On the use and interpretation of proper orthogonal decomposition of in-cylinder engine flows

Abstract

The proper orthogonal decomposition (POD) has found increasing application for the comparison of measured and computed data as well as the identification of instantaneous and time varying flow structures, particularly cyclic variability in reciprocating internal combustion engines. The patterns observed in the basis functions or modes are sometimes interpreted as coherent structures, though justification of this is not obvious from the mathematical derivations. Similarly, there is no consensus about whether or not the ensemble mean should be subtracted prior to performing POD on a data set. Synthetic flow fields are used here to reveal POD properties otherwise ambiguous in real stochastic flow data. In particular, each POD mode includes elements of all flow structures from all input snapshots and in general, several modes are needed to reconstruct physical flow structures. POD analysis of two experimental in-cylinder engine data is done: one flow condition where every cycle resembles the ensemble-averaged flow pattern, and the other with large cyclic variability such that no cycles resemble the ensemble average. The energy and flow patterns of the POD modes, derived with and without first subtracting the mean, are compared to each other and to the Reynolds decomposed flow to reveal properties of the POD modes.

Afterbody vortices of axisymmetric cylinders with a slanted base

“…The technique has been applied extensively in turbulent flows (Adrian et al 2000) and vortex-dominated flows (Graftieaux et al 2001;Wang and Gursul 2012) previously. In this paper, the analysis was performed using a MATLAB ® code (Chen et al 2012(Chen et al , 2013 which adopts the method of snapshots. The calculation was performed on the fluctuating component of the velocity field.…”

A Framework for the Development of Integrated and Computationally Feasible Models of Large-Scale Mammalian Cell Bioreactors

“…In order to achieve this, the full rank system is first solved to create time-series snapshots of distribution of cells over compartments under a specific operating condition. Then a set of orthonormal bases are generated through eigen-decomposition [55]. Bases with no significant impact on the solution profile are truncated to obtain the reduced rank model.…”

Identification of Large-Scale Structure Fluctuations in IC Engines using POD-Based Conditional Averaging

“…Here, we focus on the snapshot POD method [6,7,24]. A detailed description of the underlying theory and the application for experimental and simulation data can be found in [21,24,25].…”

“…Furthermore, the remaining fluctuations are expected not to be associated with a variation of a coherent motion but rather being smaller scale turbulent fluctuations. To achieve this, our method combines POD, which has been used previously for the identification and investigation of velocity field fluctuations based both on experimental and numerical data [3][4][5][6][7][8][9], and conditional averaging [10].…”