Cellular Ceramics / 5

509

5.6

Acoustic Transfer in Ceramic Surface Burners

Koen Schreel and Philip de Goey

5.6.1

Introduction

When using a burner of any type in a closed combustion system, noise problems can occur due to coupling between the oscillating velocity/pressure field associated with the sound and the resulting oscillating heat release by the combustion process. When using cellular ceramics as a burner material, the relevant question is how this coupling takes place. The interaction between porous materials and acoustics is treated in Chapter 4.5, but the material presented there covers the reflection/absorption of cellular materials. For the frequencies of interest for combustion applications (80–800 Hz) this (viscous) damping of the acoustic wave can be neglected. Instead, heat transfer between the flame and the porous material is the key process in coupling with the acoustic field. The use of cellular ceramics as burner materials is extensively treated in Chapter 5.5, which is recommended reading before studying this chapter. We also refer to Chapter 4.5 for an introduction to acoustics, and Chapter 4.3 for the thermal properties of cellular ceramics.

The interaction between surface-stabilized flames and acoustics belongs to the field of thermo-acoustics. Early examples of thermo-acoustic phenomena include the “singing flame” reported in 1777 by Higgins [1], the Sondhauss tube [2], and the Rijke tube [3], each showing that heat sources can produce sound when placed in a tube. Since then, these combustion-driven instabilities have been studied experimentally by numerous authors in various configurations, for example, Putnam et al. [4] and Schimmer et al. [5]. Lord Rayleigh [6] was the first to pose a theoretical criterion for acoustic instability in these devices. The so-called Rayleigh criterion states that the energy in the acoustic field increases when the following inequality holds:

ÐT

0

where p0 and q0 are the oscillating parts of the pressure and heat release, respectively, and the integration is over time. Putnam et al. [7], and Putnam [8] put this into a mathematical formulation. Raun et al. [16] presented an extensive overview. Still, the Rayleigh criterion is phenomenological, and more fundamental studies are still going on to provide the necessary information on the exact distortion of the acoustic field by the flame.

Cellular Ceramics: Structure, Manufacturing, Properties and Applications.

Michael Scheffler, Paolo Colombo (Eds.)

Copyright 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31320-6

510 Part 5 Applications

When a surface burner is operated in the blue-flame mode, Bunsen-type flames are stabilized on the surface. In this case the interaction with an acoustic field is governed mainly by flame surface variations, which were studied experimentally by, for example, Durox et al. [10] and Ducruix et al. [11] and analytically by Fleiffil et al. [21]. In the last-cited work, the flow field is described by a Poiseuille flow and the profile is assumed to be undistorted by the flame. The motion of the flame is determined by using the G equation with constant burning velocity. Although the latest results [22, 23] show significant progress in understanding, there are still unresolved issues regarding the exact nature and origin of the unsteady velocity field.

Since the operation of a porous ceramic burner in the blue-flame mode leads to higher NOx emissions, the practically more relevant case is the radiant mode, in which a flat flame is stabilized on the surface. Since the oscillating velocity field is one-dimenional, this is theoretically better understood. McIntosh et al. [12], McIntosh [13], Van Harten et al. [14], and Buckmaster [15] pioneered this area. Raun et al. [9], McIntosh [17], and, more recently, McIntosh [18] and McIntosh et al. [20] used the flame/acoustic transfer function model to investigate Rijke tube oscillations. These flames are anchored to a burner plate, and the acoustic field is calculated from the reacting flow equations that are approximated by low-Mach number and high activation energy asymptotics. From this analysis, the transfer function for the acoustic velocity arises by which the acoustic quantities outside the flame are coupled. All these analysis assume that heat transfer between the gas flow and the porous ceramic is ideal, that is, the local gas temperature is always equal to the local temperature in the ceramic.

The latest research at the Eindhoven University of Technology is also based on the acoustic interaction of flames stabilized on flat surface burners. A simple analytical model based on fluctuating heat generation due to the dynamics of flames stabilized on top of porous burners, derived by Rook et al. [24], show behavior similar to the much more complex model of McIntosh. Numerical results for a burner with ideal heat transfer were found to be in agreement with the analytical model. Experiments performed on a cooled brass perforated-plate burner confirmed these results. Local multidimensional flow and heat-transfer effects were studied by Rook et al. [25]. Schreel et al. [26] experimentally investigated the behavior of ceramic surface burners, which have a much higher surface temperature than cooled metal burners, and found reasonable agreement with the extended theory for burners with a large heat transfer. Recently, however, detailed measurements and numerical studies have shown that most realistic surface burners cannot be considered to have ideal heat transfer. If this is the case, the other material parameters, such as heat transfer aS, the effective conductivity ksss, the specific heat cp,s, and radiative properties such as the emissivity e also have an effect on the acoustic behavior [27].

In this chapter, the state-of-the-art knowledge of the interaction between acoustics and combustion on realistic porous ceramic burners is presented analytically, numerically, and experimentally. In the next section, a short introduction will be given on the network analysis of 1D acoustic systems and an extended version of acoustic transfer is introduced with respect to that given in Chapter 4.5. Furthermore, the relevant transport equations for the description of combustion are presented. In the

5.6 Acoustic Transfer in Ceramic Surface Burners 511

remaining sections, an analytical description of acoustic transfer is given, followed by experimental work on several different porous-burner materials. The last section is devoted to a full numerical simulation of the transfer function, including an accurate description of volumetric heat transfer in the porous ceramic and other relevant ceramic material properties.

5.6.2

Acoustic Transfer

When analyzing the acoustic behavior of complete systems in which a burner is used, one has to realize that, although the combustion process can be considered as a source of acoustic energy, it is the complete system geometry that determines whether spontaneous acoustic oscillations will occur or not. A generally applied method to analyze complete systems is so-called network analysis [32, 33], in which each physical element of the system is represented by a transfer function. The overall transfer function of the system can then be analyzed for resonances.

If the wavelength of the sound of interest is much longer than the typical duct diameter, the system can (acoustically) be considered as one-dimensional, and a relatively simple expression of the transfer function can be given. The velocity can be written as (cf. Chapter 4.5)

where u is the average velocity and u the acoustic fluctuations. The acoustic velocities and pressures on both sides of an element can then be related via a transfer matrix. For a burner-stabilized flat flame, it can be shown that the transfer matrix

which means that the complete transfer matrix is determined by T22, the coupling between the velocity fluctuations upstream of the burner and flame (u0u) and downstream of the flame (u0b). This matrix element can be determined by considering the detailed dynamics of the flame on top of the burner and the heat-transfer fluctuations towards the burner.

The 1D flame motion is governed by the set of N conservation equations for the

where i is the production rate of mass of species i in the flame by chemical reactions, combined with the continuity equation

Note that the momentum conservation equation reduces to a constant pressure law p = pu for low Mach numbers. The energy conservation equation describing combustion on a ceramic surface burner must be split into two parts for the two continuous phases, yielding for the gas

In the above equations, the subscripts s and g indicate whether a quantity relates to the solid material or the gas, respectively. The properties of the solid material are reflected in the volumetric heat-transfer coefficient aS, the porosity u, the heat capacity s cp;s, and the product of tortuosity and thermal conductivity (ss ks ). With regard to tortuosity, note that two tortuosities exist for a porous material. One describes the tortuosity of the “holes” and concerns the effective distance traveled by a flowing medium, and the other describes the solid and concerns the effective distance over which heat conduction takes place. In this context the latter is meant (see also Chapter 4.3).

5.6.3

Analytical Model

As an intuitive model for the interaction between the flame and the acoustic waves, a kinematic description can be applied [25] in which the heat transfer between the burner and the flame is considered to be perfect. This means that the gas temperature and the temperature of the porous solid are always the same, and Eqs. (7) and

(8) can be combined into one equation for the temperature T of the single conti-

Due to the large heat capacity of the burner, the temperature inside the material is steady in this case, and the material parameters of the burner then do not influence the flame dynamics at all. The only parameter of interest is the burner surface temperature. A variation in the standoff distance of the flame (induced by the acoustic velocity fluctuations) then results in a displacement of the complete flame structure, except for the temperature in the burner, which remains steady. This leads to a feedback loop [24, 26], by which (convective) enthalpy waves emanating from the

5.6 Acoustic Transfer in Ceramic Surface Burners 513

burner surface induce a fluctuating flame temperature and therefore also a fluctuating burning velocity of the flame. The flame motion can be amplified or damped by these enthalpy waves, depending on the frequency. The resulting transfer function reads:

In these equations, Tu , Tsurf , Tb , Tad , and Ta are the temperatures of the unburnt mixture, the surface, the flame, the adiabatic flame, and the activation temperature.

Furthermore, x^ is the frequency scaled with the flame transit time d=u, where d is the flame thickness, and wf the average flame standoff distance. For more details, the reader is refered to Ref. [24].

This transfer function shows a resonancelike behavior, as can be seen in Fig. 1. For low frequencies the magnitude of T22 is determined by the thermal expansion of the flame, then increases up to a resonance frequency, after which the magnitude falls to 1 for even higher frequencies. The resonance frequency is mainly a function of the standoff distance of the flame, and thus of the surface temperature of the burner.

Fig. 1 Absolute value of the acoustic transfer coefficient T22 as a function of frequency for a perforated brass plate. The curves were calculated with two analytical models, both assuming perfect heat transfer.

For arbitrary Lewis numbers an analytical expression for the transfer function has been found by McIntosh et al. [20], based on a matched asymptotic analysis of the full equations. Also this model shows reasonable agreement with the measurements, but the elevated burner surface temperatures of radiant burners are not

514 Part 5 Applications

accomodated in the model of McIntosh. An analytical model for acoustic transfer when the heat transfer coefficient aS is finite is not available.

5.6.4

Acoustic Transfer Coefficient for Realistic Porous Ceramics

The analytical approach presented in the Section 5.6.3 gives good insight into the physics, but it remains to be seen whether the accuracy is high enough for the purpose of acoustic modeling of a complete combustion system. The effect of realistic values of aS has been studied by Schreel et al. [27], and it was found that the assumption of infinitely fast heat transfer is not adequate for most realistic radiant burners. The experimentally observed large variation in acoustic behavior, especially for higher frequencies, can not be explained by a variation in surface temperature alone. Thus, a more realistic heat-transfer model needs to be used.

In this section, the numerical and experimental results obtained by Schreel et al. [27] are presented. Results were obtained for four different ceramic materials, completed by the results for a perforated brass plate, which serves as a reference case exhibiting infinitely fast heat transfer. Material 1 consisted of sintered fibers with a diameter of 25 mm. The fibers had an inner core of silicate, an outer shell of silicon carbide, and were arranged randomly within a layer. Material 2 was the unsintered version of material 1, with additional holes perforated in the plate. Because the material is not sintered, the porosity is noticeably larger. Material 3 was a perforated ceramic plate consisting of foamed cordierite with a closed-cell structure. The porosity was thus entirely determined by the perforation pattern, which was hexagonal (pitch 1.95 mm) with a hole diameter of 1 mm. Material 4 was a ceramic foam made of cordierite. It had a reticulated structure with 24 pores per centimeter and an average hole size of 0.3 mm. All relevant material properties are presented in Table 1. The value of the volumetric heat-transfer coefficient is based on the application of known Nusselt relations for an approximate geometry of the solid (these are discussed with the presentation of the measurements), and is normalized with respect to the volume of the plate. The porosity was derived from a comparison between the measured density of the porous material and the literature value of the density of the bulk solid. This does not take into account a distinction between microand macroporosity, nor does it consider the occurrence of closed-cell structures. For the materials used here this seems to be adequate, but in general the more elaborate techniques described in Chapter 4.3 should be applied. For the heat capacity and conductivity literature values were used. The (apparent) emissivity was assumed to be 0.85 for all materials.

First, modeling results for T22 are presented for a variation of aS, u, s cp;s , ss ks , and e. Experimental results are presented afterwards, and compared to the modeling results based on the best known values of the material properties.

5.6 Acoustic Transfer in Ceramic Surface Burners 515

5.6.4.1

Numerical Results

The porous solid can adequately be modeled with a volume-averaged continuum approach as provided by Eqs. (4)–(6), (7), and (8). These equations with the appropriate boundary conditions can in principle be solved with a good time-dependent computational fluid dynamics (CFD) solver, but the problem is quite complex and not all codes are suited for the combination of porous flow and combustion. The results presented here were obtained with the software package Chem1D, developed inhouse [37] at the Einhoven University of Technology. For the purpose of this work, the chemical model as proposed by Smooke [39] is used. This model is limited to lean CH4/air flames, but it can accurately describe the flame dynamics and offers a high computational performance gain over more complex models like GRI [40]. The diffusion was modeled by using the EGlib library of Ern and Giovangigli [41], which incorporates complex transport processes including the Dufour and Soret effects.

The actual properties of the material can be described by the parameters in Eqs. (7) and (8), which are discussed above and tabulated in Table 1. The radiation term qrad in Eq. (8) is in most cases described by the Rosseland model inside the porous material, with an extinction coefficient of 15 cm–1. At the surface the radiative heat loss is described as erT4 . An even better modeling of the radiative heat transfer near the surface could be obtained by using the discrete-ordinate method or a similar technique capable of dealing with optically thin media, but the results will show that radiative effects at the surface do not have a strong influence on the acoustic transfer function.

Table 1 Relevant properties of the burner materials.

When modeling a stationary flame, the temperature distribution inside the ceramic is clearly different for the gas and the solid (see Fig. 2 for an example). At the surface the solid temperature is significantly lower than the gas temperature due to the radiative heat loss at the surface. The solid, however, is a better heat conductor than the gas and at some position inside the flame holder the gas and solid temperature are equal. Below that point, the solid temperature is higher than the gas temperature.

From a variation of the parameters, their relative importance can be judged and from this the accuracy can be estimated with which they need to be known for modeling an arbitrary material. For all the calculations a fuel lean methane–air flame was used at a stoichiometric ratio of 0.8 and a gas mixture velocity of 17 cm s–1.

516 Part 5 Applications

Fig. 2 Temperature profile of the gas and solid for a flame on a porous ceramic material. The vertical dashed line represents the boundary of the porous material.

The volumetric heat-transfer coefficient is theoretically the parameter which determines whether it can be assumed that a material exhibits perfect heat transfer. A series of transfer function calculations with aS in the range of 1–80 W cm–3 K–1 is presented in Fig. 3. For large values of aS a resonancelike shape is found for T22, which is damped for lower values of aS. The cutoff frequency also decreases with lower values of aS. There is only influence on the low-frequency behavior of the transfer coefficient for very low values of aS. For values of aS larger than 40 W cm–3 K–1, the transfer function becomes insensitive to variations in aS, that is, heat transfer becomes ideal. The transfer function is particularly sensitive to variations in the region 1–10 W cm–3 K–1, which corresponds to the range of values encountered in the burner materials under consideration. Clearly, the approximation that heat transfer is ideal is not valid. This parameter should be given special attention when modeling an arbitrary material if no direct comparison with measurements of the transfer function is available. The measurement or modeling of the volumetric heat-transfer coefficient is not trivial [29, 42], although when great care is taken reliable results can be obtained [30]. In comparison, the analytical model gives good results for lower frequencies but fails for frequencies higher than 500 Hz.

A series of transfer functions with varying porosity u is presented in Fig. 4. Also in this case the influence on the transfer function is significant, but now the magnitude of the transfer function is affected for the frequency range below the fall-off frequency. The fall-off frequency itself is hardly affected. Although the porosity is important, it is difficult to measure it accurately enough to be able to model an arbitrary material.

The influence of the thermal conductivity ss ks is almost negligible and is not presented in a figure. We found only significant influence on the transfer function for variations of an order of magnitude. This can be understood from Eq. (8). The term containing the thermal conductivity is proportional to @Ts =@x. As can be seen from Fig. 2, the slope of the temperature is quite moderate. Normally thermal conductivity

5.6 Acoustic Transfer in Ceramic Surface Burners 517

Fig. 3 Absolute value and phase of the acoustic transfer coeffi-

cient T22 as a function of frequency for burner material 1 with aS/ W cm–3 K–1 values of 1 (lower solid curve), 2, 4, 7, and

80 (upper solid curve). The dashed curve is the analytical model by Rook.

Fig. 4 Absolute value and phase of the acoustic transfer coefficient T22 as a function of frequency for burner material 1 with porosity u of 0.7 (lower solid curve), 0.85, 0.926, and 0.96 (upper solid curve). The dashed curve is the analytical model by Rook.

is known with an accuracy better than a factor of 2, which means that no special attention is needed.

Even less significant is the heat capacity of the solid cp,s. Again from Eqs. (7) and (8) it can be seen that, since the heat capacity of the solid is three orders of magnitude larger than that of the gas, the thermal inertia of the solid is too large to feel the fast fluctuations of the gas temperature.

Figure 5 presents results for varying emissivity. Some effects can be observed, but only for unrealistic values of e. Based on this we chose a value of e = 0.85 for all materials. Although most ceramic materials have an emissivity higher than 0.9, due to the porosity the apparent emissivity is somewhat lower. Even if an error is made of –0.05, this hardly has any influence on the accuracy of the modeling.

Fig. 5 Absolute value and phase of the acoustic transfer coefficient T22 as a function of frequency for burner material 1 with emissivity e of 0.6 (lower solid curve), 0.7, 0.85, and 0.95 (upper solid curve). The dashed curve is the analytical model by Rook.

5.6.4.2

Measurements

The experimental determination of the transfer function element T22 involves accurate measurement of the velocity fluctuations directly upstream and downstream of the burner. A proven and reliable method to do this would be the four-microphone technique (see Section 4.5.4.2), if it were not for the too strong variation of the temperature in the flue gases. This can be accounted for by using additional microphones and assuming a certain function for the dependence of the velocity of sound on the distance from the flame, but this can be quite cumbersome and experimentally challenging due to the high temperatures involved. The approach used by Schreel et al. [26, 27] is to use the two-microphone technique [32, 35, 36] in the upstream (cold) part of the flow, and to directly measure the velocity immediately downstream of the flame by laser Doppler velocimetry (LDV). Details about the setup can be found in Ref. [26]. A short description is given here.

The setup consists essentially of an approximately 60 cm long tube with an inner diameter of 5 cm, placed vertically to minimize buoyancy effects. The gas inlet is located at the bottom of the tube, and the flame holder is approximately 7 cm from the exit. Some grids are fitted right after the entrance to settle the flow. In the lower part of the tube a hole is made in the side which is coupled through a flexible hose to a loudspeaker. The part of the tube downstream of the flame holder is watercooled at nominally 50 C to avoid condensation of water. The acoustic properties of the tube itself were studied, and it was found that a rather weak resonance occurs around 640 Hz, but this frequency region is not used for this research. In this case frequencies up to 800 Hz are applied, avoiding the 600–680 Hz band. Two calibrated pressure transducers are mounted in the wall of the tube upstream of the flame. Downstream of the flame optical access for the LDV measurement is provided by