Cellular Ceramics / 5

Fig. 8 Absolute value and phase of the acoustical transfer coefficient T22 as a function of frequency for burner material 3. The dashed curve is the analytical model by Rook.

Fig. 9 The absolute value and phase of the acoustical transfer coefficient T22 as a function of frequency for burner material 4. The dashed curve is the analytical model by Rook.

For a perforated ceramic plate like material 3, the structure can be quite accurately modeled as a collection of cylindrical holes. This leads to the estimation that aS = 1.24 W cm–3 K–1 for material 3, which yields a good correspondence between the numerical model and the measurements.

For material 4 (ceramic foam), the aS value was estimated using an empirical correlation [31] leading to a value of 0.5 W cm–3 K–1. Unfortunately, the numerical model shows flashback for values of aS below 1 W cm–3 K–1 (at which value the numerical curve is plotted), so no real comparison can be made, although an extrapolation of the curve of aS = 1 W cm–3 K–1 to lower values of aS seems to indicate a reasonable correspondence.

When judging the applicability of the analytical model, it can be concluded that for high values of aS and frequencies up to 500 Hz the results are good, but large discrepancies arise outside these limits.

5.6 Acoustic Transfer in Ceramic Surface Burners 521

5.6.5

Summary

Depending on the needed accuracy, the acoustic transfer function of a radiant surface burner can be obtained by using an analytical model, by measurement, or by numerical modeling. Based on experiments, it turns out that the acoustic transfer function is strongly affected by heat transfer between the flame and the flame holder. This heat transfer is mainly governed by the volumetric heat-transfer coefficient and to some extent by the porosity. It is shown that the heat transfer can be assumed to be ideal (i.e., the gas temperature and the solid temperature are identical) for values above 40 W cm–3 K–1. In practice these values do not occur for ceramic materials. Other material properties like heat capacity, heat conductivity, and emissivity are of minor importance.

The correspondence between numerical modeling and experiments is good. The key is to determine the volumetric heat-transfer coefficient, since the modeling is so sensitive to its value. This can be done on the basis of Nusselt relations, but this is not very easy for difficult geometries. The direct measurement of the volumetric heat transfer coefficient has the preference, as can be done with the methods described in Chapter 4.3 or tby Fend et al. [30]. Modeling of an arbitrary material without accurate knowledge of the volumetric heattransfer coefficient is not advisable.

References