2016/02/10 by Outi Tammisola, Tammisola, Outi · 1 citation
Engineering · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Lattice Boltzmann Simulation Studies
paper · pdf · doi:10.48550/arxiv.1602.03378
openalex publication_date 2016/02/10 · openalex created_date 2022/08/12 · openalex updated_date 2026/07/28
A method to find optimal 2nd-order perturbations is presented, and applied to\nfind the optimal spanwise-wavy surface for suppression of cylinder wake\ninstability. Second-order perturbations are required to capture the stabilizing\neffect of spanwise waviness, which is ignored by standard adjoint-based\nsensitivity analyses. Here, previous methods are extended so that (i) 2nd-order\nsensitivity is formulated for base flow changes satisfying linearised\nNavier-Stokes, and (ii) the resulting method is applicable to a 2D global\ninstability problem. This makes it possible to formulate 2nd-order sensitivity\nto shape modifications. Using this formulation, we find the optimal shape to\nsuppress the a cylinder wake instability. The optimal shape is then perturbed\nby random distributions in full 3D stability analysis to confirm that it is a\nlocal optimal at the given amplitude and wavelength. Furthermore, it is shown\nthat none of the 10 random wavy shapes alone stabilize the wake flow at Re=50,\nwhile the optimal shape does. At Re=100, surface waviness of maximum height 1%\nof the cylinder diameter is sufficient to stabilize the flow. The optimal\nsurface creates streaks by passively extracting energy from the base flow\nderivatives and effectively altering the tangential velocity component at the\nwall, as opposed to spanwise-wavy suction which inputs energy to the normal\nvelocity component at the wall. This paper presents a fully two-dimensional and\ncomputationally affordable method to find optimal 2nd-order perturbations of\ngeneric flow instability problems and any boundary control (such as boundary\nforcing, shape modulation or suction).\n