Short Time Proper Orthogonal Decomposition for State Estimation of Transient Flow Fields

2005 ◽  
Author(s):  
Stefan Siegel ◽  
Kelly Cohen ◽  
Jürgen Seidel ◽  
Thomas McLaughlin
Keyword(s):  
Proper Orthogonal Decomposition ◽  
State Estimation ◽  
Transient Flow ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Short Time ◽  
Proper Orthogonal ◽  
Transient Flow Fields

Inverse design of aircraft cabin environment using computational fluid dynamics-based proper orthogonal decomposition method

2017 ◽  
Vol 27 (10) ◽  
pp. 1379-1391 ◽  
Author(s):  
Jihong Wang ◽  
Tengfei (Tim) Zhang ◽  
Hongbiao Zhou ◽  
Shugang Wang
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Proper Orthogonal Decomposition ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Air Supply ◽  
Spatial Modes ◽  
Cabin Environment ◽  
Proper Orthogonal

To design a comfortable aircraft cabin environment, designers conventionally follow an iterative guess-and-correction procedure to determine the air-supply parameters. The conventional method has an extremely low efficiency but does not guarantee an optimal design. This investigation proposed an inverse design method based on a proper orthogonal decomposition of the thermo-flow data provided by full computational fluid dynamics simulations. The orthogonal spatial modes of the thermo-flow fields and corresponding coefficients were firstly extracted. Then, a thermo-flow field was expressed into a linear combination of the spatial modes with their coefficients. The coefficients for each spatial mode are functions of air-supply parameters, which can be interpolated. With a quick map of the cause–effect relationship between the air-supply parameters and the exhibited thermo-flow fields, the optimal air-supply parameters were determined from specific design targets. By setting the percentage of dissatisfied and the predicted mean vote as design targets, the proposed method was implemented for inverse determination of air-supply parameters in two aircraft cabins. The results show that the inverse design using computational fluid dynamics-based proper orthogonal decomposition method is viable. Most of computing time lies in the construction of data samples of thermo-flow fields, while the proper orthogonal decomposition analysis and data interpolation is efficient.

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

2020 ◽  
pp. 146808742091724
Author(s):  
Li Shen ◽  
Kwee-Yan Teh ◽  
Penghui Ge ◽  
Fengnian Zhao ◽  
David LS Hung
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Internal Combustion Engines ◽  
Temporal Evolution ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Temporal Behavior ◽  
Decomposition Approach ◽  
Cylinder Flow ◽  
Proper Orthogonal ◽  
Low Order

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.

Model order reduction using sparse coding exemplified for the lid-driven cavity

2016 ◽  
Vol 808 ◽  
pp. 189-223 ◽  
Author(s):  
Rohit Deshmukh ◽  
Jack J. McNamara ◽  
Zongxian Liang ◽  
J. Zico Kolter ◽  
Abhijit Gogulapati
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Sparse Coding ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Driven Cavity ◽  
Reduced Order ◽  
Multi Scale ◽  
Small Set ◽  
Proper Orthogonal

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

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