ERCOFTAC Bulletin - Centre Acoustique

Figure 3: Schlieren visualizations with the baseline (top) and notched (bottom) nozzle, Mj = 1.35.
4 Screech effects on the BBSAN
It has been shown in the previous section that the
notches in themselves had a small effect on the jet development.
It is thus postulated in the following that the
differences between broadband shock-associated noise
from the two nozzles come entirely from the different
screech tone levels. Some salient features are already
visible in Figure (2) : the broadband hump is usually
enhanced and shifted to higher frequencies. In order to
quantitatively analyse the first broadband hump of the
acoustic spectra in an objective way, Gaussian curves
writing
A exp(−(f − fp) 2 /(2σ 2 )) (1)
are fitted through the spectra. In expression (Eq. (1)),
A is the maximum amplitude of the hump, f the frequency,
fp the peak frequency and σ a measure of the
hump width. This procedure allows an objective set of
properties for each broadband hump to be obtained.
A detailed traverse of the Mj range from 1.0 to 1.55
has been performed for each nozzle and far field acoustic
spectra have been measured at each operating point.
For every value of Mj, the first broadband hump in the
spectra at θ = 90 ◦ has been fitted by a Gaussian curve
and the Strouhal number based on the peak frequency,
Stp, has been plotted in Figure (5). Obviously, the peak
Strouhal number is decreasing with increasing Mj, owing
to the lengthening of the shock-cells. In most cases, Stp
is larger for the notched nozzle as for the baseline. This
property is in agreement with the baffle experiments of
Norum [15]. But the most interesting feature is the tuning
existing between fp and 2 Sts for the baseline nozzle,
where Sts is the screech Strouhal number. Whereas Stp
for the notched nozzle evolves smoothly through the Mj
range, it clearly follows the staging process of screech in
the baseline configuration (the jump above Mj = 1.20 for
the notched nozzle is due to a change of interpretation
of a continuously evolving hump). This can be related
to a modification in shock spacing due to the screech
modes, which should not occur in the absence of screech.
Moreover, in ranges where two screech frequencies exist
in the baseline case, like around Mj = 1.25 and 1.40,
the broadband hump seems to settle in-between the two
tones. The existence of an effect of screech on BBSAN
is clearly demonstrated by Figure (5).
The evolution of BBSAN the peak frequency has been
estimated over all directivity angles of the far field antenna.
The non-dimensioned peak wavelength λp/D has
been plotted against cos θ in Figure (6) for Mj = 1.10 and
1.35.
Firstly, it is clear that fp is higher in the case of the
notched nozzle, over the entire θ and Mj range. Secondly,
all the curves are approximately linear. This comes from
the well-known Doppler effect arising on the far field
peak frequencies of BBSAN. Harper-Bourne & Fisher [4]
and Tam & Tanna [16] found the following expression for
St
3
2.5
2
1.5
1
0.5
0
1 1.1 1.2 1.3 1.4 1.5 1.6
M j
Figure 5: ◦ Stp for the baseline nozzle, ▽ Stp for the
notched nozzle ; • two times the screech Strouhal number
(baseline nozzle). The bars over Mj = 1.05, 1.24 and
1.53 denote the uncertainty ranges as estimated for the
notched nozzle.
Uc/Uj
Mj
1.10 1.15 1.35 1.50
baseline 0.42 0.58 0.61 0.65
notched 0.66 0.65 0.65 0.65
Table 1: Values of Uc/Uj found from linear fitting of
fp(θ = 90 ◦ )/fp(θ).
fp, with entirely different models :
fp =
Uc
L (1 − Mc cos θ)
(2)
In Eq. (Eq. (2)), Uc is the convection velocity of the vortical
structures responsible for the shock noise, Mc is Uc
divided by the ambient speed of sound and L is the shock
spacing. Seiner & Yu [17] used this relation to estimate
the convection velocity. Indeed,
fp(θ = 90 ◦ )/fp(θ) = 1 − Mc cos θ (3)
The same procedure has been applied here for the two
nozzles. The resulting values of Uc/Uj are displayed in
Table (1). There is a striking difference between baseline
and notched nozzle. While the Uc/Uj estimate for the
latter is constant with Mj, the estimate for the former
keeps rising. At Mj = 1.50, both estimates are equal owing
to a weak baseline screech. The estimate at Mj = 1.10
for the baseline nozzle appears to be very low as compared
with usual values from the literature, which could
partly arise from the limited number of data points available
and the shallow broadband hump over the turbulent
mixing noise, making detection more subjective and peak
frequencies more uncertain. Panda et al. [18] also found
a screech mode dependency of convection velocity. When
screech is removed, so is the variation of Uc/Uj as well
and Uc/Uj ≈ 2/3.
The cases Mj = 1.10 and Mj = 1.35 have also been
studied in the near field. Only Mj = 1.10 is reported
12 ERCOFTAC Bulletin 90