Large Back Pressure Ratio Results

3.5.1 Mean Results

Time-Averaged SSV Results

The results of the time-averaged SSV are shown for the W-B interaction atα= 24°in Fig. 3.10. Comparing Figs. 3.3 and 3.10, several important changes are evident in the structure of the SBLI at the elevated compression strength. The shock-induced separation length has increased considerably from α = 12°, with a spanwise average distance between the compression corner and PS of approximately 20 mm. This result is consistent with 2-D interaction theory, as the incoming boundary layer will require a longer turbulent mixing length to overcome the increased adverse pressure gradient associated with the steeper ramp angle [21]. However, the primary SBLI forα= 24° in Fig. 3.10 exhibits a significant degree of three-dimensionality as compared

to the relatively 2-D primary interaction observed for α= 12°. The streamwise interaction size is largest near the centerline of the channel, as the primary separation bulges upstream near z= 0 mm and recedes slightly as the sidewall fences are approached.

By comparison, the appearance of the corner interaction has been altered less substantially than that of the primary SBLI. The corner vortex structure noted for the mild back pressure ratio case is still observable in the top corner of the figure. While the corner separation line has moved upstream for the higher back pressure, the size of the corner vortex at α = 24° is not noticeably different from what was observed atα= 12°, with the streamwise length remaining around 11 mm. The visualization quality in the bottom corner is insufficient to resolve the flow features there.

Unsteady SSV Results

Figure 3.11 shows the time-average of the unsteady SSV carried out forα= 24°. The reattach- ment line (R) has now begun to stand off from the compression ramp leading edge, and is visible on the ramp face. The total separation length (i.e. the streamwise distance between PS and R) has a spanwise mean ofLsep = 45.4 mm. The behavior of the downstream reattachment line can

Figure 3.12: Mean of unsteady SSV in the corner junction of the W-B interaction,α= 24°. be seen to mirror that of the primary separation line, bowing downstream near the mid-span. The features in the upstream portion of the corner interaction are qualitatively consistent with the time-averaged SSV results. Downstream of the ramp leading edge, saddlepoints are visible in either corner junction.

While the primary and corner SBLI units at mild back pressures were fairly isolated, Fig. 3.11 shows that this is no longer true for α = 24°. A zoomed-in view of the top corner of the interaction is shown in Fig. 3.12. The fluid along the primary separation front (i.e. between U and PS) is swept directly toward the nearest sidewall junction. In the reversed flow regions along the floor, it can be observed that most streaklines run toward the nearest sidewall junc- tion/corner vortex. This is similar to the behavior observed by Dupont et al. [70], who also noted heavy spanwise fluid migration away from the centerline in an incident/reflected SBLI. Interestingly, while it is expected that the separation region near the sidewalls should continu- ally accumulate the streakline visualization mixture due to the heavy spanwise fluid migration, it does not become noticably brighter over the course of the video. This suggests that some open ejection mechanism is at play. If the corner vortex is indeed the separation vortex of the glancing sidewall interaction as noted by Bisek [45], it would play such a role.

Fig. 3.13 depicts an isometric view of the sidewall separation relative to the primary and corner separations along the floor plate for the α = 24° case. To attain this FOV the model was mounted from the wind tunnel ceiling. Due to the viewing angle, the sidewall nearest the camera was replaced with a blank to prevent the fence from interfering with the camera line-of-sight. As a result there is a loss of confinement and some quantitative differences in the flow structure are expected, but the qualitative nature illustrates the coupling between the floor and sidewall interactions. As was previously hypothesized, a large portion of the flow entrained by the primary separation clearly migrates toward the corner junction and is ejected by the open separation along the sidewall. This supports the supposition that the corner vortex is actually the footprint of the sidewall separation vortex along the floor plate. This notion is further bolstered by the observation that, with increasing interaction strength, the corner vortex diameter remains relatively constant when compared to the primary separation length. In a glancing interaction, the separation vortex is least susceptible to back pressure induced changes near the VCO. Therefore, if the corner vortex is the sidewall separation vortex footprint at the floor, the features of the corner vortex would also be largely impervious to changes in the back pressure ratio.

The removal of fluid from the primary separation zone near each sidewall may be partially responsible for the local reduction in primary separation length as the corner junction is ap-

Figure 3.13: Oblique view of unsteady SSV mean along the W-B interaction floor plate/sidewall, α= 24°.

proached (i.e. the curvature of the primary separation shock front previously observed in Fig. 3.11). It is not currently clear to what extent the sidewall height influences the amount of relief experienced by the SBLI unit along the floor. The current sidewall fences have a height of y ≈ 5δ0. This is expected to be tall enough to preclude substantial changes due to 3-D

relieving effects with additional sidewall height, although further investigations with different fence heights are needed to confirm this notion. The author points out that this relief is not actually equivalent to geometric 3-D relieving, which occurs irrespective of viscous effects. This phenomenon is perhaps more appropriately classified as a form of viscous relieving, as it occurs as a result of a subsonic communication channel existing between the separated flow in the in- teraction and a freestream fluid “sink,” which could effectively accomodate all the mass ejected from the W-B SBLI.

The increased interplay between the primary, corner, and sidewall SBLIs indicated by the unsteady SSV results at α = 24° can be explained logically by considering the effects of back pressure ratio on 2-D SBLIs. In general, higher compression strengths will lead to larger sep- aration bubbles [27]. A larger separation bubble translates to a larger subsonic zone through which information can readily propagate. As the subsonic regions along the floor plate, sidewall and corner junction become large enough to combine, the interactions accordingly communicate and a large increase in three-dimensionality is observed. This suggests that the SBLIs along the floor, corner junction and sidewall can no longer be considered distinct entities. From an inlet unstart perspective, the α= 24° case has begun to resemble the globally coupled SBLI system observed during the propagation phase, at least in a mean sense.

Mean Pressure Profiles

Figure 3.14 displays the normalized mean wall pressures at each transducer position along the centerline and corner junction of the W-B interaction at α= 24°. The previous time-averaged SSVs of this configuration revealed that the separation shock is pulled out at the centerline and that the corner separation lags behind slightly at a distance downstream. This is also observed

in the mean pressure profiles of Fig. 3.14, which show that the upstream influence of the primary SBLI occurs well forward of the corner SBLI. Two distinct pressure gradients separated by a kink are observable in the primary interaction profile - a larger pressure gradient region exists between −40 _/x /−20 mm that corresponds to the intermittent region of the SBLI, with a weaker pressure gradient region occuring forx'−20 mm. The transition between the steep and shallow pressure gradient marks the approximate point of mean flow separation [21], which is consistent with the centerline PS location indicated in the figure. The shallow pressure gradient downstream of separation can be attributed to the inability of the overhead free shear layer to withstand additional compression [21].

In the corner SBLI, the upstream influence and intermittent region of the interaction were measured, but transducers were not placed far enough downstream to measure the downturn occuring due to the separation of the boundary layer. The pressure gradient in the upstream portion of the corner interaction appears similar to what was observed in the centerline pressure profile. Comparing Figs. 3.10 and 3.14, it appears likely that a separation kink in the corner pressure profile may occur around x ≈ −10 mm. Pressure measurements conducted for the sidewall-mounted model in Chapters 7 & 8 will address this uncertainty.

3.5.2 Unsteady Results

RMS Pressure Profiles

The centerline and corner RMS pressure profiles for the W-B compression ramp SBLI atα= 24° are shown in Fig. 3.15. Note that the RMS pressure at each transducer is again normalized by its respective mean in Fig. 3.14 to enable direct comparisons of transient pressure magnitudes at different streamwise positions. Considering the trends inσp/pw for this elevated back pressure ratio, it can be observed that they are qualitatively consistent with the growth of the shock- induced separation observed in the SSVs. Both the primary and corner intermittent regions (identified by the most upstream peak in σp/pw) have shifted upstream. The locations of the intermittent regions occur just upstream of the local separation point from the time-averaged SSV of Fig. 3.10 in both the primary and corner SBLIs. Curiously, a secondary region of elevated σp/pw is observable in the centerline profile near x ≈ −5 mm. This second peak is interesting because it does not correspond to the physical location of a distinct flow feature in the SSV results. This may indicate that some lifted fluid structure may be influencing the unsteady loading at the wall, as will be explored further subsequently. The downstream peak in the corner profile is now clearly shifted forward of the compression corner, and corresponds approximately to the downstream periphery of the corner vortex structure observed in Fig. 3.10. Given that the sidewall interaction in Fig. 3.13 is clearly separated, it is probable that the forward and rear peaks correspond to the front and rear legs of the λ-shock system along the sidewall [38, 40]. The unsteady loading magnitude at both spanwise locations is considerably larger than was observed for theα= 12°case, a finding consistent with the observations made by Dolling & Or [28] as back pressure/mean separation size increased.

The RMS pressure curves depicted in Fig. 3.15 also enable the determination of length scales that will later prove useful for the frequency normalization of the unsteady pressure power spectra. Here, the separation length Lsep is defined as the streamwise distance from the compression ramp leading edge to the centerline intermittent region. As was noted in Sec.

Figure 3.15: RMS pressure profiles for the W-B interaction, α= 24°.

3.4.2, the two distinct peaks in pressure fluctuation present in the corner lend themselves to the definition of a separate vortex length scale Lv, which is the streamwise distance between the upstream and downstream peaks. Table 4 compares the values ofLsep and Lv forα= 12° and 24°. The length scales indicated in the table are consistent with the time-averaged SSV results, withLsep increasing andLv remaining relatively constant with increasing values ofα.

Pressure Power Spectra

Power spectral densities of the primary and corner W-B SBLI intermittent region signals (up- stream peaks inσp/pw) atα= 24°were computed in order to gain insights into the development of the characteristic separation shock motions with increasing back pressure ratio. The results

Table 3.3: Values of Lsep and Lv discerned from the RMS pressure profiles for the W-B inter- actions.

α Lsep Lv 12° 8.0 mm 7.3 mm 24° 29.4 mm 11.3 mm

are displayed in Fig. 3.16. The distance between the compression corner and the centerline RMS peak shown in Table 3.3 (Lsep = 29.4 mm) was used in the determination of the Strouhal number, which is also displayed. A comparison of Figs. 3.7 and 3.16 reveals that both the pri- mary and corner SBLIs exhibit spectral shifts toward lower frequencies for the higher ramp angle. This is generally consistent with what has been recorded in 2-D SBLI compilations [3], as the length of scale of the separation shock motions should increase in proportion with the streamwise separation length. Interestingly from Fig. 3.16, the dominant corner frequency for theα = 24°case also occurs very near where the primary SBLI begins to exhibit spectral decay at higher frequencies, although it remains to be seen if this result is physically meaningful.

While Lsep is understood to be the appropriate frequency normalization length scale for 2-D SBLIs [3], uncertainty still remains regarding the choice of a characteristic length for the frequency scaling of 3-D interactions. Previously it was shown that for the α = 12° case both Lsep and Lv produced values of peak Strouhal number consistent with 2-D SBLI literature, withLv providing slightly better agreement with LES simulations in terms of scaling the max- imum corner shock unsteadiness frequency. To determine whether these length scales are still

Figure 3.16: Pressure power spectra comparison for intermittent regions of W-B interaction, α= 24°.

applicable for the highly 3-D W-B SBLI case at α = 24°, Fig. 3.17 graphically compares the Strouhal number spectra of the primary and corner intermittent regions at each back pressure usingLsep and Lv. The unsteady signal power is normalized by its maximum value to allow for easier comparsions between the spectra. Figure 3.17(a) shows that the low-frequency portions of the primary intermittent region power spectra collaspse fairly neatly when normalized by Lsep, which suggests that the length scales of the primary separation shock motions at the centerline scale with the local separation bubble size. In Fig. 3.17(b) the corner intermittent region fluctuations for α = 12° and 24° are scaled by the RMS-discerned vortex length scale Lv. It can be seen that while the the shapes of the corner separation shock spectra remain similar between the two ramp angles, the spectrum for α= 24° is shifted toward slightly lower peak Strouhal numbers. This suggests that the corner separation shock is exhibiting motions of a lower frequency than can be explained by the slight increase in the corner vortex length observed in Table 3.3. This may be indicative of an increased interplay between the primary

(a) (b)

Figure 3.17: Comparison of Strouhal number spectra based on Lsep and Lv values from Table 3.3 (a) centerline intermittent region spectra, scaled by Lsep (b) corner intermittent region spectra, scaled byLv.

and corner SBLIs, where some low-frequency content from the interaction along the floor plate is spilling over into the corner junction. This would be qualitatively consistent with the heavy degree of spanwise flow toward the corner junction observed in the separation bubble in Figs. 3.12 & 3.13, but this is difficult to confirm from pressure data which was acquired at a single point in a highly 3-D flowfield.

A Note Regarding Two-Point Coherences with Separation Shock Unsteadiness

In a previous work of the current author [61] two-point coherences with the separation shock motions at the centerline/corner junction of the W-B interaction were performed at α = 24°. It was noted that the coherence spectra of the primary and corner separation shocks began to resemble one another for larger inviscid shock strengths, and it was therefore proposed that the centerline and corner interaction would respond as a single unit to perturbations [61]. In retrospect, this analysis was flawed in that the reference transducers were placed too close to one another, with a streamwise separation of only ∆x = 4.5 mm between the sensors. This placement was acceptable for the α = 12° W-B case, which has fairly short intermittent re- gions. However, as the separation size increases so does the intermittent region length, and it subsequently becomes necessary to increase the streamwise distance between sensors to pre- clude over-estimation of two-point coherences between transducers with similar intermittencies (i.e. comparing shock motion to itself). That the magnitude of the coherence spectra in Ref. 61 gradually increases with compression strength regardless of reference transducer location sug- gests a larger streamwise spacing was needed. Details on the determination of an appropriate minimum streamwise spacing for two-point coherences are discussed in Appendix A.6.