A nonlinear model for indirect combustion noise through a compact nozzle

2013 ◽  
Vol 733 ◽  
pp. 268-301 ◽  
Author(s):  
Maxime Huet ◽  
Alexis Giauque
Keyword(s):  
Nonlinear Response ◽  
Regime Change ◽  
Low Frequency ◽  
Maximum Amplitude ◽  
Second Order ◽  
Combustion Noise ◽  
Order System ◽  
Order Model ◽  
Describing Functions ◽  
Low Amplitude

AbstractThe present paper deals with the generation of sound by the passage of acoustic or entropy perturbations through a nozzle in the nonlinear regime and in the low-frequency limit. The analytical model of Marble and Candel for compact nozzles (J. Sound Vib., vol. 55, 1977, pp. 225–243), initially developed for excitations in the linear regime, is rederived and extended to the nonlinear domain. Full nonlinear and second-order models are written for both subcritical and supercritical nozzles in the absence of shock and a detailed methodology is provided for the resolution of the second-order system. The accuracy of the second-order model is assessed for entropy forcings. It is shown to be accurate for all waves, with the exception of the upstream generated wave for subcritical diverging geometries where higher-order nonlinear contributions cannot be neglected. In the context of indirect combustion noise, the phenomenon of regime change of the nozzle due to an incoming entropy fluctuation is also addressed. Regime change is related to a Mach number modification induced by temperature and velocity fluctuations. In the present study, it translates into a limitation of the maximum amplitude of the incoming entropy forcing. Such limitations are to be considered for subcritical nozzles with significant inlet or outlet Mach numbers, where the flow transition is observed even for very low-amplitude entropy excitations. With the constraint of those limitations, the analytical extended nozzle describing functions representing the full nonlinear response for indirect combustion noise are validated through detailed comparisons with numerical simulations.

Identifying parametric variation in second-order system from frequency response measurement

2016 ◽  
Vol 24 (5) ◽  
pp. 879-891 ◽  
Author(s):  
A Hegde ◽  
J Tang
Keyword(s):  
Frequency Response ◽  
Parametric Identification ◽  
Second Order ◽  
Order System ◽  
Model Parameters ◽  
Order Model ◽  
Response Measurement ◽  
Electrical Systems ◽  
Angle Measurements ◽  
Second Order Model

Fundamentally, second-order model is the foundation of describing the dynamic characteristics of many mechanical and electrical systems. This paper investigates a parametric identification scheme for single degree-of-freedom second-order model in which the model parameters are subject to normal variation. By utilizing frequency response magnitude and phase angle measurements, we construct a linear-in-the-parameters model and build a related maximum likelihood estimator for both parametric means as well as variances. The validity of the approach is demonstrated through a collection of case analyses, and the results show considerable levels of accuracy in the presence of sufficient data.

scholarly journals Modeling and Order Reduction for the Thermodynamics of a Diesel Oxidation Catalyst with Hydrocarbon Dosing

Catalysts ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 369
Author(s):  
Wu ◽  
Zhang ◽  
Yao ◽  
Yang
Keyword(s):  
Reduction Process ◽  
Order Reduction ◽  
Diesel Oxidation Catalyst ◽  
Second Order ◽  
Oxidation Catalyst ◽  
Order System ◽  
Storage Process ◽  
Order Model ◽  
Thermal Dynamics ◽  
Diesel Oxidation

This paper presents an order reduction for the thermal dynamics of a diesel oxidation catalyst (DOC) with hydrocarbon (HC) dosing. The original model includes the pyrolysis of diesel droplets and a wall storage process in the upstream of the DOC. The order reduction process is derived from the thermodynamics model of the DOC for further control design. The results are compared with experimental data. It is found that the DOC can be simplified as a second-order model using the HC dosing model, which has more than 94% fitness, reflecting the thermodynamics of the system. According to this research, the DOC thermal dynamics can be considered to be equivalent to a time-varying second-order system for the investigation. The second-order parameters of K, Tw, and ζ are also investigated in this paper.

Frequency response of human soleus muscle

1976 ◽  
Vol 39 (4) ◽  
pp. 788-793 ◽  
Author(s):  
P. Bawa ◽  
R. B. Stein
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Soleus Muscle ◽  
Damping Ratio ◽  
Low Frequency ◽  
Second Order ◽  
Order System ◽  
Pass Filter ◽  
Stimulus Pulse ◽  
Low Pass Filter

1. The properties of human soleus muscle were studied by systems analysis. Single stimulus pulses and random stimulus pulse trains were applied to a branch of the nerve to soleus muscle and the resultant tension fluctuations were recorded. 2. The frequency-response function between stimulus pulses and tension conforms to that of a second-order, low-pass filter. The parameters of the second-order system, low frequency gain, natural frequency, and damping ratio, varied systematically with the angle of the ankle. As the ankle was flexed (the length of the muscle was increased), the low frequency gain increased, the natural frequency decreased, and the damping ratio was unaffected or increased slightly. 3. These results are discussed in relation to the twitch responses of human soleus muscles and the responses previously observed in cat muscles.

Natural Forcing Functions in Nonlinear Systems

1958 ◽  
Vol 25 (3) ◽  
pp. 352-356
Author(s):  
T. J. Harvey
Keyword(s):  
Frequency Response ◽  
Maximum Amplitude ◽  
Second Order ◽  
Point Of View ◽  
Order System ◽  
Nonlinear Frequency ◽  
Restoring Force ◽  
Forcing Function ◽  
Special Cases ◽  
Forcing Functions

Abstract The response of nonlinear, second-order systems is examined from a new point of view which greatly simplifies presentation of the usual frequency-response diagrams. The use of “natural” forcing functions results in a general equation relating the maximum amplitude of the applied force to the maximum amplitude of the restoring force. The relationship is found to be a function of the ratio of the period of free oscillation to the period of the forcing function. The results apply for any second-order system without damping and with a nonlinear (or linear) restoring force. The special cases of a linear system and of Duffing’s equation are considered to illustrate similarities as well as differences between treatment of linear and nonlinear frequency-response problems.

Bifurcation Transition and Nonlinear Response in a Fractional-Order System

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
J. H. Yang ◽  
M. A. F. Sanjuán ◽  
H. G. Liu ◽  
G. Cheng
Keyword(s):  
Fractional Order ◽  
High Frequency ◽  
Nonlinear Response ◽  
System Parameter ◽  
Low Frequency ◽  
Transcritical Bifurcation ◽  
Fractional Order System ◽  
Order System ◽  
Saddle Node Bifurcation ◽  
Saddle Node

We extend a typical system that possesses a transcritical bifurcation to a fractional-order version. The bifurcation and the resonance phenomenon in the considered system are investigated by both analytical and numerical methods. In the absence of external excitations or simply considering only one low-frequency excitation, the system parameter induces a continuous transcritical bifurcation. When both low- and high-frequency forces are acting, the high-frequency force has a biasing effect and it makes the continuous transcritical bifurcation transit to a discontinuous saddle-node bifurcation. For this case, the system parameter, the high-frequency force, and the fractional-order have effects on the saddle-node bifurcation. The system parameter induces twice a saddle-node bifurcation. The amplitude of the high-frequency force and the fractional-order induce only once a saddle-node bifurcation in the subcritical and the supercritical case, respectively. The system presents a nonlinear response to the low-frequency force. The system parameter and the low-frequency can induce a resonance-like behavior, though the high-frequency force and the fractional-order cannot induce it. We believe that the results of this paper might contribute to a better understanding of the bifurcation and resonance in the excited fractional-order system.

Second-order classical nonlinear response theory

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 962-965
Author(s):  
Abdulmuhsen H. Ali
Keyword(s):  
Nonlinear Response ◽  
Second Order ◽  
Response Theory

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

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