A Finite Element Method for Three-Dimensional Analysis of Thermo-acoustic Combustion Instability

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
S. M. Camporeale ◽  
B. Fortunato ◽  
G. Campa
Keyword(s):  
Finite Element ◽  
Heat Release ◽  
Combustion Chamber ◽  
Growth Rates ◽  
Acoustic Waves ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Complex Eigenvalue ◽  
Governing Equations ◽  
Acoustic Instabilities

A method for predicting the onset of acoustically driven combustion instabilities in gas turbine combustor is examined. The basic idea is that the governing equations of the acoustic waves can be coupled with a flame heat release model and solved in the frequency domain. The paper shows that a complex eigenvalue problem is obtained that can be solved numerically by implementing the governing equations in a finite element code. This procedure allows one to identify the frequencies at which thermo-acoustic instabilities are expected and the growth rate of the pressure oscillations, at the onset of instability, when the hypothesis of linear behavior of the acoustic waves can be applied. The method can be applied virtually to any three-dimensional geometry, provided the necessary computational resources that are, anyway, much less than those required by computational fluid dynamics methods proposed for analyzing the combustion chamber under instability condition. Furthermore, in comparison with the “lumped” approach that characterizes popular acoustics networks, the proposed method allows one for much more flexibility in defining the geometry of the combustion chamber. The paper shows that different types of heat release laws, for instance, heat release concentrated in a flame sheet, as well as distributed in a larger domain, can be adopted. Moreover, experimentally or numerically determined flame transfer functions, giving the response of heat release to acoustic velocity fluctuations, can be incorporated in the model. To establish proof of concept, the method is validated at the beginning against simple test cases taken from literature. Over the frequency range considered, frequencies and growth rates both of stable and unstable eigenmodes are accurately evaluated. Then the method is applied to a much more complex annular combustor geometry in order to evaluate frequencies and growth rates of the unstable modes and to show how the variation in the parameters of the heat release law can influence the transition to instability.

scholarly journals Impact of the heat release distribution on high-frequency transverse thermoacoustic driving in premixed swirl flames

2016 ◽  
Vol 9 (3) ◽  
pp. 143-154 ◽  
Author(s):  
Michael Hertweck ◽  
Frederik M Berger ◽  
Tobias Hummel ◽  
Thomas Sattelmayer
Keyword(s):  
Heat Release ◽  
Combustion Chamber ◽  
High Frequency ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Elevated Pressure ◽  
Rayleigh Index ◽  
The Stability ◽  
Stability Limits ◽  
The Impact

Self-excited, high-frequency first transversal thermoacoustic instabilities in a cylindrical combustion chamber equipped with a premixed swirl-stabilized flame are investigated. Phase-locked image analysis of the phenomena shows the displacement of the flame and a higher burning rate in the region of elevated pressure. The impact of diffuser angle and fuel composition on the stability limits and the flame position is investigated. The Rayleigh-Index is computed for a three-dimensional domain based on analytical flame transfer functions for experimentally obtained data of OH*-chemiluminescence as measure for the spatial heat release. Two models from different sources are applied, which describe the interaction between flame and acoustic locally. The axial dependence of the amplitude of the transversal mode is computed by a numerical model, which takes the temperature distribution inside the combustion chamber into account. The comparison of the Rayleigh-Index of different operation points shows a correlation with the stability limits for some, but not for all investigated configurations.

Transfer Function Measurements on a Swirl Stabilized Premix Burner in an Annular Combustion Chamber

2004 ◽  
Author(s):  
Klaas Kunze ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Combustion Chamber ◽  
Acoustic Waves ◽  
Velocity Fluctuation ◽  
Transfer Functions ◽  
Flow Direction ◽  
Near Field ◽  
Thermal Power ◽  
Annular Combustor

A generic swirl stabilized premix burner for natural gas is experimentally investigated in both a single burner test rig and in an annular combustion chamber. Flame transfer functions are measured relating the fluctuation of the flame heat release to the axial velocity fluctuation at the burner outlet. The OH-chemiluminescence signal of the flame, captured with a photomultiplier tube, is taken as an estimate for flame heat release, whereas the velocity fluctuation is measured with a hot wire probe. As integral measurements of the entire flame reveal important differences between the single burner and the annular combustor, locally resolved measurements are performed observing slices of the flame that are perpendicular to the main flow direction at a variable distance from the burner outlet. In both the single and the annular combustor a near field and a far field of the dynamic flame behavior can be distinguished. The annular combustor flame has a larger near field than the single combustor flame and a different shape in the presence of circumferential acoustic waves. Variation of swirl, thermal power and mass flow and comparison of the steady state heat release distribution within the flames lead to the result that the effective swirl in the annular combustor is lower than for the identical burner in the single burner combustor. When the difference in swirl is compensated for by modifying the burner configuration in the annular combustion chamber the flame transfer function is still not equal to the single combustor flame. The remaining difference can be attributed to the circumferential acoustic waves in the annular combustor which influence the flame shape.

Performance Based Evaluation of Bridge Substructure in North Mississippi Using Nonlinear FEM and Field Vibration Measurement

2000 ◽  
Author(s):  
Chris L. Mullen ◽  
Prabin R. Tuladhar
Keyword(s):  
Finite Element ◽  
Transfer Functions ◽  
Response Spectrum ◽  
Three Dimensional ◽  
Vibration Measurement ◽  
Elastic Behavior ◽  
Evaluation Procedure ◽  
Vibration Measurements ◽  
Linear Elastic ◽  
Performance Based Evaluation

Abstract Discussion of a Performance - Based Engineering evaluation procedure for an existing interstate highway bridge in north Mississippi. The bridge is in a highly trafficked location near the Memphis Metropolitan area and is reflective of modern design practices in Mississippi. Results are presented of nonlinear damage response and displacement ductility performance of the reinforced concrete bents and their foundations predicted using static finite element (FE) computations. The model considers the composite action of the concrete and the reinforcing steel materials under axial force, shear, torsion and flexure. The performance-based evaluation includes three-dimensional computational simulations of the nonlinear bridge system, including substructures and superstructure. The response spectrum dynamic analysis method will also be carried out on the linear elastic three-dimensional model to predict the linear elastic behavior. Field vibration measurements, including ambient and hammer-impact, were performed to calibrate the models. The computed transfer functions are currently being evaluated to correlate vibration measurements and the Finite element models.

Measurement and Analysis of Flame Transfer Function in a Sector Combustor Under High Pressure Conditions

2003 ◽  
Author(s):  
W. S. Cheung ◽  
G. J. M. Sims ◽  
R. W. Copplestone ◽  
J. R. Tilston ◽  
C. W. Wilson ◽  
...  
Keyword(s):  
High Pressure ◽  
Transfer Function ◽  
Heat Release ◽  
Gas Turbine ◽  
Mass Flow ◽  
Atmospheric Pressure ◽  
Acoustic Waves ◽  
Gas Turbines ◽  
Transfer Functions ◽  
Unsteady Pressure

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. A flame transfer function describes the change in the rate of heat release in response to perturbations in the inlet flow as a function of frequency. It is a quantitative assessment of the susceptibility of combustion to disturbances. The resulting fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can result. Flame transfer functions for LPP combustion are poorly understood at present but are crucial for predicting combustion oscillations. This paper describes an experiment designed to measure the flame transfer function of a simple combustor incorporating realistic components. Tests were conducted initially on this combustor at atmospheric pressure (1.2 bar and 550 K) to make an early demonstration of the combustion system. The test rig consisted of a plenum chamber with an inline siren, followed by a single LPP premixer/duct and a combustion chamber with a silencer to prevent natural instabilities. The siren was used to induce variable frequency pressure/acoustic signals into the air approaching the combustor. Both unsteady pressure and heat release measurements were undertaken. There was good coherence between the pressure and heat release signals. At each test frequency, two unsteady pressure measurements in the plenum were used to calculate the acoustic waves in this chamber and hence estimate the mass-flow perturbation at the fuel injection point inside the LPP duct. The flame transfer function relating the heat release perturbation to this mass flow was found as a function of frequency. The same combustor hardware and associated instrumentation were then used for the high pressure (15 bar and 800 K) tests. Flame transfer function measurements were taken at three combustion conditions that simulated the staging point conditions (Idle, Approach and Take-off) of a large turbofan gas turbine. There was good coherence between pressure and heat release signals at Idle, indicating a close relationship between acoustic and heat release processes. Problems were encountered at high frequencies for the Approach and Take-off conditions, but the flame transfer function for the Idle case had very good qualitative agreement with the atmospheric-pressure tests. The flame transfer functions calculated here could be used directly for predicting combustion oscillations in gas turbine using the same LPP duct at the same operating conditions. More importantly they can guide work to produce a general analytical model.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

scholarly journals Using Welding Simulation and Ultrasonic Method to Evaluate Residual Stress in Stainless Steel Welded Plates

2012 ◽  
Author(s):  
Yashar Javadi ◽  
Mohammadreza Hadizadeh Raeisi ◽  
Hamed Salimi Pirzaman ◽  
Mehdi Ahmadi Najafabadi
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Stainless Steel ◽  
Residual Stresses ◽  
Acoustic Waves ◽  
Stress Measurement ◽  
Bulk Material ◽  
Three Dimensional ◽  
Ultrasonic Waves ◽  
Welding Simulation

When a material is under mechanical load, the stresses change the velocity of acoustic waves because of acoustoelastic effect. This property can be employed for stress measurement in the material itself when the stress concerns the surface of the material, or in the bulk material. This technique involves with critically refracted longitudinal waves that propagate parallel to the surface, i. e. LCR waves. This paper presents a three dimensional thermo-mechanical analysis to evaluate welding residual stresses in plate-plate joint of AISI stainless steel 304L. After finite element simulation, the residual stresses were evaluated by LCR ultrasonic waves. This paper introduces a combination of “Finite Element Welding Simulation” and “Ultrasonic Stress Measurement using the LCR Wave” which is called as “FELcr”. The capabilities of FELCR in residual stress measurement are confirmed here. It has been shown that predicted residual stress from three dimensional FE analyses is in reasonable agreement with measured residual stress from LCR method.

A Quantitative Comparison Between a Low Order Model and a 3D FEM Code for the Study of Thermoacoustic Combustion Instabilities

2011 ◽  
Author(s):  
Giovanni Campa ◽  
Sergio Mario Camporeale ◽  
Anai¨s Guaus ◽  
Julien Favier ◽  
Matteo Bargiacchi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Quantitative Comparison ◽  
Complex Eigenvalue ◽  
Combustion Instabilities ◽  
Order Model ◽  
Element Method ◽  
Low Order

The study of thermoacoustic combustion instabilities has an important role for safety operation in modern gas turbines equipped with lean premixed dry low emission combustion systems. Gas turbine manufacturers often adopt simulation tools based on low order models for predicting the phenomenon of humming. These simulation codes provide fast responses and good physical insight, but only one-dimensional or two-dimensional simplified schemes can be generally examined. The finite element method can overcome such limitations, because it allows to examine three-dimensional geometries and to search the complex eigenfrequencies of the system. Large Eddy Simulation (LES) techniques are proposed in order to investigate the instability phenomenon, matching pressure fluctuations with turbulent combustion phenomena to study thermoacoustic combustion oscillations, even if they require large numerical resources. The finite element approach solves numerically the Helmholtz equation problem converted in a complex eigenvalue problem in the frequency domain. Complex eigenvalues of the system allow us to identify the complex eigenfrequencies of the combustion system analyzed, so that we can have a valid indication of the frequencies at which thermoacoustic instabilities are expected and of the growth rate of the pressure oscillations at the onset of instability. Through the collaboration among Ansaldo Energia, University of Genoa and Polytechnic University of Bari, a quantitative comparison between a low order model, called LOMTI, and the three-dimensional finite element method has been examined, in order to exploit the advantages of both the methodologies.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 2: Reduced Formulations of the Problems in Haar Basis

2014 ◽  
Vol 670-671 ◽  
pp. 724-727 ◽  
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Mojtaba Aslami ◽  
Oleg A. Negrozov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Haar Wavelet ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Governing Equations ◽  
Boundary Problems ◽  
Element Method

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are transformed to corresponding localized formulations by using the discrete Haar wavelet basis and finally, with the use of averaging and reduction algorithms, the localized and reduced governing equations are obtained. Special algorithms of localization with respect to each degree of freedom are presented.

Rotordynamic Analysis of a Large Industrial Turbo-Compressor Including Finite Element Substructure Modeling

2006 ◽  
Author(s):  
J. Jeffrey Moore ◽  
Giuseppe Vannini ◽  
Massimo Camatti ◽  
Paolo Bianchi
Keyword(s):  
Finite Element ◽  
Transfer Function ◽  
Transfer Functions ◽  
Three Dimensional ◽  
Coupled Model ◽  
Element Model ◽  
7Th Edition ◽  
Curve Fit ◽  
Turbo Compressor ◽  
Fully Coupled

A rotordynamic analysis of a large turbo-compressor that models both the casing and supports along with the rotor-bearing system was performed. A three-dimensional (3-D) finite element model of the casing captures the intricate details of the casing and support structure. Two approaches are presented, including development of transfer functions of the casing and foundation, as well as a fully coupled rotor-casing-foundation model. The effect of bearing support compliance is captured, as well as the influence of casing modes on the rotor response. The first approach generates frequency response functions (FRF’s) from the finite element case model at the bearing support locations. A high-order polynomial in numerator-denominator transfer function format is generated from a curve-fit of the FRF. These transfer functions are then incorporated into the rotordynamics model. The second approach is a fully coupled rotor and casing model that is solved together. An unbalance response calculation is performed in both cases to predict the resulting rotor critical speeds and response of the casing modes. The effect of the compressor case and supports caused the second critical speed to drop to a value close to the operating speed and not compliant with API 617 7th edition requirements. A combination of rotor, journal bearing, casing, and support modifications resulted in a satisfactory and API compliant solution. The results of the fully coupled model validated the transfer function approach.

Non-Reflecting Finite Element Schemes for Three-Dimensional Acoustic Waves

1997 ◽  
Vol 05 (01) ◽  
pp. 95-115 ◽  
Author(s):  
Igor Patlashenko ◽  
Dan Givoli
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Infinite Medium ◽  
Wave Guide ◽  
Acoustic Medium ◽  
Structural Acoustics ◽  
Artificial Boundary ◽  
Finite Element Schemes

The finite element solution of problems involving three-dimensional acoustic waves in an infinite wave guide, and in the infinite medium around a structure is considered. Such problems are typical in structural acoustics, and this paper concentrates on the efficient numerical treatment of the infinite acoustic medium away from the structure. The unbounded domain is truncated by means of an artificial boundary ℬ. On ℬ, non-reflecting boundary conditions are used; these are either nonlocal Dirichlet-to-Neumann conditions, or their localized counterparts. For the high-order localized conditions, special three-dimensional finite elements are constructed for use in the layer adjacent to ℬ. The performance of the nonlocal and localized boundary conditions is compared via numerical experiments involving a three-dimensional wave guide.

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