with fifteen nodal degrees of freedom. The fuselage is permitted three translational (vertical, longitudinal, and lateral) and two rotational (pitch and roll) degrees of freedom. The formulation considers a three-dimensional gust field wherein each gust velocity component can have an arbitrary variation in space and time. Aerodynamic loads are obtained using quasisteady strip theory. Wake-induced effects are introduced through dynamic inflow modeling. Dynamic stall and reverse flow effects are also included. Equations governing the rotor-fuselage gust response are linearized about the vehicle propulsive trim state and the blade steady-state defected positions, and solved by time integration. The effects of several parameters on the helicopter gust response are illustrated, including dynamic inflow, lag stiffness, forward speed, gust profile, gust penetration rate, and gust velocity direction.

Bir, G. S.↗
NASA NTRS1986

Theoretical comments on the nature of the plasmapause

The traditional theoretical interpretations of the observed plasmapause are compared, namely, the plasmapause as: (1) The boundary between closed flux tubes that have been in the inner magnetosphere for several days and those that have recently drifted in from the magnetotail or (2) the last closed electric equipotential. Although the two interpretations become equivalent in the case where the electric-field pattern is steady for several days, interpretation 1 seems theoretically more secure for typical magnetospheric conditions, due to the essentially time-dependent nature of the magnetospheric electric field. The results of old theoretical studies of the effects of time variations in the electric-field pattern on the shape of the plasmapause are reviewed briefly. The formulation of the present version of the Rice Convection Model is also reviewed. Preliminary results of recent computations of quiet-time electric fields, carried out with this model, are presented and discussed. Quiet-time thermospheric winds are found to have only minor effects on drift paths of magnetospheric particles.

Wolf, R. A.↗
NASA NTRS1987

Shock structure in jets of arbitrary exit geometry

The shock structure and hydrodynamic stability of single and twin jets with arbitrary exit geometry are studied. Both vortex sheets and realistic mean profiles are considered for the jet shear layer. The boundary element method is used to predict the shock spacing and screech tones in a vortex sheet model of a single jet. Results are given for circular, elliptic and rectangular jets and the results compared with analysis and experiment. A finite difference technique is used to examine the effect of finite mixing layer thickness for a single jet. The hydrodynamic stability of twin circular jets is also considered. The variation of the stability characteristics are presented for the vortex sheet case for several separation distances. The formulation of the problem to account for finite thickness effects is also given.

Morris, P. J.↗
NASA NTRS1998

A Simple Model of Cirrus Horizontal Inhomogeneity and Cloud Fraction

A simple model of horizontal inhomogeneity and cloud fraction in cirrus clouds has been formulated on the basis that all internal horizontal inhomogeneity in the ice mixing ratio is due to variations in the cloud depth, which are assumed to be Gaussian. The use of such a model was justified by the observed relationship between the normalized variability of the ice water mixing ratio (and extinction) and the normalized variability of cloud depth. Using radar cloud depth data as input, the model reproduced well the in-cloud ice water mixing ratio histograms obtained from horizontal runs during the FIRE2 cirrus campaign. For totally overcast cases the histograms were almost Gaussian, but changed as cloud fraction decreased to exponential distributions which peaked at the lowest nonzero ice value for cloud fractions below 90%. Cloud fractions predicted by the model were always within 28% of the observed value. The predicted average ice water mixing ratios were within 34% of the observed values. This model could be used in a GCM to produce the ice mixing ratio probability distribution function and to estimate cloud fraction. It only requires basic meteorological parameters, the depth of the saturated layer and the standard deviation of cloud depth as input.

Smith, Samantha A.↗
NASA NTRS2017

Food Fortification Stability Study

This study aimed to assess the stability of vitamin content, sensory acceptability and color variation in fortified spaceflight foods over a period of two years. Findings will help to identify optimal formulation, processing, and storage conditions to maintain stability and acceptability of commercially available fortification nutrients. Changes in food quality were monitored to indicate whether fortification affects quality over time (compared to the unfortified control), thus indicating their potential for use on long-duration missions.

Sirmons, T. A.↗
NASA NTRSDate not supplied

Sonic Boom Ground Noise Minimization Via the Adjoint Method

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by the sonic boom of a high altitude supersonic body is presented. A Cartesian Euler flow solver is coupled with an atmospheric propagation tool to create a ground-noise analysis capability for supersonic bodies. Adjoint formulations for both the flow solver and propagation tool are also coupled to compute sensitivities of shape variations in the body in a highly efficient manner. A gradient-based optimizer is then introduced to forge a valuable design capability. Output-based mesh adaptation that is driven directly by ground-level noise is employed to increase accuracy and provide error estimation. The design method is demonstrated first on a simple axisymmetric body with few design variables to evaluate the efficacy of the optimization scheme. Guided by the results of this initial case, the problem is then repeated with somewhat different design variables to further demonstrate the capabilities of the design method. Finally, the method is applied to a real-world problem by optimizing control surface deflection settings of a low-boom aircraft to minimize ground noise while maintaining trimmed, level flight.

ARMD↗