Thermoacoustic Stability Analysis of an Annular Combustion Chamber With Acoustic Low Order Modeling and Validation Against Experiment

2005 ◽  
Author(s):  
Jan Kopitz ◽  
Andreas Huber ◽  
Thomas Sattelmayer ◽  
Wolfgang Polifke
Keyword(s):  
Transfer Function ◽  
Network Model ◽  
Transfer Functions ◽  
Model Simulation ◽  
Scaling Methods ◽  
Annular Combustor ◽  
The Stability ◽  
Operating Points ◽  
Low Order

A low order acoustic network model is used to examine the stability of an annular combustor for different operating points. The results obtained by this approach are compared against experimental data from a full annular combustor. This annular combustor, in contrast to commonly used single burners or sector rigs, was used to include also 2-dimensional effects like the influence of circumferential modes, which can occur in practical gas turbine applications. The influence of the flame enters the network model simulation through an experimentally measured flame transfer function in terms of the response of heat release to acoustic velocity fluctuations. This flame transfer function, which has been measured at a stable operating point, is then used as a basis for the determination of flame transfer functions at other operating points by means of scaling methods. The transition to instability is thereby simulated by determination of the complex eigen modes, applying methods from control theory. The analytically determined stability behavior is compared to the experimentally measured one, with the aim to enhance and validate the network model approach as a means of predicting combustion instabilities in early design stages.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

scholarly journals On the Essential Instabilities Caused by Fractional-Order Transfer Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Farshad Merrikh-Bayat ◽  
Masoud Karimi-Ghartemani
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Stability Condition ◽  
Transfer Functions ◽  
Branch Points ◽  
The Stability ◽  
Unstable Branch

The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles. So, in this case, not only the characteristic equation but the numerator term is of significant importance. In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback. Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term. The effect of unstable branch points is studied and simulations are presented.

scholarly journals The Transfer Function of the SARS-CoV-2 Spread in Different Countries with Stability, Observability, and Controllability Analysis

2021 ◽  
Author(s):  
Jasmina Lozanović Šajić ◽  
Sonja Langthaler ◽  
Sara Stoppacher ◽  
Christian Baumgartner
Keyword(s):  
Differential Equation ◽  
System Theory ◽  
Control System ◽  
System Identification ◽  
Transfer Function ◽  
State Space ◽  
Separate System ◽  
The Stability ◽  
Controllability And Observability

Abstract This paper presents the determination of the transfer function of the spreading pandemic caused by SARS-CoV-2 in different countries. The methodology of system identification, well known in control system theory, based on the number of infected was used. Appropriate hypotheses have been adopted to determine the transfer function of the system. Each country is viewed as a separate system, and comparisons of determined systems are given. The systems are also presented in the state space, the stability of the systems is analysed, and the matrices of controllability and observability are determined. After analysis, it is shown that the spread of the SARS-CoV-2, for each country, can be described with the same order of transfer function and differential equation.

scholarly journals Best L1 Piecewise Monotonic Data Approximation in Overhead and Underground Medium-Voltage and Low-Voltage Broadband over Power Lines Networks: Theoretical and Practical Transfer Function Determination

2016 ◽  
Vol 2016 ◽  
pp. 1-24 ◽  
Author(s):  
Athanasios G. Lazaropoulos
Keyword(s):  
Transfer Function ◽  
Normal Distribution ◽  
Performance Metrics ◽  
Transfer Functions ◽  
Low Voltage ◽  
Power Lines ◽  
Data Approximation ◽  
Medium Voltage ◽  
Piecewise Monotonic

This paper investigates the efficiency and accuracy of the best L1 piecewise monotonic data approximation (best L1PMA) in order either to approximate the transfer functions of distribution BPL networks or to reveal the aforementioned transfer functions when various faults occur during their determination. The contribution of this paper is quadruple. First, based on the inherent piecewise monotonicity of distribution BPL transfer functions, a piecewise monotonic data approximation is first applied in BPL networks; best L1PMA is outlined and applied during the determination of distribution BPL transfer functions. Second, suitable performance metrics such as the percent error sum (PES) and fault PES are reported and applied so as to assess the efficiency and accuracy of the best L1PMA during the determination of distribution BPL transfer functions. Third, the factors of distribution BPL networks that influence the performance of best L1PMA are identified. Fourth, the accuracy of the best L1PMA is assessed with respect to its inherent properties, namely, the assumed number of monotonic sections and the nature of faults, that is, faults that follow either continuous uniform distribution (CUD) or normal distribution (ND), during the determination of distribution BPL transfer functions. Finally, best L1PMA may operate as the necessary intermediate antifault method for the theoretical and practical transfer function determination of distribution BPL networks.

Structural Dynamics in Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—2

1965 ◽  
Vol 87 (4) ◽  
pp. 455-463 ◽  
Author(s):  
G. W. Long ◽  
J. R. Lemon
Keyword(s):  
Transfer Function ◽  
Machine Tool ◽  
Stability Theory ◽  
Transfer Functions ◽  
Phase Relationship ◽  
Structure Response ◽  
Machine Tool Structure ◽  
Machine Tool Chatter ◽  
The Stability ◽  
Tool Chatter

This paper is one of four being presented simultaneously on the subject of self-excited machine-tool chatter. Transfer-function theory is applied to obtain a representation of the dynamics of a machine-tool structure. The stability theory developed to investigate self-excited machine-tool chatter requires such a representation. Transfer functions of simple symmetric systems are derived and compared with measurements. When measured frequency-response data of more complex structures are obtained, it provides a very convenient means of data interpretation and enables one to develop the significant equations of motion that define the structure response throughout a specified frequency range. The transfer function presents the phase relationship between structure response and exciting force at all frequencies in the specified range. This knowledge of phase is essential to the proper application of the stability theory and explains the “digging-in” type of instability that is often encountered in machine-tool operation. The instrumentation used throughout these tests is discussed and evaluated. The concept of developing dynamic expressions for machine-tool components and joining these together through properly defined boundary conditions, thereby building up the transfer function of the complete machine-tool structure, is suggested as an area for further study.

DYNAMIC PROPERTIES OF A BIOLOGICALLY MOTIVATED NEURAL NETWORK MODEL

1992 ◽  
Vol 03 (04) ◽  
pp. 371-378 ◽  
Author(s):  
FRANÇOIS CHAPEAU BLONDEAU ◽  
GILBERT CHAUVET
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Transfer Function ◽  
Network Model ◽  
Neural Network Model ◽  
Dynamic Properties ◽  
Biological Significance ◽  
Neural Architecture ◽  
The Stability ◽  
Basic Features

We develop a neural network model based on prominent basic features of biological neural networks. The description keeps a simple but coherent link between the subneuronal, neuronal and network levels. In addition, the variables of the model are endowed with realistic numerical values together with their physical units. This permits to reach quantitative significance for the results. To describe the operation of the neuron, a transfer function is used that is believed to convey more biological significance compared to the usual sigmoid transfer function. It is shown that the dynamic properties of the network, which can vary from stability to chaos, are significantly influenced by the choice of the neuron transfer function. Constraints on the synaptic efficacies, as imposed by Dale’s rule, are also shown to modify the dynamic properties by increasing the stability of the network. A simple neural architecture is presented that leads to a controllable time evolution of the network activities.

A Unified Transfer Function (UTF) Approach for the Modeling and Stability Analysis of Long Slender Bars in 3-D Turning Operations

1993 ◽  
Vol 115 (2) ◽  
pp. 193-204 ◽  
Author(s):  
I. N. Tansel
Keyword(s):  
Stability Analysis ◽  
Transfer Function ◽  
Transfer Functions ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Tool Geometry ◽  
Turning Operations ◽  
Chip Area ◽  
The Stability ◽  
Unique Relationship

A new approach is introduced to model 3-D turning operations that are used for the stability analysis of long slender bars. This approach utilizes the unique relationship between externally created feed direction tool displacements (input) and the resultant thrust direction workpiece vibrations (output) to estimate stability limits in three-dimensional turning operations from the data of a single dynamic cutting test. In this paper, this unique relationship is referred to as the “Unified Transfer Function ” (UTF) and its expressions are derived from conventional cutting and structural dynamics transfer functions. For the stability analysis, the uncut chip area variations of oblique cutting are represented by a linear model having different coefficients at different depths of cuts. These coefficients are found by using a tool geometry simulation program. An iterative procedure is developed for the stability analysis. The proposed approach considers in-process structural and cutting dynamics and can be automatically implemented without any input from the operator for the traverse turning of a long slender bar. Experimental studies have validated the proposed modeling and stability analysis techniques. The UTFs can also be used to monitor machine tool structure, tool wear, and the machinability of the material.

A Note About the Stability of a String of LTI Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 472-475 ◽  
Author(s):  
Swaroop Darbha
Keyword(s):  
Transfer Function ◽  
Weak Interaction ◽  
Error Propagation ◽  
Transfer Functions ◽  
Lp Norms ◽  
The Stability

This note concerns the stability of a string of LTI systems; it is shown here that, if the “weak interaction” condition among systems in the string is satisfied (i.e., the sum of the ∞-norms of the interaction/error propagation transfer functions is less than unity), then the string is Lp stable for every p⩾1. Since the ∞-norm of a transfer function is the smallest of all its induced Lp norms, the result presented here enables one to obtain a tighter estimate of the geometric rate of attenuation of the states of systems in the string.

Study of Flame Transfer Function With Three Dimensional Calculations

2003 ◽  
Author(s):  
M. Zhu ◽  
A. P. Dowling ◽  
K. N. C. Bray
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Low Frequency ◽  
Systematic Investigation ◽  
Flow Properties ◽  
Low Frequency Oscillation ◽  
Local Flow ◽  
Shape Factors ◽  
Annular Combustor

Combustors with fuel-spray atomisers are particularly susceptible to a low-frequency oscillation at idle and sub-idle conditions. For aero-engine combustors, the frequency of this oscillation is typically in the range 70–120Hz and is commonly called ‘rumble’. The mechanism involves interaction between the plenum around the burner and the combustion chamber. In our previous work, the CFD calculation has been conducted in an idealised 2D axisymmetric annular combustor to calculate unsteady combustion flow at idle conditions. In this work, in order to investigate the effects of asymmetrical geometry and flow distributions on the transfer functions of flame and shape factors, the CFD code has been extended to fully three-dimensional geometries. The results are compared with those from 2D calculations. Though the differences of the distribution local flow properties are evident, the integrated results for the 3D flow are broadly similar to those obtained in 2D. One substantial difference arises due to the more accurate modelling of the downstream contraction near the combustor exit, which is treated as a smooth contraction in our 3D calculations and as an abrupt change in the simplified 2D geometry. The gradual downstream contraction not only accelerates the fluid near the combustor exit but also unifies the flow properties. As the consequence, we can see that, near the exit, the phase of the flame transfer function increases rapidly, and the shape factors tend toward unity. This work is a further development of our systematic investigation into the ‘rumble’ phenomenon, and gives encouragement that much of the essential physics can be captured in a quasi-one-dimensional model.

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