air expanding flames: Effect of Lewis number

Combustion and Flame 212 (2020) 1–12

Contents lists available at ScienceDirect

Combustion and Flame journal homepage: www.elsevier.com/locate/combustflame

Self-similar propagation and turbulent burning velocity of CH4 /H2 /air expanding flames: Effect of Lewis number Xiao Cai, Jinhua Wang∗, Zhijian Bian, Haoran Zhao, Meng Zhang, Zuohua Huang∗ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 6 June 2019 Revised 8 October 2019 Accepted 9 October 2019

Keywords: Turbulent burning velocity Self-similar propagation Differential diffusion Lewis number CH4 /H2 /air flame Turbulent expanding flame

a b s t r a c t In this study we clarify the role of differential diffusion characterized by effective Lewis number, Leeff , on the self-similar accelerative propagation and the associated turbulent burning velocity of turbulent expanding flames. The turbulent flame trajectories of the CH4 /H2 /air mixtures were measured using a newly developed large-scale, fan-stirred turbulent combustion chamber generating near-isotropic turbulence. It is found that the normalized turbulent propagation speed scales as the turbulent flame Reynolds number, ReT, f = (urms /SL )(r/l f ), roughly to the one-half power for the stoichiometric CH4 /H2 = 80/20 flames with unity Leeff (=1), where the average flame radius, r, is the length scale and the thermal diffusivity, α = SL l f , is the transport property, SL and lf are the laminar burning velocity and flame thickness, and urms is the root-mean-square (rms) turbulent fluctuation velocity. The propagation of the fuel lean CH4 /H2 = 20/80 flames with sub-unity Leeff (<1) is still self-similar, however, the normalized turbulent propagation speed is much higher and the power exponent is greater than 1/2 even though these two flames have almost the same laminar burning velocity, flame thickness with SL , lf and experience the similar turbulence perturbations. The stronger self-similar propagation of the Leeff < 1 flames is the consequences of the couple effects of the differential diffusion and the flame stretch on the local wrinkled flamelets within the turbulent flame brush. Based on the present experimental data, a modified possible general correlation for turbulent burning velocity is obtained in terms of the Leeff and ReT,f with differential diffusion consideration. This correlation is able to predict not only the present experimental data but also the previous turbulent burning velocities measured using both turbulent Bunsen flames and expanding flames at high pressures. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Hydrogen enriched natural gas is regarded as a promising method to store, transport and utilize hydrogen in internal combustion engines, gas turbines, and other combustion devices [1]. Combustion of fuel lean CH4 /H2 /air mixtures with high H2 concentration can yield lower CO2 emission and higher thermal efficiency. So far, a number of experimental studies have focused on the laminar burning velocity of CH4 /H2 /air mixtures [2–4], which could be used to validate and develop the chemical kinetic mechanisms. The turbulent burning velocity and flame front structure of CH4 /H2 /air mixtures with moderate H2 enrichment have also been studied using both turbulent expanding flames [5,6] and Bunsen flames [7]. In practice, combustion mode in spark ignition engines is premixed turbulent combustion in intense turbulence [8], which will signif-

∗

Corresponding authors. E-mail addresses: [email protected] (J. Wang), [email protected] (Z. Huang).

icantly enhance flame propagation and make high-speed engines possible. Thus, to design high-efficiency and low-emission CH4 /H2 spark ignition engines, it is essential to study the fundamentals of the flame propagation for highly H2 enriched CH4 mixtures in intense turbulence. The turbulent burning velocity, ST , of premixed flames is a critical important parameter in turbulent combustion, as evidenced by extensive theoretical [9–13], experimental [14–21], numerical [22–24], and review literature [25–27]. In general, under the wellaccepted concept proposed by Damkohler [28], it is believed that the turbulent burning velocity is mainly controlled by the turbulent transport of heat and mass of the mixtures and the total surface area of the wrinkled flamelets. Under the long-held assumption, the ST is a meaningful physical parameter, and there is a great interest to seek a general correlation, at least under some special turbulent flows such as those in isotropic turbulence. Furthermore, such a general correlation could be used as a sub-grid scale model for large eddy simulation (LES) of engine operations and accidental explosions. Conventionally, the most obvious choices of

https://doi.org/10.1016/j.combustflame.2019.10.019 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

2

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

flame and turbulence parameters for the ST correlation would be the laminar burning velocity, SL , the corresponding laminar flame thickness, lf , and the root-mean-square (rms) turbulent fluctuation velocity, urms , the integral length scale, LI , of turbulence. A number of experimental studies have been focused on determination of the ST and its correlation with turbulent expanding flames [20,29,30] and Bunsen flames [17,19]. To assess the existing correlations on prediction of the turbulent burning velocity with different initial conditions, fuels, and flame geometries, it is necessary to answer the question: “How important are the differential diffusion effects for fully turbulent conditions?” [27]. The differential diffusion (commonly referred to either molecular diffusion or preferential diffusion) of heat and mass which are directed normal to the flame surface is characterized by Lewis number, Le, of mixtures [31,32]. Although such differential diffusion effects on laminar flame propagation are well established as flame surface subjected to aerodynamic stretch which accounts flame curvature and strain [33,34]. While the mechanism of differential diffusion effects on turbulent flames is more complex, the role of the differential diffusion is sometimes neglected by assuming that the transport of heat and mass near the flame front is dominated by turbulent mixing such that molecular transport vanishes, especially in intense turbulence. The strong influence of differential diffusion has however been experimentally identified, through the facilitating effects on ignition [35] and propagation [19,21,36–38] of both weakly and strongly burning flames in turbulence. In addition, the differential diffusion effects on the turbulent burning velocity and the temperature and curvature dependence for the non-unity Le turbulent flames have also been discussed in several DNS analyses [39–42]. Lipatnikov and Chomiak [26] and Driscoll [27] reviewed the importance of the differential diffusion in turbulent combustion. It was suggested that the differential diffusion within the layers dominates over turbulent diffusion in the flamelets regimes, and it perhaps still plays a role in the thin reaction zone regime. The multi-scale turbulent eddies wrinkle the flamelets within the flame brush and generate a collection of both positive and negative stretched segments, where the local flame temperature and propagation speed could be enhanced or suppressed for mixtures with non-unity Le. As such, the global flame propagation speed will not be proportional to the total flame surface area. Bradley et al. [29] investigated the differential diffusion effects based on the Le and turbulent Karlovitz stretch factor, K = A(urms /SL )2 ReT −0.5 , and proposed a general correlation, ST /urms ∼ (KLe )−0.3 , where A is a coefficient, the classical turbulent Reynolds number, ReT = (urms LI )/ν , is defined based on the integral length scale (LI ) of turbulence and the kinematic viscosity (ν ) of reactants. Subsequently, Kitagawa et al. [43] rearranged the 2 −1 original scaling parameter of KLe as ReT Le−2 = [A( uSrms ) (KLe ) ]2 L and used this scaling parameter for H2 /air expanding flames at elevated pressures. They found the values of ST /SL for fuel lean H2 /air flames could be grouped into four regimes of urms /SL . Recently, Nguyen et al. [21] presented three modified general correlations for turbulent burning velocity with the consideration of Le effect based on the high pressure turbulent expanding flames data and the original correlations proposed by Kobayashi et al. [17], Chaudhuri et al. [20], and Liu et al. [30]. However, the different power constants of Le−n in the correlations were found in these studies. This reveals the insufficient understanding of differential diffusion effects on turbulent flames. In view of the importance of this issue, it therefore motivates us to assess the differential diffusion effects on non-unity Le flames experimentally with well controlled parameters (almost the same flame chemistry and turbulence property) in intense turbulence. We should note that because of the voluminous number of publications in this area, only representative references were cited herein.

In addition to the issue of differential diffusion, the accelerative propagation of turbulent expanding flame is of great interest. The spark-ignited, fan-stirred turbulent expanding flame in a combustion chamber possesses unique merits, it has a relatively simple configuration and propagates in a near-isotropic turbulence with negligible mean flow velocity, and it is more convenient to operate at high pressures than open flame configurations. Since the flame is ignited in a turbulent environment and expands outwardly, the turbulent propagation speed continuously increases and no equilibrium propagation speed has been reached [44]. Chaudhuri et al. [20] explained the accelerative propagation of the turbulent expanding flame due to the increasing of the effective hydrodynamic scale and the flame brush thickness as the flame continuously expands and developed a general correlation for ST /SL with the turbulent flame Reynolds number, ReT, f = (urms /SL )(r/l f ). The exponential correlation, ST /SL ~ ReT, f 0.5 , which was developed based on the experimental and theoretical results of unity Le flames, suggests the self-similar propagation of turbulent expanding flames. Subsequently, this correlation was validated and extended to various fuels characterized by unity and super-unity Le ( ≥ 1), and a modified correlation was experimentally obtained with the consideration of the Markstein diffusion for flames with positive Markstein number, Ma > 0 (Le ≥ 1) [37]. However, the modified correlation is invalid for negative Ma, where fuel lean CH4 /H2 /air flames are usually characterized by negative Ma. Furthermore, the diffusional-thermal instability often enhances the laminar flame propagation for mixtures with Le < 1 [45,46]. Therefore, it is the great interest to investigate the propagation dynamics of Le < 1 flames influenced by the coupling of molecular transport and turbulent mixing of heat and mass and also to seek a possible correlation for ST with the consideration of the Le effect. In view of the fundamental interest discussed above, we have two major objectives in present study. Firstly, we report the experimental results of turbulent burning velocity of fuel lean to stoichiometric CH4 /H2 /air mixtures with wide range of CH4 /H2 blending ratios measured using a newly developed fan-stirred turbulent combustion chamber generating near-isotropic intense turbulence. Secondly, the differential diffusion effects significantly enhance the self-similar propagation of sub-unity Leeff flames when compared with unity Leeff flames with almost the same laminar flame speed and flame thickness. The facilitation is due to the coupling of the differential diffusion of heat and mass of the mixtures and the flame stretch on the local wrinkled flamelets within the turbulent flame brush. In addition, we will present a modified possible general correlation with the differential diffusion consideration based on the present experimental data and compare this correlation with previous experimental data measured using both turbulent Bunsen flames and expanding flames under high pressures, showing a good agreement between the experimental data sets and the present correlation. 2. Experimental setup and methodology 2.1. Experimental setup The experiments were conducted on a newly developed, constant-volume, cylinder-type, fan-stirred combustion chamber with inner diameter of 345 mm and inner length of 307 mm, as shown in Fig. 1. A 6 kW cylinder-type heater with inner diameter of 303 mm and thickness of 20 mm is fixed into the stainless steel combustion chamber to heat the mixtures temperature up to 473 K. The chamber has been designed to conduct explosion experiments with initial pressure up to 1.0 MPa. Two quartz windows with optical diameter of 150 mm are equipped on the two ends of the chamber to allow optical access. Four fans with diameter

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

3

Fig. 1. Experimental setup: schematic configuration and experimental apparatus.

of 114 mm are orthogonally located in the chamber and are driven by four motors mounted on the outer chamber wall. The fan rotation speed can be varied from 0 to 10,0 0 0 rpm. Turbulence is generated by these fans which continuously run at a given rotation speed during the entire flame propagation event. The fuel, oxidizer, and dilution are successively introduced into a large mixing tank (with volume of 71.1 L and withstanding maximal pressure up to 30 MPa) which is previously vacuumed. The composition of mixtures is quantified using two pressure gauges (with accuracy within 0.075%) based on partial pressure law. After about 10 h waiting, the premixed combustible mixtures are filled into the combustion chamber and then ignited by two centrally located tungsten electrodes. The flame propagation images are recorded using a high-speed transmission schlieren system and a high-speed camera (Phantom v611) operating at 80 0 0 fps with 800 × 800 pixels image resolution. And the evolution of pressure inside the chamber is synchronously measured with a piezoelectric pressure sensor (PCB 112A05). The initial temperature of mixtures is measured using three thermocouples (with accuracy within 3 K) amounted on the mixing tank, pipeline, and combustion chamber. In laminar cases, the fans do not turn on, while the fans are driven at a given rotation speed before ignition in turbulent cases. In addition, the same mixtures from the mixing tank are ignited in both laminar and turbulent cases to avoid the run-to-run uncertainty due to different mixture compositions. 2.2. Turbulence characterization The non-reacting turbulent flow field inside the fan-stirred turbulent combustion chamber was characterized by a 2D particle image velocimetry (PIV). The PIV system consists a dual-cavity laser delivering laser rays of 200 mJ/pulse at 532 nm and a CCD camera. The original laser beam is expanded to a 1 mm thick laser sheet inside the turbulent combustion chamber using a semi-cylindrical lens (with focal length ~ −10 mm) located on the inner wall. The CCD camera is placed at 90° from the laser sheet and records images with the resolution of 1200 × 1600 pixels. Olive oil droplets (with average diameter of 1 μm) created with an aerosol generator are used for seeding. The uniform distribution of seed density

is obtained as the fans are activated. In each measurement, 560 couples of images were recorded with the frequency of 10 Hz. The velocity vector fields of 50 × 80 mm in the central of the chamber were calculated using software Davis 7.2 with fixed interrogation windows of 16 × 16 pixels and an overlap ratio of 50%, leading to a vector spacing of 0.76 mm. In the experiment, 2D velocity field was measured with fan rotation speeds from 500 to 20 0 0 rpm and pressures ranging from 0.05 to 0.5 MPa. The turbulent flow is always characterized by the turbulence intensity calculated by the rms turbulent fluctuation velocity and the integral length scale which is the largest length scale in turbulent flow. It is found that the mean flow velocity, uxy,mean , is negligible compared with the rms turbulent fluctuation velocity, uxy,rms , in the measured plane. The rms values of ux,rms and uy,rms in x- and y-directions around a given radius are evaluated based on the 2D PIV data of the central plane. The values of ux,rms and uy,rms are approximately equal, and the uxy,rms is the average of these two rms values. The uxy,rms is independent of the pressure and increases slightly from the central to the chamber wall, as shown in Fig. 2(a). The uxy,rms at r == 30 mm (average radius of the interrogation flame radius range, 15 to 45 mm) is used as a representative rms turbulent fluctuation velocity of the turbulent flow field. A new correlation between uxy,rms (m/s) and fan rotation speed, n (rpm), uxy,rms = 0.00181 × n, is obtained based on the 2D PIV data from 0.05 to 0.5 MPa. The maximal uxy,rms reaches 3.62 m/s, which is equivalent to those encountered in previous work [21,44]. Following the analyses of Ravi et al. [47] and Galmiche et al. [48], the longitudinal and lateral integral length scales are determined based on the spatial correlation coefficients of the turbulent fluctuation velocity. The longitudinal and lateral integral length scales are independent of the pressure but increase with the fan rotation speed, which is in accordance with the results of Shy and co-workers [30,49] and Abdel-Gayed et al. [50], as shown in Fig. 3. It is seen that the longitudinal integral length scale, Llong , is 1.8 times of the lateral integral length scale, Llat , regardless of initial pressure and fan rotation speed. This result is very close to the theoretical relation, Llong = 2 Llat , in isotropic turbulence [51]. The Llong is the representative length scale with the values from 10.6 to 16.1 mm in present work. In the following,

4

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

the urms and LI are the values of uxy,rms at r == 30 mm and Llong , respectively.

6 500 rpm 1000 rpm 1500 rpm 2000 rpm

5 4 uxy,rms (m/s)

(a)

0.05 MPa 0.1 MPa 0.2 MPa 0.5 MPa Average

2.3. Experimental conditions and data processing methods

3 2 1 0

0

10

20

30

40

50

r (mm)

uxy,rms or uxy,mean (m/s)

(b)

0.05 MPa uxy,rms 0.1 MPa uxy,mean 0.2 MPa 0.5 MPa Average uxy,rms = 0.00181*n (m/s)

4

3

2

R = 0.997

2

1

0 0

500

1000 n (rpm)

1500

2000

Fig. 2. Velocity field in turbulent combustion chamber: (a) Turbulence intensity with radius at different pressures; (b) Turbulence intensity and mean flow velocity at r == 30 mm with fan rotation speed.

20

LI (mm)

15

3. Results and discussions

Llong

0.05 MPa 0.1 MPa 0.2 MPa 0.5 MPa Average

Llat

3.1. Laminar burning velocity and turbulent combustion diagram

10

5

n

Llong = 16.44*(1-0.998 ) (mm) n

Llat = 9.35*(1-0.998 ) (mm)

0

500

1000

In experiments, mixtures of CH4 , H2 , and air were conducted with the mole ratio of CH4 /H2 ranging from 20/80 to 80/20 and the equivalence ratio varying from 0.4 to 1.0. All the experiments are performed at initial temperature of 298 K and pressure of 0.1 MPa to inhibit the development of Darrieus-Landau (DL), hydrodynamic instability for the finite flame thickness in relation to the flame size. For each concentration, the laminar and turbulent conditions (fan rotation speed from 0 to 20 0 0 rpm) were tested, and the detailed experimental conditions are listed in Table1. The instantaneous equivalence flame radius is defined as r = A f /π , which is based on the 2D projection area of the 3D flame front, Af . Because of the blurring effect of overlapping series of 2D images, the r based on schlieren image will cause a small but systematic overestimation of the mean flame radius of an actual 3D flame front in turbulent cases, and the r was suggested to correspond to the mean progress variable, c ~ 0.1 [15,52]. The downstream flame propagation speed for laminar and turbulent cases is determined by differentiating the r with respect to time, dr/dt. It should be noted that the proper flame radius range within 15 mm < r < 45 mm was used to avoid the influences of spark ignition and chamber confinement based on the results of laminar expanding flames [53]. The fundamental parameters, such as laminar burning velocity, SL , density ratio, σ , adiabatic temperature, Tad , and flame thickness, lf , were obtained by simulating the Equilibrium and 1D freely propagating flame using the CHEMKIN-Pro-Software and chemical kinetic mechanism of USC Mech 2.0 [54]. The density ratio is the ratio of the density of unburned to burned mixtures, σ = ρu /ρb . The flame thickness is defined based on the temperature profile, l f = (Tad − Tu )/(dT /dx)max , where Tu is the initial temperature, (dT/dx)max is the maximum temperature gradient [55]. The fuel Lewis number is calculated based on a volumetric fraction weighted average of the Lewis numbers of the CH4 and H2 [56]. The overall effective Lewis number, Leeff , is determined considering the influence of the excess and deficient reactants, as suggested by Addabbo et al. [57]. The Leeff of CH4 /H2 /air mixtures increases with the equivalence ratio and ranges from 0.58 to 1.19, as shown in Table 1.

1500

2

R = 0.999 2

R = 0.998

2000

n (rpm) Fig. 3. Evolution of integral length scale with fan rotation speed at different pressures. Llong and Llat are the longitudinal and lateral integral length scales, respectively.

Laminar burning velocity is the basic fundamental property of combustible mixtures and the key parameter in turbulent combustion. The SL of CH4 /H2 /air mixtures are extracted with an accurate nonlinear method (LC method) [58,59] based on the flame radius history in present large-scale combustion chamber. The experimental values of SL are compared with the previous experimental data and the numerical results in Fig. 4. It is seen that the present experimental data agree well with the SL measured using both spherically expanding flame [3] and heat flux method [4] for CH4 /H2 = 50/50 case. In general, the USC Mech. 2.0 [54] could well predict the SL under present conditions. It is found that the SL increases nonlinear with the concentration of H2 , and the enhancement in the SL becomes significant for mixtures with high H2 concentration. The experimental data of CH4 /H2 /air mixtures reported in present study were conducted at 0.1 MPa. The development of the DL instability is suppressed, and the DL cells are not observed for the propagation flames in the laminar cases. Therefore, the effect

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

5

Table 1 Laminar flame properties and turbulence information for the present experimental conditions. Initial temperature is 298 K and initial pressure is 0.1 MPa. CH4 /H2 a

φ

urms (m/s)b

LI (mm)b

σ

SL (m/s)c

lf (mm)d

Leeff e

Mac

Zef

20/80

0.4 0.6 0.8 1.0 0.6 0.8 1.0 0.6 0.8 1.0

0.91~3.62 0.91~3.62 0.91~2.72 0.91~1.81 0.91~3.62 0.91~3.62 0.91~3.62 0.91~3.62 0.91~3.62 0.91~3.62

10.4~16.1 10.4~16.1 10.4~15.6 10.4~14.2 10.4~16.1 10.4~16.1 10.4~16.1 10.4~16.1 10.4~16.1 10.4~16.1

4.37 5.58 6.54 7.17 5.59 6.65 7.38 5.59 6.70 7.49

0.126 0.395 0.748 1.045 0.192 0.381 0.529 0.098 0.268 0.378

0.753 0.463 0.342 0.299 0.644 0.418 0.366 0.817 0.494 0.434

0.58 0.70 0.89 1.19 0.80 0.90 1.07 0.92 0.96 1.03

−2.03 −1.08 −0.02 1.34 −1.02 −0.35 0.90 −0.68 1.24 1.77

12.43 8.74 6.99 6.27 9.73 7.84 6.85 10.51 8.48 7.15

50/50

80/20

a b c d e f

2

100

SL (mm/s)

10

T = 298 K P = 0.1 MPa CH4/H2/air

75

Present work Donohoe et al. (2014) Nilsson et al. (2017) USC Mech 2.0

Broken reaction zone Ka=100

CH4/H2=80/20

10

CH4/H2=50/50 CH4/H2=20/80

50

Da=1

Laminar flames

10

25

Corrugated flamelets

CH4/H2=80/20 CH4/H2=50/50 CH4/H2=20/80

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Fig. 4. Experimental and numerical laminar burning velocities of CH4 /H2 /air mixtures. Experimental data of the present work are extracted using a nonlinear method (LC method), and numerical data are calculated with USC Mech. 2.0.

of the DL instability on turbulent flames can be neglected under the same thermodynamic conditions. Figure 5 plots the present operating conditions in the turbulent combustion diagram proposed by Peters [12]. The experimental conditions range from wrinkled flamelets to thin reaction zone regimes, and many of them fall in the thin reaction zone regime. However, even in the thin reaction zone regime, the flame structure may not be dominated by turbulent transport such that the differential diffusion effects vanish. Furthermore, according to the experimental results of Skiba et al. [60], the concept of flamelet, which is invoked in most theories of turbulent combustion [61], is still valid in such regime. 3.2. Le effect on flame self-similar propagation Figure 6 shows the evolution of typical images of CH4 /H2 /air flames at CH4 /H2 = 50/50, different urms and φ . The flame propagates faster as the urms increases, and more finer scale structures emerge on the flame surface due to the reduction of the Kolmogorov length scale (inner scale), while the integral length scale (outer scale) keeps the same. Furthermore, it can be seen that more small-scale structures emerge on the flame surface for fuel lean mixtures in comparison with the stoichiometric mixtures probably due to the differential diffusion effects. From the indi-

Ka=1

ReT=1 0

0 0.2

Thin reaction zone

1

urms/ SL

125

The mole ratio of CH4 to H2 . urms = 0.00181 × n (m/s) and LI = 16.44(1−0.998n ) (mm), where n is the fan rotation speed from 500 to 20 0 0 rpm. The laminar flame speed and Markstein number are measured with a nonlinear method (LC method). The laminar flame thickness, lf = (Tad −Tu )/(dT/dx)max . The effective Lewis number is the weighted average of the Lewis numbers of excess and deficient reactants. The Zeldovich number, Ze = Ea (Tad −Tu )/(R0 Tad 2 ).

-1

10

0

10

urms=SL Wrinkled flamelets 1

10 LI / lf

2

10

3

10

Fig. 5. Regimes of present experimental conditions on turbulent combustion diagram.

cated time instants in Fig. 6, fuel lean (φ = 0.6, Leeff < 1) and stoichiometric (φ = 1.0, Leeff ~1) flames take 10.4 ms and 7.1 ms to propagate the same distance of 45 mm at urms = 1.81 m/s, respectively. However, the SL of the fuel lean flame (19.2 cm/s) is much smaller than that of the stoichiometric flame (52.9 cm/s). This means that the enhancement of flame propagation speed becomes significant for the Leeff < 1 flames in turbulent cases. Moreover, it can be found that the flame becomes more wrinkled and accelerates as it expands outwardly. Figure 7(a) shows the evolution history of the equivalence flame radius, r(t), for CH4 /H2 = 20/80 mixtures at φ = 0.6 and different urms . It is seen that the flame propagates faster as the urms increases, and all flames concave upward at different urms , indicating flame acceleration. Figure 7(b) plots the flame propagation speed dr/dt with the r. It is observed that the dr/dt increases throughout the flame propagation event. This demonstrates the acceleration of turbulent expanding flames, and no equilibrium propagation speed has been reached at least in present observation. The acceleration phenomenon is also observed at different φ and CH4 /H2 blending ratios. Bradley and co-workers [15,62] attributed the accelerative motion to the extension of turbulence spectra (on the long wavelength side) affecting the flame front as the flame expands. In the initial stage, the flame kernel is only

6

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

Fig. 6. Flame front evolution of CH4 /H2 /air mixtures under different turbulence intensities and equivalence ratios. The mole ratio of CH4 /H2 is 50/50.

imposed to part of turbulence spectra, as such only small eddies with the size smaller than the flame size could wrinkle the flame front, while larger eddies only could move it. The maximal length scale of the turbulence eddy that can affect the flame front is assumed to be the flame diameter [15]. In other words, in the early stage of flame propagation, the flame will accelerate due to the expansion of the spectrum of exposed turbulence to longer wavelength, however, the acceleration process will terminate when the flame length scale researches the largest turbulence length scale (LI ). In the present experiments, the LI is estimated to be 10.4 to 16.1 mm depending on the fan rotation speed. Thus, this mechanism could not fully explain the accelerative behavior of the turbulent expanding flames. Recently, Chaudhuri et al. [20] suggested that the acceleration mechanism of turbulent expanding flames is the increasing of effective hydrodynamic length scale, lH , and turbulent brush thickness, δ T , as flame continuously expands. A turbulent burning velocity correlation depending on flame radius (the lH in expanding flames) was proposed for unity Leeff flames,

ST ∼ SL



urms r SL l f

1 / 2 = ReT, f 1/2

(1)

where ReT,f is the turbulent flame Reynolds number, which is defined based on the averaged flame radius and the thermal diffusivity, increases as the turbulent flame expands outwardly. It is different from the classical turbulent Reynolds number, ReT = (urms LI )/ν , which is defined based on the integral length scale and the kinematic viscosity, and keeps constant in the propagation event. This correlation is the modification result by replacing LI with r from the theoretical expression for statistically turbulent planar flames in both the corrugated flamelets and the thin reaction zone regimes based on the spectrum closure of the G equation

Fig. 7. Effect of turbulence intensity on (a) equivalence flame radius and (b) flame propagation speed of CH4 /H2 /air mixtures. The mole ratio of CH4 /H2 is 20/80, and the equivalence ratio is 0.6.

by Peters [12] and Chaudhuri et al. [63]:

ST ∼ SL



urms LI SL l f

1/2

= Re T 1/2

(2)

This expression was originally presented by Damkohler for the thin reaction zone regime with the argument that turbulence only modifies the transport of the preheat zone [8,28]. In the analyses of Peters [12] and Chaudhuri et al. [63], the Damkohler’s first hypothesis, ST /SL = AT /AL , and the proportional relation of the δ T with LI , δ T ~ LI , are invoked. Firstly, the Damkohler’s first hypothesis is not valid for non-unity Leeff flames, and its validity in the flames with mean flame curvature is questionable even for unity Leeff flames [64]. Because the local burning velocity is still slightly affected by the strain and curvature even for unity Leeff flames, as the Ma is slightly larger than zero and also depends on the initial pressures [37]. In experiments, the flame radius is relatively large, and the positive mean flame curvature is small, thus the mean local burning velocity is largely kept as a constant laminar burning velocity. Therefore, it can be argued that the Damkohler’s first hypothesis is valid for unity Leeff flames with small mean flame curvature. Secondly, the proportional relation, δ T ~ LI , is obtained from the statically planar turbulent flames [12], while this is not valid in the turbulent expanding flames. Because the grow-

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

7

ence of these two correlations is within 2% in the present ReT,f range. This demonstrates that the propagation speed of unity Leeff flames can be scaled as the ReT,f roughly to one-half power, further indicating the self-similar propagation of such flames. As we know, the local flame burning velocity is insensitive to the local flame stretch rate for unity Leeff flames with small mean flame curvature, and as such the Damkohler’s first hypothesis is valid. However, for non-unity Leeff flames, the local burning velocity is modified by the local stretch rate due to the differential diffusion effects. And the dependence of the local burning velocity on local flame stretch rate is essentially nonlinear. Do the non-unity Leeff flames still propagate in a self-similar manner? The normalized flame propagation speed of highly H2 enriched CH4 lean flames (CH4 /H2 = 20/80, φ = 0.6) as a function of the ReT,f is plotted in Fig. 8(b). The experimental data at different urms and at each instant of the propagation case collapse well into one curve and follow a power-law correlation of

dr/dt = 0.065ReT, f 0.71 σ SL

Fig. 8. Plot of normalized flame propagation speed with turbulent flame Reynolds number for (a) unity Leeff (~ 1) and (b) sub-unity Leeff (< 1). Present data are compared with previous data (dash red line) for unity Leeff in (a). And the data curve obtained for unity Leeff (dash blue line with error bar) are plotted in comparison with the data for sub-unity Leeff in (b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

ing flame experiences the wrinkling of larger and larger turbulent eddies [37]. Furthermore, Chaudhuri et al. [37] suggested that the δ T is approximately proportional to the flame size, δ T ~ r, for the expanding flames using Mie scattering. Consequently, to arrive at a reasonable scaling for the turbulent expanding flames, it is S δ rationale to replace the LI to δ T or r, yielding ST ∼ ( uSrms l T )1/2 ∼ L

( uSrms L

L

f

r  1/2 ) [37]. Therefore, the Eq. (1) provided a successful prel f

diction for CH4 /air flames with unity Leeff (φ = 0.9) at different urms and initial pressures [20,65]. Figure 8(a) plots the normalized flame propagation speed of CH4 /H2 /air mixtures with turbulent flame Reynolds number at CH4 /H2 = 80/20, φ = 1.0 and different urms . It is seen that all the data collapse into a single curve and can be represented by a power-law correlation (R2 = 0.977),

dr/dt = 0.098ReT, f 0.55 σ SL

(3)

This power-law correlation agrees very well with the previous data of CH4 /air flames (see dash red line in Fig. 8(a)) with the power-law correlation of dσrS/dt = 0.102ReT, f 0.54 [20]. The differL

(4)

This suggests that the propagation of non-unity Leeff flames is also self-similar, at least in the domain of interrogation. The power exponent (0.71) is larger than the 1/2 power of the modified theoretical result of the Eq. (1), indicating a stronger acceleration process. The experimental data of (dr/dt)/(σ SL ) at CH4 /H2 = 80/20, φ = 1.0 are also plotted in Fig. 8(b) for comparison with a dash blue line. It is seen that the normalized flame propagation speed of fuel lean CH4 /H2 = 20/80 flames is much larger than that of stoichiometric CH4 /H2 = 80/20 flames. And the power exponent, α , in the correlation of dσrS/dt ∼ ReT, f α is larger for the fuel lean L CH4 /H2 = 20/80 flames. It should be emphasized that the laminar burning velocities (flame thicknesses) are similar for fuel lean CH4 /H2 = 20/80 and stoichiometric CH4 /H2 = 80/20 flames with the values of 39.5 cm/s and 37.8 cm/s (0.463 mm and 0.434 mm), respectively. In other words, both lean and stoichiometric CH4 /H2 /air flames are investigated with similar SL , lf , urms , LI , ReT , Ka (Karlovitz number), and Da (Damkohler number), which are located in almost the same places in the turbulent combustion diagram (see Fig. 5). Thus, the differences of the normalized flame propagation speed and the power exponent could only attribute to the fact that the Leeff of fuel lean CH4 /H2 = 20/80 flames (Leeff ~ 0.70) is much smaller than that of stoichiometric CH4 /H2 = 80/20 flames (Leeff ~1.03). The above differences on the flame self-similar propagation can be explained by the influence of the differential diffusion and flame stretch on the local flame structure and propagation speed within the turbulent flame brush. In specific, turbulent eddies statistically stretch inherently laminar flame front, and the local flame structure and propagation speed of the laminar flame are affected by the flame stretch [31]. The dependence of the propagation speed of laminar flame on the strain and curvature is essentially nonlinear [58], i.e.,



U+

 

2 2 ln U + R R



=



2 Ze −1 R 2

 1

Le



−1

(5)

where U is the local stretched flame propagation speed normalized by unstretched laminar flame speed, 2/R is the curvature scaled by laminar flame thickness, and Ze is the Zeldovich number. The Zeldovich number is defined as Ze = Ea (Tad − Tu )/R0 Tad 2 , where Ea is the activation energy, R0 is the universal gas constant [55]. This nonlinear equation indicates that the local flame propagation speed is enhanced (U > 1) for (2/R )(Le−1 − 1 ) > 0 and is suppressed (U < 1) for (2/R )(Le−1 − 1 ) < 0. The multi-scale turbulent eddies wrinkle the flamelets within the flame brush and generate both positive and negative stretch (curvature) on the laminar flameltes [38]. For the present fuel lean CH4 /H2 /air mixtures characterized by Leeff < 1, the propagation of the convex segments with

8

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

Fig. 9. Flame propagation speed and stretch rate as a function of flame radius for two CH4 /H2 /air mixtures characterized by unity and sub-unity Leeff in laminar cases.

positive curvature (2/R > 0) is enhanced, while the propagation of the concave segments with negative curvature (2/R < 0) is weakened, and as such both convex and concave segments move away from the mean flame position, leading to amplification of the flame surface fluctuations [27]. Since the convex segments are the typical leading points of the flamelets which propagate faster and will assist the overall flamelets to reach a higher propagation speed. Thus, the fuel lean CH4 /H2 /air flames (Leeff < 1) propagate faster than stoichiometric flames (Leeff ~ 1) due to the higher leading flame propagation speed and the larger total flame surface area. Furthermore, for Leeff < 1 mixtures, the difference of local propagation speeds between the leading and trailing segments will lead to the more curved local flamelets and stronger flame stretch (curvature) which will further exaggerate the difference of local propagation speeds between these segments [38]. This positive feedback of local flame propagation speed and flame stretch (curvature) of the leading segments in the flamelets continuously increases the leading flame propagation speed and the flame surface fluctuations. Therefore, this positive feedback causes a stronger propagation of the global flame front. Consequently, the difference of the global propagation speed increases as flame expands outwardly for the fuel lean and stoichiometric CH4 /H2 /air flame. Therefore, a higher power exponent in dσrS/dt ∼ ReT, f α is obtained from the fuel lean L mixtures characterized by Leeff < 1. It should be noted that the above physical mechanism based on Eq. (5) is derived for both strong and moderate stretch rates. And the convex segments of flamelets with positive curvature can also exist in intense turbulence with strong flame strain [26]. In addition, the diffusional-thermal instability occurs on the fuel lean CH4 /H2 /air flame front at the late stage of flame propagation in laminar case, and the promotion effect on flame propagation is negligible when compared with the influence of strong stretch rate, as illustrated in Fig. 9. Moreover, the stretch induced local extinction is not observed for these cases even at high turbulence intensity, therefore, the stronger resistant ability to local extinction of Leeff < 1 flames will not make contribution to the stronger selfsimilar propagation [66,67]. These complementary interpretations further support the importance of the leading segments with positive curvature in facilitating the propagation of turbulent flames even in intense turbulence by increasing the global propagation speed and exaggerating the flame surface fluctuations for Leeff < 1 flames.

Fig. 10. Effect of (a) equivalence ratio and (b) CH4 /H2 blending ratio on normalized turbulent burning velocity. ST,c = = 0.5 is the turbulent burning velocity at c = 0.5.

3.3. Turbulent burning velocity and possible correlation with Le effect In turbulent expanding flames, it should be noted that the turbulent burning velocity, ST , is not equal to dr/dt due to the gas expansion effect [52]. The normalized turbulent burning velocity, ST /SL , could be obtained using the density correction and mean progress variable converting factor. The simultaneous measurements using Mie scattering and schlieren imaging by Bradley et al. [15] suggest that the r obtained by schlieren imaging corresponds to c ~ 0.1, and the ratio of rc=0.1 /rc=0.5 ∼ 1.33, where rc=0.1 is the averaged flame radius of the schlieren image, rc=0.5 is the averaged flame radius corresponding to c = 0.5 based on Mie scattering. Hence, according to the density correction within the turbulent flame brush by Chaudhuri et al. [20], the normalized turbulent burning velocity at c = 0.5 can be determined by

SL,

c=0.5

SL

=

2σ dr/dt (rc=0.1 /rc=0.5 )2 σ +1 σ SL

(6)

The ST at c = 0.5 is a better choice regardless of the flame geometries, as a good agreement between turbulent expanding flames and Bunsen flames can be obtained [20]. The normalized turbulent burning velocity, ST,c = = 0,5 /SL , is plotted as a function of the ReT,f under different CH4 /H2 blending ratios, φ , and urms in Fig. 10. The self-similarity of turbulent

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

9

burning velocity is observed from these flames. It is seen that the ST,c = = 0,5 /SL is strongly enhanced for fuel lean CH4 /H2 = 20/80 flames at φ = 0.4 when compared with the stoichiometric flames. While the ST,c = = 0,5 /SL increases slightly as the CH4 /H2 blending ratio varies from 20/80 to 80/20 for CH4 /H2 /air flames at φ = 0.8. Because the Leeff of CH4 /H2 = 20/80 mixtures decreases from super-unity Leeff = 1.12 to sub-unity Leeff = 0.58 caused by the φ variation. However, the Leeff of fuel lean CH4 /H2 /air flames (φ = 0.8) is close to unity, even though the CH4 /H2 blending ratio changes greatly. The sensitivity of the ST,c = = 0,5 /SL to the φ and CH4 /H2 blending ratio can be explained by the control factor of Leeff as discussed in the previous section. A unified correlation for turbulent burning velocity that includes the differential diffusion effects is recognized as a challenge [26]. It should be noted that Chaudhuri et al. [37] proposed S 1 urms r 1/2 a power-law correlation ST ∼ ( Ma ) = (ReT, f /Ma )1/2 conS l L

L

f

sidering the effect of Ma, and it was validated for several fuels at different pressures, φ , and urms . Unfortunately, this scaling is only valid for positive Ma, while a majority of the present experimental data of the fuel lean CH4 /H2 /air flames are characterized by negative Ma, as shown in Table 1. Both the Ma and Le could characterize the differential diffusion, however, in practice, the accurate value of Ma is very difficult to measure due to the uncertainty response to the flame stretch by perturbations on flame propagation. In addition, the average fractional reduction in burning velocity of laminar flamelets was found to be proportional to KMa [29]. And the Le is almost proportional to the Ma. Hence, Bradley et al. [29] developed the ST correlation on the basis of KLe, rather than the more rigorous scaling parameter KMa, and proposed a general correlation ST /urms = 0.88(KLe )−0.3 , where K = A(urms /SL )2 ReT −0.5 is the turbulent Karlovitz stretch factor, A is a coefficient with a value of 0.157 [29] or 0.25 [15]. Subsequently, Kitagawa et al. [43] rearranged the original correlation term of KLe 2 −1 as ReT Le−2 = [A( uSrms ) (KLe ) ]2 and used a rearranged correlation L

on the basis of ReT Le−2 in H2 /air turbulent expanding flames,

 β ST = C ReT Le−2 SL

(7)

where C and β are the coefficients depending on the relative turbulence intensity, urms /SL . The general correlations of Bradley et al. [29] and Kitagawa et al. [43] are valid for mixtures with Le > 1 as well as Le < 1, however, the self-similar propagation is not well considered in these correlations. It is the great interest to seek a power-law correlation considering the self-similar propagation and differential diffusion effects. A modified correlation in terms of a rational scaling parameter of ReT, f Lee f f −2 is obtained based on the present experimental data of CH4 /H2 /air mixtures at different CH4 /H2 blending ratios, φ , and urms :



ST,c=0.5 urms r − 1 = 0.164 Lee f f −2 SL SL l f 2

R = 0.942.

0.66



= 0.164 ReT, f Lee f f −2

0.66

Fig. 11. The variation of ST,c = = 0.5 /SL −1with ReT,f /Leeff 2 for (a) CH4 /H2 = 20/80 (linear plot) and (b) different CH4 /H2 blending ratios (log-log plot). Not included in the fitting is the CH4 /H2 = 80/20, φ = 0.6 case as a widespread local extinction is observed in such flames.

(φ = 0.7) turbulent expanding flames [21] with large Leeff ~ 1.62 at elevated pressures (0.1–0.5 MPa), and fuel lean to stoichiometric H2 /air (φ = 0.4–1.0) turbulent expanding flames [43] with wide Leeff range (0.33–1.10 [53]) at elevated pressures (0.1–0.5 MPa) are presented in Fig. 12. The turbulent burning velocities determined at c = 0.1 from turbulent Bunsen flames [17] are converted to that at c = 0.5 using a correction factor with the value of 1.35 [20]. The previous experimental data and the present data line (solid black line with error bar) are plotted as ST,c=0.5 /SL − 1 versus ReT,H in Fig. 12. The ReT,H =

(8)

It is seen that all experimental data collapse quite well in Fig. 11, hence suggesting the possibility of a general ST correlation with the consideration of differential diffusion. It is also found that the power exponent, α = 0.66, is slightly larger than 1/2 power of the Eq. (1) associated with unity Leeff . This may be caused by the stronger acceleration process in the late period of Leeff < 1 flames. This correlation can be compared with the previous experimental turbulent burning velocities measured using turbulent Bunsen flames and expanding flames. The extensive experimental data of fuel lean CH4 /air (φ = 0.9) turbulent Bunsen flames [16,17] with unity Leeff over wide initial pressure (0.1–3.0 MPa) and turbulence intensity ranges, the newly measured fuel lean C3 H8 /air

urms SL

lH lf

is a turbulent Reynolds

number based on effective hydrodynamic length scale, lH , which is the burner diameter, D, for Bunsen flames and the r for expanding flames. It can be seen that the previous experimental data of hydrocarbon fuels collapse well with the present data line, while the data of H2 is slightly scattered. The previous data could be fitted as ST,c=0.5 /SL − 1 = 0.207(ReT,H Leeff −2 )0.60 with the R2 = 0.864. The power exponent is slightly smaller and the pre-factor is larger than that of Eq. (8). These differences are likely caused by the scattered data of H2 /air flames. Specifically, the ST /SL of H2 /air flames exhibits two different positive slopes with the ReT,H Leeff −2 , namely a weak power exponent when the ReT,H Leeff −2 < 800 and a strong power exponent when the ReT,H Leeff −2 > 800. This is possibly caused by the DL instability on H2 /air flames in weak turbu-

10

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

the urms /SL . Furthermore, the integral length scale, LI , should play a role in turbulent premixed combustion, but it is not considered in the present correlation. Liu et al. [30] found a general correlation based on the turbulent Damkohler number, (ST − SL )/urms ∼ Da0.5 , where Da = (LI /urms )(SL /l f ). This correlation considers the effect of LI , and it is similar to ST /SL − 1 ∼ ReT 0.5 . However, the LI only varies from 10.4 to 16.1 in the present experiments, and the promotion effect of the LI on the ST could be covered by the uncertainty of the measurements based on the correlation of Liu et al. [30]. In addition, the DL instability effect is also not included in the present correlation. Thus, a true unified correlation for turbulent burning velocity is still an open issue.

4. Conclusions

Fig. 12. Comparison of present data line with previous data of turbulent Bunsen flames from Kobayashi et al. [16,17] (CH4 /air data with open symbol) and turbulent expanding flames from Nguyen et al. [21] (C3 H8 /air data with solid symbol) and Kitagawa et al. [43] (H2 /air data with half open symbol). The length scale lH is the burner diameter for Bunsen flames and the averaged flame radius for expanding flames.

lence, and as such the ST /SL of H2 /air flames is larger than that of other flames at small ReT,H Leeff −2 . In addition, the effect of the DL instability is negligible in intense turbulence [68]. Thus, the previous data have a smaller power exponent. If the H2 /air data at ReT,H Leeff −2 < 800 were removed, the best fitting line will become ST,c=0.5 /SL − 1 = 0.172(ReT,H Leeff −2 )0.62 with the R2 = 0.882 (not shown in Fig. 12). Thus, the difference of the pre-factor is small now, and the difference of the power exponent could be accepted. It demonstrates that the present correlation could largely predict the previous data, hence suggesting that the possibility of the general turbulent burning velocity correlation for different flame geometries and Lewis numbers, when it is appropriately scaled. Considering the theoretical result and experimental data, the turbulent burning velocity could be possibly scaled as ST,c=0.5 /SL = 1 + ALeeff −1 ReT,H 0.5 . This reveals that the turbulent flame is selfsimilar regardless of initial condition, fuel type, and even flame geometry. The Le−1 dependence of the turbulent burning velocity or the mean burning rate has been suggested in previous experimental and numerical studies. Dinkelacker and co-workers [69,70] found ST,c=0.5 /SL − 1 ∼ Le−1 ReT 0.25 (urms /SL )0.3 (P/P0 )0.2 based on extensive experimental data from turbulent Bunsen flames. Chakraborty and Cant [71] also proposed an scaling relation for the mean burning rate, (ρ Sd )s ∼ Le−1 ρ0 SL , from DNS analysis. In addition, Driscoll [27] reviewed the correlation curve of Bradley [72] with the scaling parameter of KLe based on the data measured from Bunsen, spherical, and V-flame geometries and presented a similar correlation, ST /SL = 1 + Le−1 ReT 0.5 . These studies further inspire the confidence of the present correlation for turbulent burning velocity with near Le−1 dependence. The differential diffusion characterized by Leeff plays an important role in turbulent combustion even in the thin reaction zone regime. And this effect needs to be incorporated in the turbulent combustion diagram. However, the differential diffusion effect in the broken reaction zone regime is still an open question and needs further investigation. It should be further noted that a true unified correlation for turbulent burning velocity between turbulent Bunsen and expanding flames relies on the correction factors for both flames. The recent work of Brequigny et al. [73] found that the correction factor for turbulent expanding flames is not a constant value and varies with

The present study reported the flame self-similar propagation and turbulent burning velocity of fuel lean to stoichiometric CH4 /H2 /air mixtures with CH4 /H2 blending ratio from 20/80 to 80/20 and for a wide range of turbulence intensity using a newly developed fan-stirred combustion chamber generating nearisotropic turbulence. The role of differential diffusion characterized by Leeff on flame propagation were demonstrated even in intense turbulence. Then, a possible general correlation of turbulent burning velocity was obtained based on the present experimental data. The main conclusions are summarized as follows: (1) The propagation of turbulent expanding flame is self-similar regardless of Leeff . The normalized turbulent propagation speed scales as a turbulent flame Reynolds number roughly to the one-half power, dσrS/dt = 0.098ReT, f 0.55 , for the unity L

Leeff (=1) flames and dσrS/dt = 0.065ReT, f 0.71 for the subL unity Leeff (<1) flames. The normalized turbulent propagation speed is much higher, and a larger power exponent is obtained for the sub-unity Leeff flames even though these two flames have almost the same laminar burning velocity and flame thickness. (2) The stronger self-similar propagation of the Leeff <1 flames can be explained by the coupling between differential diffusion and the flame stretch on the local wrinkled flamelets caused by the multi-scale eddies of turbulence. The global propagation speed of the Leeff <1 flames is enhanced due to the stronger leading segments in the winkled flamelets with positive curvature and the continuously increased total flame surface area. (3) The normalized turbulent burning velocity increases significantly with the decreasing Leeff . A modified possible general turbulent burning velocity correlation is found based on the ReT, f Leeff −2 with differential diffusion consideration. This correlation is able to describe not only the present experimental data but also the turbulent burning velocities from literature measured using turbulent Bunsen flame and expanding flame geometries at high pressures.

Declaration of Competing Interest None.

Acknowledgments This study is supported by National Natural Science Foundation of China (No. 91841302, 51776164, 91441203). Xiao Cai acknowledges the Chinese Scholarship Council (CSC201806280104) for a joint Ph.D. scholarship at Lund University.

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

References [1] S. Verhelst, T. Wallner, Hydrogen-fueled internal combustion engines, Prog. Energy Combust. Sci. 35 (2009) 490–527. [2] Z. Huang, Y. Zhang, K. Zeng, B. Liu, Q. Wang, D. Jiang, Measurements of laminar burning velocities for natural gas-hydrogen-air mixtures, Combust. Flame 146 (2006) 302–311. [3] N. Donohoe, A. Heufer, W.K. Metcalfe, H.J. Curran, M.L. Davis, O. Mathieu, D. Plichta, A. Morones, E.L. Petersen, F. Güthe, Ignition delay times, laminar flame speeds, and mechanism validation for natural gas/hydrogen blends at elevated pressures, Combust. Flame 161 (2014) 1432–1443. [4] E.J.K. Nilsson, A. van Sprang, J. Larfeldt, A.A. Konnov, The comparative and combined effects of hydrogen addition on the laminar burning velocities of methane and its blends with ethane and propane, Fuel 189 (2017) 369–376. [5] S.S. Shy, Y.C. Chen, C.H. Yang, C.C. Liu, C.M. Huang, Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion, Combust. Flame 153 (2008) 510–524. [6] M. Fairweather, M.P. Ormsby, C.G.W. Sheppard, R. Woolley, Turbulent burning rates of methane and methane-hydrogen mixtures, Combust. Flame 156 (2009) 780–790. [7] M. Zhang, J. Wang, Y. Xie, W. Jin, Z. Wei, Z. Huang, H. Kobayashi, Flame front structure and burning velocity of turbulent premixed CH4 /H2 /air flames, Int. J. Hydrogen Energy 38 (2013) 11421–11428. [8] N. Peters, Turbulent combustion, Cambridge University Press, 20 0 0. [9] P. Clavin, F. Williams, Theory of premixed-flame propagation in large-scale turbulence, J. Fluid Mech. 90 (1979) 589–604. [10] G.I. Sivashinsky, Cascade-renormalization theory of turbulent flame speed, Combust. Sci. Technol. 62 (1988) 77–96. [11] A.R. Kerstein, W.T. Ashurst, F.A. Williams, Field equation for interface propagation in an unsteady homogeneous flow field, Phys. Rev. A 37 (1988) 2728. [12] N. Peters, The turbulent burning velocity for large-scale and small-scale turbulence, J. Fluid Mech. 384 (1999) 107–132. [13] A. Lipatnikov, J. Chomiak, Global stretch effects in premixed turbulent combustion, Proc. Combust. Inst. 31 (2007) 1361–1368. [14] R. Abdel-Gayed, D. Bradley, M. Lawes, Turbulent burning velocities: a general correlation in terms of straining rates, Proc. R. Soc. A 414 (1987) 389–413. [15] D. Bradley, M. Lawes, M.S. Mansour, Correlation of turbulent burning velocities of ethanol–air, measured in a fan-stirred bomb up to 1.2 MPa, Combust. Flame 158 (2011) 123–138. [16] H. Kobayashi, T. Tamura, K. Maruta, T. Niioka, F.A. Williams, Burning velocity of turbulent premixed flames in a high-pressure environment, Symp. (Int.) Combust. 26 (1996) 389–396. [17] H. Kobayashi, K. Seyama, H. Hagiwara, Y. Ogami, Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature, Proc. Combust. Inst. 30 (2005) 827–834. [18] S.A. Filatyev, J.F. Driscoll, C.D. Carter, J.M. Donbar, Measured properties of turbulent premixed flames for model assessment, including burning velocities, stretch rates, and surface densities, Combust. Flame 141 (2005) 1–21. [19] P. Venkateswaran, A. Marshall, D.H. Shin, D. Noble, J. Seitzman, T. Lieuwen, Measurements and analysis of turbulent consumption speeds of H2 /CO mixtures, Combust. Flame 158 (2011) 1602–1614. [20] S. Chaudhuri, F. Wu, D. Zhu, C.K. Law, Flame speed and self-similar propagation of expanding turbulent premixed flames, Phys. Rev. Lett. 108 (2012) 044503. [21] M.T. Nguyen, D.W. Yu, S.S. Shy, General correlations of high pressure turbulent burning velocities with the consideration of Lewis number effect, Proc. Combust. Inst. 37 (2019) 2391–2398. [22] J.H. Chen, H.G. Im, Correlation of flame speed with stretch in turbulent premixed methane/air flames, Symp. (Int.) Combust. 27 (1998) 819–826. [23] J. Bell, M. Day, I. Shepherd, M. Johnson, R. Cheng, J. Grcar, V. Beckner, M. Lijewski, Numerical simulation of a laboratory-scale turbulent V-flame, Proc. Natl. Acad. Sci. 102 (2005) 10 0 06–10 011. [24] F. Creta, M. Matalon, Propagation of wrinkled turbulent flames in the context of hydrodynamic theory, J. Fluid Mech 680 (2011) 225–264. [25] A. Lipatnikov, J. Chomiak, Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations, Prog. Energy Combust. Sci. 28 (2002) 1–74. [26] A. Lipatnikov, J. Chomiak, Molecular transport effects on turbulent flame propagation and structure, Prog. Energy Combust. Sci. 31 (2005) 1–73. [27] J.F. Driscoll, Turbulent premixed combustion: Flamelet structure and its effect on turbulent burning velocities, Prog. Energy Combust. Sci. 34 (2008) 91–134. [28] G. Damköhler, Der einfluss der turbulenz auf die flammengeschwindigkeit in gasgemischen, Ber. Bunsen. Phys. Chem. 46 (1940) 601–626. [29] D. Bradley, A. Lau, M. Lawes, F. Smith, Flame stretch rate as a determinant of turbulent burning velocity, Philos. Trans. R. Soc. Lond. Ser. A 338 (1992) 359–387. [30] C.-C. Liu, S.S. Shy, M.-W. Peng, C.-W. Chiu, Y.-C. Dong, High-pressure burning velocities measurements for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at constant Reynolds numbers, Combust. Flame 159 (2012) 2608–2619. [31] C.K. Law, Combustion physics, Cambridge University Press, 2010. [32] Y. Xie, X. Wang, H. Bi, Y. Yuan, J. Wang, Z. Huang, B. Lei, A comprehensive review on laminar spherically premixed flame propagation of syngas, Fuel Process. Technol. 181 (2018) 97–114. [33] M. Matalon, B.J. Matkowsky, Flames as gasdynamic discontinuities, J. Fluid Mech. 124 (1982) 239–259.

11

[34] C.K. Law, C.J. Sung, aerodynamics Structure, and geometry of premixed flamelets, Prog. Energy Combust. Sci. 26 (20 0 0) 459–505. [35] F. Wu, A. Saha, S. Chaudhuri, C.K. Law, Facilitated ignition in turbulence through differential diffusion, Phys. Rev. Lett. 113 (2014) 024503. [36] D. Bradley, M. Lawes, K. Liu, M.S. Mansour, Measurements and correlations of turbulent burning velocities over wide ranges of fuels and elevated pressures, Proc. Combust. Inst. 34 (2013) 1519–1526. [37] S. Chaudhuri, F. Wu, C.K. Law, Scaling of turbulent flame speed for expanding flames with Markstein diffusion considerations, Phys. Rev. E 88 (2013) 033005. [38] S. Yang, A. Saha, W. Liang, F. Wu, C.K. Law, Extreme role of preferential diffusion in turbulent flame propagation, Combust. Flame 188 (2018) 498–504. [39] C. Rutland, A. Trouvé, Direct simulations of premixed turbulent flames with nonunity Lewis numbers, Combust. Flame 94 (1993) 41–57. [40] N. Chakraborty, R. Cant, Effects of strain rate and curvature on surface density function transport in turbulent premixed flames in the thin reaction zones regime, Phys. Fluids 17 (2005) 065108. [41] N. Chakraborty, R.S. Cant, Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames, Combust. Flame 156 (2009) 1427–1444. [42] G. Ozel-Erol, M. Klein, N. Chakraborty, Lewis number effects on flame speed statistics in spherical turbulent premixed flames, Medical Combustion Symposium (2019). [43] T. Kitagawa, T. Nakahara, K. Maruyama, K. Kado, A. Hayakawa, S. Kobayashi, Turbulent burning velocity of hydrogen-air premixed propagating flames at elevated pressures, Int. J. Hydrogen Energy 33 (2008) 5842–5849. [44] J. Goulier, A. Comandini, F. Halter, N. Chaumeix, Experimental study on turbulent expanding flames of lean hydrogen/air mixtures, Proc. Combust. Inst. 36 (2017) 2823–2832. [45] J. Wang, Y. Xie, X. Cai, Y. Nie, C. Peng, Z. Huang, Effect of H2 O addition on the flame front evolution of syngas spherical propagation flames, Combust. Sci. Technol. 188 (2016) 1054–1072. [46] X. Cai, J. Wang, H. Zhao, M. Zhang, Z. Huang, Flame morphology and self-acceleration of syngas spherically expanding flames, Int. J. Hydrogen Energy 43 (2018) 17531–17541. [47] S. Ravi, S.J. Peltier, E.L. Petersen, Analysis of the impact of impeller geometry on the turbulent statistics inside a fan-stirred, cylindrical flame speed vessel using PIV, Exp. Fluids 54 (2013) 1424. [48] B. Galmiche, N. Mazellier, F. Halter, F. Foucher, Turbulence characterization of a high-pressure high-temperature fan-stirred combustion vessel using LDV, PIV and TR-PIV measurements, Exp. Fluids 55 (2014) 1636. [49] S. Shy, M. Lin, A new cruciform burner and its turbulence measurements for premixed turbulent combustion study, Exp. Therm. Fluid Sci. 20 (20 0 0) 105–114. [50] R. Abdel-Gayed, K. Al-Khishali, D. Bradley, Turbulent burning velocities and flame straining in explosions, Proc. R. Soc. A 391 (1984) 393–414. [51] S.B. Pope, Turbulent flows, Cambridge University Press, 20 0 0. [52] D. Bradley, M. Haq, R. Hicks, T. Kitagawa, M. Lawes, C. Sheppard, R. Woolley, Turbulent burning velocity, burned gas distribution, and associated flame surface definition, Combust. Flame 133 (2003) 415–430. [53] X. Cai, J. Wang, H. Zhao, Y. Xie, Z. Huang, Effects of initiation radius selection and lewis number on extraction of laminar burning velocities from spherically expanding flames, Combust. Sci. Technol. 190 (2018) 286–311. [54] H. Wang, X. You, A.V. Joshi, S.G. Davis, A. Laskin, F. Egolfopoulos, C.K. Law, USC Mech Version II. High-Temperature Combustion Reaction Model of H2/CO/C1C4 Compounds. http://ignis.usc.edu/USC_Mech_II.htm, May 2007. [55] G. Jomaas, C.K. Law, J.K. Bechtold, On transition to cellularity in expanding spherical flames, J. Fluid Mech. 583 (2007) 1–26. [56] N. Bouvet, F. Halter, C. Chauveau, Y. Yoon, On the effective Lewis number formulations for lean hydrogen/hydrocarbon/air mixtures, Int. J. Hydrogen Energy 38 (2013) 5949–5960. [57] R. Addabbo, J.K. Bechtold, M. Matalon, Wrinkling of spherically expanding flames, Proc. Combust. Inst. 29 (2002) 1527–1535. [58] Z. Chen, On the extraction of laminar flame speed and Markstein length from outwardly propagating spherical flames, Combust. Flame 158 (2011) 291–300. [59] A.P. Kelley, C.K. Law, Nonlinear effects in the extraction of laminar flame speeds from expanding spherical flames, Combust. Flame 156 (2009) 1844–1851. [60] A.W. Skiba, T.M. Wabel, C.D. Carter, S.D. Hammack, J.E. Temme, J.F. Driscoll, Premixed flames subjected to extreme levels of turbulence part I: flame structure and a new measured regime diagram, Combust. Flame 189 (2018) 407–432. [61] N. Peters, Laminar flamelet concepts in turbulent combustion, Symp. (Int.) Combust. 21 (1988) 1231–1250. [62] D. Bradley, M. Lawes, M.S. Mansour, Flame surface densities during spherical turbulent flame explosions, Proc. Combust. Inst. 32 (2009) 1587–1593. [63] S. Chaudhuri, V. Akkerman, C.K. Law, Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability, Phys. Rev. E 84 (2011) 026322. [64] N. Chakraborty, D. Alwazzan, M. Klein, R.S. Cant, On the validity of Damköhler’s first hypothesis in turbulent Bunsen burner flames: a computational analysis, Proc. Combust. Inst. 37 (2019) 2231–2239. [65] L.J. Jiang, S.S. Shy, W.Y. Li, H.M. Huang, M.T. Nguyen, High-temperature, highpressure burning velocities of expanding turbulent premixed flames and their comparison with Bunsen-type flames, Combust. Flame 172 (2016) 173–182.

12

X. Cai, J. Wang and Z. Bian et al. / Combustion and Flame 212 (2020) 1–12

[66] F. Wu, A. Saha, S. Chaudhuri, C.K. Law, Propagation speeds of expanding turbulent flames of c 4 to c 8 n -alkanes at elevated pressures: experimental determination, fuel similarity, and stretch-affected local extinction, Proc. Combust. Inst. 35 (2015) 1501–1508. [67] S.S. Shy, C.C. Liu, J.Y. Lin, L.L. Chen, A.N. Lipatnikov, S.I. Yang, Correlations of high-pressure lean methane and syngas turbulent burning velocities: effects of turbulent Reynolds, Damköhler, and Karlovitz numbers, Proc. Combust. Inst. 35 (2015) 1509–1516. [68] S. Yang, A. Saha, Z. Liu, C.K. Law, Role of Darrieus–Landau instability in propagation of expanding turbulent flames, J. Fluid Mech. 850 (2018) 784–802. [69] S.P.R. Muppala, N.K. Aluri, F. Dinkelacker, A. Leipertz, Development of an algebraic reaction rate closure for the numerical calculation of turbulent premixed

[70]

[71]

[72] [73]

methane, ethylene, and propane/air flames for pressures up to 1.0 MPa, Combust. Flame 140 (2005) 257–266. N. Aluri, P. Pantangi, S. Muppala, F. Dinkelacker, A numerical study promoting algebraic models for the Lewis number effect in atmospheric turbulent premixed Bunsen flames, Flow Turbul. Combust. 75 (2005) 149. N. Chakraborty, R.S. Cant, Effects of Lewis number on flame surface density transport in turbulent premixed combustion, Combust. Flame 158 (2011) 1768–1787. D. Bradley, How fast can we burn? Symp. (Int.) Combust. 24 (1992) 247–262. P. Brequigny, C. Endouard, C. Mounaïm-Rousselle, F. Foucher, An experimental study on turbulent premixed expanding flames using simultaneously Schlieren and tomography techniques, Exp. Therm. Fluid Sci. 95 (2018) 11–17.