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 $35^\circ$ 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 $Re_H=1.9 \times 10^5$ 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.

Gradient-Free Optimization in Thermoacoustics: Application to a Low-Order Model

Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms -- the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm -- to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.

A Two-Level Optimization Method for Hypersonic Periodic Cruise Trajectory

Periodic cruise has the potential to improve the fuel-saving efficiency of hypersonic cruise vehicle but is difficult to optimize. In this paper, a two-level optimization method for the trajectory of periodic cruise is proposed. Due to that the periodic cruise trajectory can be divided into an acceleration phase where engine works and a glide phase where engine is off, the two-level optimization method is proposed to optimize the trajectory in each phase by the corresponding level. In the first level, Downhill Simplex Method (DSM) is employed to find an optimal angle of attack in the acceleration phase. Subsequently, the optimal trajectory in glide phase is obtained by the Pseudo-Spectral Method (PSM) in the second optimization level. Numerical results demonstrate the effectiveness of the proposed method. Finally, through comparing with steady-state cruise, it is concluded that periodic cruise makes full use of the change of atmospheric density and lift-drag ratio; thus, fuel saving is achieved.

Gradient-Free Optimization in Thermoacoustics: Application to A Low-Order Model

Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms — the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm — to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.

From Static to Dynamic Modeling of Surfactants Micellization

Micelles and micellization appeal long lasting interest as promising drug carriers. A conventional parameter providing information about formation of micelles is critical micelle concentration (cmc). Its value roughly separates two states of the surfactant solution – namely states with and without presence of micelles. If concentration of surfactants in water solution approaches cmc some physical quantities abruptly change, and this phenomenon is a key to determine value of the cmc. From numerous approaches for determination of the cmc the paper considers the conductivity-based method. But rather than studying the mechanism of micellization that is primarily carried out by the colloid chemists, the paper is focused on the development of an information rich and optimal dynamical model of the conductivity vs. concentration dependence. The model is derived from the solutions of the 1st order differential equation. The optimal model parameters are determined by the downhill simplex algorithm and the cmc is computed on the basis of the curvature of the concentration dependence of the conductivity.