1. Although the total sound level (i.e., integrated over all frequencies) of turbulent flames has been extensively characterized, significantly less attention has been given to the spectral characteristics of the radiated sound. The limited experimental data suggests that the noise is broadband with emissions above background noise levels for frequencies from 100 Hz to over 20 kHz. It is also generally experimentally observed that flame noise levels peak in the 200- 1000 Hz frequency range9. Some data also indicates the presence of multiple peaks in the acoustic spectra14. A number of analyses have assumed a Strouhal number scaling (based on burner diameter and jet exit velocity) for this peak frequency14'15. Noting the shortcomings of these Strouhal number scalings, others '17have suggested that this frequency is kinetically controlled. At present, it is still unclear how the frequency of maximum acoustic emissions scales with relevant combustor variables.
2. where q' denotes the unsteady heat release per unit volume. In order to proceed, we neglect the effects of mean temperature/density variations in Eq. (9). The solution of Eq. (9) is then given by Eq. (10). Note that these neglected inhomogeneities cause wave refraction and reflection after they are excited by the unsteady heat release process, q'. For example, waves generated from the side of the flame which is opposite that of the observer position (i.e. 0-00180 degrees) impinge upon the other side of the flame, where they will be refracted and reflected, before reaching the observer. These processes are not accounted for in the analysis below, which assumes an isothermal medium and, thus,thatthewaves directly propagate to the observer. These reflection and refraction processes both roughly depend upon the square root of the temperaturejump across the flame. Thus, the errors due to this effect should scale as and tend tozeroasTb-»Tu. P'(XO,CD) =-ko(Y-l)
3. Figure 3 Polar directivity predicted by Eq. (21) for St=500 and 2000 (more oscillatory curve) and mean flow and flame speed Mach numbersof 0.05 and 0.01, respectively