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

Abstract

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.

Manifold reduction techniques for the comparison of crank angle-resolved particle image velocimetry (PIV) data and Reynolds-averaged Navier-Stokes (RANS) simulations in a spark ignition direct injection (SIDI) engine

“…x use different methods 24,25,43 7: Reconstruct centred data Y centre xEquation 7 8: Reintroduce the mean to get Y…”

“…x use different methods 24,25,43 and the upper piston ring) was varied for each condition to match the in-cylinder pressure trace. There was no further tuning of the physical models.…”

On the use of particle image velocimetry (PIV) data for the validation of Reynolds averaged Navier-Stokes (RANS) simulations during the intake process of a spark ignition direct injection (SIDI) engine

“…The coherent flow structures in the instantaneous flow fields (Figure 9(i)) are instead preserved in the approximated flow fields (Figure 9(a)-(h)) once sufficiently large numbers of low-order POD components are added to the ensemble mean (cf equation ( 11)). 56,57 The focus of this paper lies only on the low-order approximated flow fields and thus discussions of the individual POD mode shapes are not presented.…”

“…The POD reconstructed fields using different numbers of POD modes (equation ( 11)) for two arbitrarily selected engine cycles, Cycle A (Figure 1 11)). 56,57 The focus of this paper lies only on the low-order approximated flow fields and thus discussions of the individual POD mode shapes are not presented.…”

Propeller Position Effects over the Pressure and Friction Coefficients over the Wing of an UAV with Distributed Electric Propulsion: A Proper Orthogonal Decomposition Analysis

“…Some recent studies where the application of POD in fluid fields can be seen are the investigation of Broatch et al [16] where this tool is used to analyse acoustic fields in radial compressors, or the work of Torregrosa et al [17] where the modal decomposition helps to characterise the unsteady flow field of a combustion chamber. Like the last study, it is easy to find the application of POD in the field of thermal engines [18][19][20], but this method is also used to analyse different aerodynamic problems. These include the interpolation of transonic flows [21], the creation of reduced-order models to characterise aircraft flying at high angles of attack [22], or to generate three-dimensional flow models for supersonic aircraft that significantly reduces the need of computationally-expensive high fidelity simulations [23].…”