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Temperature and density gradient changes arising with the precessing vortex core and vortex breakdown in swirl burners
TEMPERATURE AND DENSITY GRADIENT CHANGES ARISING WITH T H E PRECESSING VORTEX CORE AND VORTEX BREAKDOWN IN SWIRL BURNERS N. SYRED,* A. K. GUPTA, A N D J. M. BE]~R
Department of Chemical Enqineerinr and Fu~l Technology, University of Sheffield, England Two main types of flow pattern occur in certain types of swirl burner for various Reynolds numbers, mixture ratios and axial fuel entry. They are as follows: (a) Flows which contain a large three-dimensional time dependent instability, called the precessing vortex core (henceforth PVC). This PVC dominates the flow. (b) Flows where the PVC amplitude is damped by at least two orders of magnitude. The large PVC case (a), occurs in non-reacting flow systems, and at. weak mixture ratios (4~:>50). Case (b), where the large PVC is greatly damped, occurs with turbulent diffusion flames when 50>4,. This paper investigates the transition, or vortex breakdown, between these two states, (a) and (b), for axial fuel entry at ~ ~50. For ~b:>50 (at very weak mixture ratios) the large PVC occurs and the flame burns in and around the PVC up to 0.3 diameters past the exit. As ~ is reduced below 50, by increased fuel input, vortex breakdown occurs and the swirling flow jumps to state (b) where the amplitude of the large PVC is damped by at least two orders of magnitude. Under these conditions the influence of the PVC is scarcely detectable and the swirling flow is virtually axi-symmetric. Measurements of the rotating temperature field, associated with the PVC, under conditions approaching vortex breakdown showed high temperatures near to the centre of the PVC (T~1250~ The end of the PVC is also sucked back into the reverse flow zone, thereby increasing the temperature of this region. From considerations of the Rayleigh stability criterion and radial density gradients, it is shown that the PVC is unstable before vortex breakdown. After vortex breakdown, the flame expands in diameter and is reduced in length; the flame now being near axisymmetric as shown by measurement of mean and fluctuating temperature. The significant effect of perturbations upon flame characteristics when operating near to the point of vortex breakdown is demonstrated. 1. I n t r o d u c t i o n I t has been demonstrated t h a t the behaviour of highly swirling flows is complicated b y several different instabilities and changes in flow pattern with variation in Reynolds and swirl number, t 1-6 First let us consider a low Reynolds number flow ( ( 1 0 0 0 ) with a swirl number greater than 0.6 (thus ensuring recireulation at high Reynolds numbers).7 As the Reynolds number is increased * Now at Department of Mechanical Engineering, University, College, University of Wales, Cardiff, Wale~ f See section 2. 587
a n instability develops called the vortex breakdown phenomenon; it is first manifest as a small closed bubble of circulating fluid 1,2 on the axis of symmetry. T h e flow returns to a stable form and than breaks down again. As the Reynolds number is fnrther increased a large three-dimensional time dependent instability, called the precessing vortex core (henceforth P V C ) develops after this second breakdown of flow? '~ T h e central forced vortex core region of flow is displaced from the axis and starts to precess about the axis of s y m m e t r y . T h e P V C is often of large diameter and of low frequency of precession (10-200 H z ) ? '~ T h i s frequency has been shown to increase linearly with Reynolds h u m -
588
FLAME-FLOW INTERACTION uolt r~t tl~[ RAOIA~
-
OlSSIP~lVE ~ E C E S ~ v o m [ i c o n e i r AXiaL t ~ li~ ~ FRO~ r ~ t t i l t
r.[
swlqL~n A~o r ~ t
Q (d
nAaAt ~CT~OU ( s
~
I//]
I~TE i'tr I~JCH ~IALL|R SANI~ OF PI~Xt$.~II~ ~OtlTEXCORfS lu~ol T~ sw~t~ ~ r ~ Jumse~c~ ~ l u t RADIAL- ~ l l t E ~
Fro. 1. (a) Flow pattern formed with the large PVC. Occurrence: Isothermal systems; premixed combustion 6>~>1,4; Axial fuel entry-weak mixture ratios 6>50. (b) Flow pattern formed by large positive radial density or pressure gradients. ber? '6 The PVC is usuaUy situated between the boundary of the reverse flow region and the zero streamline. On leaving the swirl burner the PVC is rapidly dissipated in any fully separated flow region.~ A schematic diagram of the flow field is shown in Fig. l(a). The PVC frequently occurs in non-reactlng (isothermal) swirling flows, particularly inside long devices (L/D,> 1) or in the exit? ,s In the combustive state, with ~xial fuel entry, this burner (Fig. 2) is stable over a wide range of mixture ratios? At mixture ratios leaner than 50, the PVC is sustained. * '*~ At a mixture ratio of 50, a sudden jump, or vortex breakdown, occurs and the amplitude of the PVC is damped by more than an order of magnitude, 9 [-Fig. 1(b)]. This paper examines in detail this abrupt change i21 flow structure, occurring with axial fuel entry into the burner (Fig. 2), suggesting it is another form of the vortex breakdown phenomenon. In particular, the flow states just before and after this new manifestation of vortex breakdown are examined and conclusions drawn as to the stability of the flow.
2. Experimental Apparatus and Techniques The experimental swirl burner consisted simply of a cylhldrical tube three diameters long
(Fig. 2). Air was supplied through eight tangential inle~ sets in the wall. Fuel was supplied through a 1.25 cm diameter inlet through the baseplate. The relevant dimensions are: Diameter (De), 17.6 em; Length (L), 52.8 cm; Tangentlal inlets, 35.2 cm longX0.476 cm wide; Fuel inlet, 1.25 cm diameter. Natural gas was used as fuel throughout: Composition, 94.4% CH4, 3.22%C~H~, 0.6%C~Hs, 1.46%N~; the rest higher hydrocarbons. The definition of swirl numbeF used, was
3~
where the axial flux of angular momentum
Go=
2wpWUr ~dr
and tile axial flux of linear momentum G , = rnj0~/22rp(b~_ W~/2) rdr The swirl number should be derived from experimental measurements of the various velocity profiles in the particular flow state being investigated.~ As these were not available, a swirl number, based upon geometrical parameter, is
8WIgL BURNERS useful particularly when comparing results. The swirl number used here for this particular burner is obtained as follows:
589
SWIRL PIPE 17" 5 cm. I.D.
Input axial finx of angular momentum
Gr M~. (MiD~/2p~Ar) Input axial flux of linear inomentum G.=
M~. (Mi4/p~vD~~)
The input axial flux of linear momentum due to the fuel can be neglected as
QI~-~Qo/500
and
Vs~0.8m/see
for the conditions to be investigated. Thus, S= 2Go/'DoG~= ~D,~/4A r = 1.86 for the swirl burner of Fig. 2. Frequencies and amplitudes of the PVC were measured by means of a high temperature Soiartron pressure transducer in the exit plane. Mean tmnperatures were measured by means of a Pt/Pt-13% Rh thermoeouple (0.07 mm diameter wire) coated with hexamethyldisiloxane to reduce catalytic effects upon the platinum. FluctuatiiLg temperatures were measured (using the same thermocouple) by means of a compensation network, based upon a resistance-capacitance circuit, m In the system used, the thermocouple Signal is passed through an a~lplifier (gain= 17 660) and thence to the rcslstauce-eapacitance nnit which is designed to compensate for the drop iu frequency response of the thermocouplc at frequencies greater than 2 tIz. The thermocouple time constant was measured by heating the the~Tnocouple by a radio frequency signal and observing the temperature decay. The time constant was fotmd to bc substantially lower in this highly fluctuating thne-dependant flow than is nmre usually encountered in high temperature swirling flames (large PVC damped). Scadron and Warshawskyn have shown that the time constant of a thermocouple can be given by the following correlation. ~-cc E(pc)~/(~.:) e t,o] (289/T~)~.m X
[(DJ)I!e/(MP) ~/2]
Precessing vortex cores cause large regular fluctuations in pressure (typically 0.12 atmospheres) accompanied by large temperature fluctuations (up to ll00~ in 3 msec.) Tim eomhination of pressure, temperature and velocity fluctuations is instrumental to the reduction of the thcrmocouple ~ime constant.
I A X I A L AIR OR GAS INLET 1"25 cm. I.D.
Fro. 2. Diagram of swirl burner S = 1.86 A model was constructed of the r0tatiltg temperature field associated with the PVC under combustion conditions by analysis of the regular temperature, signals as follows: Oscilloscope re~grds of these signals were obtained at sevente-en i'adial measuring stations at 0.5 cm intervals across the radius of the swirl burner. By measurement from these oscilloscope records the angular distribution of temperature could be deteiTnined at each radial measuring station. Results from at lcast twenty wavefo~T~Swere used to obtain this temperature distribution at each radial measuring station. The amplifier used, introduced some high frequency "noise" into the output sigT~l. As the frequencies of the PVC were only of the order of 50-60 iIz, this unwant~l noise (f> 500 Hz) was easily elinfillated by means of a bank of standard filters. Correlation studies between the rotating temperature and velocity field were undertaken by using a high temperature DISA hot wire probe positioned just outside the path of the rotating PVC and hence outside the flaxne front?
590
FLAME-FLOW I N T E R A C T I O N
(~)
FIG. 3. Photogrsphs of the burning PVC
O.I,
0-8
1-2
1.6
2,0
(b)
2"6
R e x lo - ~
FIo. 4. Variation of the frequency of the PVC witb Reynolds number.
SWIRL BURNERS
3. Experimental Results The two main types of flow pattern produced by this burner were as follows: Figs. 1 (a) and
1 (b). (a) With Ole large PVC present. (b) With the amplitude of the large PVC damped by at least an order of magifitude. In this section, results relevant to the transition between the flows with and without the large PVC, are discussed.
.Swirling Flowwith the Large PVC Present As has been described previously2-~,9,n undcr non-reacting (isothermal) flow conditions, the large PVC is typically about 0.2D~ in diameter, at a radius of prceession at the exit of about 0.67R. Frequencies of the PVC are typically 60 Hz for a Reynolds numbcr of 1.2X 10~. When fuel is admitted to the burner, it is entrained immediately inte the PVC and burns on the outer periphery2 Gradually, as the fuel supply is increased, burning extends to the whole length of the PVC inside the burner and (just before the transition at ~b=50) to about C.3D~ outside the burner. The effect of combnstion with axial fuel entry is both to rednce the amplitude and frequency of PVC (at ~ 5 0 by about 25%) by pulling the axis of precisslon towards the axis of s)n~nmetry, typically at the exit. Non-reacting (isothermal) state: r ~ = 0.67R; Combnstion ~ - 50: r ~ = 0.39R. Photographs of the resulting flames am shown in Fig. 3(a) and (b). From the short time exposure photograph (t= 1/250 sec) it may be seen combustion is only occurring in and around the PVC. The variation of the frequency of the PVC with Reynolds number for a given mixture ratio is linear and very similar to the non-reacting (isothermal) state, see Fig. 4, the richcr the mixture the more the frequency of precession (and the radius of precession) is reduced. I t has also been shown~ that the non dimentionalized frequency parameter fD~3/Qo tends to a constant value at high Reynolds number both for the combustive and isothermal states. Correlation m~suremcnts between the periodically fluctuating velocity and temperature signals showed a correlation cecil%lent of near + 1 (i,e., nearly in phase). This applied to both measuring positions, at the exit and --0.5D~ inside the burner. These correlation measurements were, thereforc, in agreement with the evidence of a cine film, n~unely that the natural gas was burning on the boundary of the PVC.
591
The rotating temperature fields associated with the PVC are shown iu Fig. 5(a) and (b) at two axial positions; inside the burner, at X/D,= --0.52 and at the exit at X/D,=O. For clarity reference should bc made to Fig. l(a) of the diagram of the flow field associated with the PVC. Due to the PVC the shape of the reverse flow zone is uon-axisymnmtric. The reverse flow zone, the boundaries of which are shown in Fig. 5(a) and (b), is also rotating with the PVC. The rotating temperature fields associated with the PVC show that at X,/D~=--0.52 precession has only just started as r~T=O.12R, by X/D~=O r ~ = 0.39R. This is in contrast to the isothermal state where vortex core precession extends much further down inside the burner (11). At X/D~= --0.52 maximum temperatures of 1250~ are reached inside the boundary of the PVC. This boundary is at approximately 1200~ and there also seems to be a short tail (between 0= 300 ~ and 330 ~ where some of the hot gases arc being torn off the PVC. In the reverse flow zone, directly opposite the PVC there is another area of hot gas, again at approximately 1200~ and this seems to occur for two main reasons. (a) Mass and heat transfer between the rever~ flow zone and the burning Pu (b) The top of the PVC is sucked back down into the reverse flow zone, also shown by a eine-film. At the exit a similar phenomenon occurs, Fig. 3(b). The PVC boundary achieves a temperature of approximately 1200~ maxlmmn temperatures of 1250~ being reached inside the PVC. The center of the PVC is slightly cooler at 1200~ and it is believed this is due to a high concentration of natural gas on the PVC axis. The "tail" of the PVC is now much longer than at X/'D~=--0.52, extending from 0=225 ~ to 340 ~ The sucking back of the top of the PVC into the reverse flow zone is also clearly showu by the h i g h temperature region between the PVC and the axis of symmetry. I t should be noted that between the two measuring stations at X/Do= 0 and --0.52 this high temperature region in the reverse flow zone crosses over the axis of symmetry. In the exit plane of the burner, the total high temperature region (T>300~ occupies an angular position from O= 225 ~ to 45 ~ over a normalized radius of 0 to 0.86. At X/D~=--0.52 there is a far more uniform angnlar distribution of temperature, from 0 ~ to 360~ but spread over a smaller normalized radius, from 0 to 0.6. The stability of this type of rotating flow containing the large PVC may be conveniently analysed by reference to the R~ylelgh Criterion ~ and by consideration of a stratific~tion parameter, such as the nmdified Richardson number,
FLAME-FLOW
,592
INTERACTION
270 a XlO e - - 0 S 2 0
=SO 225 ~
315Q
,~,~, ,~
/ 180 a
--0 o
1
= 5 3 " 8 REVS / s 332"5 RADIANS I s )
90 ~
Ji/De = 0
2?0=
r =50
225 ~
315~
t ~ = 53 gREYS / s 3325 RADIANS I s )
goa I~G. 5. R o t a t i n g m e a n t e m p e r a t u r e field associated w i t h t h e P V C for a m i x t u r e r a t i o of 50. (a) - 0 . 5 2 . (b) X/D,=O.
X/D,
SWIRL B U R N E R S
593
z~o. proposed by Be~r?4 The stability criterion proposed by Rayleigh was t h a t a system is: (a) x l o , 9 o $ 9 so rzs. stable if pWr increases with r (solid body r o t ~ tion), (b) neutrally stable if pWr is constant with r (free vortex), (e) unstable if pWr decreases with r. Measurements made in the isothermal state on this burner, ~2'15show t h a t the mean tangential velocity profile is of Rankine form, i.e., forced/ free vortex, with the change-over point in the velocity profile occurring at the centre of the PVC. The angular velocity of tlm PVC gives the mean tangential velocity (in the forced vortex region) through the forced vortex velocity relationship I:ZS" ~S" W~wr Thus, extrapolating to the combustive state Zeo with the large PVC present, the mean tangential NI$. E&CN .~ICCIESSIVIE DiSTRISU'rJON 15 MOVEO velocity field cau be estimated with the assump~ s ~ * 40 UNITS tion of a forced vortex profile from the axis of symmetry to the center of the PVC and a free (b) TN,s ~r R E F ~ re vortex from the PVC center to the wall of the ~+ o, r ~ P, r , . ,o" burner. With the further assumption t h a t there is little angular momentum transfer between the PVC and the surroundings, the distribution of ~ -angular momentum can then be ealeulated from the mean velocity field and the rotating
3.I R[y$ / s (:in.', S RJ~*NS I l l
1 Z49
,
NB
EACH SUCCESSIVE UPWARDS BY 0 . 4
DISTRIBUTION IS UNITS
i!
~
MOVED
S 9 320 ~ o e = 34O ~ o e= o~ o 9 = 20 ~ A e = 40 ~
I
me AXIS OF CENTRE OF P V C
4"0
II
oe, a 9 =
o. 2o"
~ e.
r
-160
I D
32
o. . . . ~ /
i
z4
i o
/y
0 ~
7
~ . . . ~ , ~
~.6
~
i
o
0s
o 0
02
I 0~
0.4
0s
10~
rlR
Fro. 6. Radial distribution of angular momentum across the PVC.
~
!+
',. . . . .
o'..
"0
5's
Fro. 7. Distributions of radial density gradient. (a) Spatially in the re plane. (b) Radially across the PVC. temperature field associated with the PVC, see Fig. 5(b). The derived radial distribution of
+++,++++++,++oom
Fig. 6.~ Just outside the PVC between a norrealized radius of 0.43 and 0.52 (for 0= 0 ~ to 40 ~ pWr decreases with r and hence the PVC is :~It is further assumed for density calculations from the rotating temperature fields that all the gases have the composition of air. The error due to this assumption will be small due to the very weak mixture ratio of 50.
594
FLAME-FLOW INTERACTION
1200
a
XID r = - 0.52
m
X/Dr
= 0
FL~E eURNOUrOCCURS A r xlo~ - O-S
240
7Oc
?"c
400 ~
0
80
0.2
0'4
r/R
0.6
0.8
0 I'0
F~o. 8. Mean and fluctuating temperatures level from the flame occurring after vortex breakdown and the large scale damping of the PVC unstable in this region. Similarly, for ~= 320~ ~ and a normalized radius of 0.45 to 0.55 pWr is virtually constant with r and so the flow is neutrally stable in this region. The modified Richardson mlmber~4 is of the form Ri* = (1/p) (Op/Or)(W~/r)
(0U/0ry
and is the ratio of the centrifugal forces in a field with density gradients to the shear forces. Stabilizing effects begin to act for Ri*>0. Be~r st al.,~4 demonstrated that laminarizatiou of turbulent flames in rotating environments occurred when Ri*> 1. As there is a lack of detailed velocity and turbulence data for this burner (and for most others) the distribution of Ri* cannot be properly calculated. However, the presence of large negative radial density gradients is sufficient to make Ri* negative and indicate instability. The spatial and radial distributions of radial density gradient are shown in Fig. 7. The spatial distribution in Fig. 7(a) shows that a large zone of negative radial density gradient extends between the axis of symmetry and the PVC. The small centrifugal force consequent to small radius makes the large negative density gradients near the axis Op/Or~,~ -- 240 Kg/ma/m between r = 0 and 0.1, Fig. 7(a) and (b) insignificant. However, signifi-
cantly large negative radial density gradients (~,-~--100 Kg/mS/m) occur between r=0.15 and 0.3 for 0 between 0 and 40 ~ Hence these distributions of radial density gradient suggest that the PVC is unstable between its centre and the axis of symmetry and is neutrally stable over a large area outside the PVC, extending over a wide range of r and 0 [-Fig. 7(a)']. The Rayleigh criterion bMieated instability between 0= 0 ~ and 40 ~ and a normalized radius of 0.43 to 0.52 and this area coincides with the area of neutral stability in the radial density gradient distribution [-Fig. 7(a)~. Thus the PVC and associated flow field is unstable both from considerations of the Rayleigh criterion for rotating flows and radial density gradients, especially in the area from 0 = 0 to 40 ~ and r=0.15 to 0.53.
Swirling Flow when the PVC Amplitude is Damped If the natural gas supply is subsequently increased so that the mixture ratio, ~, is less that 50, the large scale damping of the PVC occurs and the flow returns to near axi-symmetry with a residual prescnce of the PVC on the bomldary of the vortex core region. ~ The flame is reduced considerably in length, but expanded in diameter, and combustion is now complete i~side the burner by X/D~.~--0.5. The radial distribution of mean and fluctuating temperature in this state is
SWIRL BURNERS shown in Fig. 8. The temperature profiles follow the expected pattern for a swirl burner with the peak occurri~tg at a radius of about 0.55R at flame burnout. The peak of the rms fluctuating temperatures occurs outside the flame bouudary at r~0.65R, maxnnum rms fluctuating temperaturcs of 200 ~ being recorded. At the exit both the mean and fuctuating temperatures are reduced considerably in magnitude. Changes Occurring with Transition Breakdown
or Vortex
The pressure drop through the air register of this bnrner is both a function of mixture ration and Reynolds number2 For a constant Reynolds number there is a slow but steady decrease in pressure drop as the mixtnre ratio is decreased, until at the point of vortex breakdowul (~b~-~50) a small but sudden decrease in pressure drop occurs? Measurements have shown~ that this reduction of pressure drop is virtually independent of Reynolds number and is approximately 0.32hP/89 "~. At high Reb~lolds nmnber tim heat input to the flow necessary to achieve the large radial density gradients necessary for vortex breakdown tends to a constant value of 17.5 eals/grm of air? Some of Sarpkaya's water nrodels ~ indicate the formation of a processing vm'tex core some way behind the closed bubble of eirsulating fluid which first indicates the onset of the vortex breakdown phenomenon. Thus, the initiM onset of the PVC may be nsed to indicate the onset of the vortex breakdown phenomenon. The swirl burner u ~ d in these experiments confirms the results of Sarpkaya as to the initial onset of this phenomenon (for isothermal conditions attd for a similar swirl number), indicating the first occurrence of the PVC at a Reynolds number of B.O26X10"~(Fig. 4). We further suggest that the transition between the two flow states, one containing the large PVC and the other containing the greatly damped PVC is another manifestation of the vortex breakdown phenomenon. An elegant mathematical treatment of vortex breakdown by Brooke-Benjaminr6 has been found to be applicable2 4. Coneluslons
This paper has investigated the transition or vortex breakdown which occurs between two flow states in swirl burners at weak mixture ratios (4,~50). At very weak mixture ratios (r a three dirnensioual time dependent instability occurs with the central vortex core region precessing about the axis of symmetry.
595
The flame burns in and just arom~d this PVC causing large negative radial temperature and density gradients. At the transition or point of vortex breakdown there is a reduction in pressure drop, a stabilization of the vortex core, and an expansion in diameter. Measurenmnts have been made of the rotating temperature, radial density gradient and angular momentum fields associated with the PVC near to the point of vortex breakdoswa. By consideration of the Rayleigh criterion aml a modified Richardson nmnber, it has been demonstrated that the PVC and associated flow field is unstable at a tuixture r~tio of 5(/ ~nd liable to be damped as a result of small changes in input variables. The relevance of these results to practical applications lies in determining the relationship between perturbations of operating variables and flame characteristics near to the point of vortex breakdown. Nomenclature
AT c De Dpvc D~ f M Mi P PVC Q Qs Q0 r r~ R Ri* Re S T U V Vf W X
tangential inlet area velocity of sound exit diameter of swirl burner diameter of PVC diameter of thermocouple frequency Math number input mass flow of air static pressure processing vortex core flowrate input flowrata of fuel flowrate of air into swirl burner at STP conditions radius radius to centre of PVC radius of exit of swirl burner modified Richardson nmnber Reynolds number based on STP conditions, i.e., Re= VDJv where V=4Qo/ wD~~ swirl nmnber temperature ~ axial velocity mean average exit velocity, V=4Qo/~rD2 inlet velaeity of fuel tangential velocity axial coordinate exit of buruer is at 0.
Greek 7" o~ AP 0
thermocouple time constant angular velocity of rotation of PVC pressure drop across the swirl burner ant~dar coordinate, zero pohtt starting
FLAME-FLOW INTERACTION
596
o
on the radius from the axis of symmetry through the PVC center density mixture ratic~-defined as (volume flowrate of air at STP conditions)/['volume flowrate of fuel at STP conditionsX Stoiehiometrlc air/fuel ratio (by volume at S T P ) ]
Superscripts _r
Fluctuating quantities, i.e., ~,t
Subscripts w
pt,o i
refers to the thermoeouple refers to condition of the cold junction of the thermoc~mple refers to bflet conditions
A cb~wwledgmerd The authors gratefully acknowledge the financial support of the Science Research Council (U.X.) REFERENCES 1. 2. 3. 4.
S~YA, T.: J. Fluid Mech. 45, 545 (1971). HARVSY, J. K.: J. Fluid Mech. 1~, 585 (1962). CH~AUD, R. C.: J. Fluid Mech. 21, 111 (1965). CASSIDY, J. J., AND FAnVEY, H. T.: J. Fluid Mech. 41, 727 (1970).
5. SYaED, N. AND B~f~a, J. M.: Fourteenth (International) Symposium on Combustion, p. 537, The Combustion Institute, 1973. 6. SYnED, N. ANn BEta, J. M.: Astronaut. Acta. 17, 783 (1972). 7. BEf~Ir J. M. )~'~DCH1Oma, N. A.: Combustion Aerodynamics Applied Science Publishers Ltd., 1972. 8. SUZUKI,M.: Sei. Pap. Inst. Phys. Chem. Res. Tokyo 5~, 44 (1960). 9. SY~mv, N. AND BB~a, J. M.: Proceedings European Symposium on Combuslion, p. 542, Academic Press, 1973. 10. SttEPARD, C. E. ANn WATCSHWASKY,I.: (i) N.A.C.A. Tech. Note 2073 (1952). (ii) ISA Trans. 9, 119 (1953). 11. S c o n c e , M. D. AND WAasa~ws~Y, I.: N.A. C.A. Tech. Note 2599 (1952). 12. Svn~n, N. ANn BE~X, J. M.: Vortex Core Preeessiou in High Swril Flows, Proe. Second J.S.M.E. Symposium on Fluid Machinery and Fluidies, p. 111, Tokyo, September 1972. 13. RArbEtO~, Loan: Prec. I:L Soc. Lond. 93, 148 (1916). 14. Bs~R, J. M., Cm(~ma, N. A., DAwEs, T. W., ]~ASSINDAI,E,K.: Combuzt. Flame 16, 39 (1971). 15. SynoD, N., BrAn, J. M., CmGI~n, N. A.: Paper I3 of the Prec. Internal Flows Symposium, Salford University and the Institution of Mechanical Engineers (London), p. B.27, 1971. 16. BROOKE-BENJAMIN,T.: J. Fluid Mech. 14, 593 (1962).
COMMENTS T. K. Deague, B.H.P. Central Research Labs., Australia. What do you see as tile implications of this phenomenua for the development of high intensity burners? Do you see it as somethiug to be eliminated, or as something potentially useful?
Authors' Reply. The implications of the phenomenon of precessiug vortex cores (PVC) are important for most types of high intensity swirl burners. Remembering that the PVC can exist in two different states, as follows (Ref. 5, 6, 9, 12, and 15 of the paper). (a) In a flow state where the large PVC exists (analogous to the isothermal state)--premixed combustion (or fuels with high molecular diffusivities) excites the frequency and amplitude of the PVC substantially. (b) The large PVC may be damped, in ampli-
tude, by more than an order of ma~qlitude, this usually occurs with diffusion flames at near stoichoimetric mixture ratios. However, there is still a residual presence of the PVC close to the bomldalT of the reverse flow zone. The PVC free in either of the two forms described above, is an essential part of swirling flows, tile formation of the rccirculation zones and high levels of turbulence causes the formation of the PVC. Thus in understanding the ouset, formation of the PVC and the transition between the two flow states (a) and (b) above, we can further understand the flame stabilization and mixillg processes which occur in swirl burners. The large PVC, in a combustion system, is usually undesirable, as resonant coupling between various travelling or sta~lding waves can easily occur. It has also been shown (Ref. 1) that even the
SWIRL BURNERS damped PVC, state (b) above, cart excite resozm~lthlstability in a furnace or cavity, by couplit~g with other modes of oscillation (in this case a longitudinal mode). Thus providing data is available on the frequency (or Strouhal rlumber)-Reyaolds number reIationship of the PVC care carl be taken to mismatch the frequency of the PVC with the fundamental modes of oscillation of the furrlace or cavity.
597
An advantage of diffusion flames with precessing vortex cores is that the range of stable burning can be extended well into the region of fuel beam mixture ratios. REFERENCE 1. ~YRED I NI, HANBY 1 V. I., AND GUPTA~ A. ~.'.
J. Inst. Fuel, z;6, 402 (1973).
Department of Chemical Enqineerinr and Fu~l Technology, University of Sheffield, England Two main types of flow pattern occur in certain types of swirl burner for various Reynolds numbers, mixture ratios and axial fuel entry. They are as follows: (a) Flows which contain a large three-dimensional time dependent instability, called the precessing vortex core (henceforth PVC). This PVC dominates the flow. (b) Flows where the PVC amplitude is damped by at least two orders of magnitude. The large PVC case (a), occurs in non-reacting flow systems, and at. weak mixture ratios (4~:>50). Case (b), where the large PVC is greatly damped, occurs with turbulent diffusion flames when 50>4,. This paper investigates the transition, or vortex breakdown, between these two states, (a) and (b), for axial fuel entry at ~ ~50. For ~b:>50 (at very weak mixture ratios) the large PVC occurs and the flame burns in and around the PVC up to 0.3 diameters past the exit. As ~ is reduced below 50, by increased fuel input, vortex breakdown occurs and the swirling flow jumps to state (b) where the amplitude of the large PVC is damped by at least two orders of magnitude. Under these conditions the influence of the PVC is scarcely detectable and the swirling flow is virtually axi-symmetric. Measurements of the rotating temperature field, associated with the PVC, under conditions approaching vortex breakdown showed high temperatures near to the centre of the PVC (T~1250~ The end of the PVC is also sucked back into the reverse flow zone, thereby increasing the temperature of this region. From considerations of the Rayleigh stability criterion and radial density gradients, it is shown that the PVC is unstable before vortex breakdown. After vortex breakdown, the flame expands in diameter and is reduced in length; the flame now being near axisymmetric as shown by measurement of mean and fluctuating temperature. The significant effect of perturbations upon flame characteristics when operating near to the point of vortex breakdown is demonstrated. 1. I n t r o d u c t i o n I t has been demonstrated t h a t the behaviour of highly swirling flows is complicated b y several different instabilities and changes in flow pattern with variation in Reynolds and swirl number, t 1-6 First let us consider a low Reynolds number flow ( ( 1 0 0 0 ) with a swirl number greater than 0.6 (thus ensuring recireulation at high Reynolds numbers).7 As the Reynolds number is increased * Now at Department of Mechanical Engineering, University, College, University of Wales, Cardiff, Wale~ f See section 2. 587
a n instability develops called the vortex breakdown phenomenon; it is first manifest as a small closed bubble of circulating fluid 1,2 on the axis of symmetry. T h e flow returns to a stable form and than breaks down again. As the Reynolds number is fnrther increased a large three-dimensional time dependent instability, called the precessing vortex core (henceforth P V C ) develops after this second breakdown of flow? '~ T h e central forced vortex core region of flow is displaced from the axis and starts to precess about the axis of s y m m e t r y . T h e P V C is often of large diameter and of low frequency of precession (10-200 H z ) ? '~ T h i s frequency has been shown to increase linearly with Reynolds h u m -
588
FLAME-FLOW INTERACTION uolt r~t tl~[ RAOIA~
-
OlSSIP~lVE ~ E C E S ~ v o m [ i c o n e i r AXiaL t ~ li~ ~ FRO~ r ~ t t i l t
r.[
swlqL~n A~o r ~ t
Q (d
nAaAt ~CT~OU ( s
~
I//]
I~TE i'tr I~JCH ~IALL|R SANI~ OF PI~Xt$.~II~ ~OtlTEXCORfS lu~ol T~ sw~t~ ~ r ~ Jumse~c~ ~ l u t RADIAL- ~ l l t E ~
Fro. 1. (a) Flow pattern formed with the large PVC. Occurrence: Isothermal systems; premixed combustion 6>~>1,4; Axial fuel entry-weak mixture ratios 6>50. (b) Flow pattern formed by large positive radial density or pressure gradients. ber? '6 The PVC is usuaUy situated between the boundary of the reverse flow region and the zero streamline. On leaving the swirl burner the PVC is rapidly dissipated in any fully separated flow region.~ A schematic diagram of the flow field is shown in Fig. l(a). The PVC frequently occurs in non-reactlng (isothermal) swirling flows, particularly inside long devices (L/D,> 1) or in the exit? ,s In the combustive state, with ~xial fuel entry, this burner (Fig. 2) is stable over a wide range of mixture ratios? At mixture ratios leaner than 50, the PVC is sustained. * '*~ At a mixture ratio of 50, a sudden jump, or vortex breakdown, occurs and the amplitude of the PVC is damped by more than an order of magnitude, 9 [-Fig. 1(b)]. This paper examines in detail this abrupt change i21 flow structure, occurring with axial fuel entry into the burner (Fig. 2), suggesting it is another form of the vortex breakdown phenomenon. In particular, the flow states just before and after this new manifestation of vortex breakdown are examined and conclusions drawn as to the stability of the flow.
2. Experimental Apparatus and Techniques The experimental swirl burner consisted simply of a cylhldrical tube three diameters long
(Fig. 2). Air was supplied through eight tangential inle~ sets in the wall. Fuel was supplied through a 1.25 cm diameter inlet through the baseplate. The relevant dimensions are: Diameter (De), 17.6 em; Length (L), 52.8 cm; Tangentlal inlets, 35.2 cm longX0.476 cm wide; Fuel inlet, 1.25 cm diameter. Natural gas was used as fuel throughout: Composition, 94.4% CH4, 3.22%C~H~, 0.6%C~Hs, 1.46%N~; the rest higher hydrocarbons. The definition of swirl numbeF used, was
3~
where the axial flux of angular momentum
Go=
2wpWUr ~dr
and tile axial flux of linear momentum G , = rnj0~/22rp(b~_ W~/2) rdr The swirl number should be derived from experimental measurements of the various velocity profiles in the particular flow state being investigated.~ As these were not available, a swirl number, based upon geometrical parameter, is
8WIgL BURNERS useful particularly when comparing results. The swirl number used here for this particular burner is obtained as follows:
589
SWIRL PIPE 17" 5 cm. I.D.
Input axial finx of angular momentum
Gr M~. (MiD~/2p~Ar) Input axial flux of linear inomentum G.=
M~. (Mi4/p~vD~~)
The input axial flux of linear momentum due to the fuel can be neglected as
QI~-~Qo/500
and
Vs~0.8m/see
for the conditions to be investigated. Thus, S= 2Go/'DoG~= ~D,~/4A r = 1.86 for the swirl burner of Fig. 2. Frequencies and amplitudes of the PVC were measured by means of a high temperature Soiartron pressure transducer in the exit plane. Mean tmnperatures were measured by means of a Pt/Pt-13% Rh thermoeouple (0.07 mm diameter wire) coated with hexamethyldisiloxane to reduce catalytic effects upon the platinum. FluctuatiiLg temperatures were measured (using the same thermocouple) by means of a compensation network, based upon a resistance-capacitance circuit, m In the system used, the thermocouple Signal is passed through an a~lplifier (gain= 17 660) and thence to the rcslstauce-eapacitance nnit which is designed to compensate for the drop iu frequency response of the thermocouplc at frequencies greater than 2 tIz. The thermocouple time constant was measured by heating the the~Tnocouple by a radio frequency signal and observing the temperature decay. The time constant was fotmd to bc substantially lower in this highly fluctuating thne-dependant flow than is nmre usually encountered in high temperature swirling flames (large PVC damped). Scadron and Warshawskyn have shown that the time constant of a thermocouple can be given by the following correlation. ~-cc E(pc)~/(~.:) e t,o] (289/T~)~.m X
[(DJ)I!e/(MP) ~/2]
Precessing vortex cores cause large regular fluctuations in pressure (typically 0.12 atmospheres) accompanied by large temperature fluctuations (up to ll00~ in 3 msec.) Tim eomhination of pressure, temperature and velocity fluctuations is instrumental to the reduction of the thcrmocouple ~ime constant.
I A X I A L AIR OR GAS INLET 1"25 cm. I.D.
Fro. 2. Diagram of swirl burner S = 1.86 A model was constructed of the r0tatiltg temperature field associated with the PVC under combustion conditions by analysis of the regular temperature, signals as follows: Oscilloscope re~grds of these signals were obtained at sevente-en i'adial measuring stations at 0.5 cm intervals across the radius of the swirl burner. By measurement from these oscilloscope records the angular distribution of temperature could be deteiTnined at each radial measuring station. Results from at lcast twenty wavefo~T~Swere used to obtain this temperature distribution at each radial measuring station. The amplifier used, introduced some high frequency "noise" into the output sigT~l. As the frequencies of the PVC were only of the order of 50-60 iIz, this unwant~l noise (f> 500 Hz) was easily elinfillated by means of a bank of standard filters. Correlation studies between the rotating temperature and velocity field were undertaken by using a high temperature DISA hot wire probe positioned just outside the path of the rotating PVC and hence outside the flaxne front?
590
FLAME-FLOW I N T E R A C T I O N
(~)
FIG. 3. Photogrsphs of the burning PVC
O.I,
0-8
1-2
1.6
2,0
(b)
2"6
R e x lo - ~
FIo. 4. Variation of the frequency of the PVC witb Reynolds number.
SWIRL BURNERS
3. Experimental Results The two main types of flow pattern produced by this burner were as follows: Figs. 1 (a) and
1 (b). (a) With Ole large PVC present. (b) With the amplitude of the large PVC damped by at least an order of magifitude. In this section, results relevant to the transition between the flows with and without the large PVC, are discussed.
.Swirling Flowwith the Large PVC Present As has been described previously2-~,9,n undcr non-reacting (isothermal) flow conditions, the large PVC is typically about 0.2D~ in diameter, at a radius of prceession at the exit of about 0.67R. Frequencies of the PVC are typically 60 Hz for a Reynolds numbcr of 1.2X 10~. When fuel is admitted to the burner, it is entrained immediately inte the PVC and burns on the outer periphery2 Gradually, as the fuel supply is increased, burning extends to the whole length of the PVC inside the burner and (just before the transition at ~b=50) to about C.3D~ outside the burner. The effect of combnstion with axial fuel entry is both to rednce the amplitude and frequency of PVC (at ~ 5 0 by about 25%) by pulling the axis of precisslon towards the axis of s)n~nmetry, typically at the exit. Non-reacting (isothermal) state: r ~ = 0.67R; Combnstion ~ - 50: r ~ = 0.39R. Photographs of the resulting flames am shown in Fig. 3(a) and (b). From the short time exposure photograph (t= 1/250 sec) it may be seen combustion is only occurring in and around the PVC. The variation of the frequency of the PVC with Reynolds number for a given mixture ratio is linear and very similar to the non-reacting (isothermal) state, see Fig. 4, the richcr the mixture the more the frequency of precession (and the radius of precession) is reduced. I t has also been shown~ that the non dimentionalized frequency parameter fD~3/Qo tends to a constant value at high Reynolds number both for the combustive and isothermal states. Correlation m~suremcnts between the periodically fluctuating velocity and temperature signals showed a correlation cecil%lent of near + 1 (i,e., nearly in phase). This applied to both measuring positions, at the exit and --0.5D~ inside the burner. These correlation measurements were, thereforc, in agreement with the evidence of a cine film, n~unely that the natural gas was burning on the boundary of the PVC.
591
The rotating temperature fields associated with the PVC are shown iu Fig. 5(a) and (b) at two axial positions; inside the burner, at X/D,= --0.52 and at the exit at X/D,=O. For clarity reference should bc made to Fig. l(a) of the diagram of the flow field associated with the PVC. Due to the PVC the shape of the reverse flow zone is uon-axisymnmtric. The reverse flow zone, the boundaries of which are shown in Fig. 5(a) and (b), is also rotating with the PVC. The rotating temperature fields associated with the PVC show that at X,/D~=--0.52 precession has only just started as r~T=O.12R, by X/D~=O r ~ = 0.39R. This is in contrast to the isothermal state where vortex core precession extends much further down inside the burner (11). At X/D~= --0.52 maximum temperatures of 1250~ are reached inside the boundary of the PVC. This boundary is at approximately 1200~ and there also seems to be a short tail (between 0= 300 ~ and 330 ~ where some of the hot gases arc being torn off the PVC. In the reverse flow zone, directly opposite the PVC there is another area of hot gas, again at approximately 1200~ and this seems to occur for two main reasons. (a) Mass and heat transfer between the rever~ flow zone and the burning Pu (b) The top of the PVC is sucked back down into the reverse flow zone, also shown by a eine-film. At the exit a similar phenomenon occurs, Fig. 3(b). The PVC boundary achieves a temperature of approximately 1200~ maxlmmn temperatures of 1250~ being reached inside the PVC. The center of the PVC is slightly cooler at 1200~ and it is believed this is due to a high concentration of natural gas on the PVC axis. The "tail" of the PVC is now much longer than at X/'D~=--0.52, extending from 0=225 ~ to 340 ~ The sucking back of the top of the PVC into the reverse flow zone is also clearly showu by the h i g h temperature region between the PVC and the axis of symmetry. I t should be noted that between the two measuring stations at X/Do= 0 and --0.52 this high temperature region in the reverse flow zone crosses over the axis of symmetry. In the exit plane of the burner, the total high temperature region (T>300~ occupies an angular position from O= 225 ~ to 45 ~ over a normalized radius of 0 to 0.86. At X/D~=--0.52 there is a far more uniform angnlar distribution of temperature, from 0 ~ to 360~ but spread over a smaller normalized radius, from 0 to 0.6. The stability of this type of rotating flow containing the large PVC may be conveniently analysed by reference to the R~ylelgh Criterion ~ and by consideration of a stratific~tion parameter, such as the nmdified Richardson number,
FLAME-FLOW
,592
INTERACTION
270 a XlO e - - 0 S 2 0
=SO 225 ~
315Q
,~,~, ,~
/ 180 a
--0 o
1
= 5 3 " 8 REVS / s 332"5 RADIANS I s )
90 ~
Ji/De = 0
2?0=
r =50
225 ~
315~
t ~ = 53 gREYS / s 3325 RADIANS I s )
goa I~G. 5. R o t a t i n g m e a n t e m p e r a t u r e field associated w i t h t h e P V C for a m i x t u r e r a t i o of 50. (a) - 0 . 5 2 . (b) X/D,=O.
X/D,
SWIRL B U R N E R S
593
z~o. proposed by Be~r?4 The stability criterion proposed by Rayleigh was t h a t a system is: (a) x l o , 9 o $ 9 so rzs. stable if pWr increases with r (solid body r o t ~ tion), (b) neutrally stable if pWr is constant with r (free vortex), (e) unstable if pWr decreases with r. Measurements made in the isothermal state on this burner, ~2'15show t h a t the mean tangential velocity profile is of Rankine form, i.e., forced/ free vortex, with the change-over point in the velocity profile occurring at the centre of the PVC. The angular velocity of tlm PVC gives the mean tangential velocity (in the forced vortex region) through the forced vortex velocity relationship I:ZS" ~S" W~wr Thus, extrapolating to the combustive state Zeo with the large PVC present, the mean tangential NI$. E&CN .~ICCIESSIVIE DiSTRISU'rJON 15 MOVEO velocity field cau be estimated with the assump~ s ~ * 40 UNITS tion of a forced vortex profile from the axis of symmetry to the center of the PVC and a free (b) TN,s ~r R E F ~ re vortex from the PVC center to the wall of the ~+ o, r ~ P, r , . ,o" burner. With the further assumption t h a t there is little angular momentum transfer between the PVC and the surroundings, the distribution of ~ -angular momentum can then be ealeulated from the mean velocity field and the rotating
3.I R[y$ / s (:in.', S RJ~*NS I l l
1 Z49
,
NB
EACH SUCCESSIVE UPWARDS BY 0 . 4
DISTRIBUTION IS UNITS
i!
~
MOVED
S 9 320 ~ o e = 34O ~ o e= o~ o 9 = 20 ~ A e = 40 ~
I
me AXIS OF CENTRE OF P V C
4"0
II
oe, a 9 =
o. 2o"
~ e.
r
-160
I D
32
o. . . . ~ /
i
z4
i o
/y
0 ~
7
~ . . . ~ , ~
~.6
~
i
o
0s
o 0
02
I 0~
0.4
0s
10~
rlR
Fro. 6. Radial distribution of angular momentum across the PVC.
~
!+
',. . . . .
o'..
"0
5's
Fro. 7. Distributions of radial density gradient. (a) Spatially in the re plane. (b) Radially across the PVC. temperature field associated with the PVC, see Fig. 5(b). The derived radial distribution of
+++,++++++,++oom
Fig. 6.~ Just outside the PVC between a norrealized radius of 0.43 and 0.52 (for 0= 0 ~ to 40 ~ pWr decreases with r and hence the PVC is :~It is further assumed for density calculations from the rotating temperature fields that all the gases have the composition of air. The error due to this assumption will be small due to the very weak mixture ratio of 50.
594
FLAME-FLOW INTERACTION
1200
a
XID r = - 0.52
m
X/Dr
= 0
FL~E eURNOUrOCCURS A r xlo~ - O-S
240
7Oc
?"c
400 ~
0
80
0.2
0'4
r/R
0.6
0.8
0 I'0
F~o. 8. Mean and fluctuating temperatures level from the flame occurring after vortex breakdown and the large scale damping of the PVC unstable in this region. Similarly, for ~= 320~ ~ and a normalized radius of 0.45 to 0.55 pWr is virtually constant with r and so the flow is neutrally stable in this region. The modified Richardson mlmber~4 is of the form Ri* = (1/p) (Op/Or)(W~/r)
(0U/0ry
and is the ratio of the centrifugal forces in a field with density gradients to the shear forces. Stabilizing effects begin to act for Ri*>0. Be~r st al.,~4 demonstrated that laminarizatiou of turbulent flames in rotating environments occurred when Ri*> 1. As there is a lack of detailed velocity and turbulence data for this burner (and for most others) the distribution of Ri* cannot be properly calculated. However, the presence of large negative radial density gradients is sufficient to make Ri* negative and indicate instability. The spatial and radial distributions of radial density gradient are shown in Fig. 7. The spatial distribution in Fig. 7(a) shows that a large zone of negative radial density gradient extends between the axis of symmetry and the PVC. The small centrifugal force consequent to small radius makes the large negative density gradients near the axis Op/Or~,~ -- 240 Kg/ma/m between r = 0 and 0.1, Fig. 7(a) and (b) insignificant. However, signifi-
cantly large negative radial density gradients (~,-~--100 Kg/mS/m) occur between r=0.15 and 0.3 for 0 between 0 and 40 ~ Hence these distributions of radial density gradient suggest that the PVC is unstable between its centre and the axis of symmetry and is neutrally stable over a large area outside the PVC, extending over a wide range of r and 0 [-Fig. 7(a)']. The Rayleigh criterion bMieated instability between 0= 0 ~ and 40 ~ and a normalized radius of 0.43 to 0.52 and this area coincides with the area of neutral stability in the radial density gradient distribution [-Fig. 7(a)~. Thus the PVC and associated flow field is unstable both from considerations of the Rayleigh criterion for rotating flows and radial density gradients, especially in the area from 0 = 0 to 40 ~ and r=0.15 to 0.53.
Swirling Flow when the PVC Amplitude is Damped If the natural gas supply is subsequently increased so that the mixture ratio, ~, is less that 50, the large scale damping of the PVC occurs and the flow returns to near axi-symmetry with a residual prescnce of the PVC on the bomldary of the vortex core region. ~ The flame is reduced considerably in length, but expanded in diameter, and combustion is now complete i~side the burner by X/D~.~--0.5. The radial distribution of mean and fluctuating temperature in this state is
SWIRL BURNERS shown in Fig. 8. The temperature profiles follow the expected pattern for a swirl burner with the peak occurri~tg at a radius of about 0.55R at flame burnout. The peak of the rms fluctuating temperatures occurs outside the flame bouudary at r~0.65R, maxnnum rms fluctuating temperaturcs of 200 ~ being recorded. At the exit both the mean and fuctuating temperatures are reduced considerably in magnitude. Changes Occurring with Transition Breakdown
or Vortex
The pressure drop through the air register of this bnrner is both a function of mixture ration and Reynolds number2 For a constant Reynolds number there is a slow but steady decrease in pressure drop as the mixtnre ratio is decreased, until at the point of vortex breakdowul (~b~-~50) a small but sudden decrease in pressure drop occurs? Measurements have shown~ that this reduction of pressure drop is virtually independent of Reynolds number and is approximately 0.32hP/89 "~. At high Reb~lolds nmnber tim heat input to the flow necessary to achieve the large radial density gradients necessary for vortex breakdown tends to a constant value of 17.5 eals/grm of air? Some of Sarpkaya's water nrodels ~ indicate the formation of a processing vm'tex core some way behind the closed bubble of eirsulating fluid which first indicates the onset of the vortex breakdown phenomenon. Thus, the initiM onset of the PVC may be nsed to indicate the onset of the vortex breakdown phenomenon. The swirl burner u ~ d in these experiments confirms the results of Sarpkaya as to the initial onset of this phenomenon (for isothermal conditions attd for a similar swirl number), indicating the first occurrence of the PVC at a Reynolds number of B.O26X10"~(Fig. 4). We further suggest that the transition between the two flow states, one containing the large PVC and the other containing the greatly damped PVC is another manifestation of the vortex breakdown phenomenon. An elegant mathematical treatment of vortex breakdown by Brooke-Benjaminr6 has been found to be applicable2 4. Coneluslons
This paper has investigated the transition or vortex breakdown which occurs between two flow states in swirl burners at weak mixture ratios (4,~50). At very weak mixture ratios (r a three dirnensioual time dependent instability occurs with the central vortex core region precessing about the axis of symmetry.
595
The flame burns in and just arom~d this PVC causing large negative radial temperature and density gradients. At the transition or point of vortex breakdown there is a reduction in pressure drop, a stabilization of the vortex core, and an expansion in diameter. Measurenmnts have been made of the rotating temperature, radial density gradient and angular momentum fields associated with the PVC near to the point of vortex breakdoswa. By consideration of the Rayleigh criterion aml a modified Richardson nmnber, it has been demonstrated that the PVC and associated flow field is unstable at a tuixture r~tio of 5(/ ~nd liable to be damped as a result of small changes in input variables. The relevance of these results to practical applications lies in determining the relationship between perturbations of operating variables and flame characteristics near to the point of vortex breakdown. Nomenclature
AT c De Dpvc D~ f M Mi P PVC Q Qs Q0 r r~ R Ri* Re S T U V Vf W X
tangential inlet area velocity of sound exit diameter of swirl burner diameter of PVC diameter of thermocouple frequency Math number input mass flow of air static pressure processing vortex core flowrate input flowrata of fuel flowrate of air into swirl burner at STP conditions radius radius to centre of PVC radius of exit of swirl burner modified Richardson nmnber Reynolds number based on STP conditions, i.e., Re= VDJv where V=4Qo/ wD~~ swirl nmnber temperature ~ axial velocity mean average exit velocity, V=4Qo/~rD2 inlet velaeity of fuel tangential velocity axial coordinate exit of buruer is at 0.
Greek 7" o~ AP 0
thermocouple time constant angular velocity of rotation of PVC pressure drop across the swirl burner ant~dar coordinate, zero pohtt starting
FLAME-FLOW INTERACTION
596
o
on the radius from the axis of symmetry through the PVC center density mixture ratic~-defined as (volume flowrate of air at STP conditions)/['volume flowrate of fuel at STP conditionsX Stoiehiometrlc air/fuel ratio (by volume at S T P ) ]
Superscripts _r
Fluctuating quantities, i.e., ~,t
Subscripts w
pt,o i
refers to the thermoeouple refers to condition of the cold junction of the thermoc~mple refers to bflet conditions
A cb~wwledgmerd The authors gratefully acknowledge the financial support of the Science Research Council (U.X.) REFERENCES 1. 2. 3. 4.
S~YA, T.: J. Fluid Mech. 45, 545 (1971). HARVSY, J. K.: J. Fluid Mech. 1~, 585 (1962). CH~AUD, R. C.: J. Fluid Mech. 21, 111 (1965). CASSIDY, J. J., AND FAnVEY, H. T.: J. Fluid Mech. 41, 727 (1970).
5. SYaED, N. AND B~f~a, J. M.: Fourteenth (International) Symposium on Combustion, p. 537, The Combustion Institute, 1973. 6. SYnED, N. ANn BEta, J. M.: Astronaut. Acta. 17, 783 (1972). 7. BEf~Ir J. M. )~'~DCH1Oma, N. A.: Combustion Aerodynamics Applied Science Publishers Ltd., 1972. 8. SUZUKI,M.: Sei. Pap. Inst. Phys. Chem. Res. Tokyo 5~, 44 (1960). 9. SY~mv, N. AND BB~a, J. M.: Proceedings European Symposium on Combuslion, p. 542, Academic Press, 1973. 10. SttEPARD, C. E. ANn WATCSHWASKY,I.: (i) N.A.C.A. Tech. Note 2073 (1952). (ii) ISA Trans. 9, 119 (1953). 11. S c o n c e , M. D. AND WAasa~ws~Y, I.: N.A. C.A. Tech. Note 2599 (1952). 12. Svn~n, N. ANn BE~X, J. M.: Vortex Core Preeessiou in High Swril Flows, Proe. Second J.S.M.E. Symposium on Fluid Machinery and Fluidies, p. 111, Tokyo, September 1972. 13. RArbEtO~, Loan: Prec. I:L Soc. Lond. 93, 148 (1916). 14. Bs~R, J. M., Cm(~ma, N. A., DAwEs, T. W., ]~ASSINDAI,E,K.: Combuzt. Flame 16, 39 (1971). 15. SynoD, N., BrAn, J. M., CmGI~n, N. A.: Paper I3 of the Prec. Internal Flows Symposium, Salford University and the Institution of Mechanical Engineers (London), p. B.27, 1971. 16. BROOKE-BENJAMIN,T.: J. Fluid Mech. 14, 593 (1962).
COMMENTS T. K. Deague, B.H.P. Central Research Labs., Australia. What do you see as tile implications of this phenomenua for the development of high intensity burners? Do you see it as somethiug to be eliminated, or as something potentially useful?
Authors' Reply. The implications of the phenomenon of precessiug vortex cores (PVC) are important for most types of high intensity swirl burners. Remembering that the PVC can exist in two different states, as follows (Ref. 5, 6, 9, 12, and 15 of the paper). (a) In a flow state where the large PVC exists (analogous to the isothermal state)--premixed combustion (or fuels with high molecular diffusivities) excites the frequency and amplitude of the PVC substantially. (b) The large PVC may be damped, in ampli-
tude, by more than an order of ma~qlitude, this usually occurs with diffusion flames at near stoichoimetric mixture ratios. However, there is still a residual presence of the PVC close to the bomldalT of the reverse flow zone. The PVC free in either of the two forms described above, is an essential part of swirling flows, tile formation of the rccirculation zones and high levels of turbulence causes the formation of the PVC. Thus in understanding the ouset, formation of the PVC and the transition between the two flow states (a) and (b) above, we can further understand the flame stabilization and mixillg processes which occur in swirl burners. The large PVC, in a combustion system, is usually undesirable, as resonant coupling between various travelling or sta~lding waves can easily occur. It has also been shown (Ref. 1) that even the
SWIRL BURNERS damped PVC, state (b) above, cart excite resozm~lthlstability in a furnace or cavity, by couplit~g with other modes of oscillation (in this case a longitudinal mode). Thus providing data is available on the frequency (or Strouhal rlumber)-Reyaolds number reIationship of the PVC care carl be taken to mismatch the frequency of the PVC with the fundamental modes of oscillation of the furrlace or cavity.
597
An advantage of diffusion flames with precessing vortex cores is that the range of stable burning can be extended well into the region of fuel beam mixture ratios. REFERENCE 1. ~YRED I NI, HANBY 1 V. I., AND GUPTA~ A. ~.'.
J. Inst. Fuel, z;6, 402 (1973).