1. Loginov et al (2006) 2.95 2046 0.00205 5.19 Wu & Martin (2007) 2.9 2400 0.00217 4.74 Bookey et al (2005) 2.9 2400 0.00225 5.51 Ringuette et al (2009) 2.9 2400 0.00217 5.49 Zheltovodov et al (1990) 2.95 1826 0.00179 5.3 Table 1. Relevant parameters of simulations and experiments that the present turbulent boundary layer are compared against, in figure 9. See original references for the definition of Reθ.
2. Figure 10 presents a few more comparisons using data from Bookey et al (2005), Ringuette et al (2009), and those reported in Loginov et al (2006). Profiles of streamwise velocity u, density ρ, temperature T and Mach number M are plotted against y/δ, δ being the local boundary layer thickness (based on 99% u/u∞). Theagreementisreasonable,indicatingthatroughness-inducedtransitionresultsinafullydeveloped turbulentflowthatcompareswellwith availableresults. Thecomparisonsalsoshowthatthe flowisturbulent far upstream of the corner. By x = 6.5, for example, the profiles appear turbulent and show good agreement (figure 10). Lastly, transition appears to begin away from the wall (as seen by the unsteadiness in the snapshots, figure 7), and is reflected slightly downstream in the skin friction curves. This observation reflects the inherent difficulty in characterizing a `transition location' for unsteady transitional flows.
3. The incoming boundary layer thickness is δ ∼ 0.022 inches, and is one length scale in this flow. This however, is specific to the problem setup. The length scale that allows comparison across different simulations/experiments is the boundary layer thickness at the location of the corner, in the absence of the corner, indicated here as δ0. In the present case, δinflow/δ0is about 0.25. Figure 11 shows δ (computed as the y location of 99% u/u∞) plotted against the streamwise distance starting from the end of the roughness strip to the location of the corner, from the simulation that did not include the corner. δ is normalized by δ0. Past x = 6.0 where the flow becomes turbulent, δ rises steadily acrossthe domain, and the difference is significant. y+1001011021030 u u∞,ρρ∞,TT∞,Mx 5 6 7 8 9 Figure 14. Iso surfaces of Q criteria, colored by streamwise velocity. Figure shows turbulence in the boundary layer and the change in length scales through the interaction region. (Cartesian) distance from the present simulations. The solution shows an increase in wall pressure upstream of the corner, a plateau, and the recovery to the post-shock pressure downstream. The figure also shows experimental results from Bookey et al (2005), Ringuette et al (2009), Settles et al (1979), and DNS results of Wu & Martin (2007). Note that the agreement is reasonable. Figure 16 also shows the variation of pressure variance (√pp/pwall)withstreamwisedistance. AvailabledatafromRinguetteetalandWu& Martin (extracted from Ringuette et al) is also plotted for comparison. The curve shows a peak upstream of the corner, a decrease and another peak downstream of the corner. The increase in pressure variance is a consequence of the shock-foot motion (Loginov et al 2006). The peak p p agrees reasonably with the experiment.
4. the location corresponding to each profile, as distance from the corner xc. Up to and including xc= 0, the wall-normal coordinate is the same as the Cartesian y coordinate. Thereafter, the profiles are taken normal to the wall and are hence at an angle of 24◦with the Cartesian y axis. Mean velocity profiles at xc=-10δ0are similar to that expected of an undisturbed boundary layer. Closer to the corner, the flow begins to separate and the velocity profile indicates a decrease in the near-wall momentum. There is also a small reverse velocity observed. Past the corner, the velocity field recovers, and the profiles show an increase in the near-wall momentum and a filling up of the profile. Note that the peak velocity post-corner is less than the incoming streamwise velocity u∞. The velocity profiles shown here are qualitatively similar to those presented in Loginov et al (2006), even as the exact locations of the profiles are different. One feature of this flow field is an increase in the turbulence through the shock, as presented by Smits & Muck (1987) and Andreopoulos et al (2000). Figure 18 shows this behavior using u u and v v . The increase in turbulent intensities is significant starting at about xc= -3δ0, and the location of the peak moves farther from the wall. The turbulent intensities remain high through the separation region and post-corner. Only by about x = 10δ0do the intensity peaks appear to decrease back towardthe pre-cornerlevels. Also, turbulent activity is observed over a significantly larger ynormalextent compared to the incoming flow.