Pressure Field

Figure 5.27 - Pressure ratio (p/p∞) profiles for three sections along surface S1 parameter-ized by the cavityL/H ratio. Left and right columns correspond to angle of attackα of 10 and 20 degrees, respectively.

Figure 5.28 - Pressure ratio (p/p∞) profiles for three sections along surface S1 parameter-ized by the angle of attack α. Left and right columns correspond to cavity L/H ratio of 1 and 4, respectively.

Figure 5.29 - Pressure ratio (p/p∞) profiles for three sections along surface S3 parameter-ized by the cavityL/H ratio. Left and right columns correspond to angle of attackα of 10 and 20 degrees, respectively.

this group of plots, again, left- and right-column diagrams correspond to density ratio for angle of attack α of 10 and 20 degrees, respectively.

It may be recognized from Figure5.29 that pressure ratio profiles inside the cavity are affected not only by the cavityL/H ratio but also by the angle of attack α. It is observed that pressure ratio for theL/H = 1 case presents a similar behavior for three sectionsX_L⁰, i.e., it presents a high value at the top of the cavity, Y = 0, and decreases up to the bottom, Y = -1. However, as the L/H ratio increases from 1 to 4, the pressure ratio decreases close to the cavity backward face, X_L⁰ = 0.25, and increases at the vicinity of the cavity backward face,X_L⁰ = 0.75, as compared to the pressure ratio for theL/H = 1 case. By increasing theL/H ratio, the flow topology inside the cavity changes from that for an “open cavity” to that of a “closed cavity”, as shown in Figures 5.14, 5.15, and 5.16. As discussed earlier, the flow experiences an expansion close to the cavity backward face and a compression close to the cavity forward face. Moreover, by increasing the angle of attack from 10 to 20, these effects on the pressure ratio are more significant.

Proceeding in a manner analogous to the density earlier treatment, Figure 5.30 exhibits the pressure ratio profiles outside the cavities for the same three sections X_L⁰. According to this figure, major differences in the pressure ratio take place inside the shock layer.

In order to account for the angle-of-attack effects, Figure 5.31 illustrates the de-pendence of the density ratio on the angle of attackα, for the same three sections X_L⁰ inside the cavity. In this set of plots, left- and right-column plots correspond to cavity L/H ratio of 1 and 4, respectively. Also, a matter of comparison, results for zero-degree angle of attack, obtained by Palharini (PALHARINI,2010), are shown in this group of plots. It is recognized from this set of plots that pressure ratio increases significantly with increasing the angle of attack as compared to the case for zero-degree angle of incidence. In general, pressure ratio increased one order of magnitude as the angle of attack increased from 0 to 20 degrees. Furthermore, it is worth noting that, for section X_L⁰ = 0.25, pressure ratio decreased as the cavity L/H ratio increased from 1 to 4. Conversely, for section X_L⁰ = 0.75, pressure ratio increased as the cavityL/H ratio increased from 1 to 4.

The consequence on the pressure ratio due to variations in the cavityL/H ratio, for three sectionsX_L⁰⁰ along the cavity downstream surface, surface S5, is demonstrated in Figure5.32. In this set of plotsX_L⁰⁰represents the distance (X−L_u−L) normalized by the cavity downstream lengthL_d. Again, left- and right-column plots corresponds

Figure 5.30 - Pressure ratio (p/p∞) profiles for three sections along surface S3 outside the cavity parameterized by the cavity L/H ratio. Left and right columns correspond to angle of attackα of 10 and 20 degrees, respectively.

Figure 5.31 - Pressure ratio (p/p∞) profiles for three sections along surface S3 parameter-ized by the angle of attack α. Left and right columns correspond to cavity L/H ratio of 1 and 4, respectively.

Figure 5.32 - Pressure ratio (p/p∞) profiles for three sections along surface S5 parameter-ized by theL/H ratio. Left and right columns correspond to angle of attack α of 10 and 20 degrees, respectively.

to angle of attack of 10 and 20 degrees, respectively. Based on this set of plots, it is clearly seen that pressure ratio profiles follow a similar behavior as compared to those presented along the cavity upstream surface, surface S1. They differ from those for the flat-plate case in the shock layer at the vicinity of the cavity corner, i.e., at station X_L⁰⁰ = 0.01. In this small region, the pressure ratio for the L/H ratio and angle of attack investigated is larger than that for the flat-plate case.

In what follows, in order to gain some insight into the pressure field behavior, Fig-ures5.33,5.34, and5.35displays the distribution of pressure ratio,p/p∞, along with streamline traces inside the cavity. This family of plots covers all the cases inves-tigated for cavity L/H ratio and angle of attack α. According to these plots, it is seen that maximum values for pressure ratio take place close to the cavity corner, at surface-S4/surface-S5 junction. It is also seen that, in this region, pressure pis two orders of magnitude larger than the freestream pressure p∞, for the majority of the cases. It should be remarked that this pressure ratio is higher than that observed at the bottom of the cavities, for theL/H ratio and angle of attack α investigated.

As a result, it may be inferred in passing that particular attention should be paid to the cavity forward face in terms of the pressure loads, since the vicinity of the corner represents a zone of strong compression.