A practical guide for using proper orthogonal decomposition in engine research

Proper orthogonal decomposition has been utilized for well over a decade to study turbulence and cyclic variation of flow and combustion properties in internal combustion engines. In addition, proper orthogonal decomposition is useful to quantitatively compare multi-cycle in-cylinder measurements with numerical simulations (large-eddy simulations). However, the application can be daunting, and physical interpretation of proper orthogonal decomposition can be ambiguous. In this paper, the mathematical procedure of proper orthogonal decomposition is described conceptually, and a compact MATLAB® code is provided. However, the major purpose is to empirically illustrate the properties of the proper orthogonal decomposition analysis and to propose practical procedures for application to internal combustion engine flows. Two measured velocity data sets from a motored internal combustion engine are employed, one a highly directed flow (each cycle resembles the ensemble average), and the other an undirected flow (no cycle resembles the average). These data are used to illustrate the degree to which proper orthogonal decomposition can quantitatively distinguish between internal combustion engine flows with these two extreme flow properties. In each flow, proper orthogonal decomposition mode 1 is an excellent estimate of ensemble average, and this study illustrates how it is thus possible to unambiguously quantify the cyclic variability of Reynolds-averaged Navier–Stokes ensemble average and turbulence. In addition, this study demonstrates the benefits of comparing two different samples of cycles using a common proper orthogonal decomposition mode set derived by combining the two samples, the effect of spatial resolution, and a method to evaluate the number of snapshots required to achieve convergence.

[1]  Laurent Cordier,et al.  Proper Orthogonal Decomposition: an overview , 2008 .

[2]  L. Graftieaux,et al.  Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows , 2001 .

[3]  Thierry Poinsot,et al.  Large Eddy Simulation of a Motored Single-Cylinder Piston Engine: Numerical Strategies and Validation , 2011 .

[4]  David L. Reuss,et al.  Two-dimensional particle image velocimetry with electro-optical image shifting in an internal combustion engine , 1993, Optics & Photonics.

[5]  David L. Reuss,et al.  Cyclic Variability of Large-Scale Turbulent Structures in Directed and Undirected IC Engine Flows , 2000 .

[6]  J. Westerweel.  Fundamentals of digital particle image velocimetry , 1997 .

[7]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[8]  D. Thévenin,et al.  An experimental analysis of the turbulent structures generated by the intake port of a DISI-engine , 2010 .

[9]  Daniel C. Haworth,et al.  Application of the proper orthogonal decomposition to datasets of internal combustion engine flows , 2004 .

[10]  W. Dahm,et al.  Turbulence Properties of High and Low Swirl In-Cylinder Flows , 2002 .

[11]  Hao Chen,et al.  On the use and interpretation of proper orthogonal decomposition of in-cylinder engine flows , 2012, Measurement Science and Technology.

[12]  J. Borée,et al.  Tumbling Vortex Flow in a Model Square Piston Compression Machine: PIV and LDV Measurements , 1997 .

[13]  T. Poinsot,et al.  Large-Eddy Simulation and experimental study of cycle-to-cycle variations of stable and unstable operating points in a spark ignition engine , 2012 .

[14]  Michel L. Riethmuller,et al.  Post-processing of experimental and numerical data , 2002 .

[15]  B. Khalighi,et al.  Particle Image Velocimetry Measurements in a High-Swirl Engine Used for Evaluation of Computational Fluid Dynamics Calculations , 1995 .

[16]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[17]  Volker Sick,et al.  Analysis of misfires in a direct injection engine using proper orthogonal decomposition , 2011 .

[18]  W. Meier,et al.  Phase-resolved characterization of vortex–flame interaction in a turbulent swirl flame , 2011 .

[19]  Simona Silvia Merola,et al.  POD-based analysis of combustion images in optically accessible engines , 2010 .

[20]  S. Pope.  Ten questions concerning the large-eddy simulation of turbulent flows , 2004 .

[21]  J. Borée,et al.  Spatio-temporal structure and cycle to cycle variations of an in-cylinder tumbling flow , 2011 .

[22]  Daniel C. Haworth,et al.  Development and assessment of POD for analysis of turbulent flow in piston engines , 2011 .

[23]  Volker Sick,et al.  High-speed imaging for direct-injection gasoline engine research and development , 2010 .

[24]  P. Hutchinson,et al.  Velocity measurements in the recirculation region of an industrial burner flame by laser anemometry with light frequency shifting , 1974 .

[25]  Volker Sick,et al.  Measurement of digital particle image velocimetry precision using electro-optically created particle-image displacements , 2002 .

[26]  V. Sick,et al.  High-speed imaging analysis of misfires in a spray-guided direct injection engine , 2011 .

[27]  L Sirovich,et al.  Low-dimensional procedure for the characterization of human faces. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[28]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[29]  Xavier Baby,et al.  Investigation of the In-Cylinder Tumble Motion In a Multi-Valve Engine: Effect of the Piston Shape , 1997 .

[30]  Daniel C. Haworth,et al.  Large-Eddy Simulation of in-Cylinder Flows , 1999 .