scholarly journals A Low Order Model of SCR-in-DPF Systems with Proper Orthogonal Decomposition

2018 ◽  
Author(s):  
Seun Olowojebutu ◽  
Thomas Steffen
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Order Model ◽  
Proper Orthogonal ◽  
Low Order

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

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.

Reduced-Order Model of Unsteady Flows in a Turbomachinery Fan Modeled Using a Novel Proper Orthogonal Decomposition

2019 ◽  
Author(s):  
Elizabeth H. Krath ◽  
Forrest L. Carpenter ◽  
Paul G. A. Cizmas ◽  
David A. Johnston
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Reference Conditions ◽  
Stable Solution ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Model Rotor

Abstract This paper presents a novel, more efficient reduced-order model based on the proper orthogonal decomposition (POD) for the prediction of flows in turbomachinery. To further reduce the computational time, the governing equations were written as a function of specific volume instead of density. This allowed for the pre-computation of the coefficients of the system of ordinary differential equations that describe the reduced-order model. A penalty method was developed to implement time-dependent boundary conditions and achieve a stable solution for the reduced-order model. Rotor 67 was used as a validation case for the reduced-order model, which was tested for both on- and off-reference conditions. This reduced-order model was shown to be more than 10,000 times faster than the full-order model.

scholarly journals Reduced order model of offshore wind turbine wake by proper orthogonal decomposition

2020 ◽  
Vol 82 ◽  
pp. 108554 ◽  
Author(s):  
M. Salman Siddiqui ◽  
Sidra Tul Muntaha Latif ◽  
Muhammad Saeed ◽  
Muhammad Rahman ◽  
Abdul Waheed Badar ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Turbine Wake

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

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