Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motion

The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of $St=0.21{-}0.94$ . The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high $St$ required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex ‘rollers’. At low $St$ , these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high $St$ , the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures.

Bio-Inspired Design, Modeling, and Control of Robotic Fish Propelled by a Double-Slider-Crank Mechanism Driven Tail

This paper presents the design, modeling, and control of a three-joint robotic fish propelled by a Double-Slider-Crank (DSC) driven caudal fin. DSC is a mechanism that can use one DC motor to achieve oscillating foil propulsion. Its design is guided by a traveling wave equation that mimics a fish’s undulatory locomotion. After multiple tests, the robotic fish displayed good performance in mimicking a real fish’s swimming motion. DSC mechanism is proven to be an effective propulsion technique for a robotic fish. With the help of another servo motor at the first joint of the fish’s tail, the robotic fish can have a two-dimensional free-swimming capability. In experiments, the robotic fish can achieve a swimming speed of 0.35 m/s at 3 Hz, equivalent to 0.98 body length (BL) per second. Its steering rate is proportional to a bias angle. The DSC benefits the control of the robotic fish by independently adjusting its steering and swimming speed. This characteristic is studied in a hydrodynamic model that derives the thrust within a DSC frame. Besides the dynamic model, a semi-physics-based and data-driven linear model is established to connect bias angle to robotic fish’s heading angle. The linear model is used for designing a state feedback control, and the controller has been examined in simulation and experiments.

To estimation of the Energy Efficiency Design Index (EEDI) for a ship with energy-saving wing devices

В статье приводится оценка индекса проектной энергетической эффективности (EEDI) для судна с энергосберегающими крыльевыми устройствами на встречном регулярном волнении. Вначале на основе предыдущих работ авторов с применением линейной теории поперечных сечений определяются характеристики продольной (вертикальной и килевой) качки судна без крыльев, и такого же судна с крыльями большого удлинения, установленными на днище вблизи оконечностей с целью преобразования волновой энергии в дополнительную тягу. После определения параметров качки судна с крыльями как твердого тела, с применением теории Теодорсена колеблющегося профиля определяется средняя по периоду тяга энергосберегающих крыльевых элементов, совершающих поступательно-вращательные колебания. С другой стороны, в статье находится общее сопротивление системы «судно-крыльевые элементы». При этом применяется метод Холтропа в сочетании с теорие Бейкельмана-Герритсмы. Последняя дает возможность произвести оценку дополнительного волнового сопротивления по найденным параметрам продольной качки судна с крыльями и без крыльев. Затем оценивается значение индекса проектной энергетической эффективности (EEDI) контейнеровоза, снабженного энергосберегающими крыльями на встречном волнении. Исследование показывает, что установка на днище крыльевых элементов может использоваться как один из способов сокращения выброса углекислого газа и уменьшения в соответствии с требованиями Международной морской организации ИМО, значения индекса EEDI для репрезентативных морских условий. In this paper an estimation is presented of the Energy Efficiency Design Index (EEDI) for a ship with energy-saving wing devices in headwind regular waves. At first, based on previous works of the authors, there are determined with use of linear strip theory the characteristics of longitudinal (heaving and pitching) motions of a ship without wings and identical ship equipped with wings of large aspect ratio fitted on the bottom near extremities for the purpose of converting wave energy into additional thrust. After motions of the ship with wings as a solid boy are determined Theodorsen theory of oscillating foil is applied to calculate period averaged thrust of energy-saving wing elements, performing combined heave-pitch oscillations. On the other hand, the paper addresses the problem of determining overall drag of the “wing-plus-wings” system with use of Holtrop method combined with Beikelmann-Gerritsma theory. The latter enables carrying out an estimation of additional wave resistance based on the calculated parameters of the ship longitudinal motions with and without wings. Then follows an estimation of the EEDI for a containership equipped with wings in headwind regular waves. The study shows that fitting wing elements on the ship bottom can be seen as one of the methods for decreasing the magnitude of the EEDI for representative sea conditions as per requirements of the International Maritime Organization.

A Novel Deep Learning Model for the Flow Field Reconstruction of An Oscillating Airfoil

In this paper, a novel model is presented for reconstructing unsteady periodic fields of velocity vector and pressure scalar over an oscillating foil. This data-driven method based on convolutional neural network can be utilized to accomplish two objections: fields reconstruction from limited measurements and transient aerodynamic characteristics prediction. The verification results of an oscillating foil under low Reynolds number show that this method can accurately reconstruct all the fields only by limited pressure information at probes on the foil surface. The evaluation on aerodynamic characteristics prediction illustrates that our model outperforms four classical machine learning methods. Meanwhile, a well-trained CNN model can almost achieve real-time flow field prediction by leveraging the GPU acceleration. Finally, the exploration of the robustness for the CNN model is conducted on several aspects, including training size, probe layouts, probe numbers and measurement noises.

Experimental Validation of a Bio-Inspired Thruster

Bio-inspired solutions have been deeply investigated in the last two decades as a source of propulsive improvement for autonomous underwater vehicles. Despite the efforts made to pursue the substantial potential payoffs of marine animals' locomotion, the performance of biological swimmers is still far to reach. The possibility to design a machine capable of propelling itself like a marine animal strongly depends on the understanding of the mechanics principles underlying biological swimming. Therefore, the adoption of advanced simulation and measurement techniques is fundamental to investigate the fluid–structure interaction phenomena of aquatic animals' locomotion. Among those, computational fluid dynamics represents an invaluable tool to assess the propulsive loads due to swimming. However, the numerical predictions must be validated before they can be applied to the design of a bio-inspired robot. To this end, this paper presents the experimental setup devised to validate the fluid dynamics analysis performed on an oscillating foil. The numerical predictions led to the design of a strain gages-based sensor, which exploits the deflection and twisting of the foil shaft to indirectly measure the propulsive loads and obtain a complete dynamic characterization of the oscillating foil. The results obtained from the experiments showed a good agreement between the numerical predictions and the measured loads; the test equipment also allowed to investigate the potential benefits of a slender fish-like body placed before the spinning fin. Therefore, in future work, the system will be employed to validate the analysis performed on more sophisticated modes of locomotion.

On the issue of reduction of relative motion of the bow for a ship with energy-saving wing elements in headwind waves

В статье рассматривается относительное перемещение носовой оконечности судна с энергосберегающими крыльевыми элементами на встречном волнении, а также результаты сравнения соответствующих расчетных и экспериментальных данных. Метод расчета основан на линейной теории поперечных сечений в частотной области. Сначала производится расчет продольной (вертикальной и килевой) качки судна встречном волнении, а затем расчетные данные используются для расчета относительных перемещений точек корпуса судна. Далее, для найденных численным методом смешанных колебаний носового и кормового крыльев, с привлечением теории Теодорсена колеблющегося профиля. В ходе расчетов демонстрируется влияние на относительное перемещение удлинения и площади энергосберегающих крыльев, а также эффект реализации относительного перемещения и вертикального ускорения при совместном использовании носового и кормового крыльев по сравнению со случаем использования только одного (носового или кормового) крыла. Полученные расчетные данные позволяют получить представление о механизме и эффективности снижения относительного перемещения на встречном волнении при качке судна с энергосберегающими крыльевыми элементами. Considered in the article are relative vertical displacement of the bow extremity of a ship with energy-saving wing elements in headwind regular waves, and also comparison of corresponding computational and experimental data. The method of calculation is based on a linear strip theory in frequency domain. At first, calculation is carried out of longitudinal (heaving & pitching) motions of a ship with and without wings in headwind waves, and then calculated results are employed to determine relative displacements of ship hull points. To account for the influence of inertial and damping effects of the wings attached to the hull we make use of Theodorsen theory of oscillating foil. Demonstrated in the course of calculations are the effects of wings aspect ratio and area as well as position with respect to the hull (bow wing, stern wing and bow & stern wings). Obtained computed data brings about better understanding of the mechanism and efficiency of reduction of vertical displacements of the hull points for a ship with energy-saving wings in headwind regular waves