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Chapter 4 Fundamental Investigations of Half-Isolator Compession Ramp

4.3 Computational Setup

4.6.4 Cross-Correlation Analysis

In order to better characterize the origins of the characteristic separation shock motions, two- point cross-correlations were performed between the pressure signals at the intermittent region

with those at other locations for various compression ramp configurations. Figure 4.21 shows an example of the streamwise development of cross-correlation with the intermittent region for the taller α = 20° compression ramp interaction. The time-lag between the signals, τ, is given in ms. The ordinate, ρ(x, y), is the correlation coefficient at a given time-lag between the intermittent region signal and the streamwise station noted above each curve. A value of unity indicates perfect correlation, whereas a value of negative unity suggests signals which are perfectly anti-correlated. A negative time-lag indicates that an event in signal x temporally preceded an event in signal y.

Each cross-correlation curve in Fig. 4.21 exhibits two modes. The first is broad, typically occuring in therange of τ ≈ −1−1 ms. A second sharp mode exists atop the first at much shorter time-lags. Brusniak & Dolling [56] performed a similar analysis beneath a blunt fin SBLI, and showed that the broad mode corresponds to the low-frequency separation shock motion discussed at length previously. The second mode was found to be due to the overhead passage of turbulent boundary layer structures; that this sharp mode continually occurs at negative time lag for each station in the present work is consistent with that idea. For the station beneath the incoming boundary layer at x=−39 mm, relatively little correlation exists in the broad mode, which is in line with the diminishing role of the incoming boundary layer in driving separation shock motions for a larger separation. As the intermittent region is approached, the broad mode correlation increases. Interestingly the broad mode undergoes a sign change somewhere between −15 mm < x < −6 mm, this also occurs in every other computed cross-correlation profile. In the interest of completeness, the streamwise development of the maximum broad mode cross-correlation value,ρ(x, y)max, is shown for various compression ramp configurations in Fig. 4.22. The cross-correlation coefficient is unity by definition at the intermittent region, therefore those points are omitted from each profile. Brusniak & Dolling [56] called the location where the broad mode crosses zero a transition point. Physically, the broad mode correlation sign change implies that when pressures beneath the intermittent region are high (indicating an upstream motion of the separation shock wave), the pressure beneath the separation bubble

Figure 4.22: Maximum broad mode values of cross-correlation between separation shock mo- tion and pressure fluctuctuations at various streamwise stations for various compression ramp angles.

is low. This was attributed to a separation bubble vortex “ground effect” (i.e. the separation vortex strengthens resulting in decreased pressures when the separation shock travels upstream). Similarly, Gramann & Dolling [35] showed that the pressure fluctuations between the separation and reattachment shock feet were anti-correlated, consistent with the “breathing” motion of the separation bubble pushing the separation and reattachment points in opposite directions simultaneously.

4.7

Summary

Experiments and computations were performed for a negatively curved compression ramp SBLI at a freestream Mach number of M∞ = 2.5 to determine the extent to which axisymmetric

confinement affected the mean and unsteady structure of the shock-induced separation region. Unsteady SSVs and PSP-based wall pressure measurements indicated significantly increased values ofLsep/δ0and a more severe adverse pressure gradient for the H-I interaction as compared

RANS simulations and PLS imaging confirmed outer shock strengths in excess of the 2-D oblique limit for the H-I SBLI, which occur due to the combined influence of a streamwise area contraction effect and shock-shock interactions. The severity of these mechanisms scales with a confinement parameter,h/R, as validated by experiments at different ramp heights and constant angle for the H-I interaction. Because the captured streamtube of the H-I interaction is not completely enclosed, the effective confinement parameter reduces with distance away from the midspan due to 3-D relieving. This leads to a circumferential variation in compression strength and a swept outer shock structure. While these negative curvature confinement effects do not significantly alter the static pressure rise across the separation from that of a 2-D case, they do cause a stronger adverse pressure gradient downstream of the compression corner. This increased adverse pressure gradient may necessitate the development of a higher peak velocity on the dividing streamline and a larger separation length, similar to what has been observed for SBLIs in rectangular channels [46, 78]. An additional constriction of the virtual throat at the H-I SBLI exit was also ascertained. The effect of this area reduction is in an increase in the mass being carried toward spillage by the separation bubble, which may also result in larger Lsep values given similar wall pressure distributions across the interactions.

High-frequency WSP transuducer measurements of the H-I SBLIs at different ramp angles and heights revealed findings largely consistent with expectation from the SBLI interaction literature; larger separations were observed to lead to higher amplitude, lower frequency tran- sient mechanical loads associated with the intermittent motions of the separation shock foot. Strouhal number scaling by the streamwise distance between the compression corner and the region of peak unsteady pressure was found to collapse the intermittent region power spectra into a range representative of 2-D SBLI unsteadiness. Two-point coherence and cross-correlation computations with the intermittent region signal revealed the motions of the separation shock are driven by the classical expanding/contracting motions of the separation bubble, and that this mechanism increases in prominence as the shock-induced separation size grows.