Compressor Stability At Pulsating Condition via Gas Dynamics Responses Analysis

2021 ◽  
Author(s):  
Mengying Shu ◽  
Bijie Yang ◽  
Mingyang Yang ◽  
Ricardo F. Martinez-Botas ◽  
Weilin Zhuge
Keyword(s):  
Gas Dynamics ◽  
Forced Oscillation ◽  
Characteristic Curve ◽  
Sustained Oscillation ◽  
Operating Environment ◽  
Aerodynamic Stability ◽  
Lag Effect ◽  
1D Model ◽  
The Stability ◽  
Lower Slope

Abstract The compressor is operated at unsteady exit conditions in many scenarios such as the instability of combustion in gas turbine and denotation engine. The aerodynamic stability of the compressor is inevitably influenced by the unsteady operating environment. In this paper, a 1D model that combines pulsation and unsteady responses of the compressor is developed to investigate the stability of the compressor system. The results show that the onset of surge and the transient responses of the compressor during surge are well predicted by the method. The amplitude of the component at surge frequency obtained by FFT method is applied as a criterion to quantitively evaluate the onset and the strength of the surge. Compressor stability is enhanced at pulsating conditions due to the interaction between forced oscillation of pulsation and self-sustained oscillation of surge. An analytical model is established to understand the mechanism of the enhancement of compressor stability under pulsation. The change of total energy of the compressing system is proposed to evaluate the influence of pulsating conditions. Specifically, the energy change is reduced for pulsation conditions due to two aspects: the lower slope of compressor characteristic curve due to the lag-effect of compressor responses and the higher energy dissipation due to the non-linear throttling effect.

Soil Strength Reduction Method Induced by Variation of Water Content

2012 ◽  
Vol 170-173 ◽  
pp. 847-852
Author(s):  
Peng Ming Jiang ◽  
Zhong Lei Yan ◽  
Peng Li
Keyword(s):  
Slope Stability ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Characteristic Curve ◽  
Strength Reduction ◽  
Actual State ◽  
Soil Slope ◽  
Simple Method ◽  
The Common ◽  
The Stability

As the complexity of unsaturated soil theory, and it must have a long test period when we study the unsaturated soils, so the conventional design analysis software does not provide such analysis, so we can imagine that such a slope stability analysis does not accurately reflect the actual state of the slope. Based on the known soil moisture content，this paper use the soil water characteristic curve and strength theory of unsaturated soil to calculate the strength reduction parameters of soil which can calculate the stability of the soil slope when using the common calculation method. It is noticeable that this method can be extended and applied if we establish regional databases for this simple method, and these databases can improve the accuracy of the calculation of slope stability.

Effects of tip air injection on the aerodynamic stability of an axial flow compressor with total pressure distortion

2021 ◽  
pp. 095441002110375
Author(s):  
Baofeng Tu ◽  
Xinyu Zhang ◽  
Liang Li ◽  
Jun Hu
Keyword(s):  
Total Pressure ◽  
Critical Role ◽  
Axial Flow ◽  
Air Injection ◽  
Aerodynamic Stability ◽  
Insertion Depth ◽  
Stall Margin ◽  
Low Speed ◽  
Inlet Distortion ◽  
The Stability

The compressor is a critical component that determines the aerodynamic stability of an aero-engine. Total pressure inlet distortion decreases the thrust and shrinks the stability margin, thus inducing severe performance degradation or even flameout. Generally, tip air injection is used to reduce the adverse influence of total pressure inlet distortion on the aerodynamic stability. In the present work, an experimental investigation on the effects of tip air injection on the stability of a two-stage low-speed axial compressor with total pressure inlet distortion was carried out. A flat baffle generated the total pressure distortion at the inlet of the compressor. The stall margin of the compressor was reduced significantly by the total pressure distortion. When the dimensionless insertion depth of the flat baffle was 0.45, the stall margin decreased to 11.4%. Under the total pressure inlet distortion, tip air injection effectively improved the distortion resistance capability of the compressor. The circumferential layout of the nozzle played a critical role in the stability expansion effect of tip air injection under the inlet flow condition of the total pressure distortion. The modal wave disturbance was likely to occur in the distortion-affected region (the low-pressure region and the mixing region). Tip air injection did not inhibit the generation of the modal wave but restrained the development of the modal wave into the stall cell. It improved the low-speed compressor’s tolerance to the modal wave and allowed a higher amplitude modal wave to occur.

Dynamics of Wild and Sterile Mosquito Population Models with Delayed Releasing

2020 ◽  
Vol 30 (11) ◽  
pp. 2050218
Author(s):  
Li-Ming Cai
Keyword(s):  
Delay Differential Equations ◽  
Time Delays ◽  
Sterile Insect Technique ◽  
Sustained Oscillation ◽  
Hopf Bifurcations ◽  
Control Methods ◽  
Ode Models ◽  
Dynamical Features ◽  
The Stability ◽  
Delay Differential

To reduce the global burden of mosquito-borne diseases, e.g. dengue, malaria, the need to develop new control methods is to be highlighted. The sterile insect technique (SIT) and various genetic modification strategies, have a potential to contribute to a reversal of the current alarming disease trends. In our previous work, the ordinary differential equation (ODE) models with different releasing sterile mosquito strategies are investigated. However, in reality, implementing SIT and the releasing processes of sterile mosquitos are very complex. In particular, the delay phenomena always occur. To achieve suppression of wild mosquito populations, in this paper, we reassess the effect of the delayed releasing of sterile mosquitos on the suppression of interactive mosquito populations. We extend the previous ODE models to the delayed releasing models in two different ways of releasing sterile mosquitos, where both constant and exponentially distributed delays are considered, respectively. By applying the theory and methods of delay differential equations, the effect of time delays on the stability of equilibria in the system is rigorously analyzed. Some sustained oscillation phenomena via Hopf bifurcations in the system are observed. Numerical examples demonstrate rich dynamical features of the proposed models. Based on the obtained results, we also suggest some new releasing strategies for sterile mosquito populations.

Formulation of “Stability Equations” and Derivation of New Constructions with Complete Systems of Design-formulae for Variable-speed Control Mechanisms

1953 ◽  
Vol 167 (1) ◽  
pp. 319-339
Author(s):  
M. S. Frenkel
Keyword(s):  
Nuclear Physics ◽  
Characteristic Curve ◽  
Mathematical Formulation ◽  
Control Mechanisms ◽  
Variable Speed ◽  
Speed Governor ◽  
Minimum Number ◽  
Order Of Magnitude ◽  
The Stability ◽  
Stable Characteristic

Requirements for stability are formulated mathematically and, through the “transformatory operations of mathematics”, yield a series of “stability equations” of ascending order which are generally applicable, for example to control mechanisms, electronics†, nuclear physics, etc. From these stability equations, the equation of the stable characteristic curve of a governor, and the differential equations of the oscillations of a governor-engine system, are derived. It emerges that the first part of the new oscillatory equation is identical with the whole of the differential equation in the literature to date (unchanged since Maxwell 1868)‡, while the important second part, which consists of terms of the same order of magnitude as the first part and which is the only one containing the equation of the stable characteristic curve, is lacking in literature. The stability equations classify all possible constructions of variable-speed governor according to “order of stability”, which signifies important operating properties. This classification accounts for the known shortcomings of conventional types. The stability equations, combined with the mathematical formulation of practical requirements (speed-adjustment with only one actuating motion, etc.), lead to new basic types of variable-speed governor, with complete systems of design equations. In addition to determining all unknown dimensions, this set of equations is important because it derives constructions of which the complexity increases with order of stability and, furthermore, a simple construction which provides any required high order of stability with the minimum number of adjustable components.

Analysis of the Dynamics of Piecewise Linear Memristors

2016 ◽  
Vol 26 (13) ◽  
pp. 1650217 ◽  
Author(s):  
Fangfang Jiang ◽  
Zhicheng Ji ◽  
Qing-Guo Wang ◽  
Jitao Sun
Keyword(s):  
Piecewise Linear ◽  
Equilibrium Points ◽  
Characteristic Curve ◽  
Piecewise Linear Function ◽  
Excited Oscillation ◽  
Exciting Source ◽  
Memristive Circuits ◽  
The Stability ◽  
Straight Lines ◽  
The Mathematical Model

In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines [Formula: see text] (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results.

Impact of Exit Duct Dynamic Response on Compressor Stability

2019 ◽  
Author(s):  
Wenqiang Zhang ◽  
Mehdi Vahdati ◽  
Fanzhou Zhao
Keyword(s):  
Dynamic Response ◽  
Model Simulation ◽  
Stability Margin ◽  
Quantitative Relationship ◽  
Aerodynamic Stability ◽  
Stall Margin ◽  
Acoustic Reflection ◽  
Exit Nozzle ◽  
Fan Blade ◽  
The Stability

Abstract Abrupt distortions can appear as a result of transient crosswind or during rapid aircraft maneuvers. Such distortions are known to reduce the aerodynamic stability of engines and therefore present a major concern to all aero-engine manufacturers. To assess the aerodynamic stability of fan blades due to distortions, rig tests are usually carried out to establish the loss in stall margin. In such test campaigns, an exit duct (which is followed by a nozzle) is placed downstream of the fan blade and the operating condition of the fan is controlled by this nozzle. It is shown in this paper that in such rig tests the length of duct downstream of a fan has a significant impact on fan stall margin. The key contributor for such interaction is the dynamic response of the exit duct and the aerodynamic stability of the fan is affected by the acoustic reflection from the exit nozzle. To study the underlying physics, transient response in the exit duct downstream of a transonic fan stage was studied numerically using a simplified model. Simulation results, along with calculations based on analytical theories, confirmed the generation, propagation and reflection of waves induced by the inlet distortion. A quantitative relationship concerning the lengths of the compression system is introduced which determines whether a duct setup would have beneficial or detrimental influences on compressor aerodynamic stability. The findings of this research have great implications for the stability assessment of fans as the stability margin can be affected by the waves generated in bypass ducts.

Control of ATRIAS in three dimensions: Walking as a forced-oscillation problem

2020 ◽  
Vol 39 (7) ◽  
pp. 774-796
Author(s):  
Siavash Rezazadeh ◽  
Jonathan W Hurst
Keyword(s):  
Feedback Linearization ◽  
High Speed ◽  
Forced Oscillation ◽  
Vertical Motion ◽  
Three Dimensions ◽  
Singular Perturbation Theory ◽  
Foot Placement ◽  
Uneven Terrain ◽  
Walking Control ◽  
The Stability

In this article, we present a new controller for stable and robust walking control of ATRIAS, an underactuated bipedal robot designed based on the spring-loaded inverted pendulum (SLIP) model. We propose a forced-oscillation scheme for control of vertical motion, which we prove to be stable and contractive. Moreover, we prove that, through some mild assumptions, the dynamics of the system can be written in a hierarchical form that decouples the stability analyses of the horizontal and vertical directions. We leverage these properties to find a stabilizing class of functions for foot placement. The torso control is also proved to be decoupled using singular perturbation theory and is stabilized through a feedback linearization controller. We also take advantage of the proposed framework’s flexibility and extend it to include a new reflex-based uneven-terrain walking control scheme. We test the controller for various desired walking speeds (0 to 2.5 m/s), for stepping up and down unexpected obstacles (15 cm), and for high-speed walking on a random uneven terrain (up to 10 cm of step-ups and step-downs and up to 1.8 m/s). The results show successful performance of the controller and its stability and robustness against various perturbations.

Study on support characteristic curve of primary support structures in underground excavation considering bond-slip behavior

2020 ◽  
pp. 136943322095876
Author(s):  
Wei Lu ◽  
Huibin Sun
Keyword(s):  
Performance Test ◽  
Characteristic Curve ◽  
Mechanical Analysis ◽  
Bending Test ◽  
Underground Excavation ◽  
Bond Slip ◽  
Four Point Bending ◽  
Parametric Studies ◽  
The Stability ◽  
Shotcrete Lining

Steel reinforced shotcrete lining (SRSL) support is the primary structure to maintain the stability and mobilize the self-bearing capacity of surrounding rock. However, the structural design of SRSL in underground excavation still relies on experience-based method and lack of quantitative mechanical analysis. This paper aims to propose a modified analytical model of support characteristic curve (SCC) that represents the mechanical behavior of SRSL structures in underground construction, through which the interface bond-slip behavior between steel arch and shotcrete layer is taken into consideration. Four-point bending test of SRSL composite beam was carried out to study the bearing mechanism and failure performance. Test results show that the shotcrete-steel interface is prone to slip failure which significantly reduces the overall strength of SRSL. The laboratory test is complemented by non-liner finite element parametric studies considering the bond-slip properties to clarify the design principles and to obtain the flexural stiffness of tunnel primary lining structures. Based on above studies, the simplified formulas for the SCC of SRSL is constructed. The research results provide a theoretical basis for the design and application of SRSL structure in related projects.

Works of A.A. Samarskii on Computational Mathematics

2009 ◽  
Vol 9 (1) ◽  
pp. 5-36
Author(s):  
P.N. Vabishchevich
Keyword(s):  
Gas Dynamics ◽  
Research Output ◽  
Mathematical Physics ◽  
Natural Sciences ◽  
Stability And Convergence ◽  
Russian Mathematician ◽  
Thermal Physics ◽  
Computational Mathematics ◽  
Mathematical Proofs ◽  
The Stability

Abstract This is a review of the main results in computational mathematics that were obtained by the eminent Russian mathematician Alexander Andreevich Samarskii (February 19, 1919 – February 11, 2008). His outstanding research output addresses all the main questions that arise in the construction and justification of algorithms for the numerical solution of problems from mathematical physics. The remarkable works of A.A. Samarskii include statements of the main principles re- quired in the construction of difference schemes, rigorous mathematical proofs of the stability and convergence of these schemes, and also investigations of their algorith- mic implementation. A.A. Samarskii and his collaborators constructed and applied in practical calculations a large number of algorithms for solving various problems from mathematical physics, including thermal physics, gas dynamics, magnetic gas dynam- ics, plasma physics, ecology and other important models from the natural sciences.

scholarly journals Frequency Tuning of a Disk Resonator Gyro Via Mass Matrix Perturbation

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
David Schwartz ◽  
Dong Joon Kim ◽  
Robert T. M’Closkey
Keyword(s):  
High Performance ◽  
Frequency Tuning ◽  
Perturbation Technique ◽  
Mass Matrix ◽  
Resonant Mode ◽  
Matrix Perturbation ◽  
Operating Environment ◽  
Vibratory Gyroscopes ◽  
Resonant Modes ◽  
The Stability

Electrostatic tuning of the resonant modes in microelectromechanical vibratory gyroscopes is often suggested as a means for compensating manufacturing aberrations that produce detuned resonances. In high performance sensors, however, this approach places very stringent requirements on the stability of the bias voltages used for tuning. Furthermore, the bias voltage stability must be maintained over the operating environment, especially with regard to temperature variations. An alternative solution to this problem is to use mass perturbations of the sensor’s resonant structure for resonant mode tuning. This paper presents a new mass perturbation technique that only relies on the sensor’s integrated actuators and pick-offs to guide the mass perturbation process. The algorithm is amenable to automation and eliminates the requirement that the modal nodes of the resonator be identified by direct measurement.

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