Subscriber access provided by READING UNIV
Combustion
Comprehensive combustion stability analysis using dynamic mode decomposition Rajavasanth Rajasegar, Jeongan Choi, Brendan Joseph McGann, Anna Oldani, Tonghun Lee, Stephen D Hammack, Campbell D Carter, and Jihyung Yoo Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02433 • Publication Date (Web): 27 Aug 2018 Downloaded from http://pubs.acs.org on September 1, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
Comprehensive combustion stability analysis using dynamic mode decomposition Rajavasanth Rajasegar, Jeongan Choi, Brendan McGann, Anna Oldani, Tonghun Lee University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA Stephen D. Hammack, Campbell D. Carter U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, USA Jihyung Yoo+ Hanyang University, Seoul 04763, South Korea
Abstract Combustion stability is an important consideration for many energy systems due to its impact on performance and efficiency. Flame dynamics that govern combustion stability are often complex and difficult to resolve, particularly from experimental data. However, recent advances in post-processing techniques, such as dynamic mode decomposition (DMD), have partially enabled flame dynamic analysis. This study aims to provide a comprehensive measure of combustion stability through a detailed investigation of coherent structures and their energy contents, frequencies, and growth factors from DMD. These results were then correlated to underlying physics and chemistry that drive flame dynamics. Three different datasets were analyzed in this study. Numerically-constructed images and OH-PLIF images of laminar flames were used to characterize stable flame dynamics. OH-PLIF images of acousticallyperturbed swirl-stabilized turbulent flames were used to characterize oscillatory and unstable flame dynamics. Acoustic perturbation at various frequencies and amplitudes were introduced using a speaker. Dominant spatial structures and their energy contents in the recirculation zone or shear layer were accurately resolved. Frequencies and growth factors provided good mode-specific stability assessment. Overall, the stability analysis is an effective technique for analyzing flame dynamics and developing more stable combustion systems despite complex interaction between acoustics, fluid mechanics and combustion.
Keywords Combustion instability, Swirl stabilization, Dynamic Mode Decomposition, High-speed OH-PLIF, Acoustic perturbation
+
Corresponding author:
[email protected] ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 13
1. Introduction Advanced combustion systems designed to operate under lean, premixed conditions have great potential to substantially curtail emission and satisfy regulatory requirements [1]. Such systems, however, are more susceptible to combustion instability, which in turn can negatively impact performance and durability. Understanding and maximizing combustion stability while mitigating onset and propagation of combustion instability is therefore critical to the development of clean efficient combustion systems [2]. Nonlinear combustion instability models [3-5] or combustion model [6] coupled with global stability analysis techniques [7, 8], readily provide exact flame dynamic characteristics that can be used to study the onset and propagation of combustion instability. It is in this effort that the progressing capabilities of laser diagnostics open new possibilities of understanding the chemistry and fluid dynamics of complex reacting flows. Employing laser-based imaging techniques to extract detailed information from flames has become a common practice amongst the experimental combustion community [9]. In the last decade, new high-speed diagnostics have developed rapidly, using faster camera systems and high repetition rate lasers. Planar laser-induced fluorescence (PLIF) provides valuable flow visualization and quantitative population measurements, but the technique has been limited in speed (i.e., framing rate) by both camera and laser capabilities, long inadequate for temporally correlated sequences. However, the recent advent of high-speed diagnostic equipment, including kHz-rate CMOS cameras, image intensifiers and high-speed tunable dye lasers, has enabled signal collection at framing rates sufficient to observe transient features of reacting flows. However, the extraction of flame dynamics from temporally resolved experimental datasets [10-12] is not trivial as model equations such as linearized Navier-Stokes equation are not readily available. Rather, post-processing techniques [13, 14] are used to extract pertinent dynamics from the data, which in many cases are a series of images. A common approach for extracting spatial structures (modes) is proper orthogonal decomposition (POD) [15]. The POD algorithm ranks mutually orthogonal spatial modes by their energy content. However, this technique is ill-suited for combustion instability analysis for two reasons. First, energy content may not be the only appropriate measure of ranking contribution of each mode to the overall combustion instability mechanism. Second, temporal dynamics cannot be resolved since mutually orthogonal spatial modes are spectrally contaminated. A technique for analyzing coherent structures and their frequency response is through dynamic mode decomposition [16]. Successful DMD analysis is predicated on the proper selection of ∆t (time between images) and the number of images in the sequence. The former determines the range of frequencies that can be extracted while the latter determines the accuracy of the eigenvalue approximation. Furthermore, DMD can also perform subdomain and spatial stability analysis. The former is possible since DMD does not rely on system matrix A nor boundary conditions. The latter is made possible by mapping temporal domain to spatial domain [14, 16] for analyzing spatially evolving dynamics. DMD in combustion science is a burgeoning area and its applications are quickly growing [17-23]. However, further investigations are required to fully understand the significance of coherent structures and their Ritz values, growth factors, ACS Paragon Plus Environment
Page 3 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
and energy contents driving combustion dynamics on flame stability. This study presents comprehensive analysis of DMD results on combustion stability. Three cases (one synthetic and two experimental) are processed and their results are correlated to pertinent flame dynamics. 2. Experimental Setup 2.1 Swirl Burner The assembled radial swirl burner is shown in Figure 1. The swirler, located at the burner surface, is also shown in the figure. The latter consists of eight curved vanes, at a 60⁰ vane angle, equally distributed around the circumference of a 70mm diameter cylindrical hub. The vanes are 12mm thick, and the inlet passage is 25mm deep axially. The geometric swirl number [24] is estimated to be 1.15. A 12mm diameter, 45° conical bluff-body in centrally integrated in the swirler to enhance the swirling motion and flame stabilization. The upstream face of the radial swirler is mounted onto a 100mm diameter, 75mm long plenum chamber fitted with flow straighteners on the upstream end. The downstream end of the swirler is fitted with a quartz glass tube, 100mm long with a 100x100mm square cross-section, to provide complete optical access and to mimic realistic combustion geometries. It also serves to maintain the swirling motion inside the combustor and to prevent the entrainment of outside air. An 20cm subwoofer (Dayton Audio) was attached upstream of the plenum to acoustically excite the flow. The frequency and amplitude (sound pressure level) of the acoustic perturbations were controlled by a waveform generator (Agilent) and a 1400W power amplifier (Pyle Pro), respectively. The amplitude of the waveform generator output was fixed to be 500mV peak to peak, while the forcing frequency (single component sinusoidal variation) was varied between 0 and 370Hz. The premixed reactants, air and fuel (methane) flow rates were metered individually using two laminar flow, differential pressure, MKS mass flow controllers and fed to the combustor at ambient conditions (298K, 1.01bar).
Figure 1. Schematic layout of the radial swirl burner along with the housing and acoustic forcing setup. 2.2 Laser Diagnostics Setup The OH-PLIF setup, uses a DPSS Nd:YAG laser (EdgeWave Innoslab IS12II-E), with a maximum output power of 60W, at 532nm. The beam is used to pump a tunable dye laser (Sirah CREDO) containing DCM ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 13
dye dissolved in ethanol. The red dye laser beam is frequency doubled with an integral β-barium-borate doubling crystal, and the output pulse energy is roughly 0.2mJ/pulse. The dye laser is tuned to the Q1(12) transition of the OH A2Σ+ - X2Π (0,0) band at 310.60nm in air. Timing of the 100ns intensifier gate for fluorescence collection was aided by using a fast photodiode and oscilloscope to observe a (low energy) sampling of the laser pulse. The UV laser beam is converted into a sheet of thickness ~120µm (FWHM) in the probe region using a -25mm plano-concave cylindrical lens and a 750mm spherical plano-convex lens. Fluorescence was isolated from background scattering (at 310.6nm) and visible flame emission using two custom long-wave-pass filters (Semrock AFRL-0002) and a Schott UG-5 filter. A 100mm f/2.8 UV lens (Sodern Cerco) focuses the fluorescence signal onto a two-stage image-intensifier (Lambert HICATT) attached to a Photron SA-Z CMOS camera. The schematic layout of the laser diagnostics setup is shown in Figure 2.
Figure 2. Schematic layout of the laser diagnostics setup. 3. Results and Discussion 3.1 DMD Overview Coherent structures and their frequency response are analyzed through dynamic mode decomposition by constructing a lower-dimension companion matrix from a series of images which form a Krylov sequence under linear-tangent approximation. The eigenvalues and eigenvectors of this newly constructed matrix approximate those of a nonlinear higher dimension system matrix governing the combustion phenomena [25]. A detailed and rigorous mathematical description can be found in in [14, 16] and only a brief description will be given here. Letting ν represent data from a single experimental image, an image sequence can be defined as a Krylov sequence, V1N = {ν 1 , ν 2 ,....., ν N } [26] under linear-tangent approximation. For sufficiently large sequence, the images become linearly dependent, leading to the following formulation:
ACS Paragon Plus Environment
Page 5 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
A{ν 1 , ν 2 ,....., ν N−1} = {ν 2 , ν3 ,....., V1N-1s} + reTN-1
(1)
where s is the last column of the companion matrix A and r is the residual vector. Solving for the leastsquare solution of A, its eigenvalues (empirical Ritz values) and eigenvectors are then used to approximate coherent structures of the given reactive flow field. 3.1 DMD Validation An image (q) of synthetic numeric functions is constructed to validate the DMD results [27]. The image superimposes a stationary field (q0) and three dominant dynamic structures (q1, q2, q3) with varying characteristic temporal and spatial frequencies. q = q0 + q1 + q2 + q3
(2)
y q 0 (x, y, t) = exp − 0.7 2
(3)
x − − t + y2 m =− n n q n (x, y, t) = n (t) (−1) m exp − dn m =− 2
fn =
(4)
n 2n
(5)
Here, dn = anx+bn is the diameter of the structure, an and bn are constants, βn is the wavelength factor defined as the distance between two neighboring structures, γn is the convection velocity of the structure in the streamwise direction and αn(t) is the growth or decay factor. The dominant frequencies fn for q1, q2 and q3 are 0.5 Hz, 1.64 Hz and 4.0 Hz, respectively. Coefficient αn(t) determines variation in the convecting structures. αn(t) = 1 indicates a constant structure (q0 and q1 - no growth or decay), αn(t) < 1 and αn(t) >1 correspond to decaying (q2) and growing (q3) structures, respectively. The parameters for each function are listed in Table 1. Parameters for the numerical image. The long-term behavior of q2 and q3 reach an asymptotically stable limit despite non-zero growth factors. Hence, stability analysis based on growth factors must be taken within the context of measurement duration and not for the lifetime of the system. n
an
bn
βn
γn
f (Hz)
αn(t)
1
0.0300
0.050
0.80
0.8
0.50
1
2
0.0150
0.035
0.55
1.8
1.64
e-t/30 - 0.1
3
0.0075
0.020
0.30
2.4
4.00
1 - e-t/20 + 0.2
Table 1. Parameters for the numerical image.
ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 6 of 13
Figure 3. DMD algorithm validation using a series of numerical images. 2000 superimposed images (q) were generated at every 10ms intervals for analysis. Left panel of Figure 3 show instances of the stationary field (q0), the three different structures (q1 through q3) and the combined structure image (q). The remaining panels in Figure 3 show DMD results of the synthesized dataset. The center panel show images constructed with real parts of the first four (q0 through q3) temporal DMD modes or spatial patterns. Corresponding image constructed with imaginary part is phase-shifted by 90⁰. Extracted DMD modes are in excellent agreement with the numeric images. The right panel show Ritz values (λj) of the first four spatial patterns. Markers accurately identified the frequencies of the first four modes (0, 0.5, 1.64, and 2Hz). The corresponding growth factors (x-axis) that only reflect temporal dynamics for the duration of the dataset (20 seconds for this analysis) are also accurately identified (zero, zero, negative, positive). Results show that a positive growth factor does not necessarily indicate the onset or propagation of instability. Unlike POD, which carries out eigenvalue decomposition to produce a hierarchy of coherent structures based on the time-averaged spatial correlation tensor, DMD extract dominant features (DMD modes) while enforcing both temporal orthogonality and spatial orthogonality [14, 16]. It should be mentioned that the dynamic mode decomposition is a robust tool to identify prevalent frequencies and coherent structures, even in the presence of experimental uncertainties, measurement errors or environmental noise [14]. To substantiate this, gaussian white noise (Signal to Noise Ratio, SNR ranging from 30 to 10) and 2-D gaussian smoothing kernel (Standard deviation ranging from 1 to 10) was applied to the image (q). A typical intensified image corresponds to SNR of 20 and 2-D gaussian smoothing kernel of 3.2. This simulated the experimental noise and the blur effect caused by the image intensifier used in the experimental setup. However, no significant changes were observed in the DMD spectrum as a result. 3.2 Steady Laminar Flame Initial DMD analysis of an actual flame was conducted using OH-PLIF images of a stable methane-air laminar premixed flame (Re = 645, ϕ = 1.2). The algorithm processed 200 images taken at 60Hz and produced results as shown in Figure 4. DMD spectrum (top panel) provides a typical outcome expected for a steady flame. All but one mode has negative growth factors indicating damped response. The steady ACS Paragon Plus Environment
Page 7 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
state (0Hz, denoted as A) growth factor is positive, but is extremely close to zero and can therefore be considered stable. Its coherent structure (shown in the bottom left panel of Figure 4) represents the time averaged flame position. In addition, a group of modes clustered near 18Hz is partly due to the characteristic frequency of the burner (jet velocity: 0.4 m/s, burner exit diameter: 23 mm). The marker size is proportional to a measure of coherence for each mode (energy content of each spatial mode) and help rank the relevant structures ahead of noise-contaminated ones. Furthermore, eigenvalues Eigenvalues λj of the companion matrix S can be mapped onto a unit circle in the complex plane (as shown in the bottom right panel of Figure 4). These results demonstrate that OH-PLIF images can reliably be used to deduce dominant coherent structures from reactive flow fields.
Figure 4. DMD analysis of a steady laminar flame. 3.3 Swirl Burner DMD analyses of the swirl stabilized burner were then performed using OH-PLIF images taken at 10kHz under various operating conditions. Lean flame measurements (ϕ = 0.97) exhibited discernable oscillations but maintained attachment (no blowoffs or flashbacks) at all tested experimental conditions. The speaker in the burner assembly was driven at multiple frequencies up to 370Hz and amplitudes to observe the effects of acoustic forcing on flame stability and oscillation. The 10kHz OH-PLIF images allow for reliable DMD analysis of frequencies up to 5kHz (Nyquist criterion), which is more than enough to determine the effects of acoustic perturbation in this study. First, high-speed OH-PLIF images without acoustic perturbation is shown in the top row of Figure 5. Images show very stable flame characteristics, particularly at the recirculation zone (flame anchoring point) near the burner surface and small oscillations in the shear layer. The same flame with acoustic perturbation at 50Hz is shown in the bottom row of Figure 5. Strong oscillatory behavior near the recirculation zone and the shear layer [28] is observed at the resonant frequency. DMD analysis should
ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 8 of 13
not only provide similar findings, but also quantify these dynamics to serve as an effective combustion instability analysis technique.
Figure 5. OH-PLIF images on unperturbed (top) and acoustically-perturbed flame (bottom). 3.3.1 Unperturbed Flame DMD results for the unperturbed flame is shown in Figure 6. All 2000 images were analyzed, but only the nine most relevant modes are shown in the DMD spectrum (top panel). As expected, the mode with the highest energy content and the most stable growth factor (closest to 0) is located at the mean frequency (0 Hz, denoted by A in the figure). Its spatial structure, much like that of laminar flame, represents time-averaged flame position. Small oscillation in the shear layer, as observed in the bottom row of Figure 5, is mostly due to a pair of complex conjugate modes (denoted by B in the figure) near 110Hz. Its spatial structures are concentrated in the outer shear layer further downstream of the recirculation zone. The weaker growth factor and lower energy content of mode B results in a minor contribution to the overall flame stability. A second mode at the same frequency produces similar spatial structures, but provides an even smaller contribution. Modes with very large negative growth factors and small energy content may have negligible contribution, but the all map onto or very close to the unit circle (as shown in the bottom left panel of Figure 6), much like the case of laminar flame.
Figure 6. DMD analysis of an unperturbed swirl-stabilized flame.
ACS Paragon Plus Environment
Page 9 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
3.3.1 Acoustically Perturbed Flame Various acoustic perturbation conditions were applied to the swirl-stabilized burner. An instance of acoustic perturbation frequency (210Hz) and high amplitude is shown in Figure 7. DMD spectrum (top panel) indicates that the three relevant modes (mean, resonant frequency, and its first harmonic) all have positive growth factors. The time-averaged spatial structure (Mode A, bottom row in Figure 7) is spread outwards due to the extremely oscillatory behavior of the flame. Also, coherent structures at 210 and 420Hz are all concentrated in the recirculation zone thereby promoting oscillatory behavior.
Figure 7. DMD analysis of an acoustically perturbed flame at 210Hz, +8dB A comparison of DMD spectra at 210Hz for various forcing amplitudes is shown in Figure 8. Results show that at lower amplitude (+4dB), the coherent structures at the resonant frequency and its harmonics have negative growth factors leading to a stable flame with relatively small oscillations. The negative growth factor of the first harmonic at the lowest perturbation amplitude was much too small and could not be shown in the figure. As perturbation amplitude increases, modes quickly cross into positive growth factors leading to a highly oscillatory flame behavior. The onset of combustion instability occurs at just above +9 dB, at which point the flame is no longer controllable and flashes back violently. Interestingly, the frequency response of some non-resonant modes is blue-shifted possibly to accommodate increased energy transfers from the highly excited modes.
ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 10 of 13
Figure 8. DMD spectra of acoustically perturbed flames at 210Hz and various amplitude. The modes corresponding to various perturbation frequencies at different amplitudes is shown in Figure 9. The flame transfer function (FTF) gain for a swirl flame is non-linear [29, 30] and is characterized by a periodic occurrence of local minima and maxima [31-33] which is captured well through DMD analysis. At the lowest perturbation frequency (50Hz, first row in Figure 9), the coherent structure at the resonant frequency is very similar to mode B of an unperturbed flame shown in Figure 6, which represents oscillation in the shear layer further downstream of the recirculation zone (acoustic disturbance). This would correspond to the minimum/decreasing FTF gain portion of the cycle. For perturbation frequencies of 160 and 210Hz (second and third row, respectively, in Figure 9) the dynamic modes reveal coherent structures (vortical disturbances) in the recirculation zone (flame anchoring point), which contributes to flame oscillations (flame acts as amplifier). This would correspond to the maximum/increasing FTF gain portion of the cycle. The cyclic behavior is clearly in agreement with dynamic modes at the highest frequency (370Hz), where acoustic forcing is again shifted downstream from the recirculation zone and into the shear layer (fourth row in Figure 9).
ACS Paragon Plus Environment
Page 11 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
Figure 9. DMD modes at resonant frequency under various perturbation conditions. 4. Conclusions DMD is a power analysis technique that can extract coherent structures from experimental datasets in the absence of an underlying model. Numerically-constructed images and laminar flame OH-PLIF images served to validate DMD analysis and its application on combustion phenomenon, respectively. Based on these validations, DMD analyses using high-speed OH-PLIF images of acoustically-perturbed swirl-stabilized flames were successfully carried out. DMD analyses accurately resolved dominant spatial structures present in the recirculation zone or shear layer along with their corresponding growth rates and energy contents at various perturbation frequencies and amplitudes. DMD spectra accurately depicted the stable nature of certain highly-excited swirl-stabilized flames (370 Hz) by correlating the location of coherent spatial structures of the relevant dynamic modes in reference to the flame stabilization location which in turn was able to accurately describe its oscillatory behavior. The findings presented in this study enable a step forward for flame oscillation and combustion stability analysis. The key insight regarding the complex interaction between acoustics, fluid mechanics, and combustion is expected to serve a critical role in developing detailed combustion instability models.
ACS Paragon Plus Environment
Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 12 of 13
5. Acknowledgements The authors of this work would like to acknowledge the support of Office of Naval Research through ONR Grant #N00014-17-1-2538 with Dr. Steven Martens as program manager. 6. References [1] S.M. Correa, A Review of NOx Formation Under Gas-Turbine Combustion Conditions, Combustion Science and Technology 87 (1993) 329-362. [2] T. Lieuwen, H. Torres, C. Johnson, B.T. Zinn, A Mechanism of Combustion Instability in Lean Premixed Gas Turbine Combustors, Journal of Engineering for Gas Turbines and Power 123 (2000) 182-189. [3] N. Noiray, D. Durox, T. Schuller, S. Candel, A unified framework for nonlinear combustion instability analysis based on the flame describing function, Journal of Fluid Mechanics 615 (2008) 139-167. [4] V. Yang, S.I. Kim, F.E.C. Culick, Triggering of Longitudinal Pressure Oscillations in Combustion Chambers. I: Nonlinear Gasdynamics, Combustion Science and Technology 72 (1990) 183-214. [5] J.H. Cho, T. Lieuwen, Laminar premixed flame response to equivalence ratio oscillations, Combustion and Flame 140 (2005) 116-129. [6] B. Franzelli, E. Riber, L.Y.M. Gicquel, T. Poinsot, Large Eddy Simulation of combustion instabilities in a lean partially premixed swirled flame, Combustion and Flame 159 (2012) 621-637. [7] W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly of Applied Mathematics 9 (1951) 17-29. [8] W.S. Edwards, L.S. Tuckerman, R.A. Friesner, D.C. Sorensen, Krylov Methods for the Incompressible NavierStokes Equations, Journal of Computational Physics 110 (1994) 82-102. [9] M. Aldén, J. Bood, Z. Li, M. Richter, Visualization and understanding of combustion processes using spatially and temporally resolved laser diagnostic techniques, Proceedings of the Combustion Institute 33 (2011) 69-97. [10] W. Lang, T. Poinsot, S. Candel, Active control of combustion instability, Combustion and Flame 70 (1987) 281-289. [11] Y. Huang, V. Yang, Dynamics and stability of lean-premixed swirl-stabilized combustion, Progress in Energy and Combustion Science 35 (2009) 293-364. [12] J. O’Connor, T. Lieuwen, Recirculation zone dynamics of a transversely excited swirl flow and flame, Physics of Fluids 24 (2012) 075107. [13] J. O’Connor, Disturbance-Field Decomposition in a Transversely Forced Swirl Flow and Flame, Journal of Propulsion and Power 33 (2017) 764-775. [14] P.J. Schmid, L. Li, M.P. Juniper, O. Pust, Applications of the dynamic mode decomposition, Theoretical and Computational Fluid Dynamics 25 (2010) 249-259. [15] G Berkooz, a. P Holmes, J.L. Lumley, The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows, Annual Review of Fluid Mechanics 25 (1993) 539-575. [16] P.J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics 656 (2010) 5-28. [17] A. Renaud, S. Tachibana, S. Arase, T. Yokomori, Experimental Study of Thermo-Acoustic Instability Triggering in a Staged Liquid Fuel Combustor Using High-Speed OH-PLIF, ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, ASME, Charlotte, North Carolina, USA, 2017, pp. V04AT04A065.
ACS Paragon Plus Environment
Page 13 of 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Energy & Fuels
[18] G. Jourdain, L.-E. Eriksson, S.H. Kim, C.H. Sohn, Application of dynamic mode decomposition to acousticmodes identification and damping in a 3-dimensional chamber with baffled injectors, Journal of Sound and Vibration 332 (2013) 4308-4323. [19] A. Renaud, S. Ducruix, P. Scouflaire, L. Zimmer, Experimental Study of the Interactions Between Air Flow Rate Modulations and PVC in a Swirl-Stabilised Liquid Fuel Burner, ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, ASME, Montreal, Quebec, Canada, 2015, pp. V04AT04A063. [20] A. Ghani, T. Poinsot, L. Gicquel, G. Staffelbach, LES of longitudinal and transverse self-excited combustion instabilities in a bluff-body stabilized turbulent premixed flame, Combustion and Flame 162 (2015) 4075-4083. [21] E. Motheau, F. Nicoud, T. Poinsot, Mixed acoustic–entropy combustion instabilities in gas turbines, Journal of Fluid Mechanics 749 (2014) 542-576. [22] M. Roa, S.A. Schumaker, D.G. Talley, J. Bennewitz, A Study of Acoustic Forcing on Gas-Centered SwirlCoaxial Reacting Flows, 55th AIAA Aerospace Sciences Meeting, AIAA, Grapevine, Texas, 2017. [23] A. Johchi, L. Zimmer, M. Tanahashi. Investigation on the acoustic behavior of a turbulent swirlstabilized combustor fed with liquid fuel. In: editor^editors. 17th International Symposium on Applications of Laser Techniques to Fluid Mechanics; 2014; Lisbon, Portugal. p. [24] J.M. Beér, N.A. Chigier, Combustion aerodynamics, Applied Science Publishers Ltd, London, 1972. [25] K.K. Chen, J.H. Tu, C.W. Rowley, Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses, Journal of Nonlinear Science 22 (2012) 887-915. [26] A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, Nevada, USA. [27] Q. Zhang, Y. Liu, S. Wang, The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition, Journal of Fluids and Structures 49 (2014) 53-72. [28] J. O’Connor, Visualization of Shear Layer Dynamics in a Transversely Forced Flow and Flame, Journal of Propulsion and Power 31 (2015) 1127-1136. [29] C. Hirsch, D. Fanaca, P. Reddy, W. Polifke, T. Sattelmayer, Influence of the Swirler Design on the Flame Transfer Function of Premixed Flames, ASME Turbo Expo 2005: Power for Land, Sea, and Air2005, pp. 151-160. [30] W. Polifke, C. Lawn, On the low-frequency limit of flame transfer functions, Combustion and Flame 151 (2007) 437-451. [31] B. Jones, J.G. Lee, B.D. Quay, D.A. Santavicca, Flame Response Mechanisms Due to Velocity Perturbations in a Lean Premixed Gas Turbine Combustor, Journal of Engineering for Gas Turbines and Power 133 (2011) 021503. [32] K.T. Kim, D.A. Santavicca, Generalization of Turbulent Swirl Flame Transfer Functions in Gas Turbine Combustors, Combustion Science and Technology 185 (2013) 999-1015. [33] Preetham, H. Santosh, T. Lieuwen, Dynamics of Laminar Premixed Flames Forced by Harmonic Velocity Disturbances, Journal of Propulsion and Power 24 (2008) 1390-1402.
ACS Paragon Plus Environment
