109 research outputs found

    Adjoint characteristic decomposition of one-dimensional waves

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    Adjoint methods enable the accurate calculation of the sensitivities of a quantity of interest. The sensitivity is obtained by solving the adjoint system, which can be derived by continuous or discrete adjoint strategies. In acoustic wave propagation, continuous and discrete adjoint methods have been developed to compute the eigenvalue sensitivity to design parameters and passive devices (Aguilar, J. G. et al, 2017, J. Computational Physics, vol. 341, 163-181). In this short communication, it is shown that the continuous and discrete adjoint characteristic decompositions, and Riemann invariants, are connected by a similarity transformation. The results are shown in the Laplace domain. The adjoint characteristic decomposition is applied to a one-dimensional acoustic resonator, which contains a monopole source of sound. The proposed framework provides the foundation to tackle larger acoustic networks with a discrete adjoint approach, opening up new possibilities for adjoint-based design of problems that can be solved by the method of characteristics

    Global linear stability analysis of a slit flame subject to intrinsic thermoacoustic instability

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    The present study makes use of the adjoint modes of the Linearized Reactive Flow (LRF) equations to investigate the Intrinsic Thermoacoustic (ITA) feedback loop of a laminar premixed slit flame. The analysis shows that the ITA feedback loop is closed by vorticity generated in the boundary layer of the slit by impinging acoustic waves penetrating the slit. In this region, adjoint vorticity shows a high sensitivity of the flow. It is also hypothesised that the ITA eigenmode smoothly transitions to a purely hydrodynamic mode -- vortex shedding -- for a passive flame. The computational domain is chosen sufficiently short so as to isolate the ITA feedback loop from cavity modes. This analysis is made possible by the holistic character of the LRF model, i.e. a direct linearization of the non-linear reactive flow equations, including explicit finite rate chemistry and avoiding idealization of the flow.Comment: 11 pages, 6 figures. Presented at the International Congress on Sound and Vibration, July 2023, Pragu

    Hard-constrained neural networks for modelling nonlinear acoustics

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    We model acoustic dynamics in space and time from synthetic sensor data. The tasks are (i) to predict and extrapolate the spatiotemporal dynamics, and (ii) reconstruct the acoustic state from partial observations. To achieve this, we develop acoustic neural networks that learn from sensor data, whilst being constrained by prior knowledge on acoustic and wave physics by both informing the training and constraining parts of the network's architecture as an inductive bias. First, we show that standard feedforward neural networks are unable to extrapolate in time, even in the simplest case of periodic oscillations. Second, we constrain the prior knowledge on acoustics in increasingly effective ways by (i) employing periodic activations (periodically activated neural networks); (ii) informing the training of the networks with a penalty term that favours solutions that fulfil the governing equations (soft-constrained); (iii) constraining the architecture in a physically-motivated solution space (hard-constrained); and (iv) combination of these. Third, we apply the networks on two testcases for two tasks in nonlinear regimes, from periodic to chaotic oscillations. The first testcase is a twin experiment, in which the data is produced by a prototypical time-delayed model. In the second testcase, the data is generated by a higher-fidelity model with mean-flow effects and a kinematic model for the flame source. We find that (i) constraining the physics in the architecture improves interpolation whilst requiring smaller network sizes, (ii) extrapolation in time is achieved by periodic activations, and (iii) velocity can be reconstructed accurately from only pressure measurements with a combination of physics-based hard and soft constraints. In and beyond acoustics, this work opens strategies for constraining the physics in the architecture, rather than the training

    Degenerate perturbation theory in thermoacoustics: High-order sensitivities and exceptional points

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    In this study, we connect concepts that have been recently developed in thermoacoustics, specifically, (i) high-order spectral perturbation theory, (ii) symmetry induced degenerate thermoacoustic modes, (iii) intrinsic thermoacoustic modes, and (iv) exceptional points. Their connection helps gain physical insight into the behaviour of the thermoacoustic spectrum when parameters of the system are varied. First, we extend high-order adjoint-based perturbation theory of thermoacoustic modes to the degenerate case. We provide explicit formulae for the calculation of the eigenvalue corrections to any order. These formulae are valid for self-adjoint, non-self-adjoint or even non-normal systems; therefore, they can be applied to a large range of problems, including fluid dynamics. Second, by analysing the expansion coefficients of the eigenvalue corrections as a function of a parameter of interest, we accurately estimate the radius of convergence of the power series. Third, we connect the existence of a finite radius of convergence to the existence of singularities in parameter space. We identify these singularities as exceptional points, which correspond to defective thermoacoustic eigenvalues, with infinite sensitivity to infinitesimal changes in the parameters. At an exceptional point, two eigenvalues and their associated eigenvectors coalesce. Close to an exceptional point, strong veering of the eigenvalue trajectories is observed. As demonstrated in recent work, exceptional points naturally arise in thermoacoustic systems due to the interaction between modes of acoustic and intrinsic origin. The role of exceptional points in thermoacoustic systems sheds new light on the physics and sensitivity of thermoacoustic stability, which can be leveraged for passive control by small design modifications
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