Intensity and Directivity Prediction
The prediction of the screech tone intensity remains a challenging problem. The phenomenon of mode switching or staging adds an additional layer of complication, which makes the development of a prediction method even more intimidating. Numerical simulations, with detailed specification of the entire upstream geometry, could provide a means for computing the intensity of the screech tone for a particular geometry. Such simulations using computational aeroacoustics methods have been attempted for simple geometries. Shen and Tam (1998) carried out such a simulation for a low supersonic Mach number jet for which the toroidal instability mode is dominant. This axisymmetric numerical simulation provided good qualitative details of the screech phenomenon. Features such as mode switching and the principal radiation lobes of the fundamental and second harmonics were reproduced in this study. The predicted screech intensities were close to the values measured on a large reflecting surface placed upstream of the nozzle exit. Shen and Tam (2000) have also examined the effects of jet temperature and nozzle-lip thickness on the screech tone intensity. The results of their simulations were in agreement with the experimental observations.
It has been observed that the intensity of the screech tones decreases with increasing jet temperature. The reasons for this observed change in intensity appear to be understood. In the previous section it was shown that, in the weakest link theory, the frequency of screech is determined by the characteristics of the feedback acoustic waves. Tam et al. (1994) examined the role of the other two factors responsible for screech generation; that is, the instability waves and the shock cell structure. They suggested that the characteristics of the instability waves dictated the intensity and occurrence of screech tones. By carrying out a hydrodynamic stability analysis, they examined the evolution of the instability waves for a variety of Mach numbers and jet temperatures. This study revealed that the axisymmetric or toroidal modes have the highest total amplification at lower supersonic Mach numbers. Above a Mach number of approximately 1.3, the helical or flapping mode becomes dominant. Since the feedback mechanism is driven by the instability waves, which function as the energy source, the observed switching or staging of screech mode from toroidal to flapping at about this Mach number can be attributed to the change in the dominant instability wave mode. Secondly, the Strouhal number of the most amplified instability wave decreases with increases in jet temperature and jet Mach number. In terms of frequency, even though the jet velocity increases as fTt, the decrease in Strouhal number is greater than 1Д/Т). Hence, the frequency of the most amplified instability wave decreases with increasing temperature. The measured screech frequencies, on the other hand, increase as the jet temperature increases. The implication is that the feedback mechanism is not driven by the most amplified instability waves, thereby leading to a reduction in tone intensity. At elevated temperatures, these tones may not be easily observed above the background noise. Tam et al. (1994) summarized that the observed reduction in tone intensity or the non-occurrence of the tone is the direct result of the mismatch between the screech tone frequencies and the band of the most amplified instability waves. As mentioned earlier, screech tones are not considered to be important in most real engine applications. The non-symmetric geometric features of installed engines and the reduction of screech intensity with increase in temperature, provide an explanation of this observation.
5 Recent Developments
Research in jet noise prediction is an ongoing activity. Significant progress has been made in recent years in the direct simulation of the jet flow and the noise it radiates. An example of such a computation is the work by Shur et al. (2005). These authors used a hybrid RANS/LES method and then propagated the near field solution to the far field using a permeable surface Ffowcs Williams – Hawkings equation solution (see Ffowcs Williams and Hawkings (1969), Brentner and Farassat (1998)). In this section, three additional topics will be covered very briefly: new acoustic analogy prediction methods; new views on the role of large-scale structures; and nonlinear propagation.