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

Abstract

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.

Large eddy simulation analysis of the turbulent flow in an optically accessible internal combustion engine using the overset mesh technique

“…To obtain more information on the degree of CCV, more advanced POD techniques are developed and applied. Qin proposed a further decomposition method, the quadruple POD decomposition, 42 and a review on the application of these methods to an ICE; the original POD quadruple decomposition applied in this work can be found in a previous work by Rulli et al 33 For the sake of clarity, the proposed POD quadruple decomposition is here recalled. According to equation (8), each snapshot can be reconstructed using the whole set ( N ) of POD coefficient and modes.…”

“…This technique allows recognition of the dimension of the dominant flow structures in each reconstructed POD mode. Detailed information on the implementation of the method can be found in Rulli et al 33 The transition part of the turbulence is identified as a passage in the energy cascade between the large-scale vortices in the coherent turbulence and the smallest ones in the incoherent background turbulence. The authors deliberately avoid defining a method to objectively identify the cut-off number between the transition and the incoherent parts of the turbulent.…”

“…An evolution from the consolidated POD method was proposed by Roudnitzky et al, 32 presenting a triple decomposition of the phase-invariant POD decomposition to identify the mean, the coherent and the incoherent parts of the turbulent flow field. Rulli et al 33 performed a critical review of some methods of analysis of ICE flow fields involving POD and proposed an original POD quadruple decomposition method based on the phase-invariant POD for the analysis of experimental particle image velocimetry (PIV) data. In this article, the method is extended to compare PIV and simulation data, confirming the potential of discerning mean, coherent, transition and incoherent energy content in the analysis of turbulent flows.…”

Effect of Lagrangian-phase Modelling on Charge Stratification and Spatial Distribution of Threshold Soot Index for Toluene Reference Fuel Surrogates

“…As for commercial gasolines, carbon-atom rich fuels belonging to the aromatic hydrocarbon class [4] are more prone to generate soot, especially in fuel-rich mixture combustion, when the fuel pyrolysis process is triggered. Emissions in ICEs can be investigated with both experiments at the test bench and Computational Fluid Dynamics (CFD): accurate description of flow field [5], spray [6] [7], mixing [8], combustion [9] [10], knock [11] [12], and emission formation [13] can be achieved with advanced models. The estimation of soot production during fuel oxidation via CFD tools can be achieved both employing detailed chemistry resolution [14] and a chemistry-tabulated approach [8] [15].…”

“…To tackle this problem, actual fuels are replaced by so-called fuel surrogates, which are mixtures of fewer well-known hydrocarbons; the composition depends on the properties of the reference fuel that are to be matched. Surrogates have been extensively adopted for several applications, from commercial gasolines [16] to jet fuels [5] [6]. Although Toluene Reference Fuel (TRF) and Primary Reference Fuel (PRF) do not match the evaporation properties of the real gasolines, due to the absence of high-temperature normal boiling point components, such surrogates are widely adopted in DISI engine combustion simulations.…”