Experimental Study on the Turbulent Premixed Flame Structural

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Experimental Study on the Turbulent Premixed Flame Structural Characteristics Based on the Wavelet Transform Yanhuan Jiang, Guoxiu Li, Hongmeng Li, Lei Li, and Fusheng Li Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b02792 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 8, 2017

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Experimental Study on the Turbulent Premixed Flame Structural Characteristics Based on the Wavelet Transform Yan-huan Jiang, Guo-xiu Li*, Hong-meng Li, Lei Li, Fu-Sheng Li School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, 100044, China Abstract: To investigate the effect of the flame inherent instabilities and turbulence on the flame structural characteristics, premixed combustion experiments of 50% H2 / 50% CO at equivalence ratio 0.6, were conducted in a turbulent combustion bomb in atmospheric temperature and pressure. The correlation degree was defined to study the correlation relation between flame structural characteristics at different moments; wavelet transform was used to investigate the detail components at different scales. The results indicate that with the development of the flame, the cellular structure was enhanced, the correlation degree gradually decreased. The fluctuations of the detail components at the larger scale were stronger and included more energy, which corresponded to the main factor causing the flame front complex. With the turbulence intensity increase, the rms amplitude and the energy of the detail components increased, leading to the increase of the interaction of different disturbances, while the correlation degree of flame decreased. The correlation degree of the detail components presented a staggered distribution of higher and lower values, which indicated the complex changes of the disturbances at different scales. KEYWORDS: syngas; turbulence; wavelet transform; correlation degree; detail component.

Corresponding author. Tel: + 86 010 51682047; Fax: +86 010 51682047; Email: [email protected] (G-x. LI)

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1. Introduction Energy constitutes the most significant parameter of the national economy and citizen's livelihood; the great changes in human society can be seen as the essence of energy changes [1-3]. Throughout the history of humanity, fossil fuels play an essential role. However, the reserves of fossil fuels are very limited and a series of environmental problems associated to the usage of fossil fuels, limit the living space of mankind in a great extend [4, 5]. Clean and alternative energy exploration has become a major issue in human development [6]. Syngas has attracted increased attention due its variety of preparation methods and has been widely used in the internal combustion engines and IGCC [7-8]. The diverse compositions of syngas, are significant for the study of the fundamental combustion characteristics of syngas. Laminar burning velocity is a critical parameter of syngas and air mixture, which depends on the reactant composition, pressure and temperature [9-13]. The measurement of laminar burning velocity of syngas/air mixtures under different conditions is important. Li et al. [14] studied the laminar burning velocity of H2/CO premixed flame under different hydrogen fraction (from 0% to 100%) by using an equivalence ratio ranging from 0.4 to 1.0 in a constant volume vessel. Considering that the dilution gas has greatly effect on the syngas laminar burning velocity, the laminar burning velocity of H2/CO/N2 and H2/CO/CO2 premixed flame has been systematically investigated at different hydrogen fraction [15, 16]. Askari et al. [17] investigated the laminar burning velocity of H2/CO/air at high temperature ranging from 298K to 617K and pressure up to 5.5 atm by using a novel multi-shell model. Furthermore, the effect of the synthetic exhaust gas recirculation (SRGR) and He on the laminar premixed velocity of H2/CO was studied at high temperature and pressure [18, 19]. It is remarkable that for the expanding flame the laminar burning velocity is calculated by the period of stable flame, that is the flame dates before forming cellular structure are selected. Diffusive-thermal and hydrodynamic instability constitute the two major factors, which lead to the flame front become unstable and the area of flame surface to increase. Li et al. [20] quantitatively studied the influence of pressure ranging from 0.5 to 4 bar and an equivalence ration on the flame intrinsic instabilities at the range of 0.3 to 1.0, by using the critical flame radius and critical Peclet number. It was demonstrated that an increase of initial pressure and hydrogen fraction leads to an enhancement in flame cellular instability. To investigate the correlation of flame


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intrinsic instability and the syngas burning speed, Askari et al. [21] defined the cellularity factor to quantitatively investigate the cell formation effects on the flame front area at engine-relevant conditions. By adopting the parameter, they proved that the initial thermodynamic parameters and the hydrogen fraction have a significant effect on the cellularity factor. Xie et al. [22] established the effect of cellular structure on the flame propagation speed, based on the parameter of acceleration exponent, indicating that the acceleration exponent is not identical to that of self-turbulent flame. Jiang et al. [23] extracted and analyzed the cells information in the cellular structure to explore the correlation between cellular structure and dynamic pressure in the limited space, proving that when the flame expands to a certain degree, the effect of pressure to the cellular structure is reduced. The fractural dimension is of great significance in the flame structure research and is widely used in the combustion model [24-26]. Moreover, Fast Fourier Transform (FFT) is also applied to investigate the effect of flame intrinsic instability on the disturbance evolution in the flame front in a microscope [27]. According to the above mentioned, there are many valuable conclusions on the flame propagation characteristics of syngas/air laminar premixed flame and the influence of flame inherent instabilities on the flame structural characteristics. These can provide a sufficient theoretical background for the study of turbulent premixed combustion characteristics and also provide an important parameter in further exploration of the turbulent combustion characteristics of syngas. Liu et al. [28] measured the turbulent burning velocity of 65% CO/ 35% H2 under the initial pressure at the range of 0.1 to 1.0 MPa. Shy et al. [29] reported the effect of turbulent Reynolds, Damkohler and Karlovits number on the turbulent burning velocities of syngas/air mixture. Although the above two scholars both introduced the structure evolution of the turbulent premixed flame of syngas, their researches focused on the turbulent burning velocity. Due to the important influence of the flame structure of turbulent premixed flame on the flame propagation velocity, the research on the structural characteristics of syngas is still needs further development. The structural characteristics of the flame influence significantly on the turbulent premixed flame the laminar one. For the expanding flame, flame inherent instabilities and turbulence act on the flame front subsequently, and eventually lead to the complexity of the flame structure. Li et al. [27] used the FFT method


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to analyze the contour of the flame, and obtained the microscopic information of the disturbance on the flame front. Nevertheless, the way that the fluctuations in the flame front will evolve under turbulence environment, has never been investigated by far. In addition, considering the inherent defects of the Fourier transformation, the position information of different disturbances cannot be obtained. The wavelet transform has a solid advantage in capturing the time-frequency characteristic of the signals and has been widely used in engine detonation process and cyclic variation [30-32]. In this paper, the flame structural characteristics of 50% H2 / 50% CO turbulent premixed flame under different turbulence intensities (0m/s ~1.31m/s) and at the equivalence ratio of 0.6 was studied by using wavelet transform. 2. Experimental setup and procedures 2.1 Experimental setup All the experiments were conducted in a turbulent combustion bomb, including an inner diameter of 380mm. Two pairs of windows were fixed at the horizontal direction for inspection and flame evolution photos captures. The turbulence required for the experiment was generated by the combination of the fan and the orifice plate with a diameter of 12mm. To ensure the creation of a uniform turbulence environment, four motors were installed in the pyramid on the turbulent combustion bomb. Rotation of the fan was driven by a motor to form turbulence through the orifice. The turbulence intensity was controlled by adjusting the rotating speed of the fan. All the pressure of the gas components were calculated and supplied into the chamber, and then the motors operated at the same speed for 3 to 4 minutes. All the flame photos were recorded by a FASTCAM SA-X2 high speed camera after ignition. The schematic of the experiment setup is illustrated in Fig. 1.


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Fig. 1. Schematic of the experiment setup 2.2 Parameter definition To investigate the evolution of the disturbances on the flame front, high-precision extraction of flame contour information was essential. The flame area and the position information of flame counters in the polar coordinate were recorded by using Matlab. Since it is easier to compare the flame contours information of different positions under the Cartesian coordinate system, the obtained information of flame counters were transformed to the Cartesian coordinate system. As illustrated in Fig. 2, the fluctuations of the flame front were more intuitive under Cartesian coordinate, where the Ra and Ri represent the area equivalent radius and local flame radius, respectively. The larger the fluctuation of the local flame radius Ri in Cartesian coordinate was, the stronger the wrinkle degree of the flame front in polar coordinate.


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Fig. 2. Parameter definition and coordinate transformation The flame stretch has a significant effect on the propagation characteristics of the flame, which was defined as [33-35] （1）

K = (1/A) dA/dt

where A represents the area of the flame. The evolution of the flame front corresponds to a dynamic process under the coupling influence of multifactors. However, whether a correlation relationship exists between the flame counters at different moment and how the correlation relationship varies needs to be further studied. In this paper, correlation degree was defined to a quantitative study of the intrinsic relationship of the flame structural characteristics.

N

N

ρ m,n = ∑ ( Rim − Ram )( Rin − Ran ) / i =1

N

∑ ( Rim − Ram )2 ∑ ( Rin − Ran )2 i =1

i =1

(2)

where ρm,n represents the correlation degree of flame front at m and n moments, N stands for the number of points recorded in the flame front. Rim and Rin correspond to the flame local radius at m and n moments, respectively. Ram and Ran represent the area equivalent radius at m and n moments, respectively. The correlation degree ranges from -1 to 1. When the flame front is exactly the same at different time, the


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correlation degree is 1. When the flame front is opposite at different time, the correlation degree is -1. By decreasing the correlation degree, the wrinkle degree of the flame front intensified. To study the effect of turbulence intensity on the evolution of different scales disturbances in the flame fronts, wavelet transform was adopted to decompose the flame front information, and get the distribution of flame disturbances at different scales. In this paper, eight levels were enough to decompose the flame front information for every experimental condition. The decomposition structure of the wavelet is illustrated at Fig 3, where Ai and Di represent the approximate component and detail component, respectively. The detail component corresponds to the high frequency portion of the signal and the approximate component represents the low frequency portion of the signal. The low frequency part decomposed by the original signal is decomposed continuously, and the signals in different scales were obtained

Fig. 3. Wavelet transform decomposition structure diagram 3. Results and discussion Flame structural characteristics are the most reliable features to investigate the flame combustion mechanism. For the turbulent premixed flame, the flame was not only affected by the flame inherent instability from the flame itself, but also by the turbulence flow in the environment during the flame propagation process. The coupling of the two factors accelerated the cellular structure of the flame. Fig 4 illustrates the evolution of


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the 50% H2 / 50% CO flame under different turbulence intensities. For the laminar premixed flame, the flame front emerged cracks due to the effect of the thermal – diffusive instability when the flame radius was 10 mm. With the development of the flame, the cracks of the flame front grew rapidly, were separated and gradually form cellular structure. Compared with the flame thermal – diffusive instability, the introduction of turbulence greatly enhanced the disturbances of the flame front. When the turbulence intensity was 0.49 m/s, in the flame front a tendency appeared to deviate from the standard circle at the beginning of the flame propagation. Thus, the flame front was obviously deformed as a whole. Cracks in the flame front were significantly enhanced and formed cellular structure. By the turbulence intensity increase, the overall deformation degree of the flame front increased, and the cellular structure in the flame front was enhanced. With the development of the flame, the cellular structure has been further developed, the number of cells in the flame front increased and the area of the cells tended to be uniform. u’

10mm

20mm

30mm

40mm

Flame counters

u’=0m/s

u’=0.49m/s

u’=0.74m/s


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u’=1.08m/s

u’=1.31m/s

Fig. 4. The effect of turbulence intensity on the evolution of flame radius of 50% H2 / 50% CO / air mixture The flame counters extracted from the flame at different area equivalent radius in Fig 4 demonstrate that the image processing program can capture the local information of flame front accurately. Hence, this provides a basis for the subsequent research. In addition, it can be seen that there were significant self-similarity characteristics during the flame development and different degrees of fluctuations in the flame front existed.

(a) u ‘=0 m/s

(b) u ‘=0.74 m/s


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(c) u ‘=1.31 m/s Fig. 5. The effect of turbulence intensity on the evolution of flame front To study the evolution of the disturbances and the change of the position of different disturbances in the flame front, the flame contours under Cartesian coordinate are illustrated in Fig 5. For the laminar premixed flame, few differences existed between the flame local radius and the area equivalent radius at the same moment. The fluctuation of the flame front is relative insignificant, resulting in the flame fronts in the Cartesian coordinate close to straight lines as whole. With the development of the flame, the number of fluctuations in the flame fronts presented an increasing trend and the amplitudes of the fluctuations were slightly enhanced. The turbulence greatly enhanced the fluctuation of the flame front. As the turbulence intensity increases, the volatility of the flame front increased. In contrast to region A and B, it demonstrated that there was a complex interaction between disturbances in flame front. The most intense fluctuations in the flame indicate an increased tread for the superposition of the stronger disturbances in the flame front. Due to the offset effect by the various disturbances imposed on the flame front, the smaller ones gradually decreased. In addition, the interaction between diverse disturbances in the flame front induces a great degree of deviation of the fluctuations peak position (Region A). With the development of flame, flame stretch has a critical influence on the development of flame front disturbances. The effect of flame stretch on the disturbances of different scales is different, leading to a complex structure of the flame front.


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Fig. 6. The evolution of flame correlation degree of 50% H2 / 50% CO / air mixture under different turbulent intensities The correlation degree of the flame front offers the overall self-similarity of the flame front during the process of flame development. In the laminar and weak turbulence environment, the correlation degree of the flame fronts presented a tendency to decrease first and then increase. However, after the correlation degree reached the minimum value, the growth rate of the correlation degree was very limited. The correlation degree of the flame front gradually decreased when the turbulence intensity ranged from 0.74 m/s to 1.31 m/s. The correlation degree decreased to zero when the radius was 25 mm under the highestturbulence intensity of 1.31m/s. This indicates that with an increase of the turbulence intensity the interaction of the disturbancs in the flame front increased, leading to the retention degree of the flame shape at the beginning moment gradually decreases until it diminishes and further develops to a more complex shape.


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(a) u ‘=0 m/s

(b) u ‘=0.49 m/s

(c) u ‘=0.74 m/s

(d) u ‘=1.08 m/s

(e) u ‘=1.31 m/s Fig. 7. The effect of turbulence intensity on the cumulative probability distribution of the fluctuation of flame local radius To further investigate the effect of turbulence intensity on the flame front correlation degree, the local structural characteristics of flame front were statistically studied. Fig 7 presents that by increasing of the fluctuation value, the distribution of the cumulative probability of the fluctuation of the local flame radius tended to increase at different area equivalent radii. The growth rate of the cumulative probability increased initially and then decreased. In addition, the growth rate of cumulative probability was larger in the region near 0 and the growth rate in the region far away from 0 was smaller. By turbulence intensity increase, the range of local radius fluctuation tended to increase.


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Since the first derivative of the cumulative probability represents the probability of the corresponding fluctuation value, the probability distribution information of different fluctuation values can also be obtained. When the turbulence intensity equaled 0, the distribution of the flame local radius was near normal distribution. By the increase of the turbulence intensity, the higher fluctuation component appeared, but the proportions were relative small.

Fig. 8. The evolution of flame stretch under different turbulence intensities With the development of the flame, the flame stretch gradually reduced. In the early stage of flame propagation, the change rate of flame stretch was large. With the evolution of the flame, the change rate of flame stretch gradually slowed down. As the turbulence intensity increased, the flame stretch corresponding to the same radius tended to increase (Fig 8). The flame stretch had a significant effect on the evolution of the disturbances in the flame front. At the beginning of the flame development the greater flame stretch limited the development of the disturbances. With the further reduction of the flame stretch, the disturbances in the flame front rapidly developed and accelerated the development of the cellular structure. Although the flame stretch increased with the increase of the turbulence intensity, the turbulence applied to the flame front was stronger than the effect of flame stretch, leading to a significant reduction in the correlation degree of flame front.


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(a) 10mm

(b) 20mm

(c) 30mm

(d) 40mm

Fig 9. The evolution of different decomposition components of flame front information when the turbulence intensity was 0m/s To study the time-frequency characteristics and position information of the disturbances of different detail components during the flame propagation process, the wavelet transform was conducted to the flame front when the turbulence intensity was 0 m/s. Fig 9 illustrates that when the flame front information was decomposed into 8 levels, the approximation information of the flame front became smoother than the original information. With the increase of the scale, the time resolution was reduced and the development trend of the approximation signal was more clearly demonstrated. That is, with the increase of the scale the high-frequency information contained in the low-frequency part of the decomposition components will be reduced. In addition,


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some sudden changes occurred in the decomposition components, indicating that there were discontinuity points at the corresponding position due to the existing of high frequency disturbances. The amplitude range of the detail components of D1 to D4 was relative smaller, while these of the components D5 to D8 were relative larger, which correspond to the main components of the flame local structural characteristics. With the development of the flame, the amplitude of different components disturbances increased to a variety of degrees due to flame stretch reduction.

(a) 10mm

(b) 20mm

(c) 30mm

(d) 40mm

Fig. 10. The evolution of different decomposition components of flame front information when the turbulence intensity was 1.31 m/s


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Fig 10 illustrates the detail components of the flame front at eight different scales. Compared to that of the laminar premixed flame, with the increase of the turbulence intensity, the disturbances applied to the flame front were caused by the turbulence increase. The fluctuation of different detail components increased, and the number of the mutation points of the flame front also presented an increasing trend. Under the influence of flame inherent instability and turbulence, the fluctuation of the eight detail components of the flame front was enhanced. To quantitative study the disturbances information of different components, the rms amplitude and the energy of different decomposition components were defined as follows:

n

∑ (d

rms =

mi

− dm )2 n

i=0

(3)

n

Ei = ∑ (d mi − d m ) 2 i =0

where

(4）

d mi and d m represent the local and mean amplitude of the m th wavelet decomposition of the flame

front, respectively. n means the number of the point of the m th wavelet decomposition of the flame front.

(a) u ‘=0 m/s

(b) u ‘=0.49 m/s


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(c) u ‘=0.74 m/s

(d) u ‘=1.08 m/s

(e) u ‘=1.31 m/s Fig. 11. Evolution of rms amplitude of different detail component under different turbulence intensities Figure 11 shows the rms amplitude of the detail components of the flame front profile, which is possible to reflect the uniformity of the detail components as a whole at a certain scale. The maximum value indicates that the detail components included a large degree of fluctuations. The rms amplitude increased by increasing the scale. When the flame radius was relatively small, the growth rate of the rms amplitude initially increased and subsequently decreased with the increase of the scale. When the flame radius was approximately large, the growth rate of the rms amplitude decreased after increasing and then increased with the increase of the scale. With the development of the flame, due to the reduction of the flame stretch, the corresponding rms amplitude of the detail components at a certain scale increased. With the increase of the turbulence intensity, the rms


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amplitude corresponding to the same scale presents an increasing trend. In addition, the rms amplitude of the high-frequency information was relative small, which also indicates that the complex feature of the flame front mainly occurred due to the effect of the detail components of higher scales.

(a) u ‘=0 m/s

(b) u ‘=0.49 m/s

(c) u ‘=0.74 m/s

(d) u ‘=1.08 m/s


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(e) u ‘=1.31 m/s Fig. 12. Evolution of energy of different detail component under different turbulence intensities Figure 12 illustrates the energy contained in the detail components at different scales under different turbulence intensities. When the turbulence intensity equaled 0 m/s, the energy of the detail components at different scales initially increased and then decreased with the development of the flame. The radius corresponding to the maximum energy presents a decreasing trend with an increase of the scales. With the increase of the turbulence intensity, the energy of the detail components at lower scales successively presented initially a monotonically increasing, decreasing first and then increasing and then falls again, bimodal shape with the development of the flame. The energy of the detail components at higher scale present an increase trend with the development of the flame. Moreover, with the increase of the scale, the energy of the detail components increased.


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(a) u ‘=0 m/s

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(b) u ‘=0.49 m/s

(c) u ‘=1.31 m/s Fig. 13. The correlation degree of different detail components under different turbulence intensities The correlation degree of different detail components at a certain flame radius and the correlation degree between a moment flame radius and the one at 10mm at a certain detail component are illustrated in Fig 13. The correlation degree does not present a monotonous trend at a certain scale with the development of the flame. With the increase of the scale, the correlation degree also did not presented a monotonous trend at a certain flame radius. Thus, it is demonstrated that the correlation degree of the detail components of the flame


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front presents a staggered distribution of higher and lower values. This mainly occurred due to the complex variation of the different detail components during the flame propagation process, which induced the complex interactions of disturbances of different detail components at the same location, and eventually led to the complexities of the flame front. 4. Conclusions To study the influence of flame inherent instability and turbulence on the flame structural characteristics, wavelet transform was adopted to decompose the flame front information and to investigate the characteristics of detail components at different scales. The main conclusions from this work can be summarized as follows. 1.

With the development of the flame, the limitation of flame stretch on the flame front disturbances gradually reduced, leading to the enhancement of the flame cellular structure and the decrease of the correlation degree of flame front. With the increase of the turbulence intensity, the disturbances caused by the turbulence increased and the correlation degree at a certain radius decreased.

2.

With the increase of the fluctuation value, the cumulative probability of the fluctuation of the local flame radius increased and the growth rate of the cumulative probability initially increased and then decreased. With the increase of the turbulence intensity, the higher fluctuation component appeared, but the proportion is lower.

3.

Due to the existence of high frequency disturbances, discontinuity points occurred in the flame front. With the development of the flame, the disturbances at different scales increased for the reduction of the flame stretch. With the increase of the turbulence, the disturbances have been increased at a varying degree and the discontinuity points in the flame front increased.

4.

With the development of the flame, the corresponding rms amplitude of the detail components at a certain scale increased. With the increase of the turbulence intensity, the rms amplitude corresponding to the same scale presented an increasing trend. In addition, the rms amplitude of the high-frequency information was relative low, which also indicated that the complex feature of the flame front was mainly due to the effect of the detail components of higher scales.


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5.

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The energy of the detail components at higher scale presented an increasing trend with the development of the flame. Moreover, with the increase of the scale, the energy of the detail components presented an increasing trend. The correlation degree of the detail components of the flame front presented a staggered distribution of higher and lower values. This is mainly due to the complex variation of the different detail components during the flame propagation process

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Experimental Study on the Turbulent Premixed Flame Structural

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