Innovative energy-saving propulsion system for low-speed biomimetic underwater vehicles

: This article covers research on an innovative propulsion system design for a Biomimetic 1 Unmanned Underwater Vehicle (BUUV) operating at low speeds. The experiment was conducted 2 on a laboratory test water tunnel equipped with specialised sensor equipment to assess the 3 Fluid-Structure Interaction (FSI) and energy consumption of two different types of propulsion 4 systems. The experimental data contrasts the undulating with the drag-based propulsion system. The 5 additional joint in the drag-based propulsion system is intended to increase thrust, decrease energy input, and protect the fins from degradation due to fatigue. The tests were conducted at a variety of fins oscillation frequencies and fluid velocities. Experiments demonstrate that in the region of 8 low-speed forward movement, the efficiency of the propulsion system with the additional joint is 9 greater.

In the paper [25], a wide range of real caudal fin shape species were digitised and analysed, 71 ranging from homocercal tails with a low aspect ratio (square shape used by bluegill sunfish and 72 rainbow trout) to high aspect ratio (lunate shape adopted by tuna and swordfish), and even heterocercal 73 caudal fin adopted by sharks. The comparison of propulsive efficiency shows that large aspect ratio [28], the polycarbonate fin has a width of 0.2 mm , whereas the steel fin has a width of 0.1 mm.

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In Fig. 3 c, d the fin with the additional joint is presented for power (c) and return (d) stroke.

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The vertical position of the inflexible fin with additional joint (Fig. 3 c) generates thrust, while the 87 horizontal position (Fig. 3 d) is used to reduce resistance on the return stroke.

Laboratory test equipment and measurements method 89
The laboratory test water ring shown in Fig. 4 was designed for the characteristic dynamic 90 establishment of the singular fin without considering the effect of the underwater vehicle body. The 91 laboratory water tunnel was composed of polyethylene panels with the following dimensions: 0.09 m 92 height, 0.22 m width, and 0.02 m 2 cross-sectional area. The laboratory test determines the fin dimensions 93 to stand as well as the sensors employed. For example, too large fin may interact with the inner sides 94 of the tunnel, while too tiny a fin may generate insufficient force to be monitored by strain gauges.

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Corners were set to 45 • due to laminar flow restrictions, and an additional steering wheel was installed 96 before the place of measurement. An external water pump with adjustable fluid velocity was used to 97 provide experiments with varying fluid velocities. Using signals from the high-precision, non-invasive 98 ultrasonic flow meter the water velocity was managed in a closed-loop control system [29]. Two strain 99 gauges were positioned symmetrically on both sides of the water tunnel to assess the fluid-structure with oscillation motions of up to 7.8 Hz for unload movement. The force between the fin and the 106 water was measured directly using different fins linked to the servomechanism. Furthermore, the 107 control algorithm was used for water velocity and fin frequency, and amplitude with restrictions on 108 the desired Strouhal number. Finally, the trailing edge's peak-to-peak amplitude was measured using 109 the vision algorithm described in the authors' paper [30].

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The analysis was carried out following the Buckingham theory [31]. The principle enables the expression of all the information contained in the problem's interactions between physical variables in a very compact manner, employing a reduced number of dimensionless variables. According to a review of the literature [32], [33] and experimental results, the expression characterising the fluid-structure interaction can be described as follows: where:

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K -a geometric parameter that determines the shape of the fin; 117 where: 118 f -the fin movement frequency;

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A -a peak-to-peak amplitude measured at the fin trailing edge;  3.1. Fluid-structure-interaction force for innovative propulsion system as a function of two angles 127 According to equation (5), the force during the working and returning movement of a fin depends on the coefficient (C f ), the side area of the fin (S), both angles α and β, the square of the fluid velocity (u) and acceleration concerning the fin as well as an added mass (m).
where:  The reaction force generated by this impulsive motion in water can generate considerable thrust 136 proportional to the fin acceleration. The actual force can be difficult to assess accurately because it is 137 difficult to estimate precisely the volume of fluid that is accelerated by a particular motion. Although 138 for simple motions and shapes, some reasonable estimates can be given, here experiments in the water 139 tunnel were provided.

Efficiency of the propulsion system 141
The energy efficiency of the propulsion system [22], [37] is defined as the ratio of useful power output to the rate of power input measured over a specific time interval [38], [39].
where: forces, for that reason presented in equation (6) the net thrust defines the difference between thrust 149 and drag force (7). where: 151 T -the thrust;

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T D -the drag force.
153 For a propulsion system submerged in a viscous fluid, the propulsor thrust needs to overcome the 154 resistance force for ensuring a constant speed. A steady motion for T n = 0 means that the propulsion 155 system does not decelerate or produce thrust.

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Power input to the servomotor [40] is determined as a product of the measured voltages (U) and the electric current (I) [41] across the servomotor using the following equation (8): In Fig. 5 the two P s and P f are the power consumed by the servomotor when driving without the fin and 157 when driving the fin in water, respectively. The data reported here were achieved by experimentation 158 on the tested fin. The tests were provided for the frequency of the fin oscillation in the range from 1 to 159 7.6 Hz. force (the net thrust) was measured according to formula (7) and presented in (Fig. 7 -13).  The net efficiency is zero when the mean net thrust is zero, which means that the thrust 209 compensates for the drag force.

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If the thrust is lower than drag force, then the net efficiency is negative. It means that the fluid 211 velocity in the water tunnel is higher than the propulsion system would move forward in an unmovable 212 fluid.

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If the resistance of the investigated propulsion system were known, then the quasi-propulsive 214 efficiency defined in the paper [22] could be calculated. This could provide a more intuitive description 215 of the efficiency with including the resistance. Then, there would not be a negative value of efficiency.
216 For the propulsion system tested, the distinction between thrust and drag force cannot be made. The 217 negative efficiency means that, at constant water speed, the propulsion system cannot compensate for 218 the drag such as to keep the cruising velocity (u).
219 Figure 10. The net propulsive efficiency as a function of Strouhal number for fin: + made from polycarbonate , o with additional joint, * made from thin steel sheet The design of the propulsion system, with an additional joint, achieves the best net efficiency for 220 Strouhal numbers more significant than 1, indicating that the water velocity is equal to zero (Fig. 11) or 221 has a low value (Fig. 12). This is analogous to fish that use a pectoral fin to swim at a slow speed but 222 with high-energy efficiency [47].

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In addition, it can be shown in Fig. 11 -13 that the net thrust for propulsion system with additional 224 joint, increases with higher frequency, according to the mathematical relationship in equation (5).

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For the results presented in Fig. 11, where the water velocity is equal to zero, the thrust was 226 measured for the drag force equal to zero. It means that for that measurement condition, only the 227 thrust is generated. It can be seen from the experimental measurements, that the fin with additional 228 joint has almost two times higher thrust that the fish like flapping foils propulsion system.   The future tests are going to be provided with including body impact on the propulsion system 251 characteristics. The findings encourage further investigation into the effects of mass ratio, non-uniform 252 stiffness, and background turbulence on the unsteady dynamics.

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The future research will concentrate on the Particle Image Velocimetry (PIV) approach, which will 254 be used to conduct a more in-depth investigation of the Fluid-Structure Interaction (FSI). This analysis 255 method allows comparing the created thrust to the speed of the water near the fins. The test will be 256 provided to build a propulsion system with additional joint and flexible fins and various movement 257 styles. This can lead to a more accurate replica of the living marine organism with high-energy 258 efficiency. Finally, the promising results presented in the paper enable us to expect to obtain more 259 efficient undulating propulsion for the BUUV in the close future.