Linear State Space Interconnect Modeling of Acoustic Systems

Emmert, Thomas; Meindl, Max; Jaensch, S.; Polifke, Wolfgang

doi:10.3813/aaa.918997

Cited by 53 publications

(17 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Experimentally, instabilities have been observed for nearly anechoic conditions at the upstream inlet, with frequencies in good agreement with the theoretical predictions for ITA modes (Hoeijmakers et al 2016). In addition, Emmert et al (2016) showed that a stable system can be driven into instability, if excited at intrinsic frequencies. The work by Hosseini et al (2018) shows that, as the parameters of the system are changed, there is significant interplay between the ITA and the acoustic modes; in particular, they identify a coupling mechanism that causes ITA modes "attach and detach" from their acoustic counterparts.…”

Section: Introductionsupporting

confidence: 76%

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019

View full text Add to dashboard Cite

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

show abstract

Section: Introductionsupporting

confidence: 76%

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019

View full text Add to dashboard Cite

show abstract

“…• A linear eigenproblem is a subset of NEPs with N = A−σL, where A and L may be complex matrices. Some thermoacoustic systems, however, may be governed by linear eigenproblems (e.g., in state space models [243][244][245] or with time-delayed equations that are linearized in τ [42,153]); • The spectrum of an NEP is discrete, i.e. it does not have accumulation points.…”

Section: Features Of Nonlinear Eigenproblemsmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

View full text Add to dashboard Cite

In a thermoacoustic system, such as a flame in a combustor, heat release oscillations couple with acoustic pressure oscillations. If the heat release is sufficiently in phase with the pressure, these oscillations can grow, sometimes with catastrophic consequences. Thermoacoustic instabilities are still one of the most challenging problems faced by gas turbine and rocket motor manufacturers. Thermoacoustic systems are characterized by many parameters to which the stability may be extremely sensitive. However, often only few oscillation modes are unstable. Existing techniques examine how a change in one parameter affects all (calculated) oscillation modes, whether unstable or not. Adjoint techniques turn this around: They accurately and cheaply compute how each oscillation mode is affected by changes in all parameters. In a system with a million parameters, they calculate gradients a million times faster than finite difference methods. This review paper provides: (i) the methodology and theory of stability and adjoint analysis in thermoacoustics, which is characterized by degenerate and nondegenerate nonlinear eigenvalue problems; (ii) physical insight in the thermoacoustic spectrum, and its exceptional points; (iii) practical applications of adjoint sensitivity analysis to passive control of existing oscillations, and prevention of oscillations with ad hoc design modifications; (iv) accurate and efficient algorithms to perform uncertainty quantification of the stability calculations; (v) adjoint-based methods for optimization to suppress instabilities by placing acoustic dampers, and prevent instabilities by design modifications in the combustor's geometry; (vi) a methodology to gain physical insight in the stability mechanisms of thermoacoustic instability (intrinsic sensitivity); and (vii) in nonlinear periodic oscillations, the prediction of the amplitude of limit cycles with weakly nonlinear analysis, and the theoretical framework to calculate the sensitivity to design parameters of limit cycles with adjoint Floquet analysis. To show the robustness and versatility of adjoint methods, examples of applications are provided for different acoustic and flame models, both in longitudinal and annular combustors, with deterministic and probabilistic approaches. The successful application of adjoint sensitivity analysis to thermoacoustics opens up new possibilities for physical understanding, control and optimization to design safer, quieter, and cleaner aero-engines. The versatile methods proposed can be applied to other multiphysical and multiscale problems, such as fluid–structure interaction, with virtually no conceptual modification.

show abstract

“…For example, Sayadi et al [40] made use of a finite difference scheme to build a dynamical system representation of a one-dimensional thermoacoustic system comprising a volumetric heat source localized within the domain. A more generic direct discretization LOM is the taX Low-Order Model developed at Technical University of Munich [41] . Its modularity lies in the ability to combine in a same thermoacoustic network one-dimensional elements discretized by finite difference, geometrically complex elements discretized through FEM, and other types of elements such as FTFs and scattering matrices.…”

Section: The First Class Of Lom Is a Wave-based 1d Network Approachmentioning

confidence: 99%

“…An elegant formulation to connect subdomains is to use a state-space approach. This method, already used in [32][33][34]41] , is adopted in this work but requires to be adapted. Some implementation details are given below; further developments relative to state-space representations can be found in control theory textbooks [46] .…”

Section: State-space Formalism For Subsystems Couplingmentioning

confidence: 99%

“…However, unlike this latter method, the present example did not assume acoustically compact injectors represented as lumped elements, and the acoustic field is fully resolved within the burners. LOMs relying on direct discretization of the flow domain, although more straightforward to put into application, appears to result in more DoF and higher cost: Emmert et al [41] required 10 5 DoF and 38 CPUs to compute 5 eigenmodes of a 12-injectors annular geometry without any active flames. Finally, in contrast to mixed-method LOMs based on modal expansions alongside Riemann invariants A + /A − [14] , the proposed Low-Order Model ( Eq.…”

Section: Application To Thermoacoustic Instabilities In An Annular Comentioning

confidence: 99%

See 1 more Smart Citation

A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

Laurent

Bauerheim

Poinsot

et al. 2019

Combustion and Flame

View full text Add to dashboard Cite

This work proposes an improvement to existing methods based on modal expansions used for the prediction of thermoacoustic instabilities in zero Mach number flow conditions. Whereas the orthogonal basis made of the acoustic eigenmodes of the domain bounded by rigid walls is classically used, an alternative method based on a modal expansion onto an over-complete set of acoustic eigenmodes is proposed. This allows avoiding the misrepresentation of the acoustic velocity field often observed near non rigid-wall boundaries. A Low Order Model network utilizing a state-space framework is then built upon this novel type of modal expansion. Several test cases, going from non reacting ducts to a complex geometry with combustion, are studied to assess the potential of the approach. The methodology not only successfully mitigates the misrepresentation in the acoustic field in the presence of non-rigid-wall boundaries, but it also drastically improves the convergence speed. The modularity of the method and its ability to handle complex geometries are illustrated by considering a configuration featuring an annular chamber, an annular plenum, as well as multiple burners. This novel technique is expected to bring worthy improvements to existing Low Order Models using modal expansions for the prediction of combustion instabilities.

show abstract

Linear State Space Interconnect Modeling of Acoustic Systems

Cited by 53 publications

References 0 publications

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

Adjoint Methods as Design Tools in Thermoacoustics

A novel modal expansion method for low-order modeling of thermoacoustic instabilities in complex geometries

Contact Info

Product

Resources

About