Joint measurements of velocity and scalars in a turbulent diffusion flame with moderate swirl

Twenty-first Symposium (International) on Combustion/The Combustion Institute, 1986/pp. 1569-1577

J O I N T M E A S U R E M E N T S OF V E L O C I T Y A N D S C A L A R S I N A T U R B U L E N T D I F F U S I O N FLAME W I T H M O D E R A T E S W I R L S.H. ST&RNER AND R.W. BILGER Department of Mechanical Engineering The University of Sydney N S W 2006 Australia

Simultaneous measurements by two-component LDA and Mie scattering methods have been made in a moderately swirling, turbulent hydrogen diffusion flame in a horizontal co-flowing stream. Mean temperature is obtained separately by thermocouple. The three velocity components are measured in pairs so that all components of the stress tensor are obtained. The Mie signal is used to obtain scalar time traces. The flame expands into the freestream, which does not act as a confinement, and is shortened one third and widened around one quarter by the swirl. This contrasts with results in the literature for confined swirling flames which lengthen with increasing swirl. The difference is thought to be caused mainly by the action of the velocity pressure-gradient correlations: in a confined flame the radial pressure gradient is maintained high downstream, so these terms appear to suppress the u-v stress. In the present work, the upstream decay of streamwise velocity is increased, as is the turbulence intensity, whilst far downstream the normalized data look similar to those of unswirled flames. There is less penetration of external fluid towards the flame axis than in non-swirling flames. The v-w and u-w stress components have similar magnitudes, and it appears that the v-w stress may be dealt with by gradient transport modelling where the radial pressure gradient is not too high.

1. Introduction A substantial body o f e x p e r i m e n t a l data on n o n - r e a c t i n g , swirling flows has b e c o m e available o v e r the last twenty years. Usually, though, the object has b e e n to study some special feature, such as flame stabilization, and often the generality o f the findings has b e e n limited. Cold flow e x p e r i m e n t s i n t e n d e d to aid flame predictions also neglect the effect o f swirl on the variable density. In r e c e n t years, the p r o b l e m s o f m a k i n g detailed m e a s u r e m e n t s in swirling flames have b e e n m a d e tractable by n e w e r optical methods, but t h e r e does not yet a p p e a r to exist any set o f p u b l i s h e d data that may serve as a general b e n c h m a r k for testing predictive models. T h e ideal e x p e r i m e n t should i n c l u d e full details o f shear stress and velocity-scalar correlations as well as the usual lower m o m e n t s . U n w a n t e d features that may add c o m p l e x i t y such as buoyancy, finite chemistry, stabilization devices and c o m p l e x g e o m e t r y should be suppressed. T h e w e l l - d o c u m e n t e d 1'2 horizontal t u r b u l e n t H2 flame in a co-flowing s t r e a m is well suited for this p u r p o s e . T h e aim o f the p r e s e n t w o r k is thus to e x p a n d the data base for this flame to include

m o d e r a t e swirl. M e a s u r e m e n t s are p r e s e n t e d h e r e o f centerline data a n d vertical traverses at 26, 40 and 80 fuel j e t d i a m e t e r s f r o m the nozzle, and also i n c l u d e d are full details of initial conditions. Implications for m o d e l l i n g are discussed a n d the effect o f swirl on t u r b u l e n t kinetic e n e r g y p r o d u c t i o n is e x a m i n e d .

2. Equipment and Data Reduction T h e basic a p p a r a t u s and data r e d u c t i o n m e t h o d have b e e n d e s c r i b e d by S t e r n e r 2 and only the modifications n e e d e d for g e n e r a t i o n a n d m e a s u r e m e n t o f swirl are detailed here. A central h y d r o g e n fuel jet, seeded with M g O particles o f n o m i n a l l y 1 ~xm size, issues f r o m a 1 m long horizontal tube o f i n n e r d i a m e t e r D = 9.90 m m and o u t e r d i a m e t e r 10.72 m m with a bulk velocity o f 139 m/s and a Reynolds n u m b e r o f 1.3 x 104. It is s u r r o u n d e d by a tube o f 18.4 m m i n n e r a n d 19.1 m m o u t e r diameters, which c o n d u c t s swirling air at nominally 37.8 m/s axial velocity. Swirl is g e n e r a t e d in the a n n u l u s by an 18 m m l o n g helix, cut as a screw with six entries f o r m i n g 0.7 m m thick vanes at 45 ~ angle to the axial direction, based

1569

1570

TURBULANT COMBUSTION

vanes at 45 ~ angle to the axial direction, based on the mean diameter of the annulus. The helical swirler is placed with its exit 26 m m upstream of the jet exit plane. This assembly is placed centrally at the 305 m m square entry to the glass-walled working section which is bolted to a 9:1 contraction of the windtunnel, from which the co-flowing air enters the working section with a velocity ue = 12.0 m/s. The two-colour, two-component, dual beam, forward scatter LDA system is shown in Fig. 1. Bragg ceils are used for the radial (v) and circumferential (w) velocity components, with two cells for each component, so that a shift frequency of 10 MHz is obtained. The velocity components are measured sequentially in pairs: u-v, u-w and v-w All traverses are made in the vertical direction. T h e measurement volume dimensions are a r o u n d 0.2 x 1.0 ram. T o obtain a Mie scattering signal for scalar measurements, an unfocused beam of a third laser colour, 476 ram, is directed vertically upwards, with the scattered light detected at 50 ~ from the forward direction. T h e measurement volume has dimensions of approz~imately 1.3 x 1.5 mm. The scattered light from a He-Ne laser, not shown in Fig. 1, is recorded to monitor the seeding density at the jet exit. The velocity signals are processed in counter-type timers and recorded on analogue tape together with the Mie scatter and monitor traces and also data indicating the occurrence of velocity validations. The taped information is played back into a VAX computer. Mean temperatures have been obtained by a Pt-5Rh/Pt-20Rh thermocou-

/ ~,BBnm

Y FIG. I. Isometric sketch of optical layout.

pie with 0.2 m m head, where the compensation for radiation loss has been made, following Kent ~ assuming a thermal emissivity of 0.3. Scalar information is derived from the Mie signal as described by Stfwner 2. The viability of this technique has been demonstrated by an experiment in an isothermal air jet z. T h e intermittency factor -/(-=7, where I(t) is unity in the fuel stream a n d zero in the free-stream) is determined by fitting a Gaussian form to the zero spike of the Mie signalt. It is found that velocity-scalar correlations are obtained with good accuracy, provided that the scalar component is first order, whilst scalar variances and correlations where scalars appear in higher order may show bias a n d increased scatter. Velocity bias correction for the effect of seeding only the fuel stream is also described in ref. 2 together with detailed error estimates. Briefly, errors in the streamwise velocity (u) are estimated to be within 3 a n d 6% of axis values for mean and rms data, respectively. This applies also to the rms values of the v and w components. The accuracy of ~ (the Reynolds average) is estimated to have an error limit of 10% of maximum values for all traverses. Shear stresses and velocity-scalar correlations have larger errors, up to 15% of peak values at each axial location.

3. Results and Discussion

3.1 Measured Initial Conditions

Figure 2 shows radial profiles of all velocity components at x/d = 0.2, x being the streamwise distance from the jet exit. T h e complicated profiles of turbulence intensity arise from the four b o u n d a r y layers at the inner and outer nozzle walls. T h e lack of complete symmetry in the ~ and % profiles is probably caused by wakes from the swirl vanes. T h e measured mean temperature profile shows the location of stoichiornetric mean composition and the width of the mixing layer in which combustion occurs. The working section has a constant crosssection, and the measured mean axial pressure gradient in the ~co-flowing stream, as an average from x/D = 0 to 100, is - 3 3 Pa/m. At x/D = 26, 40 and 80, the pressure gradient is - 4 4 , -- ~0 and - 2 5 Pa/m, respectively.

tValues of ~/ thus obtained are known4 to be somewhat too low due to differential diffusion of fuel ,' d marker particles.

J O I N T MEASUREMENTS OF VELOCITY AND SCALARS

1571 -

10

o

2000

D

O3

2000

u.

o

02

~u.

o

T

lOOO 5oo

K 0.5 1000

o1~~

A "

9

,I!

~',

/

~"1~/~.

LL

0.15

I~)~

02

01 00s

01

0

~ 01

0

i

o lOO

FIG. 3. Centerline profiles of axial turbulence intensity and mean temperature. Present results: o swirling flame; Anon-swirling flame.--Glass and Bilger 6. -Til

0.3

ao

ture t h r o u g h o u t , without lift-off or instability in the initial region. M e a n t e m p e r a t u r e (Fig. 3) on the centerline indicates a flame l e n g t h f of 75 to 80 nozzle d i a m e t e r s c o m p a r e d with a r o u n d 130 d i a m e t e r s for the unswirled flame o f K e n t and Bilger 5. T h e excess velocity halfradius L~ (i.e. the radius w h e r e the excess m e a n velocity is half o f its axis value), normalized by the fuel nozzle radius R = D/2, has values 5.42, 6.16 and 7.66 at x/D = 26, 40 and 80, respectively. T h i s is l a r g e r than the data for the unswirled flame o f Glass and Bilger 6, 4.7 and 6.6 at x/D = 40 and 80.

=J0 2

1

1

r/R

2

FIG. 2. Initial profiles of mean temperature T,

streamwise (u), circumferential (w) and transverse (v) velocity components: means and turbulence intensities at x/D = 0.2. Centerline velocity Uo = 177.1 m/s; co-flowing air velocity u~ = 12.0 m/s. Fuel nozzle radius R = 4.95 mm. Rhs of graph is above centerline. T h e nominal swirl n u m b e r , based on meas u r e d initial conditions, is 0.60, a value normally associated with the onset o f recirculation. H o w e v e r , the high velocity central jet, a l t h o u g h strongly r e t a r d e d initially, is far f r o m reversing. In the p r e s e n t results, the 'unswirled' flame r e f e r r e d to has the same initial conditions as the swirled flame e x c e p t that the axial velocity in the a n n u l u s is r e d u c e d to 4.0 m/s. This results in negligible swirl n u m b e r , ~ 0.02, whilst a v o i d i n g recirculation in the wake of the a n n u lus exit.

3.2 General features T h e main effect o f i n t r o d u c i n g swirl is a s h o r t e n i n g and b r o a d e n i n g o f the flame. Shad o w g r a p h p h o t o g r a p h s show t u r b u l e n t struc-

3.3 Mean Velocity and Temperature F i g u r e 4 shows the c e n t e r l i n e decay o f axial m e a n m i x t u r e fraction and excess m e a n velocity Uo -= u0 - u~, n o r m a l i z e d by the value at the j e t exit, Uo. Also shown are data for unswirled J H2 flames. T h e swirling flame initially loses m o m e n t u m rapidly d u e to the strong adverse axial p r e s s u r e gradient, but d o w n s t r e a m values a p p r o a c h those o f the unswirled flames. Radial p r o f i l e s f t o f m e a n excess velocity U -= u - u~ are shown in Fig. 5 t o g e t h e r with m e a n tangential velocity w a n d m e a n t e m p e r a t u r e T. T h e shear rate OU/0~q is some 1 0 - 1 5 % greater below the axis than above it. T h i s is known to originate f r o m a very small m i s a l i g n m e n t between the axial directions o f the central fuel j e t and the a n n u l a r swirling jet. It was f o u n d that this a l i g n m e n t is critical; the central fuel pipe has to be p r e v e n t e d f r o m any b e n d i n g by fitting

fThe flame length is defined as the length to maximum mean temperature and stoichiometric mean mixture fraction. f f T h e transformed co-ordinate "q = ylk,, is Cartesian, y being the vertical distance from the centerline. Hence, "q is negative below the axis of the flame.

1572

TURBULANT COMBUSTION t, z~lz= &

t=t,

oo~o~ o %~

05 o

o

o

&

O2

[]

~

o A &o

o

a

2O00

t=

a~ ~=o~a T

K

o o~ ~ e o

~ 1 7 6 1 7 6 1 7 6 1 746~176

t,o o o o o

10410

&o

10

o

io

uy%

o

0.7

01

005

500

o

2

5

10

20 x/0

50

100

FIG. 4. Axial decay of mean mixture fraction ~ ([]) and streamwise excess mean velocity Uo (o swirling flame; A non-swirling flame).--Glass and Bilger6. several supports relative to the annulus. T h e misalignment for the present results is less than 0.2 ~ yet this is still sufficient to p r o d u c e measureable asymmetry t h r o u g h o u t the flame. T h e m a x i m u m m e a s u r e d t e m p e r a t u r e in the flame is 2120 K (Fig. 3) on the axis atx/D = 7 0 80. The equivalent m e a s u r e m e n t by Kent and Bilger 5 in the unswirled flame yielded 2135K, a very close result. T h e profiles of tangential velocity w shown in Fig. 5 intersect the abscissa a little below the nominal flame axis, as determined from U profiles. This d o w n w a r d shift is visible also in the peaks o f the U profiles. T h e r e is some asymmetry in the ~ profiles which have larger peaks below the axis, again thought to arise from the slightly diverging axes o f the central and annular jets. Also shown in Fig. 5 is the intermittency factor -/. Whilst unswirled flames show intermittency on the axis from x/D = 60 onwards which grows with axial distance, there is no intermittency in the swirling flame inside the normalized radius "q = 0.6 at x/D = 80.

05

075

o

2

"ii

o 02

ooo~ ,o o

01

YUo

o

o o~

A ~, r t" & A~,

A

&ao

~ ~ ~' . . .~. =,~ ~ g 0gcx~ o

-0~

oo

oo

i -1

~176176

-~ z

1

11

FIG. 5. Radial devlopment of excess mean velocity U, tangential velocity w, mean temperature -T and intermittency factor ~ for the swirling flame,

i

02

ooOO

xl0 = ~6 oOO o ~ ~ 1 7 6 1 7 6

o o~ O o A 13

0,

~ O OO OOOO O O O='~O

oo~

~

0 090 ago

02

3.4 Turbulence Components T h e axial variation in centerline turbulence intensity (u-~)1/2 Uo shown in Fig, 3 is much enlarged u p s t r e a m by the swirl, but at x/D = 40 it is below that o f the non-swirling flame. Values for the non-swirling flame are below the results of Glass a n d Bilger ~ an effect which may arise from differences in nozzle configuration. Radial profiles o f all turbulence components for the swirling flame are shown in Fig. 6 together with the u-component for the nonswirling flame at x/D = 40. Whilst peak values are the same, the swirl.._~pears to result in s~gnificant reduction o f (u ,''z)1/2 near the axis. T h r o u g h o u t , the magnitude of the swirl (w)

40

&

'~o

= ) 01 *, i 0

o

~ 99 oo

~ o

~oo

9 9o~r o x / O : ~,0 o 9 t , t , & A t ~,

o o

0z

-

o

o

x / O : 60 o ~ ~ ~

o

0 a~

8 ~

0 -z

i -1

O

L 1

q

FIG. 6. Radial profiles of turbulence intensities. Swirling flame: o (u---72,)I/2 /Uo; [] (v~' ) v2 IUo; A (w~2') v~ /Uo. Non-swirling flame: V (u--72'v2/Uo. )

JOINT MEASUREMENTS OF VELOCITY AND SCALARS c o m p o n e n t lies between those o f the streamwise and radial components u a n d v. T h e v and w-components are equal on the axis, as required by symmetry. (The downward shift is again seen here). T h e w-component does show off-axis peaks, but less so than for the u-component. This is reasonable, as the w-turbulence is produced both directly t h r o u g h - 2v--r~w'/r O(r ~v)/br and indirectly by redistribution from the u-component. T h e direct route is much weaker than the generation o f u-turbulence via the larger -2u-V-V-rV ' O-ff/~r; hence the lower off-axis peaks and lower overall level. T h e relative magnitudes of the three components of turbulent kinetic eners~y agree with results for isothermal swirling jets ''s.

1573

correlation is much weaker at a r o u n d one third of u ' v ' upstream, weakening further with x/D, and with R~w typically less than 0.5 Ru~. The relatively poorer symmetry and larger scatter originates from this weakness: v ' w ' =- v w - ~ , a difference between two nearly equal quantities. One would expect the results to be zero on the centerline and positive elsewhere. The negative values shown near the axis may stem from minor alignment or LDA bias problems. T h e axial flux u ' w ' has roughly the same magnitude as v ' w ' , a n d thus suffers from the same sources of error. However, it is generally positive, as also f o u n d by Takagi et al ~~ for a confined swirling flame. 3.6 M i x t u r e Fraction Fluxes

3.5 S h e a r Stresses Figure 7 shows radial profiles of the three velocity correlations u ' v ' , u ' w ' and v-b-r~w ', all normalized by centerline excess velocity. T h e u - v correlation 6'~, shows peaks at radii of maxim u m mean strain rate, and the correlation coefficient R,~ has maxima a r o u n d 0.4. T h e v - w

Figure 8 shows the velocity-mixture fraction correlations u'---~,~ and w'---~.Since the radial gradients o f U and ~ have the same sign, profiles o f the axial flux ~ can be expected to be positive everywhere, as is the case here. T h e behaviour shown in Fig. 8 is similar to that in an unswirled flame a and in a heated jet ~l, both as

1S t, A

10

0 0

~o ~ ~

--61--.

'

v ~

o t:

o~| o -0.5

A oz '

.__

6~oOO o

Ob O 0

o

8~ A

~S a

A

O5

A

O

zx A

0

,~, t~ o

o o

o

~~

o

~ 1 7 6 1 7o~6

o I

o os

o o

_

,~

o p._O~

oo

o

o~

9~0 -1.0

[] oo

zs z~

-15

^,, o~A.

o

10 "

r[] 1&7 6

05

0

qf,~ % t,

A ~' C : ~

I[ ~ ~

o ~oPo8~ oa~ o a A ~

z~ A"~~

0

~o

x/D

0 AAO0

O~

00~ S~176176176

100v~

A A ~000

o 0

0

o

26

o

z.O

~,

G0

O0

-0 .Oz.

1.0

o~

o o

0.02

WI~ 0S Uo~, 0

100u-~"

T

Bo ~ 0Q

~

.

o -0 5

;~ " S

-0.02

L

-2

-1

0

1

11

FIG. 7. Radial profiles of shear stress components. o, [~, ,~ swirling flame; ~7 non-swirling flame; line through data at x/D = 26.

-006. -2

,

-1

0

1

q

FIG. 8. Radial profiles of normalized mixture fraction fluxes. The centerline values of ~o are 0.19, 0.11 and 0.04 at x/D = 26, 40 and 80, respectively.

1574

TURBULANT COMBUSTION

to shape an d magnitude; the normalized flux grows with x/Dand has off-axis peaks. Similarity with the unswirled flame 2 applies also to the radial flux v'----~; peak values are of the same magnitude, b u t the increase in values with x/D is less obvious here. 3.7 Favre Quantities Favre (density weighted) averages are increasingly favoured in flame predictions because of the much simplified equations that result. To enable to simple comparison with the Reynolds averaged data presented in this work the ratios o f Favre averages (denoted by tilde overbars) and Reynolds averages are shown for some representative data in Fig. 9. For any two quantites P and Q have

Q -~ vQ/p = Q + p'Q'/p

1 "0 ,fi-/L u

1"0

c 0.98

0.8

0.96

0.6

0,%

1'2t

(])

p , Q , _~ pp"Q"/~

/

= p ' Q ' + p'p'Q'/~

(a)

(b)

(p,p,p,Q,)/~2,

_

(2)

(c)

where p is the density. It is seen that zi is lower than t2 by a few percent; thus p-7"U-7/pis negative and small, relative to ti. Since the w turbulence intensity is much larger than the u-component intensity, ~7-~7~ is much more important, so, at the maxima, ~ -~ 2zb. For the variances ~t2 and ~,2 (simply setting P = Q in Eq.(2)) the triple correlation (b) dominates over term (c). It is positive n e a r the axis and negative at the edge, whilst the double correlations in (c) are always negative. T h e same applies to the u-v and u-w stresses. However, in the v-w stress, term (c) dominates n e a r the axis so the ratio is less than unity there.

Discussion

-

O lu v Or + v w r ~ j ,_

-

-

(a)

_of -~ ~ r - " (c)

1

(b)

~,a~ ~' (d)

where p is the pressure.

1.0 0'~ 0"6 \ \

,

0.4.

In the balance equation for turbulent kinetic energy k, the production terms are written, in boundary layer axisymmetric Favre form:

Sk =

1.2

(3)

0

1

N tl

2

Fro. 9. Ratios of Favre to conventional time averages at x/D = 40. T h e neglected redistributive part, p'au'~/axk of the velocity pressure-gradient correlations is not i m p o r t a n t here as it does not greatly alter the energy level (in c o n s t a n ~ f l o w , au~/aXk --- 0). T h e diffusive part, b(p'u~)/bxk, is usually included with the turbulent diffusion terms. A calculation for the radial position "q = 0.65 at x/D = 26 shows that term (a) in Eq.(3) dominates; the ratios o f terms are: (b)/(a) = 0.08,

1575

JOINT MEASUREMENTS OF VELOCITY AND SCALARS (c)/(a) = - 0 . 0 8 and (d)/(a) = 0.09. As we have also seen, the normalized u-v correlation and turbulence intensities are not markedly affected by the swirl. However, for a closely confined, moderately swirling flame1", Takagi et al 1~ r e p o r t strong suppression o f the u-v stress. T h e y attribute the u-v suppression to the mean pressure gradient term - u " op/Or in the u-v balance equation. (They neglect the correlations u'[ op'/Oxj for lack o f data. Whether such neglect is valid here is a moot point; experiments in a heated j e t 12 show that in the u-v balance equation these correlations are large, and that they roughly balance the leading production term.) T h e large suppression by - u'~ ~/Or (at x/D = 43 it has lost only a quarter of its initial value), because the angular moment u m cannot diffuse into s u r r o u n d i n g air, so a strong positive 0p /Or persists. The reduced shear stress and turbulence are consistent with the finding 1~ that the swirl lengthens the flame. T h e present results, however, show a flame that is shortened by the r a p i d expansion of the annular swirling air j e t into the freestream; this expansion causes a strong adverse (positive) op/Ox near the nozzle, with r a p i d decay of axial j e t m o m e n t u m and radial o f angular momentum, so that, as seen above, term (c) in Eq. (3) is small already at x/D = 26. Thus, the flame length will shorten if there is fluid outside the swirling j e t into which the angular m o m e n t u m can diffuse. This is certainly so for the free, p r e m i x e d flame o f Chigier a n d Chervinsky 1~. It appears also to be the case for the confined diffusion flame of Lockwood et a114 where an annular jet of 44.5 m m d i a m e t e r (surrounding the fuel jet) issues into a 210 mm diameter furnace; this flame also shortens with increasing swirl, contrasting with that of Takagi et al, where all the s u r r o u n d i n g air is swirling. It is common in the literature to find v'w' modelled by . v'w'=-v,/o~

(0(~/,)) ~r~-r J,

shows (Fig. 10) that v'w' would be fairly well predicted using the model in Eq. (4) (except perhaps near the axis, but here the accuracy is rather low) with ~rw near unity. However, this model would clearly be inadequate in flows like that of Takagi et al, where the pressure gradient term in the v-w balance equation, '---7 w op/Or would be of the same order. T h e u-w stress c o m p o n e n t appears more complex to model, since in its balance equation, all of the production terms,

(a)

(b)

(c)

W

(6)

Ox '

(d) are large. However, if we make the aproximations N

u"v"

off

= - v t a~- and

o%"=

-~,r

(7)

O(~lr) Or

(8)

and re-arrange, Eq. (6) reduces to

(9) I

& o

Z

t=&~_ __

(4)

where the bracketed part is the circumferential strain rate, analogous to OU/Or. A calculation using present results at x/D = 26, with the turbulent diffusivity vt given by measured values: UrU t

v,- - OU/Or'

(5)

?The jet Reynolds number of the flame of Takagi et al is a low 1600, indicating that transition to fully turbulent flow may be incomplete; hence, comparisons must be viewed with this caution in mind.

-1

-1

1 11

FIG. 10. Comparison of measured stress ~ (0) and the model -vtra(r~/r)/ar (A) at x/D = 26 for the swirling flame.

1576

TURBULANT COMBUSTION

This suggests the model N u " w " ~-

V~ a~ a ~ C~w k Or Or

.

(I0)

With a value of cu~ = 8, Eq. (10) yields a satisfactory fit to the data at x/D = 26, reproducing the zero crossing in the inner part of the shear layer, since a~/ar changes sign. However, the fit is poor at x/D = 40 and 80 where all the measured data are positive. The mixture fraction flux v"~" for an unswirled flame has been shown previously2 to be satisfactorily modelled by

~"U=

-,',/a~ a--;'

ql ~ k )

with cr~ = 0.7, the usually quoted value in the literature. T h e nresent results show the same basic behavtour of v"~" as for the unswirled flame, but the model in Eq.(11) yields predictions a r o u n d 40% too large. The cause of this overshoot is possibly the radial pressure gradient, which although only slightly augmented by the swirl, acts to suppress the measured scalar flux, throu/u h the term - - ~ b ~ in the balance equation v"~". Where the swirl effect is stronger, such as in the flame of Takagi et al, this term is likely to dominate, so the model of Eq. (11) fails, and solution of the ~ balance equation becomes necessary.

5. Conclusions

The aim of this work has been to make direct measurements of modelled quantities for a simple diffusion flame with moderate swirl. Second order velocity and scalar properties have been obtained, including the complete shear stress tensor, to enable direct submodel examination 9 It is f o u n d that the swirl shortens and broadens the flame. Scrutiny of the production terms in the balance equations for second order quantities indicates that the effect of swirl on flame length can d e p e n d on the degree of confinement 9 T h e present flow is essentially unconfined, and angular m o m e n t u m diffuses quickly into the freestream. The resulting adverse axial pressure gradient retards and widens the jet initiallly, whilst the normalised downstream turbulence components and

stresses are close to those in non-swirling flames. By contrast, narrow confinement, as reported by others 9, appears to lengthen the flame due to suppression of shear stress by the pressure-gradient terms, as the angular mom e n t u m cannot diffuse freely, thus maintaining a high radial pressure gradient. Downstream in the present flame, the v-w component of the stress tensor and the mixture fraction flux seem amenable to simple gradient flux modelling. However, upstream, where pressure gradients are high, such models would be inadequate.

Acknowledgement This work is supported by a grant from the Australian Research Grants Scheme.

REFERENCES 1. STXRNER, S.H., AND BILGER, R.W.: Eighteenth Symposium (International) on Combustion, p. 921, The Combustion Institute, 1981. 2. STERNER, S.H.: Combust.Sci.Technol., 30, 145 (1983). 3. KENT,J.H.: Turbulent Jet Diffusion Flames, Ph.D. thesis. The University of Sydney, 19729 4. DRAKE,M.C., ST.~RNER,S.H., AND BILGER, R.W.: Nineteenth Symposium (International) on Combustion, p. 459, The Combustion Institute, 1982. 5. KENT, J.H., AND BILGER, R.W.: Fourteenth Symposium (International) on Combustion, p. 615, The Combustion Institute, 1973. 6. GLASS, M., AND BILGER, R.W.: Combust.Sci. Technol., 18, 165 (1978), 7. RIBEIRO, M.M., AND WHITELAW,J.H.: J. Fluid Mech., 96, 769 (1980)9 8. PRATTE,B.D., AND KEFFER,j.F.:j. Basic Engineering, 94, 739 (1972). 9. ST~tRNER, S.H.: Combust.Sci.Technol., 48, 99

(1986). 10. TAKAGI, T.,

OKAMOTO, T., TAJI, M., AND NAKASUJI, Y.: Twentieth Symposium (International) on.Combustion, p. 251, The Combustion Institute, 1985.

11. ANTONIA, R..A.., PRABHU, A., AND STEPHENSON, S.E.: J. Fluid Mech., 72, 455 (1975)9 12. ANTONIA,R.A., ANDPP,aBHU, A.: AIAAJ., 14, 221 (1976). 13. CHIGIER, N.A., AND CHERVINSKY, A.: Eleventh Symposium (International) on Combustion, p. 489, The Combustion Institute, 1967. 14. LOCKWOOD, F.C., EL-MAMALLAWY, F.M., AND SPALDING, D.B.: Comb. Flame, 23, 283 (1974).

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COMMENTS H. A. Becker, Queen's University, Canada. 1. Why would angular momentum not be conserved in your flame? 2. Did you compute the angular momentum flux as a function of streamwise position and so actually check the conservation (or lack thereof) of angular momentum? Author's Reply. In this flame, which is a free shear flow, angular momentum must be conserved. The important point here is that, due to the lack of confinement, the annular, swirling air jet issuing from the nozzle is free to expand into the co-flowing stream. (Photographs show an included cone angle of around 55 ~ for the first 1-2 nozzle diameters). It follows from the conservation o f angular momentum

that this expansion reduces the mean angular velocity z'v in inverse porportion to the radius. Turbulent diffusion of angular momentum into the non-swirling co-flow also reduces zb. Therefore, the mean radial pressure gradient, Op/Or ~ f) ~)2/r, diminishesquickly with distance from the nozzle so that the suppression effect on the u-v stress and turbulent kinetic energy becomes insignificant compared to the case of a confined flow where ~ can be kept high. We have computed the angular momentum flux but have found the largest contribution to the integral at the outer edge of the flame where the density is highest, and where our measurements end. This makes integration by extrapolation uncertain, but our results do not appear to be inconsistent with the conservation requirement.