The first flow bifurcation, in channels with a sudden geometry contraction, is controlled through shape optimization to delay the onset of asymmetry. First, we confirm the existence of a pitchfork type bifurcation instability, already reported in similar geometries. The global mode responsible for this bifurcation leads to asymmetric flow for Reynolds numbers beyond a critical value. Second, we propose a global shape optimization methodology to introduce small modifications in the channel geometry that lead to flows with enhanced stability. Our results include three contraction ratios C = 2, 4, and 8, where C is the ratio of upstream to downstream channel widths. The shape optimization aims at minimizing the growth rate of the unstable mode responsible for asymmetry. Sensitivity analysis is used to find an appropriate geometry parametrization, which is defined through super-elliptic curves, and limited to small deformations. Additionally, a dynamically updated surrogate model (based on radial basis functions) is developed to drive the optimization. This substitutes expensive function evaluations, each requiring the solution of a steady Navier-Stokes base flow computation and a solution of an eigenvalue problem (linear stability analysis). Finally, a mode tracking algorithm identifies the eigenmode responsible for the onset of asymmetry during the optimization. The optimized geometries show rounded corners and are stable for Reynolds numbers well beyond the original values. For all contraction ratios, the critical Reynolds number increases by at least 7.9 times with respect to the original values. Three-dimensional simulations confirm that the optimized geometry is more stable than the original when periodic boundaries are used on the side walls. When comparing the drag of the optimized geometry to the original, we obtain a reduction of at least 64%.

A scheme for generating boundary layers is described and applied to an infinite swept wing model with wavy surface deformations. Steady laminar mean flow is extracted directly from solutions of the Navier–Stokes system of equations, which is validated against computations of a compressible boundary-layer method. Furthermore, the routines capture separated boundary-layer profiles, overcoming the constraints of the conventional methods. The stability of crossflow disturbances is investigated using both the parabolized stability equation and linearized Navier–Stokes methods, and the effect of chordwise waviness of variable wavelength, amplitude, and phase is considered. Wavy surfaces are found to influence the growth of crossflow disturbances, suggesting that the onset of transition may also be affected by the variations in the surface geometry.

We derive a discrete framework for the calculation of eigenvalue sensitivity to geometric deformations. We apply the technique to the steady compressible Navier-Stokes and Reynolds-averaged Navier-Stokes (RANS) flows. The analysis enables one to control (reduce or increase) the amplification rate or frequency associated to the least stable global mode, which is identified using stability analysis. A methodology using a discrete framework is proposed, allowing one to recover the gradients in compressible and turbulent flows. The potential of the resulting shape gradients is evaluated on the well-known circular cylinder flow problem and on a RANS turbulent flow scenario to control the buffet onset on a NACA0012 airfoil. The predicted deformations show excellent performance on the stabilization or excitation, and frequency control, of the global modes and for the two cases tested.

Turbine blades operating in transonic–supersonic regime develop a complex shock wave system at the trailing edge: a phenomenon that leads to unfavorable pressure perturbations downstream and can in...

The stability of flow over a complex high-lift configuration with significant regions of separated flow is analyzed. Current state-of-the-art flow solvers encounter difficulties in predicting both the onset of flow separation over similar configurations and the progression of the separated region when the angle of attack is increased. The present analysis provides useful insights into the mechanisms responsible for limiting the maximum lift on multielement wing configurations by relating flow separation with the onset of flow instability. A steady solution based on a finite volume discretization is used as the basic state for the linear stability analysis. The resulting generalized eigenvalue problem has been solved using a Krylov subspace projection technique in the form of the Arnoldi iterative method. This methodology is first applied to a NACA0012 test case at subsonic and transonic conditions. Then, for the first time, the stability of flow over an industrial multicomponent geometry involving the A310 airfoil has been investigated in order to identify the low-frequency instabilities related to flow separation. One important conclusion is that, for both configurations, one unstable mode related to flow separation appears at an angle of attack greater than that corresponding to the maximum lift coefficient condition. Finally, the adjoint problem is solved in order to evaluate the receptivity characteristics and the structural sensitivity of both configurations, identifying the regions of flow that can be manipulated to yield the largest change in the flowfield.