SEARCH · Search NASA

Results for “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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

NASA NTRS1978

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response: (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate dependent aerodynamic phenomena characteristic of airfoils in low speed dynamic stall; the second permits a description of the double valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies.

Tobak, M.↗

NASA NTRS1977

An element formulation for perturbed motion about the center of mass

The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements: l, the magnitude of the angular momentum vector; h, the total energy; delta and epsilon, two linear functions of the independent variable; and psi(1) and theta (1), two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body.

Donaldson, J. D.↗

NASA NTRS1978

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate-dependent aerodynamic phenomena characteristic of airfoils in low-speed dynamic stall; the second permits a description of the double-valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies.

Tobak, M.↗

NASA NTRS1978

CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

Lee, C. H.↗

NASA NTRS1979

Dynamic loads analysis system (DYLOFLEX) summary. Volume 1: Engineering formulation

The DYLOFLEX computer program system expands the aeroelastic cycle from that in the FLEXSTAB computer program system to include dynamic loads analyses involving active controls. Two aerodynamic options exist within DYLOFLEX. The analyst can formulate the problem with unsteady aerodynamics calculated using the doublet lattice method or with quasi-steady aerodynamics formulated from either FLEXSTAB or doublet lattice steady state aerodynamics with unsteady effects approximated by indicial lift growth functions. The equations of motion are formulated assuming straight and level flight and small motions. Loads are calculated using the force summation technique. DYLOFLEX consists of nine standalone programs which can be linked with each other by magnetic files used to transmit the required data between programs.

Miller, R. D.↗

NASA NTRS1979

The computation of isentropic atmospheric trajectories using a 'discrete model' formulation

An explicit technique for calculating atmospheric trajectories is presented as an alternative method to the standard implicit scheme of Danielsen (1961). The technique uses the inviscid equations of motion and the discrete model formulation derived by Greenspan (1972, 1973) to compute trajectories on isentropic surfaces, assuming adiabatic flow. The discrete model formulation is designed specifically for a Lagrangian system and objectively accounts for the geostrophic departures, local psi-tendencies, and the subsequent accelerations along the entire length of the trajectory. Application of the discrete formulation to a diagnostic case study yielded favorable results.

Petersen, R. A.↗

NASA NTRS1979

A general and computationally fast formulation for radiative transfer with scattering

A general formulation of monocromatic radiative transfer with scattering has been developed for plane-parallel geometry. The inhomogeneous and nonisothermal medium absorbs, emits, and anisotropically scatters radiation. Surfaces can emit and scatter radiation in any specified manner. The solution procedure uses the fact that phase incoherent scattering is linear in radiative sources. Certain basic scattering functions are then defined and calculated by an adding computer code using matrix algebra. These scattering functions are weighted by the temperature field and summed (superimposed) to obtain the solution for any specific problem. Numerical results for exiting intensities and one-sided heat fluxes from general media bound by one arbitrary surface are presented. These parametric studies demonstrate the effects of scattering particles and surfaces on radiative transfer from inhomogeneous and nonisothermal media. Application of the formulation to radiative equilibrium is also discussed. The conclusion is that all problems in plane-parallel radiative transfer with scattering can be solved by a common and computationally fast algorithm based on this formulation.

Cogley, A. C.↗

NASA NTRS1980

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade.

Stephens, W. B.↗

NASA NTRS1981

An analytic formulation for heating source memory in the thermospheric composition

Numerical calculations from a spectral circulation model are utilized to construct an analytic Green's function formulation describing the meridional, time-dependent thermospheric composition and temperature response during magnetic storms. The purpose is to develop a formulation that embodies source memory while being sufficiently simple to serve as a heuristic guide for empirical modeling. By passing from the discrete Fourier series representation, utilized for the numerical circulation model, to a continuous Fourier integral representation, explicit waves are obtained for the thermospheric response times. The response times are altitude and species dependent and can exceed two days below 200 km. Thus, for certain storm scenarios, pronounced source memory signatures for the composition and temperature are predicted. Response times obtained from the formulation are shown to give a response consistent with previously published neutral composition data from AE-C for the February 1974 storm when an ap dependent heat source is employed.

Porter, H. S.↗

NASA NTRS1984

A formulation and analysis of combat games

Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games.

Heymann, M.↗

NASA NTRS1985

Characterization-curing-property studies of HBRF 55A resin formulations

Characterization curing property investigations on HBRF 55A resin formulations are reported. The initial studies on as received cured samples cut from a full-size FWC are reviewed. Inadequacies of as-received and aged samples are pointed out and additional electron microscopic evidence is offered. Characterization of as-received ingredients of HBRF 55A formulation is described. Specifically, Epon 826, Epon 828, EpiRez 5022, RD-2 and various amines, including Tonox and Tonox 60.40, were characterized. Cure kinetics of various formulations are investigated. Changes in physical/thermal properties (viscosity, specific heat, thermal conductivity and density) during cure are described.

Pearce, E. M.↗

NASA NTRS1985

A formulation and analysis of combat games

Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum differential game. Otherwise the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequencies may not exist, approximate of delta-combat games are also formulated leading to approximate or delta-optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games.

Heymann, M.↗

NASA NTRS1985

Scalar/Vector potential formulation for compressible viscous unsteady flows

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Morino, L.↗

NASA NTRS1982

Results of tests of K5NA and a revised formulation of EPDM/cork patch material in MSFC Hot Gas Facility

During prelaunch procedures at Kennedy Space Center some of the EPDM Thermal Protection System material was damaged on the Solid Rocket Booster stiffener stubs. The preferred solution was to patch the damaged areas with a cork-filled epoxy patching compound. Before this was done, however, it was requested that this patching technique be checked out by testing it in the MSFC Hot Gas Facility. Two tests were run in the HFG in 1980. The results showed the patch material to be adequate. Since that time, the formulation of the cork-filled epoxy material has been changed. It became necessary to retest this concept to be sure that the new material is as good as or better than the original material. In addition to the revised formulation material, tests were also made using K5NA as the patch material. The objectives of the tests reported herein were to: (1) compare the thermal performance of the original and the new cork-filled epoxy formulations, and (2) compare the K5NA closeout material to these epoxy materials. Material specifications are also discussed.

Dean, W. G.↗

NASA NTRS1985

On the convergence of an iterative formulation of the electromagnetic scattering from an infinite grating of thin wires

Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.

Brand, J. C.↗

NASA NTRS1984

Aeroelastic formulations for turbomachines and propellers

The task of the aeroelastic analysis is to combine the formulations of the structural dynamic and unsteady aerodynamic models in a consistent manner, to solve the resulting aeroelastic model to determine the dynamic behavior (e.g., stability, forced vibration), and to interpret those results for both qualitative trends, and quantitative detail. A review of the various formulations of the aeroelastic problem and a comparison of their relative advantages will be the subject of this paper. Specifically, the topics to be addressed are: the formulation of the aeroelastic problem, including a summary of the relations necessary to transform various diverse structural and aerodynamic models to a consistent notation for oscillatory motion; an approximate transformation for arbitrary temporal behavior; and a brief review of the applicable solution techniques.

Crawley, E. F.↗

NASA NTRS1986

Prediction of helicopter rotor discrete frequency noise: A computer program incorporating realistic blade motions and advanced acoustic formulation

A computer program has been developed at the Langley Research Center to predict the discrete frequency noise of conventional and advanced helicopter rotors. The program, called WOPWOP, uses the most advanced subsonic formulation of Farassat that is less sensitive to errors and is valid for nearly all helicopter rotor geometries and flight conditions. A brief derivation of the acoustic formulation is presented along with a discussion of the numerical implementation of the formulation. The computer program uses realistic helicopter blade motion and aerodynamic loadings, input by the user, for noise calculation in the time domain. A detailed definition of all the input variables, default values, and output data is included. A comparison with experimental data shows good agreement between prediction and experiment; however, accurate aerodynamic loading is needed.

Brentner, K. S.↗

NASA NTRS1986

Electrically conductive, black thermal control coatings for spacecraft application. I - Silicate matrix formulation

The formulation of the graphite silicate paints MH-11 and MH-11Z, which will serve as electrically conductive, heat-resistant thermal control coatings for the Galileo spacecraft's 400 Newton engine plume shield, 10 Newton thruster plume shields, and external shunt radiators, is described, and performance results for these paints are reported. The MH-11 is produced by combining a certain grade of graphite powder with a silicate base to produce a black, inorganic, electrically conductive, room temperature cure thermal control paint having high temperature capability. Zinc oxide is added to the MH-11 formulation to produce the blister resistant painta MH-11Z. The mechanical, chemical, thermal, optical, and radiation characteristics of the coatings are reported. The formulation, mixing, application, and surface preparation of the substrates are described, and a method of determining the electrical resistance of the coatings is demonstrated.

Bauer, J. L.↗