ignition and flame development in mixing layers with ... · zhiyan wang1* john abraham1,2 1school...

* Corresponding author: [email protected]

8th

U. S. National Combustion Meeting

Organized by the Western States Section of the Combustion Institute

and hosted by the University of Utah

May 19-22, 2013

Ignition and Flame Development in Mixing Layers with

Applications to CI Engines

Zhiyan Wang1*

John Abraham1,2

1School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088, USA

2School of Mechanical Engineering, University of Adelaide, Adelaide, South Australia 5005,

Australia

Abstract

In prior studies, ignition and flame development in compositionally stratified n-heptane/air

mixtures have been studied under uniform high pressure and temperature conditions with

application to compression-ignition engines. It was concluded that ignition occurs in the rich

mixture and an ignition front then propagates to the flame stabilization location near the

stoichiometric mixture fraction. The front propagation was accelerated with increasing

gradients when the gradients were smaller than a critical value but decelerated with

increasing gradients when the gradients were higher than the critical value. In this work, more

realistic engine conditions where both compositional and thermal stratification are

simultaneously present are studied. It is shown that ignition again occurs in the rich mixture,

but the mixture fraction values are lower than in the uniform temperature case. Ignition delay

is reduced with increasing stratification gradient until a critical value is reached after which

ignition delay grows as gradient further increases. The mixture fraction where ignition

initiates is less sensitive to changes in level of compositional stratification than to initial

temperature variation. The studies are then extended to a biodiesel surrogate and to an

application relevant to a dual-fuelled engine.

1. Introduction

In direct-injection diesel engines in which fuel is injected into the combustion

chamber, there is insufficient mixing of the fuel and air prior to the start of combustion. This

results in a mixture where compositional and thermal stratification are present. It is important

to understand the influence of the stratification on ignition and flame development in such

engines because these processes influence the phasing of the combustion with respect to the

chamber volume which, in turn, influences engine performance (Heywood, 1988). There

have been prior studies of the influence of compositional stratification on ignition

characteristics at elevated pressure and temperature conditions (Mastorakos et al., 1997; Im

et al., 1998; Sreedhara and Lakshmisha, 2000; Mastorakos, 2009; Bansal et al., 2009;

Owston and Abraham, 2010; Mukhopadhyay and Abraham, 2011). In the present work, the

focus will be on autoigniting mixing layers.

Paper # 070IC-0130 Topic: Internal Combustion Engines

[2]

Mastorakos et al. (1997) performed two-dimensional direct-numerical simulation

of methane/air diffusion layers at pressure of 1 bar and temperature ranging from 1000 K to

1200 K. They found that ignition delay is reduced by increasing initial diffusion layer

thickness. Pitsch and Peters (1998) studied the influence of scalar dissipation rate on

autoignition of n-heptane/air mixture using a one-dimensional flamelet model and observed

that decreasing scalar dissipation rate will facilitate ignition. Mukhopadhyay and Abraham

(2011) performed a one-dimensional simulation of a reacting laminar n-heptane/air diffusion

layer at uniform pressure and initial temperature of 40 bar and 1000 K, respectively and

observed that ignition always occurred in the rich mixture and then a front (which they

referred to as an “ignition front”) propagated to the flame stabilization location near the

stoichiometric mixture fraction. In addition, it was reported that the front propagation was

accelerated with increasing gradients when the gradients were smaller than a critical value

but decelerated with increasing gradients when the gradients were higher than the critical

value.

This paper is an extension of the work of Mukhoadhyay and Abraham (2011, 2012).

Whereas they considered primarily compositional stratification, in the present work we will

consider both compositional and thermal stratification. n-Heptane whose ignition behavior

has been quite well-understood is again selected as one of the fuels. In addition, we include a

study of the behavior of a biodiesel surrogate which is of interest in biodiesel-fuelled

compression-ignition engines. We also study the mixing layers of n-heptane and a

homogeneous-charge of a less reactive fuel and air that is of relevance to natural gas engines

in which a pilot quantity of diesel fuel is injected to ignite the mixture (Karim, 1980;

Korakianitis et al., 2011). These studies are also relevant to homogeneous-charge

compression-ignition engines where a pilot quantity of more reactive fuel is injected to

control ignition of a less reactive fuel (Hanson et al., 2012).

This paper is structured in the following manner. The numerical model and reaction

mechanisms employed are briefly discussed in Section 2. Section 3 presents the results

pertaining to n-heptane combustion in air, biodiesel surrogate combustion in air, and finally

n-heptane combustion in a homogeneous mixture of methane and air. The paper then closes

with summary and conclusions in Section 4.

2. Computational Methods and Setup

The FLEDS numerical code which has been employed by Mukhopadhyay and

Abraham (2011) for their studies of ignition in mixing layers is employed in this work. The

code has been employed in many other studies in the past (Anders et al., 2008; Owston and

Abraham, 2010; Venugopal and Abraham, 2008; Mukhopadhyay and Abraham, 2011, 2012;

Reddy and Abraham, 2011). The prior papers may be consulted for details of the numerical

method. In brief, the code employs the sixth-order compact finite-difference scheme of Lele

(1992) to solve mass, momentum, energy and species conservation equations for

compressible, multi-component reacting gaseous mixtures. At the boundaries, non-reflective

outflow conditions are specified. Chemical kinetic source terms are computed through an

interface with CHEMKIN-like subroutines (Kee et al., 1999). The code is written in

FORTRAN 90 using the message passing interface (MPI) library for parallel computing. In

addition to the FLEDS code, a 1-D laminar flamelet code is also employed to solve the

unsteady flamelet equations in the mixture fraction ( ) space for some of the studies


[3]

(Gopalakrishnan, 2003). This code has also been discussed in the literature (Gopalakrishnan,

2003; Venugopal, 2008).

Studies involving n-heptane autoignition in air and methane/air homogeneous

mixture are carried out using a 37-species, 70-step reaction mechanism developed by Peters

et al. (2002). For validation purpose, a more detailed oxidation mechanism for n-heptane

developed by Seiser et al. (2002) is employed which consists of 159 species and 1540

reaction steps. A 115-species, 460-step chemical mechanism (Luo et al., 2012;

http://www.engr.uconn.edu/~tlu/mechs/mechs.htm) is employed to model the oxidation of the

biodiesel surrogate.

Figure 1 shows a typical computational domain that is adopted for carrying out our

numerical simulations with the FLEDS code. The domain measures 0.25 and 2.5 mm in x-

and y-directions, respectively, and a uniform mesh with 25 x 250 points is used. This gives

rise to a spatial resolution of 10 µm in both directions. Pressure condition at 40 bar is

imposed and the temperature of air is chosen to be 1000 K while that of the fuel is 373 K to

emulate the typical engine conditions. The mass fraction of fuel and temperature distribution

inside the domain shown in Fig. 1 is given by a hyperbolic tangent profile, which is described

mathematically by the equation below:

(1)

Here, is a general parameter that in this specific case represents mass fraction of species

and temperature . and are the upper and lower values of the variable respectively.

represents the location where is half-way between the maximum and minimum values and

it has been chosen to coincide with the center of the computational domain to achieve

symmetry. The parameter is a measure of the diffusion layer thickness. For a hyperbolic

tangent profile, the separation between 99 percentile and 1 percentile of the distribution is

typically three times the value. Note that the size of the computational domain is varied for

different values of . Furthermore, the spatial resolution is selected to ensure that there are at

least 10 cells within the diffusion layer thickness (Vervisch and Poinsot, 1998).

Fig. 1 Schematic of the computational domain.


[4]

The 1-D laminar flamelet code solves the flamelet equations in the mixture fraction

( ) space rather than in the physical space. The Z-space is discretized by a non-uniform grid

with points concentrated near the stoichiometric mixture fraction, . Instead of

specifying a characteristic length scale , the scalar dissipation rate, is

used to represent the compositional gradient between fuel and air. Such a profile of scalar

dissipation rate is obtained from the initial distribution of as a function of mixture fraction

for various diffusion layer thicknesses in FLEDS. In the flamelet code, unity Lewis number

is assumed whereas the FLEDS code uses mixture-averaged diffusivities for the species.

3. Results and Discussion

We will initially present results for a mixing layer thickness of 120 µm. Figure 2

shows the evolution of temperature profiles as a function of mixture fraction when the

initial temperature is uniform in the computational domain at 1000 K and Fig. 3 shows the

same profiles when the initial air temperature is 1000 K and the fuel temperature is 373 K. In

Fig. 2 the initial rise in temperature is observed at a time of approximately 0.15 ms at

and as the temperature increases, the value of at which the peak temperature is observed

becomes smaller and finally stabilizes at which is close to the stoichiometric

value, . The stabilization occurs at approximately 0.25 ms. Mukhopadhyay

and Abraham (2011) have characterized this propagation of the “front” from the initial

ignition location to the stabilization location as an “ignition front propagation” suggesting

that it is primarily driven by ignition occurring at progressively lower values of . Hence, in

this case the duration of ignition front propagation is about 0.1 ms. In Fig. 3, the initial rise in

temperature is observed at a time of approximately 0.19 ms at of approximately 0.073. This

difference in value of Z with respect to the previous case is a result of the variation in

temperature with the higher temperature occurring on the air side and preferentially

promoting ignition. After the initial rise in temperature, the location of peak temperature

initially shifts to richer , suggesting that the richer Z is primed for ignition provided

temperature are sufficiently high, and then shifts back towards the leaner and stabilizes at

. The shift occurs at about 0.3 ms. The flame stabilization occurs at a time of about

0.45 ms. In other words, the duration of ignition front propagation is approximately 0.25 ms.

Fig 2. Temperature evolution as a function of

mixture fraction for and uniform initial

temperature at 1000K.

Fig 3. Temperature evolution as a function of

mixture fraction for and initial air

temperature at 1000K and fuel (n-heptane)

temperature at 373K.


[5]

Figures 4 and 5 show results for cases with initial of 30 µm and 400 µm,

respectively. Both simulations are performed under realistic temperature conditions where the

fuel is at 373 K and air at 1000 K. It is again shown that initial temperature rise occurs at a

rich mixture fraction where is approximately 0.091. The ignition front initially travels

toward the richer mixture as in Fig. 3. For , it appears that the shift toward the

richer mixture fraction is more pronounced compared to the previous case where Figure 6 shows the at the location of maximum temperature rise as a function of

time for the three cases where . It can be seen that for the case

where , the ignition front shifts to before it moves in the opposite

direction toward the leaner mixture at about 0.57 ms, and eventually reaches steady-state at

.

It is interesting to note that the instant when ignition front propagation changes

direction coincides with the onset of the second stage of ignition. Figure 7 shows the peak

temperature rise relative to the initial temperature at that location as a function of time. For

, the shift in the direction of ignition front propagation coincides with the

time when the second stage of ignition begins, i.e. at 0.57 ms and 0.32 ms, respectively. This

behavior can be explained considering that ignition of the n-heptane and air mixture is

Fig 6. Mixture Fraction at the location of maximum

temperature rise inside the domain as a function of

time for .

Fig 7. Maximum temperature rise inside the domain

as a function of time for .

Fig 4. Temperature evolution in mixture fraction

space for and initial air temperature at

1000K and fuel (n-heptane) temperature at 373K.

Fig 5. Temperature evolution in mixture fraction

space for and initial air temperature at

1000K and fuel (n-heptane) temperature at 373K.


[6]

facilitated by two factors: 1) high local temperature, and 2) relatively high local mixture

fraction. In the presence of both compositional and thermal gradient, ignition will not occur at

, as in the uniform temperature case of Fig. 2, since the richer mixture also corresponds

to lower local temperature. Instead ignition starts at the location where the combined effects

of local temperature and mixture fraction provide the optimal condition for ignition. During

the first stage of ignition, heat generated from oxidation of n-heptane at the location of

ignition diffuses down the thermal gradient toward the richer mixture making it more

favorable for ignition. This results in the initial shift of ignition front toward the richer

mixture. In this stage, mixture fraction is more dominant than temperature in the ignition

process. When the second stage of ignition starts, it is accompanied by rapid generation of

heat and a relatively large increase in temperature. The temperature then becomes the

dominant factor and consequently ignition front reverses and propagates toward the lean

mixture which is at a much higher temperature. In fact, this second stage of propagation may

be more akin to flame front propagation rather than ignition front propagation.

A similar trend is evident in Fig. 5 that illustrates the evolution of temperature profiles

for a case where . Ignition is again initiated in the rich mixture and propagates

toward the richer mixture in the first stage of ignition. After the second stage of ignition

occurs at 0.32 ms, the ignition front travels into the leaner mixture and eventually stabilizes

near the location where composition of fuel/air mixture is close to stoichiometric

Fig 8. Time evolution of maximum temperature inside the computational domain under various compositional and

thermal gradients for different values of for n-heptane and air combustion.

Figure 8 shows the evolution of the maximum temperature in the domain as a function

of time for several values of . Here we will define the ignition delay to be the time elapsed

for the peak temperature inside the domain to reach 1500 K. It is evident from Fig. 8 that as

increases from 30 µm to 120 µm, ignition delay is shortened from 0.57 ms to 0.31 ms.

However, when diffusion thickness further increases from 120 µm to 400 µm, the opposite

trend is observed where ignition delay grows longer from 0.31 ms to 0.33 ms. This suggests

that ignition front propagation is initially accelerated by decreasing the diffusion layer

thickness and hence by increasing diffusion gradients until a critical diffusion gradient is

reached after which further increase in diffusion gradients will increase ignition delay. In this

specific case, the critical gradient corresponds to the composition profile of .


[7]

This behavior is consistent with the observation made earlier by Mukhopadhyay and

Abraham (2011) under uniform initial temperature conditions.

In order to verify the results we have obtained are not mechanism-dependent, the

same set of computations were repeated in the flamelet code using a more detailed 159-

species, 1540-step chemical mechanism (Seiser et al., 2002). Results have indicated that the

influence of composition gradient on ignition delay exhibits the same trend as characterized

in the FLEDS simulations above and the critical gradient is again found at a diffusion

thickness of 120 µm.

It is interesting to examine if the behavior that has been discussed above is shown by

other fuels or is specific to n-heptane. As reported by Mukhopadhyay and Abraham (2011),

and shown by our work with the flamelet code, results similar to those discussed above can

be obtained by solving the flamelet equations. A biodiesel surrogate is selected for this part of

the study (Luo et al., 2012). The study is carried out by solving the flamelet equations

because direct simulations with the larger biodiesel-surrogate chemical kinetic mechanism

are computationally intensive in FLEDS. Figure 9 shows the evolution of the maximum

temperature inside the domain as a function of time for the same values of shown in Fig. 8.

Unlike the behavior of n-heptane/air, the dependence between ignition delay and the initial

compositional gradient is monotonic: as increases from 30 µm to 1 mm, i.e. compositional

gradient decreases, the ignition delay, i.e. time to reach 1500 K, decreases monotonically

from 1.8 ms to 0.4 ms. In other words, there is no change in behavior of ignition delay with

respect to as observed earlier.

Fig 9. Maximum temperature within the computational domain as a function of time under various compositional

and thermal gradients for biodiesel and air combustion.

The difference between the dependence of n-heptane/air and biodiesel/air autoignition

on compositional gradients is an interesting topic that is worthy of further investigations. As

discussed by Mukhopadhyay and Abraham (2011), there are two competing effects that

control the behavior: on the one hand, high gradient leads to faster loss of radicals and heat

which retard ignition, i.e. ignition delay increases; on the other hand, high gradient also

facilitates faster ignition front propagation from the initial location of ignition to the

stabilization location near the stoichiometric mixture fraction, i.e. ignition delay decreases. In

the case of biodiesel autoignition, it appears that the first stage of ignition is dominated by the

former effect as evident in Fig. 9 that time elapsed to reach second stage of ignition increases


[8]

as compositional gradient decreases. It is only in the second stage of ignition when the latter

effect starts to manifest. As shown in Fig. 10, the movement from the rich mixture fraction

toward the stabilization point slows down as is increased, i.e. gradient decreases. However

in the case of n-heptane reaction, the critical gradient effect discussed earlier is manifest in

the first stage of ignition. The detailed reasoning behind this behavior is still unclear and it

will require further studies.

Fig 10. Time evolution of mixture fraction at the location of peak temperature.

The study presented above is of interest to both conventional diesel engines and

advanced engines like homogeneous-charge compression-ignition engines when stratification

is employed to control the rise of pressure and/or formation of carbon monoxide and

unburned hydrocarbons. As discussed in the Introduction section, there is another

compression-ignition scenario which is of interest to homogeneous-charge compression-

ignition engines and lean-burn natural gas fuelled engines. In both cases, a more reactive fuel

that auto-ignites easily can be employed to control ignition. In this situation, the more

reactive fuel is injected into the chamber where air and less reactive fuel are premixed. To

study the ignition characteristics of this system, computations will be carried out in a domain

similar to the one shown in Fig. 1. However, the air side will be replaced by a homogeneous

mixture of air and fuel. In the present work, methane, a surrogate for natural gas fuel, will be

the fuel.


[9]

Fig 11. Initial temperature (a) and fuel mass fraction (b) profiles in the y-direction (see Fig. 1) for the dual-fuel setup

with equivalence ratio of for the CH4/air mixture.

Figure 11 shows the initial temperature and fuel mass fractions as a function of the y-

coordinate of Fig. 1. The initial temperature of n-heptane is at 373K while that of the

CH4/air mixture is 1000 K. Four homogeneous mixture compositions corresponding to

, are studied. The evolution of the maximum temperature rise over

the initial temperature at the same location is shown in Fig. 12. It is seen that for all four

equivalence ratios of CH4/air mixture at , the initial rise in

temperature occur at approximately 0.15 ms and the second stage of ignition occurs at

approximately 0.34 ms. Figure 13 illustrates the y-location in the domain where the local

temperature has the greatest increment over the initial value as a function of time. As

equivalence ratios of CH4/air mixture are varied from 0.5 to 1.0, the y-location where

temperature first rises stays roughly constant at 0.18 mm below the midpoint of the

computational domain where the mass fraction of n-heptane is around 0.048. Note that this

mass fraction is significantly lower than in the n-heptane/air mixing layer. The presence of

the methane has a noticeable effect on the location of ignition.

This y-location, representative of the ignition front, will initially shift toward the n-

heptane side similar to the single-fuel cases of n-heptane and biodiesel until it reaches about

0.13 mm below the center point, covering a total distance of 50 µm which is almost half of

the diffusion layer thickness. Then it reverses and propagates toward the homogeneous

mixture of methane and air. This propagation is that of a flame front which is similar to flame

propagation in the premixed combustion. On the whole, the ignition behavior during the first

stage of ignition is almost identical for all four cases. In the second stage of ignition, the

effects of equivalence ratio begin to manifest. From Fig. 12, it is evident that the richer the

premixed mixture is, the longer it takes for the flame to reach the steady peak temperature.

Such observation is consistent with results shown in Fig 13: as equivalence ratio increases

from 0.5 to 1.0, the speed at which flame front travels decreases from 2.1 ms-1

to 1.7 ms-1

.

This occurs because the combination of n-heptane and methane mass fractions makes the

mixture overly rich as the methane mass fraction increases, thereby decreasing flame speed.


[10]

4. Summary and Conclusions

Computations of autoignition behavior in compositionally and thermally stratified

n-heptane/air mixtures reveal that ignition occurs in the rich mixture and an ignition front

then propagates into the richer mixture. Following the second stage of ignition, the front

propagates into the leaner mixture and stabilizes near the stoichiometric mixture fraction. As

compositional gradients are increased, ignition delay initially decreases but then increases.

This behavior reflects the balance between the competing effects of increasing loss of

radicals/heat and faster front propagation as gradient is increased. In the case of biodiesel

ignition, two stages of ignitions are observed similar to n-heptane reactions but with the

important difference that the critical gradient observed in n-heptane autoignition is absent, i.e.

ignition delay decreases monotonically as gradients decrease. In the case of autoignition of n-

heptane in a background of premixed methane/air mixture, the early stages of ignition are

controlled by the autoignition characteristics of n-heptane/air mixture but the time for a stable

flame front to develop is controlled by the local equivalence ratio based on n-heptane and

methane concentrations.

Acknowledgements

Financial support provided by Caterpillar, Inc. is gratefully acknowledged. The

authors thank Professor Vinicio Magi for useful discussions related to this work and his

assistance with the numerical code. Computational resources for this work were provided by

the National Institute of Computational Sciences (NICS) at University of Tennessee, and by

the National Computing Infrastructure (NCI), Australia.

Fig 12. Maximum temperature rise as a function of

time for with initial fuel (n-heptane)

temperature at 373K and CH4/air mixture

temperature at 1000K of various .

Fig 13. Time evolution of the y-location where

maximum temperature rise is observed for with initial fuel (n-heptane) temperature at

373K and CH4/air mixture temperature at 1000K of

various .


[11]

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