Influence of thermal conductivity and aspect ratio on stable combustion inside a refractory tube

Energy Convers. Mgmt Vol. 38, No. 10-13, pp. 1051-1059, 1997

Pergamon P l l : S0196-41904(96)00135-5

© 1997 Elsevier Science Ltd All rights reserved. Printed in Great Britain o196-89o4/97 $17.oo + o.oo

I N F L U E N C E OF T H E R M A L C O N D U C T I V I T Y A N D ASPECT R A TI O ON STABLE C O M B U S T I O N I N S I D E A REFRACTORY TUBE RAPEPUN KANSUNTISUKMONGKOL~ and HIROYUKI O Z O E 2. qnterdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga Koen 6-1, Kasuga, Fukuoka 816, Japan and 2Institute of Advanced Material Study, Kyushu University, Kasuga Koen 6-1, Kasuga, Fukuoka 816, Japan

Abstract--The characteristics of combustion flame for premixed propane and air flowing inside an adiabatic refractory tube without a flameholder were numerically investigated. The effect of thermal conductivity of a tube wall kw and a tube aspect ratio L = l/D on the flume front was studied for the stable combustion at multiple locations. It is revealed that both upstream and downstream flame locations are shifted into the center of the tube with decreasing the thermal conductivity of the tube wall. Then the extinguishment occurs in the center of the tube because of insufficient thermal feedback. As the tube aspect ratio is decreased by the increase of tube diameter, either locus of the flame front moves to an inlet. On the contrary, when the tube aspect ratio is increased by the increase of tube length, the upstream flame location is almost the same place. The downstream flame location, however, moves to an exit. The location of stable flame appears to be determined by the distance to the nearest openings to the outside due to the thermal energy balance. The results are quite different from those for conventional combustion. © 1997 Elsevier Science Ltd. Refractory tube

Thermally stabilized combustion

Thermal conductivity

Tube aspect ratio

NOMENCLATURE A¢ = Area for conduction (m 2) Af = Frequency factor of chemical reaction (m3/kg.s) B ( Z ) = Radiosity (W/m 2) Bi = Biot number = Dh/kw Bi, = D[hj + EaT3(O3w+ 0~0~ + OwO~+ 03)]/kw Bi~ =

C = D = E = Fro-. = F(Z) =

G = h = H(Z) =

-AH

= I= J= k =

K(Z) =

I= L = P = R = St =

T W X z

= = = =

O[ho +

e#T~(O~ + 0~0o + Ow02o + 03o)]/k.

Specific heat capacity (J/kg.K) Tube diameter (m) Energy of activation (J/mole) Shape factor for radiation from surface rn to surface n Configuration factor from disk plane at a tube end to differentialring Dimensionless rate of reaction = x D ~ , / 4 W Heat transfer coefficient0 V / m " K ) Irradiosity0 V / m 2) Heat of reaction (J/kg) Dimensionless parameter = - A H D y / h T ~ Dimensionless parameter = h~D3/kwAo Thermal conductivity (W/m. K) Configuration factor between two differentialrings on the inside surface of the tube at distance Z apart Tube length (m) Tube aspect ratio = I/D Pressure (N/m 2) Universal gas constant (J/mole.K) Stanton number -- h x D 2 / 4 W C B Teraperature (K) Mass flow rate of mixture (kg/s) Mass fraction Distance from an inlet (m)

*Corresponding author. I051

1052 KANSUNTISUKMONGKOLand OZOE: STABLECOMBUSTION INSIDE A REFRACTORY TUBE Z:m Dimensionless distance = z/D

Greek letters

Emissivity of tube wall 0 = Dimensionless temperature = T/T~

Fuel-air ratio = fuel mass/air mass Dummy variable 7 = Reaction rate (kg/m3.s) Iz = Viscosity (kg/m.s) p = Density (kg/m~) Stefan-Boltzmann constant (W/m2.K~) Subscripts Inlet disk plane Outlet disk plane dA: Surface at a distance z from an inlet g = Gas mixture i = Inlet •40 m

o = Outlet w = Tube wall C3HB= Propane 02 = Oxygen

INTRODUCTION The stable, steady combustion in a refractory tube for propane with uniformly sized hexane droplets and ethane used as fuel was theoretically and experimentally investigated by Churchill and co-workers (Chen, Bernstein, Choi, Goepp, Tang, Pfefferle e t a l . ) [ 1 - 6 ] . They found that the behavior of combustion inside a refractory tube without a flameholder is unique and radically different from that for conventional combustion. For instance, the flame is invisible, quiet and very stable, whereas with conventional combustion, the flame responds rapidly to even minor perturbations and may become unstable. It is named as "thermally stabilized combustion" and its characteristics are concluded by Churchill [7]. Thermally stabilized combustion is one of the combustion process to enhance the efficiency and minimize pollutants. In the previous all works, there appear to be few studies on the dependence of flame front on various combustion parameters. The aim of this work is to study these effects for propane-air lean mixed gas. THEORETICAL ANALYSIS The combustion system for the present study consists of a propane-supply system, an air-supply system, a mixing chamber and a combustion chamber. The combustion chamber is a straight and CONDUCTION

FLAME FRONT Fig. I. Schematic of the thermally stabilized combustion system considered in this work.

KANSUNTISUKMONGKOL

and OZOE:

STABLE COMBUSTION INSIDE A REFRACTORY TUBE

1053

refractory ceramic tube, 254 mm long and 9.525 mm in diameter and well insulated in the radial direction. Premixed gas of propane and air from the mixing chamber is fed, ignited and burned inside the combustion tube without a flameholder. Pollutants, such as NOx and CO, are exhausted from an outlet of the tube. The flame is stabilized by thermal feedback process as schematically illustrated in Fig. 1. Thermal energy is convected from the hot burned gas to the tube wall at the downstream of the flame front. This thermal energy is then conducted and radiated from the hot downstream portion of the tube wall to the colder upstream portion of the tube wall. Finally, the entering gas is heated to the point of ignition by convection somewhere at the upstream portion of the tube wall. The principal postulates introduced for the analysis are as follows: (1) (2) (3) (4) (5)

The mixed gas is in plug flow with perfect radial mixing. The mixed gas is an ideal gas and transparent. Axial mixing, conduction, diffusion and pressure variation in the gas phase are negligible. The tube wall is well insulated in a radial direction. The reservoirs at both ends of the tube are black body and tube wall is gray surface.

The theoretical model for a steady state combustion consists of one integro-differential energy balance for a tube wall, differential energy and propane mass fraction balance for gas mixture as well as a reaction rate equation. They are expressed in dimensionless form as follows: d20w~- J [ B ( Z ) ~ T f - I ( Z )

(Og-0w)]

dog _ St[4(Ow - 0~) + I] dZ

(1) (2)

dXc~H~

dZ

= -G

(3)

where

B(z) = (1 - e)H(z) + eaTS(z); H(z) = trT~ F(z) + a T 4 F(I - z) + J = hrcD3/kwAc; I = -AHDy/hT~;

i

I

B(~)IK(z - ¢)1 de;

St = hnD2/4WCg; G = gD3"~/4W;

0, is the dimensionless wall temperature, 0s is the dimensionless gas temperature, E is the emissivity of tube wall, a is Stefan-Boltzmann constant (W/m:.K4), ~ is the dummy variable and ~ is the reaction rate (kg/m3.s). The reaction rate is modeled by using the Arrhenius law and an analogy with the result of butane-oxygen reaction rate which was carried out by Appleby et al. [8] owing to the fact that the flame speed for propane is nearly the same as that of butane. Therefore, the reaction rate is expressed as follows: _ .4 ^2v3/2 ]rl/2 e-E/RTw. ~) - - ElfPgAC3Ha,,xO2

(4)

d0w d Z - Bi:(Ow - Oi)

(5)

0s = 1

(6)

4, XC3H8- 1 --{-(~"

(7)

Boundary conditions At the inlet, Z = 0

1054 K A N S U N T I S U K M O N G K O L and OZOE:

STABLE COMBUSTION INSIDE A R E F R A C T O R Y TUBE

2200 2000 18oo 1600 1400 4e~

1200

m

lOOO i~.

800

Z"

600 400

•"

.-

200 0 k=..,

0.00

0.04

0.08

0.12

0.16

0.20

0.24

D i s t a n c e from an inlet [m] Fig. 2. Comparison of predicted wall temperature profiles (solid lines) with experimental data [1]. Computed gas temperature profiles (dashed lines) are also shown. Multiple solutions, curve 1. T.,~= 340.78 (K) and curve 2. T.,~=312.94 (K) were obtained for the same mass flow rate W = 4,528 x 10 -4 (kg/s). See Table 1 for other conditions.

At the outlet, Z = L

dOw

=

Bi (Ow Oo).

(8)

-

dZ

Overall energy balance is obtained from the following equation. W(-AH)'Xc3H, + nDtr (1 - :¢-e -2z) ( 7 + To') I

= l'f"(Cs,o Ts,o - Cs,iTg,i ) +

I

B(z)nD(FdA,-A, +

FdA,--Ao)dz

+h~Ao(Tw,~ - Ti) + hoAo(Tw,o - To) +EaA~(T~w,i- T~) + EoA¢(T~,o -- TO`)

(9)

where ps is the density of gas mixture (kg/m3), tk is the fuel-air ratio = fuel mass/air mass. The transport properties of the mixed gas such as the viscosity #g (kg/m.s), the heat capacity C~ (J/kg. K) and the heat transfer coefficient hs (W/m2"K) inside a tube and so on, that change with gas temperature, are also taken into account. These equations were solved numerically by the fourth-order Runge--Kutta-Gill integration scheme. Solutions which satisfy the boundary conditions and overall energy balance were found by trial and error. RESULTS AND DISCUSSION

The computed results are shown in Fig. 2. The circular symbols are the experimental wall temperature of Chen and Churchill [1]. The solid lines and dashed lines are the computed wall and gas temperature profiles, respectively. The predictions are in good accord with the experimental data. The dimensions and physical properties employed in the experiment and calculation are described in Table 1. Multiple steady state solutions do not always occur. There are a number of

K A N S U N T I S U K M O N G K O L and OZOE:

STABLE C O M B U S T I O N INSIDE A R E F R A C T O R Y T U B E

1055

Table 1. Dimensions and physical properties employed in the experiment and calculation Representative properties

Value

Area for conduction Frequency factor Tube diameter Energy of activation Heat of reaction Thermal conductivity of tube Tube length Pressure Universal gas constant Inlet temperature Outlet temperature Mass flow rate Emissivity of the tube wall Fuel-air ratio Stefan-Boltzmann constant

Ac Ar D E -AH k. / P R T, To W E 4) a

Unit

2.903 x 10 -4 4.7168 × 109 0.9525 x 10 -2 1.1396 × 105 4.6357 × 107 4.327 0.254 1.013 x 105 8.314 299.44 299.44 4.528 x 10 -4 0.21 0.0533 5.669 x 10 -8

me mJ/kg.s m J/mole J/kg W/m.K m N/m 2 J/mole.K K K kg/s --W/m2.K 4

appropriate conditions for this occurrence. Influence of the thermal conductivity and the aspect ratio on the multiple locations of the steady state flame front are to be investigated.

Effect of the thermal conductivity of a tube wall The effect of the thermal conductivity of the tube wall on the location of flame front was then computationally studied. For thermal conductivity less than 4.2 (W/m. K), no solutions were found (note that steady state solution may exist, but was not found by this work). For thermal conductivity greater than 4.9 (W/m.K), single stable solution in downstream regime was found. Since we are interested in multiple steady solutions, these results are not considered. Figure 3 shows gas temperature profiles obtained by the present computation for various combinations of the thermal conductivity and the inlet wall temperature as listed in Table 2. As the thermal conductivity of the wall increases from 4.2 (W/m.K) to 4.9 (W/m.K), the upstream flame front backwardly recedes to the inlet direction from 0.0996 (m) to 0.0772 (m) and the downstream flame front moves

2200 2000 7r /

/

/

;

.-,./:/

1800

: ;:

e

!

1600

;

.

t

Iml

~ 1400 i

" ;

1200

E lOOO

/

:

i

' :

/,

, o

O W m

¢3

J

800

600

'i ,'I

400

"

t,

/" i

:

/ ,

.'

200 0 ~

0.00

0.04

0.08

0.12

0.16

0.20

0.24

Distance from an Inlet [m] Fig. 3. Predicted gas temperature profiles for various combinations of thermal conductivity kw and inlet wall temperature Tw., Curve 1, kw ffi 4.2 (W/m.K); curve 2, k, = 4.4 (W/m.K); curve 3, k, ffi 4.6 ( W / m . K ) and curve 4, k~ = 4.8 (W/m.K).

1056 K A N S U N T I S U K M O N G K O L and OZOE:

STABLE C O M B U S T I O N INSIDE A R E F R A C T O R Y T U B E

Table 2. S u m m a r y of good combinations of the thermal conductivity o f tube wall and the inlet tube wall temperature that give the multiple steady state solutions displayed in Fig. 3 Thermal conductivity kw ( W / m . K )

No. 1 2 3 4 5 6 7 8

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

334.442 339.580 343.434 346.431 349.722 351.788 353.827 355.537

0.25

--

Flame location (m) upstream downstream

Inlet temperature (K) upstream downstream

I

I

315.415 313,064 312.076 311.268 310.639 309.890 308.184 308.723

I

I

I

9.96 9.30 8.79 8.48 8.18 8.03 7.87 7.72

I

× x x x × x x x

10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 l0 -2 10 -2

I

14.38 15.34 16.00 16.46 16.92 17.48 18.49 18.44

x x x x × x x x

10 -2 10 -2 10 -2 10 .2 10 -2 10 -2 10 -2 10 -2

I

0.20

O

=.

0.15

0.10

0.05

-

0.00 4.1

I 4.2

I 4.3

I 4.4

I 4.5

I 4.6

I 4.7

I 4.8

I 4.9

5.0

Thermal conductivity [W/m.K] Fig. 4. Dependence o f the flame location on the thermal conductivity k..

Table 3. S u m m a r y of good combinations o f the tube aspect ratio and the inlet tube wall temperature that give the multiple steady state solutions displayed in Figs 5 and 6 No.

Tube length 1 (m)

AI A2 A3 A4 A5 A6 A7 BI B2 B3 B4 B5 B6 B7

0.254 0.254 0.254 0.254 0.254 0.254 0.254 0.240 0.260 0.280 0.300 0.320 0.340 0.360

Diameter D (m) 0.9 1.0 1.1 1.2 1.3 1.4 1.8 0.9525 0.9525 0.9525 0.9525 0.9525 0.9525 0.9525

x x x x × × x x x x × x × ×

10 -2 10 -2 l0 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2 10 -2

Tube aspect ratio L 28.222 25.400 23.091 21.167 19.538 18.143 14.111 25.197 27.296 29.396 31.496 33.596 35.695 37.795

Inlet temperature upstream downstream 1.135510 1.145470 1.146650 1.144530 1.140300 1.146460 1.158550 1.135900 1.137560 1.141040 1.146530 1.146723 1.148137 1.149378

1.04450 1.04560 1.05195 1.05970 1.06785 1.06660 1.10080 1.06600 1.03960 1.02320 1.01377 1.00760 1.00410 1.00220

Flame location upstream downstream 10.05 8.992 8.313 8.213 7.659 7.112 6.068 9.670 9.554 9.407 9.197 9.205 9.138 9.071

17.10 15.49 14.13 12.70 11.49 11.07 8.523 14.72 16.98 19.40 21.67 24.12 26.42

28.80

KANSUNTISUKMONGKOL and OZOE: STABLE COMBUSTION INSIDE A REFRACTORY TUBE 1057 7

"~" 6 .o

E

; ; ;

4

':// i J i i

i ;

t~

.."

O)

3

,/

i

'

.9o 2

i

J

t-

0

4

8

12

Dimensionless

16

20

24

28

d i s t a n c e f r o m a n Inlet [-]

Fig. 5. Predicted gas temperature profiles for various combinations of tube aspect ratio L = I/D (1 is constant whereas D is changed) and inlet wall temperature Tw,~.Curve 1, L = 21.167; curve 2, L = 23.091; curve 3, L = 25.4 and curve 4, L = 28.222.

from 0.1438 (m) to 0.1844 (m) to the outlet direction. Note that the flame location is defined as a p o s i t i o n where the gas temperature gradient becomes m a x i m u m . The locus o f the flames vs the thermal conductivity is displayed in Fig. 4. As the thermal c o n d u c t i v i t y o f the tube wall increases, conductive heat from the hot d o w n s t r e a m p o r t i o n to the colder u p s t r e a m p o r t i o n o f the wall increases. The u p s t r e a m flame location can be stable t o w a r d the inlet because the cold reactants rise to its ignition p o i n t quicker owing to more thermal feedback. By the same energetic a r g u m e n t , the d o w n s t r e a m flame location can be shifted toward

I

I

I f

# - - 1 - "- , '

6

l,.~ ~!

;

I]

,

;

'

i

/

,

/

-

,°' ;

:

:

' /

i

, ;~,, ,. :. '

! /

;

" ;

f

~

I

-:

i"

:

, :

I

;:

, ,

'

t:

' ~)

m

(

3

~)

I¢

o

,~

2

I

:

.'

,~

;

J'

I

/ ",~7iL 7

" ~)

!

//i

, ,

_L..,"_ ........

t

,'

" ...

/

. ....

.~

,

.,'

.....

1

E

,1

0

0

I

I

I

I

5

10

15

20

Dimensionless

25

I

I

30

35

d l s t e n c e f r o m a n inlet

[-]

Fig. 6. Predicted gas temperature profiles for various combinations of tube aspect ratio L - - I/D (1 is changed whereas D is constant) and inlet wall temperature Tw.,Curve 1, L ffi 25.197; curve 2, L ffi 27.296; curve 3, L ffi 29.369; curve 4, L ffi 31.496; curve 5, L ffi 33.596; curve 6, L ffi 35.695 and curve 7, L = 37.795.

1058 K A N S U N T I S U K M O N G K O L and OZOE:

40

'

I

STABLE COMBUSTION INSIDE A R E F R A C T O R Y TUBE

'

I

'

I

I

'

I

'

35 3O

m.

g

25 2O 15 10 5 I 16

~

I 20

~

I 24

,

I 28

~

I 32

~ 36

I 40

Tube aspect ratio [-] Fig. 7. Dependence o f the flame location on the tube aspect ratio I/D. ZX 1 = 0.254 (m) and D = 0.9 x 10 -z ~ 1.8 x 10 -2 (m); O l = 0.24 ~ 0.36 (m) and D = 0.009525 (m); • total tube length for each case.

an exit since larger thermal conductivity of the wall can supply enough energy for the heat loss to the tube end opening. It is evident that both upstream and downstream flame locations move into the center of a tube with the decrease of thermal conductivity and a minimum value exists (for a given set of other conditions). If thermal conductivity of the wall is lower than this critical value, the flame will 14

I

I

I

I

I

I

[

13 12 •"~-

11

v

~

8

m

7

~ 0

6

E N

v

.?_

distance from upstream

f l a m e location to the Inlet distance from downstream f l a m e l o c a t i o n to the e x i t

c •

~

4

3 2 1 0 24

I 26

i 28

I 30

J 32

I 34

I 36

38

40

Tube aspect ratio [-] Fig. 8. The stable dimensionless distance from the upstream flame front to the inlet (the circular symbols) or the downstream flame front to the end of the tube (the square symbols).

KANSUNTISUKMONGKOL and OZOE: STABLECOMBUSTION INSIDE A REFRACTORY TUBE 1059 become extinct because of insufficient thermal feedback. The effect of thermal conductivity on the downstream solution is slightly more prominent than that on the upstream solution. Effect o f the tube aspect ratio

The effect of the tube length vs the tube diameter on the flame location is studied next by changing both I and D. The range of variables are listed in Table 3. Series A are for tube length kept at 1 = 0.254 (m) with various diameters. Series B are for constant diameter D = 0.9525 × 10 -5 (m) with various tube lengths. Stationary gas temperature profiles for various combinations of the tube aspect ratio and the inlet wall temperature are indicated in Figs 5 and 6. Figure 7 shows dependence of the flame locations on the tube aspect ratio. Triangle symbols are the results when the tube length is constant and the tube diameter is changed. Circular symbols are the results when the tube length is changed while the tube diameter is constant. Total tube lengths are also indicated by additional black square symbols. It suggests that influence of tube diameter differs from that of tube length. As the tube diameter is increased from 0.9 × 10 -2 (m) to 1.8 × 10 -2 (m), both upstream and downstream flame fronts move to upstreamward direction from 10.05 (in dimensionless term) to 6.068 and from 17.1 to 8.523, respectively. Increasing the diameter D results in the increase of G in equation (3) and greater decrease of Xc3n8 in the downstream. Thus, the ignition occurs more rapidly and both loci of flame front are shifted toward the inlet. Increasing the diameter also decreases the average velocity and both flame fronts move to the inlet. With the increase of the tube length from 0.24 (m) to 0.36 (m), the dimensionless upstream flame front location is nearly constant at 9. However, the dimensionless downstream flame front location moves to downstreamward direction from 14.72 to 28.8. Such behavior of the flame front occurs in order to maintain overall energy balance. The stable upstream location keeps almost the same distance from an inlet. On the other hand, the downstream flame is always at the location 9 to 10.5 from the exit. These are further shown in Fig. 8 in which distance from the inlet to the upstream flame front (the circular symbols) or distance from the downstream flame front to the outlet (the square symbols) are almost the same in spite of the difference in the tube length. The location of stable flame appears to be determined by the distance to the nearest openings to the outside due to the satisfaction of the thermal energy balance. CONCLUSION Influence of the thermal conductivity and the aspect ratio on the location of the flame front was numerically studied. These results are expected to be useful for the improvement of the efficiency of combustion system. REFERENCES

1. Chen, J. L.-P. and Churchill, S. W., Combustion and Flame, 1972, 18, 27-42. 2. Bernstein,M. H. and Churchill, S. W., Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1977, pp. 1737-1745. 3. Choi, B. and Churchill, S. W., Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1979, pp. 917-925. 4. Goepp, J. W., Tang, S. K., Lior, N. and Churchill, S. W., AIChE J., 1980, 26, 855-858. 5. Tang, S. K., Lior, N. and Churchill, S. W., Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1981, pp. 73-80. 6. Pfefferle,L. D. and Churchill, S. W., Proceedings Worm Congress Ill of Chemical Engineering, Tokyo, 1986, Vol. 4, pp. 68-71. 7. Churchill, S. W., Chem. Engng Technol., 1989, 12, 249-254. 8. Appleby, W. G., Avery, W. H., Meerbott, W. K. and Sartor, A. F., J. Am. Chem. Soc., 1953, 75, 1809-1814.