Nonlinear Optimization in High-Speed Boundary Layers: The Most Unstable Nonlinear disturbances & Robust Flow Design
Abstract
Laminar-to-turbulence transition in high-speed flows is a fundamental scientific problem with significantimplications on drag and heat transfer. Its importance has motivated researchers to investigatethe various pathways whereby the flow can break down to turbulence. These studies invariablystart from the amplification of either one or a weighted superposition of linear instability modes,and proceed to evaluate their growth, interaction and breakdown to turbulence. As a result of thesensitivity of transition to the disturbance environment, changes in the initial perturbation can leadto unpredictable changes in the breakdown mechanism and location. These difficulties exacerbatethe challenge of robust flow design and control. In the present effort, we adopt a different approachto the study of transition, which does not suffer from these difficulties. Instead of starting from linearinstability modes, we evaluate the nonlinearly most dangerous disturbance. This perturbationis the most potent initial disturbance that (i) satisfies the full nonlinear Navier-Stokes equations; (ii)undergoes the fastest energy amplification; (iii) and undergoes the fastest breakdown to turbulence.It provides a minimum bound on transition Reynolds number and, as such, a benchmark for robustflow design. We also perform nonlinear shape optimization for robust designs, with stability guaranteesindependent of the disturbance environment. The theoretical and computational predictionswill be paralleled by an experimental campaign at the U.S. Air Force Academy in order to verifyour theory and demonstrate its applicability in real high-speed flows. The experiments will be performedin the Ludwieg tube test facility, at Mach 6. A novel design of the fast-acting piston valvewill enable us to vary the background noise level and examine the impact on transition location,in both the reference and optimized models, across the operating range of Reynolds numbers. Thecombined theoretical (formulation of the optimization problem), computational (nonlinear simulationsof forward and adjoint equations) and experimental (Ludwieg tube testing) campaign willensure that the proposed activity yields substantive progress in transition research and robust flowdesign.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 05, 2017
- Source ID
- N000141712339
Entities
People
- Tamer A. Zaki
Organizations
- Johns Hopkins University
- Office of Naval Research
- United States Navy