4.1. Evolution process – ‘schlieren on’

As described in § 2.3, two GA experiments were performed in this campaign. In this section, the results from the GA experiment with the schlieren optics inside the otherwise anechoic chamber will be described. The fitness function utilized is described by (3.2), with the algorithm attempting to maximize the $OASPL$ reduction at any microphone, starting from random actuator configurations. The number of individuals on each generation tested was 30. A chart of the GA evolution over the course of 22 generations ($MaxGenerations=22$) is provided in figure 4(a), summarizing the measurements from 660 different configurations of actuators tested. Although the fitness function $J$ defined in (3.2) did not prioritize any microphone direction, it was observed that the GA sought to minimize the $OASPL$ at the $\phi =90^\circ$ microphone as the GA evolved. Therefore, figure 4(a) presents the $OASPL$ measured at $\phi =90^\circ$. As can be noted, convergence is quickly reached by Generation  6, but the experiment was allowed to run for a longer time to ensure breakthrough solutions would not appear. Note on figure 4(c) that the best individual configurations after Generation  6 are very similar. Further analysis of the latter generations indicated significant reduction in population diversity, reaching $d<0.5$ for the last generations. Thus, a GA breakthrough was considered unlikely within the time scales of the experiment. The total run time of the experiment was approximately one and a half hours, which included pauses midexperiment to ensure $NPR$ was within the uncertainty bounds.

Figure 4.

Results from the first GA experiment with the schlieren on. (a) Evolution of the $OASPL$ captured by the microphone at $\phi =90^\circ$ against the baseline case. Blue band represents variability between baseline cases. (b) Setpoint of EPRs for best individual on each generation. (c) Number of active actuators for the best individual on each generation.

In figure 4(b), the pressure setpoint for each EPR is presented for the best individuals of each generation. The GA quickly hovered around 70–90 psig as it moved beyond generation 10. Defining a secondary stream pressure ratio ($SPR$) as

(4.1)\begin{equation} SPR=\frac{P_{EPR}}{P_{0}}, \end{equation}

where $P_{EPR}$ is the setpoint EPR pressure, and $P_0$ is the stagnation pressure of the main nozzle. The $SPR$ is between 1.65 and 2.15 for the optimal configurations found by the GA. The effect of $SPR$ is more readily noted in figure 5, where the $OASPL$ at the $\phi =90^\circ$ microphone is plotted as a function of $SPR$. It is evident that the $OASPL$ reduces as $SPR$ is increased for the three most downstream rings (R2, R3 and R4). Ring R1 is not plotted in figure 5, as it was inactive in a large fraction of the experiments. Furthermore, the effect of $SPR$ asymptotes at approximately $SPR\sim 1.7$, at least within the upper limit of the EPRs (100 psig; $SPR=2.42$).

Figure 5.

Effect of $SPR$ on the measured $OASPL$ for the ‘schlieren on’ GA experiment.

A representation of the best actuator configuration is shown in figure 4(c) by tabulating the number of active actuators on each ring for the best individual of each generation. Note the number of active actuators corresponds to the actuator arrangements represented in figure 3. It is quickly noted that the GA deactivated the actuators on ring R1, which are absent after Generation  4. Ring R1 is the only ring upstream of the nozzle throat, and the fact the GA deactivates the actuators on this ring implies that actuating on the converging section of the nozzle is detrimental to the GA goal (noise reduction). The actuator configuration stabilizes around Generation  6, hovering about $\{{\rm R}1,{\rm R}2,{\rm R}3,{\rm R}4\}=\{0,6,12,6\}$ and spuriously adding or removing one actuator from any of the rings. The ‘schlieren on’ GA solution, therefore, will be called the $\{0,6,12,6\}$ solution for the remainder of this manuscript. The configuration with the lowest noise occurs in Generation  11, with $OASPL=101.9$ dB at the $\phi =90^\circ$ microphone, representing a reduction of 8.6 dB with respect to the baseline $OASPL=110.5$ dB. During the automated experimental campaign, the reduction in perceived noise as the actuation schemes evolved was qualitatively noticeable. This is an achievement that exceeds the best efforts in the literature using air as the actuation fluid, to the knowledge of the authors. Most of the past efforts are summarized by Henderson (Reference Henderson2010), and the highest $\Delta OASPL$ reported in the literature to the knowledge of the authors is slightly lower than 6 dB by Morris et al. (Reference Morris, McLaughlin and Kuo2013). In the work of Morris et al. (Reference Morris, McLaughlin and Kuo2013), the fluidic actuation also occurs at the diverging section of the nozzle, the maximum reduction occurring at a more downstream direction ($\phi =40^\circ$). Reaching such significant reductions in jet noise demonstrates the potential of the GA, as well as other machine-learning-based techniques, to enhance our ability to control flows and potentially perform multiobjective optimization considering other relevant optimization objectives such as thrust, actuation power, among others.

At this point in the experimental campaign, however, it was very concerning that the microphone that was favoured by the GA ($\phi =90^\circ$) was exactly the microphone most shadowed by the schlieren mirror. More specifically, the $\phi =90^\circ$ microphone was located about 500 mm from the $12$ in. (305 mm) diameter mirror, directly behind it as required by the schlieren optical set-up. It could be possible that the higher frequency acoustic waves, which diffracted around the mirror, would be under-represented in the spectrum of the measurements made. This concern was cleared later by repeating the measurements without the schlieren set-up including the microphones. These results are presented in § 4.4. As the chamber was not anechoic during this experiment, the directivity plots and frequency spectra will not be presented for the ‘schlieren on’ experiment.

4.2. Flow visualization

The images obtained for the ‘schlieren on’ GA solution can now be examined to further understand the potential mechanisms leveraged by the GA. An average schlieren image from 100 image samples is presented in figure 6 for the unactuated baseline case and the $\{0,6,12,6\}$ solution obtained by the GA. The baseline image in figure 6(a) corresponds to a typical overexpanded jet, at $NPR=2.80$, presenting a repeating shock diamond train pattern that shows sharp interactions at the jet shear layers. The $\{0,6,12,6\}$ solution mean schlieren image in figure 6(b), on the other hand, shows a highly complex structure of shock cells, resulting from the addition of new bow shocks inside of the diverging section of the nozzle due to the presence of the actuators. Inside the diverging section of the nozzle, the microjets act as jets in supersonic cross-flow (Knast Reference Knast2020). The small bow shocks in front of the microjets disrupt the formation of a strongly defined shock cell structure such as the baseline case of figure 6(a). Note the disruption is so significant that the Mach disk present in the baseline case of figure 6(a) is not evident in the actuated case of figure 6(b), suggesting it was greatly weakened.

Figure 6.

Mean schlieren images (vertical cutoff) of the (a) baseline and (b) GA solution obtained in § 4.1, plotted in the same colour scale. Scaled nozzle drawing overlaid to clarify actuator locations. Vertical schlieren cutoff used to acquire images.

In this sense, the extra shocks introduced by the microjets are expected to have two effects. On one hand, additional shocks originating from within the nozzle interact with the jet shear layer, increasing the minimum wavenumber $k_1$ of the waveguide modes according to the model proposed by Tam (Reference Tam1995), which would be expected to increase the frequencies related to the BBSAN produced by the jet. On the other hand, the magnitude of the BBSAN sources may be greatly diminished if the shocks are spread out in space such that the velocity jumps across each shock are smaller in magnitude, which may explain the significant reduction in $OASPL$ accomplished by the GA solution. A similar effect was observed by Morris et al. (Reference Morris, McLaughlin and Kuo2013) by also actuating at the diverging section of the C–D nozzle, being highly effective in reducing noise.

The presence of the microjets blowing at the shear layer also disrupts the feedback loop mechanism responsible for screech, similar to what is observed by Alvi et al. (Reference Alvi, Lou, Shih and Kumar2008). This is readily observed in the standard deviation of the schlieren images, shown in figure 7. The unactuated case of figure 7(a), which produces screech tones at 5.7 kHz and 11.5 kHz, presents periodically spaced regions of high standard deviation outside of the jet shear layer, indicated in (a1). This structure is similar to what is observed by Edgington-Mitchell (Reference Edgington-Mitchell2019) and referred to as a standing wave pattern, characterizing the screech of the baseline jet. As the jet is actuated, as shown in figure 7(b), the standing wave pattern vanishes and the screech tone is eliminated from the spectrum, as will be further discussed in § 4.4, indicating the effectiveness of the control mechanism to eliminate jet screech.

Figure 7.

Standard deviation of the schlieren images for the (a) baseline and (b) GA solution obtained in § 4.1, plotted in the same colour scale.

Lastly, it can be noted that the addition of microjets is also observed to increase the shear layer growth close to the first two shock cells in figure 7, although the growth rate seems to be lower in the most downstream portions of the jet. This effect has also been observed by Alvi et al. (Reference Alvi, Lou, Shih and Kumar2008). The effect is also evident in figure 6, where the supersonic (shock cell containing) portion of the jet core is extended farther downstream – possibly due to the reduced mixing resultant from a lower shear layer growth rate.

4.3. Evolution process – anechoic

The success obtained by the GA described in § 4.1 was highly encouraging, but the fact the GA targeted the minimization of noise as measured by the microphone behind the schlieren mirror raised questions about the generality of the solution achieved. Thus, a second GA experiment was performed after removing the schlieren optics and reinstalling all acoustic wedges back into the anechoic chamber, restoring the fully anechoic state of the chamber.

During the second GA run, 25 generations of 30 individuals were considered for a total of 750 configurations tested. The summary of the GA evolution is presented in figure 8. Once again, the GA quickly sought to minimize the sideline noise ($\phi =90^\circ$), as the largest $\Delta OASPL$ indeed occurred at that angle. Thus, once again the evolution plot of figure 8(a) shows the evolution of $OASPL$ at the $\phi =90^\circ$ microphone. Convergence was slower during the second run, reaching a converged state approximately by Generation  15. However, note that the optimal actuator pattern for the second run, shown in figure 8(c), is different than the optimal actuator pattern in the previous run figure 4(c). In this second experiment, the pattern $\{0,0,13,12\}$ was reached as the optimal pattern. As the maximum number of actuators was 25, this pattern used all actuators made available for the GA. The actuator pressures shown in figure 8(b), were approximately the same in the optimal case as the previous solution, and the $OASPL$ dependence on $SPR3$ and $SPR4$ is very similar to what is previously shown for the ‘schlieren on’ experiment in figure 5, with an asymptotic behaviour about $SPR\sim 1.7$. The pressure for EPR1 and EPR2 are not shown in figure 8(b) as they had no active actuators in most of the best cases on each generation.

Figure 8.

Results from the second GA experiment without a schlieren (fully anechoic). (a) Evolution of the $OASPL$ captured by the microphone at $\phi =90^\circ$ against the baseline case. Blue band represents variability between baseline cases. (b) Setpoint of EPRs for best individual on each generation. (c) Number of active actuators for the best individual on each generation.

Once again, the actuator patterns in figure 8(c) indicate actuating at ring R1 (in the converging section of the nozzle) is highly ineffective. In fact, plotting the measured $OASPL$ at $\phi =90^\circ$ against the mass flow rate at the ring R1 ($\dot {m}_{R1}$) for all the cases explored in the anechoic GA run reveals an interesting pattern, shown in figure 9(a). The mass flow rate was measured by an Omega FMA5410 mass flow meter with the main nozzle inactive for all actuators as a function of the pressure at the EPR, and a quadratic curve fit based on these measurements is used to estimate the mass flow rate during the experiment. The main nozzle mass flow rate ($\dot {m}_{Nozzle}=336.5\ {\rm g}\ {\rm s}^{-1}$) is estimated from the 1-D isentropic relations for the overexpanded $NPR=2.80$. Figure 9(a) shows that as the mass flow rate in the ring R1 is increased (i.e. increasing number of active actuators and the corresponding $SPR$), the minimum $OASPL$ attained by the GA increases. This would suggest that actuating at the converging section of the nozzle is not only ineffective, but potentially detrimental to the goal of noise reduction. This effect is further evidenced by a measurement performed for the $\{16,0,0,0\}$ configuration (i.e. only a full R1 ring) at a mass flow ratio of $\dot {m}_{R1}/\dot {m}_{Nozzle}=0.7\,\%$, which yielded a small increase in $OASPL$ at the $\phi =90^\circ$ microphone of 1.1 dB. At the position where the actuators R1 are located, the local cross-sectional area of the nozzle channel is 1.043 times the throat area, meaning the local Mach number is approximately 0.96. Thus, actuating at R1 may significantly change the boundary layer and flow conditions at the throat, as well as the effective throat area. Unfortunately, the data gathered in this experiment is not sufficient to specify how such changes to the throat conditions would increase the noise produced by the main jet.

Figure 9.

Effect of mass flow rate at (a) ring R1 and (b) all rings on the $OASPL$ for the fully anechoic GA experiment.

As presented in figure 9(b), the total mass flow rate used by all actuators is always maintained under $\dot {m}_{Total}/\dot {m}_{Nozzle}<1.7\,\%$. The same general trend previously observed in figure 5 is also observed in figure 9(b), that is, increasing the actuator mass flow rate has a generally beneficial effect to noise reduction up until a threshold value ($\dot {m}_{Total}/\dot {m}_{Nozzle} \sim 1\,\%$), and further increases in mass flow rate then have little effect on $OASPL$ within the range observed. For the optimal configuration with most noise reduction, $\dot {m}_{Total}/\dot {m}_{Nozzle} = 1.4\,\%$ and $J=\max (\Delta OASPL_m)=7.3$ dB.

4.4. Far field acoustics

In this section, a more detailed analysis of the acoustics of the different cases explored will be presented. All acoustical data presented in the following sections consists of measurements performed in the fully anechoic configuration, with 10 s-long data sets for improved statistical convergence.

The directivity of the jet noise captured by the microphone array is presented in figure 10(a), comparing the baseline unactuated case with the two GA solutions obtained in the experiments described in §§ 4.1 and 4.3. The difference between the baseline $OASPL$ and the $OASPL$ of the anechoic GA solution $\{0,0,13,12\}$ is annotated in figure 10(a) in red. Note the largest $\Delta OASPL$ occurs at the sideline $\phi =90^\circ$ noise, which is plotted over time in figure 10(b) together with the baseline case to show the drastic difference in waveform amplitude as the actuators are toggled. A significant reduction is observed in all radiation directions, ranging from $-3.3$ dB to $-7.3$ dB, which is an accomplishment considering the approach used is model-free. The more upstream microphones, closer to the sideline $\phi =90^\circ$ direction, observed the largest noise reductions. This is a similar behaviour to what was observed in a recent study (Liu et al. Reference Liu, Khine, Saleem, Rodriguez and Gutmark2022) on a faceted C–D nozzle, which reports the application of 12 microvortex generators at the diverging walls of the nozzle, also observing noise reduction of 5–6 dB at the sideline and upstream directions. Thus, introducing small disturbances at the diverging section is a reasonable strategy for supersonic jet noise reduction in the sideline and upstream directions, which was effectively leveraged by the GA. Both GA solutions have approximately the same effect on the overall noise, however, the $\{0,0,13,12\}$ solution is slightly more effective ($\sim$0.5 dB) at reducing jet noise than the $\{0,6,12,6\}$ beyond the ($\pm$0.02 dB) uncertainty on the statistical convergence of $OASPL$. Considering the solutions were attained in two different runs of the GA with different random seeds, it is reasonable to say they are equivalent solutions, at least from the perspective of the goal function $J$ defined.

Figure 10.

(a) Effect of the actuation schemes found by the GA on jet noise directivity. Red numbers represent $\Delta OASPL$ for the $\{0,0,13,12\}$ solution. All cases evaluated in anechoic conditions. (b) Time series of the $\phi =90^\circ$ microphone as the $\{0,0,13,12\}$ actuators are toggled.

Closer examination of figure 10(b) indicates that the baseline time traces are positively skewed (${\rm skewness} = 0.22$), even though their mean is zero. The skewness is removed in the actuated case. As noted by Greska, Krothapalli & Arakeri (Reference Greska, Krothapalli and Arakeri2003) and Krothapalli, Venkatakrishnan & Lourenco (Reference Krothapalli, Venkatakrishnan and Lourenco2000), the skewness is attributed to crackle events, which are sudden, large deviations from the mean over short time scales. The use of microjets in the GA solution, similarly to what was found in Greska et al. (Reference Greska, Krothapalli and Arakeri2003), eliminates this effect, which may also contribute to a significant fraction of the noise reduction observed.

A closer look at the spectral content captured by the microphones at selected angles is provided in figure 11 in both physical and normalized frequencies, obtained through the averaged periodogram method (Welch Reference Welch1967) with 4096 averages. The Strouhal frequencies ($St_{D_e}=f D_e/U_e$) are normalized by the exit diameter $D_e=27.55$ mm and exit velocity $U_e=431\ {\rm m}\ {\rm s}^{-1}$, estimated through isentropic relations. As is typical, the more downstream angles $\phi =30^\circ$ and $\phi =45^\circ$ in figure 11(a,b) contain higher energy at lower frequencies $St_{D_e}\sim 0.2$, which are related to turbulent mixing noise and are broadband in nature. At these angles, the noise reduction promoted by the GA actuation schemes is lower but is consistent across most frequencies in the spectrum. At very low frequencies ($St_{D_e}< 0.08$), however, the GA solutions are mostly ineffective at reducing very large-scale mixing noise. Noting that this very low frequency part of the spectrum ($St_{D_e}< 0.08$) contains a very small fraction of the total noise energy in the baseline case (0.25 % for $\phi =90^\circ$ and 3.7 % for $\phi =30^\circ$), it was not prioritized during the optimization in face of significantly larger noise sources, such as the screech tone and the BBSAN.

Figure 11.

Effect of GA-based actuation on the noise spectra at different polar directions.

At the two more upstream angles $\phi =60^\circ$ and $\phi =90^\circ$ in figure 11(c,d), a greater reduction in noise is observed at all frequencies. Evidently, this reduction across the entire spectrum culminates in the larger reduction in $OASPL$ at these locations. Also important to note is the disappearance of the screech tones at $St_{D_e}= 0.364$ and $St_{D_e}=0.735$, which agrees with the disappearance of the standing wave observed in the schlieren standard deviation images of figure 7. Note that the energy contained in the screech tones of the baseline case at $\phi =90^\circ$ was 37 % of the total power contained in the spectrum, meaning the elimination of the screech tone would contribute to a $-10\log _{10} (1-0.37)=2.03$ dB reduction in $OASPL$. Thus, although the overall spectrum experiences a reduction in $OASPL$, a portion of the reduction in noise is due to the elimination of the screech tone.

A spectral hump is observed at $\phi =90^\circ$ in both baseline and actuated cases, peaking at $St_{D_e}\sim 0.85$ and $St_{D_e}\sim 1.1$, respectively. This high-frequency broadband peak is typically associated with the BBSAN. In the baseline case, the broadband peak occurs around $f\sim 12.3$ kHz, matching the predicted BBSAN peak by the early model of Harper-Bourne & Fisher (Reference Harper-Bourne and Fisher1977), considering the measured shock cell spacing of 25.7 mm (figure 6). In the baseline case at $\phi =90^\circ$, 59.4 % of the total noise energy is contained within the high ($f>8$ kHz) frequency range, excluding the screech tone peak, indicating the BBSAN is also a noise source worthwhile targeting during the noise optimization process. In the $\{0,0,13,12\}$ solution, the energy in this high-frequency ($f>8$ kHz) range is reduced to 28 % of the baseline value, demonstrating how the GA successfully targeted the BBSAN mechanism to effectively reduce the noise produced by the main jet.

Furthermore, the fact the actuated cases shift the peak frequency of the BBSAN to a higher frequency is further evidence that the mechanism proposed in § 4.2 (i.e. that the extra shocks produced by the microjets increase the wavenumbers of the waveguide modes) plays a role in the shaping of the acoustic spectrum. However, since the shock cell spacings are uneven, it is unclear whether the simple model by Harper-Bourne & Fisher (Reference Harper-Bourne and Fisher1977) still applies. The effectiveness of this actuation scheme on targeting the BBSAN also explains why the GA targeted the $\phi =90^\circ$ microphone during the optimization process, as it was the most readily available mechanism to be leveraged using the microjet locations provided. Utilizing a more downstream location, such as the $\phi =30^\circ$ microphone, for the definition of the goal function may have yielded a solution with more focus on noise reduction at the lower frequencies associated with turbulent mixing.

Also worth discussion is the strong similarity of the spectra between the two GA solutions (red and blue curves in figure 11), as well as the $OASPL$ values in figure 10(a). This similarity would suggest the two actuation schemes, although activating different rings, are accomplishing a very similar overall result in the acoustic field. Further examination of the GA evolution process in the ‘schlieren on’ phase of this experiment indicate that ring R2 may not have been a key contributor to the GA solution. Through the ‘teleport ring’ function in the GA mutation procedure, two rings can be swapped, generating alternative configurations that can be examined. Remembering that the optimal $\Delta OASPL=8.6$ dB for the $\{0,6,12,6\}$ solution in the ‘schlieren on’ configuration at $\phi =90^\circ$, alternative configurations with similar EPR values are found at $\{12,6,0,6\}$ ($\Delta OASPL=4.4$ dB), and $\{6,0,12,6\}$ ($\Delta OASPL=7.6$ dB). Note the former configuration swaps rings R1 and R3, moving the actuators of R3 to a less effective location (R1), yielding significant performance drop on the $\Delta OASPL$ and indicating the 12 actuators on ring R3 are essential to the solution. Conversely, swapping rings R1 and R2 (i.e. configuration $\{6,0,12,6\}$) does not yield a significant performance drop, indicating ring R2 is not as essential to the solution as ring R3 and potentially its presence was a limiting factor on the evolution of the GA in the ‘schlieren on’ experiment, as the maximum number of actuators was limited to 25. Under the light of this observation, one could conclude the ‘anechoic’ GA solution may be slightly more optimal, as it maximizes the available number of actuators at the rings that are most effective (i.e. rings R3 and R4).

An examination of the cases where actuation is provided as a full ring of actuators at ring R3 ($\{0,0,16,0\}$) and ring R4 ($\{0,0,0,16\}$) at a corresponding $SPR=1.7$ can be useful to isolate the effects of the two rings in the ‘anechoic’ GA solution $\{0,0,13,12\}$. The $\phi =90^\circ$ spectra of the single-ring actuation schemes are presented in figure 12(a) in solid magenta and green lines, accompanied by the spectra of the previously discussed GA solutions as dashed lines. It is immediately noticed that the actuation only at ring R3 (magenta line) does not eliminate the screech tone, also slightly lowering its frequency as well as the BBSAN hump peak frequency. The overall levels of the BBSAN hump, however, are significantly lowered in the full R3 case, indicating the addition of new, weaker shock cells positively contributes to broadband shock noise reduction. A lengthening of the first shock cell is also observed when comparing the shadowgraphs of figures 12(b) and 12(c), which is consistent with the lowering of the peak frequencies in the spectrum. Conversely, actuating only ring R4 (green line in figure 12a) increases the BBSAN hump peak frequency, eliminates the screech tone and reduces the length of the first shock cell, as can be noted in figure 12(d). Thus, it appears that actuating the shear layer of the jet is responsible for disrupting the feedback loop that causes the jet to screech, also having a smaller effect on the reduction of the BBSAN noise amplitude. The effects of rings R3 and R4 compound on the GA solution found in anechoic conditions $\{0,0,13,12\}$, resulting in significant reduction of BBSAN as well as the elimination of the screech tone.

Figure 12.

(a) Comparison of the spectra of the GA-based actuation schemes with the single full ring actuation at $\phi =90^\circ$, $SPR=1.7$. All spectra captured at anechoic conditions. (b–d) Shadowgraphs of the first two shock cells for the baseline and full ring cases.

4.5. Effect of $NPR$

Utilizing the optimal GA-based actuator scheme yielded 7.3 dB $OASPL$ reduction at the most effective direction ($\phi =90^\circ$). A follow-up question is how effective this actuation scheme would be at different operational conditions of the main jet. In this section, the effect of $NPR$ will be examined for the baseline and the $\{0,0,13,12\}$ solution obtained in the anechoic GA experiment. The results herein noted also apply very closely to the $\{0,6,12,6\}$ solution, which was also tested for $NPR$ effects but is omitted for clarity of the discussion. Thrust, including potential losses, could not be estimated in the present study as it was designed to focus on acoustics.

For this experiment, a parametric scan of $NPR$ was performed by sequentially opening the main jet control valve and acquiring data for 10 s, while maintaining the remaining conditions fixed (i.e. one scan for the baseline case and another for the actuated case). Between $2.7< NPR<2.9$, an increased number of points was taken to ensure repeatability of the results previously described. The parameter scan is summarized in figure 13 by showing the $OASPL$ measured by selected microphones as a function of $NPR$ for both baseline and GA solution cases. The difference between the cases ($\Delta OASPL$) was computed by linearly interpolating the baseline/actuated data sets prior to computing the difference, as the $NPRa$ of each data set were slightly mismatched. The mismatch did not exceed $\Delta NPR=0.02$ in any case considered.

Figure 13.

Effect of $NPR$ on the $OASPL$ produced by the jet at different polar directions.

Figure 13(d) shows that the peak noise reduction occurred, serendipitously, very close to the $NPR=2.80$ chosen for the experiment. More specifically, the peak reduction of 7.9 dB at $\phi =90^\circ$ occurred at $NPR=2.73$. As is typically observed in C–D nozzles, the sideline noise trend for the baseline case has an ‘N’ shape, with the noise levels increasing for the overexpanded jet and then decreasing as the nozzle approaches ideally expanded conditions, where a local noise minimum occurs as the strength of the shocks is minimized. The $NPR$ where this minimum occurs in this experiment is $NPR=3.45\pm 0.15$, which is slightly different from the design $NPR_d=3.69$. Increasing pressure past this $NPR$ then monotonically increases the noise levels. Actuating the nozzle with the GA $\{0,0,13,12\}$ solution changes this ‘N’ curve into a simple monotonic increase in $OASPL$ as a function of $NPR$, which is observed in all polar directions. At the downstream directions $\phi =30^\circ$ and $\phi =45^\circ$ the actuated cases always reduce noise, even close to ideally expanded $NPR$ values, as is shown in figure 13(a,b). Note in this experiment that the $SPR$ of the microjet actuators is not being increased, meaning the ratio of actuator mass flow with respect to the main nozzle is greatly decreasing as the $NPR$ is increased.

Conversely, a crossover behaviour can be observed in the more upstream microphones $\phi =60^\circ$ and $\phi =90^\circ$. As the $NPR$ is increased towards ideally expanded conditions, the actuation becomes less effective and then becomes detrimental to noise reduction between $3.35< NPR<3.9$, increasing the noise produced by up to 2.1 dB in the worst case at $\phi =90^\circ$ and $NPR=3.45$. This stands to reason as the microjets always induce a bow shock that will lead to a shock train within the jet, which by itself is an important source of noise. When the baseline case does not produce strong shocks, as is the case close to ideally expanded conditions, then actuating adds undesirable noise sources. At underexpanded conditions, the benefit of actuating becomes significantly lower, only reaching 0.5 dB noise reduction at the highest $NPR$ considered of 4.1. As the actuator experimental set-up would need increased supply pressures to maintain similar mass flow ratios or similar momentum coefficients, it is possible that significantly better noise reduction could be achieved with the same actuator distribution found by the GA. The mass flow ratio is estimated to be $\dot {m}_{Total}/\dot {m}_{Nozzle} = 0.9\,\%$ at the most underexpanded case ($NPR=4.1$). It is likely that different optimal configurations of microjet actuators exist for the underexpanded and ideally expanded cases, which would require a dedicated optimization experiment.

The observed trends in $OASPL$ as a function of $NPR$ for the baseline and actuated cases are more readily understood by analysing the spectral content of the corresponding cases. Spectra for representative $NPR$ values are presented in figure 14. Note in all cases the low-frequency turbulent mixing noise is slightly reduced, and this reduction is more pronounced around $NPR=3.0$ as shown in figure 14(b). Also, in all cases the frequency of the BBSAN-associated hump is increased, which is noted in figure 14 by the grey arrows. The case $NPR=3.45$, displayed in figure 14(c) and selected because its baseline $OASPL$ was the lowest in the parameter scan, has a negligible BBSAN content and is likely the closest this real nozzle is to ideally expanded conditions. Evidently, the addition of actuators that introduce shocks introduces a BBSAN-related hump in the spectrum, which is clearly seen as a hump that peaks around 25 kHz. This effect can readily be observed in the long-exposure (10 ms) schlieren photographs of figure 15, which were also captured at the design $NPR$ of this nozzle (3.67), although for the ‘schlieren on’ GA solution $\{0,6,12,6\}$. The introduction of microjets introduces shocks that enable the production of BBSAN that were absent in the unactuated jet. Note this additional noise source is solely responsible for the 2.1 dB increase in $OASPL$ noise levels in the $NPR=3.45$ case, as the remainder of the spectral content (i.e. at frequencies lower than 15 kHz) is lower in energy than the baseline.

Figure 14.

Effect of $NPR$ on the spectra of the $\phi =90^\circ$ microphone for the baseline and actuated cases. Grey arrows indicate BBSAN peak frequency shift.

Figure 15.

Schlieren images (horizontal cutoff) of (a) unactuated and (b) $\{0,6,12,6\}$ actuation at $NPR=3.67$.

At underexpanded conditions ($NPR=4.1$, figure 14d), an appreciable reduction in the BBSAN hump is also observed. Although not investigated herein, it is possible further improvement may be possible through increased actuation mass flow rate. Finally, at highly overexpanded conditions ($NPR=2.4$, figure 14a), the addition of the microjets resulted in an overall reduction in noise ($\Delta OASPL=1.4$ dB) by elimination of the screech tone and reduction in turbulent mixing noise, but the actuator mass flow rate may have been excessive, as the BBSAN levels increased. A parametric scan on the mass flow rate parameter was not performed at this time, but it is reasonable to assume that if the BBSAN noise reduction mechanism is related to the spreading of the shock train there would be an optimal point beyond which additional actuator power would produce bow shocks that are stronger than the original baseline shock, resulting in an increased production of noise.

4.6. Effect of temperature

An experiment at a higher stagnation temperature of $T_0=560\pm 3$ K and $NPR=2.80\pm 0.04$ was performed to understand the effect of temperature on the effectiveness of the actuator schemes found by the GA for a cold jet as described in the previous sections. The cases with $T_0=560$ K will be considered ‘hot’ cases through this section, at a nozzle temperature ratio of $NTR=1.88$, although the stagnation temperature is not as high as is typical in supersonic engines. All cases are measured under fully anechoic conditions. As the actuator assembly materials were not appropriate to run for extended periods of time under the ‘hot’ conditions, the experiments were limited to 5 min, which prevented the deployment of the GA in this part of the study.

The effect of temperature on the noise directivity is presented in figure 16 for both actuation schemes found by the GA. Comparing the red and black lines from the respective hot and cold baseline cases, a general increase in $OASPL$ is observed in all directions, with the largest increase at the most downstream microphone ($\phi =30^\circ$). At the sideline microphone, a marginal increase in $OASPL$ of $0.4$ dB is observed as the baseline jet temperature is increased. Utilizing the actuation schemes encountered by the $GA$ is not as effective in the hot cases, however. A maximum reduction of 4.7 dB in $OASPL$ at the sideline microphone $\phi =90^\circ$ is observed, which is much lower than the 7.3 dB reduction observed for the cold jet. Once again, both actuation schemes perform similarly in the hot case, but the {0,0,13,12} pattern is slightly more effective by ${\sim }0.5$ dB. A lower degradation in actuator effectiveness for the hot case is observed at the downstream stations ($\phi <60^\circ$), with similar $\Delta OASPL$ results when compared with the cold case of figure 10.

Figure 16.

Effect of the temperature jet noise directivity for baseline and GA actuated cases. Magenta numbers represent $\Delta OASPL$ for the $\{0,0,13,12\}$ solution.

To understand the reduced effectiveness of the actuation schemes, a closer look at the spectra of microphones at two different polar angles is presented in figure 17. Both microphones at figure 17(a,b) detect an overall increase in low-frequency turbulent mixing noise for the baseline hot case, when compared with the baseline cold case. At $\phi =30^\circ$, in figure 17(a), the mixing noise increases in amplitude at the higher frequencies, which explains the greatly increased $OASPL$ at this directivity angle. Additionally, the screech tone now radiates towards the $\phi =30^\circ$ microphone, presenting a peak at 6.3 kHz and contributing to the increased noise levels. At $\phi =90^\circ$, in figure 17(b), an increase in the low-frequency mixing noise is observed for the baseline hot case, but the higher frequency BBSAN remains approximately constant. The screech tone slightly drops in amplitude, resulting in a negligible increase in $OASPL$ at this radiation angle.

Figure 17.

Comparison between the spectra of the baseline and actuated cases at two stagnation temperatures.

Comparing the magenta (actuated, hot) and red (baseline, hot) lines in figure 17(b), a significant reduction of $SPL$ through the spectrum can still be observed. However, the drop in $SPL$ is lower in magnitude and does not occur for ultrasonic frequencies ($f>20$ kHz). The screech tones are, once again, eliminated in the actuated case. The BBSAN-related hump is also shifted to significantly higher frequencies, but the lack of effect at the ultrasonic frequencies seems to be responsible for the overall performance degradation observed in figure 16.

As the ‘anechoic’ GA solution $\{0,0,13,12\}$ utilized all 25 available solenoids during the optimization experiment, it was conjectured that using all available actuators in the two downstream rings (R3, R4) would probably be the optimal solution if that constraint was not enforced. Thus, prior to running the hot experiments, a few checks and modifications to the solenoid power supply were performed to enable the usage of two full rings (32 actuators) for a limited amount of time. The directivity plot for the full (R3, R4) rings under hot conditions is compared with the GA solution in figure 18(a). Curiously, using the full (R3, R4) rings ($\{0,0,16,16\}$ in figure 18a) leads to a change in the directivity characteristics of the actuated jet. On one hand, the $\{0,0,16,16\}$ solution causes further reduction in $OASPL$ at the downstream $\phi =30^\circ$ microphone (4.4 dB reduction instead of 3.9 dB reduction). On the other hand, the sideline $\phi =90^\circ$ microphone observes an increase in $OASPL$ when compared with the $\{0,0,13,12\}$ solution (3.6 dB reduction instead of 4.7 dB reduction). Thus, from the $J$ fitness function perspective, the GA solution is indeed better, as there is a directivity trade-off between rings R3 and R4.

Figure 18.

Directivity comparison of the $\{0,0,13,12\}$ GA solution with manually selected actuator configurations utilizing full rings. All cases evaluated under high temperature ($T_0=560$ K).

As observed by Castelain et al. (Reference Castelain, Sunyach, Juvé and Béra2008), a corrugation of the shear layer on the main jet occurs due to the microjets impinging on it, corresponding to ring R4 in the current experiment. This shear layer corrugation was observed to be correlated to a $\sim$1 dB reduction of turbulent mixing noise for a $M=0.9$ jet. In the current experiment, increasing the number of jets on ring R4 from 12 ($\{0,0,13,12\}$ in figure 18a) to 16 ($\{0,0,16,16\}$ in figure 18a) provides a further 0.5 dB noise reduction at the downstream $\phi =30^\circ$ microphone, which would suggest this shear layer corrugation effect may be responsible for a portion of the turbulent mixing noise reduction.

The effect of the individual rings R3 and R4 was also investigated at this stage of the experimental campaign. A plot of directivity for the individual, but fully actuated rings R3 and R4 is presented in figure 18(b) and compared with the baseline and GA solution $\{0,0,13,12\}$ cases. Note that each individual ring causes a reduction in $OASPL$ at all directivity angles, however, the reduction in $OASPL$ obtained by the GA solution $\{0,0,13,12\}$ cannot be fully explained by only one of the rings. In past literature studies (Greska & Krothapalli Reference Greska and Krothapalli2005; Castelain et al. Reference Castelain, Sunyach, Juvé and Béra2008; Zaman Reference Zaman2010), it was very common to use actuation at a ring externally mounted to the nozzle (like ring R4), which presents operational advantages such as interchangeability between nozzles. However, actuating ring R4 is not optimal, yielding only 2.1 dB $OASPL$ reduction at the sideline $\phi =90^\circ$ direction as can be noted in figure 18(b), which is comparable to the results found by Castelain et al. (Reference Castelain, Sunyach, Juvé and Béra2008). Actuating inside the nozzle diverging section, at ring R3, is significantly more effective, yielding 3.5 dB reduction at the sideline direction. Ring R3 is not as effective in the downstream $\phi =30^\circ$ direction, however, yielding only 0.7 dB $OASPL$ reduction in that microphone. Thus, it is a combination of the two rings, such as the GA solution $\{0,0,13,12\}$ case, which yields maximum $OASPL$ reduction across all directivity angles.

The reduced effectiveness of the individual rings R3 and R4 can be broken down when analysing the spectra presented in figure 19, which is shown for $\phi =90^\circ$. Ring R3 (black line) has an appreciable impact in low frequency turbulent mixing noise, as well as in the high-frequency BBSAN region. However, actuating ring R3 does not eliminate the screech tones, although it does reduce their amplitude ($\sim$7.5 dB). Conversely, actuating externally to the nozzle (ring R4, blue line in figure 19) is very effective in reducing low frequency turbulent mixing noise, which further supports the shear layer corrugation effect observed by Castelain et al. (Reference Castelain, Sunyach, Juvé and Béra2008) is related to large scale mixing noise reduction. Furthermore, actuating ring R4 also eliminates the screech tone, but increases the high-frequency BBSAN above the baseline level, which leads to poor $OASPL$ reduction. By actuating both rings with the optimal number of actuators, the GA found this compromise between screech, turbulent mixing noise and BBSAN that is by no means straightforward, reaching the significant reductions in noise levels observed in this study.

Figure 19.

Comparison between the spectra of baseline and individual ring (R3 or R4) cases, measured at $\phi =90^\circ$. All cases evaluated under high temperature ($T_0=560$ K).

Finally, it is worth noting that a GA optimization was not performed with the heated jet in this study. However, it is evident in figure 16 that the noise levels are significantly increased at the $\phi =30^\circ$ direction, reaching 127.4 dB. The $OASPL$ at $\phi =30^\circ$ is thus 10.5 dB higher than at the sideline $\phi =90^\circ$ direction, meaning it poses a greater risk of hearing damage if one considers an aircraft carrier application where noise from heated supersonic jets is of interest. Thus, from an application perspective, it may be more appropriate to define $J$ as a cost function that considers the worst-case noise direction (e.g. minimize $J=\max [OASPL_{actuated,m}]$).