Phase-invariant Proper Orthogonal Decomposition Research Articles

Temporal evolution analysis of in-cylinder flow by means of proper orthogonal decomposition

In-cylinder flow fields and their temporal evolution have strong effect on the combustion dynamics of internal combustion engines. Proper orthogonal decomposition is a statistical tool to analyze these flow fields by decomposing them into flow patterns (known as proper orthogonal decomposition modes) and corresponding coefficients with their contribution to the ensemble flow kinetic energy successively maximized. However, neither of the two prevailing proper orthogonal decomposition approaches satisfactorily describes the temporal behavior of the flow fields. The phase-dependent proper orthogonal decomposition approach is limited to analyzing spatial flow structures at a certain engine phase. The phase-invariant proper orthogonal decomposition approach attempts to account for both spatial and temporal variations, but at the expense of diminished statistical and physical significance. In this article, we seek to understand the temporal behavior of tumble flow fields by analyzing the evolution of low-order phase-dependent proper orthogonal decomposition modes over multiple crank angles. The concept of relevance index is first generalized to enable comparison between two vectorial fields of different sizes. This metric is then used to quantify the directional similarities between the two lowest proper orthogonal decomposition modes obtained at sequential crank angles. The mode shapes are observed to evolve gradually and naturally over most crank angles, but change significantly at certain crank angles during intake. The results indicate that each of the low-order modes features strong velocity fluctuations in different regions of the tumble plane, and different numbers of modes are needed to represent the dominant features of tumble flow at different engine phases. Based on this understanding, we propose to use the partial sum of those proper orthogonal decomposition modes and their coefficients to form a low-order approximation model of the in-cylinder tumble flow, in order to reduce flow field complexity and noise while retaining its major spatial and temporal features.

A critical review of flow field analysis methods involving proper orthogonal decomposition and quadruple proper orthogonal decomposition for internal combustion engines

Experimental techniques like particle image velocimetry provide a powerful technical support for the analysis of the spatial and temporal evolution of the flow field in internal combustion engines. Such techniques can be used to investigate both ensemble-averaged flow structures and their cyclic variations. These last are among the major causes of cycle-to-cycle variability of the engine processes (mixture formation, combustion, heat transfer, emission formation), the reduction of which has become a paradigm recently in engine development. Proper orthogonal decomposition has been largely used in conjunction with particle image velocimetry to analyze flow field characteristics. Several methods involving proper orthogonal decomposition have been proposed in the recent years to analyze engine cycle-to-cycle variability. In this work, phase-invariant proper orthogonal decomposition analysis, conditional averaging and triple and quadruple proper orthogonal decomposition methods are first introduced and applied to a large database of particle image velocimetry data from a well-known research engine. Results are discussed with particular emphasis on the capability of the methods to perform both quantitative and qualitative evaluations on cycle-to-cycle variability. Second, a new quadruple proper orthogonal decomposition methodology is proposed and compared to those available in the literature. All the methods are found to be helpful to identify the turbulent structures responsible for cycle-to-cycle variability. They can be equally applied to both experimental and numerical datasets to analyze turbulent fields in detail and to make comparisons.

On the Application of Proper Orthogonal Decomposition (POD) for In-Cylinder Flow Analysis

Proper orthogonal decomposition (POD) is a coherent structure identification technique based on either measured or computed data sets. Recently, POD has been adopted for the analysis of the in-cylinder flows inside internal combustion engines. In this study, stereoscopic particle image velocimetry (Stereo-PIV) measurements were carried out at the central vertical tumble plane inside an engine cylinder to acquire the velocity vector fields for the in-cylinder flow under different experimental conditions. Afterwards, the POD analysis were performed firstly on synthetic velocity vector fields with known characteristics in order to extract some fundamental properties of the POD technique. These data were used to reveal how the physical properties of coherent structures were captured and distributed among the POD modes, in addition to illustrate the difference between subtracting and non-subtracting the ensemble average prior to conducting POD on datasets. Moreover, two case studies for the in-cylinder flow at different valve lifts and different pressure differences across the air intake valves were presented and discussed as the effect of both valve lifts and pressure difference have not been investigated before using phase-invariant POD analysis. The results demonstrated that for repeatable flow pattern, only the first mode was sufficient to reconstruct the physical properties of the flow. Furthermore, POD analysis confirmed the negligible effect of pressure difference and subsequently the effect of engine speed on flow structures.

Large-eddy simulation of in-cylinder flow in a DISI engine with charge motion control valve: Proper orthogonal decomposition analysis and cyclic variation

The application of the charge motion control valve is an effective and flexible way to reduce cycle-to-cycle variations (CCV) and improve engine performance. The objective of this research is to investigate the influence of the tumble flap (i.e., a specific type of charge motion control valve) placed in the intake port on the in-cylinder aerodynamics and CCV inside a non-reacting, direct injection spark ignition (DISI) engine by means of multi-cycle large-eddy simulation (LES) and proper orthogonal decomposition (POD). Extensive POD analyses involving the phase-dependent POD and phase-invariant POD were carried out. Furthermore, the POD quadrapole decomposition method was employed to gain more insight into the stochastic nature of in-cylinder flow. Results indicate that the tumble flap greatly affects the in-cylinder flow field and the first three subfields, but its effect on turbulent part is insignificant. With the closed tumble flap, more intense tumble motion, improved volumetric efficiency, increased energy portion of the mean part, decreased rate of energy decay, and reduced CCV could be achieved compared with the open tumble flap. It is also found that the phase-invariant POD is a useful tool to assess the effect of the tumble flap on the evolution characteristics.

Evaluating Large-Eddy Simulation (LES) and High-Speed Particle Image Velocimetry (PIV) with Phase-Invariant Proper Orthogonal Decomposition (POD)

This study is part of a program to understand the stochastic variations in IC engine flows; in particular, it is a comparison of measured (PIV) and computed (LES) velocity from multiple cycles of the same motored engine. Comparison procedures included traditional RANS (Reynolds Averaged Navier-Stokes) decomposition (ensemble-averaged and RMS (Root Mean Square) velocity), phase-dependent, and phase- invariant POD. Phase-dependent POD was performed on the PIV and LES samples separately and on the combined samples, thus creating separate or a single POD mode sets, respectively. The phase- invariant POD was performed both on normalized snapshots and on snapshots where the original energy was conserved. Initial comparisons of the mass-specific kinetic energies of the ensemble average and RMS velocities revealed that the PIV and LES data sets differed significantly during most of the intake stroke. This discrepancy was quantifiedfirst by comparing the relevance indices calculated between ensemble average velocity fields and, second, using phase-dependent POD, which quantified cycle-to-cycle flow variations of the RANS average and turbulence. Phase-dependent POD was applied separately to the PIV and LES data sets during the intake stroke (76° ATDCE, After Top Dead Center Exhaust), where the intake-valve jet is strong and the PIV and LES data were earlier found to be significantly different. The cyclic variability of the LES ensemble average was estimated to be significantly higher than that of the PIV data set. POD was also applied to the combined sample of LES and PIV snapshots for quantitative comparison creating a single set of modes, so that comparison could be made with POD coefficients alone. Example comparisons were made at again for data at 76° and also 330° ATDCE, which is a viable spark timing in a fired engine. The results at 76° ATDCE were similar to those obtained with the POD analysis of the separate samples. At 330° ATDCE, the PIV ensemble average and RMS velocities showed somewhat more cyclic variability. Phase-invariant POD was applied to the combined PIV and LES velocity data from all crank angles to study the flow evolution over the crank angle range. Conclusions derived from the two different energy transformations are contrasted. When the energy of each velocity field is normalized, the phase-invariant POD results focus on differences in flow structures and their evolution. On the other hand, when the energy of each velocity field is conserved, the phase-invariant POD results also take into account differences in energy between the PIV and LES data.

Large-eddy Simulation of Motored Flow in a Two-valve Piston Engine: POD Analysis and Cycle-to-cycle Variations

Large-eddy simulation (LES) has been performed for a single-cylinder, two-valve, four-stroke-cycle piston engine through 70 consecutive motored cycles. Initial comparisons of ensemble-averaged velocity fields have been made between LES and experiment, and proper orthogonal decomposition (POD) has been used to analyze the complex in-cylinder turbulent flows. Convergence of POD modes has been quantified, several POD variants have been explored, and sensitivity of results to analyzing different subsets of engine cycles has been studied. In general, it has been found that conclusions that were drawn earlier from POD analysis of a simplified non-compressing piston-cylinder assembly with a fixed valve carry over to the much more complex flow in this motored four-stroke-cycle engine. For the cases that have been examined, the first POD mode essentially corresponds to the ensemble-averaged mean velocity. The number of engine cycles required to extract converged POD modes increases with mode number, and varies with phase (piston position). There is little change in the lower-order phase-invariant POD modes when as few as 24 phases per cycle (30° between samples) are used, and complex 3-D time-dependent in-cylinder velocity fields through full engine cycles can be reconstructed using a relatively small number of POD modes. Quantification of cycle-to-cycle variations and insight into in-cylinder flow dynamics can be extracted through analysis of phase-invariant POD modes and coefficients.

Spatio-temporal structure and cycle to cycle variations of an in-cylinder tumbling flow

The aim of this paper is to make use of PIV and high-speed PIV in a research engine of moderate tumbling ratio in order to analyze both the spatial structure of the flow and its temporal evolution during series of consecutive cycles. Appropriate analyzing tools are introduced, and four different points are addressed: (1) the chain of events driving the generation of the three-dimensional mean tumbling motion is investigated; (2) a Lagrangian analysis of the roll-up of the tumbling jet in individual cycles demonstrates a strong cycle to cycle variation during the compression phase (the rms of the position of the jet front being approximately 10% of the piston stroke); (3) focussing on the “breakdown” phase, phase invariant proper orthogonal decomposition enables us to distinguish cycles according to their structure near top dead center (TDC). We show that when the coherent energy of the flow is conserved, there is no increase in the fluctuating kinetic energy; (4) finally, the phase-averaged Reynolds stresses is decomposed into a contribution of the in-cycle coherence and the turbulence carried by the flow states. Approximately 30% of the fluctuating kinetic energy is due to cycle to cycle fluctuations in this chamber near TDC.

Coupling time-resolved PIV flow-fields and phase-invariant proper orthogonal decomposition for the description of the parameters space in a transparent Diesel engine

Particle image velocimetry (PIV) results obtained from one transparent Diesel engine with a cylindrical bowl-in piston are investigated in this paper. Beyond the standard statistical description of in-cylinder flows, time-resolved PIV (TRPIV) now allows to access the in-cycle evolution. However, due to experimental and data storage limitations, the number of cycles obtained with TRPIV is evidently too low to perform any reliable statistical analysis and this is a general problem when TRPIV is used. However, this in-cycle information is very useful and should be associated in an optimal way to classical statistical data bases obtained in such engines. To overcome this issue, a coupling approach between TRPIV data and phase-invariant proper orthogonal decomposition (POD) applied on statistically converged data is proposed. To describe the large-scale motions and to reveal the low order flow dynamics, it is necessary to combine in an optimal way the statistically converged PIV datasets and the limited number of in-cycle TRPIV measurements. The POD modes resulting from the decomposition of the first dataset are used as an energetic basis for the projection of the time-resolved flow-fields during the whole compression stroke. The in-cycle evolution of the POD random coefficients is analysed. This method gives a low order description of the evolution of the compressed flow structure and dynamics and we prove that the fluctuations associated with both the intensity and the displacement of the swirling motion increase during the compression stroke, particularly during the transfer in the bowl. Normalized projections associated with the fluctuations identified are finally introduced to describe the parameters space for the available number of flow realisations. We show that they vary over the full parameter space during one compression.

Phase invariant proper orthogonal decomposition for the study of a compressed vortex

We propose here an experimental investigation of a vortex submitted to a radial perturbation while being compressed. This experiment reproduces a model situation of the complex flows that take place in a real engine cylinder. An isolated tumbling flow is first submitted to an injection of fluid and then compressed and measurements are realised by Particle Image Velocimetry (PIV). The Proper Orthogonal Decomposition is known to be an unbiased method to identify the coherent structures of turbulent flows. It is possible to make this decomposition for a given phase or to create a set of basis functions with the whole set of compression stroke velocity fields. First, the experimental set-up will be presented, then the second part provides the POD principle. Results of phased POD decomposition of the compression of the unperturbated vortex will be presented. Finally results from the time invariant POD will be discussed to study the influence of the jet perturbation in the compression of a vortex.