During wind tunnel testing of the LSLB inlet configurations, the time stamps on the schlieren images and high-speed pressure measurements were not accurately synchronized. Thus, direct correlations between the pressure and schlieren data are not possible. However, if the onset of buzz is captured with both the high-speed schlieren and pressure measurements, a comparison between the time signals can be approximated by aligning the shock fluctuations with the intersection of pressure waves at the inlet entrance. Figure 100 shows an x-t diagram of the static pressure and shock position within the inlet throughout the course of two buzz cycles, starting at a time interval prior to onset. The data in Fig. 100 were obtained using the U4D5 (small split-ramps/small vanes with downwash) single-stream inlet configuration in a Mach 1.7 flow. The inlet geometry is provided along with the transducer locations to help clarify wave propagation and shock oscillations (Fig. 100). Please note that the coarse distribution of static pressure Kulites through the diffuser and cold pipe (Fig. 100a, no transducer between x = 64.8 -
(a)
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307.3 cm (x = 25.5 - 121 in)) results in a substantial interpolation between the centerbody and downstream near-mass-flow plug transducers. The shock position measured from the schlieren images at each of the five heights (heights 1, 2, 3, 4, and 5 corresponding to the centerbody, the centerbody throat, halfway between the throat and cowl tip, the cowl tip, and above the cowl tip, respectively) are included in Figs. 100a and 100b with the same color scheme as displayed in Figs. 91 and 92. It appears that the shock position measured at heights 2 and 3 most precisely aligns with the pressure fluctuations, likely because the flow at heights 2 and 3 is within the streamtube of the inlet (Figs. 91 and 92). In Fig. 100, downstream-propagating (right-running compression or expansion) waves have a positive slope from left to right, while upstream-propagating (left-running) waves have a negative slope from left to right. Using the shock/pressure wave interaction near t = 0.05 s, the shock wave position and static pressure oscillations were aligned with surprisingly high-resolution and accuracy. Iteratively changing the shock- position delay time in Fig. 100b and measuring where the angle of wave propagation intersects the shock helped facilitate the time series alignment to within ±0.0005 s. Measuring the intersection of the shock with additional pressure waves confirms the accuracy of the alignment method.
Figure 100: Contour plot of inlet static pressure against space and time (x-t diagram), during two buzz cycles with corresponding shock wave position at five heights (Figs. 91-92), inlet geometry, and transducer locations included: (a) entire inlet apparatus, and (b) inlet measurements upstream of AIP.
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Figure 100b confirms the hypothesis that the onset of buzz is triggered by separation along the compression spike. This conclusion is reached by the fact that the static pressure is absent of fluctuations until separation results in the transmission of a brief pressure rise downstream from the compression spike followed by an expansion wave as the shock reaches the spike tip and the large separation area reduces the mass-flow rate. The expansion wave propagates all the way to the mass-flow plug upon which it is reflected and returned upstream (Fig. 100a). The exact time of buzz onset is more clearly viewed in Fig. 101, which plots the aligned shock position at height 3 with the static pressure at the upstream Kulite (probe 1, Fig. 88b) in Fig. 101a, the static pressure at the AIP Kulite (probe 8, Fig. 88b) in Fig. 101b, the average stagnation pressure at the AIP (probes 1, 3, 5, and 7, Fig. 88c) in Fig. 101c, and the mass-flow rate at the AIP in Fig. 101d. The mass-flow rate was calculated using the same method as previously discussed without inclusion of the long-pass filter.
Figure 101: Normalized shock oscillations (height 3 in red) over two cycles compared with: (a) upstream centerbody static pressure fluctuations (probe 1, Fig. 88b), (b) AIP centerbody static pressure fluctuations (probe 8, Fig. 88b), (c) average AIP stagnation pressure fluctuations (probes 1, 3, 5, and 7, Fig. 88c), and (d) AIP mass-flow rate.
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Using Figs. 100 and 101 to approximate the onset of buzz at t = 0.008 s, it appears that the initial small compression wave and subsequent expansion wave, do not return to the shock until t = 0.03 s. This period of wave propagation results in a frequency of 45 Hz and is extremely close to a frequency peak in both the pressure and shock wave fluctuation signals (Figs. 94, 95, 97 and 98). This frequency most likely corresponds to the first even mode acoustic frequency since it correlates with the time it takes for a weak wave to propagate the length of the inlet and back. A plausible explanation for the discrepancy between the measured and theoretical first even mode frequency in Table 14 is a small error in the estimated Mach number and/or speed of sound in the inlet. After the return of the first reflected wave, a complex interaction ensues with numerous pressure waves transmitting through the inlet making it difficult to decipher the propagation of a specific wave (Fig. 100). The interaction of pressure waves with the shock can clearly be observed, but following specific waves further into the inlet is challenging past the first buzz cycle.
The shock and pressure oscillations during the first spike-buzz phase are significantly more periodic and regular than the spike-buzz phase of the second buzz cycle due to the reflecting pressure waves (Figs. 100 and 101). Analyzing the first buzz cycle reveals that the dominant spike buzz frequency varies between fsb = 200, 222, and 250 Hz. The binning of the frequency content into these three peaks occurs
because of the temporal resolution of the 2000 fps schlieren images. The significance of this is that it appears that spike buzz creates pressure waves at a frequency between 200 and 250 Hz. Thereafter, these waves enter and travel through the inlet system eventually occupying the even and odd acoustic frequency modes of the duct. Both modes appear to arise due to the variation in acoustic impedance of the inlet entrance as a result of the periodic flow separation.
Looking at the correlation between shock position and pressure measurements in Fig. 101 exposes the phase shift or delay between the signals as the measurement locations increase in distance downstream; this is also apparent in the x-t diagram of Fig. 100. Precise correlation of shock position and mass-flow rate in Fig. 101d confirms the overall analysis and phases of the buzz cycle in addition to the alignment of the shock position and pressure signals. The most downstream shock position matches the maximum mass-flow rate into the inlet and the repressurization phase of the cycle, while a shock location near the spike tip has a low mass-flow rate with a depressurizing inlet. The average static pressure distribution along the centerbody was calculated during choked-flow and spike-buzz using a threshold of one standard deviation above and below the mean mass-flow rate, respectively, as an indicator of pressure points corresponding to each phase of buzz (Fig. 102). The resulting calculations do appear to show the likely presence of a weak secondary shock downstream of the geometric throat inside the subsonic diffuser of the inlet (Fig. 102a) for the choked phase, as indicated by the steep pressure rise immediately downstream
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of the throat, similar to the surface-oil flow visualization in Fig. 93. The reduced pressure at the throat in Fig. 102a also indicates that the flow is continuing to expand at that position and likely chokes. The pressure distribution along the centerbody during spike buzz reveals the possible depressurization of the inlet from its downstream end. However, during spike buzz, the large separation regions near the inlet entrance make it challenging to accurately interpret the static pressure distribution along the centerbody.
Figure 102: Average centerbody static pressure distribution during buzz cycle (inlet geometry in blue): (a) choked phase, and (b) spike-buzz phase.
5.6 Summary and Conclusions
Analysis of the large-scale low-boom inlet with high-speed schlieren imaging and pressure measurements has revealed the dominant frequency of shock wave oscillation at the buzz condition for the single- and dual-stream U0D0 inlets at Mach 1.7 and 0º AOA to be 21.0 Hz and 15.7 Hz, respectively. The best description for the observed buzz cycle in the single-stream inlet was put forth by Trapier et al. [127, 133, 134] using Dailey’s criterion (large separation along the compression surface) [130] for buzz onset and was also applied to the dual-stream inlet buzz analysis by Chima [123]. The description consists of four parts for one buzz cycle; (1) shock advance, (2) spike buzz, (3) shock retreat, and (4) choked flow. The shock wave proceeds upstream during the first part of the buzz cycle (shock advance) due to boundary-layer separation on the centerbody spike creating an unstable shock system. A high-frequency oscillation (spike buzz) is observed during the second component of the buzz cycle resulting from the pulsation/oscillation of the shock wave between a lambda shock and bow shock configuration. This generates large, separated vortices and pressure waves that travel throughout the system. Once the inlet pressure has dropped sufficiently, the shock shifts back downstream (shock retreat) where the inlet experiences choked flow during its repressurization. The shock continues to oscillate during the choked flow part of the buzz cycle due to the returning pressure waves reflected from the mass-flow plug.
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Eventually the compression and expansion waves propagating through the system occupying the even and odd acoustic wave frequencies. Power-spectral density analysis of the shock position time series from schlieren images and high-speed pressure fluctuation measurements reveals the characteristic frequencies associated with each part of the buzz cycle.
Dailey’s [130] driving mechanism for a buzz cycle has been confirmed for the LSLB inlet through the analysis of the single- and dual-stream buzz frequencies by calculating that the ratio of the dominant buzz frequencies for the two inlets is the same as the ratios of their rates of depressurization and repressurization. This investigation showed that both the upstream and downstream VGs had little effect on the inlet buzz cycle, but that Mach number variations had the greatest effect on high-frequency spike buzz oscillations. The primary effect of the VGs was to trigger buzz at a higher MFR, mostly likely by reducing pressure recovery either through increased drag and/or reduced inlet area.
Furthermore, the investigation found that the single best indicator for the onset of buzz in the LSLB inlet was shock position triggering massive flow separation on the compression spike as a result of the incoming Mach number. Pressure fluctuations as indicators for the imminent onset of buzz were not present, and only a sensor locating the shock position/pressure gradient on the compression spike for a given freestream Mach number can provide warning of buzz onset in the LSLB inlet.
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