THE ACOUSTIC RESPONSE OF BURNER-STABILIZED PREMIXED FLAT FLAMES

Transcription

1 Proceedings of the Combstion Institte, Volme 29, 2002/pp THE ACOUSTIC RESPONSE OF BURNER-STABILIZED PREMIXED FLAT FLAMES K. R. A. M. SCHREEL, R. ROOK and L. P. H. DE GOEY Eindhoven University of Technology Faclty of Mechanical Engineering Section of Combstion Technology P.O. Box MB Eindhoven, The Netherlands The behavior of acostically driven flat flames has been analyzed experimentally. In this stdy, pressre transdcers and laser Doppler velocimetry are sed to characterize the acostical waves pstream and downstream of a flat flame stabilized on a flame holder. Two different flame holders have been sed, a perforated brass plate and a ceramic foam, exhibiting very different srface temperatres. From these experiments, the acostical transfer fnction can be derived. This transfer fnction shows a resonance-like behavior, of which the shape and peak freqency is governed mainly by the srface temperatre of the brner and the velocity of the nbrned mixtre. The brass brner exhibits a resonance freqency arond 140 Hz, where the resonance of the ceramic brner seems to have shifted to mch higher freqencies and is mch more damped. All reslts can be nderstood very well with an analytical model in terms of Zeldovich nmber, standoff distance, and heat condctivity. Apart from the analytical model for the brass flame holder, nmerical simlations with detailed chemistry have also been performed. Again, the correspondence is good. The most interesting application is the acostic behavior of central heating systems, in which these brners are freqently sed. For the prpose of modeling the acostical behavior of complete boiler systems, the analytical model can be sed with minor jstments to the Zeldovich nmber and heat condctivity, yielding a fairly accrate semiempirical model describing the transfer fnction. Introdction Since the introdction of low-no x premixed brners with a large modlation range, severe noise problems hamper frther developments of modlating domestic heating boilers. In recent years, a fndamental change has occrred in boiler design. In the past, the brner operated only at one or a few discrete thermal los. Noise problems cold be solved by trial and error methods. Crrent developments, however, se designs where the brner lo is allowed to vary continosly. The major drawback of this approach is that many different acostic instabilities are now triggered, and phenomena like high whistling noises and low vibrational excitations of the complete system occr. To analyze these instabilities, the whole system mst be considered. A way to do this is by sing the transfer matrix method [1], in which every acostic element is characterized by a (freqency-dependent) transfer matrix which coples the acostic fields on both sides of the element. At relatively low freqencies (1000 Hz), the acostic field in a boiler system can be described as a planar wave of flctations in pressre (p) and velocity (): ū p p p (1) The average vales of the velocity and pressre are denoted by ū and p, respectively. For a brner-stabilized flat flame, it can be shown [2] that the transfer matrix has (in the approximation that the Mach nmber Ma r 0) the following form: p b 1 0 p (2) 0 T b 22 which means that the complete transfer matrix is determined by T 22, the copling between the velocity flctations pstream () and downstream () b of the flame. Since the acostical properties of flat brner-stabilized flames are important for practical applications, the availability of an (analytical) model describing the transfer fnction is needed. On the sbject of acostics and combstion, extensive theoretical and experimental stdies have been performed; for an overview, see the paper by Ran [3]. Work on the forced oscillation of dct-confined free flames has been done by Fleifil et al. [4], while Searby [5] worked on spontaneos oscillations of dct-confined free flames. Dowling [6] also stdied self-excitation, bt of a dct-confined trblent flame. Matsi [7] worked on the forced oscillation of arrays of Bnsen flames, and Dcrix et al. [8] stdied the forced oscillation of a single Bnsen flame. The sbject of this paper, forced oscillation of brner-stabilized flames, was covered by McIntosh 115

2 116 COMBUSTION DYNAMICS AND CONTROL Fig. 1. Schematic graph showing the enthalpy ( J), temperatre (T ), and fel mass fraction (Y ) in the vicinity of the flame holder (at x 0) and flame front (at x x f ). Changes in flame standoff distance reslt in enthalpy waves. and coworkers dring several years time. This reslted in a rather complex bt mathematically rigoros analytical model [9,10]. The basis of their analysis is formed by a one-step chemistry description of the combstion and an ideal flame holder, that is, a flame holder with an infinite heat transfer coefficient and an infinite heat capacity. Conseqently, the flame holder has the same temperatre as the pstream nbrned gases. Their reslts were obtained via large activation energy asymptotics, copling the different acostic zones, and show good correspondence with experiments obtained in a Rijke tbe brner. Recently, Rook and De Goey derived an alternative analyical model [11,12], which is also based on one-step chemistry and the infinite heat transfer assmption, bt allows for the flame holder having a higher temperatre than the gas pstream of the flame holder. Their analysis is based on the decopling of the nstey conservation eqations into the G-eqation, describing the motion of the flame, and a flamelet system, describing the inner strctre and the mass brning rate. Additionally, it is assmed that the Lewis nmber is nity, which is of minor importance as long as methane/air flames are considered. Recent experimental work has been performed by Chen and Chen [13,14], bt their focs was on the mittance of the brner and not on the transfer coefficient. Also, no direct comparison was me with a model. As an intitive model for the interaction between the flame and the acostic waves, consider Fig. 1. Following the G-eqation description, a variation in the standoff distance of the flame (indced by the acostic velocity flctations) reslts in a displacement of the complete flame strctre, except for the temperatre. The temperatre remains fixed at the flame holder. De to a varying fel concentration at the flame holder, the enthalpy varies with it. Ths, an oscillating flame position reslts in enthalpy waves traveling toward the flame front. When this wave has the right phase relationship with respect to the motion of the flame front, amplification or damping of the flame front motion can occr. Some kind of resonance behavior is then expected for certain freqencies. As an estimation for the lowest mode, consider the pstream flow velocity (on the order of 10 cm/s) and the standoff distance (on the order of 1 mm), yielding 100 Hz as an order-of-magnitde estimate for the position of the resonance. From this intitive pictre, it can be seen that one of the most important parameters is the srface temperatre of the flame holder, since this determines the standoff distance to a great extent. Higher harmonics are not expected, since high-freqency enthalpy waves damp qickly de to diffsion. In this paper, an experimental characterization of the T 22 element of the transfer matrix is presented for a brner-stabilized flat flame in a tbe with fixed diameter. The diameter of the tbe is chosen to be mch smaller than the acostical wavelengths of interest, and a one-dimensional description of the acostics is valid. Two brner types are sed: a perforated brass plate, closely resembling the ideally cooled brner as assmed in the model by McIntosh, and a ceramic foam plate, which has a significantly higher srface temperatre. The reslts are compared to nmerical calclations obtained with a model derived previosly by Rook et al. [2,16], with the analytical model derived by McIntosh and Rylands [10], and with the simple analytical model derived previosly by Rook et al. [11,12]. Experiment The measrement of the transfer matrix element copling the acostic velocities before and after the flame-brner combination involves the time-correlated measrement of the velocity pstream and downstream of the flame. An established way of determining pressre waves inside a tbe is by means of mltiple pressre transdcers fitted in the wall of the tbe [1,15]. If the medim in the tbe has constant properties (density and temperatre), two microphones sffice to characterize the waves traveling in both directions. From the pressre wave and the properties of the medim and the tbe, the velocity wave can be reconstrcted. The pstream region of the flame does have the desired constant density and temperatre, bt the downstream region does not, becase the hot gas cools down rapidly. Therefore, we have chosen to se the two-microphone method in the pstream region, bt a direct measrement of the velocity in the downstream region by means of laser Doppler velocimetry (LDV). A difficlty that arises when sing

3 ACOUSTIC RESPONSE OF FLAT FLAMES 117 Fig. 2. Sketch of the brner he showing one pressre transdcer, the laser beams of the laser Doppler velocimeter, and the flame holder. The flame holder and the pper part of the tbe are (thermostatically) cooled. The total length of the tbe below the flame holder is approximately 45 cm. LDV to measre a repetitive signal is that, de to the very natre of the measrement techniqe, the signal obtained by LDV is a random sample of the flctations. This means that a Forier transform cannot be sed in a straightforward way. This was solved by monitoring the otpt of the conterprocessor (Disa 55L series) in real time together with the reference signal. When a valid LDV measrement occrs, the velocity is registered together with several sample points of the reference wave. From sch a recording, the phase of the reference wave can be calclated at the time of the LDV measrement. When a large nmber of sch measrements are assembled, a data set is obtained which can be analyzed by fitting a cosine together with some higher harmonics to the data set. This is eqivalent to a Forier transform, provided that the velocity flctations contain only those signals which the fit takes into accont pls some random noise. The brner essentially consists of a 50 cm long tbe with a diameter of 5 cm (Fig. 2). The bottom is closed with a flange, in which a small hole serves as entrance for the premixed CH 4 /air mixtre. Some grids are fitted right after the entrance to settle the flow. In the lower part of the tbe, a hole is me in the side and copled with a flexible hose to a lodspeaker. The top is an open end, to allow the exhast gas to escape. The open end acts nearly as a perfect reflector with, in first the order, a velocity antinode at the opening. A small portion of the acostic energy, however, is riated ot, and a small transfer region exists in which the velocity flctations decrease strongly from the vales associated with the wave inside the tbe to the vales otside the tbe. The length of this region is approximately eqal to the ris of the tbe. The brner plate is placed approximately 7 cm below the exit, at sfficient distance from the transition zone. The part of the tbe downstream of the flame holder and the flame holder itself are water cooled at nominally 50 C to avoid condensation of water. The acostical properties of the tbe itself have been stdied, and it was fond that when the tbe is excited by broband noise, while some freqencies are copled in more effectively than others, no clear resonace shows p. Since measrements are only performed at a single freqency, this can be compensated for by an jstment of the amplifier gain. The absence of any inflence of the tbe characteristics on the transfer coefficient is spported by a mearement of the transfer coefficient withot flame, which (within the experimental error) yields nity for all freqencies sed. Two materials are sed for the flame holder. The first is a perforated plate me of brass with a thickness of 2 mm. The perforation pattern is hexagonal, with a hole diameter of 0.5 mm and a pitch of 0.7 mm. The hole size is small enogh that a flat methane/air flame stabilizes on top of it. The other is me of a ceramic foam, with a porosity of 90% and an average pore size of 45 pores/in. The ceramic foam is sed in commercial applications. To allow for the se of the two-microphone method, two pressre transdcers are monted on the wall of the tbe. Optical access to the downstream region of the flame is somewhat difficlt, since the flame holder is placed 7 cm before the open end. Three small holes have been me in the downstream part of the brner. Their size is small enogh not to inflence the acostical wave in the tbe. Two holes serve as an entrance for the two LDV laser beams, and throgh the third hole the scattered laser light is detected. In this way, the velocity is measred in the middle of the tbe at 4 mm above the flame holder. In principle, one does not measre the transfer matrix element of the flame in this way, bt the transfer matrix element of the flame combined with the flame holder. Test measrements showed, however, that the transfer matrix element of the flame holder itself is very close to nity for all materials at the freqencies of interest and can be neglected. The inflence of the srface temperatre of the brner, however, cannot be neglected. Since the flame is brner stabilized, some heat loss will occr via the flame holder. For the perforated brass brner, the temperatre is mainly determined by the temperatre at the edge. Heat loss from the flame to the brner is condcted away via the flame holder. This also means that the temperatre in the middle of the flame holder will be somewhat larger than at the edge. To calclate this rial dependence of the temperatre (T(r)), consider the eqation describing the heat

4 118 COMBUSTION DYNAMICS AND CONTROL Fig. 3. The freqency dependence of the transmission coefficient for the brass flame holder and ū 14 cm/s and 0.8. Clearly, a resonance can be identified, which is well predicted by the nmerical simlation. flow throgh the flame holder in cylindrical coordinates, 1 rkd T qc p(t T b) (3) r r r in which d is the thickness of the flame holder, k the effective heat condctivity of the flame holder in the rial direction, q the density, the flow velocity of the flame of interest, c p the (mixtre-averaged) heat capacity, and T and T b the temperatres of an iabatic flame and the flame of interest, respectively. The temperatre T b can be derived from the wellknown empirical relation between the brning velocity and the flame temperatre sing data of an iabatic flame [17], E K exp a (4) 2RT b with E a the effective activation energy. When temperatre variations perpendiclar to the flame holder are neglected and a perfect cylindrical symmetry is assmed, a soltion to eqation 3 can be written as 2 2 Q T(r) T(R) (R r ) (5) 4kd This soltion is based on the bondary condition that the temperatre at the edge (r R) of the flame holder (T(R)) is fixed and known. For or perforated brass brner, it trns ot that T(0) T(R) is approximately 40 K higher than at the edge. The nonniform temperatre distribtion across the flame holder reqires, in principle, a two-dimensional treatment, bt since the downstream velocity is measred very close to the flame holder, we will assme a srface temperatre (T srf ) eqal to the temperatre directly below the measrement point, that is, T srf T(0). For the ceramic brner, another mechanism comes into play for accommodating the heat loss from the flame to the brner. Since the condction coefficient of the ceramic material is very low, the heat can only be riated away. A reasonable estimate of the srface temperatre can be obtained by eqating the heat loss of the the flame to the brner (right-hand side of eqation 3) to the heat loss of the 4 4 srf srr brner via riation (er(t T )). When sing eqation 4 to calclate T b, this yields for the srface temperatre [18] qc p T T 4 T 4 srf srr er 2RT ln s L (6) 2RT ln E with e the emissivity of the flame holder, r the Stefan-Boltzmann constant, and T srr the temperatre of the srrondings. s L Analytical Models The experimental reslts are compared to two analytical models. McIntosh et al. [10] derived a model based on an exact asymptotic soltion of the governing eqations with one-step chemistry. When inserting the condition that Le 1, the following expression can be derived for the transfer coefficient [19]: b 1 Tb 1 2 T T r exp rx 1,f T 2 2 b w r exp(2rx 1,f) h(1 T /T b) 1 where r w (7) 4 In this eqation, x 1,f is the mass-weighted standoff distance or iabaticity, a

5 ACOUSTIC RESPONSE OF FLAT FLAMES 119 T T x ln (8) T T 1,f with T the temperatre of the nbrned gases. The dimensionless complex freqency w and the dimensionless activation energy h are given by k E a w ix, h (9) 2 ū qc RT p b b When deriving this model, it was assmed that T srf is eqal to T, bt this does not reflect the experimental conditions. At first glance, the model cold easily be jsted by stating T T srf, bt a closer examination les to the conclsion that in fact a complete workover of the model wold be reqired. We choose not to jst this model, and this needs to be kept in mind when comparing the experimental reslts to the models. The analytical model derived by Rook et al. [11] is based on a G-eqation description, yielding for the transfer coefficient b Tsrf Tb Tsrf A( ˆx) T T with T T T exp(w) 1 1 A( ˆx) (1 1 4 ˆx) (10) 2 ˆx MN A( ˆx) MN ˆx Ze 1 M 2 T T N (T b T ) exp(w) W exp (1 1 4 ˆx) 2 The freqency ˆx is defined as ˆx wt /T srf. The dimensionless standoff distance W is given by T T W ln (11) T Tb Tsrf T and is eqal to the iabaticity for T srf T. The Zeldovich nmber (Ze) arises from the assmption that the ratio of the mass brning rate flctations (m) and temperatre flctations (T) is eqal to m/t Ze. This is tre for small and slow flctations, bt will break down for high amplitdes and freqencies. A vale of Ze 13 is sed, derived from nmerical simlations for 0.8. Another ncertain vale is that of the heat condctivity. An approximate vale of W/K m for a pre methane/air mixtre is reasonable, bt the actal vale might differ, de to diffsion and thermal inflences. Fig. 4. The dependence of the transmission coefficient on the freqency for three different temperatres of the flame holder. The conditions are ū 14 cm/s and 0.8. Reslts In Fig. 3, the freqency dependence of the transmission coefficient is plotted for the perforated brass flame holder with 0.8 and ū 14 cm/s. One can clearly see the resonance at abot 150 Hz. For low freqencies, the absolte vale of the transmission coefficient tends to a vale arond 7, which corresponds to the stationary limit, where ū b (T b /T )ū. For higher freqencies, the transmission coefficient drops to vales arond 1. The correspondence to the simlation is good. Both the phase and the absolte vale of the transmission coefficient are qantitatively close to the measred vales. This reslt means that for low freqencies, a flat flame is inherently nstable with regard to acostical problems. When monted in a system, the damping of low freqencies needs special attention. The position of the resonance is mainly governed by the standoff distance of the flame. A straightforward way to vary the standoff distance is by varying the temperatre of the flame holder. Two temperatre settings were achieved by varying the temperatre of the cooling water which flows throgh the ring arond the brass flame holder. Another (high) temperatre is obtained by sing the ceramic foam. In Fig. 4, the reslts are plotted. Even for the relatively small temperatre difference of 40 K, a significant shift of the resonance freqency is noticed. For the temperatre of T srf 878 K, the resonance seems to be absent, bt can be regarded as being moved so far into the highfreqency region that its magnitde is severely decreased. This is spported by an inspection of the phase of the transfer coefficient (Fig. 7). This behavior follows the argment in the introdction where a higher resonance freqency is expected for shorter standoff distances.

6 120 COMBUSTION DYNAMICS AND CONTROL Fig. 5. The freqency dependence of the transmission coefficient for the perforated brass brner with 0.8 and ū 10, 14, 18, and 22 cm/s. Fig. 6. The freqency dependence of the transmission coefficient for the ceramic foam brner with 0.8 and ū 10 cm/s. A more complex way of changing the acostical behavior is to change the flow velocity. In the case of the brass flame holder, experiments have been carried ot for for different vales of the flow velocity at 0.8 and with the lowest possible cooling water temperatre of 50 C (Fig. 5). In the figre, the reslts of both analytical models are also plotted. One can see that for both of them, the correspondence is reasonable, bt the model by McIntosh nderestimates the resonance freqency and the model of Rook lacks magnitde. The nderestimation of the resonance freqency by the model of Mc- Intosh is probably de to the assmption of an ideally cooled srface, which is 100 K lower than the real srface temperatre. As explained above, we did not jst T and ū to accont for the presence of a warm flame holder. In Fig. 6, two reslts for the ceramic foam flame holder are presented for vales of ū 10. The experimental reslts of all velocity settings below the iabatic velocity of 23.9 cm/s are nearly indistingishable. The model of Rook shows good correspondence for low freqencies, bt overestimates the high-freqency behavior. As noted before, the vales of some qantities sed in calclating the analytical reslts are sbject to ncertainty. If, for example, the heat condctivity is decreased by a factor of 2, the model of McIntosh shows nearly perfect agreement with the measred reslts. Also for the model by Rook, small changes in the vale of Ze reslt in nearly perfect agreement, as shown in Fig. 7. Althogh jsting Ze seems qestionable, one has to take into accont that the model by Rook assmes perfect heat transfer between the flame holder and the nbrned gases. Since Ze expresses the sensitivity of the flame to the enthalpy wave emerging from the flame holder, Ze can be jsted to accommodate non-perfect heat transfer. This opens the way to accrately describing the acostical behavior of flat flames with a semiempirical model. For this practical prpose, the model by Rook seems to be versatile, since it can accommodate elevated brner srface temperatres. Conclsions Experiments have been carried ot to determine the transfer coefficient between the acostic velocity

7 ACOUSTIC RESPONSE OF FLAT FLAMES 121 Fig. 7. The freqency dependence of the transmission coefficient for the perforated brass plate and ceramic foam brner with 0.8 and ū 14 cm/s. The solid lines are obtained by fitting the analytical model of Rook et al. with varying Ze and k. pstream and downstream of a brner-stabilized flat flame. Downstream of the flame, LDV has sccessflly been sed to measre the acostic velocities, while the pstream acostic amplitde has been measred with pressre transdcers. The reslts show a clear resonance type of behavior for a flat flame, with amplification factors as high as 18. The resonance depends strongly on the srface temperatre of the brner and on the flow properties. For shorter standoff distances (i.e., higher flame holder temperatre), higher resonance freqencies are observed. The resonance freqency takes on lower vales for low mass flow, increases for medim mass flows, bt rapidly decreases again near blowoff. The region where amplification occrs ( / b 1) extends to abot 300 Hz, indicating that flat flames are inherently nstable in this region, with more dramatic effects for cooled srface brners. The correspondence to nmerical simlations performed with a model developed by Rook et al. [2,16] is good, both qalitatively and qantitatively. The correspondence to analytical models is reasonable, bt can be me nearly perfect by jsting one or two constants within physical limits. This opens the way to describe the acostical properties of an anchored flat flame with a semiempirical model. REFERENCES 1. Mnjal, M. L., Acostics of Dcts and Mfflers, Wiley- Interscience, Chichester, UK, Rook, R., Schreel, K. R. A. M., De Goey, L. P. H., Somers, L. M. T., and Parchen, R., Acostic Response of Brner Stabilized Flat Flames, paper 46, Seventeenth International Colloqim on the Dynamics of Explosions and Reactive Systems, Heidelberg, Germany, Jly 25 30, Ran, R. L., Beckste, M. W., Finlinson J. C., and Brooks, K. P., Prog. Energy Combst. Sci. 19:313 (1993). 4. Fleifil, M., Annaswamy, A. M., Ghoniem, Z., and Ghoniem, A. F., Combst. Flame 106:487 (1996). 5. Searby, G., Combst. Sci. Technol. 81:221 (1992). 6. Dowling, A., J. Flid. Mech. 346:271 (1997). 7. Matsi, Y., Combst. Flame 43:199 (1981). 8. Dcrix, S., Drox, D., and Candel, S., Proc. Combst. Inst. 28:765 (2000). 9. McIntosh, A. C., Combst. Sci. Technol. 91:329 (1993). 10. McIntosh, A. C., and Rylands, S., Combst. Sci. Technol :273 (1996). 11. Rook, R., Acostics in Brner Stabilized Flames, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2001, available at Rook, R., De Goey, L. P. H., Somers, L. M. T., Schreel, K. R. A. M., and Parchen, R., Combst. Theory Modeling 6:223 (2002). 13. Chen, T.-Y., and Chen, M.-G., J. Sond Vibration 221:221 (1999). 14. Chen, T.-Y., and Chen, M.-G., Exp. Flids 31:457 (2001). 15. Paschereit, C. O., Gtmark, E., and Weisenstein, W., AIAA 38:1025 (1998). 16. Rook, R., Schreel, K. R. A. M., De Goey, L. P. H., and Parchen, R., Response of Brner Stabilized Flames to Acostic Waves, Proceedings of the Second Eropean Conference on Small Brner and Heating Technology, Stttgart, Germany, March 16 17, Kaskan, W. F., Proc. Combst. Inst. 6:134 (1956). 18. Boma, P. H., Methane-Air Combstion on Ceramic Foam Srface Brners, Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1997, available at Ran, R. L., and Beckste, M. W., Combst. Flame 94:1 (1993).

8 122 COMBUSTION DYNAMICS AND CONTROL COMMENTS Sébastien Dcrix, Laboratoire EM2C CNRS, France. Can the crve giving / k b as a fnction of the freqency be considered as the amplitde of the flame transfer fnction? In this case, cold the peak observed at 100 Hz be seen as the reslt of an amplification mechanism? Resonance wold then be obtained in the whole system for a proper match of the different time delays. Athor s Reply. This crve is indeed the amplitde. The peak is the reslt of an amplification mechanism formed by the feedback of heat generated by the flame via the flame holder to the nbrned gas.