A model for flame kernel growth at aircraft relight conditions

Twenty-FifthSymposium(International)on Combustion/TheCombustionInstitute,1994/pp.261-268

A M O D E L FOR FLAME K E R N E L G R O W T H AT AIRCRAFT RELIGHT CONDITIONS DERYUH LIOU Combustion Technology Division Industrial Technology Research Institute Chutung, Taiwan, ROC DOMENIC A. SANTAVICCA Turbulent Combustion Laboratory The Pennsylvania State University University Park, PA, USA A one-dimensional (1D); comprehensive numerical model for the prediction of flame kernel development at high altitude relight conditions in aircraft gas turbines is proposed and tested. The main purpose of this study is to develop a new methodology to numerically solve the very complicated governing equations involved in the flame kernel initiation and propagation in turbulent flowfields. Generally speaking, the surface area of a wrinkled fame cannot be directly described by one-dimensional approaches. However, this problem is overcome by incorporating a fractal model into the one-dimensional governing equations. Meanwhile,the concept of high-activation-energyasymptoticanalysisis also applied to provide the relationships between the average turbulent transport coefficients and reaction rate and their laminar counterparts. An artificial thermal conductivity submodel is used to reflect the fact that rapid mixing always exists inside spark kernels in the early stages of kernel development. The effect of flame stretch, which plays an important role in flame propagation, is also included in the model. Numerically, the governing equations are first discretized by the power-law scheme and then solved by the PISO algorithm. In general, the numerical predictions are in good agreement with the ex~perimentalresults. With minor modification, this numerical approach may be applied to spark ignition problems in SI engines as well.

Introduction Flameout in aircraft gas turbines poses a potential threat to pilots and passengers. In-flight flameout is more apt to occur at high altitudes [1,2] where the inlet pressure and temperature are much lower than those on the ground. Whenever flameout occurs, combustion has to be re-establishedin the combustors. Capacitor-type surface discharge igniters have been widely adopted to deliver the necessary heat sources for relight. During sparking, the electric energy is locally converted to thermal energy to raise the temperature of a combustible mixture to alevel at which the reaction is rapid and self-sustaining. One of the requirements for successfulignition in a combustor is that the kernel must grow fast enough to reach the recirculation region in the primary zone before it is swept away. Therefore, flame kernel development is an important factor to the relight performance of gas turbines [2]. In this study, a one-dimensional (1D) comprehensive model is developed to predict flame kernel propagation at relight conditions. Although many numerical models have been proposed for the prediction of kernel development, only a few of them [3,4] have been exclusively developed for spark ignition in tur-

bulent flows, e.g., Akindele et al. [3] studied flame kernel growth in turbulent fuel-air mixtures and Herweg and Maly [4] developed a one-dimensional model to predict flame kernel growth inside SI engines. The model in this paper incorporates the concept of high-activation-energy asymptotic analysis and the fractal description for wrinkled flame surfaces. Theoretically, two- or three-dimensional models are superior to one-dimensional approaches in terms of providing a detailed description of the flame surface. However, due to the extremely small characteristic scales involved in the spark ignition process, these models may be computationally inefficient at present. In our one-dimensional model, the description of the wrinkled flame surface area is obtained from the wellknown fractal models, and the equivalent turbulent transport properties are derived from the concept of high-activation-energyasymptotic analysis.

Formulation and Modeling Mathematical Formulation: Spark ignition can be mathematically described by the conservation equations of mass, species, momentum, and energy. To simplify the approach, two as-

261

262

PRACTICALASPECTS OF COMBUSTION

sumptions are made. First, it is assumed that the diffusion of species is governed by Fick's law, namely, Y+Vi = DiVYi, where V+, Y+, and Dt are the diffusion velocity, mass fraction, and mass diffusivity of species i, respectively. Second, it is assumed that viscous dissipation and heat radiation are negligible. Consequently, the mass-weighted, 1D conservation equations in spherical coordinates are [5] 0/3 + 1 a(/Sr2ti) _ 0 at r z Or

o(~f,) -

-

(2)

external heat source, and Qto+sdenotes energy loss through walls or electrodes; Di,o, #o, and ko denote the overall mass, momentum, and heat transport coefficients, respectively. Each overall transport coefficient consists of the molecular and turbulent transport coefficients. The terms QF, Wi, and Ah~'ddenote heat of combustion per unit mass of fuel consumption, molecular weight of species i, and heat of formation of species i, respectively. Due to the relatively small value of the summation term in Eq. (4), the molecular mass diffusion coefficient is directly replaced by an overall diffusion coefficient to make the energy equation applicable to both laminar and turbulent flows. Numerical evidence shows that this replacement does not significantly affect the solution. Moreover, if the mixture is assumed to be ideal, the following equation of state for ideal gas is used:

(3)

where R~ is the universal gas constant and M denotes the mean molecular weight of the mixture.

(1)

+

Ot

r2

Or 1 a(prZD+oag,/ar) + (d)+)r re Or

O([~a) at

1 a ( ~ r ~ 2) r2 Or

a[~ 1 a(#or2&i/Or) Or r 2 Or

cp o(~f) + c__pa(,~-hTf) at

r2

DP Dt

Modeling:

Or

1 O(rekoOT/Or) r2 Or

0-7

~

+ Q/~)~" - q~os~ + s (4)

The surface area of a wrinkled flame cannot be directly described by one-dimensional approaches. To overcome this problem, an equivalent planar flame model is suggested. For a wrinkled flame in the flamelet regime, an equivalent planar flame, which has the same preheat volume as the wrinkled flame but a different flame propagation speed at any point on the flame surface, is proposed. Thus, AT/AL = (6v)T/(6V)C

where e

m r W~(v7 +=1 LWF(v'b

- z,

1);) v'v)

"(Ah~,f + ]r~ Cp.+dT)]

(5)

Cp

(6)

--- ~

f, Cp,,

In arriving at Eqs. (2) through (4), mixing length models have been proposed for the turbulent flux terms to solve the problems of closure. Thus, a general form is employed for the turbulent flux terms: pgt~'u " = - ~Fr(O(hlOr )

(7)

where Fr is a turbulent transport coefficient, T represents any physical quantity, and 7t" is any massweighted fluctuating quantity, the tilde represents Favre average, and the overbar denotes mean average. Meanwhile, d)i is the chemical production rate of species i; S is the energy deposition rate of an

(9)

where A is surface area and & represents the thickness of the preheat zone. Tehis equivalent planar flame is schematically shown in Fig. 1. Meanwhile,. as suggested by DamkiShler [6], the ratio of the furbulent flame speed to the laminar flame speed is equal to the ratio of the wrinkled flame area to the planar flame area. However, neither the turbulent flame speed nor the wrinkled flame area is known. In recent years, Gouldin [7] has proposed that turbulent flame fronts could be treated as constant property surfaces embedded in turbulent flows. As a result, turbulent flame surfaces may be characterized by the mathematics of fractals. In their proposal, the fractal behavior of turbulent flames are limited by an upper bound and a lower bound, which are also referred to as the outer cutoff (e0) and inner cutoff (e~), respectively. Based on Damk6hler's and Gouldin's hypotheses, the relationship between the flame surface area, the flame speed, and the fractal cutoffs is given as [8,9] sO/s 0 = AT/A L = (eolai)~-2~(L/q)m 2

(10)

A MODEL FOR FLAME KERNEL GROWTH AT AIRCRAFT RELIGHT CONDITIONS $1.

AL

263

A v x 6 L ' ALx 6T Areo A L

Areo ^v

L

~--

Burned

Unburned

Burned

$v Unburned

\ ROBe! ion Priho01 Zone Zone

VR I NKLED FLAME

Reocllon Zone

Prohoo! Zone

EGUIVALENT PLANAR FLAME

where ~t is the fractal dimension that is a measure of surface roughness, L is the integral scale, r/is the Komolgorov scale, and superscript 0 denotes the unstretched state. Since the kernel size measured in our experiments is always greater than integral scale, a fixed value, integral scale L, is used to replace outer cutoff (s0). From asymptotic analysis, a laminar flame of laigh activation energy can be divided into two zones: a relatively thick preheat zone followed by a very thin reaction zone. The analysis shows that convection and diffusion are dominant in the preheat zone, while reaction balances diffusion in the reaction zone. By applying these results to the equivalent flame, the values of the turbulent transport coefficients can be found. Due to the convection-diffusion balance in the preheat zone, integrating Eq. (4) over the preheat zone, 0 + to 0 + + (tip)r, yields CpPuS~

- ~'u) ~-~ ko(?b - ~'u)/(tp)T

(1l)

where linear approximation is used for the temperature gradient, and continuity, pt/ = Pu ST = constant, is applied. Subscripts b and u represent the burned and the unburned states, and To+ is approximately equal to Tb. As a result, Eq. (11) can be further simplified as ko/( tp) T ~ Cpp u S O.

FIc. 1. Schematic illustration of the equivalent planar flame model for a wrinkled flame in laminar flamelet regime.

(lC2)

Similarly, integration of the species Eq. (2) over the mass diffusion zone, 0 + to 0 + + (tin) T, yields

From the diffusion-reaction balance in the reaction zone, the heat conduction term in Eq. (4) is equal to the rate of chemical heat release. After integration, Eq. (4) becomes

ko(l"b - I"o+)/(tR)T ~ (CheF}T"OF

(14)

where ((J)F)T and (tR) T a r e the integrated reaction rate of fuel over the reaction zone and the thickness of the reaction zone, respectively. Similar integrations for a laminar unstretched flame yields kL /(tp) L ~" CptOu SO

(15)

pb(DiL)b/(tm)L ~ [u S~

(16)

kL(T~ - T~176

~ <-~FF>L'QF

(17)

where subscript L represents laminar state. Dividing Eq. (12) by Eq. (15) gives ko/k L ~. [(tp)T/(tp)LJ " [S~

0]

(18)

In order to obtain Eq. (18), Eqs. (9) and (10) are employed. Meanwhile, from Eqs. (13) and (16), the ratio of the turbulent and the laminar mass diffusivity is given by Oio/OiL

~

(tm)T/(tm)

L 9

[S~ 0]

(19)

(tm)T/(tm) L " (E0/ei)a-2

P~ (Dio)b/(6m)r ~- P, S O

(13)

where (tin) r is the thickness of mass diffusion zone.

where the ratio ofpb to Pb is assumed to be close to unity. The two diffusion-zone thicknesses, (tm)L and

264

PRACTICALASPECTS OF COMBUSTION may be related to the preheat zone thicknesses,

(r

(~p)L and (~p)r. As derived by Chung and Law [10], the flame thickness ratio of (~m)L to (~p)L in laminar flows is equal to the inverse of the Lewis number. However, in well-stirred combustion, diffusion processes in the flame are expected to be controlled by turbulence rather than molecular diffusion. Thus, all of the turbulent transport coefficients are expected to have the same value at a very high Reynolds numbers. Hence, the ratio of (fi,~)r to (~p)T approaches unity as the strength of turbulence increases. Between these two extremes, turbulence and molecular motion contribute to the transport process; however, the degree of contribution from each mechanism is not clear so far. Therefore, a relationship between the thickness of the mass diffusion zone, tim, and the thickness of the preheat zone & at different turbulence levels must be given. In this study, the ratio of ~m to ~k" which is assumed to be a function of turbulence intensity, laminar flame speed, and the Lewis number, is given as

~m/6p = 1/f(u'/SL, Le)

imaginary planar flame with a speed about four times greater than the laminar speed in the laminar flame calculation at this stage. The momentum equation is usually not used for spark ignition simulation in a homogeneous and electrode-free and wall-free flow field after the breakdown phase. In arriving at Eqs. (18), (22), and (24), the flame is totally unstretched. For a stretched flame, a stretch factor I 0 [12] is used to take account of the effect of flame stretch. For a stretched flame, when the stretch factor is not strongly related to the wrinkled surface area to volume ratio, Eqs. (18), (22), and (24), maybe expressed as

ko/kL = [to" (e0/eY-2] z

Dio/DiL = [Le/f(u'/SL, Le)l" [Io" (eo/ei)e-z] 9 ~i~ = ~5~. to2. [(eo/e,)~-~] ~

(26) (27)

Solution Procedure

(20)

where

(25)

Diseretization:

f(u'lS ~

Le)

=

I -

[(1 -

Le)t(1

+

u'fS~ (21)

Equation (20) is a heuristic model [5] that considers the contribution from the laminar and the turbulent parts. In Eq. (21), the function f increases or decreases monotonically to unity when the turbulence intensity increases from 0 to an extremely high level. Thus, the ratio (~m/(~p is correctly described by Eq.s (20) and (21) for flames in laminar and very turbulent flows. Therefore, the ratio of the turbulent mass diffusivity to the laminar mass diffusivity is

Dio/D~L = [Le/f(u'/Sr, Le)]-[(e0/ei)a-2] 2.

(22)

From Eqs. (14) and (17), the ratio of the two reaction rates is expressed as (69~)T/(d)~)L = (k0/kL)" [(~O)y(~R)T]

(23)

where the assumption of (Tb - T0+) -- (Tg - TO+) is made. However, the ratio of the two reaction zone thicknesses, (~)L/(~R)T, is unknown. It is reasonable to expect that this reaction rate ratio is dependent on large and small length scales of the turbulent field [11]. If we further assume that the dependency can be represented by a simple function, the ratio is expressed as ((j)F}T/(~OF}L ~, [(F,O/Si)~t-2]2+y = [(/~O/gi)~, 2]z

(24)

where z = 2 + y and is determined by using an

The governing equations of the model are integrated over control volumes first and then discretized into finite-difference equations by using the powerlaw scheme [13]. The discretized equations are then solved by the PISO algorithm [14]. The computation domain is a cone-shaped region that extends outward from the origin of the coordinates with a solid angle ~ . M1 physical quantities in a control volume are calculated and stored at the corresponding nodal points. In this study, the minimum grid spacing is 0.02 mm, and the time increment is 5/ts.

Linearization of Reaction Rate: The production rate of any species i may be expressed in an Arrhenius form (~i)L = [Wi(v" -

v')/W~(v~

-

vi~)]B

(2S)

. pa+b. T n . e x p ( - E/RuT). Y~. Ybo

where B is the pre-exponent frequency factor, E is the activation energy, and v~' and v' are the stoichiometric coefficients of species i on the production and reaction sides, respectively. For spark ignition in Calls-air mixtures, five species, C3H8, 02, H20, CO2, and Nz, are considered. The reaction orders, a and b, are 0.65 and 1.15 [15], respectively. The pre-exponent factor is obtained from a laminar flame calculation by correctly reproducing the laminar flame speed [16]. Meanwhile, due to mass conservation, species i at time steps I + 1 and 1 are satisfied by

A MODEL FOR FLAME KERNEL GROWTH AT AIRCRAFT RELIGHT CONDITIONS (y]+l _ Y~)/rhi = Constant

(29)

where mi is the mass of species i created in the reaction. By performing a Taylor expansion of Eq. (28) and substituting Eq. (29) into the expanded equation, a linear form for the reaction rate of species i is derived. Initial Size of Spark:

The size of a spark channel is not a constant value during sparking. However, Sloane has shown [17] that the numerical results obtained with a fixed channel size differ only a few percent or less from those obtained with a variable channel size. Therefore, constant channel radius assumption is employed to simplify the numerical approach. The equivalent radius of a semispherical spark is given by r 0 = (3/8"In" Era) I/3

(30)

where I,~ and V,n are the measured current (in A) and voltage (in V) of an arc-type cylindrical spark channel [18]. Meanwhile, the energy discharge rate per unit volume as a function of radius is given by [17] Pw(r) = Pwo/(1 + exp[(r - ro)/~r])

(31)

where Pwo is the maximum power density during sparking, and 5r is a steepness parameter. The parameter ~r indicates the degree of the edge of a square waveform being smoothed [16], and a value of 0.5 mm is used in this study. Artificial Thermal Conductivity:

It has been shown [19] that the spark energy discharged in the first few microseconds produces violent turbulence inside a flame kernel. Apparently, the spark-induced turbulence can efficiently distribute spark energy inside the kernel and may cause different kernel growth. A model with artificial thermal conductivity inside a flame kernel is introduced as ka~ = k. (T - Tad)5" 10 -3

(32)

where kart is the artificial thermal conductivity. The molecular-level thermal conductivity, and other transport properties like mass diffusivity, viscosity, and specific heat at constant pressure can be calculated from formulas in the literature [20,21]. Stretch Factor:

The stretch factor is mathematically derived as [4]

Zo

~

1

-

(5~/sL)

9[KT + (1 + pu/pb)/rf]

9[1/Le - (Le - 1/Le). Ta/2Tad ]

(33)

265

where Ta and T~d are the activation temperature and adiabatic flame temperature, respectively, 5l is the laminar flame thickness, and Kr is the turbulent strain rate and can be evaluated using the formula shown byAbdel-Gayed et al. [22]. However, Eq. (33) can only be used when the Lewis number is greater or less than unity. When the Lewis number is very close to unity, the stretch factor should be approximately equal to 1. Results and Discussion

In order to provide data for comparison, spark ignition experiments were conducted in a turbulent flow reactor [5]. The turbulent flow reactor can generate homogeneous turbulence and uniform velocity in the test section. A high-speed schlieren photographic system was used to record the images of the flame kernels. The equivalent kernel radius, which is defined as a semi-circle with the projected area the same as that of the kernel, can be calculated. In this experiment, a surface discharge ignition system typical of those used in aircraft is employed to initiate combustion. The spark energy is 1.8 J, and the discharge duration is about 100/xs. The tip of the igniter is flush with the wall of the test section. The test conditions and turbulent characteristics are listed in Table 1. To solve the discretized equations, the exponent z in Eq. (27) has to be known first. From planar flame calculations, the values ofz vary slightly over the test pressures. It is 1.44 for p = 0,6 atm and 1.45 for p = 1.0 atm. These values are reasonable because the thickness of the reaction zone of the equivalent flame should not increase linearly as that of the preheat zone or diffusion zone does. The exponent of almost constant value means that the ratio of reaction rates is controlled by the characteristic scales of turbulent field only. Since no dissociation or ionization process is considered in the spark ignition model, the thermal conductivity directly obtained from the JANAF table [19] are usually underestimated. An artificial conductivity model, Eq. (32), is used in our calculation. To examine the validity of the proposed artificial thermal conductivity model, test calculations have been performed for a 30 mJ arc-discharge spark in a stoichiometric propane-air mixture. Heat loss through the electrode or the wall is not considered, and a 50% energy-transfer efficiency is assumed in these calculations. Figure 2 shows the temperature profiles of two flame kernels with and without artificial thermal conductivity. For spark ignition with artificial thermal conductivity, the temperature inside the flame kernel is evenly spread within a short period of time. However, without artificial thermal conductivity, the temperature profile still does not reach a uniform state at 1 ms after spark initiation.

PRACTICAL ASPECTS OF COMBUSTION

266

TABLE 1 Summary of the test conditions, turbulence characteristics, and discharge characteristics Pressure (atm) Parameters Mixture Equivalence ratio Turbulence intensity u' (m/s) Temperature T (K) Integral length scale L (mm) Discharge type Spark energy

10000

0.6

1.0 C3Hs-Air

0.8, 1.0, 1.4 0.17, 1.60 300 --5

0.8, 1.0, 1.4 0.17, 1.60 300 --5 Arc

1.8J

i

" ~

P = 1.0 atm

\

8000 ,

V, 9..... O,---Zh , - -

41, = 1.0 E = 30 m J

L

u'

4=0.0 41,= 1 . 0 ~ - 1.4

= 0.17

m/=

O0 /~s

6000

...i~,

2

" 4000 "-"

200 /~s

500 bcs

ooo

100

0

#

t

I

I

1

2

3

Distance

( mm

1 ms

4 )

FIG. 2. The predicted temperature profiles for flame kernels initiated by a 30-mJ spark in atmospheric, stoichiometric Calls-air mixture. Dash lines: no artificial conductivity; solid lines: with artifieial conductivity.

Compared with Maly's results [23], the temperature profiles obtained with the artificial thermal conductivity model are more reasonable. Moreover, the flame kernel propagation rate is also different. Thus, at a given time, the kernel front spreads to a farther distance when the artificial thermal conductivity model is applied. Numerical simulations of spark ignition in propane-air mixtures were carried out at various test conditions. The comparison between the predicted and the measured kernel radii at p = 1.0 and 0.6 atm are presented in Figs. 3 through 6. Turbulence is not included in the computation scheme in the first 0.9 ms since the spark-induced turbulence is usually strong in this period. The numerical predictions are, in fact, in very good agreement with the experimental results. Although, for certain cases, the difference between the prediction and the measurement is

0

, 0

l

l

l

l

l 5

l

l

Time

l

l

l

( ms

l l l0

l 15

)

FIG. 3. Comparison between the predicted and the measured kernel radii at P = 1.0 atm and u' = 0.17 m/s, where u' is turbulence intensity, ~ is equivalence ratio, symbols represent measurements, and lines denote predictions. about 15%, this deviation is, however, relatively small and usually acceptable in turbulent combustion simulations. It is also interesting to note that, for the ignition at fuel-rich and low turbulence intensity conditions, most of the prediction inaccuracy appears in the first 3/xs. This may be due to the exclusion of spark-generated radicals in our calculation. In Fig. 6, the predictions and measurements show that the kernel growth curves for q5 = 1.0 and 1.4 are almost identical, while kernel growth in the ~b = 0.8 mixture is the slowest, although the laminar flame speed at = 1.4 (Le = 0.98) is about 30% slower than that at q5 = 1.0 (Le = 1.34) and is approximately equal to that at 9 = 0.8 (Le = 1.67). Thus, for a mixture with nonunity Le, flame kernel behavior is not only controlled by the laminar flame speed but is also affected by flame stretch. However, for unity Le flow,

A MODEL FOR FLAME KERNEL GROWTH AT AIRCRAFT BELIGHT CONDITIONS

60

~r

- .....

1, =

0.8

13 .

----

4.=

1.0

~ . - -

=

u'

1.60

m/s

9r fi

60

4,=1.4

o

9. . . . .

u'

4 = 0 . 8

,-----

# -

1.0

z x . - -

4=

1.4

=

267

1.60

m/s

4o

40

.= /" " ,TF

i "i

20

g

0

i

,

,

,

i

i

,

i

,

5

I

,

i

,

Time

i

i

10

15

( ms )

l~

60

.

.

.

V

,

i

9. . . . .

[]

----

Z ~ , - -

"~

"d

.

.

4,

=

0,8

4.

m

1.0

41,=

.

.

i

.

.

.

u'

=

,

i

.

0.17

m/:

1,4

40

"d q)

i

i

,

,

i

i

,

i

i

5

I 10

Time

( me

,

i 15

i

,

=

I 10

Time

FIG. 4. Comparison between the predicted and the measured kernel radii at P = 1.0 atm and u' = 1.60 m/s, where u' is turbulence intensity, q~ is equivalence ratio, symbols represent measurements, and lines denote predictions. .

,

5

(

ms

15

)

FXG. 6. Comparison between the predicted and the measured kernel radii at P = 0.6 atm and u' = 1.60 m/s, where u' is turbulence intensity, 9 is equivalence ratio, symbols represent measurements, and lines denote predictions. ysis is developed to predict flame kernel growth in turbulent flow fields. With the use of an artificial thermal conductivity inside the flame kernel, the model successfully predicted flame kernel development at various operating conditions. Although this model has been initially designed for the prediction of kernel behavior at in-flight flameout conditions, it is expected that this model can be applied to spark ignition in SI engines, if the effect of electrode geometry is properly dealt with in the early stages. The model may also provide a means to estimate the average turbulent transport properties. In order to improve this model, future extensive study of flame stretch and surface area of a wrinkled flame must be conducted experimentally and theoretically, and more advanced modeling approaches [24] should be considered.

)

FIG. 5. Comparison between the predicted and the measured kernel radii at P = 0.6 atm and u' = 0.17 m/s, where u' is turbulence intensity, 9 is equivalence ratio, symbols represent measurements, and lines denote predictions.

Acknowledgment

This work was supported by Garrett Engine Division, Allied-Signal Aerospace Company, USA.

REFERENCES as for the ~ = 1.4 case, stretch has no effect on flame propagation.

Conclusions

A one-dimensional comprehensive model that incorporates a fractal description and asymptotic anal-

1. Lefebvre, A. H., Gas Turbine Combustion, McGrawHill, New York 1983. 2. Low, H. C., Wilson, C. W., Abdel-Gayed, R. G., and Bradley, D., Evaluation of Novel Igniters in a Turbulent Bomb Facility and a Tubo-Annular Gas Turbine Combustor, AIAA/ASME/SAE/ASEE 25th Joint Propulsion Conference, July 10-12, 1989.

268

PRACTICAL ASPECTS OF COMBUSTION

3. Akindele, O. O., Bradley, D., Mak, P. W., and McMahon, M., Combust. Flame 47:129-155 (1982). 4. Herweg, R., and Maly, R. R., SAE Technical Paper

922243. 5. Liou, D., "Flame Kernel Development in Atmospheric and Subatmospheric Turbulent Flows," Ph.D. Thesis, Pennsylvania State University, University Park, PA, 1994. 6. Damkshler, G., Z. Electrochem. 46:601 (1940). 7. Gouldin, F. C., Combust. Flame 39:249-266 (1987). 8. Santavicca, D. A., Liou, D., and North, G. L., SAE Technical Paper 900024. 9. Matthews, R. D., and Chin, Y.-W., SAE Technical Paper 910079. 10. Chung, S. H., and Law, C. K., Combust. Flame 72:325-336 (1988). 11. Spalding, D. B., Thirteenth Symposium(International) on Combustion, 649-657. 12. Bray, K. N. C., Proc. R. Soc. London A The Combustion Institute, Pittsburgh, 1970, pp. 431:315-335 (1990). 13. Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980.

14. Issa, R. I., Ahmadi-Befrui, B., Beshay, K. R., and Gosman, A. D., J. Comput. Phys. 93:388-410 (1991). 15. Westbrook, C. K., and Dryer, F. L., Prog. Energy Combust. Sci. 10:1-57 (1984). 16. Law, C. K., Zhu, D. L., and Yu, G., Twenty-First Symposium (International) on Combustion, 1988, pp. 1381-1402. 17. Sloane, T. M., Combust. Sci. Technol. 73:367-381 (1990). 18. Raizer, Y. R., Gas Discharge Physics, Springer-Verlag, New York, 1991. 19. Au, S., Haley, R., and 8my, P. R., Combust. Flame 88:50-60 (1992). 20. Chase, M. W., et. al., ]ANAF Thermochemical Tables, 3rd ed.,]. Phys. Chem. Ref Data 14(1) (1985). 21. Kee, R. J., et. al., Sandia Report SAND86-8246, UC401, reprint 1990. 22. Abdel-Gayed, R. G., Bradley, D., and Lawes, M., Proc. R. Soc. London A 414:389-413 (1987). 23. Maly, R., in Fuel Economy in Road Vehicles Powers by Spark Ignition Engines, (J. C. Hillard and G. S. Springer, Eds.), Plenum Press, 1984, pp. 91-148. 24. Pope, 8. B., Prog. Energy Combust. Sci. 11:119-192 London (1985).

COMMENTS C. T. Avedisian, Cornell University, USA. This is an interesting and potentially useful study concerning the influence of a spark on ignition. I have several questions for clarification. i. How important is the term dP/dt in the energy equation for the conditions of your calculation (was pressure assumed to be constant)? 2. You mentioned that the spark created "violent turbulence." Did you calculate the "decay" of the turbulence created? 3. How long was the spark kept on in the experiments, and did you vary the spark duration in the calculation? Author's Reply. 1. In a constant-pressure environment, dp/dt significantly affects flame kernel development in the blast-wave phase. Since the electric discharge system used in our study was an arc discharge, the pressure was assumed to be constant. 2. The turbulence of flow field would dominate the kernel growth process within a few hundred microseconds after spark onset. Therefore, we did not consider the effect of the decay of spark-generated turbulence in the report. 3. Because the spark duration and energy (90,us and 1.8 J) were very typical to the discharge systems used in aircraft gas turbines nowadays, we did not vary the discharge duration, energy, and/or power profiles in our experiment or calculation.

I. P. Nikolova, Bureau of Mines, USA. If the round shape

is the sole one, which shape is expected to be obtained by this model? I was pleased to hear that kernel hemispherical at origin distorts: I have had experience in modeling a kernel evolution, originally spherical, that distorts due to convection during the time of evolution.

Author's Reply. Based on experimental observation, kernel shape could be spherical for surface discharge igniters or cylindrical for electrode-type igniters at the initial stage. However, those initially cylindrical kernels would transform to be spherical ones in - 1 0 0 ,us. In our study, since the igniter tip was flush with the wall of the test chamber, the initially spherical kernels would become semispherical kernels within 200 ,us. Meanwhile, kernels were also slightly distorted along the flow direction. To simplify the numerical approach, a semispherical-kernel assumption was employed in our calculation.

N. Shah, Sundstrand Power Systems, USA. The abstract implied a high-altitude relight study; however, the temperature and pressure studies, which are the critical two parameters, were not reported. Author's Reply. Only operating conditions at 0.6 and 1.0 atm were reported in this paper at this time; however, other conditions (e.g., 0.3 atm) can be found in Liou's Ph.D. thesis [5]. Meanwhile, although the study was conducted at room temperature, the effect of low mixture temperature will be investigated in our future study.