Computation of Acoustic Transfer Matrices of Swirl Burner with Finite Element and Acoustic Network Method

Abstract

For a gas turbine combustor, an accurate transfer matrix of the burner is an essential prerequisite for stability analysis of combustion instability. This paper describes two numerical methods for the computation of burner transfer matrix (BTM) derived from the experimental method and an experimental validation. In the numerical study, Helmholtz equation with the boundaries of plane wave radiation is solved by employing a finite element code. As alternative to the finite element method (FEM), the BTM is also assessed through using acoustic network method (ANM). In the experimental study, complex acoustic pressure at the combustion chamber firstly can be evaluated based on multi-microphone method (MMM) from three measurement points in the plenum and BTM calculated by the FEM or ANM, then be compared with the measurement for the BTM validation at resonance frequency self-excited by the combustion instability of the combustor consisting of a supply plenum, a premixed swirlstabilized burner and a combustor chamber. The validation shows that the three calculated values are essentially the same as the experimental data, when resonance frequency approximately equal to194, 243 and 290Hz. The results indicate that acoustic behavior of the complex swirl burner can be evaluated successfully by mapping the burner to a network consisting of simple elements.

Numerical optimization of straight multi-array side-branched mufflers using differential evolution method

“…With this, the STL of muffler discussed in 2000 Hz is almost within the cutoff frequency. 33,34 Moreover, based on equation (4), the back pressures with respect to mufflers A-H constrained with 0.5 m in length is 0.000003 Pa. Therefore, the backpressure is small enough and can be neglected.…”

Numerical assessment of two-chamber mufflers hybridized with multiple parallel perforated plug tubes using simulated annealing method

“…The acoustical four-pole matrix between nodes 1-2, nodes 2-3, nodes 3-4, nodes 8-9, nodes 9-10, and nodes 10-11 is the same as equations (1)-(3) and equations (9)- (11). As derived in Appendix 4, for a two chambers muffler connected with four parallel perforated plug tubes, the four-pole matrices between nodes 5 (1) -7 (1) , 5 (2) -7 (2) , 5 (3) -7 (3) , and 5 (4) -7 (4) nodes can be combined to an equivalent matrix…”

“…Therefore, to analyze the sound transmission loss ( STL ) of two-chamber mufflers equipped with multiple parallel perforated plug tubes that are optimally designed to perform within a limited space, three kinds of two-chamber mufflers linked together by multiple perforated plug tubes (muffler A: a two-chamber muffler internally equipped with one perforated plug tube; muffler B: a two-chamber muffler internally equipped with two perforated and parallel plug tubes; muffler C: a two-chamber muffler internally equipped with four perforated and parallel plug tubes) are introduced. Because the geometric shapes of mufflers A–C are complicated, the numerical method such as the finite element method 10,11 will be predictably time-consuming when doing a broadband noise reduction assessment. In order to quickly and efficiently approach best design values, the numerical decoupling methods used in forming a four-pole matrix are in line with the simulated annealing method and presented in the article.…”

Sound field study of a building near a roadway via the boundary element method

“…1,2 Nowadays, scholars have proposed numerous methods to calculate the acoustic attenuation, which include the experimental modeling method, 3,4 the geometrical acoustics method, 5,6 and the numerical simulation method. [7][8][9] The experimental modeling method produces scene-adaptive models that generate results that more closely approximate the real sound pressure level (SPL). However, the method is limited in use as it requires substantial equipment and manpower.…”