Downstream of the linear growth region, nonlinear interactions must be modeled in the study of hypersonic transition physics. The bow shock is very close to the edge of the boundary layer and a quantitative description of the finite shock-layer thickness on transition modeling requires a nonlinear solution.
In addition to the discussions about transition in 2-D and axisymmetric flows, linear theory alone is not so successful as a tool for modeling the physics associated with 3-D boundary layers in which the crossflow instability is observed. Concerning crossflow, the past decade has seen the identification of important factors with our team members providing leadership in many of these discoveries (Saric et al. 2003). (1) Linear theories predict that travelling crossflow waves are more amplified than stationary waves. But, whereas travelling crossflow waves are observed in noisy tunnels, the dominant structure in flight is a stationary crossflow vortex that can only be observed in quiet tunnels. (2) Crossflow vortices show extreme sensitivity ultra small surface roughness near the attachment line. (3) Nonlinear effects and modal interaction play an early and important role because of the presence of stationary co-rotating vortices. These vortices distort the meanflow to include inflection points and these destabilize a high-frequency secondary instability and rapid breakdown to turbulence.
These advances would not have been possible without cohesive groups performing complementary computations and experiments. Our team set a successful precedent studying incompressible swept-wing boundary layers. Integrated experiments and computations resolved the effects of curvature and nonlinearities and validated NPSE (Haynes and Reed 2000; Reibert et al. 1996. Figure 4), and together elucidated a novel idea of applying subcritically spaced, micron-sized roughness (DREs) near the leading edge to maintain laminar flow on a swept wing (Saric et al. 1998). This is being considered for extension to high-speed 3-D boundary layers (Saric et al. 2004. See Sec. 2.4). As we aspire to understand the effects of freestream and surface disturbances in hypersonic flight this kind of collaboration becomes even more critical because detailed measurements are more difficult and costly in these flows.
CFD formulations validated to date demonstrate that if the environment and operating conditions can be modeled and input correctly, NPSE and DNS agree quantitatively with the experiments. To accurately model nonlinear growth and interactions, we propose to develop NPSE and DNS formulations with appropriate thermochemistry nonequilibrium models and the bow shock. Chemistry-model sensitivity results from LST will feed into our formulations, as will the expertise of our team in chemistry and results from T5 and the TAMU Hypersonic Shock Tunnel. It is also proposed to work with M6QT and M3.5QT experiments and receptivity and transient growth activities to establish appropriate initial conditions for NPSE and DNS for hypersonics, including disturbance amplitude and content.
Comparison of NPSE and experimental results for stationary crossflow vortices. Streamwise-velocity contours: experiment (top left), NPSE (bottom left). N-factor comparison (right). LST and PSE are insufficient; NPSE successfully duplicates the experiment.
The expected results are robust NSPE and DNS prediction tools (including initial conditions and thermochemistry models), the identification of relevant physics in all regions of the hypersonic parameter space and the competition and interaction of the mechanisms, and physics-based control strategies. Also, NPSE and DNS will guide the experiments and aid in identifying those effects most important to measure and validate.