Imperial College London

ProfessorPeterSchmid

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics
 
 
 
//

Contact

 

peter.schmid

 
 
//

Location

 

753Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Publication Type
Year
to

105 results found

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

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

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

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

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

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

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

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

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

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

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

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: 2470-0045

JOURNAL ARTICLE

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: 0022-1120

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

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

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

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

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

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

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

JOURNAL ARTICLE

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

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

Flinois TLB, Morgans AS, 2015, Projection-free approximate balanced truncation of large unstable systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 1539-3755

JOURNAL ARTICLE

Flinois TLB, Morgans AS, Schmid PJ, 2015, Projection-free approximate balanced truncation of large unstable systems., Phys Rev E Stat Nonlin Soft Matter Phys, Vol: 92

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

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

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

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: 1756-8277

JOURNAL ARTICLE

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

Request URL: http://wlsprd.imperial.ac.uk:80/respub/WEB-INF/jsp/search-html.jsp Request URI: /respub/WEB-INF/jsp/search-html.jsp Query String: respub-action=search.html&id=00793828&limit=30&person=true