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At least 433 records · Page 24

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NASA NTRS1979

A finite element formulation of the eigenvalue problem in lined ducts with flow

A finite element method is used to formulate the eigenvalue problem for a lined duct with flow. Either two dimensional or axially symmetric ducts with sheared flows can be studied, although the examples cited are two dimensional. The primitive variables of velocity and pressure are used with quadratic shape functions in each element. Results indicate that a useful level of accuracy can be achieved with a modest number of elements. Spurious eigenvalues, easily identified by obviously inconsistent eigenvectors, occur in certain instances. If the number of elements is not too small, these spurious modes are among the higher order eigenvalues of otherwise questionable accuracy. The possibility of using higher order elements which have slope continuity is proposed for future investigations to eliminate the spurious results.

Astley, R. J.↗

NASA NTRS1979

Evaluation of finite element formulations for transient conduction forced-convection analysis

Numerical studies clarifying the advantages and disavantages of conventional versus upwind convective finite elements are presented along with lumped versus consistent formulations for practical conduction forced-convection analysis. A finite-element procedure for treatment of negligible capacitance fluid nodes is presented. The procedure is based on procedures used in finite-element structural dynamics to treat nodes with negligible structural mass. Two finite-element programs and a finite-difference lumped-parameter program used in the studies are discussed. Evaluation studies utilizing three convection and two combined conduction-convection problems are then presented and discussed. Additionally, the computational time saving offered by the finite element procedure is considered for a practical combined conduction-convection problem.

Thornton, E. A.↗

NASA NTRS1979

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Daniele, C. J.↗

NASA NTRS1980

The analysis of delays in simulator digital computing systems. Volume 1: Formulation of an analysis approach using a central example simulator model

The effects of spurious delays in real time digital computing systems are examined. Various sources of spurious delays are defined and analyzed using an extant simulator system as an example. A specific analysis procedure is set forth and four cases are viewed in terms of their time and frequency domain characteristics. Numerical solutions are obtained for three single rate one- and two-computer examples, and the analysis problem is formulated for a two-rate, two-computer example.

Heffley, R. K.↗

NASA NTRS1978

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Lee, S. S.↗

NASA NTRS1980

Nonlinear finite element analysis: An alternative formulation

A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.

Merazzi, S.↗

NASA NTRS1979

Formulation of coupled rotor/fuselage equations of motion

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which can be used to study coupled rotor/fuselage dynamics in forward flight. The methodology of rotor/fuselage coupling is clearly described and the importance of an ordering scheme in deriving consistent nonlinear equations of motion is reviewed. The final equations which are presented in partial differential form can be used to model coupled rotor/fuselage aeroelastic response or stability problems.

Warmbrodt, W.↗

NASA NTRS1979

Evaluation of finite element formulations for transient conduction forced-convection analysis

Conventional versus upwind convective finite elements, and lumped versus consistent formulations for practical conduction/forced convection analysis are evaluated on the basis of numerical studies, with finite element and finite difference lumped-parameter temperatures compared to closed-form analytical solutions for convection problems. Attention is given to two practical combined conduction and forced convection applications, stressing that the finite element method, showing superior accuracy, is competitive with the finite difference lumped-parameter method. Also considered are the computational time savings offered by the zero capacitance nodes procedure and comparative finite element and finite difference lumped-parameter computer times. The present study has reference to the design of actively cooled engine and airframe structures for hypersonic flight.

Thornton, E. A.↗

NASA NTRS1979

Formulations and applications of large structure actuator and sensor placements

A new approach based on the steady-state solutions of the optimal control and estimation problems is presented to study respectively the actuator and sensor locations for large flexible structures. A simple and computer-implementable formulation for minimizing the steady state optimal cost function and the state estimation error inherent in the estimation process is given. In conjunction with the new approach, two criteria are established relating the actuator and the sensor placement optimalities respectively to the minimums of the optimal cost function and the state estimation error. To illustrate the concepts of this paper, we present the results of some numerical and analytical studies on the actuator and the sensor locations of several simple flexible beam modes.

Juang, J.-N.↗

NASA NTRS1980

The finite element duct eigenvalue problem - An improved formulation with Hermitian elements and no-flow condensation

Hermitian elements are used in a finite element solution for the eigenvalue problem in lined ducts with flow. These elements give significantly greater accuracy for reduced dimensionality when compared with Lagrangian elements. Spurious mode generation associated with the Lagrangian formulation is eliminated. A dramatic improvement in the ratio of the number of reliable eigenvalues to the total number of computed eigenvalues is effected by the use of a condensation scheme based on the no-flow eigenvectors. Results are presented for two dimensional and axisymmetric ducts. In the axisymmetric case good resolution is obtained even for high order, high frequency modes by the use of continuously graded meshes.

Astley, R. J.↗

NASA NTRS1980

Formulation and evaluation of C-Ether fluids as lubricants useful to 260 C

Three base stocks were evaluated in bench and bearing tests to determine their suitability for use at bulk oil temperatures (BOT) from -40 C to +260 C. A polyol ester gave good bearing tests at a bulk temperature of 218 C, but only a partially successful run at 274 C. These results bracket the fluid's maximum operating temperature between these values. An extensive screening program selected lubrication additives for a C-ether (modified polyphenyl ether) base stock. One formulation lubricated a bearing for 111 hours at 274 C (BOT), but this fluid gave many deposit related problems. Other C-ether blends produced cage wear or fatigue failures. Studies of a third fluid, a C-ether/disiloxane blend, consisted of bench oxidation and lubrication tests. These showed that some additives react differently in the blend than in pure C-ethers.

Clark, F. S.↗

NASA NTRS1981

Case studies of clear air turbulence using the diagnostic Richardson Number Tendency formulation

The results of four case studies of clear air turbulence (CAT) using the diagnostic Richardson number tendency (DRT) formulation are highlighted. The performance of this technique in resolving regions of documented CAT encounters is encouraging. Its operational adaptability appears particularly attractive in that input data can be supplied by the currently operational rawinsonde system. Two CAT indices are calculated deterministically, sensing synoptic scale changes in static stability and vertical wind shear conductive for supporting mesoscale CAT layers. These two indices reveal volumes of the troposphere which act as source regions for patches of CAT. The first, the time to reach the critical Richardson number necessary for the initiation of turbulent conditions, was first used by Oard (1974). A second index is devised which is an adaptation of Roach's (1970) work relating synoptic scale and mesoscale energetical coupling and gives more information on the relative intensity of these source regions. The output from the DRT computer module highlights specific regions of the atmosphere which can be interpreted operationally in terms of a CAT encounter probability.

Keller, J. L.↗

NASA NTRS1980

Payloads minimum EIRP formulations

The effective isotropic radiated power (EIRP) of the payloads is formulated. The EIRP consists of three components; EIRP = P sub T + G sub T + L sub TX, where P sub T is the transmitter total RF output power, G sub T is the transmitting antenna gain, and L sub TX is all transmitter circuit losses.

Source record↗

NASA NTRS1980

A note on a Lagrangian formulation for motion about the collinear points

A Lagrangian formulation for the three-dimensional motion of a satellite in the vicinity of the collinear points of the circular-restricted problem is reconsidered. It is shown that the influence of the primaries can be expressed in the form of two third-body disturbing functions. By use of this approach, the equations for the Lagrangian and for the motion itself are readily developed into highly compact expressions. All orders of the non-linear developments are shown to be easily obtainable using well-known recursive relationships. The resulting forms for these equations are well suited for use in the initial phase of canonical or non-canonical investigations.

Richardson, D. L.↗

NASA NTRS1981

Forecasting of Clear Air Turbulence using a Diagnostic Richardson Number Tendency formulation

The results of several case studies of Clear Air Turbulence (CAT) using the Diagnostic Richardson Number Tendency (DRT) formulation are highlighted. The performance of this technique in resolving regions of documented CAT encounters is encouraging. Its operational adaptability seems particularly attractive in that the input data can be supplied by the currently operational Rawinsonde system. A CAT index is calculated deterministically, sensing synoptic-scale changes in static stability and vertical wind shear conducive for supporting meso-scale CAT layers. This index reveals volumes of the troposphere which act as 'source regions' of Kelvin-Helmholtz instabilities. The results suggest that these regions are particularly efficient with respect to the synoptic/meso-scale energetical coupling necessary for supporting significantly turbulent layers. The output highlights specific regions of the atmosphere which can be interpreted operationally in terms of CAT-encounter probabilities.

Keller, J. L.↗

NASA NTRS1980

Analysis of aromatic polyamine mixtures for formulation of LARC-160 resin

An investigation was conducted to identify a potential substitute for the aromatic polyamine mixture, Jeffamine AP-22, currently used to formulate LARC-160 polyimide precursor resin. Jeffamine AP-22 was characterized by high pressure liquid chromatography and mass spectrometry. Eleven different aromatic amines in the mixture were isolated and identified. Subsequent liquid chromatographic analysis of nine additional commercially available aromatic polyamine mixtures identified three candidates that are similar in composition to AP-22.

Young, P. R.↗

NASA NTRS1980

Generic multi-body formulation of heavy lift airship equations of motion

This paper describes the formulation of a comprehensive set of equations which describe the dynamic behavior of a generic heavy lift airship (HLA). They are being used in a digital computer simulation to investigate the response dynamics and flying qualities of HLAs operating with various payloads in a variety of operational environments. A key feature is the separate treatment of each component body making up the HLA. This allows the analyst to vary the configuration (e.g., number of lift-propulsion units, presence or absence of slung payload, etc.) without rewriting the equations. It further provides measures of key structural and control loads acting on the HLA and eases the task of modeling wind disturbances.

Ringland, R. F.↗

NASA NTRS1981

Formulation of a dynamic analysis method for a generic family of hoop-mast antenna systems

Analytical studies of mast-cable-hoop-membrane type antennas were conducted using a transfer matrix numerical analysis approach. This method, by virtue of its specialization and the inherently easy compartmentalization of the formulation and numerical procedures, can be significantly more efficient in computer time required and in the time needed to review and interpret the results.

Gabriele, A.↗