Structures induced by periodic acoustic excitation of a diffusion flame

Structures Induced by Periodic Acoustic Excitation of a Diffusion Flame M. R. DAVIS* and LI HA1 L I N Department of Civil and Mechanical Engineering, University of Tasmania,

GPO Box 252C Hobart, Tasmania 7001,Australia Signal recovery techniques have been used to measure the periodic structures formed in a coannular diffusion flame due to acoustic excitation of the flow from upstream. The flow response was sensed using the quantitative schlieren technique, and consistent results were obtained on the basis of both axial and transverse optical beam deflections and appropriate analysis of signal records. The two dominant modes of response were identified as a series of alternating disturbances along the flow axis at the higher frequency, and a series of alternating ring disturbances containing on axis disturbances of opposite sign at the lower frequency. The former mode is essentially associated with the fuel jet shear layer, while the latter is associated with the outer annular shear layer surrounding the air flow from the outer nozzle. The strength of disturbances was consistent with mixing fluctuations between cold fuel gas and the products of combustion. Structures induced in the outer shear layer weakened rapidly with distance from the nozzle, indicating a relatively sudden breakup of coherent structures caused by excitation near to the nozzle.

NOMENCLATURE di

do

f

?.

St/ St0 t U X Y x, y, z

Subscripts and Superscripts

i n n e r n o z z l e d i a m e t e r (m) o u t e r nozzle d i a m e t e r (m) f r e q u e n c y (Hz) r a d i a l c o o r d i n a t e f r o m axis (m) S t r o u h a l n u m b e r b a s e d o n an i n n e r nozzle ( f d i / U i) S t r o u h a l n u m b e r b a s e d o n o u t e r nozzle ( f d o / U o) t i m e (s) p e r i o d i c t i m e (s)

a c i i o p t

velocity ( m / s ) d i s t a n c e f r o m nozzle to m e a s u r e m e n t p l a n e (m) d i s t a n c e f r o m axis to sensing b e a m (m) c o o r d i n a t e d i r e c t i o n s , origin at nozzle c e n t e r (m)

A n u m b e r o f visualization studies o f diffusion flames have r e v e a l e d the p r e s e n c e o f r e g u l a r large scale d i s t u r b a n c e s in t h e mixing r e g i o n b e t w e e n t h e fuel a n d o x i d a n t flows [1-5]. T h e s e effects a r e p a r t i c u l a r l y e v i d e n t in small diffusion flames w h e r e the physical scales a n d high t e m p e r a t u r e c o m b i n e to p r o d u c e relatively low local R e y n o l d s n u m b e r s at t h e m o d e s t velocities at which c o m b u s t i o n is stable. In a d d i t i o n to this t e n d e n c y for u n e x c i t e d flames to exhibit r e g u l a r mixing structures, it is also well k n o w n t h a t diffusion flames have a c o n s i d e r a b l e sensitivity to acoustic excitation [6-8] a n d t h a t und e r such c o n d i t i o n s t h e r e g u l a r i t y o f i n d u c e d mixing s t r u c t u r e s can b e c o n s i d e r a b l y enhanced. M e a s u r e m e n t o f t h e r e s p o n s e o f diffusion flames is g e n e r a l l y c o m p l i c a t e d by the pres-

Greek Symbols ~:, ~, ~" c o o r d i n a t e d i s p l a c e m e n t s f r o m m e a s u r e m e n t p o i n t (m) r e f r a c t i v e index 6 constant of integration t~ r beam deflection (radians) 0

* Corresponding author.

axial d i r e c t i o n convection integer i n n e r nozzle o u t e r nozzle periodic transverse direction

INTRODUCTION

COMBUSTIONAND FLAME 103:151-160 (1995) Copyright © 1995 by The Combustion Institute Published by Elsevier Science Inc.

0010-2180/95/$9.50 SSDI 0010-2180(95)00050-G

152 ence of turbulent components of the mixing region, which occur with or without regular excitation. Also many probe sensing systems are adversely affected by the high temperature within a diffusion flame and may not give a clear indication of a particular flow parameter. The hot wire probe in particular is made difficult to use for these reasons as it responds to velocity, temperature and composition of the flow. In the present work these difficulties are overcome by using the laser schlieren detection system [9-11] which requires no probe to be inserted into the flow and which has a well defined response to mixture refractive index. The refractive index becomes an effective reaction progress variable [12] as it is dominantly related to local temperature and progress of reaction as represented by the extent to which combustion of mixture components has occurred. In addition, the application of a regular periodic acoustic excitation of the diffusion flame provides a phase referenced excitation signal so that measured signals from the laser schlieren sensing system can be averaged to eliminate random or turbulent signal components and recover the component due to the excitation. Moreover, the line-integrating nature of the optical sensing system used makes it inherently more sensitive to coherent components, which influence the complete sensing beam in the cross section of the flow, than to turbulent components of the signal which tend to vary randomly along the sensing beam due to their smaller scale and thus contribute at a reduced level to the total detected signal [12]. Thus the laser-schlieren system is well suited to the task of sensing the response of a flame to excitation, However, as will be discussed in the following section, it is necessary to develop a suitable approach to the analysis of averaged signal records recovered from the sensing beam deflection system. Previous investigations of acoustically excited flames have dealt with laminar diffusion flames without co-flow [17], turbulent flames with co-flow [18], and flames with a large smooth co-flow [19]. Of particular interest in these investigations is the identification of two scales of mixing structure associated with the flow and mixing from the fuel jet and with

M. R. DAVIS AND LI HAI LIN mixing of the buoyant plume. Under certain conditions these two structures become coupled together [19]. Conditions in the experiments conducted here were somewhat different, as the external co-flowing system is itself a jet flow which mixes with the quiescent surrounding air. Also, the flame in the present experiments was stabilized on the annular face between inner (fuel) and outer air flows, allowing operation at higher velocity where conditions are more strongly turbulent and where buoyancy effects are relatively much smaller. Also, in the present work, acoustic excitation was applied symmetrically from upstream through the outer (air) flow nozzle, whereas in these previous investigations it was applied through the fuel flow nozzle. It can be said that the overall goal of such investigations of acoustic excitation is that it may provide a route to control of the mixing and combustion process, with implications for the intensity, rate, and progress of the combustion process and consequent size of flame, peak temperatures and pollutant formation [18]. It has been found previously [16] that two modes of mixing dominated for the coaxial diffusion flame to be investigated and accordingly the present investigation set out specifically to detect the inner and outer flow mixing structures corresponding to the frequency for each of these modes. This objective is somewhat similar to that of previous investigations [17-19], although in the present experiments the outer structure is controlled by mixing of the outer annular flow rather than by buoyancy. R E S P O N S E OF THE LASER SCHLIEREN SYSTEM

As indicated in the introduction, the present work involves the acquisition of averaged output signals referenced to a particular time or phase in the excitation signal. This is a standard method of recovering regular signals related to a known phase reference from a signal containing random or turbulent components. We are therefore concerned with the analysis of the regular, recovered signal records which can be obtained with the laser schlieren sensing beam intersecting the flow at a variety of

PERIODIC ACOUSTIC EXCITATION OF A DIFFUSION FLAME

DEFLECTION SENSING DIODE \~ ~t

Output Xi

] ~ I j}/ TURBULENT I , ~DIFFUSION FLAME

~ "iX.' MICROPHONE ll) / ~10utput Pi

153

distribution of 6 is an axisymmetric function of radial distance from the nozzle axis (r) and of time (t) referenced to the excitation signal. It follows that the measured signal Oi(t) can be expressed as

Oi(Y,t) = 2 Jy f~

06(r, t) Ox i

dr (1 -

(Y/r)2) 1/2'

(2)

where Y is the perpendicular distance from the sensing beam to the axis of the nozzle system. In the case where axial beam deflections (i = a) are sensed, Eq. 2 becomes

-Oa(Y, t) = 2 f : GASINLET~ N O Z Z L E ACOUSTICEXCITATION Fig. |. Genera]arrangementof combustionnozz]esystem and m e a s u r e m e n t

system.

physical locations. The present work is based on the use of a number of averaged signal records obtained as the sensing beam is traversed over the cross section of the flow as illustrated in Fig. 1, the perpendicular distance of the detection beam (Y) from the flow axis being the traverse variable. Averaged angular deflection signal records as a function of time 0i(t, Y) are then recorded at different positions Y and form the basis for reconstruction of the structure in the flow due to periodic upstream acoustic excitation as sensed by the optical detection system. The recovered averaged signal -Oi(t,Y) can be measured with the beam deflection angle transverse to the axis of the nozzle (i = t) or parallel to the axis (i = a). The beam deflection is determined by standard optical refraction as

-Oi = f 3X i ae

(1)

where x/ = ~ or xi = ~" for the axial and transverse deflection measurements, respectively, and the local refractive index in the flame is 6. Since the acoustic excitation to be applied emanates from within the upstream nozzle system in a symmetrical form we now assume that the

c~6(r, t) 0so

dr ( 1 --

( Y / r ) 2 ) 1/2"

(3)

This is an Abel integral equation at any particular time (t) for the radial distribution of the axial gradient of the refractive index and can be solved from the measured distribution 0a(Y, t) with traverse distance Y. Minerbo and Levy [13] give details of techniques for numerical solution of the Abel integral equation in terms of polynomial representations of the solution which were used here. In the case where the averaged signal is derived from the transverse deflection of the sensing beam Or(Y, t) the axisymmetry of the refractive index disturbance function 6(r,t) leads to a zero circumferential component of the refractive index gradient. The resulting form of the relation for the measured signal is then:

-O'(Y't) = 2fl

06(r, t) (Y/r)dr Or V/l _ (Y/r)2

(4)

This equation can be treated as an Abel integral equation for solution of the radial distribution function {(1/r)O6(r,t)/c~r} from the experimentally determined distribution of ( 1 / Y )'Ot(Y, t). Thus we can obtain from the radial deflection measurements 0t(Y, t) the radial distribution of (c~6(r, D/Or)by use of the Abel transform and multiplication of the transform function result by the radius (r). From the foregoing discussion a basis thus exists for determination of radial distribution of the axial refractive index gradient as a func-

154

M. R. DAVIS AND LI HA1 LIN

tion of time ( a 6 ( r , t ) / @ ) and also of the radial distribution of the radial refractive index gradient as a function of time (06(r, t)/Or). If the structure in the mixing region is moving at a convection velocity U~ then the time and axial coordinates are related simply by ~ = Uct. This relationship (sometimes called the frozen pattern hypothesis) has been generally found to be a reasonable representation of turbulent mixing regions as the rate of deformation of the mixing structures is usually found to take place relatively slowly compared with the dominant convective motion with the flow. We may thus identify two approaches to the determination of the excited structure 6(r, t~ = Uct) from the experimental data. Firstly, at each time step the radial gradient data may be integrated from a point outside the flow (r = r 0 say) to give

a(r, ~ = Uct) =

[r Oa(r, t) Jro Or

dr.

(5)

A series of such integrations at each time step may then be assembled to form the complete distribution of the convecting refractive index in the flow (6(r, ~ = Uct). The second approach is to work from the axial deflection data on the basis of the frozen pattern hypothesis and integrate in the axial direction from the data,

6(r, ~ = Uct) = I~ ¢/U~ ~o

36(r,

~/v~) a~

d~ + 6r(r). (6)

This integration from the data is then performed at each radial position to form the complete distribution 6(r, ~). The constant of integration (6r(r)) is determined on the basis that the disturbance induced by the excitation represents a perturbation about a zero average value. Therefore at each radial position 6r(r) was adjusted iteratively until:

fo~P6(r, ~ / U c) ds¢ = O,

(7)

where ~p = Uc/T p and Tp = periodic time of

the applied excitation and recovered response record. EXPERIMENTAL OBSERVATION OF RESPONSE TO EXCITATION The experimental observations were made with a turbulent diffusion flame formed above an upward directed coaxial nozzle. The Reynolds number of the nozzle flow was not very large, and it could be said that the flame is of a transitional rather than a fully turbulent nature. The center nozzle (6.0 mm diameter, d i) provided a jet of propane gas whilst the outer nozzle (inner diameter 10 mm, outer diameter 20 mm, d 0) discharged an air flow. The flame was stabilised on the fiat annular surface between inner and outer nozzles and the general arrangement of the nozzle system is as shown in Fig. 1. The flow rates of propane and air were metered in the supply lines so that nozzle discharge rates could be calculated, and the nozzle system was designed so that both nozzles had an upstream settling chamber with a smooth contraction to the nozzle exits. The diffusion flames formed by this nozzle system have been the subject of previous investigations of turbulent flame structure [12] and of flame response to broadband excitation [16]. These earlier investigations under random excitation showed that the diffusion flame exhibited two dominant modes of response: a lower-frequency mode generally associated with the mixing of the flame with the surrounding ambient air and a higher-frequency mode associated with the mixing of the inner fuel jet with the coannular air jet surrounding it. These experiments with random excitation required the use of specialized signal analysis methods to identify the flame response (minimum mean square error identification and homomorphic deconvolution) and it was not possible to make detailed observations of the structures induced under these conditions. However, within certain limits [16] the response increased linearly with the amplitude of the random excitation and the two modes could generally be identified as being associated with inner and outer regions of the diffusion flame. In the experiments to be described here, pure tone excitation was applied at the two frequencies of

PERIODIC ACOUSTIC EXCITATION OF A DIFFUSION FLAME dominant response identified in the previous random excitation experiments with the intention of determining the detailed structure of the two dominant modes of response of the flame. In both series of experiments the acoustic excitation was applied by a loudspeaker located in the rear of the settling chamber of the outer (air flow) coannular nozzle so as to induce symmetrical disturbances in the flame. During the experiments to be described the diffusion flame was operated with a central propane jet velocity of 2.5 m / s (Ui) and a coannular outer air jet velocity of 2.0 m / s (U0). This produced a turbulent flame with a visable length of approximately 300 mm, with evidence of inner and outer mixing structures [16] in schlieren photographs taken with a conventional photographic schlieren visualisation system. The sound pressure level produced by the acoustic excitation from within the air flow settling chamber was measured with a microphone located adjacent to the nozzle exit. From standard acoustic relations it was thus calculated that the excitation applied produced a

(a)

155

periodic velocity fluctuation of peak amplitude 0.13 m / s at 40 Hz (the lower frequency of dominant broadband response) and 0.19 m / s at 420 Hz (the higher frequency of dominant broadband response). These correspond to 6.5% and 9.5% of the exit velocity of the outer coannular airstream, so that the acoustic excitation was applying a significant level of velocity fluctuation at the nozzle exit and could thus be expected to produce substantial effects on the development of the mixing shear layers in the flame. The Reynolds number of the outer nozzle air stream was 2700. The level of acoustic excitation applied was the maximum that could be generated by the loudspeaker without distortion. The overall structure of the test diffusion flame is shown in Fig. 2 under natural mixing conditions. There is clear evidence of both the inner and outer regions of mixing, the latter having a much larger physical scale. Of particular interest is the effectiveness of the Prewitt signal enhancement filter algorithm (Fig. 2b) in clearly delineating the structures embedded in

(b)

Fig. 2. Visualizations of the diffusion flame. (a) Instantaneous schlieren image. (b) Image enhanced by Prewitt filter algorithm.

156

M. R. DAVIS AND LI HAI LIN

the original schlieren image (Fig. 2a). The Prewitt window applies a ( - 1 , 0 , 1) weighting to pixels successively in the two coordinate directions, and effectively compounds the image density gradients in the image. When excitation is applied to the flame there was apparent a strengthening of the internal structure if higher-frequency (420 Hz) excitation was applied, and a strengthening of the outer structure when low frequency excitation was applied. These photographs have been published previously [16]. With the flame in operation and acoustic excitation applied at one of the two selected frequencies, records were made of the averaged time record of the laser deflection signal in either axial direction or transverse to the flow. The lasers used were 0.5 mW Spectra Physics h e l i u m - n e o n lasers with a beam diameter of approximately 0.5 mm. The deflection sensors used were United Detector Technology PIN-SC-10 solid state devices. This signal averaging was carried out using a Nicolet 660B digital signal analyzer having a 1024-point signal record length. The averaged time history of the laser signal was relative to a fixed but

arbitrary trigger point on the periodic excitation signal. Averaging was carried out over many thousand cycles of excitation and response record. The dominant uncertainty in the averaged record was mainly due to the inevitable small long term fluctuations in the flow conditions. There were no comparable uncertainties due to the convergence of the signal averaging process in the presence of random fluctuations caused by the natural turbulent mixing in the flame which was not associated directly with the excitation. Thus the limiting factor was the maintenance of steady gas supply flow rates rather than signal analysis methods. The averaged or recovered signal records are shown in Figs. 3 and 4 for axial and transverse beam deflections, respectively. We see that in the main the records are quite smooth and regular except for records with the laser on or near the nozzle axis with low frequency excitation or far away from the nozzle axis with high frequency excitation. In the former case, the signal is quite small (less than 10% of the maximum) and it appears that the irregularity apparent is due to the other dominant mode of

-1

:b 4"t 0.0

1,0

(a)

o

lO

(b)

0

10

(c)

Fig. 3. Time averaged axial deflection signal records extracted from the schlieren output signal by signal recovery methods. (Phase referenced to fixed point on excitation input, axial direction deflection records "Oa(r, t), vertical ordinate radian 2 104, horizontal ordinate A x / d i = A ' r U , . / d i , Y / d i values as marked, Y = distance from axis) (a) 420 Hz, x / d i = 11.7. (b) 40 Hz = x / d i = 5.8. (c) 40 Hz, x / d i = 11.7.

P E R I O D I C A C O U S T I C E X C I T A T I O N OF A D I F F U S I O N F L A M E

,ok 0,4. -0.4

/%,.,

-2o I- ~

-1

157

~

J

8 3

0

10

0

(a)

10

0

10

(b)

(c) Fig. 4. Time-averaged transverse deflection signal records (as Fig. 3, Or(r, t)). mixing at approximately ten times the excitation frequency. The existence of a small but finite averaged result on the axis in these cases thus suggests that the excitation is not perfectly symmetrical (due to the small excitation frequency component) and that the highfrequency inner structure although not being directly excited has a tendency to phase lock to the lower excitation frequency. This is evidenced by a near regular fluctuation on the averaged record, However, these effects are quite small and are apparent only in observations with the laser passing through the flow axis. The averaged records at the outer edge of the flow with high-frequency excitation also show the presence of more random fluctuations, but this is merely a consequence of the very small response to high-frequency excitation in this region of the flow. Values from the averaged signal records shown in Figs. 3 and 4 at a series of time values and for various radial locations of the sensing beam were used to form a distribution of beam deflection with laser position (Y) at each time instant as described in the previous section. The resulting functions were then transformed by the Abel integral transform to obtain the radial distribution of the axial refractive index gradients (Eqs. 3 and 4 as appropriate: (c?6/c)~) and (1/r)(O6/Or). Since the

Abel transform essentially proceeds by an inward progression from the outermost data point, these distributions all begin with a zero value at the outer edge. As we are computing the axial density gradient at a series of time values by this transformation there is no particular requirement for zero values to apply on the flow axis. In order to carry out the transformation from a set of values that are functions of time to values that are functions of axial displacement it is necessary to know the convection velocity of the disturbances. This was obtained by using a second laser beam located orthogonally to the first but displaced in an axial direction by varying distances. Observation of the time delay of peak cross correlation ( r ) between the two beams thus indicates convection velocity of the structures in the flow as shown in Fig. 5, the slope of these results giving a velocity of 2.07 m / s for the lowfrequency (40 Hz) structures and 2.7 m / s for the high-frequency (420 Hz) structures. It will be noted that the latter value is slightly higher than the nominal exit velocity of the central gas nozzle flow, but it should be borne in mind that the system senses the reacting structures in the flow which undergo significant volumetric expansion due to combustion. The velocities of flow and structures induced are consid-

158

M . R . DAVIS A N D LI H A I LIN

~c 0.5 10 ¸

(ms)

S 0.o

1

(a) 0

I

I

I

I

2

4

6

8

& x / d ~,

Fig. 5. Convective motion of mixing structures as shown by time delay to peak correlation. (Cross correlation of signals from orthogonal laser beams through flow axis, fixed beam located 10 inner nozzle diameters from nozzle exit) ×: 40 Hz, slope 2.07 m / s . Q: 420 Hz, slope = 2.7 m / s (slope of line gives phase velocity from values of time scale and nozzle size).

erably greater than velocities due to buoyant motion [17-19] which is therefore considered to be negligible in this case. The final stage of the analysis is to transform the results of axial density gradient by integration at each radial position in the axial or transverse directions (Eqs. 5 and 6) to form the distribution of local refractive index over the complete radial/axial cross section of the axisymmetric disturbances induced by the excitation. The result of this process is shown in the form of contour diagrams in Figs. 6 - 8 for the two frequencies of excitation applied and at two axial locations. Adjustment of the constant of integration in the axial direction at each radial position has been made to give a zero average value of the refractive index disturbance about the mean value according to Eq. 7. At the higher excitation frequency (Fig. 6) we see that quite small sized disturbances are induced near the flow axis with alternating maxima and minima of refractive index having an overall wavelength of approximately 1.2 times the inner (fuel) nozzle diameter. At this higher frequency there was no evidence of the larger external flow structures that could be detected. At the observation point (11.7 inner nozzle diameters from the nozzle exit) the disturbances have a transverse diameter which is approximately twice the fuel nozzle diameter,

o

1

(b)

Fig. 6. Structures induced by excitation of flame at St i = 1.01 (a) Identified from transverse deflection records (Eqs. 4 and 5) (b) Identified from axial beam deflection records (equations (3), (6) and (7)). ( f = 420 Hz, d i = 6 mm, U~ = 2.5 m / s , U0 = 2.0 m / s , Uc = 2.7 m / s , x / d i = 11.7, figures marked indicate extremes of 105 & Ordinate: a r / d i. Abscissa: A x / d i ) .

and are of alternating sign along the flow axis. The magnitude of the alternating peaks and minima in refractive index give an overall range of variation of 0.00011 from the axial deflection data and 0.00018 from the transverse deflection data, an average of 0.00014. For these higher frequency small disturbances the discrepancy between the two methods of analysis from axial or transverse deflection records is due to the relatively small diameter of the inner fuel nozzle system (6.0 mm) and finite size of the measuring beam ( ~ 0.5 mm). However, subject to this limitation due to resolution, the results of the two sets of analysis indicate fluctuations which are ___23% of the refractive index of the ambient air or + 6.5% of the refractive index of the propane fuel when cold. The range of possible variation of refractive index which results from the combustion of propane and air depends on the extent of reaction and relative mixture concentration achieved [12], but for complete combustion of a stoichiometric mixture the refractive index can reduce to 10% of the refractive index of cold air at ambient conditions. This indicates the potential for combustion to contribute a maximum reduction of refractive index by 90% of that of cold air. Hence the present observations with fluctuations of + 23% of the refractivity of cold air indicate quite severe fluctuations of conditions along the flow axis, but nonetheless fluctuations which are well within (+_5.1%) the overall

PERIODIC ACOUSTIC EXCITATION OF A DIFFUSION FLAME maximum possible range (0.00137) set by the lower limit of complete stoichiometric combustion and the u p p e r limit of cold, unreacted propane. The results of m e a s u r e m e n t s and computation at the lower excitation frequency are shown in Figs. 7 and 8 for two locations of the measuring system at 5.8 and 11.7 inner nozzle diameters from the nozzle exit. The physical scale of the disturbances is much larger, the outer train of ringlike structures having a diameter 3.8 times the inner nozzle diameter or 1.15 times the outer nozzle outer diameter. Clearly these outer ring structures are centered on the shear layer between the outer (air) flow and the surrounding laboratory air. The axial scale of the disturbances is also much larger, the periodic length being 5.2 times the outer nozzle outer diameter or 8.7 times the inner fuel nozzle diameter. The results show a tendency for axial length to increase and diameter to decrease from the nozzle exit. These outer structures have alternating maxim u m and minimum refractive index, the range of variation diminishing sharply from +0.00017 at 5.8 diameters from the nozzle exit to +0.00004 at 11.7 diameters from the nozzle exit. This represents a reduction from + 12% to + 3 % of the refractive index differential between the propane fuel and fully reacted stoichiometric mixture. These disturbances are strong but within the range limitation set by the extremes of refractive index of fuel and stoichiometric reacted mixture. The rapid reduction of observed strength of disturbances with distance from the nozzle is consistent with the initial formation of very regular ring-like structures which undergo rapid distortion and fragmentation as they move downstream. Inside the ringlike structures induced in the outer shear layer by the lower frequency excitation there is also evidence of an inner chain of disturbances on the flow axis (Figs. 7 and 8). Owing to some residual noise in the averaged signal records (Figs. 3 and 4) near the flow axis which appears to be associated with the inner flow mixing structures as discussed, the transverse deflection results gave erratic results at the inner position ( x / d i = 5.8) near to the nozzle. However, the axial deflection records and all results at the outer position ( x / d ~ =

3

159

) ,~J~

;

rJq-x

i +0,'~ I llrlJll

0

10

0

(a)

10

(b)

Fig. 7. S t r u c t u r e s i n d u c e d by e x c i t a t i o n of f l a m e at St 0 = 0.38 ((a) and (b) as F i g u r e 5, f = 40 Hz, d o = 20 mm, U / = 2.5 m / s , U 0 = 2. 0 m / s , Uc = 2.1 m / s , x / d i = 5.8).

11.7) were not subject to this problem, and the inner structures were fairly clearly resolved (Figs. 7 and 8). The inner structures have the same axial length scale as the outer structures and are also of alternating sign but in the opposite sense to the sign of the outer structure at the same axial position. There is a tendency for the inner disturbances (of opposite sign) to precede the outer structures very slightly in all cases. Nearer to the nozzle ( x / d i = 5.8) the strength of inner and outer disturbances was similar, but further away from the nozzle exit ( x / d i = 11.7) the outer structures weakened more rapidly and the inner structures were then somewhat stronger. The form of the inner structures at both m e a s u r e m e n t positions was that of a series of pufflike structures of alternating sign, there being no evidence of a ringlike form but rather a form with a maximum disturbance strength on the flow axis. It appears that these inner structures are locked into the outer structures, a phe-

o

(a)

(b)

lO

Fig. 8. S t r u c t u r e s i n d u c e d by e x c i t a t i o n of flame at St o = 0.38 (as for figure 6, x / d i = 11.7).

160 n o m e n o n similar to that observed for buoyant flames [18, 19]. CONCLUSIONS It has been found that signal averaging or recovery from noise by phase reference to an acoustic excitation is an effective means of determining structures induced in a diffusion flame. Generally consistent results for the structure and strength of induced disturbances have been obtained by signal recovery from both axial and transverse schlieren b e a m deflections, although there are some limitations in the present results due to the relatively small coannular nozzle system and flame investigated. Two quite distinct physical modes of response have been detected at the two Strouhal numbers that were known from previous investigations to be the most responsive for the particular nozzle system and flame configuration investigated. At the higher excitation frequency and Strouhal n u m b e r of 1.01, the excitation at 9.5% of inner nozzle exit velocity produced a + 5 . 1 % fluctuation of refractive index normalized on the upper bound for refractive index fluctuations, that is the difference between the refractivity of the propane fuel and the fully reacted stoichiometric mixture. The structures formed were a series of alternating disturbances centered along the central nozzle axis with a repeating wavelength of twice the inner nozzle diameter. These small inner flow disturbances showed a very slow rate of reduction of strength with distance from the nozzle and thus would persist for a substantial distance from the nozzle. At the lower excitation frequency and Strouhal number of 0.38 based on the outer nozzle parameters an excitation of 6.5% of the exit velocity induced a + 12% fluctuation of refractive index. In this case the structure induced in the flow was a series of alternating ring structures of approximately the same diameter as the outer nozzle and with a repetition wavelength 5.2 times the outer nozzle diameter. Contained within these ringlike structures were a series of

M.R.

D A V I S A N D LI H A I L I N

alternating disturbances along and centered on the flow axis, of opposite sense to the surrounding ring structure. These larger scale disturbances weakened rapidly with distance from the nozzle, indicating a rapid breakup of the regular ringlike structures between the two measuring points at x/D = 5.8 and 11.7. REFERENCES 1. Miake-Lye, R. C., and Toner, S. R., Combust. Flame 67:9-26 (1987). 2. Eickhoff, H., and Winandy, A., Combust. Flame 60:99-101 (1985). 3. Lysaght, A. J. R., Bilger, R. W., and Kent, J. H., Combust. Flame 46:104-108 (1982). 4. Chen, L. D., and Roquemore, W. M., Combust. Flame 66:81-86 (1986). 5. Gutmark, E., Parr, T. P., Hanson-Parr, D. M., and Schadow, K. C., Combust. Flame 75:229-240 (1989). 6. Cabelli, A., Pearson, I. G., Shepherd, I. C., and Hamilton, N. B., First World Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Dubrovnik, 1988. 7. Ha, J., Proctor, D., Pierson, I. G., and Brumale, S. Proceedings of the Eleventh Australasian Fluid Mechanics, Conference, Hobart, Paper 4B-8, pp. 443-446 (1992). 8. Pierson, I. G., Cabelli, A., Shepherd, I. C., and Hamilton, N. B., Proceedings of the Tenth Australasian Fluid Mechanics Conference, Melbourne, Paper 5C-2, pp 5.27-5.30 (1989). 9. Davis, M. R., J. Fluid Mech. 70 (3):463-479 (1975). 10. Winarto, H., and Davis, M. R., Proc. R. Soc. Lond. A 395:203-228 (1984). 11. Davis, M. R., Combust. Sci. Technol. 64:51-65 (1989). 12. Davis, M. R., and Rerkshanandana, P., Exp. Thermal Fluid Sci. 6:402-416 (1993). 13. Minerbo, G. N., and Levy, M. E., SIAM J. Num. Anal. 6:598-616 (1969). 14. Davis, M. R., and Rerkshanandana, P., Int. J. Heat Mass Trans. 34:1633-1647 (1991). 15. Davis, M. R., and Rerkshanandana, P. Exp. Thermal Fluid Sci. 6:402-416 (1993). 16. Davis, M. R., and Jumppanen, P. C., Combust. Flame 93:349-374 (1993). 17. Vandsburger, U., Lewis, G., Seitzman, J. M., and Allen, M. G., Western States Section, The Combustion Institute Fall Meeting, University of Arizona, Paper 86-19 (1986). 18. Lovett, J. A., and Turns, S. R., A/AA J. 28:38-46 (1990). 19. Strawo, A. W., and Cantwell, B. J., Phys. Fluids 28:2317-2320 (1985). Receiued 12 June 1994; revised 6 February 1995