Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

Fractal Characteristics of Combustion Noise

[+] Author and Article Information
Aditya Saurabh

Chair of Fluid Dynamics,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: aditya.saurabh@outlook.de

Hassan Imran

School of Mechanical, Aerospace
and Civil Engineering,
University of Manchester,
Manchester M13 9PL, UK

Holger Nawroth

Chair of Fluid Dynamics,
Technische Universität Berlin,
Berlin 10623, Germany

Christian Oliver Paschereit

Chair of Fluid Dynamics,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: oliver.paschereit@tu-berlin.de

Lipika Kabiraj

Fluid Dynamics,
Technische Universität Berlin,
Berlin 10623, Germany
e-mail: lipika.kabiraj@iitrpr.ac.in

1Corresponding author.

2Present address: Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, India

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received September 5, 2017; final manuscript received October 19, 2017; published online August 30, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(12), 121507 (Aug 30, 2018) (7 pages) Paper No: GTP-17-1494; doi: 10.1115/1.4038766 History: Received September 05, 2017; Revised October 19, 2017

Fractal analysis is undertaken to characterize flame surface fluctuations on an unconfined turbulent premixed flame and the resulting far-field acoustics fluctuations. Results indicate that combustion noise is monofractal and is characterized by an anticorrelated structure with a Hurst exponent less than 0.5. The anticorrelated nature was identified in the pressure fluctuations as well as flame surface fluctuations for small time-scales. Additionally, results suggest that flame surface fluctuations are multifractal for large time scales. The calculated Hurst exponent increases noticeably with the equivalence ratio and decreases slightly with Reynolds number for the investigated operating conditions. Variation in the Hurst exponent for combustion noise data is compared with a case study of synthetic fluctuations comprised of linear combinations of white and 1/f2 noise. These results provide a more detailed characterization of the temporal structure of flame surface fluctuations and resulting noise emission from turbulent premixed flames than is presently known.

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Grahic Jump Location
Fig. 1

MFDFA results showing q-order rms fluctuations, Fq, against scale, w, on a double-log scale for the case of monofractal (left) and multifractal (right) time series. Values of q range from −4 till 4 with positive q denoted by red markers and negative q by blue markers (color online). The slope of linear fits to the fluctuations equate to the q-order hurst exponents, and are q-dependent for the multifractal case where the slopes decrease with increasing q values.

Grahic Jump Location
Fig. 2

(a) Three-dimensional cad model of the test rig under investigation, (b) section view of the burner exit indicating the fuel arrangement of the pilot flames, (c) instantaneous OH* chemiluminescence image of the turbulent flame (Re = 1.5 × 104, ϕ = 0.9), and (d) the pressure microphone is located in the plane of the burner exit, 30 burner diameters in the radial direction

Grahic Jump Location
Fig. 3

Pressure time trace spectra for combinations of Reynolds numbers, isothermal cases (ϕ = 0) and equivalence ratios, indicated in the legend as Re, ϕ pairs. The dashed line indicates the power-law decay of the spectra (Re = 1.5 × 104, ϕ = 0.9) and has a slope of 1.94 (color online).

Grahic Jump Location
Fig. 4

Detrended fluctuation analysis for combustion noise: fluctuation curves for different combinations of Reynolds numbers and equivalence ratios. Approximate crossover scales are marked by vertical gray lines in (a). The slopes significantly change with variation in equivalence ratios, while the effect of Reynolds number variation is not significant. The y-axis is scaled by w0.5. Thus, the Hurst exponent for scales below the crossover scale is 0.5.

Grahic Jump Location
Fig. 5

Fluctuation curves for varying values of q (positive:red, negative:blue, and zero:black; color online) for ϕ = 0.7 and varying Reynolds numbers. As the slope of the curves does not change with q, the pressure time series is not multifractal in nature.

Grahic Jump Location
Fig. 6

Fluctuation curves for varying values of q (positive:red, negative:blue, and zero:black; color online) for Re = 15000 and varying equivalence ratios. As the slope of the curves does not change with q, the pressure time series is not multifractal in nature.

Grahic Jump Location
Fig. 7

Time series (left) and fluctuations curves (middle, right), for varying values of Q (positive:red, negative:blue, and zero:black; color online) for Re = 15,000 and ϕ = 0.7, 0.9. Bold, black lines denote slopes for q = 2 and the dashed gray lines plotted for scales larger than 27 datapoints are slopes for various q values. The spread in the dashed lines suggests the presence of multifractality.

Grahic Jump Location
Fig. 8

Fluctuation curves, Fw, for synthetic data generated by combinations of white noise, ξ0.5 and f–2 noise, ξ2. Increasing the relative contribution of the long-range correlated f–2 noise gradually increases the slope of the fluctuation curves. The crossover from 0.5 occurs at successively lower scales as f–2 is increased.



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