Adjoint-based analysis of thermoacoustic coupling

Lemke, Mathias; Reiß, Julius; Sesterhenn, Jörn

doi:10.1063/1.4825966

Cited by 10 publications

(7 citation statements)

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“…Other implementations of adjoint methods in steady reacting flow solvers can be found in [143][144][145]. In time-dependent problems, Lemke et al [146,147] showed that adjoint equations of one-and two-dimensional compressible reacting flows provide accurate gradient information even with stiff nonlinear reaction rates. The sensitivities and optimal initial conditions to maximize the integrated heat release were computed for a three-dimensional reacting jet crossflow [148].…”

Section: Reacting Flowsmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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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.

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Section: Reacting Flowsmentioning

confidence: 99%

Adjoint Methods as Design Tools in Thermoacoustics

Magri

2019

Applied Mechanics Reviews

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“…Of course, the resulting interface is different from the desired interface, identified by the solid line in the figure, and hence the need for an optimization procedure. Note, that the figure shows the initial and the end location of the particle, but the evolution of the interface at all times is considered in the objective function, defined by Equation (14). As opposed to the one-dimensional problem, the linearization of the THINC flux (and therefore, its transpose Equation (40)) in the two-dimensional setting, gives rise to discontinuities away from the interface, where the interface direction γ changes sign.…”

Section: Two-dimensional Testsmentioning

confidence: 99%

“…The use of adjoint methods for design and optimization has been an active area of research, which started with the pioneering work of Pironneau [9] with applications in fluid mechanics and later in aeronautical shape optimization by Jameson and co-workers [10][11][12]. Ever since these groundbreaking studies, adjoint-based methods have been widely used in fluid mechanics, especially in the fields of acoustics and thermo-acoustics [13,14]. These areas provide a suitable application for adjoint-based methods, which are inherently linear, since they too are dominated by linear dynamics.…”

Section: Introductionmentioning

confidence: 99%

Control and Optimization of Interfacial Flows Using Adjoint-Based Techniques

Fikl

Chenadec

Sayadi

2020

Fluids

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The applicability of adjoint-based gradient computation is investigated in the context of interfacial flows. Emphasis is set on the approximation of the transport of a characteristic function in a potential flow by means of an algebraic volume-of-fluid method. A class of optimisation problems with tracking-type functionals is proposed. Continuous (differentiate-then-discretize) and discrete (discretize-then-differentiate) adjoint-based gradient computations are formulated and compared in a one-dimensional configuration, the latter being ultimately used to perform optimisation in two dimensions. The gradient is used in truncated Newton and steepest descent optimisers, and the algorithms are shown to recover optimal solutions. These validations raise a number of open questions, which are finally discussed with directions for future work.

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“…This gradient is computed in the form of algebraic expressions based on the problem's Lagrange multipliers or adjoint variables, which in turn is used in standard optimization algorithms that rely on Jacobian information (such as the conjugate-gradient family). This approach, although more involved, is gaining traction especially in the field of acoustics and thermoacoustics [13,15,6]. Recently, nonlinear problems have also been tackled, within the context of optimal control of separation on a realistic high-lift airfoil or wing, enhancement of mixing efficiency, minimal turbulence seeds and shape optimization [19,25,22,5].…”

Section: Introductionmentioning

confidence: 99%