Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called the explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex method, the random restart simplex, Latin hypercube sampling, Monte Carlo sampling and the genetic algorithm. EGM is applied to minimize the net drag power of the two-dimensional fluidic pinball benchmark with three cylinder rotations as actuation parameters. The net drag power is reduced by 29% employing direct numerical simulations at a Reynolds number of 100 based on the cylinder diameter. This optimal actuation leads to 52% drag reduction employing Coanda forcing for boat tailing and partial stabilization of vortex shedding. The price is an actuation energy corresponding to 23% of the unforced parasitic drag power. EGM is also used to minimize drag of the 35. slanted Ahmed body employing distributed steady blowing with 10 inputs. 17% drag reduction are achieved using Reynolds-averaged Navier-Stokes simulations at the Reynolds number Re-H = 1.9 x 10(5) based on the height of the Ahmed body. The wake is controlled with seven local jet-slot actuators at all trailing edges. Symmetric operation corresponds to five independent actuator groups at top, middle, bottom, top sides and bottom sides. Each slot actuator produces a uniform jet with the velocity and angle as free parameters, yielding 10 actuation parameters as free inputs. The optimal actuation emulates boat tailing by inward-directed blowing with velocities which are comparable to the oncoming velocity. We expect that EGM will be employed as efficient optimizer in many future active flow control plants as alternative or augmentation to pure gradient search or explorative methods.

Automated summary

The explorative gradient method (EGM) addresses the challenge of optimizing multiple actuation parameters by alternately performing exploitative and explorative steps, ensuring convergence rate of a gradient based method and exploration of better minima. EGM outperforms other optimization methods in analytical tests and applications to flow control problems.