Análisis del Equipo de Protección Auditivo

The uncontrolled flow configurations examined have helped to detail a number of the less well understood aspects of normal SWBLIs.

Firstly, by varying the position of the normal shock relative to the di↵user, the strong influence of the post-shock geometry and therefore post-shock adverse-pressure-gradient has been documented. By moving the position of the shock wave from far upstream to the di↵user entrance, it has been demonstrated that the positioning of the shock relative to the subsonic di↵user is critically important.

When the shock is far enough upstream, in this case around 6 o, of the di↵user, the flow is relatively benign, with little, if any, separation at centre-span. Wall-pressure measurements indicated that the adverse-pressure-gradient from the shock and di↵user are separated in space and that prior to the di↵user entrance the interaction did not vary from that of the constant area duct. In addition to this, the flow visualizations do not look dissimilar to the constant-area duct case, and these are shown here in figure 11.1 to illustrate this. The fact that the flow with the shock in position 1 behaves similarly to that in the constant-area duct case is further evidence that the adverse-pressure-gradient from the downstream di↵user is having little influence on the SWBLI.

The reason why the floor boundary layer does not separate at this Mach number, although Mach 1.4 is higher than the traditionally accepted limit of Mach 1.3, can be nicely illustrated using the plot of shock-induced separation limit based on geometry presented by Bruce et al. (2011). Adding the configuration examined here to this plot results in a position below the line which demarcates unseparated and separated flow. This fact is shown in figure 11.2.

However, when the shock is moved downstream to position 2, where the shock is only o upstream of the di↵user entrance, the flow is entirely di↵erent to that of the constant-area duct. The corner separations become very large and extensive separation is introduced in the centre-

Chapter 11. Further Discussion

span region. The cumulative detrimental e↵ect of the shock-induced pressure rise and di↵user pressure rise in quick succession gives the boundary layer little time to recover and the boundary layer separates in the di↵user.

Further movement of the shock downstream to position 3 results in a flow where the two pressure rises have e↵ectively merged. As a result, centre-span separation occurs underneath the shock due to the combined e↵ect of the shock and di↵user. Although the strength of the shock itself remains unchanged—the incoming Mach number is still Mach 1.4—the combination of the two adverse-pressure-gradients results in a very strong interaction with a substantial length of fully reversed flow.

While the minimum distance required between the shock and the di↵user for the floor bound- ary layer not to separate has not been determined, it must lie somewhere between o and 6 o for this configuration.

The importance of the downstream area variation has consequences for the shock-induced separation limit predicted by Bruce et al. (2011). Unfortunately, figure 11.2 does not in any way take into consideration the influence of downstream pressure gradients. For this reason, figure 11.2 cannot be used as a definitive estimator of shock-induced separation. The importance of downstream geometry indicates that it may not even be a good estimator as the position of the line dividing attached from separated interactions will inevitably move depending on the post shock geometry. Nevertheless, this should not detract from the observed trend by Bruce et al. (2011) of increasing shock-induced separation limit with increasing three-dimensionality, large ⇤/wtunnel.

The changes in the flow-field that are observed as the shock is moved closer to the di↵user clearly demonstrate that this flow-field is not only a function of the upstream Mach number, but also a strong function of geometry. The streamwise area variation and therefore downstream pressure gradient is having a strong bearing on the interaction. While this in itself is not necessary unexpected, the extent of the separation produced, 37 o, and accompanying losses increase, a nearly 5% increase, is undoubtably noteworthy.

Turning our attention to the observed near-wall flow topologies: once conditions are such that separation is initiated in the vicinity of the shock, a comparison of the separation topol- ogy observed here in position 3 with that observed by Sawyer and Long (1982) (presented in figure 3.3) exemplifies a large deviation between the two cases. While the flow-field produced here is dominated by separation originating in the corners, the separation in the case of Sawyer and Long (1982) is initiated near centre-span. It is not immediately clear though why this is the case; clearly there must be a di↵erence in the separation mechanisms at work. Interestingly, however, the separation topologies observed on the sidewalls are not too dissimilar.

To help determine why such a variation in the near-wall topologies exists between these two cases, a number of other studies in which the separation topology was investigated were collated. Some of the surface-flow visualizations by these authors are shown in figure 11.3. During this search of the literature, the author could only find one other study, that of Doer↵er and Dallmann (1989), where a similar flow topology was obtained to that observed in this investigation. Two examples of typical flow visualizations obtained by Doer↵er and Dallmann (1989) are shown in figure 11.3. The surface flow topology of figure 11.3a most closely resembles the flow topology obtained here in positions 2 and 3; figure11.3b is only included for completeness because a

Chapter 11. Further Discussion

corresponding topological interpretation was provided by the authors and is shown here in figure11.3c. The topologies of Doer↵er and Dallmann (1989) are quite similar to those obtained here: much like in this investigation, separation is initiated in the corners; the centre-span flow is entrained into the foci on either side of the centre-line; and the separation is terminated by a single separation saddle point (in the symmetric case).

Other than the investigation of Doer↵er and Dallmann (1989), in instances in the literature where surface-flow visualizations were available, the flow topology tends to look more similar to that obtained by Sawyer and Long (1982). Two further examples of this type of topology are shown in figure 11.3. These topologies shown in figure11.3d and 11.3e and f were performed by Zare Shahneh and Motallebi (2009) and Schofield (1985) respectively. In each of these cases, flow separation is initiated at centre-span and the reversed flow near the initial separation line travels towards the two sidewalls before being entrained into a focus on each side. In these cases the foci rotate in the opposite direction to the flow-fields presented here and those of Doer↵er and Dallmann (1989).

To determine why such topological variations exist, the test conditions and geometric pa- rameters for this investigation is compared with those of the other investigations presented in figure 11.3 in table 11.1.

Table 11.1: Test conditions for a variety of transonic SWBLIs

Investigation M₁ configuration Re_⇥10 6 C ⇤/wtunnel AR

This investigation 1.40 spillage-di↵user 31.5 0.13 6 0.93

Sawyer and Long (1982) 1.54 constant-area duct 10 0.16 4.5 1.20

Schofield (1985) 1.40 duct-di↵user 30 0.08 3.7 1.8

Doer↵er and Dallmann (1989) 1.43 2D bump 16.7 0.18 6.4 0.4

Zare Shahneh and Motallebi (2009)

1.40 duct-di↵user 16 0.23 6 1

Inspection of table 11.1 demonstrates, unsurprisingly, that all these investigations were per- formed under di↵erent conditions. However, there is one factor that di↵erentiates this investi- gation and that of Doer↵er and Dallmann (1989) from the others, and this is the wind tunnel aspect ratio. While this investigation and that of Doer↵er and Dallmann (1989) utilized a work- ing section where the tunnel is taller than it is wide (AR < 1), all the other utilized facilities with a working section wider than they are tall (AR >1). These results indicate that the wind tunnel aspect ratio is influential in the establishment of the separated flow topology. Neverthe- less, following this argument further one might expect the sidewall topology of a configuration with AR >1 to be similar to that of the floor flow forAR <1, i.e., the separation topology in the entire duct is the same but rotated through 90o. However, this is not the case: for example, the sidewall topologies in position 2 and 3 do not look like the floor flow of Sawyer and Long (1982) or vice versa. The flow physics is more complicated than a direct switch between the floor and sidewall.

What is more, the use of ⇤/wtunnel as a first approximation of the importance of the corner separations used by Bruce et al. (2011) fails to deliver a trend in this instance: the experiment

Chapter 11. Further Discussion

here and that of Zare Shahneh and Motallebi (2009) have a very similar value of ⇤/wtunnel, but the topology is not similar. This is perhaps surprising as it is the prominence of the corner separations which di↵erentiates the two di↵ering topologies.

It is difficult to conclude from the available data why these topological variations exist. The observed trend with aspect ratio cannot be easily explained and requires further examination. It is possible that this trend is a coincidence as only five investigations have been compared. This is unfortunately due to the fact that most SWBLI investigations do not include surface- flow visualizations. What is clear is the strong three-dimensionality in all of these interactions, and this clearly demonstrates the need to achieve three-dimensional measurements whenever possible.

These results have a number of implications for SWBLI studies that are designed to be rel- evant to supersonic inlet aerodynamics. Due to the importance of downstream geometry, the constant-area channel normal SWBLI, which has been widely used as a test-case for inlet SWB- LIs and flow control studies, is unlikely to be a good representation of typical inlet conditions as these rarely include a constant area section. Thus matching the upstream Mach number is not enough as inlets very often have post terminal shock divergence and flow turning. It is therefore important to set up more realistic flow conditions. The flow-field investigated here is thought to be a step in the right direction, because it imposes a more realistic adverse-pressure-gradient (without the added complication of an actual inlet geometry). And it is the adverse-pressure- gradient which is of foremost importance to the flow-field. In addition to this, it has been shown that by altering the shock position relative to the di↵user in this configuration the severity of the adverse-pressure-gradient can be nicely adjusted.

In spite of the advantages to this configuration just discussed, the configuration here ex- hibited very prominent corner separations, which is not necessarily typical of an inlet. The importance of the corner separations here is in large part due to the low aspect ratio of this wind tunnel, and real inlets do not have such low aspect ratios (see figure 6.6). As a result, the flow-field established here has three-dimensional e↵ects that are not typical of most inlet flows—especially axisymmetric inlets which have very little three-dimensionality. Yet, as al- ready discussed, fundamental geometries have an important role to play in helping to improve our understanding of inlet SWBLIs. Hence, it is very important to appreciate corner interactions and their influence on the performance of small-scale geometries. This is important if we are to interpolate e↵ectively from small-scale test data to real inlet performance.

Chapter 11. Further Discussion

inflow ( M_∞ )

scale 2:5 origin of corner flow separation area of low shear stress primarily attached flow

s

s

Figure 11.1: Flow visualizations in the constant-area duct case (Bruce (2008))

Mach number 1.6 1.5 1.4 1.3 1.2 1.1 1 Fully Developed Centre-line Separation Attached flow or Intermittent Separation 0 2 4 6 8 10 δ* w_tunnelx 103 This investigation

Figure 11.2: Experimental shock induced separation limit, Mach number vs geometry ( ⇤/wtunnel); unseparated flows (open symbols) and separated flows (closed symbols); adapted from Bruce et al. (2010))

C h ap te r 11. F u rt h er D is cu ss ion

(a) Doerffer and Dallmann (1989) (b) Doerffer and Dallmann (1989) (c) topological interpretation of the flow in (b)

(f) topological interpretation of the flow in (e)

(d) Zare Shahneh and Motallebi (2009) (e) Schofield (1985)

Figure 11.3: Surface-flow visualizations from a variety of transonic facilities

Chapter 11. Further Discussion