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At least 91 records · Page 5

Recent developments in finite element analysis for transonic airfoils

The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.

Hafez, M. M.↗

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗

Structural expansions for the ground state energy of a simple metal

A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.

Hammerberg, J.↗

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗

Global sensitivity to velocity errors at the libration points

The global effects on non-linear stability are investigated at and around the triangular libration points. The model of the circular restricted problem of three bodies is used, considering the earth and the moon as the primaries. Areas of the initial conditions in the configuration space leading to stability with zero initial velocity around the equilibrium points are compared to stable areas in the phase space with variable initial velocity and zero initial deviations at the equilibrium points. The behavior of the system concerning errors due to initial conditions in the configuration space is studied for 6 years and the effects of initial velocity errors are considered for 7.73 years.

Szebehely, V.↗

Estimation of effective hydrologic properties of soils from observations of vegetation density

An existing one-dimensional model of the annual water balance is reviewed. Slight improvements are made in the method of calculating the bare soil component of evaporation, and in the way surface retention is handled. A natural selection hypothesis, which specifies the equilibrium vegetation density for a given, water limited, climate-soil system, is verified through comparisons with observed data and is employed in the annual water balance of watersheds in Clinton, Ma., and Santa Paula, Ca., to estimate effective areal average soil properties. Comparison of CDF's of annual basin yield derived using these soil properties with observed CDF's provides excellent verification of the soil-selection procedure. This method of parameterization of the land surface should be useful with present global circulation models, enabling them to account for both the non-linearity in the relationship between soil moisture flux and soil moisture concentration, and the variability of soil properties from place to place over the Earth's surface.

Tellers, T. E.↗

Squeeze-film dampers for turbomachinery stabilization

A technique for investigating the stability and damping present in centrally preloaded radially symmetric multi-mass flexible rotor bearing systems is presented. In general, one needs to find the eigenvalues of the linearized perturbation equations, though zero frequency stability maps may be found by solving as many simultaneous non-linear equations as there are dampers; and in the case of a single damper, such maps may be found directly, regardless of the number of degrees of freedom. The technique is illustrated for a simple symmetric four degree of freedom flexible rotor with an unpressurized damper. This example shows that whereas zero frequency stability maps are likely to prove to be a simple way to delineate multiple solution possibilities, they do not provide full stability information. Further, particularly for low bearing parameters, the introduction of an unpressurized squeeze film damper may promote instability in an otherwise stable system.

Mclean, L. J.↗

Raman Scattering from Atmospheric Nitrogen in the Stratosphere

The Mark II laser radar system at Kingston, Jamaica, has been used to make observations on the Raman shifted line from atmospheric nitrogen at 828.5 nm. The size of the system makes it possible to detect signals from heights of up to 40 kilometres. The effects of aerosol scattering observed using a single wavelength are almost eliminated, and a profile of nitrogen density may be obtained. Assuming a constant mixing ratio, this may be interpreted as a profile of atmospheric density whose accuracy is comparable to that obtained from routine meteorological soundings. In order to obtain an accurate profile several interfering effects have had to be examined and, where necessary, eliminated. These include: 1) Fluorescence in optical components 2) Leakage of signal at 694.3 nm. 3) Overload effects and non-linearities in the receiving and counting electronics. Most of these effects have been carefully examined and comparisons are being made between the observed atmospheric density profiles and local meteorological radio-sonde measurements. Good agreement has been obtained over the region of overlap (15 - 30 KID), discrepancies being of the same order as the experimental accuracy (1-10%), depending on height and length of period of observation.

Garvey, M. J.↗

Computer program for post-flight evaluation of the control surface response for an attitude controlled missile

A FORTRAN IV coded computer program is presented for post-flight analysis of a missile's control surface response. It includes preprocessing of digitized telemetry data for time lags, biases, non-linear calibration changes and filtering. Measurements include autopilot attitude rate and displacement gyro output and four control surface deflections. Simple first order lags are assumed for the pitch, yaw and roll axes of control. Each actuator is also assumed to be represented by a first order lag. Mixing of pitch, yaw and roll commands to four control surfaces is assumed. A pseudo-inverse technique is used to obtain the pitch, yaw and roll components from the four measured deflections. This program has been used for over 10 years on the NASA/SCOUT launch vehicle for post-flight analysis and was helpful in detecting incipient actuator stall due to excessive hinge moments. The program is currently set up for a CDC CYBER 175 computer system. It requires 34K words of memory and contains 675 cards. A sample problem presented herein including the optional plotting requires eleven (11) seconds of central processor time.

Knauber, R. N.↗

In-Situ Scanning Electron Microscope Experiments for Microscale Mechanical Testing and Validated Modeling of Fiber Reinforced Thermoplastics

A novel, in-situ, scanning electron microscope (SEM) mechanical testing capability for materials at the microscale which provides experimental validation to a machine learning (ML) toolset for full-field validation of physics-based micromechanics models is being developed by researchers at NASA Glenn Research Center. These are enabling technologies for the integration of multiscale digital twins for materials into system level models which will result in the improved performance, material discovery, reduced production cost and time, rapid characterization, and prognostic structural health monitoring (SHM) for materials and structures for extreme environments in support of NASA space exploration missions. In order to bridge the material structure-to-system gap for digital twins, physics-based models must be experimentally validated at multiple length scales. Seminal microscale experiments, conducted at the Air Force Research Laboratory (AFRL), were limited to transverse compression of single-layer, unidirectional thermoset polymer matrix composite (PMC) micropillar specimens [1]. The early phases of the current project followed those initial results and setup to reproduce the compression testing of PMC material on the custom-built piezoelectric actuated micromechanical testing rig built by MicroTesting Solutions LLC. In this work, samples of thermoplastic PMC material were first machined into 3 mm cubes, and then further machining and final milling was done using a Focused Ion Beam (FIB). The initial experiment was done on a pillar roughly 20 µm x 20 µm x 40 µm tall. Additional pillars were milled with final sizes ranging from 20 µm x 20 µm x 40 µm tall to 40 µm x 40 µm x 65 µm tall. A speckle pattern for in-situ full-field measurements using Digital Image Correlation (DIC) was applied with platinum, which was coated on the surface, and then the FIB was used to mill away some of the coating to produce an irregular pattern of Pt on the pillar surface. The samples were loaded into the custom testing rig and placed into the SEM and loaded under compression until failure. Images were collected in the SEM during testing. Post-processing of the images was conducted using DIC to obtain full-field displacement and strain measurements elucidating the role of the matrix as well as fiber-fiber interaction at the microscale within the composite subjected to compression loading well into the non-linear regime of the material. Moreover, the evolution of fiber-matrix debonding and matrix cracking is observed in-situ at the microscale. This data, along with images segmented with a newly developed ML toolset [2], was used to create and validate physics-based micromechanics models. An image of the failed micropillar is shown in Figure 1. The techniques developed in the initial compression experiment was tailored to the validation needs of the models and expanded to include different sized samples as well as possibly tension and fatigue.

Laura Wilson↗

Dual characterizations of optimal systems.

The complementary variational principle developed in a Hilbert space setting provides a duality principle in the calculus of variations with dynamic constraints. This concept is adopted in this paper to investigate dual characterizations of optimal control systems. Systems under consideration include those with dynamics governed by linear ordinary differential equations, linear partial differential equations and non-linear ordinary differential equations.

Chan, W. L.↗

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Mukhopadhyay, A. K.↗

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.

Shamie, J.↗

Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow

The instability of the laminar boundary layer flow along a concave wall was studied. Observations of these three-dimensional boundary layer phenomena were made using the hydrogen-bubble visualization technique. With the application of stereo-photogrammetric methods in the air-water system it was possible to investigate the flow processes qualitatively and quantitatively. In the case of a concave wall of sufficient curvature, a primary instability occurs first in the form of Goertler vortices with wave lengths depending upon the boundary layer thickness and the wall curvature. At the onset the amplification rate is in agreement with the linear theory. Later, during the non-linear amplification stage, periodic spanwise vorticity concentrations develop in the low velocity region between the longitudinal vortices. Then a meandering motion of the longitudinal vortex streets subsequently ensues, leading to turbulence.

Bippes, H.↗

Non-linear duct acoustics and its application to fan noise

Quite often the scalar Helmholtz equation is assumed to be the fundamental equation of duct acoustics and various relations are derived from it. An investigation is, therefore, conducted regarding the underlying assumptions leading to the Helmholtz equation. It is found that serious errors, even well below 186 dB, are possible if the assumption of linearity were to be made. In duct acoustics these errors are highest near the cutoff points and in the case of ducts with transonic flow. It is pointed out that serious errors could arise if a nonlinear problem is analyzed by linear methods. At times, an entire phenomenon remains unpredictable by linear methods. Attention is given to the characteristics of nonlinear systems, the phenomenon of multiple pure tones in the case of noise from the aircraft engine fans, the limitations of the conventional acoustics equation, duct shape and nonlinearity, and the numerical simulation of a fan with 8 blades.

Vaidya, P. G.↗

A digital strategy for manometer dynamic enhancement

Application of digital signal processing techniques to improve the non-linear dynamic characteristics of a sonar-type mercury manometer is described. The dynamic enhancement strategy quasi-linearizes the manometer characteristics and improves the effective bandwidth in the context of a wind-tunnel pressure regulation system. Model identification data and real-time hybrid simulation data demonstrate feasibility of approach.

Stoughton, J. W.↗

Identification and dual adaptive control of a turbojet engine

The objective of this paper is to utilize the design methods of modern control theory to realize a 'dual-adaptive' feedback control unit for a highly non-linear single spool airbreathing turbojet engine. Using a very detailed and accurate simulation of the non-linear engine as the data source, linear operating point models of unspecified dimension are identified. Feedback control laws are designed at each operating point for a prespecified set of sampling rates using sampled-data output regulator theory. The control system sampling rate is determined by an adaptive sampling algorithm in correspondence with turbojet engine performance. The result is a 'dual-adpative' control law that is functionally dependent upon the sampling rate selected and environmental operating conditions. Simulation transients demonstrate the utility of the dual-adaptive design to improve on-board computer utilization while maintaining acceptable levels of engine performance.

Merrill, W.↗

Surprisal analysis of rotational-translational energy transfer - Non-linear versus linear rotors

Surprisal versus energy gap analyses of state-to-state cross sections are presented for a number of linear rigid rotors excited by collisions with atoms for H2-H, H2-He, HCl-He, HCl-Ar, CO-He, CS-H2 (j=0) OCS-H2 (j=0) and HN2(+)-He, where (j=0) indicates that the hydrogen molecule was constrained to remain in its lowest level. Different systems exhibit wide variations in the slope of the surprisal plot and in certain cases, enough to indicate that the energy gap may not be the static dynamical constraint. Similar analyses are presented for nonlinear rotors excited by atoms for H2CO-He and H2O-He. For these, the data show a great deal of scatter, indicating that the reduced energy gap is probably not the appropriate independent variable.

Green, S.↗