Adjoint based optimisation of reactive compressible flows

Lemke, Mathias; Reiß, Julius; Sesterhenn, Jörn

doi:10.1016/j.combustflame.2014.03.020

Cited by 30 publications

(21 citation statements)

References 6 publications

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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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“…which can encode a design goal in terms of optimisation [21], a target state for data assimilation [24,35], or a QoI for sensitivity analysis. For the latter, it is defined as the squared norm of the difference between the system state q and a modified state q (mod) (see Section 4 for a detailed discussion):…”

Section: Adjoint-based Sensitivitymentioning

confidence: 99%

“…In particular for complex reaction kinetics, the analytic derivation as well as the numerical implementation of the operator A lin T can be challenging. For example, the temperature dependence of the material parameters was excluded in the adjoint analysis of [21,25].…”

Section: Adjoint Operatormentioning

confidence: 99%

“…For example, in fluid mechanics, the influence of the geometry on lift and drag of an aerofoil, as a QoI, is commonly analysed by the adjoint approach [20]. The adjoint method was applied to several reactive systems for different applications such as optimisation [21], uncertainty quantification [22,23], data assimilation [24], and sensitivity analysis [25].…”

Section: Introductionmentioning

confidence: 99%

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Adjoint-based sensitivity analysis of quantities of interest of complex combustion models

Lemke

Cai

Reiß

et al. 2018

Combustion Theory and Modelling

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An adjoint-based approach for the sensitivity analysis of complex reaction mechanisms is presented. It builds purely on the evaluation of the governing equations. No adjoint equations have to be derived explicitly. Instead, the required adjoint operator is constructed numerically. The approach can be utilised for various kinetic models and in existing codes with minimal implementation effort. All dependencies on the state and on model parameters are fully evaluated without simplifications. Sensitivities are calculated more efficiently and more robustly compared with the often-used brute-force method. The approach is demonstrated for a homogeneous (zero-dimensional) reactor with different complex reaction mechanisms including several reaction types.

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“…This type of approach is well-known and widely used in sensitivity analyses of non-reacting flows, 46 but has only recently been applied to reactive flows. 47,48 This strategy also differs from the acoustic perturbation equation formulation that has been developed to analyze combustion noise. 49 In this hybrid approach, the noise sources are extracted from large-eddy simulations and the sound field is computed with an aeroacoustic solver, but the flame does not respond to the incident sound field.…”

Section: Introductionmentioning

confidence: 99%

Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

Blanchard

Schuller

Sipp³

et al. 2015

Physics of Fluids

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International audienceThe response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated

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Adjoint based optimisation of reactive compressible flows

Cited by 30 publications

References 6 publications

Adjoint Methods as Design Tools in Thermoacoustics

Adjoint Methods as Design Tools in Thermoacoustics

Adjoint-based sensitivity analysis of quantities of interest of complex combustion models

Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

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