scholarly journals Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Nicholas Hamilton ◽  
Murat Tutkun ◽  
Raúl Bayoán Cal
Keyword(s):  
Turbulent Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Anisotropic Character ◽  
Proper Orthogonal ◽  
Low Order

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.

Proper orthogonal decomposition applied to turbulent flow in a square duct

1994 ◽  
Vol 6 (9) ◽  
pp. 3086-3092 ◽  
Author(s):  
R. S. Reichert ◽  
F. F. Hatay ◽  
S. Biringen ◽  
A. Huser
Keyword(s):  
Turbulent Flow ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Square Duct ◽  
Proper Orthogonal

Turbulence characteristics of a thermally stratified wind turbine array boundary layer via proper orthogonal decomposition

2017 ◽  
Vol 828 ◽  
pp. 175-195 ◽  
Author(s):  
N. Ali ◽  
G. Cortina ◽  
N. Hamilton ◽  
M. Calaf ◽  
R. B. Cal
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Atmospheric Boundary Layer ◽  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Commercial Application ◽  
Surface Boundary ◽  
Stable Regime ◽  
Proper Orthogonal

A large eddy simulation framework is used to explore the structure of the turbulent flow in a thermally stratified wind turbine array boundary layer. The flow field is driven by a constant geostrophic wind with time-varying surface boundary conditions obtained from a selected period of the CASES-99 field experiment. Proper orthogonal decomposition is used to extract coherent structures of the turbulent flow under the considered thermal stratification regimes. The flow structure is discussed in the context of three-dimensional representations of key modes, which demonstrate features ranging in size from the wind turbine wakes to the atmospheric boundary layer. Results demonstrate that structures related to the atmospheric boundary layer flow dominate over those introduced by the wind farm for the unstable and neutrally stratified regimes; large structures in atmospheric turbulence are beneficial for the wake recovery, and consequently the presence of the turbulent wind turbine wakes is diminished. Contrarily, the flow in the stably stratified case is fully dominated by the presence of the turbines and highly influenced by the Coriolis force. A comparative analysis of the test cases indicates that during the stable regime, higher-order modes contribute less to the overall character of the flow. Under neutral and unstable stratification, important turbulence dynamics are distributed over a larger range of basis functions. The influence of the wind turbines on the structure of the atmospheric boundary layer is mainly quantified via the turbulence kinetic energy of the first ten modes. Linking the new insights into structure of the wind turbine/atmospheric boundary layer and their interaction addressed here will benefit the formulation of new simplified models for commercial application.

scholarly journals Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Alejandro Marquez ◽  
Jairo José Espinosa Oviedo ◽  
Darci Odloak
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Linear Model ◽  
Predictive Control ◽  
Linear Time ◽  
Orthogonal Decomposition ◽  
Galerkin Projection ◽  
Operating Condition ◽  
Order Linear ◽  
Proper Orthogonal ◽  
Low Order

This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.

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