Influence of nozzle external geometry on wavepackets in under-expanded supersonic impinging jets

2021 ◽  
Vol 929 ◽  
Author(s):  
Shahram Karami ◽  
Julio Soria
Keyword(s):  
Shear Layer ◽  
Spectral Decomposition ◽  
Travelling Waves ◽  
Near Field ◽  
High Amplitude ◽  
Impinging Jets ◽  
The Other ◽  
Mode Shapes ◽  
Reflected Shock ◽  
Spatial Modes

In this study, large-eddy simulations are utilised to unravel the influence of the nozzle's external geometry on upstream-travelling waves in under-expanded supersonic impinging jets. Three configurations, a thin-lipped, a thin-lipped with a sponge and an infinite-lipped nozzle are considered with the other non-dimensionalised geometrical and flow variables identical for the three cases. Spectral proper orthogonal decomposition is applied to the Mack norm, i.e. the energy norm based on the stagnation energy, to obtain the spatial modes at their corresponding frequency. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies is used to isolate the wavepackets into upstream- and downstream-propagating waves based on their phase velocity. It is found that the external geometry of the nozzle has a significant influence on the first-order statistics even though the governing non-dimensional parameters are the same for all three cases. Multiple peaks emerge in the energy spectra at distinct frequencies corresponding to axisymmetric azimuthal modes for each case. The downstream-propagating wavepackets have a high amplitude at the shear layer of the three jets with the mode shapes resembling Kelvin–Helmholtz instability waves, while the upstream-travelling wavepackets exist in the three regions of the near field, shear layer and inside of the jet. The barrel shock at the nozzle exit appears as a flexible shield, which prevents upstream-travelling waves from reaching the internal region of the nozzle, where the upstream-travelling waves travel obliquely with one side of the wavefront is crawling on the reflected shock while the other side is guided by the shear layer. These latter waves can reach the nozzle lip via inside of the jet. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies show that all three forms of the near field, shear layer and inside jet upstream-travelling wavepackets contribute to the receptivity process while their contributions and strength are altered by the change of the external geometry of the nozzle.

Application of partial eigenvalue assignment techniques to dampen electromechanical oscillations in multi-machine power systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Erick Baleeiro da Silva ◽  
José Mário Araújo
Keyword(s):  
Power Systems ◽  
The Other ◽  
Mode Shapes ◽  
Eigenstructure Assignment ◽  
Power System Stabilizers ◽  
Control Effort ◽  
Electromechanical Oscillations ◽  
Oscillation Modes ◽  
Partial Controllability

AbstractIn this study, a methodology for partial eigenstructure assignment (PEVA) is applied to dampen electromechanical oscillations in electrical multi-machine power systems. The approach is anchored in allocating a small number of undesirable eigenvalues, for example, which are poorly damped, preserving the other eigenvalues in the system - the so-called no-spillover spectrum. The new position of the selected eigenvalues is carried out based on the partial controllability analysis of the system, in order to minimize the control effort. Simulation examples using a system with 68 buses, 16 generators and five areas showed that the presented methodology is efficient in dampening the local and inter-area oscillation modes when compared to the classic power system stabilizers (PSS). The quality of the solution is illustrated through computer simulations, eigenvalues tables and mode-shapes.

Nonlinear Combination Resonances in Cantilever Composite Plates

1995 ◽  
Author(s):  
Kyoyul Oh ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Low Frequency ◽  
Composite Plates ◽  
High Amplitude ◽  
Mode Shapes ◽  
Laser Vibrometer ◽  
Combination Resonance ◽  
Response Curves

Abstract We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

Torsional Vibration Analysis of Shafts With Sections of Tapered Diameter

1993 ◽  
Author(s):  
John R. Baker ◽  
Keith E. Rouch
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Displacement Function ◽  
The Other ◽  
Mode Shapes ◽  
Axial Distance ◽  
Rotational Degree ◽  
Rotor Systems ◽  
Constant Diameter

Abstract This paper presents the development of two tapered finite elements for use in torsional vibration analysis of rotor systems. These elements are particularly useful in analysis of systems that have shaft sections with linearly varying diameters. Both elements are defined by two end nodes, and inertia matrices are derived based on a consistent mass formulation. One element assumes a cubic displacement function and has two degrees of freedom at each node: rotation about the shaft’s axis and change in angle of rotation with respect to the axial distance along the shaft. The other element assumes a linear displacement function and has one rotational degree of freedom at each node. The elements are implemented in a computer program. Calculated natural frequencies and mode shapes are compared for both tapered shaft sections and constant diameter sections. These results are compared with results from an available constant diameter element. It is shown that the element derived assuming a cubic displacement function offers much better convergence characteristics in terms of calculated natural frequencies, both for tapered sections and constant diameter sections, than either of the other two elements. The finite element code that was developed for implementation of these elements is specifically designed for torsional vibration analysis of rotor systems. Lumped inertia, lumped stiffness, and gear connection elements necessary for rotor system analysis are also discussed, as well as calculation of natural frequencies, mode shapes, and amplitudes of response due to a harmonic torque input.

Are Epileptic Spasms a Seizure Type for the Insular Region?

2020 ◽  
Vol 51 (04) ◽  
pp. 295-297 ◽  
Author(s):  
Volodymyr Kharytonov ◽  
Olivier Dulac
Keyword(s):  
Slow Wave ◽  
Late Onset ◽  
Motor Program ◽  
High Amplitude ◽  
The Other ◽  
Seizure Type ◽  
Wave Characteristic ◽  
The Third ◽  
Epileptic Spasms ◽  
Insular Region

AbstractTwo patients with insular and striatal postnatal scar had epileptic spasms (ES) that were asymmetrical and the only seizure type, whereas none of the usual ictal symptoms of insular seizures occurred. Ictal electroencephalography (EEG) showed the high-amplitude slow-wave characteristic of ES. Vigabatrin remained efficient for over 4 years for one patient and right into the third decade for the other one. Such ES are distinct from infantile and late onset spasms. Furthermore, these observations suggest that in ES insular epilepsy triggers paroxysmal activation of the striatum, and that vigabatrin inhibits the striatal startle motor program, thus interrupting the corticostriatal loop.

scholarly journals Prediction of the Resonant Response of Frictionally Constrained Blade Systems Using Constrained Mode Shapes

1998 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Contact Point ◽  
Element Model ◽  
The Other ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Cyclic Symmetry ◽  
Resonant Response ◽  
Friction Contact ◽  
Blade System ◽  
Free Mode

In this paper, the concept of constrained mode shapes is employed to predict the resonant response of a frictionally constrained blade system. For a tuned blade system, the constrained mode shapes can be calculated using a finite element model of a single blade along with the cyclic symmetry constraint that simulates a fully stuck friction contact. The resulting constrained mode shapes are often complex and can be used to obtain the constrained receptance of the frictionally constrained blade. It is shown that by examining each mode’s contribution to the receptance at the friction contact point, the importance of each individual modes to the prediction of the resonant response of a frictionally constrained blade can be determined. Furthermore, by comparing the receptances calculated from free mode shapes and those from constrained mode shapes, it is found that in the neighborhood of the fully slipping region, the prediction of resonant response requires fewer number of modes when using free mode shapes compared to using constrained mode shapes. On the other hand, in the neighborhood of the fully stuck region, it requires fewer number of modes if constrained mode shapes are used. Therefore, when high preload at the friction contact is desirable, such as for shrouded blade systems, using the constrained mode shapes for the prediction of resonant response is preferred. Moreover, the concept of hybrid receptance is introduced so as to yield very accurate prediction of the resonant response based on only very few vibration modes.

Nonmodal Solution of Spherical Shells With Cutouts Excited by High-Frequency Axisymmetric Forces

1970 ◽  
Vol 37 (4) ◽  
pp. 977-983 ◽  
Author(s):  
M. C. Junger
Keyword(s):  
Boundary Conditions ◽  
High Frequency ◽  
Near Field ◽  
Closed Form Solution ◽  
Radial Force ◽  
Form Solution ◽  
Mode Shapes ◽  
High Frequency Response ◽  
Circular Cutout ◽  
Line Loads

A closed-form solution is obtained for the high-frequency response of a thin spherical shell embodying a circular cutout and excited axisymmetrically by a concentrated radial force. The solution is constructed by combining the shell response to the radial exciting force with its response to radial, tangential, and moment line loads applied along the cutout boundary, these line loads being selected to match the boundary conditions. Concise expressions for the shell response are obtained by applying the Sommerfeld-Watson transformation to the slowly converging high-frequency modal series which is thereby reduced to only two terms, viz., an exponentially decaying near-field and a standing or propagating-wave field. These two terms are in the nature of the creeping waves commonly used to formulate electromagnetic or acoustic diffracted wave fields in the short-wavelength limit. The method is illustrated for the simple case of a circular cutout with a clamped boundary, but lends itself to more complicated boundary conditions, viz., intersecting shells or wave guides. The natural frequencies and mode shapes are found from a single, characteristic equation involving trigonometric functions.

Transition to global instability in transverse-jet shear layers

2010 ◽  
Vol 661 ◽  
pp. 294-315 ◽  
Author(s):  
J. DAVITIAN ◽  
D. GETSINGER ◽  
C. HENDRICKSON ◽  
A. R. KARAGOZIAN
Keyword(s):  
Shear Layer ◽  
Near Field ◽  
Single Mode ◽  
Shear Layers ◽  
Global Instability ◽  
Frequency Tracking ◽  
Transverse Jet ◽  
Critical Range ◽  
Crossflow Velocity ◽  
Lock In

In a recent paper (Megerianet al.,J. Fluid Mech., vol. 593, 2007, pp. 93–129), experimental exploration of the behaviour of transverse-jet near-field shear-layer instabilities suggests a significant change in the character of the instability as jet-to-crossflow velocity ratiosRare reduced below a critical range. The present study provides a detailed exploration of and additional insights into this transition, with quantification of the growth of disturbances at various locations along and about the jet shear layer, frequency tracking and response of the transverse jet to very strong single-mode forcing, creating a ‘lock-in’ response in the shear layer. In all instances, there is clear evidence that the flush transverse jet's near-field shear layer becomes globally unstable whenRlies at or below a critical range near 3. These findings have important implications for and provide the underlying strategy by which active control of the transverse jet may be developed.

The potential flow bounded by a mixing layer and a solid surface

1984 ◽  
Vol 395 (1809) ◽  
pp. 265-290 ◽  
Keyword(s):  
Shear Layer ◽  
Solid Surface ◽  
Turbulent Mixing ◽  
Potential Flow ◽  
Near Field ◽  
Mixing Layer ◽  
Detailed Comparison ◽  
Mixing Layers ◽  
Turbulent Shear ◽  
Spatial Correlations

Phillips's ( Proc. Camb. Phil. Soc . 51, 220 (1955)) analysis of the potential 'near field' forced by a turbulent shear layer is extended to include calculation of velocity spectra, spatial correlations and the effect of a solid surface at a finite distance from the shear layer. In the region away from the influence of the wall the theory predicts that correlation scales depend principally on the effective distance from the turbulence. This result suggests that the large correlation scales measured outside turbulent mixing layers do not necessarily demonstrate the essential tow-dimensionality of the large turbulent eddies and shows why mixing layers are more influenced by potential flow effects than are other shear layers. The detailed comparison of the theory to measurements made outside a high Reynolds number single-stream turbulent mixing layer results in an unphysical negative regions are caused by an error in a basic assumption of the theory. However, all the measured correlation scales appear to increase linearly with distance from the turbulence and therefore are consistent with the main result of the analysis. As the potential flow becomes affected by the wind tunnel floor, u 2 — and w 2 — are amplified significantly more than the theory predicts, while v 2 — is not attenuated. These discrepancies are attributed partly to the streamwise inhomogeneity of the flow, which was not incorporated into the analysis.

Viscous constraints on microorganism approach and interaction

2018 ◽  
Vol 851 ◽  
pp. 715-738 ◽  
Author(s):  
Mehdi Jabbarzadeh ◽  
Henry Chien Fu
Keyword(s):  
Reynolds Number ◽  
Near Field ◽  
Reynolds Numbers ◽  
Suspended Particles ◽  
The Other ◽  
Direct Approach ◽  
Low Reynolds Numbers ◽  
Physical Constraints ◽  
Low Reynolds ◽  
Viscous Hydrodynamics

Microorganisms must approach other suspended organisms or particles in order to interact with them during a host of life processes including feeding and mating. Microorganisms live at low Reynolds number where viscosity dominates and strongly affects the hydrodynamics of swimmer and nearby cells and objects. Viscous hydrodynamics makes it difficult for two surfaces to approach closely at low Reynolds numbers. Nonetheless, it is observed that microorganisms in fluid are still able to approach closely enough to interact with each other or suspended particles. Here, we study how the physical constraints provided by viscous hydrodynamics affects the feasibility of direct approach of flagellated and ciliated microorganisms to targets of different sizes. We find that it is feasible for singly flagellated swimmers to approach targets that are the same size or bigger. On the other hand, for squirmers, the feasibility of approach depends on near-field flows that can be controlled by the details of their swimming strokes.

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