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Direct simulation of thermoacoustic instability in gas generators using “CABARET” scheme
N. A. Afanasievab, V. M. Golovizninab, V. N. Semenovc, A. M. Sipatovd, S. S. Nesterovd a Keldysh Institute of Applied Mathematics RAS
b Lomonosov Moscow State University
c IBRAE RAS
d UEC-Aviadvigatel, Perm
Abstract:
It is shown that it is possible to use the non-dissipative CABARET scheme to find the
conditions for the occurrence of thermoacoustic instability (vibrational combustion) in
the combustion chambers of gas turbine engines. The propagation of long waves in the
gas-dynamic channel is described quite accurately by a system of quasilinear equations
of gas dynamics, averaged over the cross section. Numerical modeling of the dynamics
of acoustic disturbances and their interaction with the combustion zone (in the presence
of feedbacks) using non-dissipative difference schemes (direct modeling) is a real alternative to the so-called low-order network models that replace the acoustic channel (by
analogy with AC power grids) with a sequence of four-port or six-port networks. The advantages of direct modeling include the simple accounting for geometric factors, nonlinear effects, and the possibility of using more realistic combustion models.
As an example of using the direct method, a model problem of the excitation of sound
vibrations in a tube in the presence of heat sources (Rijke tube) is solved. The results
demonstrated the high accuracy of the method in determining the growth rate of unstable
modes, comparable to the accuracy of the results obtained using low-order network models.
Keywords:
thermal acoustics, vibration combustion, balance-characteristic methods,
CABARET scheme, Rijke tube.
Received: 17.09.2020 Revised: 17.09.2020 Accepted: 30.11.2020
Citation:
N. A. Afanasiev, V. M. Goloviznin, V. N. Semenov, A. M. Sipatov, S. S. Nesterov, “Direct simulation of thermoacoustic instability in gas generators using “CABARET” scheme”, Matem. Mod., 33:2 (2021), 3–19; Math. Models Comput. Simul., 13:5 (2021), 820–830
Linking options:
https://www.mathnet.ru/eng/mm4258 https://www.mathnet.ru/eng/mm/v33/i2/p3
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