Shape optimization approach for cambered otter board using neural network and multi-objective genetic algorithm

Abstract

The shape optimization approach of the cambered otter board has been performed by the integration of the neural network model and the multi-objective genetic algorithm (MOGA). Because the excellent performance of an otter board is expressed by great lift and less drag force, in this study the lift and drag coefficients were chosen as objective functions to obtain the optimal otter board. The Bézier curve represented the cambered otter board as a simple structure with five control points resulting in the six coordinates, which were adopted as the design variables. The hydrodynamic characteristics of twenty-five otter board models were calculated in a two-dimension computational fluid dynamics (CFD) analysis at an attack angle of 20°. The implicit fitness function in the MOGA algorithm was then obtained by the backpropagation neural network model based on the estimated results of CFD calculation. A set of thirty optimal otter board models were extracted in the optimal solutions of the MOGA, and two optimal models were selected to verify the feasibility of the approach by hydrodynamic and visualization experiments with a comparative hyper-lift trawl door (HLTD). The model 1 showed greatest lift-to-drag ratio before the attack angle of 30° as a high lift-to-drag ratio otter board, and the model 2 showed a large lift coefficient and lift-to-drag ratio than the HLTD before the attack angle of 25° as a large lift force otter board. Through the flow distribution around the model 2, it is observed that the flow separation on the suction side is prevented as a result of less drag owing to the modified shape. In summary, the shape optimization approach is efficient in designing optimal otter board to satisfy supposed needs in otter trawling.

Introduction

Otter boards, or trawl doors, are devices that fulfill the crucial task of ensuring a suitable horizontal net opening at the required depth. They generate a hydrodynamic lift force at the cost of introducing a drag force that adds to the total resistance the trawler must overcome (Fig. 1). Although the otter board is small compared to the trawl net, it would be responsible for roughly 10-30% of the total drag of the entire assembly (otter board, warp, and trawl net). The hydrodynamic efficiency of the otter board, which has excellent spread performance and less drag force at the same time, is often described by its lift-to-drag ratio [1,2,3]. In general, a low lift-to-drag ratio of an otter board results in high trawler consumption. Diminishing the drag of the otter board is a favorable choice for fuel consumption savings by the optimization design of the otter board to improve the lift-to-drag ratio.

Drag force of the otter board can be mainly ascribed to three components: friction, pressure drag, and lift-induced drag. In this work, the otter board is assumed to be operated in the pelagic trawling, not contacting the seabed. The friction drag would not be considered. Secondly, the pressure drag is determined by its shape, generated by the pressure difference between the suction and pressure sides of the otter board. Thirdly, the coefficient of the lift-induced drag is proportional to the lift coefficient square and inversely proportional to the aspect ratio [λ = b/c, defined as span length (b) divided by the chord length (c)] of the otter board [4]. Thus, the non-dimensional lift-induced drag can be reduced by increasing the span length of the otter board with the same chord length as a result of a high aspect ratio. Based on our previous studies, when the aspect ratio is more than or equal to 2, the coefficient of the lift-induced drag of the otter board becomes likely less. Simultaneously, the wing-tip flow formed around the wing-tip plate of the otter board has less contribution to the improvement of the lift force [5,6,7]. Considering the object in this study assumed as a customarily conventional pelagic otter board with the aspect ratio more than 2, reducing the pressure drag determined by the geometry is to be the aim through modifying the otter board with a high lift-to-drag ratio.

Many modern otter boards are the simple design, improved through practical trials until they work well enough to be used commercially. Meanwhile, model experiments are conducted over the years to improve the hydrodynamic performance of the otter board. However, these methods are time-intensive and costly. Recently, a computational fluid dynamic (CFD) approach is used to design the otter board. The feasibility of the CFD analysis has been confirmed in several studies [4,8]. Coupled with the CFD analysis, some optimization methods using local surrogate models [9] and multi-objective genetic algorithm (MOGA) [10] were proposed for multi-element or biplane type otter board. However, the fundamental and customarily monoplane type otter board has not yet mentioned. And few attempts of proof work are conducted with experimental data, compared with those obtained by the optimization methods.

In this study, the shape of a monoplane type otter board was represented using the Bézier curve, completed by five control points on the suction side of the otter board. Three control points were considered as design variables, whose level was five in its upper and lower limits. The lift and drag coefficients (C_L and C_D) of all twenty-five models designed by a five-level orthogonal array were calculated in CFD analysis. Based on those results, an implicit fitness function between the design variables and lift/drag coefficients was obtained using a neural network model. For the optimization formula, lift and drag coefficients were employed for the objective function such that C_L was maximized, and C_D was minimized. After that, a multi-objective genetic algorithm (MOGA) was used to produce new otter boards whose hydrodynamic characteristics were predicted by the above fitness function, and to select the superior model which meet the optimization formula in every generation. Finally, thirty optimal otter board models were obtained. Two representative models from the thirty optimal models were selected to confirm the feasibility of the new shape optimization approach, termed as model 1 and model 2. Hydrodynamic experiments of model 1 and model 2 were conducted in a flume tank, compared with a model as the hyper-lift trawl door (HLTD) [11,12]. Moreover, visualization experiments of the flow field around the optimal and comparative otter boards using particle image velocimetry (PIV), were further conducted to explain the difference in drag characteristics generated by the shape.