Numerical study on dynamics of local flame elements in

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Numerical study on dynamics of local flameelements in turbulent jet premixed flamesTo cite this article K Yamayaki et al 2010 IOP Conf Ser Mater Sci Eng 10 012032

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Numerical Study on Dynamics of Local Flame Elements in Turbulent Jet Premixed Flames

K Yamayaki1 Y-S Shim1 N Fukushima 1 M Shimura1 M Tanahashi1 and T Miyauchi1 1Department of Mechanical and Aerospace Engineering Tokyo Institute of Technology Meguro-ku Tokyo 152-8550 Japan

kyamawaknaviermestitechacjp

Abstract Direct numerical simulations (DNSs) of turbulent jet premixed flames have been conducted to investigate dynamics of local flame elements Behaviors of turbulent jet flames are discussed by considering characteristics of local flame elements such as flame displacement speed local turbulent burning velocity curvature and tangential strain rate The peak of probability density function (pdf) of the local turbulent burning velocity locates at laminar burning velocity whereas the maximum turbulent burning velocity reaches to about 5 times laminar one and the minimum burning velocity is negative The result indicates that dynamics of turbulent flame cannot be explained by the flamelet concept The concept of flame stretch is evaluated by growth rate of the flame area which is a function of flame displacement speed flame curvature and tangential strain rate In the concept of flame stretch the time-averaged growth rate must be zero because flame front should stay in a certain area statistically However in DNS the mean growth rate is not zero which suggests that flame does not exist as a statistically steady state The present results indicate a possibility of the existence of flame elements which cannot be explained by the flamelet concept and the concept of flame stretch

1 Introduction The turbulent combustion model has significant effects on accuracy of numerical prediction of combustors Recently many approaches [1-6] have been attempted to develop high accuracy turbulent combustion model and these developed models are validated by using results of numerical simulation or experiment As for modeling of turbulent premixed flames the description of dynamics of flame front has been one of the most important subjects in the turbulent combustion research since that is the basis of turbulent combustion models in the flamelet concept in which local burning velocity is not so far from laminar burning velocity In the concept of the flame stretch increasing rate of the flame area is expressed by flame displacement speed flame curvature and tangential strain rate at the flame front [37]

The effects of the strain rate have been discussed based on the Markstein number [48] In the previous studies [910] the curvature and strain rate effects have been investigated in the steady or unsteady laminar flames because the flame elements in turbulent flames are assumed to be laminar flame under weak stretch with small curvature To confirm the theory of the flame stretch experimentally measurements of the flame displacement speed in turbulent premixed flames are required In general shadowgraph or laser tomography has been adopted to estimate flame displacement [1011] However in these studies flame propagation normal to the flame front is

WCCMAPCOM 2010 IOP PublishingIOP Conf Series Materials Science and Engineering 10 (2010) 012032 doi1010881757-899X101012032

ccopy 2010 Published under licence by IOP Publishing Ltd 1

Table 1 Numerical parameters for DNS

φ Reλ Rel urmsSL lδF lδL Case 1 10 538 1282 155 827 154 Case 2 10 1180 3861 333 1157 216 Case 3 06 538 1282 197 650 145 Case 4 06 1180 3861 424 911 203

01

1

101

102

103

01 1 101 102 103 104

urm

s S L

lδF

broken reaction zones

corrugated flamelets

wrinkled flamelets

thin reaction zones Ka = 1

Kaδ = 1Case 1

Case 4Case 3Case 2

Figure 1 Turbulent combustion diagram

assumed In turbulent flames the flame elements do not always move into the flame normal direction due to strong convection effects of turbulence Planar laser induced fluorescence (PLIF) [1213] of molecules and radicals produced in chemical reactions such as OH [14] CO [15] CH [16-18] and CH2O [19] has been commonly used to investigate turbulent flame structures experimentally Although the conventional PLIF measurement has been a very powerful tool to obtain instantaneous local flame structures investigation of dynamics of flame structures in turbulence has been difficult due to the limitation of time resolution Recently several time-resolved PLIF measurements have been reported [20-26] In our previous study [27] CH double-pulsed PLIF measurement has been developed to estimate local flame displacement speed in turbulent premixed flame However these experimental techniques are required to be more sophisticated and to be applied for lots of combustion conditions

Direct numerical simulation (DNS) with detailed kinetic mechanism is the most precise computational method Hence DNS has been conducted to understand the physics of turbulent combustion and to develop high-accuracy turbulent combustion models In the numerical investigations by DNS [28-33] fuel consumption speed or local heat release rate is commonly used to represent characteristics of flamelet instead of the flame displacement speed However they do not always coincide with the flame displacement speed In this study two-dimensional DNS of turbulent jet premixed flames has been conducted to investigate dynamics of local flame elements Behaviors of turbulent jet flames are discussed by considering flame displacement speed local burning velocity curvature and tangential strain rate

2 DNS of hydrogen-air turbulent jet premixed flame In this study two-dimensional DNS of turbulent jet premixed flame which is based on conservation equations of mass momentum energy and species has been conducted The DNS code developed in our previous study [3134] has been modified for turbulent jet premixed flame Details of the governing equations have been shown by our previous study [35] In this study Soret effect Dufour


2

Figure 2 Distributions of heat release rate for cases 1(a) 2(b) 3(c) and 4(d)

effect pressure gradient diffusion bulk viscosity and radiative heat transfer are assumed to be negligible The detailed kinetic mechanism which includes 27 elementary reactions and 12 reactive species (H2 O2 H2O O H OH HO2 H2O2 N2 N NO2 and NO) is used to represent hydrogen-air reaction in turbulence The detailed kinetic mechanism has been picked up from Miller and Bowman [36] Smooke and Giovangigli [37] and Kee et al [38] The temperature dependence of the viscosity the thermal conductivity and the diffusion coefficients are considered by linking Chemkin II packages with several modifications for vector and parallel computations

The governing equations are discretized by the 4th-order finite difference scheme in all directions To eliminate high frequency oscillations higher than spatial resolution of finite difference scheme the 4th-order compact finite difference filter [39] is applied in all directions Time integration is conducted by the 3rd-order Runge-Kutta scheme The boundary condition in all directions is Navier-Stokes characteristic boundary condition (NSCBC) [4041]

Numerical parameters for DNS are presented in table 1 In this table φ urms SL l and δF denote equivalence ratio turbulent intensity laminar burning velocity integral length and laminar flame thickness respectively Reynolds numbers based on Taylor micro-scale of initial and inflow turbulence are set to 538 and 1180 Computational domains are selected to be 20 mm times 20 mm and 769 times 769 grid points are used The slot width is 5mm A hydrogen-air mixture in unburnt side is set to φ = 06 and 10 at 01 MPa and 700K The inflow velocities of unburnt gas are 100 ms in cases 1 and 3 and 200 ms in cases 2 and 4 respectively The inflow velocities of burnt gas are 10 ms in all cases As for inflow boundary condition a homogeneous isotropic turbulence by the preliminary DNS with spectral method is superimposed on uniform flow Figure 1 shows the location of the numerical conditions on the turbulent combustion diagram [4] In this study all cases are classified in the corrugated flamelets

(a) (b)

A

(c) (d)

C

B

high

low


3

Figure 3 Distributions of mole fraction of H atom O atom and OH radical for case 1(a) and case 3(b)

3 Dynamics of local flame element Figure 2 shows instantaneous distributions of heat release rate for different Reynolds numbers and equivalence ratios Here a part of the computation domain is visualized Figures 2(a) and (b) show the cases for φ = 10 As shown in our previous study [32] the flame which is convex towards the burnt side tends to show high heat-release rate Along the flame fronts the heat release rates are fluctuating highly due to the turbulence motion of unburnt gas The fluctuations of heat release rate in high Reynolds number are larger than those in low Reynolds number The significantly wrinkled flames convex towards the burnt side appear in both cases and cusp structures appear These cusp structures of the flame move towards the burnt side and then the unburnt mixture islands appear behind the flame front as shown in figures 2(a) and (b) These unburnt mixtures seem to be isolated in the burnt gas and burn out rapidly In case 2 the area of the unburnt mixture island is smaller than that of case 1 due to the high fluctuations of flame front in high Reynolds number and the unburnt mixture islands are frequently created as shown by arrow B in figure 2(b) Figures 2(c) and (d) show the cases for φ = 06 The flame which is convex towards the burnt side tends to show high heat-release rate similar to the cases for φ = 10 However the heat-release rate is distributed lower than that of the cases for φ = 10 The flame area increases and reaches to further downstream region The region C in figure 2(c) shows the cusp of the flame just before the formation of the unburnt mixture island This cusp of the flame moves towards the burnt side and then the unburnt mixture island is formed behind the flame front after 20 μs (not shown here) The formation of unburnt mixture island in the case for φ = 06 requires

XH XO XOH

XH XO XOH

(a)

(b)

high

low


4

Figure 4 Distributions of reaction rate of R6 and mole fraction of HO2 for case 1

Figure 5 Dynamics of flame fronts (black 1st and red 2nd) longer time than that in the cases for φ = 10 due to lower laminar burning velocity In the cases for φ = 06 the unburnt mixture islands appear rarely compared to the cases for φ = 10 and the flame front shows complicated structures due to the turbulence and vortex motions

Figure 3 shows instantaneous distribution of H and O mole fractions and OH radical for cases 1 and 3 In case 1 the distributions of H and OH mole fractions seem to be relatively uniform along flame front This result is similar to the results obtained in DNS of hydrogen-air planar turbulent premixed flame reported by our previous study [32] The O mole fraction tends to increase behind flame with high heat release rate and forms elongated structures compared to those of planar hydrogen-air turbulent premixed flames In case 3 the distribution of H mole fraction seems to be relatively uniform along the flame front like as case 1 However the H mole fraction tends to be high behind flame convex towards the unburnt side compared to the case 1 The O mole fraction tends to be high behind flame front but it cannot show the elongated structure like as that in case 1 The distribution of O mole fraction seems to be relatively uniform along the flame front whereas the OH mole fraction tends to be high near the flame front and its structure is very complicate The equivalence ratio has effects on flame curvature and tangential strain rate at the flame front Therefore the flame structure can be changed by equivalence ratio

Figure 4 show instantaneous distributions of reaction rate of R6 and mole fraction of HO2 for case 1

ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4

Figure 6 Probability density function (pdf) of local burning velocity

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2

Figure 7 Correlation diagram between tangential strain rate at and kSLl and time average (red line)

R6 H + O2 + M hArr HO2 + M

The temperature of unburnt mixture island behind the flame front as shown by circle in figure 4 increases due to the heat conduction from surrounding burnt gas with high temperature This means that the temperature of the unburnt mixture behind flame front increases due to the heat conduction from surrounding burnt gas This temperature rise causes enhancement of the reaction of R6 Therefore the mole fraction of HO2 tends to show high concentration in the unburnt mixture island which results in enhancement of the turbulent burning velocity

To investigate local burning velocity the flame displacement speed and fluid velocity have been required because the local burning velocity is determined by the difference between flame displacement speed and fluid velocity In this study the flame displacement speed is evaluated by applying the cross-correlation method to a pair of distributions of flame fronts and the fluid velocity in unburnt region close to the flame front is identified as convection velocity of the flame front Figure 5 shows temporal development of the flame front of case 2 The flame front can be determined as the plane where heat release rate shows the peak value Black and red lines correspond to the flame fronts of the 1st and the 2nd images respectively In DNS the temporal development of flame front can be


6

investigated exactly Therefore the local burning velocity can be determined preciously by DNS with the method which has been developed in our previous study [27]

Figure 6 shows probability density function (pdf) of the local turbulent burning velocity In the flamelet concept local turbulent burning velocity is not so far from laminar burning velocity The peak of the pdf locates at laminar burning velocity whereas variance of the local burning velocity is relatively large The maximum burning velocity reaches to about 5 times laminar burning velocity and the minimum one is negative velocity Negative local burning velocity which means flame propagation toward unburnt side might be caused by following reasons In enormously strong turbulent field the time scale of fluid is very short compared to the laminar flame time scale In such strong turbulent field fluid flow often changes before fluid velocity is reflected to dynamics of flame front (or combustion chemistry) Therefore there is a possibility that the dynamics of turbulent flame cannot be explained by the flamelet concept

In the concept of flame stretch growth rate of the flame area (A) is written as

lLt kSatA

A dd1

minus= (1)

where SLl k and at denote flame displacement speed flame curvature and tangential strain rate respectively It should be noted that SLl in equation (1) is local burning velocity of each flame element In this study since the measured local burning velocity has large variance each flame element is assumed to have laminar burning velocity Figure 7 shows a correlation diagram between two-dimensional tangential strain rate (at) and kSLl in cases 1 and 2 Ensemble averages of the two values are denoted by red lines In the concept of flame stretch since flame front should stay in a certain area statistically ensemble average of the right hand side of equation (1) should be zero Figure 7 shows that ensemble average of kSLl is zero whereas the time average of tangential strain rate is around 20times105 and 34times105 in cases 1 and 2 respectively This result suggests that flame does not exist as a statistically steady state Therefore conventional description for the growth rate of flame area (equation (1)) might be modified It should be noted that the assumption of SLl = SL does not change this result significantly because the curvature is instantaneous property However both of the curvature and the tangential strain rate might be modified by the two dimensional effects To investigate these effects further complicated simultaneous measurements and simulations will be required in future works

4 Conclusions In this study DNSs of turbulent jet premixed flames have been conducted to investigate dynamics of local flame elements Behaviors of turbulent jet flames were discussed by considering characteristics of local flame elements such as flame displacement speed local burning velocity curvature and tangential strain rate

The flame which is convex towards the burnt side tends to show a high heat-release rate The largely wrinkled flame convex towards the burnt side appears and then the unburnt mixture island appears behind the flame front This unburnt mixture contributes the increase of turbulent burning velocity The temperature of unburnt mixture island behind the flame front increases because of the heat conduction from surrounded burnt gas which results in high concentration of HO2 inside of this unburnt mixture and enhance the turbulent burning velocity

The peak of the pdf of the local burning velocity locates at laminar burning velocity whereas the maximum burning velocity reaches to about 5 times laminar one and the minimum burning velocity is negative In the concept of flame stretch the time-averaged growth rate must be zero because flame front should stay in a certain area statistically However in DNS the mean growth rate is not zero which suggests that flame does not exist as statistically steady state

The present DNS results indicate a possibility of the existence of flame elements which cannot be explained by the flamelet concept and the concept of the flame stretch To understand these effects in detail further measurements and simulations will be required


7

5 Acknowledgment This work is partially supported by Grant-in-Aid for Young Scientists (S) (No 20676004) of Japan

Society for the Promotion of Science

References [1] Clavin P 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows Prog

Energy Combust Sci 11 1 [2] Williams F A 1985 Combustion theory (California Benjamin Cummings) [3] Pope S B 1988 The evolution of surface in turbulence Int J Eng Sci 26 445 [4] Peters N 2000 Turbulent combustion (London Cambrige Press) [5] Law C K and Sung C J 2000 Structure aerodynamics and geometry of premixed flamelets

Prog Energy Combust Sci 26 459 [6] Williams F A 2000 Progress in knowledge of flamelet structure and extinction Prog Energy

Combust Sci 26 657 [7] Candel S M and Poinsot T J 1990 Flame stretch and the balance equation for the flame area

Combust Sci Technol 70 1 [8] Clavin P 2000 Dynamics of combustion fronts in premixed gases from flames to detonations

Proc Combust Inst 28 569 [9] Poinsot T J Echekki T and Mungal M G 1992 A study of the laminar flame tip and implications

for premixed turbulent combustion Combust Sci Technol 81 45 [10] Sinibaldi J O Driscoll J F Muller C J Donbar J M and Carter C D 2003 Propagation speeds

and stretch rates measured along wrinkled flames to assess the theory of flame stretch Combust Flame 133 323

[11] Kido H Nakahara M Nakashima K and Hashimoto J 2002 Influence of local flame displacement velocity on turbulent burning velocity Proc Combust Inst 29 1855

[12] Dyer M J and Crosley D R 1985 Fluorescence imaging for flame chemistry Proc Int Conf Laser 84 211

[13] Hanson R K 1986 Combustion diagnostics planar imaging techniques Proc Combust Inst 21 1677

[14] Smooke M D Xu Y Zurn R M Lin P Frank J H and Long M B 1992 Computational and experimental study of OH and CH radicals in axisymmetric laminar diffusion flames Proc Combust Inst 24 813

[15] Seitzman J M Haumann J and Hanson R K 1987 Quantitative two-photon LIF imaging of carbon monoxide in combustion gases Appl Opt 26 2892

[16] Allen M G Howe R D and Hanson R K 1986 Digital imaging of reaction zones in hydrocarbon-air flames using planar laser-induced fluorescence of CH and C2 Opt Lett 11 126

[17] Carter C D Donbar J M and Driscoll J F 1998 Simultaneous CH planer laser-induced fluorescence and particle imaging velocimetry in turbulent nonpremixed flames Appl Phys 66 129

[18] Mansour M S Peters N and Chen Y C 1998 Investigation of scalar mixing in the thin reaction zone regime using a simultaneous CH-LIFRayleigh laser technique Proc Combust Inst 27 767

[19] Bockle S Kazenwadel J Kunzelmann T Shin D-I Schulz C and Wolfrum J 2000 Simultaneous single-shot laser-based imaging of formaldehyde OH and temperature in turbulent flames Proc Combust Inst 28 279

[20] Kychakoff G Paul P H van Cruyningen I and Hanson R K 1987 Movies and 3-D images of flow fields using planar laser-induced fluorescence Appl Opt 26 2498

[21] Seitzman J M Miller M F Island T C and Hanson R K 1994 Double-pulse imaging using simultaneous OHacetone PLIF for studying the evolution of high-speed reacting mixing layers Proc Combust Inst 25 1743

[22] Schefer R W Namazian M Filtopoulos E E J and Kelly J 1994 Temporal evolution of


8

turbulencechemistry interactions in lifted turbulent jet flames Proc Combust Inst 25 1223 [23] Kaminski C F Hult J and Alden M 1999 High repetition rate planar laser induced fluorescence

of OH in turbulent non-premixed flame Appl Phys B 68 757 [24] Nygren J Richter M Hult J Kaminski C F and Alden M 2001 Temporally resolved single-

cycle measurements of fuel and OH distributions in spark ignition engine using high speed laser spectroscopy Proc Fifth int Symp on diagnostics and modeling of combustion in internal combustion engines(COMODIA) p 572

[25] Watson K A Lyons K M Carter C D and Donbar J M 2002 Simultaneous two-shot CH planar laser induced fluorescence and particle image velocimetry measurements in lifted CH4air diffusion flames Proc Combust Inst 29 1905

[26] Hult J Meier U Meier W Harvey A and Kaminski CF 2005 Experimental analysis of local flame extinction in a turbulent jet diffusion flame by high repetition 2-D laser techniques and multi-scalar measurements Proc Combust Inst 30 701

[27] Tanahashi M Taka S Shimura M and Miyauchi T 2008 CH double-pulsed PLIF measurement in turbulent premixed flame Exp Fluids 45 323

[28] Haworth D C and Poinsot T J 1992 Numerical simulations of Lewis number effects in turbulent premixed flames J Fluid Mech 244 405

[29] Baum M Poinsot T J Haworth D C and Darabiha N 1994 Direct numerical simulation of H2O2N2 flames with complex chemistry in two-dimensional turbulent flows J Fluid Mech 281 1

[30] Echekki T and Chen J H 1996 Unsteady strain rate and curvature effects in turbulent premixed methane-air flames Combust Flame 106 184

[31] Tanahashi M Fujimura M and Miyauchi T 2000 Coherent fine-scale eddies in turbulent premixed flames Proc Combust Inst 28 529

[32] Nada Y Tanahashi M and Miyauchi T 2004 Effect of turbulence characteristics on local flame structure of H2-air premixed flames J Turbulence 5 16

[33] van Oijen J A Groot G R A Bastiaans R J M and de Goey L P H 2005 A flamelet analysis of the burning velocity of premixed turbulent expanding flames Proc Combust Inst 30 657

[34] Tanahashi M Nada Y Ito Y and Miyauchi T 2002 Local flame structure in the well-stirred reactor regime Proc Combust Inst 29 2041

[35] Miyauchi T Tanahashi M Sasaki K and Ozeki T 1996 Transport phenomena in combustion (Washington DC Taylor and Francis)

[36] Miller J A and Bowman C T 1989 Mechanism and modeling of nitrogen chemistry in combustion Prog Energy Combust Sci 15 287

[37] Smooke M D and Giovangigli V 1991 Formulation of the Premixed and Nonpremixed Test Problems Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames (Berlin Springer)

[38] Kee R J Rupley F M Meeks E and Miller J A 1996 Chemkin-III a fortran chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics Sandia Report SAND96-8216

[39] Lele S K 1992 Compact finite difference schemes with spectral-like resolution J Comput Phys 103 16

[40] Poinsot T J and Lele S K 1992 Boundary conditions for direct simulations of compressible viscous flows J Comput Phys 101 104

[41] Baum M Poinsot T and Thevenin D 1994 Accurate boundary conditions for multicomponent reactive flows J Comput Phys 106 247


9

Numerical Study on Dynamics of Local Flame Elements in Turbulent Jet Premixed Flames

K Yamayaki1 Y-S Shim1 N Fukushima 1 M Shimura1 M Tanahashi1 and T Miyauchi1 1Department of Mechanical and Aerospace Engineering Tokyo Institute of Technology Meguro-ku Tokyo 152-8550 Japan

kyamawaknaviermestitechacjp

Abstract Direct numerical simulations (DNSs) of turbulent jet premixed flames have been conducted to investigate dynamics of local flame elements Behaviors of turbulent jet flames are discussed by considering characteristics of local flame elements such as flame displacement speed local turbulent burning velocity curvature and tangential strain rate The peak of probability density function (pdf) of the local turbulent burning velocity locates at laminar burning velocity whereas the maximum turbulent burning velocity reaches to about 5 times laminar one and the minimum burning velocity is negative The result indicates that dynamics of turbulent flame cannot be explained by the flamelet concept The concept of flame stretch is evaluated by growth rate of the flame area which is a function of flame displacement speed flame curvature and tangential strain rate In the concept of flame stretch the time-averaged growth rate must be zero because flame front should stay in a certain area statistically However in DNS the mean growth rate is not zero which suggests that flame does not exist as a statistically steady state The present results indicate a possibility of the existence of flame elements which cannot be explained by the flamelet concept and the concept of flame stretch

1 Introduction The turbulent combustion model has significant effects on accuracy of numerical prediction of combustors Recently many approaches [1-6] have been attempted to develop high accuracy turbulent combustion model and these developed models are validated by using results of numerical simulation or experiment As for modeling of turbulent premixed flames the description of dynamics of flame front has been one of the most important subjects in the turbulent combustion research since that is the basis of turbulent combustion models in the flamelet concept in which local burning velocity is not so far from laminar burning velocity In the concept of the flame stretch increasing rate of the flame area is expressed by flame displacement speed flame curvature and tangential strain rate at the flame front [37]

The effects of the strain rate have been discussed based on the Markstein number [48] In the previous studies [910] the curvature and strain rate effects have been investigated in the steady or unsteady laminar flames because the flame elements in turbulent flames are assumed to be laminar flame under weak stretch with small curvature To confirm the theory of the flame stretch experimentally measurements of the flame displacement speed in turbulent premixed flames are required In general shadowgraph or laser tomography has been adopted to estimate flame displacement [1011] However in these studies flame propagation normal to the flame front is


ccopy 2010 Published under licence by IOP Publishing Ltd 1



01

1

101

102

103

01 1 101 102 103 104

urm

s S L

lδF



wrinkled flamelets


Kaδ = 1Case 1

Case 4Case 3Case 2






2





(a) (b)

A

(c) (d)

C

B

high

low


3



XH XO XOH

XH XO XOH

(a)

(b)

high

low


4





ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9



01

1

101

102

103

01 1 101 102 103 104

urm

s S L

lδF



wrinkled flamelets


Kaδ = 1Case 1

Case 4Case 3Case 2






2





(a) (b)

A

(c) (d)

C

B

high

low


3



XH XO XOH

XH XO XOH

(a)

(b)

high

low


4





ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9





(a) (b)

A

(c) (d)

C

B

high

low


3



XH XO XOH

XH XO XOH

(a)

(b)

high

low


4





ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9



XH XO XOH

XH XO XOH

(a)

(b)

high

low


4





ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9





ｗR6 XHO2

small large Δt


5

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 1Case 2

00

05

10

15

20

25

-5 -4 -3 -2 -1 0 1 2 3 4 5

p

SLlSL

Case 3Case 4


-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 1

-3

-2

-1

0

1

2

3

-200 -150 -100 -50 0 50 100 150 200

a t (1

s)

kSLl (1s)

(x105)

Case 2






6




lLt kSatA

A dd1

minus= (1)







7
























8






















9




lLt kSatA

A dd1

minus= (1)







7
























8






















9
























8






















9






















9

Numerical study on dynamics of local flame elements in

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