Combustor-inlet interactions in a low-order dynamic model of ramjet engines

2020 ◽  
Vol 124 (1282) ◽  
pp. 2001-2018
Author(s):  
K. Liu ◽  
T. Cui
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Nonlinear Effects ◽  
Physical Parameters ◽  
Nonlinear Phenomena ◽  
Stable States ◽  
Dynamic Framework ◽  
Ramjet Engine ◽  
Multiple Stable States ◽  
Ramjet Engines

ABSTRACTThe coexistence of multiple stable states is indicative of self-organising processes occurring in the course of the combustor-inlet interactions in a ramjet engine and give rise to the appearance of various nonlinear phenomena. This paper provides a dynamic model that can describe the multiple stable states and the corresponding nonlinear effects to further investigate the dynamic interactions between combustor and inlet in a ramjet engine. Our study shows the whole engine can display distinct dynamic behaviours ranging from irreversibility to hysteresis and to various mode transitions, depending on different physical parameters. With the model, we also illustrate the role of the instability of the normal shock wave in impacting the whole engine’s nonlinear dynamics. Additionally, we extend the previous studies of the classification of combustor-inlet interactions from a static framework to a dynamic framework, which helps to clarify the transient processes of the nonlinear interactions. This work offers a quantitative illustration of the combustor-inlet interactions in a ramjet engine by revealing its nonlinear dynamics and associated characteristics, therefore advancing our understanding of the nonlinear phenomena that exhibit in ramjet engines.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

A Dynamic Model for the Design of Methanol to Hydrogen Steam Reformers for Transportation Applications

2004 ◽  
Vol 126 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Gregory L. Ohl ◽  
Jeffrey L. Stein ◽  
Gene E. Smith
Keyword(s):  
Response Time ◽  
Dynamic Model ◽  
First Principles ◽  
Initial Conditions ◽  
Design Parameters ◽  
Physical Parameters ◽  
Steam Reformer ◽  
Powerful Means ◽  
Steam Reformers ◽  
Transportation Applications

As an aid to improving the dynamic response of the steam reformer, a dynamic model is developed to provide preliminary characterizations of the major constraints that limit the ability of a reformer to respond to the varying output requirements occurring in vehicular applications. This model is a first principles model that identifies important physical parameters in the steam reformer. The model is then incorporated into a design optimization process, where minimum steam reformer response time is specified as the objective function. This tool is shown to have the potential to be a powerful means of determining the values of the steam reformer design parameters that yield the fastest response time to a step input in hydrogen demand for a given set of initial conditions. A more extensive application of this methodology, yielding steam reformer design recommendations, is contained in a related publication.

Trapped liquid drop in a microchannel: Multiple stable states

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Zhengjia Wang ◽  
Cheng-Chung Chang ◽  
Siang-Jie Hong ◽  
Yu-Jane Sheng ◽  
Heng-Kwong Tsao
Keyword(s):  
Liquid Drop ◽  
Stable States ◽  
Multiple Stable States

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

Dynamic Instability in Quartering Seas—Part III: Nonlinear Effects on Periodic Motions

1997 ◽  
Vol 41 (03) ◽  
pp. 210-223 ◽  
Author(s):  
K. J. Spyrou
Keyword(s):  
Periodic Motion ◽  
Horizontal Plane ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Nonlinear Effects ◽  
Ship Motions ◽  
Nonlinear Phenomena ◽  
Specific Sequence ◽  
The Stability ◽  
Two Stages

The loss of stability of the horizontal-plane periodic motion of a steered ship in waves is investigated. In earlier reports we referred to the possibility of a broaching mechanism that will be intrinsic to the periodic mode, whereby there will exist no need for the ship to go through the surf-riding stage. However, about this point the discussion was essentially conjectural. In order to provide substance we present here a theoretical approach that is organized in two stages: Initially, we demonstrate the existence of a mechanism of parametric instability of yaw on the basis of a rudimentary, single-degree model of maneuvering motion in waves. Then, with a more elaborate model, we identify the underlying nonlinear phenomena that govern the large-amplitude horizontal ship motions, considering the ship as a multi-degree, nonlinear oscillator. Our analysis brings to light a very specific sequence of phenomena leading to cumulative broaching that involves a change in the stability of the ordinary periodic motion on the horizontal plane, a transition towards subharmonic response and, ultimately, a sudden jump to resonance. Possible means for controlling the onset of such undesirable behavior are also investigated.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

scholarly journals Population dynamics of synthetic Terraformation motifs

2016 ◽  
Author(s):  
Ricard V. Solé ◽  
Raúl Montañez ◽  
Salvador Duran Nebreda ◽  
Daniel Rodriguez-Amor ◽  
Blai Vidiella ◽  
...  
Keyword(s):  
Habitat Degradation ◽  
Ecological Engineering ◽  
Ecological Interactions ◽  
Stable States ◽  
Population Extinction ◽  
Intensive Exploitation ◽  
Engineering Designs ◽  
Synthetic Organisms ◽  
Multiple Stable States ◽  
Catastrophic Shifts

Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation, and human-driven habitat degradation. Such threats are pushing ecosystems to the brink of collapse. Because of a general presence of multiple stable states, including states involving population extinction, and due to intrinsic nonlinearities associated with feedback loops, collapse can occur in a catastrophic manner. Such catastrophic shifts have been suggested to pervade many of the future transitions affecting ecosystems at many different scales. Many studies have tried to delineate potential warning signals predicting such ongoing shifts but little is known about how such transitions might be effectively prevented. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. Four classes of such ecological engineering designs orTerraformation motifshave been defined in a qualitative way. Here we develop the simplest mathematical models associated with these motifs, defining the expected stability conditions and domains where the motifs shall properly work.

Dynamic Behavior Analysis of Three-Span Rotor-Bearing System with Rub-Impact Fault

2012 ◽  
Vol 460 ◽  
pp. 160-164 ◽  
Author(s):  
Song He Zhang ◽  
Yue Gang Luo ◽  
Bin Wu ◽  
Bang Chun Wen
Keyword(s):  
Nonlinear Dynamics ◽  
Behavior Analysis ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Rotor System ◽  
System Response ◽  
Rotor Bearing ◽  
Set Up ◽  
Bearing System ◽  
Main Influence

The dynamic model of the three-span rotor-bearing system with rub-impact fault was set up. The influence to nonlinear dynamics behaviors of the rotor-bearing system that induced by rub-impact of one disc, two discs and three discs were numerically studied. The main influence of the rotor system response by the rub-impact faults are in the supercritical rotate speed. There are mutations of amplitudes in the responses of second and third spans in supercritical rotate speed when rub-impact with one disc, and there are chaotic windows in the response of first span, and jumping changes in second and third spans when rub-impact with two or three discs.

scholarly journals Multiple stable states of tree cover in a global land surface model due to a fire-vegetation feedback

2016 ◽  
Vol 43 (12) ◽  
pp. 6324-6331 ◽  
Author(s):  
G. Lasslop ◽  
V. Brovkin ◽  
C. H. Reick ◽  
S. Bathiany ◽  
S. Kloster
Keyword(s):  
Land Surface ◽  
Land Surface Model ◽  
Tree Cover ◽  
Surface Model ◽  
Stable States ◽  
Vegetation Feedback ◽  
Global Land ◽  
Multiple Stable States
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