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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

A Fundamental Study of Bifurcation Acoustic Treatment Effects on Aft-Fan Engine Noise

Increasing air traffic and more stringent aircraft noise regulations continue to expand requirements on aircraft noise levels for conventional and unconventional aircraft configurations. A major component of the overall aircraft noise is the sound associated with the propulsion system mounted in the engine nacelle. Acoustic liners mounted in the aircraft engine nacelles provide a significant portion of the current fan noise reduction. However, they must be further optimized if challenging noise reduction goals are to be achieved. One location within the aft bypass duct that may be an excellent candidate for increased attention is the acoustic treatment on the engine bifurcations (i.e., engine pylon and lower bifurcation). This paper presents the continuation of a fundamental study of the effects of bifurcation treatment on simulated aft fan noise and the validation of numerical tools to predict such effects. Five bifurcation configurations (four treated and one hardwall) were fabricated and tested in the NASA Langley Curved Duct Test Rig. Results show that mode scattering may occur due to both the presence of the bifurcation, as well as variable impedance distributions on the bifurcation surface. Future work will also include optimization of bifurcation treatments for testing in the Curved Duct Test Rig. These initial results are promising and this work provides valuable information for further study and improvement of the performance of bifurcation acoustic treatments.

bifurcation effects↗
NASA NTRSDate not supplied

A Fundamental Study of Bifurcation Acoustic Treatment Effects on Aft-Fan Engine Noise

Increasing air traffic and more stringent aircraft noise regulations continue to expand requirements on aircraft noise levels for conventional and unconventional aircraft configurations. A major component of the overall aircraft noise is the sound associated with the propulsion system mounted in the engine nacelle. Acoustic liners mounted in the aircraft engine nacelles provide a significant portion of the current fan noise reduction. However, they must be further optimized if challenging noise reduction goals are to be achieved. One location within the aft bypass duct that may be an excellent candidate for increased attention is the acoustic treatment on the engine bifurcations (i.e., engine pylon and lower bifurcation). This paper presents the continuation of a fundamental study of the effects of bifurcation treatment on simulated aft fan noise and the validation of numerical tools to predict such effects. Five bifurcation configurations (four treated and one hardwall) were fabricated and tested in the NASA Langley Curved Duct Test Rig. Results show that mode scattering may occur due to both the presence of the bifurcation, as well as variable impedance distributions on the bifurcation surface. Future work will also include optimization of bifurcation treatments for testing in the Curved Duct Test Rig. These initial results are promising and this work provides valuable information for further study and improvement of the performance of bifurcation acoustic treatments.

bifurcation effects↗
NASA NTRSDate not supplied

A Fundamental Study of Bifurcation Acoustic Treatment Effects on Aft-Fan Engine Noise

Increasing air traffic and more stringent aircraft noise regulations continue to expand requirements on aircraft noise levels for conventional and unconventional aircraft configurations. A major component of the overall aircraft noise is the sound associated with the propulsion system mounted in the engine nacelle. Acoustic liners mounted in the aircraft engine nacelles provide a significant portion of the current fan noise reduction. However, they must be further optimized if challenging noise reduction goals are to be achieved. One location within the aft bypass duct that may be an excellent candidate for increased attention is the acoustic treatment on the engine bifurcations (i.e., engine pylon and lower bifurcation). This paper presents the continuation of a fundamental study of the effects of bifurcation treatment on simulated aft fan noise and the validation of numerical tools to predict such effects. Five bifurcation configurations (four treated and one hardwall) were fabricated and tested in the NASA Langley Curved Duct Test Rig. Results show that mode scattering may occur due to both the presence of the bifurcation, as well as variable impedance distributions on the bifurcation surface. Future work will also include optimization of bifurcation treatments for testing in the Curved Duct Test Rig. These initial results are promising and this work provides valuable information for further study and improvement of the performance of bifurcation acoustic treatments.

bifurcation effects↗
NASA NTRS1985

Bifurcation theory applied to aircraft motions

Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (subcritical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with experiments.

Hui, W. H.↗
NASA NTRS1985

Bifurcation theory applied to aircraft motions

The bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (critical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with the experiments.

Hui, W. H.↗
NASA NTRS2000

Experiment Evaluation of Bifurcation in Sands

The basic principles of bifurcation analysis have been established by several investigators, however several issues remain unresolved, specifically how do stress level, grain size distribution, and boundary conditions affect general bifurcation phenomena in pressure sensitive and dilatant materials. General geometrical and kinematics conditions for moving surfaces of discontinuity was derived and applied to problems of instability of solids. In 1962, the theoretical framework of bifurcation by studying the acceleration waves in elasto-plastic (J2) solids were presented. Bifurcation analysis for more specific forms of constitutive behavior was examined by studying localization in pressure-sensitive, dilatant materials, however, analyses were restricted to plane deformation states only. Bifurcation analyses were presented and applied to predict shear band formations in sand under plane strain condition. The properties of discontinuous bifurcation solutions for elastic-plastic solids under axisymmetric and plane strain loading conditions were studied. The study focused on theory, but also references and comparisons to experiments were made. The current paper includes a presentation of a summary of bifurcation analyses for biaxial and triaxial (axisymmetric) loading conditions. The Coulomb model is implemented using incremental piecewise scheme to predict the constitutive relations and shear band inclination angles. Then, a comprehensive evaluation of bifurcation phenomena is presented based on data from triaxial experiments performed under microgravity conditions aboard the Space Shuttle under very low effective confining pressure (0.05 to 1.30 kPa), in which very high peak friction angles (47 to 75 degrees) and dilatancy angles (30 to 31 degrees) were measured. The evaluation will be extended to include biaxial experiments performed on the same material under low (10 kPa) and moderate (100 kPa) confining pressures. A comparison between the behavior under biaxial and triaxial loading conditions will be presented, and related issues concerning influence of confining pressure will be discussed.

Alshibi, Khalid A.↗
NASA NTRS2019

An Investigation of Bifurcation Acoustic Treatment Effects on Aft-Fan Engine Nacelle Noise

Increasing air traffic and more stringent aircraft noise regulations continue to expand requirements on aircraft noise reduction capabilities for conventional and unconventional aircraft configurations. A major component of the overall aircraft noise is the sound associated with the propulsion system mounted in the engine nacelle. Acoustic liners mounted in the aircraft engine nacelles provide a significant portion of the current fan noise reduction. However, they must be further optimized if challenging noise reduction goals are to be achieved. One area within the aft bypass duct that may be an excellent candidate for increased attention is the acoustic treatment on the engine bifurcations (i.e., engine pylon and lower bifurcation). This paper describes a fundamental study of the effects of bifurcation treatment on simulated aft fan noise, as well as the validation of numerical tools to predict such effects. Five bifurcation configurations (four treated and one hardwall) were fabricated and tested in the NASA Langley Curved Duct Test Rig. Results show that mode scattering may occur due to both the presence of the bifurcation, as well as variable impedance distributions on the bifurcation surface. Future work will also include optimization of bifurcation treatments for testing in the Curved Duct Test Rig. These initial results are promising and this work provides valuable information for further study and improvement of the performance of bifurcation acoustic treatments.

Nark, Douglas M.↗
NASA NTRS1981

Bifurcation and post-buckling analysis of laminated composite plates via reduced basis technique

A reduced basis technique and a problem-adaptive computational algorithm are presented for the bifurcation and post-buckling analysis of laminated anisotropic plates. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the bifurcation point. The plate is discretized by using displacement finite element (or finite difference) models. The special symmetries exhibited by the response of the anisotropic plate are used to reduce the size of the analysis region. The vector of unknown nodal parameters is expressed as a linear combination of a small number of basis vectors, and a Rayleigh-Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the bifurcation point and the associated eigenmode of the panel. In the second stage of the bifurcation buckling mode is used to obtain a nonlinear solution in the vicinity of the bifurcation point and new (updated) sets of basis vectors and reduced equations are generated. In the third stage the reduced equations are used to trace the post-buckling paths. The effectiveness of the proposed technique for predicting the bifurcation and post-buckling behavior of plates is demonstrated by means of numerical examples for plates loaded by means of prescribed edge displacements.

Noor, A. K.↗
NASA NTRS2004

Effects of Bifurcations on Aft-Fan Engine Nacelle Noise

Aft-fan engine nacelle noise is a significant factor in the increasingly important issue of aircraft community noise. The ability to predict such noise within complex duct geometries is a valuable tool in studying possible noise attenuation methods. A recent example of code development for such predictions is the ducted fan noise propagation and radiation code CDUCT-LaRC. This work focuses on predicting the effects of geometry changes (i.e. bifurcations, pylons) on aft fan noise propagation. Beginning with simplified geometries, calculations show that bifurcations lead to scattering of acoustic energy into higher order modes. In addition, when circumferential mode number and the number of bifurcations are properly commensurate, bifurcations increase the relative importance of the plane wave mode near the exhaust plane of the bypass duct. This is particularly evident when the bypass duct surfaces include acoustic treatment. Calculations involving more complex geometries further illustrate that bifurcations and pylons clearly affect modal content, in both propagation and radiation calculations. Additionally, results show that consideration of acoustic radiation results may provide further insight into acoustic treatment effectiveness for situations in which modal decomposition may not be straightforward. The ability of CDUCT-LaRC to handle complex (non-axisymmetric) multi-block geometries, as well as axially and circumferentially segmented liners, allows investigation into the effects of geometric elements (bifurcations, pylons).

Nark, Douglas M.↗
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
NASA NTRS1987

Multigrid methods for bifurcation problems: The self adjoint case

This paper deals with multigrid methods for computational problems that arise in the theory of bifurcation and is restricted to the self adjoint case. The basic problem is to solve for arcs of solutions, a task that is done successfully with an arc length continuation method. Other important issues are, for example, detecting and locating singular points as part of the continuation process, switching branches at bifurcation points, etc. Multigrid methods have been applied to continuation problems. These methods work well at regular points and at limit points, while they may encounter difficulties in the vicinity of bifurcation points. A new continuation method that is very efficient also near bifurcation points is presented here. The other issues mentioned above are also treated very efficiently with appropriate multigrid algorithms. For example, it is shown that limit points and bifurcation points can be solved for directly by a multigrid algorithm. Moreover, the algorithms presented here solve the corresponding problems in just a few work units (about 10 or less), where a work unit is the work involved in one local relaxation on the finest grid.

Taasan, Shlomo↗
NASA NTRS1982

Bifurcation analysis of nonlinear stability of aircraft at high angles of attack

The problem of stability of steady flight of an aircraft flying at high angles of attack subject to finite-amplitude disturbances in pitch is studied using bifurcation theory, taking account of the interactions between the pitching motion and the unsteady flow. The aerodynamic responses to large-amplitude slow oscillations of the aircraft are obtained from that of infinitesimal amplitude case. Increasing the angle of attack past some critical angle for which the damping vanishes, the steady flight becomes unstable and Hopf bifurcation sets in, resulting in a periodic motion. A simple criterion in terms of the aerodynamic coefficients is given for determining the stability of the bifurcating period motion. For supersonic/hypersonic flat plate airfoils the bifurcating periodic motion is found to be unstable. This implies that when the angle of attack is increased past that of neutral damping, there will be drastic changes of the motion of the aircraft from its steady flight condition at the critical angle, including, e.g. hysteresis.

Hui, W. H.↗
NASA NTRS1984

Bifurcation analysis of aircraft pitching motions near the stability boundary

Bifuraction theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single degree of freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion is represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. This information is deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.

Hui, W. H.↗
NASA NTRS1989

A torus bifurcation theorem with symmetry

Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.

Vangils, S. A.↗
NASA NTRS1990

Bifurcation analysis of axial flow compressor stability

With a one-mode truncation it is possible to reduce the Moore-Greitzer model for compressor instability to a set of three ordinary differential equations. These are approached from the point of view of bifurcation theory. Most of the bifurcations emerge from a degenerate Takens-Bogdanov bifurcation point. The bifurcation sets are completed using the numerical branch tracking scheme AUTO. Despite the severity of the truncation, the agreement with experimental results is excellent.

Mccaughan, F. E.↗
NASA NTRS1993

Bifurcation analysis of a simple analytic model of self-propagating star formation

We investigate the structure and stability of rotationally symmetric nonhomogeneous time-independent solutions derived from a simple analytic model of self-propagating star formation. For this purpose we employ two methodologies: We use bifurcation theoretical methods to prove the existence of nonhomogeneous axisymmetric stationary solutions of an appropriate nonlinear evolution equation for the stellar density. We show that the nonhomogeneous solution branch bifurcates from the homogeneous one at a critical parameter value of the star formation rate. Further, the analytical theory allows us to show that the new solution set is stable in the weakly nonlinear regime near the bifurcation point. To follow the solution branch further, we use numerical methods. The numerical calculation shows the structure and stability of these solutions. We conclude that no periodic time-dependent solutions of this special model exist, and no further bifurcations can be found. The same results have been found in simulations of stochastic self-propagating star formation based on similar models. Therefore, our findings provide a natural explanation, why long-lived large-scale structure have not been found in those simulations.

Neukirch, Thomas↗
NASA NTRS2003

Retinal ganglion cell projections to the hamster suprachiasmatic nucleus, intergeniculate leaflet, and visual midbrain: bifurcation and melanopsin immunoreactivity

The circadian clock in the suprachiasmatic nucleus (SCN) receives direct retinal input via the retinohypothalamic tract (RHT), and the retinal ganglion cells contributing to this projection may be specialized with respect to direct regulation of the circadian clock. However, some ganglion cells forming the RHT bifurcate, sending axon collaterals to the intergeniculate leaflet (IGL) through which light has secondary access to the circadian clock. The present studies provide a more extensive examination of ganglion cell bifurcation and evaluate whether ganglion cells projecting to several subcortical visual nuclei contain melanopsin, a putative ganglion cell photopigment. The results showed that retinal ganglion cells projecting to the SCN send collaterals to the IGL, olivary pretectal nucleus, and superior colliculus, among other places. Melanopsin-immunoreactive (IR) ganglion cells are present in the hamster retina, and some of these cells project to the SCN, IGL, olivary pretectal nucleus, or superior colliculus. Triple-label analysis showed that melanopsin-IR cells bifurcate and project bilaterally to each SCN, but not to the other visual nuclei evaluated. The melanopsin-IR cells have photoreceptive characteristics optimal for circadian rhythm regulation. However, the presence of moderately widespread bifurcation among ganglion cells projecting to the SCN, and projection by melanopsin-IR cells to locations distinct from the SCN and without known rhythm function, suggest that this ganglion cell type is generalized, rather than specialized, with respect to the conveyance of photic information to the brain. Copyright 2003 Wiley-Liss, Inc.

NASA Discipline Neuroscience↗
NASA NTRSDate not supplied

AMOC Stability in GISS-E2-1-G: A Case of Stochastic Bifurcation

A 10-member ensemble simulation using the NASA GISS-E2-1-G climate model shows a clear bifurcation in the Atlantic Meridional Overturning Circulation (AMOC) strength under the SSP2-4.5 future scenario, leading to 8 stable AMOC-on and 2 stable AMOC-off climate states after 400 years of integration, despite identical forcing of each ensemble member. Ocean models have previously shown a tipping point where sufficient forcing (e.g. by freshwater inputs) can shut down the AMOC. A variety of fully coupled models have demonstrated this, either through hosing experiments or increased precipitation and warming at high latitudes due to increased concentrations of greenhouse gases. In the GISS simulations, there are no external freshwater perturbations. The bifurcation arises freely in the coupled system and is the result of stochastic variability associated with sea-ice transport and melting in the Irminger Sea following a slowing of the GHG concentration increase at the end of the twenty-first century. We believe this is the first time that a CMIP-class model has shown such a bifurcation across an initial condition ensemble.

GISS ModelE2.1↗