Combustion System Damping Augmentation With Helmholtz Resonators

1998 ◽  
Author(s):  
D. L. Gysling ◽  
G. S. Copeland ◽  
D. C. McCormick ◽  
W. M. Proscia
Keyword(s):  
System Dynamics ◽  
Small Amplitude ◽  
Linear Instability ◽  
Side Branch ◽  
System Stability ◽  
Simplified Model ◽  
Model Parameters ◽  
Combustion System ◽  
Pressure Oscillations ◽  
Helmholtz Resonators

This paper describes an analytical and experimental investigation to enhance combustion system operability using side branch resonators. First, a simplified model of the combustion system dynamics is developed in which the large amplitude pressure oscillations encountered at the operability limit are viewed as limit cycle oscillations of an initially linear instability. Under this assumption, increasing the damping of the small amplitude combustion system dynamics will increase combustor operability. The model is then modified to include side branch resonators. The parameters describing the side branch resonators and their coupling to the combustion system are identified, and their influence on system stability is examined. The parameters of the side branch resonator are optimized to maximize damping augmentation and frequency robustness. Secondly, the model parameters for the combustor and side branch resonator dynamics are identified from experimental data. The analytical model predicts the observed trends in combustor operability as a function of the resonator parameters and is shown to be a useful guide in developing resonators to improve the operability of combustion systems.

Combustion System Damping Augmentation With Helmholtz Resonators

1999 ◽  
Vol 122 (2) ◽  
pp. 269-274 ◽  
Author(s):  
D. L. Gysling ◽  
G. S. Copeland ◽  
D. C. McCormick ◽  
W. M. Proscia
Keyword(s):  
System Dynamics ◽  
Small Amplitude ◽  
Linear Instability ◽  
Side Branch ◽  
System Stability ◽  
Simplified Model ◽  
Model Parameters ◽  
Combustion System ◽  
Pressure Oscillations ◽  
Helmholtz Resonators

This paper describes an analytical and experimental investigation to enhance combustion system operability using side branch resonators. First, a simplified model of the combustion system dynamics is developed in which the large amplitude pressure oscillations encountered at the operability limit are viewed as limit cycle oscillations of an initially linear instability. Under this assumption, increasing the damping of the small amplitude combustion system dynamics will increase combustor operability. The model is then modified to include side branch resonators. The parameters describing the side branch resonators and their coupling to the combustion system are identified, and their influence on system stability is examined. The parameters of the side branch resonator are optimized to maximize damping augmentation and frequency robustness. Secondly, the model parameters for the combustor and side branch resonator dynamics are identified from experimental data. The analytical model predicts the observed trends in combustor operability as a function of the resonator parameters and is shown to be a useful guide in developing resonators to improve the operability of combustion systems. [S0742-4795(00)00602-5]

Model Parameter Identification of Nonlinear Dynamics Systems by Trajectory Pattern Method

2010 ◽  
Author(s):  
Jahangir Rastegar ◽  
Dake Feng ◽  
Kavous Jorabchi
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Parameter Identification ◽  
System Stability ◽  
Model Parameters ◽  
System Dynamics Model ◽  
Dynamics Model ◽  
Higher Order Terms ◽  
Trajectory Pattern ◽  
Trajectory Pattern Method

In this paper, a new method is presented for model parameter identification of a large class of fully controlled nonlinear dynamics systems such as robot manipulators. The method uses trajectory patterns with feed-forward controls to identify model parameters of the system. The developed method ensures full system stability, does not require close initial estimated values for the parameters to be identified, and provides a systematic method of emphasizing on the estimation of the parameters associated with lower order terms of the system dynamics model and gradually upgrading the accuracy with which the model parameters, particularly those associated with the higher order terms of the system dynamics model are estimated. The developed method is based on Trajectory Pattern Method (TPM). In this method, for a pattern of motion the inverse dynamics model of the system is derived in algebraic form in terms of the trajectory pattern parameters. The system dynamics model parameters are then identified using a systematic algorithm which ensures system stability as well as accurate estimation of the model parameters associated with lower as well as higher order terms. Mathematical proof of convergence of the developed method and an example of its application are provided.

Model Parameter Identification for Non-Fully Controlled Nonlinear Dynamics Systems Using Trajectory Pattern Method

2013 ◽  
Author(s):  
Dake Feng ◽  
Jahangir Rastegar
Keyword(s):  
Nonlinear Dynamics ◽  
System Dynamics ◽  
Parameter Identification ◽  
Mathematical Proof ◽  
System Stability ◽  
Model Parameters ◽  
Model Parameter ◽  
Trajectory Pattern ◽  
Model Parameter Identification ◽  
Trajectory Pattern Method

In this paper, a new method is presented for model parameter identification of a large class of nonlinear dynamics systems that are not fully controlled. The method uses trajectory patterns with feed-forward controls to identify model parameters of the system. The developed method ensures full system stability, does not require close initial estimated values for the parameters to be identified, and provides a systematic method of emphasizing on the estimation of the parameters associated with lower order terms of the system dynamics model and gradually upgrading the accuracy with which the model parameters, particularly those associated with the higher order terms of the system dynamics, are estimated. The developed method is based on Trajectory Pattern Method (TPM). The mathematical proof of convergence of the developed method and results of its implementation on a typical system with highly non-linear dynamics are provided.

Sound Attenuation in a Flow Duct Periodically Loaded With Micro-Perforated Patches Backed by Helmholtz Resonators

2018 ◽  
Author(s):  
T. Bravo ◽  
C. Maury
Keyword(s):  
Separation Distance ◽  
Side Branch ◽  
Optimal Choice ◽  
Sound Attenuation ◽  
Limited Area ◽  
Frequency Noise ◽  
Matrix Formulation ◽  
Wave Regime ◽  
Helmholtz Resonators ◽  
Periodic Distribution

Mitigating the propagation of low frequency noise sources in ducted flows represents a challenging task since wall treatments have often a limited area and thickness. Loading the periphery of a duct with a periodic distribution of side-branch Helmholtz resonators broadens the bandwidth of the noise attenuated with respect to a single resonator and generates stop bands that inhibit wave propagation. However, significant flow pressure drop may occur along the duct axis that could be reduced using micro-perforated patches at the duct-neck junctions. In this study, a transfer matrix formulation is derived to determine the sound attenuation properties of a periodic distribution of MPPs backed by Helmholtz resonators along the walls of a duct in the plane wave regime. In the no-flow case, it is shown that an optimal choice of the MPP parameters and resonators separation distance lowers the frequencies of maximal attenuation while maintaining broad stopping bands. As observed in the no-flow and low-speed flow cases, these frequencies can be further decreased by coiling the acoustic path length in the resonators cavity, albeit at the expense of narrower bands of low pressure transmission. The achieved effective wall impedances are compared against Cremer optimal impedance at the first attenuation peak.

scholarly journals Methods for the Calculation of Thermoacoustic Stability Margins and Monte Carlo-Free Uncertainty Quantification

2017 ◽  
Author(s):  
Georg A. Mensah ◽  
Luca Magri ◽  
Jonas P. Moeck
Keyword(s):  
Monte Carlo ◽  
Factor Analysis ◽  
Risk Factor ◽  
Uncertainty Quantification ◽  
Frequency Domain ◽  
Gas Turbines ◽  
Network Models ◽  
System Stability ◽  
Risk Factor Analysis ◽  
Model Parameters

Thermoacoustic instabilities are a major threat for modern gas turbines. Frequency-domain based stability methods, such as network models and Helmholtz solvers, are common design tools because they are fast compared to compressible CFD computations. Frequency-domain approaches result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Nonlinear functions of the frequency are, for example, the n–τ model, impedance boundary conditions, etc. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, which are obtained by experiments with some uncertainty, may have a great impact on stability. The assessment of how parameter uncertainties propagate to system stability is therefore crucial for safe gas turbine operation. This question is addressed by uncertainty quantification. A common strategy for uncertainty quantification in thermoacoustics is risk factor analysis. It quantifies the uncertainty of a set of parameters in terms of the probability of a mode to become unstable. One general challenge regarding uncertainty quantification is the sheer number of uncertain parameter combinations to be quantified. For instance, uncertain parameters in an annular combustor might be the equivalence ratio, convection times, geometrical parameters, boundary impedances, flame response model parameters etc. Assessing also the influence of all possible combinations of these parameters on the risk factor is a numerically very costly task. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the eigenfrequency problem is using adjoint perturbation theory. Though adjoint perturbation methods were recently applied to accelerate the risk factor analysis, its potential to improve the theory has not yet been fully exploited. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo simulations, making it particularly attractive for industrial purposes. Using network models and the open-source Helmholtz solver PyHoltz it is also discussed how to apply the method with standard modeling techniques. The theory is exemplified based on a simple ducted flame and a combustor of EM2C laboratory for which experimental validation is available.

DETERMINATION OF MODEL PARAMETERS OF ROCKET STABILIZATION SYSTEM IN FLIGHT

2021 ◽  
Vol 6 ◽  
pp. 78-92
Author(s):  
Volt Avdejev ◽  
Keyword(s):  
Relative Weight ◽  
Stability Margin ◽  
Current Data ◽  
System Stability ◽  
System Of Nonlinear Equations ◽  
Model Parameters ◽  
Control Law ◽  
Stabilization System ◽  
Measuring Devices ◽  
Perturbation Compensation

The dynamic characteristics of the system that includes the controlled object and the regulator largely depend on the choice of the control law, which is determined based on the nominal values of the parameters of the mathematical model of the stabilization process and its priority indicator. Due to the deviation of the missile parameters and, accordingly, the model from the nominal values, the designers set the safety factors based on the most unfavorable conditions, which negatively affects the overall performance, in particular, the relative weight of the payload. Therefore, there is a need to develop algorithms for adjustment that is identification model parameters during the flight using the signals of measuring devices and the capabilities of on-board computers. This will increase the efficiency of methods of choosing the control law based on such indicators as stabilization accuracy, stability margin and power requirements of the actuator. The aim of the article is to develop methods for refining the parameters of the rocket stabilization system in the yawing plane, which are based on the use of current data of measuring devices of the part of coordinates of the state vector, and verify the effectiveness of refinement in terms of the above indicators. A linear stationary model of a system for stabilizing the perturbed motion of a rocket taking into account the inertia of the actuator in the form of ordinary fifth-order differential equations is adopted. Two approaches are proposed to approximate the model parameters to their actual values. In the first in the model parameter space there is a minimum of the integral of the distance between the points of the trajectory according to the signals of the measuring devices and the trajectory obtained by modeling the perturbation compensation process. In the second, the actual values of the parameters are the result of solving a system of nonlinear equations, which includes data from measuring devices and the corresponding data obtained by simulation. On the example of space rocket parameters it is shown that the choice of the control law based on the actual coefficients of the model leads to a significant reduction of deviations from the set value of the system stability margin, stabilization error and power of the actuator.

STABILITY OF SISO NONLINEAR SYSTEMS WITH PARAMETERS DISTURBANCES

2012 ◽  
Vol 26 (25) ◽  
pp. 1246008
Author(s):  
OLGA SHPILEVAYA
Keyword(s):  
Nonlinear Systems ◽  
System Dynamics ◽  
Control Systems ◽  
Lyapunov Method ◽  
Switched System ◽  
System Stability ◽  
Single Input Single Output ◽  
Single Output ◽  
System Output ◽  
Single Input

We study single-input single-output (SISO) control systems with the rapid piecewise-smooth parameters disturbances. The system dynamics are described by switched system models. The system output is regulated with the help of the nonlinear astatic controller with parameters which depend on some disturbance properties. The system stability is studied by second Lyapunov method.

scholarly journals Simplified Building Thermal Model Development and Parameters Evaluation Using a Stochastic Approach

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2899
Author(s):  
Abhinandana Boodi ◽  
Karim Beddiar ◽  
Yassine Amirat ◽  
Mohamed Benbouzid
Keyword(s):  
Reference Model ◽  
Model Development ◽  
Network Models ◽  
Real Data ◽  
Stochastic Approach ◽  
Simplified Model ◽  
Model Parameters ◽  
Order Model ◽  
Parameter Values ◽  
Low Order

This paper proposes an approach to develop building dynamic thermal models that are of paramount importance for controller application. In this context, controller requires a low-order, computationally efficient, and accurate models to achieve higher performance. An efficient building model is developed by having proper structural knowledge of low-order model and identifying its parameter values. Simplified low-order systems can be developed using thermal network models using thermal resistances and capacitances. In order to determine the low-order model parameter values, a specific approach is proposed using a stochastic particle swarm optimization. This method provides a significant approximation of the parameters when compared to the reference model whilst allowing low-order model to achieve 40% to 50% computational efficiency than the reference one. Additionally, extensive simulations are carried to evaluate the proposed simplified model with solar radiation and identified model parameters. The developed simplified model is afterward validated with real data from a case study building where the achieved results clearly show a high degree of accuracy compared to the actual data.

scholarly journals Black-Box Behavioral Modeling of Voltage and Frequency Response Characteristic for Islanded Microgrid

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2049 ◽  
Author(s):  
Yong Shi ◽  
Dong Xu ◽  
Jianhui Su ◽  
Ning Liu ◽  
Hongru Yu ◽  
...  
Keyword(s):  
Frequency Response ◽  
Least Squares Method ◽  
Model Identification ◽  
Response Characteristic ◽  
Black Box ◽  
System Stability ◽  
Model Parameters ◽  
Response Model ◽  
Modeling Process ◽  
Damped Least Squares

The voltage and frequency response model of microgrid is significant for its application in the design of secondary voltage frequency controller and system stability analysis. However, most models developed for this aspect are complex in structure due to the difficult mechanism modeling process and are only suitable for offline identification. To solve these problems, this paper proposes a black-box modeling method to identify the voltage and frequency response model of microgrid online. Firstly, the microgrid system is set as a two-input, two-output black-box system and can be modeled only by data sampled at the input and output ports. Therefore, the simplicity of modeling steps can be guaranteed. Meanwhile, the recursive damped least squares method is used to realize the online model identification of the microgrid system, so that the model parameters can be adjusted with the change of the microgrid operating structure, which makes the model more adaptable. The paper analyzes the black-box modeling process of the microgrid system in detail, and the microgrid platform, including 100 kW rated power inverters, is employed to validate the analysis and experimental results.

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