scholarly journals Active attenuation of a trailing vortex inspired by a parabolized stability analysis

2018 ◽  
Vol 855 ◽  
Author(s):  
Adam M. Edstrand ◽  
Yiyang Sun ◽  
Peter J. Schmid ◽  
Kunihiko Taira ◽  
Louis N. Cattafesta
Keyword(s):  
Stability Analysis ◽  
Unstable Mode ◽  
Control Strategies ◽  
Three Dimensional ◽  
Suboptimal Control ◽  
Effective Control ◽  
Streamwise Vorticity ◽  
Control Scheme ◽  
Set Up ◽  
The Stability

Designing effective control for complex three-dimensional flow fields proves to be non-trivial. Often, intuitive control strategies lead to suboptimal control. To navigate the control space, we use a linear parabolized stability analysis to guide the design of a control scheme for a trailing vortex flow field aft of a NACA0012 half-wing at an angle of attack $\unicode[STIX]{x1D6FC}=5^{\circ }$ and a chord-based Reynolds number $Re=1000$ . The stability results show that the unstable mode with the smallest growth rate (fifth wake mode) provides a pathway to excite a vortex instability, whereas the principal unstable mode does not. Inspired by this finding, we perform direct numerical simulations that excite each mode with body forces matching the shape function from the stability analysis. Relative to the uncontrolled case, the controlled flows show increased attenuation of circulation and peak streamwise vorticity, with the fifth-mode-based control set-up outperforming the principal-mode-based set-up. From these results, we conclude that a rudimentary linear stability analysis can provide key insights into the underlying physics and help engineers design effective physics-based flow control strategies.

scholarly journals Systematic stability analysis, evaluation and testing process, and platform for grid-connected power electronic equipment

2020 ◽  
Author(s):  
Ziqian Zhang ◽  
Robert Schürhuber ◽  
Lothar Fickert ◽  
Katrin Friedl ◽  
Guochu Chen ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Power System ◽  
Control Strategies ◽  
Three Dimensional ◽  
Electronic Equipment ◽  
Three Dimensions ◽  
Power Electronic ◽  
System Behavior ◽  
Linear Behaviour ◽  
The Stability

AbstractThe proportion of grid-connected power electronic equipment is already large enough to influence the dynamic characteristics of the modern power system. Ensuring the stability of grid-connected power electronic equipment in all relevant situations is one of the foundations for reliable power system operation. In contrast to conventional rotating machines, the stability of power electronic devices mostly depends on the applied control strategy, and a large diversity of different complex control strategies are in practical use. Also, the investigation of stability of such systems needs to take into account the non-linear behaviour of the power electronic equipment. These are the main reasons why the system behavior of grid-connected power electronic equipment cannot be reproduced satisfactorily when aplying a single method of stability analysis, evaluation and testing method. During the last years, faults which led to tripping of converters due to stability problems occurred frequently even though standardized fault compliance tests were performed on these converters. In this paper these stability issues are analyzed. Also, a three-dimensional stability analysis method is suggested in order to comprehensively cover system behavior. The three dimensions are the time/scale dimension, the equipment number dimension and the local or global range of the stability analysis dimension. Based on this three-dimensional framework, this paper proposes a stability evaluation as well as a test process applying a hardware-in-the-loop test concept. Through the verification and testing of the stability of the actual grid-connected power electronic equipment, the method proposed in this paper is verified for up-to-date equipment.

scholarly journals The Stability Analysis of a Multi-Port Single-Phase Solid-State Transformer in the Electromagnetic Timescale

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2250 ◽  
Author(s):  
Rui Wang ◽  
Qiuye Sun ◽  
Qifu Cheng ◽  
Dazhong Ma
Keyword(s):  
Stability Analysis ◽  
Solid State ◽  
Single Phase ◽  
Control Strategies ◽  
Current Source ◽  
Practical Stability ◽  
Stability Assessment ◽  
Solid State Transformer ◽  
The Stability ◽  
Signal Sinusoïdal

This paper proposes an overall practical stability assessment for a multi-port single-phase solid-state transformer (MS3T) in the electromagnetic timescale. When multiple stable subsystems are combined into one MS3T, the newly formed MS3T has a certain possibility to be unstable. Thus, this paper discusses the stability assessment of the MS3T in detail. First and foremost, the structure of the MS3T and its three stage control strategies are proposed. Furthermore, the stability analysis of each of the MS3T’s subsystems is achieved through the closed loop transfer function of each subsystem, respectively, including an AC-DC front-end side converter, dual active bridge (DAB) with a high-frequency (HF) or medium-frequency (MF) transformer, and back-end side incorporating DC-AC and dc-dc converters. Furthermore, the practical impedance stability criterion in the electromagnetic timescale, which only requires two current sensors and one external high-bandwidth small-signal sinusoidal perturbation current source, is proposed by the Gershgorin theorem and Kirchhoff laws. Finally, the overall stability assessment, based on a modified impedance criterion for the MS3T is investigated. The overall practical stability assessment of the MS3T can be validated through extensive simulation and hardware results.

Three-dimensional stability analysis for a salt-finger convecting layer

2018 ◽  
Vol 841 ◽  
pp. 636-653
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Grashof Number ◽  
Significant Difference ◽  
The Stability ◽  
Mode A

A three-dimensional linear stability analysis is carried out for a convecting layer in which both the temperature and solute distributions are linear in the horizontal direction. The three-dimensional results show that, for $Le=3$ and 100, the most unstable mode occurs invariably as the longitudinal mode, a vortex roll with its axis perpendicular to the longitudinal plane, suggesting that the two-dimensional results are sufficient to illustrate the stability characteristics of the convecting layer. Two-dimensional results show that the stability boundaries of the transverse mode (a vortex roll with its axis perpendicular to the transverse plane) and the longitudinal modes are virtually overlapped in the regime dominated by thermal diffusion and the regime dominated by solute diffusion, while these two modes hold a significant difference in the regime the salt-finger instability prevails. More precisely, the instability area in terms of thermal Grashof number $Gr$ and solute Grashof number $Gs$ is larger for the longitudinal mode than the transverse mode, implying that, under any circumstance, the longitudinal mode is always more unstable than the transverse mode.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Stability and Robustness of a 3D Slip Model for Walking Using Lateral Leg Placement Control

2012 ◽  
Author(s):  
Dominik Budday ◽  
Fabian Bauer ◽  
Justin Seipel
Keyword(s):  
Humanoid Robot ◽  
Performance Test ◽  
Control Mechanism ◽  
Sagittal Plane ◽  
Control Strategies ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Slip Model ◽  
The Stability

The SLIP model has shown a way to easily represent the center of mass dynamics of human walking and running. For 2D motions in the sagittal plane, the model shows self-stabilizing effects that can be very useful when designing a humanoid robot. However, this self-stability could not be found in three-dimensional running, but simple control strategies achieved stabilization of running in three dimensions. Yet, 3D walking with SLIP has not been analyzed to the same extent. In this paper we show that three-dimensional humanoid SLIP walking is also unstable, but can be stabilized using the same strategy that has been successful for running. It is shown that this approach leads to the desired periodic solutions. Furthermore, the influence of different parameters on stability and robustness is examined. Using a performance test to simulate the transition from an upright position to periodic walking we show that the stability is robust. With a comparison of common models for humanoid walking and running it is shown that the simple control mechanism is able to achieve stable solutions for all models, providing a very general approach to this problem. The derived results point out preferable parameters to increase robustness promising the possibility of successfully realizing a humanoid walking robot based on 3D SLIP.

On the stability of nonlinear waves coexisting with plasma beams

1975 ◽  
Vol 13 (1) ◽  
pp. 173-187 ◽  
Author(s):  
E. Infeld ◽  
G. Rowlands
Keyword(s):  
Nonlinear Wave ◽  
Growth Rates ◽  
Three Dimensional ◽  
Stationary Waves ◽  
One Dimensional ◽  
Long Wavelength ◽  
Long Wave ◽  
Set Up ◽  
The Stability ◽  
The One

In this paper we consider the stability of one-dimensional stationary waves set up by two counter-streaming beams of electrons in a background of stationary ions. The perturbations considered are long-wave in a direction perpendicular to the wave. The presence of a uniform magnetic field in the direction of the wave and the effect of a perpendicular pressure are taken into account. In the long-wavelength limit growth rates are diminished by the nonlinear wave. When the amplitude of this wave tends to its maximum value, the growth rates tend to zero. Thus the wave has a stabilizing effect for long-wave perturbations. Three- dimensional effects lead to additional instabilities which are also quenched by the nonlinear wave, but not as fast as the one-dimensional calculation indicates.

Stability Analysis of a 3D Vertical Slope with Transverse Earthquake Load and Surcharge

2011 ◽  
Vol 90-93 ◽  
pp. 676-679 ◽  
Author(s):  
Ting Kai Nian ◽  
Ke Li Zhang ◽  
Run Qiu Huang ◽  
Guang Qi Chen
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Failure Mode ◽  
Factor Of Safety ◽  
Three Dimensional ◽  
Strength Reduction ◽  
Reduction Procedure ◽  
Interesting Issue ◽  
Earthquake Load ◽  
The Stability

The stability and failure mode for a 3D vertical slope with transverse earthquake load and surcharge have been an interesting issue, especially in building excavation and wharf engineering. In order to further reveal the seismic and surcharge effect, a three-dimensional elasto-plastic finite element(FE) code combined with a strength reduction procedure is used to yield a factor of safety and failure mode for a vertical slopes under two horizontal direction pseudo-static(PS) coefficient and surcharge on the slope top, respectively. Comparative studies are carried out to investigate the effect of seismic coefficient, surcharge intensity and location on the stability and the failure mechanism for a 3D vertical slope including an inclined weak layer. Several important findings are also achieved.

Three-dimensional stability analysis for slurry-filled trench wall in cohesionless soil

1996 ◽  
Vol 33 (5) ◽  
pp. 798-808 ◽  
Author(s):  
Jiin-Song Tsai ◽  
Jia-Chyi Chang
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Slip Surface ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Soil Mass ◽  
Cohesionless Soil ◽  
Cohesionless Soils ◽  
Slurry Trench ◽  
The Stability

On the basis of the limiting equilibrium and arching theory, a three-dimensional analysis is proposed for slurry-supported trenches in cohesionless soils. This analytical approach is developed by considering the trench stability problem as a vertical soil cut within a fictitious half-silo with a rough wall surronding. Arching effects are considered not only in the vertical direction but also in the horizontal direction. A shell-shaped slip surface of the sliding soil mass is defined by Mohr-Coulomb criterion. The factor of safety is defines as the ratio of the resisting force induced by slurry pressure to the horizontal force required to maintain the stability of the trench wall. Results of the proposed method have been compared with those of two existing analytical methods for a typical trench stability problem. Key words: stability analysis, slurry trench wall, cohesionless soil.

On Three and Two-Dimensional Disturbances of Pipe Flow

1960 ◽  
Vol 27 (3) ◽  
pp. 381-389 ◽  
Author(s):  
Kurt Spielberg ◽  
Hans Timan
Keyword(s):  
Order Differential Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Main Flow ◽  
Two Dimensional ◽  
Straight Pipe ◽  
Special Cases ◽  
Set Up ◽  
The Stability ◽  
The Given

A system of ordinary, coupled differential equations is set up for three-dimensional disturbances of Poiseuille flow in a straight pipe of circular cross section. The commonly treated equations are shown to be special cases arising from particular assumptions. It is shown that in the nonviscous, and therefore also in the general case, there exists, in contrast to the analogous problem in Cartesian co-ordinates, no transformation reducing the given problem to a two-dimensional one. A fourth-order differential equation is derived for disturbances independent of the direction of the main flow. The solutions, which are obtained, show that those two-dimensional disturbances, termed cross disturbances, decay with time and do therefore not disturb the stability of the main flow. Explicit expressions for the cross disturbances are obtained and a discussion of their nature is given.

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