Extraction of low-order non-linear inductor models from a high-order physics-based representation

2006 ◽  
Vol 21 (3) ◽  
pp. 813-817 ◽  
Author(s):  
L. Qu ◽  
P.L. Chapman
Keyword(s):  
High Order ◽  
Non Linear ◽  
Low Order

Reduced Order Modeling of Aeroacoustic Systems for Stability Analyses of Thermoacoustically Non-Compact Gas Turbine Combustors

2015 ◽  
Author(s):  
Tobias Hummel ◽  
Constanze Temmler ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Gas Turbine ◽  
Time Domain ◽  
Order Reduction ◽  
High Order ◽  
Essential Information ◽  
Reduced Order ◽  
Stability Analyses ◽  
Modal Reduction ◽  
Non Linear ◽  
Low Order

A methodology is presented to model non-compact thermoacoustic phenomena using Reduced Order Models (ROM) based on the Linearized Navier-Stokes Equations (LNSE). The method is applicable to geometries with a complex flow field as in a gas turbine combustion chamber. The LNSE, and thus the resulting ROM, include coupling effects between acoustics and mean fluid flow, and are hence capable of describing propagation and (e.g. vortical) damping of the acoustic fluctuations within the considered volume. Such a ROM then constitutes the main building block for a novel thermoacoustic stability analysis method via a low-order hybrid approach. This method presents an expansion to state-of-the-art low-order stability tools, and is conceptually based on three core features: Firstly, the multi-dimensional and volumetric nature of the ROM establishes access to account spatial variability and non-compact effects on heat release fluctuations. As a result, it is particularly useful for high frequency phenomena such as screech. Secondly, the LNSE basis grants the ROM the capability to reconstruct complex acoustic performances physically accurate. Thirdly, the formulation of the ROM in state-space allows convenient access to the frequency and time domain. In the time domain, non-linear saturation mechanisms can be included, which reproduce the non-linear stochastic limit cycle behavior of thermoacoustic oscillations. In order to demonstrate and verify the ROM’s underlying methodology, a test case using an orifice-tube geometry as the acoustic volume is performed. The generation of the ROM of the orifice-tube is conducted in a two-step procedure. As the first step, the geometrical domain is aeroacoustically characterized through the LNSE in frequency domain, and discretized via the Finite Element Method (FEM). The second step concerns the actual derivation of the ROM. The high-order dynamical system from the LNSE discretization is subjected to a modal reduction as order reduction technique. Mathematically, this modal reduction is the projection of the high-order (N ∼200,000) system into its truncated left eigenspace. An order reduction of several magnitudes (ROM order: Nr ∼100) is achieved. The resulting ROM contains all essential information about propagation and damping of the acoustic variables, and efficiently reproduces the aeroacoustic performance of the orifice-tube. Validation is achieved by comparing ROM results against numerical and experimental benchmarks from LNSE-FEM simulations and test rig measurements, respectively. Excellent agreement is found, which grants the ROM modeling approach full eligibility for further usage in the context of thermoacoustic stability modeling. This work is concluded by a methodological demonstration of performing stability analyses of non-compact thermoacoustic systems using the herein presented ROMs.

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

Polynomial Moving Fitting Method for Edge Identification

2011 ◽  
Vol 308-310 ◽  
pp. 2560-2564 ◽  
Author(s):  
Xiang Rong Yuan
Keyword(s):  
Edge Detection ◽  
Curve Fitting ◽  
Polynomial Function ◽  
High Order ◽  
Polynomial Fitting ◽  
Fitting Method ◽  
Order Polynomial ◽  
Better Than ◽  
Low Order

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

High-Order Non-Linear Optical Effects in Organic Luminogens with Aggregation-Induced Emission

2015 ◽  
Vol 27 (14) ◽  
pp. 2332-2339 ◽  
Author(s):  
Jun Qian ◽  
Zhenfeng Zhu ◽  
Anjun Qin ◽  
Wei Qin ◽  
Liliang Chu ◽  
...  
Keyword(s):  
High Order ◽  
Aggregation Induced Emission ◽  
Optical Effects ◽  
Non Linear ◽  
Linear Optical
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