Abstract
The cycle-to-cycle variation of engine in-cylinder flow is critical for the improvement of performance for spark-ignition internal combustion engines. Proper orthogonal decomposition (POD), with its ability to extract the most energetic fluctuation structure, is widely used to analyze the in-cylinder flow and understand the variation of its evolution in different cycles. However, both of the two existing approaches to use POD for engine flow analysis encounter difficulties when applied for this purpose. Phase-dependent POD decomposes a data set in which all samples are taken at a certain engine phase (crank angle) from different cycles, but the POD results at neighboring engine phases do not necessarily evolve coherently. Phase-invariant POD, when applied to analyze tumble flow, stretches/compresses and interpolates the flow fields obtained at different engine phases onto the same grid, and this deformation means that phase-invariant POD results are no longer significant in energy sense. To overcome these difficulties, we propose an adaptation of conditional space-time POD to work with engine flow, with which the flow within a range of engine phases in each cycle is considered as one sample. It is shown that the low-order modes obtained with conditional space-time POD capture fluctuation structures that evolve coherently, and these results are compared and contrasted with those of the two existing POD approaches. A reduced-order model of the engine in-cylinder flow is constructed based on the partial sum of the modes and coefficients obtained from the conditional space-time POD, and it is shown that this new reduced-order model identifies structure that is both coherent spatially and temporally.
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
