Imperial College London

ProfessorPeterSchmid

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

peter.schmid

 
 
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Location

 

753Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

118 results found

Yang D, Sogaro FM, Morgans AS, Schmid PJet al., 2019, Optimising the acoustic damping of multiple Helmholtz resonators attached to a thin annular duct, Journal of Sound and Vibration, Vol: 444, Pages: 69-84, ISSN: 0022-460X

© 2018 Helmholtz resonators (HRs) are widely used to damp acoustic oscillations, including in the combustors of aero-engines and power gas turbines where they damp thermoacoustic oscillations. The geometries of such combustors are often annular in shape, which means that low frequency acoustic modes exhibit both longitudinal and circumferential modeshapes, the latter across different circumferential wave numbers. For linear acoustic disturbances downstream of the flame, the presence of HRs leads to modal coupling and mode shape shifts, which makes design and placement of multiple HRs very complicated. A procedure which ensures that the design and placement of the HRs can be optimised for good acoustic damping performance would be very valuable, and such a procedure is presented in this work. A simplified linear, low-dimensional model for the acoustic behaviour in a hot annular duct sustaining a mean flow is extended to account for the attachment of multiple HRs. The HRs are assumed to sustain a cooling mean bias flow through them, towards the combustor, such that they can be modelled using linear, lumped element Rayleigh conductivity models. An optimisation method based on the gradient derived from adjoint sensitivity analysis is then applied to the low order network acoustic modelling framework for hot annular ducts incorporating HR models, for the first time. It is used to optimise over multiple HR geometry and placement parameters, to obtain optimum acoustic damping over all acoustic modes in a given frequency range. These optimisation procedures are validated via multi-dimensional parameter sweep results. Thus a novel and efficient tool for HR optimisation for thin annular ducts is presented.

JOURNAL ARTICLE

Skene CS, Schmid PJ, 2018, Adjoint-based parametric sensitivity analysis for swirling M-flames, JOURNAL OF FLUID MECHANICS, Vol: 859, Pages: 516-542, ISSN: 0022-1120

JOURNAL ARTICLE

Edstrand AM, Sun Y, Schmid PJ, Taira K, Cattafesta LNet al., 2018, Active attenuation of a trailing vortex inspired by a parabolized stability analysis, JOURNAL OF FLUID MECHANICS, Vol: 855, ISSN: 0022-1120

JOURNAL ARTICLE

Eggl MF, Schmid PJ, 2018, A gradient-based framework for maximizing mixing in binary fluids, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 368, Pages: 131-153, ISSN: 0021-9991

JOURNAL ARTICLE

Edstrand AM, Schmid PJ, Taira K, Cattafesta LNet al., 2018, A parallel stability analysis of a trailing vortex wake, Journal of Fluid Mechanics, Vol: 837, Pages: 858-895, ISSN: 0022-1120

Trailing vortices are generated in aeronautical and maritime applications and produce a variety of adverse effects that remain difficult to control. A stability analysis can direct flow control designers towards pertinent frequencies, wavelengths and locations that may lead to the excitation of instabilities, resulting in the eventual breakup of the vortex. Most models for trailing vortices, however, are far-field models, making implementation of the findings from stability analyses challenging. As such, we perform a stability analysis in the formative region where the numerically computed base flow contains both a two-dimensional wake and a tip vortex generated from a NACA0012 at a angle of attack and a chord-based Reynolds number of . The parallel temporal and spatial analyses show that at three chord lengths downstream of the trailing edge, seven unstable modes are present: three stemming from the temporal analysis and four arising in the spatial analysis. The three temporal instabilities are analogues to three unstable modes in the spatial analysis, with the wake instability dominating in both analyses. The helical mode localized to the vortex co-rotates with the base flow, which is converse with the counter-rotating instabilities of a Batchelor vortex model, which may be a result of the formative nature of the base-flow vortex. The fourth spatial mode is localized to the tip vortex region. The continuous part of the spectrum contains oscillatory and wavepacket solutions prompting the utilization of a wavepacket analysis to analyse the flow field and group velocity. The structure and details of the full bi-global spectrum will help navigate the design space of effective control strategies to hasten decay of persistent wingtip vortices.

JOURNAL ARTICLE

Sogaro F, Schmid P, Morgans AS, 2018, Sensitivity analysis of thermoacoustic instabilities, Pages: 2063-2070

Copyright © (2018) by International Institute of Acoustics & Vibration.All rights reserved. Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land-based gas turbines. The thermoacoustic oscillations of these systems are of significant importance as they can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. In this work we use a low-order network model representation of a combustor where linear acoustics are solved together with appropriate boundary conditions and flame jump conditions. Special emphasis is directed towards the interaction between instabilities associated with acoustic modes and flame-intrinsic modes. Adjoint methods are used to perform a receptivity and sensitivity analysis of the spectral properties of the system to changes in the parameters involved. To better analyse the extreme sensitivities that arise in the neighbourhood of a modal interaction, we compare the results with a time domain model that allows us to perform a pseudospectra analysis. The results provide key insights into the interplay between mode types.

CONFERENCE PAPER

Horn S, Schmid PJ, 2017, Prograde, retrograde, and oscillatory modes in rotating Rayleigh-Benard convection, JOURNAL OF FLUID MECHANICS, Vol: 831, Pages: 182-211, ISSN: 0022-1120

JOURNAL ARTICLE

Schmid PJ, Fosas de Pando M, Peake N, 2017, Stability analysis for n-periodic arrays of fluid systems, Physical Review Fluids, Vol: 2, ISSN: 2469-990X

A computational framework is proposed for the linear modal and nonmodal analysis of fluid systems consisting of a periodic array of n identical units. A formulation in either time or frequency domain is sought and the resulting block-circulant global system matrix is analyzed using roots-of-unity techniques, which reduce the computational effort to only one unit while still accounting for the coupling to linked components. Modal characteristics as well as nonmodal features are treated within the same framework, as are initial-value problems and direct-adjoint looping. The simple and efficient formalism is demonstrated on selected applications, ranging from a Ginzburg-Landau equation with an n-periodic growth function to interacting wakes to incompressible flow through a linear cascade consisting of 54 blades. The techniques showcased here are readily applicable to large-scale flow configurations consisting of n-periodic arrays of identical and coupled fluid components, as can be found, for example, in turbomachinery, ring flame holders, or nozzle exit corrugations. Only minor corrections to existing solvers have to be implemented to allow this present type of analysis.

JOURNAL ARTICLE

Horn S, Schmid P, 2017, Prograde, retrograde and oscillatory modes in rotating Rayleigh-Benard convection

WORKING PAPER

Symon S, Dovetta N, McKeon BJ, Sipp D, Schmid PJet al., 2017, Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil, EXPERIMENTS IN FLUIDS, Vol: 58, ISSN: 0723-4864

JOURNAL ARTICLE

Qadri UA, Schmid PJ, 2017, Effect of nonlinearities on the frequency response of a round jet, PHYSICAL REVIEW FLUIDS, Vol: 2, ISSN: 2469-990X

JOURNAL ARTICLE

Pier B, Schmid PJ, 2017, Linear and nonlinear dynamics of pulsatile channel flow, JOURNAL OF FLUID MECHANICS, Vol: 815, Pages: 435-480, ISSN: 0022-1120

JOURNAL ARTICLE

Schmid PJ, Sayadi T, 2017, Low-dimensional representation of near-wall dynamics in shear flows, with implications to wall-models, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 375, ISSN: 1364-503X

JOURNAL ARTICLE

Schmid PJ, Sayadi T, 2017, Low-dimensional representation of near-wall dynamics in shear flows, with implications to wall-models, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 375, Pages: 20160082-20160082, ISSN: 1364-503X

JOURNAL ARTICLE

Fosas de Pando M, Schmid PJ, Sipp D, 2017, On the receptivity of aerofoil tonal noise: an adjoint analysis, JOURNAL OF FLUID MECHANICS, Vol: 812, Pages: 771-791, ISSN: 0022-1120

JOURNAL ARTICLE

Qadri UA, Schmid PJ, 2017, Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity, PHYSICAL REVIEW FLUIDS, Vol: 2, ISSN: 2469-990X

JOURNAL ARTICLE

Sogaro F, Schmid P, Morgans AS, 2017, Sensitivity analysis of thermoacoustic instabilities

Thermoacoustic instability is a phenomenon that occurs in numerous combustion systems, from rockets to land based gas turbines. The resulting acoustic oscillations can result in severe vibrations, thrust oscillations, thermal stresses and mechanical loads that lead to fatigue or even failure. This propensity to instability has been found to occur much more frequently in lean premixed combustion, one of the recent methods used in the gas turbine industry of aeroengines and power gas turbines to reduce NOx emissions. In this work we consider a simplified combustion system, and analyse the sensitivity of its thermoacoustic modes to small changes in the flame and combustor geometry parameters. Such a sensitivity analysis offers insights on how best to change the combustion system so as to "design-out" instability. The simplified combustor is modelled using a low order network representation: linear plane acoustic waves are combined with the appropriate acoustic boundary and flame jump conditions and a linear n-tau flame model. A sensitivity analysis is then performed using adjoint methods, with special focus on the sensitivity of the modes to parameters, such as reflection coefficients and flame model gain and time delay. The gradient information obtained reveals how the thermoacoustic modes of the system respond to changes to the various parameters. The results offer key insights into the behaviour and coupling of different types of modes - for example acoustic modes and so-called "intrinsic" modes associated with the flame model. They also provide insights into the optimal configuration for the design of such combustors.

CONFERENCE PAPER

Fosas de Pando M, Schmid PJ, 2017, Optimal frequency-response sensitivity of compressible flow over roughness elements, JOURNAL OF TURBULENCE, Vol: 18, Pages: 338-351, ISSN: 1468-5248

JOURNAL ARTICLE

Noack BR, Stankiewicz W, Morzynski M, Schmid PJet al., 2016, Recursive dynamic mode decomposition of transient and post-transient wake flows, JOURNAL OF FLUID MECHANICS, Vol: 809, Pages: 843-872, ISSN: 0022-1120

JOURNAL ARTICLE

Noack B, Stankiewicz W, Morzynski M, Schmid Pet al., 2016, Recursive dynamic mode decomposition of a transient wake flow

WORKING PAPER

Fosas de Pando M, Schmid PJ, Sipp D, 2016, Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 324, Pages: 194-209, ISSN: 0021-9991

JOURNAL ARTICLE

Dunne R, Schmid PJ, McKeon BJ, 2016, Analysis of Flow Timescales on a Periodically Pitching/Surging Airfoil, AIAA JOURNAL, Vol: 54, Pages: 3421-3433, ISSN: 0001-1452

JOURNAL ARTICLE

Sayadi T, Schmid PJ, 2016, Parallel data-driven decomposition algorithm for large-scale datasets: with application to transitional boundary layers, THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS, Vol: 30, Pages: 415-428, ISSN: 0935-4964

JOURNAL ARTICLE

Schmid PJ, Sipp D, 2016, Linear control of oscillator and amplifier flows, PHYSICAL REVIEW FLUIDS, Vol: 1, ISSN: 2469-990X

JOURNAL ARTICLE

Edstrand AM, Davis TB, Schmid PJ, Taira K, Cattafesta LNet al., 2016, On the mechanism of trailing vortex wandering, JOURNAL OF FLUID MECHANICS, Vol: 801, ISSN: 0022-1120

JOURNAL ARTICLE

Edstrand A, Davis TB, Schmid P, Taira K, Cattafesta Let al., 2016, On the mechanism of trailing vortex wandering

WORKING PAPER

Sujith R, Juniper M, Schmid P, 2016, Non-normality and nonlinearity in thermoacoustic instabilities

WORKING PAPER

Sujith RI, Juniper MP, Schmid PJ, 2016, Non-normality and nonlinearity in thermoacoustic instabilities, INTERNATIONAL JOURNAL OF SPRAY AND COMBUSTION DYNAMICS, Vol: 8, Pages: 119-146, ISSN: 1756-8277

JOURNAL ARTICLE

Inigo JG, Sipp D, Schmid PJ, 2016, Recovery of the inherent dynamics of noise-driven amplifier flows, JOURNAL OF FLUID MECHANICS, Vol: 797, Pages: 130-145, ISSN: 0022-1120

JOURNAL ARTICLE

Blanchard M, Schmid PJ, Sipp D, Schuller Tet al., 2016, Pressure wave generation from perturbed premixed flames, JOURNAL OF FLUID MECHANICS, Vol: 797, Pages: 231-246, ISSN: 0022-1120

JOURNAL ARTICLE

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