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Optical-acoustic feedback applied to a turbulent diffusion flame
Experimental Thermal and Fluid Science 16 (1998) 237±246
Optical-acoustic feedback applied to a turbulent diusion ¯ame M.R. Davis *, P.C. Jumppannen Department of Civil and Mechanical Engineering, University of Tasmania, G.P.O Box 252-65, Hobart 7001, Australia Received 13 March 1995; received in revised form 28 October 1996; accepted 12 March 1997
Abstract A laser schlieren sensing system has been coupled to provide feedback acoustic excitation of a co-annular turbulent diusion ¯ame of propane and air. It is found that positive feedback oscillation was induced at a level of feedback gain that was consistent with open loop broad band response measurements. The frequency of feedback induced oscillation was consistent with the disturbances moving at the speed of the ¯ow from the fuel nozzle, and the frequency showed regular cyclical variation as the sensing beam was moved slowly along the nozzle axis. This corresponded to regular physical stretching or compression of the induced structure so that an integral number of disturbances lay between an apparent origin (just outside the nozzle) and the sensing beam. Without ®ltering the feedback system tended predominantly to lock into higher frequency, smaller structures associated with the inner mixing region. However, with appropriate band pass ®ltering in the feedback ampli®er it was possible to induce either inner or outer structures by feedback. Temperature increases of between 40°C and 60°C were induced in the ¯ame centre line temperatures, these increases extending far downstream of the location of the sensing beam. It appeared that feedback moved the apparent origin of the ¯ame towards the nozzle as a consequence of enhanced mixing. Ó 1998 Elsevier Science Inc. All rights reserved. Keywords: Combustion; Turbulence; Feedback; Acoustic; Optical; Flame; Diusion
1. Introduction Gaseous jet diusion ¯ames formed by gas burner nozzles are of necessity operated at only moderate nozzle velocities in order to stabilise the ¯ame and avoid lifto from the nozzle of the combustion zone or extinction of reaction [1±3]. As a consequence the nozzle Reynolds number which is achieved is strongly determined by nozzle size and is often relatively low for small nozzles. This aspect is compounded by the temperature within the ¯ame, which generally increases local viscosity of the ¯ow and tends to lower the local Reynolds number still further. Thus, the region of ¯ow near to a burner nozzle is quite likely to be in¯uenced by relatively strong regular mixing structures between fuel, oxidant and surrounding gases [4±8]. Detection of regular, coherent mixing structures in a turbulent ¯ame is facilitated by the use of optical refractive index based sensing systems which do not rely on the insertion of a probe into the ¯ow. The schlieren or shadowgraph based methods, which respond to ®rst and second derivatives of the unsteady refractive index *
Corresponding author. Tel.: +61 3 6226-2074; fax: +61 3 62234611. 0894-1777/98/$19.00 Ó 1998 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 9 7 ) 1 0 0 2 4 - 3
®eld, are generally the simplest to implement physically [9±11]. Also, the integrating feature of optical beam methods gives an averaged time dependent signal for the whole sensing beam and thereby enhances the contribution of coherent disturbances over turbulent disturbances, the latter tending to average out to a small total eect when integrated along the complete sensing beam [12,13]. In this way an unsteady signal which is strongly indicative of coherent mixing structures is obtained and provides a better means [14,15] of detecting coherent structures than does a point sensing probe, which is dominantly in¯uenced by local turbulence. The eect of acoustic excitation from upstream on a turbulent diusion ¯ame has been shown [16±18] to stimulate the formation of regular vortex mixing structures near the nozzle which subsequently break up as they move downstream. It would appear, therefore, that a sensing system such as the thin penetrating schlieren beam system, which is very sensitive to such large scale structures, would have the potential for providing ampli®cation of mixing if it were coupled in a feedback loop to drive the acoustic excitation. The objective of the investigation described here is to combine acoustic upstream excitation, which has been shown [11,12] to induce regular structures in a diusion
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¯ame, with a feedback driving signal derived from an optical sensing beam in order to modify and strengthen the mixing and reaction process. The optical system selected is the single beam schlieren system [10±12] as this can be implemented very easily with only a low cost laser source and a de¯ection sensitive photo diode, thus obviating the need for any complex optical components or elaborate optical layout. The use of a slab sensing beam [19] may give a greater sensitivity to coherent structures relative to turbulent structures as it introduces spatial integration over the whole cross section of the ¯ow. Such a system does however require the formation of a slab beam and then focusing of this down to a single detector, optical requirements which inevitably complicate the optical sensing arrangements appreciably. For this reason the slab sensing beam has not been investigated in the context of feedback excitation, and the present paper deals only with the very simple laser source/ de¯ection sensing diode arrangement. For convenience this is termed a laser schlieren system, although the advantage of the relatively simple laser source is that it forms a high intensity narrow beam rather than its coherent properties which are not used directly in this application. Whilst the term schlieren is generally applied to a full ®eld optical imaging system, such systems rely on beam de¯ection and so the term has been used elsewhere to include the laser schlieren system in which beam de¯ection is sensed directly by a photodiode. There is, of course, no cut o knife edge used in this present method, system signals being generated by de¯ection of the laser spot which is analogous to the variation of optical intensity in a conventional schlieren caused by ray de¯ection at the knife edge. 2. Open loop response of the combustion and optical system The combustion facility used in this work comprised a vertical nozzle system having a pair of co-annular nozzles with the propane gas ¯ow through the central nozzle and an air ¯ow through the outer nozzle. The ¯ame was stabilised on the annular surface between the nozzles. The performance of this burner system has been described previously [14,15] for experiments in which the ¯ame was subjected to symmetrical acoustic excitation (without feedback) from upstream in the outer (air ¯ow) nozzle settling chamber. Fig. 1 illustrates the nozzle system in detail, the central gas nozzle having a diameter of 6 mm and the outer (air ¯ow) nozzle inner and outer diameters of 10 and 20 mm, respectively. The turbulent diffusion ¯ame formed by this nozzle had a visible height of approximately 300 mm overall depending upon ¯ow conditions, and schlieren images [14,15] show the presence of inner and outer mixing layers near to the nozzle, rapidly merging into a fully turbulent image across the whole ¯ow cross section. A co-annular diusion ¯ame was used here as it presents a much more turbulent structure than can be achieved at laboratory scale with a single jet diusion ¯ame, and is therefore more indicative of what
might be achieved in larger scale burner systems. A single ¯ame condition was used in the present work which corresponded to the maximum fuel and air velocities for which the turbulent ¯ame remained stably attached to the nozzle system. The co-annular diusion ¯ame appears much more turbulent, without such visible regularities and has a much shorter visual length than a single jet diusion ¯ame from the same nozzle. Stoichiometric and similar detail for this burner system has been discussed previously [14]. The burner system was operated approximately 1 m below a large air extractor hood and the coannular ¯ame was not signi®cantly disturbed by minor disturbances in laboratory air. The response of the ¯ame to excitation is detected by means of a penetrating laser beam and a de¯ection sensing photo diode. This sensing system has been described in detail previously [10,11,13±15] and is shown in Fig. 1. A full indication of the experimental uncertainty associated with this system has been given previously [14]. The laser beam is refracted by unsteady temperature or composition gradients in the turbulent mixing zone and the total unsteady angular de¯ection of the beam is sensed by the photo diode and translated into an unsteady output voltage. Mixing and reaction produce a lowering of the refractive index, so that the system essentially responds to the progress of reaction towards completion in the burning mixture. The sensing photo diode detects de¯ections in two perpendicular directions so that sensitivity to axial or transverse gradients of refractive index can be introduced. In the present work only the axial component sensitivity was used so that the unsteady output signal from the optical sensing system can be written as Z R0 od x; y; t E00 t Ah0a t A dy; ox ÿR0 where the integral extends across a complete diameter of a ¯ow, ÿR0 < y < R0 where R0 is some outer limit to the zone of signi®cant mixing and reaction. The constant A includes the photo diode and associated ampli®er displacement sensitivity and the system geometry (in particular distance from ¯ow to sensor). The system is calibrated directly by transversing the photo diode so that the laser beam moves across its sensing face. Measurement of the beam de¯ection by photo-sensors was accurate to better than 0.25 mm or 2 ´ 10ÿ6 rad, and the resolution of the signal analysis system was accurate to approximately 0.1% of the measured signal magnitude and frequency. These accuracies can be translated to the various measurements reported in this paper of spectral density, frequency and cross correlation. Temperatures were measured to within 5°C using a calibrated thermocouple system, whilst probe positioning was to within 1 mm approximately. The open loop sensitivity of the optical detection system has been measured using both broad band and discrete frequency excitation applied through the loudspeaker. The broad band investigation was carried out using pseudo-random binary noise inputs to the loudspeaker [15] and Fig. 2 shows that the system exhib-
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Fig. 1. General arrangement of coaxial nozzle and optical feedback systems.
Fig. 2. Open loop response spectra under pseudo-random binary excitation (identi®ed by minimum mean square response identi®cation methods [15]. (a) x=D 1:3, (b) x=D 4:7, (c) x=D 11:3, (d) x=D 17:3.) Flow conditions: co-axial diusion ¯ame, fuel (propane) speed 2:5 m=s, co-annular air ¯ow speed 2 m=s.
its two dominant modes of response: a low frequency mode at about 100±200 Hz (depending upon position) which gave rise to larger scale regular structures in the outer mixing region with the surrounding ambient air, and a high frequency mode at about 750±800 Hz which produced much smaller scale disturbances in the inner mixing region between the fuel gas and co-¯owing air streams. The occurrence of these preferred modes is attributed to the combined eect of modal acoustic resonances in the nozzle system and the instability of the mixing shear layers. Both outer and inner excited structures were found to convect at close to the exit velocity of the fuel gas nozzle (2.5 m/s), the inner structures being relatively stronger and, as would be expected, decaying more rapidly with axial movement as shown by Fig. 2. The results of Fig. 2 were obtained by a ®ltered minimum mean square signal analysis and identi®cation method [15]. Similar open loop response results to those of Fig. 2 were also obtained by the alternative signal analysis technique of homomorphic deconvolution [15]. More recent investigations carried out using periodic excitation and signal recovery by phase locked averaging [20] have shown that the inner structures are in the form of a series of disturbances centred on the axis of alternating sign spaced at intervals of approximately one inner nozzle radius, whilst the outer structures were again of alternating sign but with embedded inner structures of opposite sign spaced axially at about four inner nozzle diameters (or just over one outer nozzle diameter).
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The eect of open loop excitation from upstream is also illustrated in Fig. 3 which shows the variation with axial position of the cross correlation coecient to two orthogonal sensing beams, both sensing axial density gradients and both passing through the ¯ow axis at the same distance from the nozzle. More detailed and extensive measurements with this cross beam system [10±14] show that very similar indications of turbulent convection velocities are obtained to those using other anemometry techniques. Even without any feedback the eect of upstream excitation is to produce substantial increases in the cross correlation over the ®rst six fuel nozzle diameters from the nozzle exit, with a maximum eect at approximately three nozzle diameters from the nozzle exit. The magnitude of the excitation applied in this case corresponds approximately to a velocity ¯uctuation in the co-¯owing air stream of 0.07 m/s or 3.5% of the average speed of this ¯ow. We were not able to measure the natural, unexcited turbulence level in the mixing ¯ow, but in the light of the substantial information available on turbulence in mixing jets the level would be expected to be about 0.15 (i.e. 0.3 m/s), much larger than that due to acoustic excitation eects here. This is somewhat more than the excitation required to induce a maximum response in the ¯ow (0.02 m/s [15]) and thus represents about the greatest enhancement of ¯ow coherence which might be expected to be achieved by open loop excitation as excitation above the limit of a proportionate range [15] was found to produce an almost constant or saturated levels of response. For proportionate range excitation (i.e. up to 0.02 m/s perturbation of the air stream approximately) it was found that at 5.7 inner nozzle diameters from the nozzle exit plane the overall open loop excitation/ response sensitivity was 0.075 rad/Pa between the excitation pressure at the nozzle exit (observed by a microphone adjacent to the nozzle exit [15]) and the angular de¯ection of the optical schlieren beam. Thus when the feedback from the optical sensor to the ampli®er of the excitation loudspeaker is connected it is expected that self sustaining positive feedback will occur when the gain in the feedback path is sucient to exceed about
Fig. 3. Cross correlation between orthogonal schlieren beams crossing at the nozzle axis (¯ow conditions as for Fig. 2). (Acoustic excitation applied at 76 Hz from upstream in the air ¯ow nozzle, velocity ¯uctuation induced 0:07 m=s at nozzle exit.)
13.3 Pa/rad of exit plane pressure per unit angular de¯ection of the optical schlieren beam. It should be noted that whilst there is virtually no signi®cant delay or phase change between the optical beam and the output from the ampli®er driving the loudspeaker (Fig. 1), the geometry of the nozzle system and settling chambers will impose some phase changes of the output pressure ¯uctuation at the nozzle exit with respect to the loudspeaker input signal. However, this eect is relatively small corresponding to loudspeaker phase shift and acoustic transport delay through the nozzle settling chamber of approximately 0.001 s compared with convection delays associated with the ¯ow of about 0.02 s (at about eight fuel nozzle diameters from the nozzle exit, which varies depending on location downstream of the nozzle). The combined eect of delays or phase lags due to loudspeaker, nozzle and ¯ow convection effects is thus expected to be dominated by the ¯ow convection delay time and this should have a signi®cant in¯uence on the closed loop, positive feedback system as will be seen in the following section. 3. System characteristics with optically derived excitation feedback With the feedback connected as shown in Fig. 1 from a single schlieren sensing beam passing through the ¯ow axis, essentially two parameters can be controlled, these being the axial location of the sensing beam (i.e. its distance x from the nozzle exit) and the overall gain applied to the feedback signal as it drives the loudspeaker. The eect of the gain in the feedback loop is illustrated in Fig. 4, which shows the power spectral density of the schlieren optical signal for a set of values of the feedback gain varying from zero (i.e. no feedback) to the maximum gain level which was the level for which the spectral response peak reached its maximum (i.e. saturated) value. It must be recognised that the de®nition of reaching a maximum saturated value is subject to some uncertainty, although this condition was visually observed without diculty and thus the spectral levels indicated in Fig. 4 are subject to this de®nition and in an exact sense should be treated as relative levels. It can be seen that the rather broader schlieren optical signal spectrum with no feedback becomes progressively dominated by a very strong discrete component at approximately 800 Hz as the feedback gain is increased. Also it is quite evident that the magnitude of the peak spectral density rises quite sharply over a relatively small range of gains. This is more clearly indicated in Fig. 5, where an increase of 4 dB in feedback gain increases the level of the spectral peak by approximately 16 dB. It is evident that once the gain is increased beyond a particular critical value the net feedback becomes positive and the system goes into strong discrete oscillation. Measurement or de®nition of a minimum threshold for the onset of this discrete feedback oscillation is obviously dicult, and therefore a nominal threshold has been
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Fig. 5. Variation of peak spectral density of schlieren signal with feedback gain. Vertical axis: peak/spectral density of schlieren signal relative to maximum (saturation) value. Horizontal axis: feedback gain relative to gain required to produce saturated response. (Dashed lines indicate nominal threshold gain to produce response 3 dB below saturated value.)
Fig. 4. Power spectral density of sensing schlieren beam signal for different levels of feedback gain (¯ow conditions as for Fig. 3, schlieren beam across centre line at x=D 5:7). Vertical axis: spectral density, middle and upper spectra displaced upwards by one decade for clarity (arbitrary units): (a) Solid line: no feedback. Dotted line: (maximum gain ÿ20) dB. Dashed line: maximum gain; (b) Solid line: (maximum gain ÿ6) dB. Dotted line: (maximum gain ÿ4) dB. Dashed line: (maximum gain ÿ2) dB.
selected for which the optical spectral peak has a level 3 dB below its maximum as shown in Fig. 5. If the schlieren beam location is moved in the axial direction whilst maintaining the feedback sensing beam through the nozzle axis it is found that both the magnitude of the threshold gain and the frequency of the resonant spectral peak are altered. Fig. 6 shows the regular pattern of variation of frequency which was observed. The regular, progressive and cyclical reductions in frequency which occur, separated by sharp rises in frequency at distinct axial locations, show that as the convection time from nozzle to beam is increased so the period of the feedback oscillation also increases with a corresponding increase of interval between successive disturbances. This regular stretching of the induced structure as the sensing beam is moved downstream is broken at intervals where a complete additional cycle of the structure is preferentially ®tted in between the nozzle and sensing beam at a shorter cycle length and higher
frequency. There is evidence of overlap or hysteresis in the sudden transition that occurs as the feedback system responds to conditions where a longer or shorter wavelength train of disturbances produces the stronger preferred feedback. The introduction of the feedback path has thus modi®ed the overall system eigenvalues. The results of Fig. 6 can be used to determine the apparent convection speed (Uc ) of the moving structure, the number (n) of wavelengths (k Uc / f, where f observed frequency) between the sensing beam and the nozzle and the feedback loop / acoustic time delay (T0 ) on the presumption that the wavelength and convection speed do not vary with x:
Fig. 6. Variation of frequency of feedback oscillation with distance between nozzle exit plane and sensing beam. (Sensing beam through nozzle axis, ¯ow conditions as for Fig. 2.)
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Period T0 x=Uc T0 nk=Uc m=f ; where m is an integer. The parameter n need not be an integer if the eective origin of the induced structure is not exactly at the nozzle exit. Fitting lines to the data of Fig. 6 and using selected points on these it is thus possible to solve for T0 , Uc and n. This yields values of T0 0.0047 s for the feedback / acoustic delay, Uc 2.64 m/s for the convection speed of the induced disturbances and n 4.24 for the number of cycles between the x 4.7D position and the nozzle. The convection speed conforms closely with the velocity of the fuel jet (2.5 m/s) and also with cross beam correlation measurements of convection speed in the unexcited ¯ame. Whilst the observations of feedback oscillation extended only over the range 1.7 < x / D < 5.7 for the sensing optical beam, the calculated value of n 4.24 suggests that the eective origin of the excited structure is centred around a position x / D 0.125, so that four complete cycles then extend to the x / D 4.7 position with both these positions representing a condition where the sensing beam is neither stretching or compressing the induced structure, but rather inducing an average wavelength structure by feedback. The apparent origin of the induced system at x / D 0.125 is consistent with there being a ®nite minimum distance from the nozzle at which the induced ¯ow structure can physically be formed, this position being quite small at about one-eighth of the wavelength of the structure from the nozzle exit as might be expected. Also, as would be expected, the average frequency of the induced structures of 800 Hz corresponds closely with the maximum open loop response associated with the inner structures in the ¯ame (Fig. 2), and we see that the range of axial location over which feedback oscillation occurred (x / D < 5.7) corresponds to general to the region for which the open loop response tests showed signi®cant inner structure response at the higher frequency of this nozzle system (f 800 Hz, Strouhal number fD / Uc 1.9). The induced structures are thus seen to have a wavelength of 1.14 times the fuel nozzle diameter, to convect at the speed of the fuel jet and to commence at 0.125 times the fuel jet diameter from its exit. The stretching or compressing and consequent frequency changes of the induced structures is consistent with their being locked in by the sensing beam at its position and at a frequency determined by their convective motion. Some variations in the nominal threshold gain required to induce feedback oscillation as described above were observed as the sensing beam was moved axially as shown in Fig. 7. For most conditions a threshold gain of about 20 Pa/rad was found, but in some cases of high or low frequency oscillation where the induced structure was being compressed or stretched from its average length, signi®cantly higher threshold gains in the range up to 66 Pa/rad were required to induced feedback oscillation. This appears consistent with the notion that the average wavelength structures are generally more easily induced than those
Fig. 7. Variation of threshold feedback gain with frequency of feedback oscillation. Vertical axis: threshold gain (Pa/rad). Horizontal axis: frequency (Hz). (Flow conditions as for Fig. 2.)
where the sensing beam location demands a modi®cation of induced structure length. Open loop testing of the system response (e.g. Fig. 2 and [15]) also yielded values of the response sensitivity at the point of dominant spectral response. This was found to lie in the range 0.07±0.08 rad / Pa. Thus we see that for positive feedback to reinforce oscillations so as to overcome dissipative eects or drive the system to an amplitude limit, it is expected that a feedback loop gain of 13.3 Pa / rad would be needed in the feedback system. This result is quite consistent with the minimum observed threshold value of approximately 17 Pa / rad (Fig. 7), bearing in mind that the threshold has been de®ned as the level required to produce a response which is 3 dB below the maximum response level and for which it would be expected that the system would have feedback signi®cantly beyond the marginal limit to just induce a relatively small feedback oscillation. 4. The in¯uence of feedback and excitation on temperature pro®les Centreline temperature pro®les serve as an indication of mixing rate in diusion ¯ames. The temperature of a ¯ame will be related to the rate of energy release from the burning fuel and the degree to which complete combustion takes place. For the ¯ame in question incomplete local combustion is the norm as is indicated by the yellow appearance of the ¯ame. An increase in mixing should therefore result in increased rates of combustion leading to higher temperatures. Centreline temperature pro®les were measured using an Analog Devices lMAC-4000 thermocouple signal conditioner and data acquisition system coupled to an AT compatible personal computer via the RS-232C port. Temperature readings were averaged over 256 independent samples to improve on the variance of the measurements. An aspirated, iso-kinetic, shielded sampling probe was used. The response time of the temperature measurements was therefore much slower than that of
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eddies in the ¯ow, and only an average temperature was recorded. Temperature pro®les were obtained for both feedback and open loop excitation cases to give an indication of the relative performance of each technique. In both cases the natural ¯ow axial temperature pro®les served as a reference condition. Furthermore, because of the presence of two types of coherent structure in the ¯ow, excitation and feedback were applied in such a way as to promote either the inner or outer structure but not both. Comparison of the two modes of excitation / feedback should then give an indication of the relative importance of each structure in the process of mixing. To promote the self excitation of a low frequency structure the feedback ampli®er ®lter settings were set to give a band pass response from 10 to 100 Hz. The loop gain was adjusted to give an appreciable level of feedback excitation close to the level at which lift-o of the ¯ame occurs. The open loop excitation case was based upon the feedback case, and the level of excitation was set to a level comparable to the feedback case and the frequency of excitation was set to the feedback resonant frequency. Fig. 8 shows a comparison of the ®ltered schlieren signal spectra for the feedback and open loop excitation cases. The feedback case shows a strong resonance at 38 Hz with greatest amplitude in the second harmonic. Also there appears to be a degree of resonance in the inner structure which may require consideration when interpreting the temperature pro®le results. Fig. 9(a) and (b) show the corresponding temperature pro®les for the open loop excitation and feedback cases. Crosses correspond to the feedback or open loop excitation temperature pro®les and diamonds correspond to the natural temperature pro®le. The sample points have been ®tted by least squares optimisation using a third order polynomial. From Fig. 9(a) we see that the presence of feedback has lifted the temperature pro®le by about 40°C relative to the natural ¯ow case. This temperature dierence is approximately constant over the position range from
Fig. 8. Power spectral density of the laser schlieren signal (x=D 5:7, feedback ®ltered to 10±100 Hz ®rst order pass band to induce outer ¯ow structures). Solid line: open loop excitation at 38 Hz. Dashed line: closed loop feedback (displaced upwards by two decades for clarity). Horizontal axis: frequency (Hz). Vertical axis: power spectral density, arbitrary datum.
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Fig. 9. Axial distribution of centreline temperatures (conditions as for Fig. 8): (a) x ± with feedback. e ± natural ¯ow; (b) x ± with excitation. e ± natural ¯ow.
13.3D to 33.3D from the exit plane. The presence of schlieren-acoustic feedback thus alters the rate of combustion near the nozzle exit plane which can be seen as a net origin shift of around 3.3D. The improvement in combustion rate near the nozzle exit plane in re¯ected in the downstream temperature pro®le by the temperature increase of 40°C. By comparison the open loop excitation case of Fig. 9(b) demonstrates a temperature improvement of around 60°C over the position range from 10D to 30D from the exit plane. Direct open loop excitation thus shows here a rather greater improvement in mixing over the feedback case for the outer structure, and the improvement is observed in the form of an origin shift brought about by improvements in mixing near the nozzle exit plane. To promote the self excitation of the inner high frequency structure the feedback ampli®er ®lter settings were set to give a band pass response from 300 Hz to 3 kHz. The loop gain was adjusted to give an appreciable level of feedback in this case being limited by loudspeaker saturation rather than ¯ame lift-o. The open loop excitation case was based upon the feedback case in terms of frequency and magnitude as with the low frequency open loop excitation case. Fig. 10 shows a comparison of the ®ltered schlieren signal spectra for the feedback and open loop excitation cases. Both feedback and open loop excitation cases have responses of comparable strength; a feature not observed in the outer structure responses. The feedback case appears to the more coherent (indicated by the reduced level of broad band components) and shows a degree of oscillation in
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Fig. 10. Power spectral density of the laser schlieren signal (x=D 5:7, feedback ®ltered in 300 Hz to 3 kHz ®rst order pass band to induce inner ¯ow structures). Solid line: open loop excitation at 740 Hz. Dashed line: closed loop feedback. Horizontal axis: frequency (Hz). Vertical axis: power spectral density, arbitrary datum.
the outer structure. This is shown by the presence of sidebands in the inner structure response. The open loop excitation case also has outer structure sidebands but at a signi®cantly lower level as in the outer structure itself. The modulation mechanism could be either amplitude modulation or narrow band frequency modulation. To determine which, it is necessary to know the phase relationship between the sidebands. This information cannot be obtained through conventional spectrum analysis (i.e. FFT spectrum analyser) as it only yields the energy content and not absolute phase information. To extract this information would require a more so-
phisticated signal analysis strategy than was available for this investigation. Fig. 11(a) and (b) show the corresponding centreline temperature pro®les for the higher frequency feedback and open loop excitation case. For the feedback case there is an increase in the centreline temperature of around 50°C from 60 to 200 mm from the exit plane whilst open loop excitation only achieves an improvement of around 30°C over a similar position range. It is possible that this dierence in performance is due to the presence of a signi®cant outer structure component in the feedback case. If the outer structure plays the more dominant role (as is suggested by the results) then it is expected that the feedback case should yield a higher temperature change due to the greater strength of the outer structure. To verify this fully would require re-performing this experiment with a more sophisticated ®lter (not available here) to avoid exciting out of band modes. In this case the ®rst order ®ltering of the feedback ampli®er does not have sucient stop band attenuation to avoid exciting the out of band mode. That aside, it is clear that excitation and feedback have a signi®cant eect upon mixing in diusion ¯ames, primarily through the mechanism of the vortex structures formed in the shear layers. The temperature rise of 50°C is possibly all that can be expected from an under-ventilated ¯ow condition (the co-annular air ¯ow mass ¯ow rate is less than that required for a stoichiometric mixture). It appears that excitation and feedback have generally similar eects as regards overall improvement in mixing, the feedback being rather more eective in relation to the higher frequency inner structures in the ¯ame and somewhat less eective in relation to the outer mixing structures. The increased local temperatures can be seen as suggesting a shift of the apparent origin of the ¯ame caused by enhanced mixing relatively near the nozzle. Also it should be noted that only centreline temperatures have been observed here, and that a more comprehensive evaluation of the eect of feedback on mixing would involve transverse temperature surveys as well.
5. Conclusions
Fig. 11. Axial distribution of centreline temperature (conditions as for Fig. 10): (a) x ± with feedback. e ± natural ¯ow; (b) x ± with excitation. e ± natural ¯ow.
Open loop excitation of the turbulent co-annular diffusion ¯ame has shown two dominant modes of response, a small scale, high frequency disturbance at a Strouhal number of 1.9 based on fuel nozzle conditions associated with mixing between fuel and air ¯ows and a larger scale, lower frequency disturbance at a Strouhal number of 0.38 based on outer nozzle conditions associated with mixing between the ¯ame and surroundings. When the acoustic excitation was coupled in feedback to the optical sensing system it was found that a self sustained feedback oscillation could be maintained at a level of feedback gain that was consistent with broad band,
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open loop excitation response testing. As the sensing beam was moved along the nozzle axis so the feedback oscillation frequency varied in a manner that was consistent with the expected convection speed of mixing structures in the ¯ow at the speed of the fuel jet ¯ow. This variation was also consistent with the induced structure having an eective origin 0.125 times the fuel nozzle diameter outside the fuel nozzle exit and also with regular steps in frequency as the system selected an integral number of disturbance cycles between this origin and the sensing beam. This process involved the stretching or compression of the train of induced disturbances to the extent required. There was evidence of hysteresis in the preferred structure generated by the feedback system. Without ®ltering in the feedback system it was found that the inner, high frequency structures dominated the feedback conditions. However, if band pass ®ltering was applied it was found possible to restrict the feedback effect so that either the inner or outer structures were excited. Whilst feedback oscillations could only be obtained with the sensing beam relatively close to the nozzle (up to six fuel nozzle diameters from the nozzle exit plane), the eect of feedback was to increase local ¯ame temperatures in both cases by between 40°C and 60°C at distances up to 40 fuel nozzle diameters. This corresponded to an equivalent movement of the apparent origin of the axial temperature pro®le by approximately 3.5 fuel nozzle diameters. Generally similar increases of local temperature were obtained by direct open loop excitation at a similar frequency and level of response in the ¯ow. However, the un®ltered feedback system was found to lock into the inner, high frequency structure more strongly and when ®ltered the feedback eect was greater than that due to similar open loop excitation when the higher frequency structures were selected by the feedback ®lter. 6. Signi®cance of results and future investigations It has been found that optically derived acoustic feedback will enhance mixing and reaction in a diusion ¯ame using a system where the acoustic disturbance source is located in the upstream plenum chamber of the outer air ¯ow. Future investigations should be directed at producing the feedback disturbance directly adjacent to the shear layer so that the delay time involved is reduced and better conditions for strongly coherent feedback are obtained with the feedback acting more directly on the shear layer. Also, consideration should be given to deriving the feedback from a slab sensing beam [19], which increases sensitivity to large scale structures in the ¯ow at the cost of some increase in optical complexity associated with beam expansion and contraction. The practical signi®cance of this work is to demonstrate the potential for using a relatively simple optical feedback system to increase the rate of mixing in turbulent diusion ¯ames.
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Nomenclature A
voltage sensitivity to angular beam de¯ection, V/ rad D nozzle diameter, m f frequency, Hz n number of wavelengths from nozzle exit R0 outer radius of turbulent region, m T0 acoustic time delay, s Uc turbulent convection speed, m/s x,y,z coordinate directions, m d refractive index of gas k wavelength, m ha angular de¯ection of beam in axial direction, rad
References [1] G.T. Kalghatgi, Blowout stability of gaseous jet diusion ¯ames, pt I: In still air, Combustion Science and Technology 26 (1981) 233±239. [2] G.A. Karim, I. Wierzba, M. Hanna, The blowout limit of a jet diusion ¯ame in a co¯owing stream of lean gaseous fuel-air mixtures, Combustion and Flame 57 (1984) 283±288. [3] A.D. Birch, D.R. Brown, D.K. Cook, G.K. Hargrave, Flame stability in underexpanded natural gas, Combustion Science and Technology 58 (1988) 267±280. [4] L.D. Chen, W.M. Roquemore, Visualisation of jet ¯ames, Combustion and Flame 66 (1986) 81±86. [5] J.P. Dumont, R. Borghi, A qualitative study by laser tomography of the structure of turbulent ¯ames, Combustion Science and Technology 48 (1986) 107±128. [6] E. Gutmark, T.P. Parr, D.M. Parr, K.C. Schadow, Planar imaging of vortex dynamics in ¯ames, Transactions of the ASME series, Journal of Heat Transfer 111 (1989) 148±155. [7] M.G. Mungal, P.S. Karasso, A. Lozano, The visible structure of turbulent jet diusion ¯ames: Large-scale structure and ¯ame tip oscillation, Combustion Science and Technology 76 (1991) 165± 185. [8] E. Gutmark, T.P. Parr, D.M. Hanson-Parr, K.C. Schadow, Simultaneous OH and schlieren visualisation of premixed ¯ames at the lean blow-out limit, Experiments in Fluids 12 (1991) 10±16. [9] M.R. Davis, Determination of turbulent ¯ow properties by a penetrating beam dynamic shadowgraph method, Journal of Physics E 20 (1987) 1271±1277. [10] M.R. Davis, Intensity, scale and convection of turbulent density ¯uctuations, Journal of Fluid Mechanics 70 (3) (1975) 463±479. [11] H. Winarto, M.R. Davis, Fluctuations of density, pressure and temperature in a turbulent mixing region, Proceedings of the Royal Society. Series A 395 (1984) 203±228. [12] M.R. Davis, Coherence between large scale jet mixing structure and its pressure ®eld, Journal of Fluid Mechanics 116 (1982) 31± 57. [13] M.R. Davis, P. Rerkshanandana, The in¯uence of large eddies on thermal mixing, International Journal of Heat and Mass Transfer 34 (7) (1991) 1633±1647. [14] M.R. Davis, P. Rerkshanandana, Schlieren measurement of turbulent structure in a diusion ¯ame, Experimental Thermal and Fluid Science 6 (4) (1993) 402±416. [15] M.R. Davis, P.C. Jumppanen, Optical detection of the response of a diusion ¯ame to excitation, Combustion and Flame 93 (4) (1993) 349±374.
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[16] A.W. Strawa, B.J. Cantwell, Investigation of an excited jet diusion ¯ame at elevated pressure, Journal of Fluid Mechanics 200 (1989) 309±336. [17] S. Zikikout, S. Candel, T. Poinsot, A. Trouve, E. Esposito, High frequency combustion oscillations produced by mode selective acoustic excitation, Proceedings of the 25th Symposium (International) on Combustion, The Combustion Institute, 1986, pp. 1427±1434. [18] Y.C. Chao, M.S. Jeng, J.M. Han, Visualisation and image processing of an acoustically excited jet ¯ow, Experiments in Fluids 12 (1991) 29±40.
[19] M.R. Davis, Phase spectral evidence for vortex structures in turbulent mixing, Journal of Sound and Vibration 116 (2) (1987) 303±321. [20] M.R. Davis, H.L. Li, Structures induced by periodic acoustic excitation of a diusion ¯ame, Combustion and Flame 103 (1995) 151±160.
Optical-acoustic feedback applied to a turbulent diusion ¯ame M.R. Davis *, P.C. Jumppannen Department of Civil and Mechanical Engineering, University of Tasmania, G.P.O Box 252-65, Hobart 7001, Australia Received 13 March 1995; received in revised form 28 October 1996; accepted 12 March 1997
Abstract A laser schlieren sensing system has been coupled to provide feedback acoustic excitation of a co-annular turbulent diusion ¯ame of propane and air. It is found that positive feedback oscillation was induced at a level of feedback gain that was consistent with open loop broad band response measurements. The frequency of feedback induced oscillation was consistent with the disturbances moving at the speed of the ¯ow from the fuel nozzle, and the frequency showed regular cyclical variation as the sensing beam was moved slowly along the nozzle axis. This corresponded to regular physical stretching or compression of the induced structure so that an integral number of disturbances lay between an apparent origin (just outside the nozzle) and the sensing beam. Without ®ltering the feedback system tended predominantly to lock into higher frequency, smaller structures associated with the inner mixing region. However, with appropriate band pass ®ltering in the feedback ampli®er it was possible to induce either inner or outer structures by feedback. Temperature increases of between 40°C and 60°C were induced in the ¯ame centre line temperatures, these increases extending far downstream of the location of the sensing beam. It appeared that feedback moved the apparent origin of the ¯ame towards the nozzle as a consequence of enhanced mixing. Ó 1998 Elsevier Science Inc. All rights reserved. Keywords: Combustion; Turbulence; Feedback; Acoustic; Optical; Flame; Diusion
1. Introduction Gaseous jet diusion ¯ames formed by gas burner nozzles are of necessity operated at only moderate nozzle velocities in order to stabilise the ¯ame and avoid lifto from the nozzle of the combustion zone or extinction of reaction [1±3]. As a consequence the nozzle Reynolds number which is achieved is strongly determined by nozzle size and is often relatively low for small nozzles. This aspect is compounded by the temperature within the ¯ame, which generally increases local viscosity of the ¯ow and tends to lower the local Reynolds number still further. Thus, the region of ¯ow near to a burner nozzle is quite likely to be in¯uenced by relatively strong regular mixing structures between fuel, oxidant and surrounding gases [4±8]. Detection of regular, coherent mixing structures in a turbulent ¯ame is facilitated by the use of optical refractive index based sensing systems which do not rely on the insertion of a probe into the ¯ow. The schlieren or shadowgraph based methods, which respond to ®rst and second derivatives of the unsteady refractive index *
Corresponding author. Tel.: +61 3 6226-2074; fax: +61 3 62234611. 0894-1777/98/$19.00 Ó 1998 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 9 7 ) 1 0 0 2 4 - 3
®eld, are generally the simplest to implement physically [9±11]. Also, the integrating feature of optical beam methods gives an averaged time dependent signal for the whole sensing beam and thereby enhances the contribution of coherent disturbances over turbulent disturbances, the latter tending to average out to a small total eect when integrated along the complete sensing beam [12,13]. In this way an unsteady signal which is strongly indicative of coherent mixing structures is obtained and provides a better means [14,15] of detecting coherent structures than does a point sensing probe, which is dominantly in¯uenced by local turbulence. The eect of acoustic excitation from upstream on a turbulent diusion ¯ame has been shown [16±18] to stimulate the formation of regular vortex mixing structures near the nozzle which subsequently break up as they move downstream. It would appear, therefore, that a sensing system such as the thin penetrating schlieren beam system, which is very sensitive to such large scale structures, would have the potential for providing ampli®cation of mixing if it were coupled in a feedback loop to drive the acoustic excitation. The objective of the investigation described here is to combine acoustic upstream excitation, which has been shown [11,12] to induce regular structures in a diusion
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¯ame, with a feedback driving signal derived from an optical sensing beam in order to modify and strengthen the mixing and reaction process. The optical system selected is the single beam schlieren system [10±12] as this can be implemented very easily with only a low cost laser source and a de¯ection sensitive photo diode, thus obviating the need for any complex optical components or elaborate optical layout. The use of a slab sensing beam [19] may give a greater sensitivity to coherent structures relative to turbulent structures as it introduces spatial integration over the whole cross section of the ¯ow. Such a system does however require the formation of a slab beam and then focusing of this down to a single detector, optical requirements which inevitably complicate the optical sensing arrangements appreciably. For this reason the slab sensing beam has not been investigated in the context of feedback excitation, and the present paper deals only with the very simple laser source/ de¯ection sensing diode arrangement. For convenience this is termed a laser schlieren system, although the advantage of the relatively simple laser source is that it forms a high intensity narrow beam rather than its coherent properties which are not used directly in this application. Whilst the term schlieren is generally applied to a full ®eld optical imaging system, such systems rely on beam de¯ection and so the term has been used elsewhere to include the laser schlieren system in which beam de¯ection is sensed directly by a photodiode. There is, of course, no cut o knife edge used in this present method, system signals being generated by de¯ection of the laser spot which is analogous to the variation of optical intensity in a conventional schlieren caused by ray de¯ection at the knife edge. 2. Open loop response of the combustion and optical system The combustion facility used in this work comprised a vertical nozzle system having a pair of co-annular nozzles with the propane gas ¯ow through the central nozzle and an air ¯ow through the outer nozzle. The ¯ame was stabilised on the annular surface between the nozzles. The performance of this burner system has been described previously [14,15] for experiments in which the ¯ame was subjected to symmetrical acoustic excitation (without feedback) from upstream in the outer (air ¯ow) nozzle settling chamber. Fig. 1 illustrates the nozzle system in detail, the central gas nozzle having a diameter of 6 mm and the outer (air ¯ow) nozzle inner and outer diameters of 10 and 20 mm, respectively. The turbulent diffusion ¯ame formed by this nozzle had a visible height of approximately 300 mm overall depending upon ¯ow conditions, and schlieren images [14,15] show the presence of inner and outer mixing layers near to the nozzle, rapidly merging into a fully turbulent image across the whole ¯ow cross section. A co-annular diusion ¯ame was used here as it presents a much more turbulent structure than can be achieved at laboratory scale with a single jet diusion ¯ame, and is therefore more indicative of what
might be achieved in larger scale burner systems. A single ¯ame condition was used in the present work which corresponded to the maximum fuel and air velocities for which the turbulent ¯ame remained stably attached to the nozzle system. The co-annular diusion ¯ame appears much more turbulent, without such visible regularities and has a much shorter visual length than a single jet diusion ¯ame from the same nozzle. Stoichiometric and similar detail for this burner system has been discussed previously [14]. The burner system was operated approximately 1 m below a large air extractor hood and the coannular ¯ame was not signi®cantly disturbed by minor disturbances in laboratory air. The response of the ¯ame to excitation is detected by means of a penetrating laser beam and a de¯ection sensing photo diode. This sensing system has been described in detail previously [10,11,13±15] and is shown in Fig. 1. A full indication of the experimental uncertainty associated with this system has been given previously [14]. The laser beam is refracted by unsteady temperature or composition gradients in the turbulent mixing zone and the total unsteady angular de¯ection of the beam is sensed by the photo diode and translated into an unsteady output voltage. Mixing and reaction produce a lowering of the refractive index, so that the system essentially responds to the progress of reaction towards completion in the burning mixture. The sensing photo diode detects de¯ections in two perpendicular directions so that sensitivity to axial or transverse gradients of refractive index can be introduced. In the present work only the axial component sensitivity was used so that the unsteady output signal from the optical sensing system can be written as Z R0 od x; y; t E00 t Ah0a t A dy; ox ÿR0 where the integral extends across a complete diameter of a ¯ow, ÿR0 < y < R0 where R0 is some outer limit to the zone of signi®cant mixing and reaction. The constant A includes the photo diode and associated ampli®er displacement sensitivity and the system geometry (in particular distance from ¯ow to sensor). The system is calibrated directly by transversing the photo diode so that the laser beam moves across its sensing face. Measurement of the beam de¯ection by photo-sensors was accurate to better than 0.25 mm or 2 ´ 10ÿ6 rad, and the resolution of the signal analysis system was accurate to approximately 0.1% of the measured signal magnitude and frequency. These accuracies can be translated to the various measurements reported in this paper of spectral density, frequency and cross correlation. Temperatures were measured to within 5°C using a calibrated thermocouple system, whilst probe positioning was to within 1 mm approximately. The open loop sensitivity of the optical detection system has been measured using both broad band and discrete frequency excitation applied through the loudspeaker. The broad band investigation was carried out using pseudo-random binary noise inputs to the loudspeaker [15] and Fig. 2 shows that the system exhib-
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Fig. 1. General arrangement of coaxial nozzle and optical feedback systems.
Fig. 2. Open loop response spectra under pseudo-random binary excitation (identi®ed by minimum mean square response identi®cation methods [15]. (a) x=D 1:3, (b) x=D 4:7, (c) x=D 11:3, (d) x=D 17:3.) Flow conditions: co-axial diusion ¯ame, fuel (propane) speed 2:5 m=s, co-annular air ¯ow speed 2 m=s.
its two dominant modes of response: a low frequency mode at about 100±200 Hz (depending upon position) which gave rise to larger scale regular structures in the outer mixing region with the surrounding ambient air, and a high frequency mode at about 750±800 Hz which produced much smaller scale disturbances in the inner mixing region between the fuel gas and co-¯owing air streams. The occurrence of these preferred modes is attributed to the combined eect of modal acoustic resonances in the nozzle system and the instability of the mixing shear layers. Both outer and inner excited structures were found to convect at close to the exit velocity of the fuel gas nozzle (2.5 m/s), the inner structures being relatively stronger and, as would be expected, decaying more rapidly with axial movement as shown by Fig. 2. The results of Fig. 2 were obtained by a ®ltered minimum mean square signal analysis and identi®cation method [15]. Similar open loop response results to those of Fig. 2 were also obtained by the alternative signal analysis technique of homomorphic deconvolution [15]. More recent investigations carried out using periodic excitation and signal recovery by phase locked averaging [20] have shown that the inner structures are in the form of a series of disturbances centred on the axis of alternating sign spaced at intervals of approximately one inner nozzle radius, whilst the outer structures were again of alternating sign but with embedded inner structures of opposite sign spaced axially at about four inner nozzle diameters (or just over one outer nozzle diameter).
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The eect of open loop excitation from upstream is also illustrated in Fig. 3 which shows the variation with axial position of the cross correlation coecient to two orthogonal sensing beams, both sensing axial density gradients and both passing through the ¯ow axis at the same distance from the nozzle. More detailed and extensive measurements with this cross beam system [10±14] show that very similar indications of turbulent convection velocities are obtained to those using other anemometry techniques. Even without any feedback the eect of upstream excitation is to produce substantial increases in the cross correlation over the ®rst six fuel nozzle diameters from the nozzle exit, with a maximum eect at approximately three nozzle diameters from the nozzle exit. The magnitude of the excitation applied in this case corresponds approximately to a velocity ¯uctuation in the co-¯owing air stream of 0.07 m/s or 3.5% of the average speed of this ¯ow. We were not able to measure the natural, unexcited turbulence level in the mixing ¯ow, but in the light of the substantial information available on turbulence in mixing jets the level would be expected to be about 0.15 (i.e. 0.3 m/s), much larger than that due to acoustic excitation eects here. This is somewhat more than the excitation required to induce a maximum response in the ¯ow (0.02 m/s [15]) and thus represents about the greatest enhancement of ¯ow coherence which might be expected to be achieved by open loop excitation as excitation above the limit of a proportionate range [15] was found to produce an almost constant or saturated levels of response. For proportionate range excitation (i.e. up to 0.02 m/s perturbation of the air stream approximately) it was found that at 5.7 inner nozzle diameters from the nozzle exit plane the overall open loop excitation/ response sensitivity was 0.075 rad/Pa between the excitation pressure at the nozzle exit (observed by a microphone adjacent to the nozzle exit [15]) and the angular de¯ection of the optical schlieren beam. Thus when the feedback from the optical sensor to the ampli®er of the excitation loudspeaker is connected it is expected that self sustaining positive feedback will occur when the gain in the feedback path is sucient to exceed about
Fig. 3. Cross correlation between orthogonal schlieren beams crossing at the nozzle axis (¯ow conditions as for Fig. 2). (Acoustic excitation applied at 76 Hz from upstream in the air ¯ow nozzle, velocity ¯uctuation induced 0:07 m=s at nozzle exit.)
13.3 Pa/rad of exit plane pressure per unit angular de¯ection of the optical schlieren beam. It should be noted that whilst there is virtually no signi®cant delay or phase change between the optical beam and the output from the ampli®er driving the loudspeaker (Fig. 1), the geometry of the nozzle system and settling chambers will impose some phase changes of the output pressure ¯uctuation at the nozzle exit with respect to the loudspeaker input signal. However, this eect is relatively small corresponding to loudspeaker phase shift and acoustic transport delay through the nozzle settling chamber of approximately 0.001 s compared with convection delays associated with the ¯ow of about 0.02 s (at about eight fuel nozzle diameters from the nozzle exit, which varies depending on location downstream of the nozzle). The combined eect of delays or phase lags due to loudspeaker, nozzle and ¯ow convection effects is thus expected to be dominated by the ¯ow convection delay time and this should have a signi®cant in¯uence on the closed loop, positive feedback system as will be seen in the following section. 3. System characteristics with optically derived excitation feedback With the feedback connected as shown in Fig. 1 from a single schlieren sensing beam passing through the ¯ow axis, essentially two parameters can be controlled, these being the axial location of the sensing beam (i.e. its distance x from the nozzle exit) and the overall gain applied to the feedback signal as it drives the loudspeaker. The eect of the gain in the feedback loop is illustrated in Fig. 4, which shows the power spectral density of the schlieren optical signal for a set of values of the feedback gain varying from zero (i.e. no feedback) to the maximum gain level which was the level for which the spectral response peak reached its maximum (i.e. saturated) value. It must be recognised that the de®nition of reaching a maximum saturated value is subject to some uncertainty, although this condition was visually observed without diculty and thus the spectral levels indicated in Fig. 4 are subject to this de®nition and in an exact sense should be treated as relative levels. It can be seen that the rather broader schlieren optical signal spectrum with no feedback becomes progressively dominated by a very strong discrete component at approximately 800 Hz as the feedback gain is increased. Also it is quite evident that the magnitude of the peak spectral density rises quite sharply over a relatively small range of gains. This is more clearly indicated in Fig. 5, where an increase of 4 dB in feedback gain increases the level of the spectral peak by approximately 16 dB. It is evident that once the gain is increased beyond a particular critical value the net feedback becomes positive and the system goes into strong discrete oscillation. Measurement or de®nition of a minimum threshold for the onset of this discrete feedback oscillation is obviously dicult, and therefore a nominal threshold has been
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Fig. 5. Variation of peak spectral density of schlieren signal with feedback gain. Vertical axis: peak/spectral density of schlieren signal relative to maximum (saturation) value. Horizontal axis: feedback gain relative to gain required to produce saturated response. (Dashed lines indicate nominal threshold gain to produce response 3 dB below saturated value.)
Fig. 4. Power spectral density of sensing schlieren beam signal for different levels of feedback gain (¯ow conditions as for Fig. 3, schlieren beam across centre line at x=D 5:7). Vertical axis: spectral density, middle and upper spectra displaced upwards by one decade for clarity (arbitrary units): (a) Solid line: no feedback. Dotted line: (maximum gain ÿ20) dB. Dashed line: maximum gain; (b) Solid line: (maximum gain ÿ6) dB. Dotted line: (maximum gain ÿ4) dB. Dashed line: (maximum gain ÿ2) dB.
selected for which the optical spectral peak has a level 3 dB below its maximum as shown in Fig. 5. If the schlieren beam location is moved in the axial direction whilst maintaining the feedback sensing beam through the nozzle axis it is found that both the magnitude of the threshold gain and the frequency of the resonant spectral peak are altered. Fig. 6 shows the regular pattern of variation of frequency which was observed. The regular, progressive and cyclical reductions in frequency which occur, separated by sharp rises in frequency at distinct axial locations, show that as the convection time from nozzle to beam is increased so the period of the feedback oscillation also increases with a corresponding increase of interval between successive disturbances. This regular stretching of the induced structure as the sensing beam is moved downstream is broken at intervals where a complete additional cycle of the structure is preferentially ®tted in between the nozzle and sensing beam at a shorter cycle length and higher
frequency. There is evidence of overlap or hysteresis in the sudden transition that occurs as the feedback system responds to conditions where a longer or shorter wavelength train of disturbances produces the stronger preferred feedback. The introduction of the feedback path has thus modi®ed the overall system eigenvalues. The results of Fig. 6 can be used to determine the apparent convection speed (Uc ) of the moving structure, the number (n) of wavelengths (k Uc / f, where f observed frequency) between the sensing beam and the nozzle and the feedback loop / acoustic time delay (T0 ) on the presumption that the wavelength and convection speed do not vary with x:
Fig. 6. Variation of frequency of feedback oscillation with distance between nozzle exit plane and sensing beam. (Sensing beam through nozzle axis, ¯ow conditions as for Fig. 2.)
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Period T0 x=Uc T0 nk=Uc m=f ; where m is an integer. The parameter n need not be an integer if the eective origin of the induced structure is not exactly at the nozzle exit. Fitting lines to the data of Fig. 6 and using selected points on these it is thus possible to solve for T0 , Uc and n. This yields values of T0 0.0047 s for the feedback / acoustic delay, Uc 2.64 m/s for the convection speed of the induced disturbances and n 4.24 for the number of cycles between the x 4.7D position and the nozzle. The convection speed conforms closely with the velocity of the fuel jet (2.5 m/s) and also with cross beam correlation measurements of convection speed in the unexcited ¯ame. Whilst the observations of feedback oscillation extended only over the range 1.7 < x / D < 5.7 for the sensing optical beam, the calculated value of n 4.24 suggests that the eective origin of the excited structure is centred around a position x / D 0.125, so that four complete cycles then extend to the x / D 4.7 position with both these positions representing a condition where the sensing beam is neither stretching or compressing the induced structure, but rather inducing an average wavelength structure by feedback. The apparent origin of the induced system at x / D 0.125 is consistent with there being a ®nite minimum distance from the nozzle at which the induced ¯ow structure can physically be formed, this position being quite small at about one-eighth of the wavelength of the structure from the nozzle exit as might be expected. Also, as would be expected, the average frequency of the induced structures of 800 Hz corresponds closely with the maximum open loop response associated with the inner structures in the ¯ame (Fig. 2), and we see that the range of axial location over which feedback oscillation occurred (x / D < 5.7) corresponds to general to the region for which the open loop response tests showed signi®cant inner structure response at the higher frequency of this nozzle system (f 800 Hz, Strouhal number fD / Uc 1.9). The induced structures are thus seen to have a wavelength of 1.14 times the fuel nozzle diameter, to convect at the speed of the fuel jet and to commence at 0.125 times the fuel jet diameter from its exit. The stretching or compressing and consequent frequency changes of the induced structures is consistent with their being locked in by the sensing beam at its position and at a frequency determined by their convective motion. Some variations in the nominal threshold gain required to induce feedback oscillation as described above were observed as the sensing beam was moved axially as shown in Fig. 7. For most conditions a threshold gain of about 20 Pa/rad was found, but in some cases of high or low frequency oscillation where the induced structure was being compressed or stretched from its average length, signi®cantly higher threshold gains in the range up to 66 Pa/rad were required to induced feedback oscillation. This appears consistent with the notion that the average wavelength structures are generally more easily induced than those
Fig. 7. Variation of threshold feedback gain with frequency of feedback oscillation. Vertical axis: threshold gain (Pa/rad). Horizontal axis: frequency (Hz). (Flow conditions as for Fig. 2.)
where the sensing beam location demands a modi®cation of induced structure length. Open loop testing of the system response (e.g. Fig. 2 and [15]) also yielded values of the response sensitivity at the point of dominant spectral response. This was found to lie in the range 0.07±0.08 rad / Pa. Thus we see that for positive feedback to reinforce oscillations so as to overcome dissipative eects or drive the system to an amplitude limit, it is expected that a feedback loop gain of 13.3 Pa / rad would be needed in the feedback system. This result is quite consistent with the minimum observed threshold value of approximately 17 Pa / rad (Fig. 7), bearing in mind that the threshold has been de®ned as the level required to produce a response which is 3 dB below the maximum response level and for which it would be expected that the system would have feedback signi®cantly beyond the marginal limit to just induce a relatively small feedback oscillation. 4. The in¯uence of feedback and excitation on temperature pro®les Centreline temperature pro®les serve as an indication of mixing rate in diusion ¯ames. The temperature of a ¯ame will be related to the rate of energy release from the burning fuel and the degree to which complete combustion takes place. For the ¯ame in question incomplete local combustion is the norm as is indicated by the yellow appearance of the ¯ame. An increase in mixing should therefore result in increased rates of combustion leading to higher temperatures. Centreline temperature pro®les were measured using an Analog Devices lMAC-4000 thermocouple signal conditioner and data acquisition system coupled to an AT compatible personal computer via the RS-232C port. Temperature readings were averaged over 256 independent samples to improve on the variance of the measurements. An aspirated, iso-kinetic, shielded sampling probe was used. The response time of the temperature measurements was therefore much slower than that of
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eddies in the ¯ow, and only an average temperature was recorded. Temperature pro®les were obtained for both feedback and open loop excitation cases to give an indication of the relative performance of each technique. In both cases the natural ¯ow axial temperature pro®les served as a reference condition. Furthermore, because of the presence of two types of coherent structure in the ¯ow, excitation and feedback were applied in such a way as to promote either the inner or outer structure but not both. Comparison of the two modes of excitation / feedback should then give an indication of the relative importance of each structure in the process of mixing. To promote the self excitation of a low frequency structure the feedback ampli®er ®lter settings were set to give a band pass response from 10 to 100 Hz. The loop gain was adjusted to give an appreciable level of feedback excitation close to the level at which lift-o of the ¯ame occurs. The open loop excitation case was based upon the feedback case, and the level of excitation was set to a level comparable to the feedback case and the frequency of excitation was set to the feedback resonant frequency. Fig. 8 shows a comparison of the ®ltered schlieren signal spectra for the feedback and open loop excitation cases. The feedback case shows a strong resonance at 38 Hz with greatest amplitude in the second harmonic. Also there appears to be a degree of resonance in the inner structure which may require consideration when interpreting the temperature pro®le results. Fig. 9(a) and (b) show the corresponding temperature pro®les for the open loop excitation and feedback cases. Crosses correspond to the feedback or open loop excitation temperature pro®les and diamonds correspond to the natural temperature pro®le. The sample points have been ®tted by least squares optimisation using a third order polynomial. From Fig. 9(a) we see that the presence of feedback has lifted the temperature pro®le by about 40°C relative to the natural ¯ow case. This temperature dierence is approximately constant over the position range from
Fig. 8. Power spectral density of the laser schlieren signal (x=D 5:7, feedback ®ltered to 10±100 Hz ®rst order pass band to induce outer ¯ow structures). Solid line: open loop excitation at 38 Hz. Dashed line: closed loop feedback (displaced upwards by two decades for clarity). Horizontal axis: frequency (Hz). Vertical axis: power spectral density, arbitrary datum.
243
Fig. 9. Axial distribution of centreline temperatures (conditions as for Fig. 8): (a) x ± with feedback. e ± natural ¯ow; (b) x ± with excitation. e ± natural ¯ow.
13.3D to 33.3D from the exit plane. The presence of schlieren-acoustic feedback thus alters the rate of combustion near the nozzle exit plane which can be seen as a net origin shift of around 3.3D. The improvement in combustion rate near the nozzle exit plane in re¯ected in the downstream temperature pro®le by the temperature increase of 40°C. By comparison the open loop excitation case of Fig. 9(b) demonstrates a temperature improvement of around 60°C over the position range from 10D to 30D from the exit plane. Direct open loop excitation thus shows here a rather greater improvement in mixing over the feedback case for the outer structure, and the improvement is observed in the form of an origin shift brought about by improvements in mixing near the nozzle exit plane. To promote the self excitation of the inner high frequency structure the feedback ampli®er ®lter settings were set to give a band pass response from 300 Hz to 3 kHz. The loop gain was adjusted to give an appreciable level of feedback in this case being limited by loudspeaker saturation rather than ¯ame lift-o. The open loop excitation case was based upon the feedback case in terms of frequency and magnitude as with the low frequency open loop excitation case. Fig. 10 shows a comparison of the ®ltered schlieren signal spectra for the feedback and open loop excitation cases. Both feedback and open loop excitation cases have responses of comparable strength; a feature not observed in the outer structure responses. The feedback case appears to the more coherent (indicated by the reduced level of broad band components) and shows a degree of oscillation in
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Fig. 10. Power spectral density of the laser schlieren signal (x=D 5:7, feedback ®ltered in 300 Hz to 3 kHz ®rst order pass band to induce inner ¯ow structures). Solid line: open loop excitation at 740 Hz. Dashed line: closed loop feedback. Horizontal axis: frequency (Hz). Vertical axis: power spectral density, arbitrary datum.
the outer structure. This is shown by the presence of sidebands in the inner structure response. The open loop excitation case also has outer structure sidebands but at a signi®cantly lower level as in the outer structure itself. The modulation mechanism could be either amplitude modulation or narrow band frequency modulation. To determine which, it is necessary to know the phase relationship between the sidebands. This information cannot be obtained through conventional spectrum analysis (i.e. FFT spectrum analyser) as it only yields the energy content and not absolute phase information. To extract this information would require a more so-
phisticated signal analysis strategy than was available for this investigation. Fig. 11(a) and (b) show the corresponding centreline temperature pro®les for the higher frequency feedback and open loop excitation case. For the feedback case there is an increase in the centreline temperature of around 50°C from 60 to 200 mm from the exit plane whilst open loop excitation only achieves an improvement of around 30°C over a similar position range. It is possible that this dierence in performance is due to the presence of a signi®cant outer structure component in the feedback case. If the outer structure plays the more dominant role (as is suggested by the results) then it is expected that the feedback case should yield a higher temperature change due to the greater strength of the outer structure. To verify this fully would require re-performing this experiment with a more sophisticated ®lter (not available here) to avoid exciting out of band modes. In this case the ®rst order ®ltering of the feedback ampli®er does not have sucient stop band attenuation to avoid exciting the out of band mode. That aside, it is clear that excitation and feedback have a signi®cant eect upon mixing in diusion ¯ames, primarily through the mechanism of the vortex structures formed in the shear layers. The temperature rise of 50°C is possibly all that can be expected from an under-ventilated ¯ow condition (the co-annular air ¯ow mass ¯ow rate is less than that required for a stoichiometric mixture). It appears that excitation and feedback have generally similar eects as regards overall improvement in mixing, the feedback being rather more eective in relation to the higher frequency inner structures in the ¯ame and somewhat less eective in relation to the outer mixing structures. The increased local temperatures can be seen as suggesting a shift of the apparent origin of the ¯ame caused by enhanced mixing relatively near the nozzle. Also it should be noted that only centreline temperatures have been observed here, and that a more comprehensive evaluation of the eect of feedback on mixing would involve transverse temperature surveys as well.
5. Conclusions
Fig. 11. Axial distribution of centreline temperature (conditions as for Fig. 10): (a) x ± with feedback. e ± natural ¯ow; (b) x ± with excitation. e ± natural ¯ow.
Open loop excitation of the turbulent co-annular diffusion ¯ame has shown two dominant modes of response, a small scale, high frequency disturbance at a Strouhal number of 1.9 based on fuel nozzle conditions associated with mixing between fuel and air ¯ows and a larger scale, lower frequency disturbance at a Strouhal number of 0.38 based on outer nozzle conditions associated with mixing between the ¯ame and surroundings. When the acoustic excitation was coupled in feedback to the optical sensing system it was found that a self sustained feedback oscillation could be maintained at a level of feedback gain that was consistent with broad band,
M.R. Davis, P.C. Jumppannen / Experimental Thermal and Fluid Science 16 (1998) 237±246
open loop excitation response testing. As the sensing beam was moved along the nozzle axis so the feedback oscillation frequency varied in a manner that was consistent with the expected convection speed of mixing structures in the ¯ow at the speed of the fuel jet ¯ow. This variation was also consistent with the induced structure having an eective origin 0.125 times the fuel nozzle diameter outside the fuel nozzle exit and also with regular steps in frequency as the system selected an integral number of disturbance cycles between this origin and the sensing beam. This process involved the stretching or compression of the train of induced disturbances to the extent required. There was evidence of hysteresis in the preferred structure generated by the feedback system. Without ®ltering in the feedback system it was found that the inner, high frequency structures dominated the feedback conditions. However, if band pass ®ltering was applied it was found possible to restrict the feedback effect so that either the inner or outer structures were excited. Whilst feedback oscillations could only be obtained with the sensing beam relatively close to the nozzle (up to six fuel nozzle diameters from the nozzle exit plane), the eect of feedback was to increase local ¯ame temperatures in both cases by between 40°C and 60°C at distances up to 40 fuel nozzle diameters. This corresponded to an equivalent movement of the apparent origin of the axial temperature pro®le by approximately 3.5 fuel nozzle diameters. Generally similar increases of local temperature were obtained by direct open loop excitation at a similar frequency and level of response in the ¯ow. However, the un®ltered feedback system was found to lock into the inner, high frequency structure more strongly and when ®ltered the feedback eect was greater than that due to similar open loop excitation when the higher frequency structures were selected by the feedback ®lter. 6. Signi®cance of results and future investigations It has been found that optically derived acoustic feedback will enhance mixing and reaction in a diusion ¯ame using a system where the acoustic disturbance source is located in the upstream plenum chamber of the outer air ¯ow. Future investigations should be directed at producing the feedback disturbance directly adjacent to the shear layer so that the delay time involved is reduced and better conditions for strongly coherent feedback are obtained with the feedback acting more directly on the shear layer. Also, consideration should be given to deriving the feedback from a slab sensing beam [19], which increases sensitivity to large scale structures in the ¯ow at the cost of some increase in optical complexity associated with beam expansion and contraction. The practical signi®cance of this work is to demonstrate the potential for using a relatively simple optical feedback system to increase the rate of mixing in turbulent diusion ¯ames.
245
Nomenclature A
voltage sensitivity to angular beam de¯ection, V/ rad D nozzle diameter, m f frequency, Hz n number of wavelengths from nozzle exit R0 outer radius of turbulent region, m T0 acoustic time delay, s Uc turbulent convection speed, m/s x,y,z coordinate directions, m d refractive index of gas k wavelength, m ha angular de¯ection of beam in axial direction, rad
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