Extreme role of preferential diffusion in turbulent flame propagation

Combustion and Flame 188 (2018) 498–504

Contents lists available at ScienceDirect

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

Extreme role of preferential diffusion in turbulent flame propagation Sheng Yang a, Abhishek Saha a,∗, Wenkai Liang a, Fujia Wu a, Chung K. Law a,b a b

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544-5263, USA Center for Combustion Energy, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 5 June 2017 Revised 17 July 2017 Accepted 25 September 2017

Keywords: Turbulent flame Flammability limit Preferential diffusion

a b s t r a c t In this paper we demonstrate the essential role of molecular diffusion in the structure and propagation of turbulent flames. We first show that mixtures whose concentrations are near or beyond the conventional flammability limits can be rendered to burn strongly in turbulence, provided the controlling molecular mass diffusivity of the mixture exceeds its thermal diffusivity, namely the mixture Lewis number (Le) is less than unity. The associated turbulent flame speeds in such cases can be orders of magnitude greater than the corresponding laminar flame speeds, with distinctive finger-shape structures on the flame surfaces. Furthermore, this facilitation effect is completely flipped for Le > 1 mixtures, leading to actual weakening of the nominally enhancing effect of turbulence on their burning intensity. Mechanistically, such opposite effects are consequences of the coupling between preferential diffusion and the wrinkled laminar flamelets constituting the turbulent flame structure. © 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction The propagation speeds and the associated fuel consumption rates of premixed flames in turbulent environments are of canonical importance in combustion phenomena. In general, based on the fundamental concept advanced by Damköhler [1], it is believed that turbulence enhances the global turbulent flame propagation by increasing the effective heat and mass transport of the mixture, and by increasing the surface area of the embedded laminar flamelets by wrinkling them. Conventionally, the extent of enhancement has been quantified by a normalized turbulent flame speed [2], ST = ST /SL0 , where ST is the turbulent flame speed of a reactive premixture of given composition, temperature and pressure, subjected to a certain turbulence intensity, and SL0 is the propagation speed of the corresponding idealized, steady, adiabatic, planar, laminar flame in a quiescent ambient in the doubly-infinite domain. There have been theoretical [3–7], experimental [8–13] and computational [14–16] studies, as well as review articles [2,17–19] on the determination of ST and its correlation with the turbulence intensity, which can be quantified by the turbulent Reynolds number, ReT = u LI /ν, where u is the turbulence intensity, LI the integral length scale, and ν the kinematic viscosity of the unburned mixture. Recognizing the technological attractiveness of intense burning, and the fundamental

∗

Corresponding author. E-mail address: [email protected] (A. Saha).

interest of understanding the interaction between turbulence and flame propagation so as to answer the question: “How fast can we burn?”, as eloquently posed by Bradley [17], attempts have been made to achieve as large an ST as possible. As of now, among all the different flame configurations and flame speed definitions, the highest ST reported is around 2200 for flame propagation at elevated pressures [13]. We note in passing that because of the voluminous amount of publications in this research area, only representative references are cited herein. Although the effect of aerodynamic stretch on laminar flame propagation through the imbalance of molecular diffusion (commonly referred to as either differential diffusion or preferential diffusion) between heat and the controlling species, represented by the mixture’s Lewis number (Le), is well known [20–22], the role of such preferential diffusion in turbulent flames is sometimes neglected by assuming the dominance of turbulent transport over molecular transport, namely an effective unity Lewis number [2]. The essential role of Le has however been experimentally identified quite early [23], through results on turbulent burning velocities. Some recent experiments with hydrogen as well as hydrocarbon flames [9,13,24–26] have further confirmed the strong influence of molecular diffusion on turbulent flame propagation; Lipatnikov and Chomiak [19] reviewed the subject matter up to 2005. Most of the studies referenced above involved mixtures that are considered to be well within the conventionally defined flammability limits [27–30], characterized by their respective adiabatic flame temperatures. Consequently a more severe, and ambitious, degree of facilitation is to explore situations in which burning can be

https://doi.org/10.1016/j.combustflame.2017.09.036 0010-2180/© 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

enabled for mixtures whose concentrations are near or perhaps even beyond these limits, with the corresponding relatively lower adiabatic flame temperatures. Since the SL0 of such mixtures are necessarily very small, it is reasonable to expect that the corresponding ST can assume quite large magnitudes. In the present study, we report experimental results of extremely facilitated turbulent burning obtained with mixtures whose compositions are near or beyond these limits. We have furthermore identified that the facilitation is due to the coupled effects of Le < 1, molecular preferential diffusion of the mixture and the aerodynamic stretch experienced by the embedded laminar flamelets constituting the turbulent flame ensemble; and that under strong turbulence intensities, these flames exhibit local fingerlike structures and subsequently transform a connected flame element to disjointed flame segments through local extinction. The potential extreme facilitation by turbulence of such weak mixtures not only broadens the experimental and computational conditions in fundamental research, but it also offers opportunities for new operating conditions in practical combustion devices. In addition, we have also demonstrated that, by flipping the nature of preferential diffusion, the coupling for Le > 1 mixtures would instead weaken the nominally enhancing effect of turbulence on flame propagation, leading to slower rates of propagation.

499

(a) Oxidizer Outer Chamber

M-1

Fuel

Fan W

2. Methodology 2.1. Experimental setup The experiments were conducted using a well-vetted, dualchamber, constant-pressure vessel with four orthogonally located fans to generate near homogeneous and isotropic turbulence, whose intensity was calibrated by high-speed Particle Image Velocimetry (PIV), as reported in Ref. [31]. Figure 1 shows the experimental setup. To explore the facilitating effects of preferential diffusion for Le < 1 mixtures, the experiments were conducted using lean mixtures of hydrogen (H2 ) as fuel and oxygen (O2 ) as oxidizer, such that the mass diffusion of the deficient and hence controlling species, H2 , was enhanced because of its high mobility. In addition, carbon dioxide (CO2 ) was used as the inert, bath gas so as to reduce thermal diffusion, and as such further increase the effects of preferential diffusion. Radiation heat loss of the mixture was facilitated through the CO2 dilution, so as to promote flame extinction and demonstrate the facilitation near the flammability limits. The primary experiments were conducted at various turbulence intensities at 10 atm, with equivalence ratio (φ ) of 0.3 and CO2 dilution ratio, defined as CO2 /(CO2 + O2 ) in molar concentrations, of 81.8%, with initial temperature of 298 K. A mixture of mole fraction, H2 : O2 : CO2 = 0.6 : 1 : 4.5, was centrally spark-ignited, with the spark energy about 160 mJ, and the ensuing flame expansion was recorded using high-speed (8500 fps) Schlieren imaging. Additionally, to demonstrate local extinction for weak laminar flames, shadowgraph images were also acquired for their higher sensitivity to the density gradient. In most cases, we used the standard edge detection technique to identify the flame edges and enclosed area (A) from the Schlieren images [12,26,32], while in the case of disjointed flames, we used the Pixel-PDF method, which counts the number of pixels to estimate A from the images. The instantaneous mean  radius, R, was calculated based on the enclosed area, as R = A/π , and the propagation speeds of these turbulent flames were evaluated as the time derivative of the instantaneous mean radius, as ST = dR/dt. Both these methods are detailed in the Supplementary Materials. The flame speeds were evaluated from individual experiments, while multiple experiments were performed to assess the run-to-run variation.

M-3

E

W

High Speed Camera Inner Chamber

High Energy Hg Lamp

M-2

(b)

E

M-4

Fig. 1. Experimental setup: (a) experimental apparatus; (b) schematic configuration.

2.2. Laminar flame computations Laminar flames at 10 atm were computationally simulated using detailed chemistry (NUIG mechanism) [33] and a radiation model for the nonadiabatic cases [34]. We first evaluated the flammability limits and the associated fundamental properties, such as the flame speeds, flame temperatures and flame thicknesses of the unstretched laminar flames under nonadiabatic and adiabatic conditions, using the 1D steady CHEMKIN-PREMIX code. We, then, studied the evolution of the nonadiabatic spherical laminar flames near the flammability limits by using the 1D spherically symmetric code, ASURF [35], with the flame initiated by a centrally located hot kernel of 2500 K and radius of 2 mm. A variety of kernel sizes and temperatures were tested, all of which yielded similar quantitative results. 3. Results 3.1. Evaluation of flammability limits Before presenting the results on the turbulent flames, we evaluate the flammability of lean H2 /O2 /CO2 mixtures at the initial temperature of 298 K and pressure of 10 atm. In order to properly interpret the results reported herein, we first note that since the flammability of a mixture can be influenced by external effects, such as stretch and buoyancy, there exist a number of definitions for the flammability limit. Consequently, we shall explore the three widely-adopted perspectives through which the flammability of a mixture is evaluated. First, we recognize that the fundamental flammability limit of a given fuel-oxidizer system is defined as the concentration limit

500

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

(a)

(b)

2cm (I)

(II) 5ms

(III) 15ms

(c)

(IV) 25ms

50ms

Fig. 2. Laminar results for H2 /O2 /CO2 at φ = 0.3 and P = 10 atm (a) Computational flame speed and temperature for unstretched 1D laminar flame under adiabatic and nonadiabatic conditions for different dilution ratios, CO2 /(CO2 + O2 ). (b) Flame radius, R (red), and maximum heat release rate, HHRmax (black), of expanding laminar flames from simulation for dilution ratios, CO2 /(CO2 + O2 ) = 81.8%. (c) Experimental shadowgraph images of the flame development for dilution ratios, CO2 /(CO2 + O2 ) = 81.8%. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

of the controlling reactant beyond which steady propagation of the idealized, nonadiabatic planar one-dimensional flame in the doubly infinite domain fails, due to the progressive weakening of the chain branching reactions relative to the chain termination reactions, and the omnipresent radiation heat loss [27–30]. Consequently this limit is specific only to the fuel-oxidizer system and as such is independent of any external factors, such as stretch and buoyancy. To evaluate this fundamental flammability limit, Fig. 2(a) shows the downstream planar laminar flame speed, SL0, b , and the maximum flame temperature, Tmax , as functions of the dilution ratio for H2 /O2 /CO2 mixtures at φ = 0.3 and 10 atm. For such a nonadiabatic case (solid lines), it is found that the fundamental flammability limit, indicated by the turning point in Fig. 2(a), is at the dilution ratio of CO2 /(CO2 + O2 )=52.5% with Tmax and SL0, b

of 1580 K and 4.5 cm/s, respectively. Consequently, the dilution ratio employed in the present experiments (81.8%) is far beyond the fundamental flammability limit, and as such a nonadiabatic laminar planar flame does not exist under this condition. We have also calculated the corresponding adiabatic laminar flame speeds, for propagation without radiation heat loss, which would serve as a reference to assess the effect of turbulence on flame propagation through the scaled turbulent flame speed, ST . The dash lines in Fig. 2(a) show that at the dilution ratio of 81.8%, the adiabatic flame temperature and the downstream flame speed are 856 K and 0.002 cm/s, respectively. Second, recognizing that the positive stretch experienced by an expanding flame can also strengthen the burning intensities of the present Le < 1 mixtures [27], whose hydrogen-dominated Lewis number is estimated as Le = LeH2 ≈ 0.23, nonadiabatic expanding flames in quiescence were simulated to further test the flammability of the mixture (H2 /O2 /CO2 , φ = 0.3, CO2 /(CO2 + O2 )=81.8%). Figure 2(b) shows the development of the maximum heat release rate, HHRmax , and flame radius, R, defined as the radial location of HHRmax subsequent to ignition. It is seen that R decreases after progressing for about 0.4 mm, with the time history of the heat release rate showing that the amount of the heat release at the maximum flame radius is orders of magnitude smaller than the initial heat release. Consequently, the flame can be considered to be extinguished at such a small radius, indicating that the mixture is nonflammable even with the enhancing curvature effect through preferential diffusion. Third, while the present mixture is clearly beyond the fundamental flammability limit, the assessment does not account for buoyancy. We have therefore also performed (laminar) flame experiments for the same mixture in quiescence, which are obviously subjected to the omnipresent buoyancy force owing to very weak propagation speed. The high-speed experimental shadowgraph images of these laminar nonadiabatic expanding flames are shown in Fig. 2(c). Since shadowgraph and Schlieren images respectively capture the second and first spatial derivatives of density, the former is more sensitive to the spatial variation and as such was adopted to demonstrate the evolution of the weakly burning flame. From the images in Fig. 2(c), it is seen that sharp edges (representing sharp temperature gradient) are initially formed due to the large ignition energy, followed by a brief period of propagation in the radial direction due to the strong curvature/stretch effect, which is also captured in the simulation. Subsequently, the entire burned gas pocket moves upward due to buoyancy (Fig. 2(c)(IV)). It is then seen that at this stage the bottom segment of the “gaspocket” quickly becomes blurred, indicating the absence of density gradient and therefore the occurrence of flame extinction, while the top edges still remain sharp. This result therefore suggests that a laminar flame segment for this mixture can be sustained with the assistance of (upward) buoyancy. The effect of buoyancy on weakly propagating flames and thus flammability limits is of course well recognized [28], and consequently two separate limits, upward and downward, have been reported for measurements using the standard flammability tube [36]. As buoyancy facilitates upward propagation and restricts downward propagation, the former limit corresponds to a weaker mixture than the latter [36]. It is also important to recognize that neither of these limits are absolute as they depend on the experimental setup and the intensity of buoyancy (as well as any accelerative body force), while the buoyancy-free, fundamental limit is independent of these external effects. From the simulation and the experiments with laminar flames we can therefore infer that the chosen mixture is certainly substantially beyond the fundamental flammability limit, while buoyancy could assist in the sustenance of some local flame segments for the global flame propagation in quiescence. Regardless, it is

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

t (ms): 3.53

7.06

10.59

501

14.12

fan speed 1500rpm

(a)

3000rpm

(b)

5100rpm

(c)

(a)

Fig. 3. Sequential Schlieren images of flame development with the mixture of H2 /O2 /CO2 at φ = 0.3, CO2 /(CO2 + O2 ) = 81.8%, P = 10 atm, with different fan speeds (turbulent intensities); The central black areas are the locations of the flame fronts. The size of each view is 8 cm × 8 cm.

evident that the mixture is extremely weak, as its adiabatic flame temperature is merely 856 K. In fact, we have found that further increase in dilution would render spark ignition impossible in the experiments. 3.2. Extreme facilitation in turbulence for mixtures with Le < 1 After establishing that the present mixture is very weak and beyond the fundamental flammability limit, we now present the experimentally observed flame response in the presence of turbulence. Figure 3 shows the Schlieren images of the flame development under various fan speeds and hence turbulence intensities. Panels (a) to (c) are turbulent flames with increasing turbulence intensity, with (a) and (b) showing successful and robust propagation of turbulent flames, while (c) showing weakened burning with the occurrence of local extinction. In Fig. 4(a), we plot the turbulent flame speed (ST ) and its normalized value (ST ) for various fan speeds, from 900 to 3900 rpm. The results show turbulent flame speeds of 53–298 cm/s. As a comparison, the (downstream, nonadiabatic) laminar flame speed of the similar mixture (same φ , less dilution) at the fundamental flammability limit and the same pressure is merely 4.5 cm/s (Fig. 2(a)), which is one to two orders smaller than the present measured turbulent flame speeds. Considering the nonflammable nature of the mixture in quiescent environments, the facilitating role of turbulence in augmenting its burning is evident. As an alternate appraisal, by taking the computed propagation speed of about 2 × 10−3 cm/s for the adiabatic laminar planar flame of this mixture, which is obviously unrealistic and unattainable in the presence of heat loss, the enhanced mass burning rates by turbulence yields an (exaggerated) augmentation factor of 105 . The above result on the enhancement by turbulence can be explained by the influence of preferential diffusion on the local flamelets constituting the turbulent flame brush. Specifically, it is well established that the propagation speed of a laminar flame (both nonadiabatic and adiabatic) under aerodynamic stretch, SL , is modified from its unstretched value, SL0 , through the relation [27],

S2 lnS2 = −α K,

(1)

where S is the local, stretched flame speed (SL ) scaled by its laminar unstretched flame speed (SL0 ), K the stretch rate scaled by the laminar flame time, and α the Markstein number, which quantifies the sensitivity of the flame propagation speed to stretch, and can

(b)

Fig. 4. Experimental turbulent flame speeds with the mixture of H2 /O2 /CO2 at φ = 0.3, CO2 /(CO2 + O2 ) = 81.8%, P = 10 atm, with different fan speeds (turbulent intensities): (a) Turbulent flame speeds ST = dR/dt and ST = ST /SL0,b as they grow under different fan speeds (turbulent intensities) and radii; (b) Maximum turbulent flame speeds (ST )max and (ST )max observed with different fan speeds and ReT . Error bar shows run to run variation; Open circles indicate the flames with large local extinctions.

be approximately expressed as,

  α ≈ −Ze Le−1 − 1 .

(2)

Here Ze = Ea (Tb − Tu )/RTb2 is the Zel’dovich number, R the universal gas constant, and Tb and Tu the burned and unburned gas temperatures, respectively. Eq. (1) shows that the response of S depends on the sign of α K. As a result, since Ze > 0, the local flame propagation is promoted (S > 1) for α K < 0, implying either (Le < 1, K > 0) or (Le > 1, K < 0). Consequently, the observed enhancement can be explained through the combined effects of preferential diffusion, represented by Le, and flame stretch through turbulence, which wrinkles the laminar flamelets within the turbulent flame brush through the multi-scale eddies, and generates a collection of both positively and negatively stretched flamelets. Subsequently, for the present Le < 1 mixture, while propagation of the negatively stretched (K < 0) flame segments is retarded or even inhibited, the positively stretched segments (K > 0) are rendered to burn stronger and in the process will col l ectivel y assist the flame to propagate at higher overall flame speeds. Furthermore, since typical leading segments of the flamelet with positive curvature and hence positive stretch propagate faster than the trailing segments with negative curvature, the local flamelets become more curved leading to stronger stretch effects. Such a positive feedback between preferential diffusion and curvature/stretch sustains the burning of

502

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

Finger-like Structure and Subsequent Local Extinction

burned

unburned

higher T, SL unburned burned

high T, SL

low T, SL

(c) higher T, SL unburned

2.94

(d) high T, SL burned

(b)

2.35

unburned extinction

burned

(a)

1.76

burned

t (ms): 1.18

Fig. 5. Evolution of the local flame-front with Le < 1. Top row is sequential Schlieren images (background subtracted and intensity inverted) of local flame development for H2 /O2 /CO2 (φ = 0.3, CO2 /(CO2 + O2 ) = 81.8% and P = 10 atm) with high fan speeds (30 0 0 rpm, ReT = 680 0). Gray areas are the locations of flame fronts. Bottom row is the schematic configuration of the corresponding flame-front development of the finger-like structure. The black lines are flame-fronts separating unburned and burned sides and the arrows represent flame propagation. The size of the view is zoomed to be 1 cm × 1 cm.

rence of such finger elements and local extinction proliferate, as shown in Fig. 3(c). Such local behaviors of the flamelets are reflected by the global turbulent flame speeds, which integrate the propagation of the constituting local flamelets. Furthermore, while we have demonstrated and explained the facilitating effect of preferential diffusion in turbulence, it is reasonable to expect that this facilitating effect would eventually attenuate as the turbulence intensity continuously increases, with the progressive occurrence of frequent local extinction. As noted in Fig. 4(a), the increase in the flame speed with increasing fan speed ceases beyond 30 0 0 rpm. Also, owing to the frequent local extinction, the flame speed at 3900 rpm (black open circles) shows large fluctuations. To clarify the effect of turbulence intensity, the maximum turbulent flame speeds are plotted in Fig. 4(b). The nonmonotonic trend further demonstrates that with increasing turbulence intensity or ReT , burning becomes stronger (shown by filled circles in Fig. 4(b)) until local extinction starts to occur frequently, hence reducing the overall burning rate and thus the flame speed (shown by open circles in Fig. 4(b)). It is also noted that since extinction is random and intermittent in nature, especially for these cases with high turbulence intensities, large run-to-run variations (shown with error bars in Fig. 4(b)) were observed. Similar behavior has also been reported with flames under different conditions [26,41–45]. 3.3. Moderated burning for mixtures with Le > 1

positively curved/stretched flamelets and therefore causes the robust propagation of the entire flame. Similar effects for strongly burning flames have been reported and verified with laser diagnostics [37]. The above interpretation, based on Eqs. (1) and (2) derived for weakly stretched flames, also carries over to strongly stretched flames through the concept of flame balls [38], whose radii of curvature are of the order of the flame thicknesses. In particular, it has been shown through theories and simulations of laminar flames that there exists a range of positive curvature for which the flames can sustain their burning with finite propagation speeds, beyond the flammability limits, due to the effect of preferential diffusion (Le < 1), even under strong radiation heat loss [39,40]. Furthermore, it has been reported that these positively curved flamelets can also survive under strong flow straining in intense turbulent environments [19]. These two complementary interpretations, applicable for weak and strong limits of stretch, are self-consistent, demonstrating the importance of the propagation of the positively curved flamelets in Le < 1 mixtures in facilitating the propagation of the global flame. In addition to the facilitating effect on turbulent flame speeds through the coupling between the Le < 1 preferential diffusion and local curvature/stretch, the coupling also leads to the evolution of distinctive finger-like structures appearing on the flame-fronts, as shown in Fig. 5. Mechanistically, the local straining of the flame surface through turbulent eddies initially generates the outwardly convex surface element with positively curved tip, as shown in Fig. 5(a). Due to preferential diffusion, the tip segment of positive curvature/stretch burns stronger and propagates faster as compared to the neighboring segments, forming finger-like flame elements shown in Fig. 5(b). With these finger flamelets being elongated, local positive curvatures as well as stretch rates of the tip segments increase, triggering even stronger effects of preferential diffusion. Such positive feedback, thus, asserts further acceleration to the tip segment with positive curvature. On the other hand, the neck region of the finger with almost zero curvature is subjected to less preferential diffusion effect, and thus burns weaker, as shown in Fig. 5(c). Eventually, the weak burning at the neck may extinguish through local straining, leading to disconnected flame segments in Fig. 5(d). With increasing turbulence intensity, the occur-

To further scrutinize the above results, we next examine the response of (Le > 1) mixtures with flipped preferential diffusion influences, accomplished by working with rich mixtures of H2 , O2 and helium (He) such that the controlling reactant is the less mobile O2 , while the thermal diffusivity is boosted by using the more mobile He instead of CO2 as the inert bath gas. By flipping the enhancing effect of turbulence observed above, not only turbulence is not expected to enhance burning of the Le > 1 mixtures, but it is also reasonable to expect that the burning intensity could actually be reduced from values obtained by considering the generally enhancing effect of turbulence alone. We demonstrate such moderating effect for the rich H2 /O2 /He mixture of φ = 3.0, He/(He + O2 ) = 90.9% and P = 10 atm and initial temperature of 298 K, whose Le = LeO2 = 2.24 > 1 and the calculated adiabatic Tad is 1485 K and SL0, b is 3.2 m/s. It is noted that this mixture is within the fundamental flammability limit, and that further increase of dilution renders ignition impossible. Figure 6(a) shows the Schlieren images of the development of such flames at 10 atm and 30 0 0 rpm. It is found that the flame morphology is quite different from that of the lean cases. Specifically, even though the pressure is still 10 atm, the flame surface shows fewer fine structures such that the flame area in Fig. 6(a) is not totally dark. However, besides the case with local extinctions in Fig. 3(c), the flame areas for the cases with Le < 1 in Fig. 3(a) and (b) are dark, covered by pervasive wrinkles on the flame surface. Moreover, finger flamelets are not observed anymore for these cases. The Schlieren images were further processed to obtain the propagation speeds of the turbulent flames with Le > 1 mixtures, in Fig. 6(b) and (c). It is first noted that with increasing turbulence intensity, the maximum flame speed marginally increases. The experimentally achieved maximum turbulent flame speed reaches up to 4.5 m/s, with ST max being only about 1.5. This limited enhancement of the flame speed is therefore consistent with the role of preferential diffusion in turbulence. Specifically, as the mixture Lewis number (Le) flips from sub-unity ( < 1) to super-unity ( > 1), the response of the flamelets to stretch also reverses such that the leading segments of the flamelets with positive curvature (K > 0) burn weaker and may extinguish with strong curvature/stretch,

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

t (ms): 3.53

7.06

10.59

14.12

(a)

(b)

503

4. Conclusions In summary, the present study has identified the following understanding on the role of preferential diffusion on the structure and propagation of turbulent flames. First, we have demonstrated that molecular diffusion can actually assert leading-order effects and consequently lead to qualitatively opposite trends when the relative preferential diffusion of heat and mass reverses. Second, the significance of such effects has been prominently identified by the substantial facilitation of the flame speeds with Le < 1 mixtures near or beyond the flammability limits in the presence of turbulence; recognizing nevertheless that the assessment of flammability limits depends on the specific reference—whether fundamental or assisted/retarded through flame curvature and buoyancy effects. The presence of the finger-like structure on flame-fronts and their subsequent extinction offer fresh insight into the fine structure of the Le < 1, turbulence-enhanced flames. Furthermore, the study has also demonstrated that the enhancement effect for Le < 1 mixtures is reversed by flipping the controlling Lewis numbers to Le > 1, in that the turbulent flame speeds can be actually closer to the corresponding laminar flame speeds, without much nominally expected augmentation of the flame speeds due to turbulence. This result is therefore contrary to the notion that turbulence always substantially promotes flame propagation because of the corresponding increase in the flame surface area and mixing, and hence provides further evidence of the essential role of molecular diffusion on the structure and propagation of turbulent flames. The need to consider molecular diffusion in the study of turbulent flames is therefore clearly demonstrated, with the concomitant recognition of the potential of extreme facilitation of the burning of Le < 1 limit mixtures. Acknowledgment This work was supported by the US National Science Foundation (CBET, grant no. 1510142). Supplementary material

(c)

Supplementary material associated with this article can be found, in the online version, at 10.1016/j.combustflame.2017.09.036 References

Fig. 6. Turbulent flames with the mixture of H2 /O2 /He at φ = 3.0, He/(He + O2 ) = 90.9%, P = 10 atm. (a) Sequential Schlieren images of flame development with fan speeds 30 0 0 rpm; The central black areas are the locations of the flame fronts. The size of each view is 8 cm × 8 cm. (b) Turbulent flame speeds ST = dR/dt and ST = ST /SL0,b as they grow under different fan speeds (turbulent intensities) and radii; (c) Maximum turbulent flame speeds (ST )max and (ST )max observed with different fan speeds and ReT . Error bar shows run to run variation.

while the trailing segments with negative curvature (K < 0) burn stronger. Then, the strongly burning, trailing segments catch up with the weakly burning, leading segments, and subsequently render the flamelet smoother and reduce the effect of preferential diffusion. Consequently, with the reversal of Le, such negative feedback between preferential diffusion and curvature not only inhibits propagation of the leading flame segments and hence the occurrence of figure-like structures as shown in Fig. 6(a), but it actually also moderates the augmentation of global burning through turbulence.

[1] G. Damköhler, Der einfluss der turbulenz auf die flammengeschwindigkeit in gasgemischen, Ber. Bunsen. phys. Chem. 46 (11) (1940) 601–626. [2] N. Peters, Turbulent combustion, Cambridge University Press, 20 0 0. [3] S.B. Pope, PDF methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11 (2) (1985) 119–192. [4] 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) 2728–2731, doi:10.1103/PhysRevA.37.2728. [5] K.N.C. Bray, Studies of the turbulent burning velocity, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 431 (1882) (1990) 315–335. [6] G.I. Sivashinsky, Cascade-renormalization theory of turbulent flame speed, Combust. Sci. Technol. 62 (1–3) (1988) 77–96. [7] N. Peters, The turbulent burning velocity for large-scale and small-scale turbulence, J. Fluid Mech. 384 (1999) 107–132. [8] R. Abdel-Gayed, D. Bradley, M. Lawes, Turbulent burning velocities: a general correlation in terms of straining rates, Proc. R. Soc. A 414 (1847) (1987) 389–413. [9] H. Kido, M. Nakahara, K. Nakashima, J. Hashimoto, Influence of local flame displacement velocity on turbulent burning velocity, Proc. Combust. Inst. 29 (2) (2002) 1855–1861. [10] 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 (1) (2005) 1–21. [11] 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 (1) (2005) 827–834. [12] S. Chaudhuri, F. Wu, D. Zhu, C.K. Law, Flame speed and self-similar propagation of expanding turbulent premixed flames, Phys. Rev. Lett. 108 (4) (2012) 044503.

504

S. Yang et al. / Combustion and Flame 188 (2018) 498–504

[13] P. Venkateswaran, A.D. Marshall, J.M. Seitzman, T.C. Lieuwen, Turbulent consumption speeds of high hydrogen content fuels from 1–20 atm, J. Eng. Gas Turbines Power 136 (1) (2014) 011504. [14] J.H. Chen, H.G. Im, Correlation of flame speed with stretch in turbulent premixed methane/air flames, Symp. (Int.) Combust. 27 (1) (1998) 819–826. [15] J.B. Bell, M.S. Day, I.G. Shepherd, M.R. Johnson, R.K. Cheng, J.F. Grcar, V.E. Beckner, M.J. Lijewski, Numerical simulation of a laboratory-scale turbulent v-flame, Proc. Natl. Acad. Sci. USA 102 (29) (2005) 10 0 06–10 011. [16] F. Creta, M. Matalon, Propagation of wrinkled turbulent flames in the context of hydrodynamic theory, J. Fluid Mech. 680 (2011) 225–264. [17] D. Bradley, How fast can we burn? Proc. Combust. Inst. 24 (1) (1992) 247–262. https://doi.org/10.1016/S0 082-0784(06)80 034-2 [18] J.F. Driscoll, Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities, Prog. Energy Combust. Sci. 34 (1) (2008) 91–134. [19] A. Lipatnikov, J. Chomiak, Molecular transport effects on turbulent flame propagation and structure, Prog. Energy Combust. Sci. 31 (1) (2005) 1–73. [20] M. Matalon, B.J. Matkowsky, Flames as gasdynamic discontinuities, J. Fluid Mech. 124 (1982) 239–259. [21] P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Prog. Energy Combust. Sci. 11 (1) (1985) 1–59. [22] C.K. Law, C.J. Sung, Structure, aerodynamics, and geometry of premixed flamelets, Prog. Energy Combust. Sci. 26 (4) (20 0 0) 459–505. [23] K. Wohl, L. Shore, H. Von Rosenberg, C. Weil, The burning velocity of turbulent flames, Proc. Combust. Inst. 4 (1) (1953) 620–635. [24] 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 (1) (2013) 1519–1526. [25] S. Chaudhuri, F. Wu, C.K. Law, Scaling of turbulent flame speed for expanding flames with Markstein diffusion considerations, Phys. Rev. E 88 (3) (2013) 033005. [26] F. Wu, A. Saha, S. Chaudhuri, C.K. Law, Propagation speeds of expanding turbulent flames of C4 to C8 n-alkanes at elevated pressures: experimental determination, fuel similarity, and stretch-affected local extinction, Proc. Combust. Inst. 35 (2) (2015) 1501–1508. [27] C.K. Law, Combustion physics, Cambridge University Press, 2006. [28] D.B. Spalding, A theory of inflammability limits and flame-quenching, Proc. R. Soc. A 240 (1220) (1957) 83–100, doi:10.1098/rspa.1957.0068. [29] C.K. Law, F.N. Egolfopoulos, A unified chain-thermal theory of fundamental flammability limits, Proc. Combust. Inst. 24 (1) (1992) 137–144. [30] M.N. Bui-Pham, J.A. Miller, Rich methane/air flames: burning velocities, extinction limits, and flammability limit, Symp. (Int.) Combust. 25 (1) (1994) 1309– 1315. https://doi.org/10.1016/S0082-0784(06)80772-1

[31] S. Chaudhuri, A. Saha, C.K. Law, On flame turbulence interaction in constantpressure expanding flames, Proc. Combust. Inst. 35 (2) (2015) 1331–1339. https://doi.org/10.1016/j.proci.2014.07.038 [32] S. Yang, A. Saha, F. Wu, C.K. Law, Morphology and self-acceleration of expanding laminar flames with flame-front cellular instabilities, Combust. Flame 171 (2016) 112–118. [33] A. Kromns, W.K. Metcalfe, K.A. Heufer, N. Donohoe, A.K. Das, C.-J. Sung, J. Herzler, C. Naumann, P. Griebel, O. Mathieu, M.C. Krejci, E.L. Petersen, W.J. Pitz, H.J. Curran, An experimental and detailed chemical kinetic modeling study of hydrogen and syngas mixture oxidation at elevated pressures, Combust. Flame 160 (6) (2013) 995–1011. https://doi.org/10.1016/j.combustflame.2013.01.001 [34] Y. Ju, H. Guo, F. Liu, K. Maruta, Effects of the Lewis number and radiative heat loss on the bifurcation and extinction of CH4 /O2 –N2 –He flames, J. Fluid Mech. 379 (1999) 165–190. [35] W. Liang, F. Wu, C.K. Law, Extrapolation of laminar flame speeds from stretched flames: Role of finite flame thickness, Proc. Combust. Inst. 36 (1) (2017) 1137–1143. [36] L. Lovachev, V. Babkin, V. Bunev, A. V’Yun, V. Krivulin, A. Baratov, Flammability limits: an invited review, Combust. Flame 20 (2) (1973) 259–289. https://doi. org/10.1016/S0010-2180(73)80180-4 [37] M. Haq, C. Sheppard, R. Woolley, D. Greenhalgh, R. Lockett, Wrinkling and curvature of laminar and turbulent premixed flames, Combust. Flame 131 (1) (2002) 1–15. [38] Y.B. Zeldovich, G.A. Barenblatt, V.B. Librovich, D.V. Makhviladze, Mathematical theory of combustion and explosions, 1985. [39] J. Buckmaster, G. Joulin, P. Ronney, The structure and stability of nonadiabatic flame balls, Combust. Flame 79 (3–4) (1990) 381–392. [40] Z. Chen, Y. Ju, Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame, Combust. Theory Model. 11 (3) (2007) 427–453. [41] V. Karpov, A. Lipatnikov, V. Zimont, A test of an engineering model of premixed turbulent combustion, Symp. (Int.) Combust. 26 (1) (1996) 249–257. https://doi.org/10.1016/S0082- 0784(96)80223- 2 [42] V. Karpov, E. Severin, Effects of molecular-transport coefficients on the rate of turbulent combustion, Combust. Explosion Shock Waves 16 (1) (1980) 41–46. [43] M. Nakahara, H. Kido, A study of the premixed turbulent combustion mechanism taking the preferential diffusion effect into consideration, Mem. Faculty Eng. Kyushu Univ. 58 (2) (1998) 55–82. [44] 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 (4) (2003) 415–430. [45] A. Aspden, M. Day, J. Bell, Turbulence–flame interactions in lean premixed hydrogen: transition to the distributed burning regime, J. Fluid Mech. 680 (2011) 287–320.