Energetically Consistent Computation of Combustor Stability With a Model Consisting of a Helmholtz-FEM-Domain and a Low-Order Network

2020 ◽  
Author(s):  
Gerrit Heilmann ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Fundamental Problem ◽  
Acoustic Energy ◽  
Special Treatment ◽  
Transfer Matrices ◽  
Mean Flow ◽  
Acoustic Damping ◽  
Spatially Resolved ◽  
Low Order

Abstract An efficient approach for the detection of the acoustic damping of gas turbine combustors is the combination of spatially resolved FEM approaches based on the Helmholtz equation with low-order networks for all elements leading to acoustic damping. A fundamental problem of such hybrid approaches is that the flow is considered in the networks, but not in the spatially resolved FEM area. Without special treatment of the coupling plane and the boundary conditions this leads to serious errors in the calculation of the damping rate. The purpose of the paper is the derivation of the required correction procedures, which allow the energetically consistent formulation of such hybrid models and lead to correct damping rates. The time averaged equation of acoustic energy flux for non-uniform fluid flows is expressed in terms of reflection coefficients and compared to the equivalent formulation for vanishing mean flows. An existing transformation for boundary conditions to obtain equal energy flux at the interface between network and Helmholtz domain is analyzed in detail. The findings are then used to derive an energetically consistent transformation of transfer matrices to couple two FEM domains via a network model. The relevance of energetically consistent transfer matrices for stability analysis is demonstrated with a generic test case. The central partition is acoustically characterized via a low order model considering mean flow. The resulting acoustic two-port is transformed to obtain an energetically consistent transfer matrix for a subsequent FEM discretized eigenvalue analysis of the remaining geometry. The eigenvalues of energetically consistent calculations are finally compared to eigenvalues of energetically inconsistent setups.

Energetically Consistent Computation of Combustor Stability with a Model Consisting of a Helmholtz-Fem-Domain and a Low-Order Network

2021 ◽  
Author(s):  
Gerrit Heilmann ◽  
Christoph Hirsch ◽  
Thomas Sattelmayer
Keyword(s):  
Boundary Conditions ◽  
Energy Flux ◽  
Fundamental Problem ◽  
Acoustic Energy ◽  
Special Treatment ◽  
Transfer Matrices ◽  
Mean Flow ◽  
Acoustic Damping ◽  
Spatially Resolved ◽  
Low Order

Abstract An efficient approach for the detection of the acoustic damping of gas turbine combustors is the combination of spatially resolved FEM approaches based on the Helmholtz equation with low-order networks for all elements leading to acoustic damping. A fundamental problem of such hybrid approaches is that the flow is considered in the networks, but not in the spatially resolved FEM area. Without special treatment of the boundary conditions this leads to serious errors in the calculation of the damping rate. The purpose of the paper is the derivation of the required correction procedures, which allow the energetically consistent formulation of such hybrid models and lead to correct damping rates. The time averaged equation of acoustic energy flux is expressed in terms of reflection coefficients and compared to the equivalent formulation for vanishing mean flows. An existing transformation for boundary conditions to obtain equal energy flux at the interface between network and Helmholtz domain is analyzed in detail. The findings are then used to derive energetically consistent transformations of transfer matrices to couple two FEM domains via a network model. The relevance of energetically consistent transfer matrices for stability analysis is demonstrated with a generic test case. The central partition is acoustically characterized via low order models considering mean flow. The resulting acoustic two-port is transformed to obtain an energetically consistent transfer matrix for a subsequent FEM discretized eigenvalue analysis of the remaining geometry. The eigenvalues of energetically consistent calculations are finally compared to eigenvalues of energetically inconsistent setups.

scholarly journals Swirler geometry effects (dh/do ratio) on synthetic gas flames. Part 2: dynamic flame behaviour at external y altered acoustic conditions

Energetika ◽  
2021 ◽  
Vol 67 (1) ◽  
Author(s):  
Harun Yilmaz ◽  
Omer Cam ◽  
Ilker Yilmaz
Keyword(s):  
Boundary Conditions ◽  
Pressure Sensors ◽  
Acoustic Energy ◽  
Acoustic Boundary Conditions ◽  
Acoustic Damping ◽  
Pressure Profiles ◽  
Flame Response ◽  
Scale Variable ◽  
A Minor ◽  
Flame Behaviour

In a combustion device, unsteady heat release causes acoustic energy to increase when acoustic damping (energy loss) is not that effective, and, as a result, thermo-acoustic flame instabilities occur. In this study, effects of the swirler dh/do ratio (at different swirl numbers) on dynamic flame behaviour of the premixed 20%CNG/30%H2/30%CO/20%CO2 mixture under externally altered acoustic boundary conditions and stability limits (flashback and blowout equivalence ratios) of such mixture were investigated in a laboratory-scale variable geometric swirl number combustor. Therefore, swirl generators with different dh/do ratios (0.3 and 0.5) and geometric swirl numbers (0.4, 0.6, 0.8, 1.0 1.2 and 1.4) were designed and manufactured. Acoustic boundary conditions in the combustion chamber were altered using loudspeakers, and flame response to these conditions was perceived using photodiodes and pressure sensors. Dynamic flame behaviour of respective mixture was evaluated using luminous intensity and pressure profiles. Results showed that the dh/do ratio has a minor impact on dynamic flame behaviour.

scholarly journals Disturbance energy transport and sound production in gaseous combustion

2012 ◽  
Vol 707 ◽  
pp. 53-73 ◽  
Author(s):  
Michael J. Brear ◽  
Frank Nicoud ◽  
Mohsen Talei ◽  
Alexis Giauque ◽  
Evatt R. Hawkes
Keyword(s):  
Energy Flux ◽  
Sound Production ◽  
Energy Transport ◽  
Source Term ◽  
Sole Source ◽  
Conservation Equation ◽  
Acoustic Energy ◽  
Far Field ◽  
Source Terms ◽  
Mean Flow

AbstractThis paper presents an analysis of the energy transported by disturbances in gaseous combustion. It extends the previous work of Myers (J. Fluid Mech., vol. 226, 1991, 383–400) and so includes non-zero mean-flow quantities, large-amplitude disturbances, varying specific heats and chemical non-equilibrium. This extended form of Myers’ ‘disturbance energy’ then enables complete identification of the conditions under which the famous Rayleigh source term can be derived from the equations governing combusting gas motion. These are: small disturbances in an irrotational, homentropic, non-diffusive (in terms of species, momentum and energy) and stationary mean flow at chemical equilibrium. Under these assumptions, the Rayleigh source term becomes the sole source term in a conservation equation for the classical acoustic energy. It is also argued that the exact disturbance energy flux should become an acoustic energy flux in the far-field surrounding a (reacting or non-reacting) jet. In this case, the volume integral of the disturbance energy source terms are then directly related to the area-averaged far-field sound produced by the jet. This is demonstrated by closing the disturbance energy budget over a set of aeroacoustic, direct numerical simulations of a forced, low-Mach-number, laminar, premixed flame. These budgets show that several source terms are significant, including those involving the mean-flow and entropy fields. This demonstrates that the energetics of sound generation cannot be examined by considering the Rayleigh source term alone.

Thermoacoustic Stability of Quasi-One-Dimensional Flows—Part II: Application to Basic Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 645-653 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Acoustic Energy ◽  
System Stability ◽  
Combustion Stability ◽  
Mean Flow ◽  
One Dimensional ◽  
Numerical Formulation ◽  
The Mean ◽  
Flow Gradients ◽  
The Stability

In this paper, applications of a previously developed numerical formulation (Prasad, D., and Feng, J., 2004, “Thermoacoustic stability of Quasi-One-Dimensional Flows—Part I: Analytical and Numerical Formulation,” J. Turbomach., 126, pp. 636–643. for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.

scholarly journals Flux Density through Guides with Microstructured Twisted Clad DB Medium

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
M. A. Baqir ◽  
P. K. Choudhury
Keyword(s):  
Boundary Conditions ◽  
Flux Density ◽  
Energy Flux ◽  
Pitch Angle ◽  
Inner Core ◽  
Eigenvalue Equation ◽  
Dispersion Characteristics ◽  
The Core ◽  
Energy Flux Density ◽  
Low Order

The paper deals with the study of flux density through a newly proposed twisted clad guide containing DB medium. The inner core and the outer clad sections are usual dielectrics, and the introduced twisted windings at the core-clad interface are treated under DB boundary conditions. The pitch angle of twist is supposed to greatly contribute towards the control over the dispersion characteristics of the guide. The eigenvalue equation for the guiding structure is deduced, and the analytical investigations are made to explore the propagation patterns of flux densities corresponding to the sustained low-order hybrid modes under the situation of varying pitch angles. The emphasis has been put on the effects due to the DB twisted pitch on the propagation of energy flux density through the guide.

Thermoacoustic Stability of Quasi-One-Dimensional Flows: Part II — Application to Basic Flows

2004 ◽  
Author(s):  
Dilip Prasad ◽  
Jinzhang Feng
Keyword(s):  
Boundary Conditions ◽  
Acoustic Energy ◽  
System Stability ◽  
Combustion Stability ◽  
Mean Flow ◽  
One Dimensional ◽  
Numerical Formulation ◽  
The Mean ◽  
Flow Gradients ◽  
The Stability

In this paper, applications of a previously developed numerical formulation (Prasad and Feng 2004) for the stability analysis of spatially varying one-dimensional flows are investigated. The results are interpreted with the aid of a generalized acoustic energy equation, which shows that the stability of a flow system depends not only on the nature of the unsteady heat, mass and momentum sources but also on the mean flow gradients and on the inlet and exit boundary conditions. Specifically, it is found that subsonic diffusing flows with strongly reflecting boundary conditions are unstable, whereas flows with a favorable pressure gradient are not. Transonic flows are also investigated, including those that feature acceleration through the sonic condition and those in which a normal shock is present. In both cases, it is found that the natural modes are stable. Finally, we study a simplified ducted flame configuration. It is found that the length scale of the mean heat addition affects system stability so that the thin-flame model commonly used in studies of combustion stability may not always be applicable.

Frequency Domain Predictions of Acoustic Wave Propagation and Losses in a Swirl Burner With Linearized Navier-Stokes Equations

2015 ◽  
Author(s):  
Max Zahn ◽  
Moritz Schulze ◽  
Christoph Hirsch ◽  
Michael Betz ◽  
Thomas Sattelmayer
Keyword(s):  
Stokes Equations ◽  
Low Cost ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Swirl Flow ◽  
Acoustic Energy ◽  
Acoustic Properties ◽  
Mean Flow ◽  
Swirl Burner ◽  
Acoustic Damping

A low-cost, high-quality hybrid CFD/CAA-methodology is used to predict the acoustic properties of a swirl burner including its complex swirl flow conditions. The numerically determined burner transfer matrix is validated against experimental data. The results demonstrate the capability of this low-cost hybrid approach to predict the acoustic characteristics of combustor components with high geometrical complexity. Most importantly it captures the effect of mean flow quantities on the fluctuating field. This causes the loss of acoustic energy and thus constitutes sources of acoustic damping. In this regard, reliable data can be obtained to characterize complex acoustic components at relatively low computational cost. Therefore, experimental efforts can be reduced which are generally required to provide data e.g. to set up low-order network models. The insight into the field of fluctuating quantities allows the analysis of linear acoustic damping phenomena. Essentially, in the context of isentropic conditions acoustic energy is lost due to the formation of vorticity disturbances. Source regions for vorticity disturbances are identified at flow separation edges and within the multiple shear layers of the complex swirl flow.

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

Sidewall finite-conductivity effects in confined turbulent thermal convection

2002 ◽  
Vol 473 ◽  
pp. 201-210 ◽  
Author(s):  
ROBERTO VERZICCO
Keyword(s):  
Boundary Conditions ◽  
Thermal Convection ◽  
Lateral Wall ◽  
Finite Conductivity ◽  
Mean Flow ◽  
Number Range ◽  
Additional Heat ◽  
Low Aspect Ratio ◽  
Temperature Boundary ◽  
The Mean

The effects of a sidewall with finite thermal conductivity on confined turbulent thermal convection has been investigated using direct numerical simulation. The study is motivated by the observation that the heat flowing through the lateral wall is not always negligible in the low-aspect-ratio cells of several recent experiments. The extra heat flux modifies the temperature boundary conditions of the flow and therefore the convective heat transfer. It has been found that, for usual sidewall thicknesses, the heat travelling from the hot to the cold plates directly through the sidewall is negligible owing to the additional heat exchanged at the lateral fluid/wall interface. In contrast, the modified temperature boundary conditions alter the mean flow yielding significant Nusselt number corrections which, in the low Rayleigh number range, can change the exponent of the Nu vs. Ra power law by 10%.

scholarly journals Waves in Microstructured Conducting Sheath Helix Embedded Optical Guides with Chiral Nihility and Chiral Materials

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
N. Iqbal ◽  
M. A. Baqir ◽  
P. K. Choudhury
Keyword(s):  
Boundary Conditions ◽  
Flux Density ◽  
Energy Flux ◽  
Pitch Angle ◽  
Electromagnetic Waves ◽  
The Core ◽  
Dispersion Behavior ◽  
Chiral Materials ◽  
Energy Flux Density

The paper deals with the sustainment of electromagnetic waves in circularly cylindrical optical guide with chiral nihility and chiral materials in the core and the clad sections, respectively. A perfectly conducting tightly wound helix is introduced at the core-clad interface. The eigenvalue relation for such a complex optical microstructured guide is deduced by applying suitable boundary conditions at the core-clad interface, and the dispersion behavior is analyzed by varying the pitch angle of helix. The sustainment of energy flux density in such optical guides is estimated under various structural conditions, and the density patterns in core-clad sections are anatomized analytically.

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