Forward and Backward Uncertainty Propagation for Discontinuous System Response Using the Padé-Legendre Method

Chantrasmi, Tonkid; Iaccarino, Gianluca

doi:10.1615/int.j.uncertaintyquantification.2011003503

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…All other parameters were supposed to be xed. Even for this reduced set of uncertain input parameters, a 38 dimension space is still a very large one and an active subspace method [168] was used to reduce this dimension before using UQ analysis. A typical result is displayed in Fig.…”

Section: Uq (Uncertainty Quanti Cation) For Combustion Instabilitiesmentioning

confidence: 99%

Prediction and control of combustion instabilities in real engines

Poinsot

2017

Proceedings of the Combustion Institute

594

216

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This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 17713Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. To cite this version: AbstractThis paper presents recent progress in the eld of thermoacoustic combustion instabilities in propulsion engines such as rockets or gas turbines. Combustion instabilities have been studied for more than a century in simple laminar con gurations as well as in laboratory-scale turbulent ames. These instabilities are also encountered in real engines but new mechanisms appear in these systems because of obvious differences with academic burners: larger Reynolds numbers, higher pressures and power densities, multiple inlet systems, complex fuels. Other differences are more subtle: real engines often feature speci c unstable modes such as azimuthal instabilities in gas turbines or transverse modes in rocket chambers. Hydrodynamic instability modes can also differ as well as the combustion regimes, which can require very different simulation models. The integration of chambers in real engines implies that compressor and turbine impedances control instabilities directly so that the determination of the impedances of turbomachinery elements becomes a key issue. Gathering experimental data on combustion instabilities is dif cult in real engines and large Eddy simulation (LES) has become a major tool in this eld. Recent examples, however, show that LES is not suf cient and that theory, even in these complex systems, plays a major role to understand both experimental and LES results and to identify mitigation techniques.

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Section: Uq (Uncertainty Quanti Cation) For Combustion Instabilitiesmentioning

confidence: 99%

Prediction and control of combustion instabilities in real engines

Poinsot

2017

Proceedings of the Combustion Institute

594

216

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“…Studying uncertainty quantification for the acoustic damping, for example through impedance boundary conditions, is just as straightforward [15]. This is called "forward problem", as opposed to the "inverse problem" [22], because the focus is on how uncertainties in the input parameters a↵ect the output, which is the eigenfrequency. We assume we know the maximum and minimum values of the uncertain flame parameters.…”

Section: Forward Uncertainty Quantificationmentioning

confidence: 99%

Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification

Mensah

Magri

Moeck

2018

Journal of Engineering for Gas Turbines and Power

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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 flow computations. They result in an eigenvalue problem, which is nonlinear with respect to the eigenvalue. Thus, the influence of the relevant parameters on mode stability is only given implicitly. Small changes in some model parameters, 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. 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. A new and fast way to obtain algebraic parameter models in order to tackle the implicit nature of the problem is using adjoint perturbation theory. This paper aims to further utilize adjoint methods for the quantification of uncertainties. This analytical method avoids the usual random Monte Carlo (MC) 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 data are available.

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“…..,N so that D = 38 for N = 19 burners. This problem is known as the forward uncertainty-propagation problem (Chantrasmi & Iaccarino 2012) where the output is viewed as the result of a 'black box', which can be an experiment, a low-order model or a numerical solver, characterized by an unknown function g:…”

Section: The Classical Monte Carlo Analysismentioning

confidence: 99%

Symmetry breaking of azimuthal thermoacoustic modes: the UQ perspective

et al. 2016

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Since its introduction in the late 19th century, symmetry breaking has been found to play a crucial role in physics. In particular, it appears as one key phenomenon controlling hydrodynamic and acoustic instabilities in problems with rotational symmetries. A previous paper investigated its desired potential application to the control of circumferential thermoacoustic modes in one annular cavity coupled with multiple flames (Bauerheim et al., J. Fluid Mech., vol. 760, 2014, pp. 431–465). The present paper focuses on a similar problem when symmetry breaking appears unintentionally, for example when uncertainties due to tolerances are taken into account. It yields a large uncertainty quantification (UQ) problem containing numerous uncertain parameters. To tackle this well-known ‘curse of dimensionality’, a novel UQ methodology is used. It relies on the active subspace approach to construct a reduced set of input variables. This strategy is applied on two annular cavities coupled by 19 flames to determine its modal risk factor, i.e. the probability of an azimuthal acoustic mode being unstable. Since each flame is modelled by two uncertain parameters, it leads to a large UQ problem involving 38 parameters. An acoustic network model is then derived, which yields a nonlinear dispersion relation for azimuthal modes. This nonlinear problem, subject to bifurcations, is solved quasi-analytically. Results show that the dimension of the probabilistic problem can be drastically reduced, from 38 uncertain parameters to only 3. Moreover, it is found that the three active variables are related to physical quantities, which unveils underlying phenomena controlling the stability of the two coupled cavities. The first active variable is associated with a coupling strength controlling the bifurcation of the system, while the two others correspond to a symmetry-breaking effect induced by the uncertainties. Thus, an additional destabilization effect appear caused by the non-uniform pattern of the uncertainty distribution, which breaks the initial rotating symmetry of the annular cavities. Finally, the active subspace is exploited by fitting the response surface with polynomials (linear, quadratic and cubic). By comparing accuracy and cost, results prove that 5 % error can be achieved with only 30 simulations on the reduced space, whereas 2000 are required on the complete initial space. It exemplifies that this novel UQ technique can accurately predict the risk factor of an annular configuration at low cost as well as unveil key parameters controlling the stability.

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Forward and Backward Uncertainty Propagation for Discontinuous System Response Using the Padé-Legendre Method

Cited by 4 publications

References 17 publications

Prediction and control of combustion instabilities in real engines

Prediction and control of combustion instabilities in real engines

Methods for the Calculation of Thermoacoustic Stability Boundaries and Monte Carlo-Free Uncertainty Quantification

Symmetry breaking of azimuthal thermoacoustic modes: the UQ perspective

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