Comparison of strongly and weakly nonlinear flame models applied to thermoacoustic instability

2021 ◽  
Vol 33 (9) ◽  
pp. 094108
Author(s):  
Lijun Yang ◽  
Bosheng Pang ◽  
Jingxuan Li
Keyword(s):  
Weakly Nonlinear ◽  
Thermoacoustic Instability

Predicting Thermoacoustic Instability in an Industrial Gas Turbine Combustor: Combining a Low Order Network Model With Flame LES

2017 ◽  
Author(s):  
Y. Xia ◽  
A. S. Morgans ◽  
W. P. Jones ◽  
J. Rogerson ◽  
G. Bulat ◽  
...  
Keyword(s):  
Gas Turbine ◽  
Acoustic Waves ◽  
Gas Turbine Combustor ◽  
Network Modelling ◽  
Weakly Nonlinear ◽  
Thermoacoustic Instability ◽  
Reduced Chemistry ◽  
Flame Describing Function ◽  
Industrial Gas Turbine ◽  
Low Order

The thermoacoustic modes of a full scale industrial gas turbine combustor have been predicted numerically. The predictive approach combines low order network modelling of the acoustic waves in a simplified geometry, with a weakly nonlinear flame describing function, obtained from incompressible large eddy simulations of the flame region under upstream forced velocity perturbations, incorporating reduced chemistry mechanisms. Two incompressible solvers, each employing different numbers of reduced chemistry mechanism steps, are used to simulate the turbulent reacting flowfield to predict the flame describing functions. The predictions differ slightly between reduced chemistry approximations, indicating the need for more involved chemistry. These are then incorporated into a low order thermoacoustic solver to predict thermoacoustic modes. For the combustor operating at two different pressures, most thermoacoustic modes are predicted to be stable, in agreement with the experiments. The predicted modal frequencies are in good agreement with the measurements, although some mismatches in the predicted modal growth rates and hence modal stabilities are observed. Overall, these findings lend confidence in this coupled approach for real industrial gas turbine combustors.

Investigating Dynamics of One Weakly Nonlinear System with Delay Argument

2018 ◽  
Vol 50 (1) ◽  
pp. 20-38 ◽  
Author(s):  
Denis Ya. Khusainov ◽  
Jozef Diblik ◽  
Jaromir Bashtinec ◽  
Andrey V. Shatyrko
Keyword(s):  
Nonlinear System ◽  
Weakly Nonlinear ◽  
Delay Argument ◽  
System With Delay ◽  
Weakly Nonlinear System

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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