Imperial College London

ProfessorPeterSchmid

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics
 
 
 
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peter.schmid

 
 
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753Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

121 results found

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: 1469-7645

Numerical simulations and perturbation analysis of a radially imploding laminar premixed flame are used to study the mechanisms responsible for the generation of pressure fluctuations at flame fronts for various Lewis numbers. The relative importance of mechanisms based on unsteady heat release and on vorticity is investigated using an optimization methodology. Particular attention is paid to the influence of non-axisymmetric conditions and local flame curvature. It is shown that vorticity-based noise generation prevails for high-wavenumber, non-axisymmetric disturbances at all curvatures, while heat-release-driven noise generation dominates the axisymmetric and low-wavenumber regimes. These results indicate that short-wavelength vorticity waves actively participate in flame acoustic activity and can surpass acoustic output mechanisms based on heat-release fluctuations in the vicinity of the flame front.

Journal article

Caruso A, Vesipa R, Camporeale C, Ridolfi L, Schmid PJet al., 2016, River bedform inception by flow unsteadiness: a modal and nonmodal analysis, Physical Review E, Vol: 93, ISSN: 1539-3755

River bedforms arise as a result of morphological instabilities of the stream-sediment interface. Dunes and antidunes constitute the most typical patterns, and their occurrence and dynamics are relevant for a number of engineering and environmental applications. Although flow variability is a typical feature of all rivers, the bedform-triggering morphological instabilities have generally been studied under the assumption of a constant flow rate. In order to partially address this shortcoming, we here discuss the influence of (periodic) flow unsteadiness on bedform inception. To this end, our recent one-dimensional validated model coupling Dressler's equations with a refined mechanistic sediment transport formulation is adopted, and both the asymptotic and transient dynamics are investigated by modal and nonmodal analyses.

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: 1469-7645

Unsteadiness in noise amplifier flows is driven and sustained by upstream environmental perturbations. A dynamic mode decomposition performed with snapshots taken in the statistically steady state extracts marginally stable dynamic modes, which mimic the sustained dynamics but miss the actual intrinsic stable behaviour of these flows. In this study, we present an alternative data-driven technique which attempts to identify and separate the intrinsic linear stable behaviour from the driving term. This technique uses a system-identification algorithm to extract a reduced state-space model of the flow from time-dependent input–output data. Such a model accurately predicts the values of the velocity field (output) from measurements of an upstream sensor that captures the effect of the incoming perturbations (input). The methodology is illustrated on a two-dimensional boundary layer subject to Tollmien–Schlichting instabilities, a canonical example of flow acting as a noise amplifier. The spectrum of the identified model compares well with the results reported in literature for the full-order system. Yet the comparison appears to be only qualitative, due to the poor robustness properties of eigenvalue spectra in noise-amplifier flows. We therefore advocate the use of the frequency response between the upstream sensor and the flow dynamics, which is revealed to be a robust quantity. The frequency response is validated against full-order computations and compares well with a local spatial stability analysis.

Journal article

Sipp D, Schmid PJ, 2016, Linear Closed-Loop Control of Fluid Instabilities and Noise-Induced Perturbations: A Review of Approaches and Tools, Applied Mechanics Reviews, Vol: 68, ISSN: 0003-6900

This review article is concerned with the design of linear reduced-order models and control laws for closed-loop control of instabilities in transitional flows. For oscillator flows, such as open-cavity flows, we suggest the use of optimal control techniques with Galerkin models based on unstable global modes and balanced modes. Particular attention has to be paid to stability–robustness properties of the control law. Specifically, we show that large delays and strong amplification between the control input and the estimation sensor may be detrimental both to performance and robustness. For amplifier flows, such as backward-facing step flow, the requirement to account for the upstream disturbance environment rules out Galerkin models. In this case, an upstream sensor is introduced to detect incoming perturbations, and identification methods are used to fit a model structure to available input–output data. Control laws, obtained by direct inversion of the input–output relations, are found to be robust when applied to the large-scale numerical simulation. All the concepts are presented in a step-by-step manner, and numerical codes are provided for the interested reader.

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: 1432-2250

Many fluid flows of engineering interest, though very complex in appearance, can be approximated by low-order models governed by a few modes, able to capture the dominant behavior (dynamics) of the system. This feature has fueled the development of various methodologies aimed at extracting dominant coherent structures from the flow. Some of the more general techniques are based on data-driven decompositions, most of which rely on performing a singular value decomposition (SVD) on a formulated snapshot (data) matrix. The amount of experimentally or numerically generated data expands as more detailed experimental measurements and increased computational resources become readily available. Consequently, the data matrix to be processed will consist of far more rows than columns, resulting in a so-called tall-and-skinny (TS) matrix. Ultimately, the SVD of such a TS data matrix can no longer be performed on a single processor, and parallel algorithms are necessary. The present study employs the parallel TSQR algorithm of (Demmel et al. in SIAM J Sci Comput 34(1):206–239, 2012), which is further used as a basis of the underlying parallel SVD. This algorithm is shown to scale well on machines with a large number of processors and, therefore, allows the decomposition of very large datasets. In addition, the simplicity of its implementation and the minimum required communication makes it suitable for integration in existing numerical solvers and data decomposition techniques. Examples that demonstrate the capabilities of highly parallel data decomposition algorithms include transitional processes in compressible boundary layers without and with induced flow separation.

Journal article

Sipp D, Schmid P, 2016, Linear closed-loop control of fluid instabilities and noise-induced perturbations: a review of approaches and tools

Working paper

Dovetta N, Schmid PJ, Sipp D, 2016, Uncertainty propagation in model extraction by system identification and its implication for control design, Journal of Fluid Mechanics, Vol: 791, Pages: 214-236, ISSN: 1469-7645

In data-based control design, system-identification techniques are used to extract low-dimensional representations of the input–output map between actuators and sensors from observed data signals. Under realistic conditions, noise in the signals is present and is expected to influence the identified system representation. For the subsequent design of the controller, it is important to gauge the sensitivity of the system representation to noise in the observed data; this information will impact the robustness of the controller and influence the stability margins for a closed-loop configuration. Commonly, full Monte Carlo analysis has been used to quantify the effect of data noise on the system identification and control design, but in fluid systems, this approach is often prohibitively expensive, due to the high dimensionality of the data input space, for both numerical simulations and physical experiments. Instead, we present a framework for the estimation of statistical properties of identified system representations given an uncertainty in the processed data. Our approach consists of a perturbative method, relating noise in the data to identified system parameters, which is followed by a Monte Carlo technique to propagate uncertainties in the system parameters to error bounds in Nyquist and Bode plots. This hybrid approach combines accuracy, by treating the system-identification part perturbatively, and computational efficiency, by applying Monte Carlo techniques to the low-dimensional input space of the control design and performance/stability evaluation part. This combination makes the proposed technique affordable and efficient even for large-scale flow-control problems. The ARMarkov/LS identification procedure has been chosen as a representative system-identification technique to illustrate this framework and to obtain error bounds on the identified system parameters based on the signal-to-noise ratio of the input–output data sequence. The procedur

Journal article

Mariappan S, Sujith RI, Schmid PJ, 2015, Experimental investigation of non-normality of thermoacoustic interaction in an electrically heated Rijke tube, International Journal of Spray and Combustion Dynamics, Vol: 7, Pages: 315-352, ISSN: 1756-8285

An experimental investigation of the non-normal nature of thermoacoustic interactions in an electrically heated horizontal Rijke tube is performed. Since non-normality and the associated transient growth are linear phenomena, the experiments have to be confined to the linear regime. The bifurcation diagram for the subcritical Hopf bifurcation into a limit cycle behavior has been determined, after which the amplitude levels, for which the system acts linearly, have been identified for different power inputs to the heater. There are two main objectives for this experimental investigation. The first one deals with the extraction of the linear eigenmodes associated with the acoustic pressure from experimental data. This is accomplished by the Dynamic Mode Decomposition (DMD) technique applied in the linear regime. The non-orthogonality between the eigenmodes is determined for various values of heater power. The second objective is to identify evidence of transient perturbation growth in the system. The total acoustic energy in the duct has been monitored as the thermoacoustic system evolves from its initial condition. Transient growth, on the order of previous theoretical studies, has been found, and its parameteric dependence on amplitude ratio and phase angle of the initial eigenmode components has been determined. This study represents the first experimental confirmation of non-normality in thermoacoustic systems.

Journal article

Flinois TL, Morgans AS, Schmid PJ, 2015, Projection-free approximate balanced truncation of large unstable systems, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 92, Pages: 023012-023012, ISSN: 1063-651X

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the Gramians (including the unstable subspace). We then apply the method to a spatially developing unstable system and show that it results in reduced-order models of similar quality to the ones obtained with existing methods. Due to the unbounded growth of unstable modes, a practical restriction on the final impulse response simulation time appears, which can be adjusted depending on the desired order of the reduced-order model. Recommendations are given to further reduce the cost of the method if the system is large and to improve the performance of the method if it does not yield acceptable results in its unmodified form. Finally, the method is applied to the linearized flow around a cylinder at Re = 100 to show that it actually is able to accurately reproduce impulse responses for more realistic unstable large-scale systems in practice. The well-established approximate balanced truncation numerical framework therefore can be safely applied to unstable systems without any modifications. Additionally, balanced reduced-order models can readily be obtained even for large systems, where the computational cost of existing methods is prohibitive.

Journal article

Flinois TLB, Morgans AS, Schmid PJ, 2015, Projection-free approximate balanced truncation of large unstable systems, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol: 92, ISSN: 1539-3755

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition algorithm theoretically yields a converged transformation that balances the Gramians (including the unstable subspace). We then apply the method to a spatially developing unstable system and show that it results in reduced-order models of similar quality to the ones obtained with existing methods. Due to the unbounded growth of unstable modes, a practical restriction on the final impulse response simulation time appears, which can be adjusted depending on the desired order of the reduced-order model. Recommendations are given to further reduce the cost of the method if the system is large and to improve the performance of the method if it does not yield acceptable results in its unmodified form. Finally, the method is applied to the linearized flow around a cylinder at Re = 100 to show that it actually is able to accurately reproduce impulse responses for more realistic unstable large-scale systems in practice. The well-established approximate balanced truncation numerical framework can therefore be safely applied to unstable systems without any modifications. Additionally, balanced reduced-order models can readily be obtained even for large systems, where the computational cost of existing methods is prohibitive.

Journal article

Flinois T, Morgans A, Schmid P, 2015, Projection-free approximate balanced truncation of large unstable systems

Working paper

Meneghello G, Schmid PJ, Huerre P, 2015, Receptivity and sensitivity of the leading-edge boundary layer of a swept wing, JOURNAL OF FLUID MECHANICS, Vol: 775, ISSN: 0022-1120

Journal article

Zhang M, Martinelli F, Wu J, Schmid PJ, Quadrio Met al., 2015, Modal and non-modal stability analysis of electrohydrodynamic flow with and without cross-flow, Journal of Fluid Mechanics, Vol: 770, Pages: 319-349, ISSN: 1469-7645

We report the results of a complete modal and non-modal linear stability analysis of the electrohydrodynamic flow for the problem of electroconvection in the strong-injection region. Convective cells are formed by the Coulomb force in an insulating liquid residing between two plane electrodes subject to unipolar injection. Besides pure electroconvection, we also consider the case where a cross-flow is present, generated by a streamwise pressure gradient, in the form of a laminar Poiseuille flow. The effect of charge diffusion, often neglected in previous linear stability analyses, is included in the present study and a transient growth analysis, rarely considered in electrohydrodynamics, is carried out. In the case without cross-flow, a non-zero charge diffusion leads to a lower linear stability threshold and thus to a more unstable flow. The transient growth, though enhanced by increasing charge diffusion, remains small and hence cannot fully account for the discrepancy of the linear stability threshold between theoretical and experimental results. When a cross-flow is present, increasing the strength of the electric field in the high- Poiseuille flow yields a more unstable flow in both modal and non-modal stability analyses. Even though the energy analysis and the input–output analysis both indicate that the energy growth directly related to the electric field is small, the electric effect enhances the lift-up mechanism. The symmetry of channel flow with respect to the centreline is broken due to the additional electric field acting in the wall-normal direction. As a result, the centres of the streamwise rolls are shifted towards the injector electrode, and the optimal spanwise wavenumber achieving maximum transient energy growth increases with the strength of the electric field.

Journal article

Paramati M, Tirumkudulu MS, Schmid PJ, 2015, Stability of a moving radial liquid sheet: experiments, Journal of Fluid Mechanics, Vol: 770, Pages: 398-423, ISSN: 1469-7645

A recent theory (Tirumkudulu & Paramati, Phys. Fluids, vol. 25, 2013, 102107) for a radially expanding liquid sheet, that accounts for liquid inertia, interfacial tension and thinning of the liquid sheet while ignoring the inertia of the surrounding gas and viscous effects, shows that such a sheet is convectively unstable to small sinuous disturbances at all frequencies and Weber numbers [mathematical formula]. Here, [mathematical symbol] and [mathematical symbol] are the density and surface tension of the liquid, respectively, [mathematical symbol] is the speed of the liquid jet, and [mathematical symbol] is the local sheet thickness. In this study we use a simple non-contact optical technique based on laser-induced fluorescence (LIF) to measure the instantaneous local sheet thickness and displacement of a circular sheet produced by head-on impingement of two laminar jets. When the impingement point is disturbed via acoustic forcing, sinuous waves produced close to the impingement point travel radially outwards. The phase speed of the sinuous wave decreases while the amplitude grows as they propagate radially outwards. Our experimental technique was unable to detect thickness modulations in the presence of forcing, suggesting that the modulations could be smaller than the resolution of our experimental technique. The measured phase speed of the sinuous wave envelope matches with theoretical predictions while there is a qualitative agreement in the case of spatial growth. We show that there is a range of frequencies over which the sheet is unstable due to both aerodynamic interaction and thinning effects, while outside this range, thinning effects dominate. These results imply that a full theory that describes the dynamics of a radially expanding liquid sheet should account for both effects.

Journal article

Blanchard M, Schuller T, Sipp D, Schmid PJet al., 2015, Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver, PHYSICS OF FLUIDS, Vol: 27, ISSN: 1070-6631

Journal article

Camporeale C, Schmid PJ, 2015, Parametric resonance in unsteady watertable flow, JOURNAL OF FLUID MECHANICS, Vol: 768, ISSN: 0022-1120

Journal article

Sayadi T, Schmid PJ, Richecoeur F, Durox Det al., 2015, Parametrized data-driven decomposition for bifurcation analysis, with application to thermo-acoustically unstable systems, PHYSICS OF FLUIDS, Vol: 27, ISSN: 1070-6631

Journal article

Statnikov V, Sayadi T, Meinke M, Schmid P, Schroeder Wet al., 2015, Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition, PHYSICS OF FLUIDS, Vol: 27, ISSN: 1070-6631

Journal article

Inigo JG, Sipp D, Schmid PJ, 2015, A dynamic observer to capture and control perturbation energy in noise amplifier flows, IUTAM/ABCM Symposium on Laminar Turbulent Transition, Publisher: ELSEVIER SCIENCE BV, Pages: 337-343, ISSN: 2210-9838

Conference paper

Fosas de Pando M, Schmid PJ, Sipp D, 2015, Nonlinear model-order reduction for oscillator flows using POD-DEIM, IUTAM/ABCM Symposium on Laminar Turbulent Transition, Publisher: ELSEVIER SCIENCE BV, Pages: 329-336, ISSN: 2210-9838

Conference paper

Foures DPG, Dovetta N, Sipp D, Schmid PJet al., 2014, A data-assimilation method for Reynolds-averaged Navier-Stokes-driven mean flow reconstruction, JOURNAL OF FLUID MECHANICS, Vol: 759, ISSN: 0022-1120

Journal article

Inigo JG, Sipp D, Schmid PJ, 2014, A dynamic observer to capture and control perturbation energy in noise amplifiers, JOURNAL OF FLUID MECHANICS, Vol: 758, Pages: 728-753, ISSN: 0022-1120

Journal article

de Pando MF, Schmid PJ, Sipp D, 2014, A global analysis of tonal noise in flows around aerofoils, JOURNAL OF FLUID MECHANICS, Vol: 754, Pages: 5-38, ISSN: 0022-1120

Journal article

Juillet F, McKeon BJ, Schmid PJ, 2014, Experimental control of natural perturbations in channel flow, JOURNAL OF FLUID MECHANICS, Vol: 752, Pages: 296-309, ISSN: 0022-1120

Journal article

Sayadi T, Le Chenadec V, Schmid PJ, Richecoeur F, Massot Met al., 2014, Thermoacoustic instability - a dynamical system and time domain analysis, Journal of Fluid Mechanics, Vol: 753, Pages: 448-471, ISSN: 1469-7645

This study focuses on the Rijke tube problem, which includes features relevant to the modelling of thermoacoustic coupling in reactive flows: a compact acoustic source, an empirical model for the heat source and nonlinearities. This thermoacoustic system features both linear and nonlinear flow regimes with complex dynamical behaviour. In order to synthesize accurate time series, we tackle this problem from a numerical point of view, and start by proposing a dedicated solver designed for dealing with the underlying stiffness – in particular, the retarded time and the discontinuity at the location of the heat source. Stability analysis is performed on the limit of low-amplitude disturbances by using the projection method proposed by Jarlebring (PhD thesis, Technische Universität Braunschweig, 2008), which alleviates the problems arising from linearization with respect to the retarded time. The results are then compared with the analytical solution of the undamped system and with the results obtained from Galerkin projection methods commonly used in this setting. This analysis provides insight into the consequences of the various assumptions and simplifications that justify the use of Galerkin expansions based on the eigenmodes of the unheated resonator. We demonstrate that due to the presence of a discontinuity in the spatial domain, the eigenmodes in the heated case predicted by using Galerkin expansion show spurious oscillations resulting from the Gibbs phenomenon. Finally, time series in the fully nonlinear regime, where a limit cycle is established, are analysed and dominant modes are extracted. By comparing the modes of the linear regime to those of the nonlinear regime, we are able to illustrate the mean-flow modulation and frequency switching, which appear as the nonlinearities become significant and ultimately affect the form of the limit cycle. Analysis of the saturated limit cycles shows the presence of higher-frequency modes, which are linearly s

Journal article

Sayadi T, Schmid PJ, Nichols JW, Moin Pet al., 2014, Reduced-order representation of near-wall structures in the late transitional boundary layer, JOURNAL OF FLUID MECHANICS, Vol: 748, Pages: 278-301, ISSN: 0022-1120

Journal article

Foures DPG, Caulfield CP, Schmid PJ, 2014, Optimal mixing in two-dimensional plane Poiseuille flow at finite Peclet number, JOURNAL OF FLUID MECHANICS, Vol: 748, Pages: 241-277, ISSN: 0022-1120

Journal article

Schmid PJ, Brandt L, 2014, Analysis of Fluid Systems: Stability, Receptivity, Sensitivity, APPLIED MECHANICS REVIEWS, Vol: 66, ISSN: 0003-6900

Journal article

Jovanovic MR, Schmid PJ, Nichols JW, 2014, Sparsity-promoting dynamic mode decomposition, PHYSICS OF FLUIDS, Vol: 26, ISSN: 1070-6631

Journal article

Foures DPG, Caulfield CP, Schmid PJ, 2013, Localization of flow structures using infinity-norm optimization, JOURNAL OF FLUID MECHANICS, Vol: 729, Pages: 672-701, ISSN: 0022-1120

Journal article

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