Broadband Shock-Associated Noise
A convergent nozzle operated at supercritical pressure ratios always produces expansions and shocks in the plume. This results in the appearance of shock-associated noise. The same situation occurs when a convergent – divergent (C-D) nozzle is operated at off-design conditions. Shock-associated noise generally consists of discrete tones and broadband components. Though it is possible to design a shock-free C-D nozzle for laboratory investigation, C-D nozzles in commercial and military applications are usually constructed with straight conical sections, so some level of shock noise is present even at
Figure 8. Normalized spectra from heated jets at 90°. Tt/Ta = 3.2, D = 1.5 in. Symbols: subsonic Mach numbers; lines: supersonic Mach numbers. Velocity exponent n = 5.53. (From Viswanathan (2006))
the supposed design conditions. Harper-Bourne and Fisher (1974) were the first to provide a comprehensive experimental study and model of broadband shock-associated noise. They operated a convergent nozzle at supercritical pressure ratios and at ambient reservoir temperatures, and observed a dramatic increase in noise in the forward quadrant. They identified this noise source as being associated with the quasi-periodic shock cell structure in the jet plume. From an examination of their cold data, together with hot jet data from Rolls-Royce, they showed that the intensity of shock noise is only a function of nozzle pressure ratio and is nearly independent of jet reservoir temperature and hence jet velocity. Subsequently, Tanna (1977), Seiner and Norum (1979), Seiner and Norum (1980), Norum and Seiner (1982a), Norum and Seiner (1982b), Tam and Tanna (1982), Seiner (1984), Seiner and Yu (1984), Yamamoto et al. (1984) and, more recently, Viswanathan et al. (2009) have carried out extensive studies that have formed the basis for our understanding of shock-associated noise.
Figure 9. Extracted components of turbulent mixing noise and broadband shock-associated noise from total measured noise. M = 1.24, Tt/Ta = 3.2, inlet angle = 70°. Solid: shock noise; dashed: mixing noise; symbols and dotted line: total noise. (From Viswanathan (2006))
The experiments conducted at NASA Langley Research Center by Seiner, Norum and Yu included measurements of the aerodynamic characteristics, as well as the near and far field acoustics of shock containing plumes in order to uncover the physical mechanisms responsible for the generation of shock noise. Both convergent and C-D nozzles were tested. Whereas a convergent nozzle can only be operated supersonically at underexpanded conditions (pe/pa > 1), where pe and pa are the exit and ambient pressures respectively, a C-D nozzle can be operated at either overexpanded (pe/pa < 1) or underexpanded conditions.
Figure 10 from Norum and Seiner (1982a) shows typical narrowband noise spectra from a C-D nozzle with design Mach number of 1.5 at a fully expanded Mach number of 1.8 (NPR=4.72), and unheated. Several spectra are shown that cover polar angles from 30° to 120°. Also shown are predictions by Tam (1987): see Section 4.3. This figure displays all the three noise components. A screech tone is clearly visible in all the spectra, with its amplitude more than 10 dB above the broadband noise in the forward angles. The distinct peak to the right of the screech tone is the broadband shock-associated noise. The broadband noise contains one dominant peak, with a secondary peak sometimes evident, and the peak frequency of the radiation increases with angle from the inlet. The half-width of the broadband spectral peak widens as the radiation angle increases and in the aft quadrant the peak is very broad. The broadband shock noise component is dominant in the forward quadrant. The peak to the left of the screech tone is the turbulent mixing noise, which is most easily identified at 120°. The peak frequency of the broadband shock noise increases with angle. The spectral level of the shock noise is nearly unaffected by jet temperature at a fixed Mach number. Though recent experiments by Viswanathan et al. (2009) and Kuo et al. (2011) show that the addition of small amounts of heating increases the peak levels, but then the levels become effectively independent of jet temperature.
The intensity of shock noise depends on the degree of mismatch between the design Mach number, Md and the fully expanded Mach number, Mj. Figure 11, from Seiner and Yu (1981), shows the variation of noise intensity obtained with a C-D nozzle of design Mach number 1.5 operated over a range of fully expanded Mach numbers. The jet was operated unheated and the radiation angle shown is 30°. Also shown on this plot (denoted by dark circles and solid line) is the turbulent mixing noise obtained by operating the three nozzles at their design Mach numbers of 1.0, 1.5 and 2.0. The difference between the open circles (and dashed line) and the dark circles (and solid line) is an estimate of the shock noise contribution. When the Mach number of a C-D nozzle is progressively increased from subsonic to slightly supersonic conditions, the flow is highly overexpanded with strong shocks in the plume. Depending on the degree of overexpansion, a Mach disc may be present in the plume. The total noise of the jet in the forward quadrant increases with contributions from shock noise. As the Mach number is increased from unity, the noise level increases until the Mach disc disappears. This Mach number is denoted by point C. At higher Mach numbers, there is a decrease in noise due to the weakening of the shock strength and the minimum noise occurs at the design point A. With a further increase in Mach number, the nozzle is operated at underexpanded conditions and the shock noise again begins to increase following the trend AB. When the flow is highly underexpanded, normal shocks appear again and a Mach disc is formed, point B. The spectral level reaches a peak at approximately this condition and any further increase in Mach number results in a slight decrease initially and then no further change in the noise level. The diameter
Figure 10. Narrow band noise spectra for a convergent-divergent nozzle operated at Mach numbers of 1.67. Design Mach number = 1.5. D = 5.08 cm. (Adapted from Norum and Seiner (1982a) and Tam (1987)).
Figure 11. Variation of noise intensity with Mach number at 30° to the inlet axis. Design Mach number = 1.5. O, Imperfectly expanded jet; •, perfectly expanded jet. (Adapted from Seiner and Yu (1981)).
and the downstream location of the Mach disc increases with the degree of underexpansion. Seiner and Norum (1980) recommended that a distinction should be made between plumes with strong shocks and plumes with weak expansion and compression waves. In the latter case the flow is supersonic while in the former case there are mixed supersonic and subsonic flow regimes, due to the presence of the normal shocks. These strong shocks reduce the extent of the supersonic flow and weaken the strength of the downstream shocks.
These experiments also showed that though the first shock cell has the greatest strength, the downstream shocks are responsible for shock noise production. The main region of shock noise production was found to occur near the end of the potential core for both underexpanded and overexpanded supersonic jets. Flow and near-field acoustic correlations indicated a spatial coherence of several shock wavelengths, with the shock noise appearing to originate from the vicinity of each oblique shock wave. These results suggested strongly that broadband shock noise is produced by the interaction of turbulent flow structures with the periodic shock cell system.
The relative importance of broadband shock-associated noise and turbulent mixing noise is a strong function of radiation angle and jet operating conditions. For a fixed Mach number, the turbulent mixing noise level increases as the jet temperature is increased, while the amplitude of the broadband shock noise remains nearly unaltered. Hence, the magnitude of the shock noise over the mixing noise is a maximum for cold jets, as seen in Figure 10. The shock noise radiation is fairly omnidirectional, whereas the mixing noise radiates principally in the aft directions. The jet temperature then sets the relative levels of the two components. Figure 12 shows the effect of total temperature ratio on the OASPL from a convergent nozzle operated at a fully-expanded Mach number of 1.36 (underexpanded). The shock noise is see to be relatively omindirectional for each temperature ratio. The increase at some angles near 90 degrees in the unheated case is due to the presence of screech tones. The mixing noise is highly directional and dominates the shock noise in level for large angles to the inlet axis. In the unheated case, the peak levels of the shock and mixing noise are similar (within 5 dB when the screech tones are neglected). At the highest temperature ratio the peak mixing noise OASPL is approximately 15 dB higher than the shock noise.