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Hydrodynamic performance of an unmanned wave glide vehicle

Weixing Liu,1 Ningyu Li,1,a) Yumin Su,1 Yazhou Zhu,2 and Zhiyang Zhang3

1Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001,

China

2School of Naval Architecture & Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang

212003, China

3Deepwater Engineering Research Center, Harbin Engineering University, Harbin 150001, China

a)Author to whom correspondence should be addressed: liningyu123@aliyun.com

Abstract: A principle prototype of the unmanned wave glide vehicle (UWGV) “Voyager I” was

designed and constructed. A hydrostatic resistance test in a tank, a self-propelled experiment and a

free-sailing experiment in a regular wave were carried out. The component of hydrostatic

resistance of the UWGV was investigated. The effect of the wavelength and amplitude on the

heaving amplitude, pitch angle, thrust of the wave glider propulsor (WGP) and free-sailing

velocity of the UWGV were analyzed. The changing trends of various parameters for a series of

wavelengths and amplitudes were obtained. The experimental results provide a new research

direction for numerical computation and a technical foundation for the development of an

unmanned surface vehicle with long voyage and low-carbon capabilities.

Keywords: unmanned wave glide vehicle; tandem foil configuration; regular wave; hydrodynamic

performance

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1. Introduction

With the development of marine resources, marine exploration and territorial sea safety have

received significant attention from various countries, which has prompted changes in ocean

observation, such as three-dimensional ocean observation, platform diversification, and systematic

and networked ocean observation. The need for observing platforms to undertake long-term,

large-scale, economical, flexible, reliable and autonomous observing missions is urgent. An

unmanned boat is an intelligent sports platform capable of performing various maritime

explorations and monitoring tasks, and it has the capability for autonomous navigation. Therefore,

unmanned boats in the civil and military fields have an extensive range of applications [1].

Conventional unmanned boats generally use fuel or batteries as a driving force with limited load

capacity. Therefore, they have low endurance and a short voyage capability and pollute the marine

environment. An unmanned wave glide vehicle (UWGV) is an unmanned boat that is completely

dependent on the use of absorbing waves to promote movement and has the advantages of long

voyage capability, long cycles, minimal pollution, and strong environmental adaptability. AUWGV,

as a marine surveillance platform, produces low noise levels, has excellent stealth, can easily carry

out laying group operations, and so on. A representative of this type of unmanned boat is the Wave

Glider series manufactured by Liquid Robotics Inc, United States[2], which yields excellent

performance in marine applications [3-4].

A UWGV consists of a floating body, a wave glide propulsor (WGP) and a connecting

umbilical cable. WGP thrust is caused by a series of tandem-arranged foils do the heave and pitch

movements with the ups and downs of waves. This process is similar to the process of swimming

of fish by oscillating tail; thus, both theoretical models can be attributed to bionic flapping foils.

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Jones et al. [5] used a two-dimensional panel method and a test method to verify the propulsion

performance of single and tandem flapping foils. The results indicate that the propulsion

efficiency of the tandem foils is significantly higher than the propulsion efficiency of a single foil.

Yu Xianzhao et al [6] employed the sliding mesh method to calculate the performance of the

flapping foil and the stationary foil in tandem and to give the performance difference among the

different positions of the foils. Broering et al. [7-8] investigated the effect of the front-to-rear foil

phase angle and spacing on the aerodynamic performance of two-dimensional and

three-dimensional tandem foils using an overlapping grid method. The results indicate that the

same phase flapping increases the thrust of the tandem foils. When the phase difference is 90 °, the

motion efficiency of the tandem will be improved. Liu Peng et al. [9] employed the finite volume

method to analyze the hydrodynamic performance of tandem asynchronous foils with a gliding

wave propeller as the prototype, which provided an important reference for the selection of

experimental parameters for a UWGV prototype. In a UWGV marine trial study, Smith et al. [10]

made a preliminary prediction of the velocity of the Wave Glider by using the velocity

measurement in a real marine environment for a long period. Bingham et al [11] completed a

UWGV actual detection application test using a UWGV equipped with active and passive sonar to

perform field measurements of the test area.

Apart from the aforementioned, most existing research on flapping foils is also focused on

simulations and experiments of the foils that mimic the active locomotion of fish fins [12-20] or

are used for the appendages of ships and submarines [21-24]. However, the number of studies that

have investigated the passive motion of the WGP foil with wave is rare. Moreover, existing

experiments also comprise a qualitative test of the practical application performance of a UWGV

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but cannot provide thrust, heave amplitude, resistance and other performance parameters of the

WGP for different marine environments and cannot provide a reference for UWGV hydrodynamic

performance research. We designed and built the UWGV prototype “Voyager I”. A resistance test

in hydrostatic environment, a hydrodynamic performance experiment and velocity measurements

of free sailing in regular waves were conducted in the Harbin Engineering University towing tank.

The resistance components of the UWGV and the influence of different regular wave parameters

on the performance of the UWGV were analyzed.

2. UWGV basic principles

When sailing on waves, the floating body of the UWGV will perform heaving movements as

the waves fluctuate and convert the wave energy into its kinetic energy and potential energy. The

UWGV passes the heaving motion of the floating body to the WGP through the umbilical cable,

and the kinetic energy and potential energy of the heaving and pitching movements of the WGP

foils are transformed into the kinetic energy of the UWGV. The state of the floating body and

WGP foils and their force bearing during the movement are shown in Figure 1 [25]. In the figure,

λ represents the wavelength, h denotes the wave height, a 0 represents the wave amplitude, L

denotes the length of the floating body, and C 0 represents the foil chord length. When navigating

in the ocean, the UWGV continues to encounter waves and can continue to convert the wave

energy into its forward kinetic energy to achieve a long voyage and long-term operation.

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Figure 1 UWGV working principle diagram

3. UWGV design and experimental scheme

3.1 UWGV design and model

Based on reference to and analysis of existing research results, the profile design and

three-dimensional (3D) modeling of the UWGV floating body and WGP were completed.

Considering the influence of the profile structure of the floating body and the WGP structure on

the hydrodynamic performance of the UWGV, theoretical optimization of the design was

conducted, and the 3D design model of the UWGV prototype was determined and completed.

Figure 2 Three-dimensional UWGV model

The floating body is a large flat structure, the length of the vehicle L = 2m, the width of the

vehicle B = 0.6m, the depth of the vehicle H = 0.25m, and the designed draft is 0.15m.The WGP

foils were hinged in pairs on both sides of the beam, and no relative rotation occurs between the

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pairs of foils. A NACA0012 airfoil was employed for the foil board, the length of the single foil

chord C 0 = 0.16m, the extended length S 0 = 0.54m, and the foil oscillation angle stopper was

installed on the beam. The floating body, WGP and rigid umbilical cable were hinged and can

achieve a single degree of freedom movement respectively. The UWGV prototype is shown in

Figure 3.

(A) Floating body model

(B) Gliding wave propeller model

Figure 3 UWGV prototype

3.2 Tank test program

A UWGV tank test was completed in the Harbin Engineering University towing tank. The

tank length × width × depth = 108m × 7m × 3.5m; the test tank wave was generated by the

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pushing plate, and the maximum wave height was 0.4m with a wave period of approximately 0.4

~ 4s. Prior to the test, a trial voyage was conducted with different test parameters to obtain

effective test parameters, save test time and protect the test prototype and tank equipment; the

final test parameters are shown in Table 1. In the table, “*”denotes the test point, and“—”indicates

serious green water on the floating body; in this case, the experiment cannot be effectively

performed.

Table 1 Test point selection of the wave (drag velocity 0.412m/s)

Firstly, the resistance of the individual floating body and the UWGV in still water was

measured. In the various tests in wave environment, the UWGV was in the condition of head sea.

In the self-propelled experiment in the regular wave, the resistance, maximum pitch angle and

heave amplitude of the UWGV in different wave conditions were recorded by the Seaworthiness

Measurement Data Acquisition System. In the free-sailing experiment in head sea, the average

velocity of the UWGV in different regular wave environment was preliminarily measured. The

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UWGV test situation is shown in Figure 4.

(A) Self-propelled experiment

(B) Free-sailing experiment in head sea

Figure 4 UWGV tank test

4 Results and discussion

According to the principle of WGP thrust production, the heaving amplitude and motion

cycle of the WGP foil are primarily affected by the wave height and wavelength. In the test, the

distance between the leading edge of the rear foil and the trailing edge of the front foil of the WGP

was 0.08m, and the oscillation angle stopper limits the oscillation angle to ± 15°for each foil.

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The velocity of the trailer for the self-propelled experiment in the wave is V = 0.412 m/s = 0.8 kn.

The Froude number Fr =v/(gL)0.5, the dimensionless wave height n = h/L, and the dimensionless

wavelength m = λ/L were introduced as non-dimensional parameters.

4.1 Hydrostatic resistance of the floating body and UWGV

The UWGV umbilical cable length was designed as 6m; due to the tank conditions, the

length was shortened to 2.5m in the test. According to the surface characteristic of wave motion

[26], the WGP can be considered to be unaffected by the surface waves for the majority of the test

wave parameters. The hydrostatic resistance test of the individual floating body and the UWGV

was performed to qualitatively investigate the proportion of the WGP resistance in the UWGV

resistance, which provided a reference for the optimal design of the UWGV.

The changes of the resistance Rt of the individual floating body and the UWGV for different

Fr in still water are shown in Figure 5. The hydrostatic resistance value calculated from the

equivalent plate theory is employed as a comparison.

Figure 5 Hydrostatic resistances of the floating body and UWGV for different Froude numbers

The resistance of the individual floating body and UWGV increased in nearly quadratic form

with an increase in Fr; when joined onto the WGP, the static water resistance of the UWGV

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rapidly increased in comparison with that of the individual floating body for the same Fr.

Moreover, the greater Fr is, the greater the resistance difference. The UWGV resistance is more

than ten times the individual floating body resistance. Thus, the WGP resistance accounted for

approximately 90% of the UWGV hydrostatic resistance components. Therefore, the follow-up

UWGV performance optimization should focus on reducing the resistance of the WGP.

4.2 Heaving amplitude of the UWGV floating body for different wavelengths and wave

heights

The magnitude of the heaving amplitude of the UWGV had a direct impact on the WGP

heaving amplitude, which affected the magnitude of the WGP thrust. Figure 6 shows the changes

of the heaving amplitude of the UWGV floating body y for different dimensionless wavelengths m

and wave height n.

Figure 6 UWGV heaving amplitude for different wavelengths and wave heights

As shown in Fig. 6 (a), the UWGV heaving amplitude gradually became close to the wave

height n with an increase in m. This finding indicated that the UWGV sailing in the waves in the

test required a certain amount of time to respond to the waves. For the same n, a small m value

corresponded to a short wave period; the UWGV entered the next status when it had not yet

responded to the wave in this case. Therefore, for a small m, the actual heaving amplitude of the

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UWGV deviated the set value largely, whereas a large m value was more conducive to the UWGV

response to the waves. As shown in Fig. 6 (b), with a fixed m and an increase in n, the heaving

amplitude of the UWGV gradually increased with a certain degree of deviation from the amplitude

set value. The smaller the value of m is, the greater the deviation. When n <0.08, the heaving

amplitude of the UWGV increased in a nearly linear form with an increase in n, whereas when n >

0.08, the growth rate of the UWGV heaving amplitude decreased and an increasing difference

from the amplitude set value was observed. This is because that with a fixed m, the UWGV

motion cycle is the same; and the greater n is, the greater the heaving velocity, and moreover the

relationship of the WGP resistance was quadrilateral to the UWGV’s velocity.

4.3 UWGV floating body pitch angle for different wavelengths and wave heights

In the prototype arrangement, the WGP is suspended on the front position of the middle part

of the floating body bottom—approximately 0.45L from the bow. Therefore, the pitch angle of the

UWGV floating body has a significant impact on not only the total security of the UWGV and the

stability of the UWGV after the instrument is deployed but also the generation of the WGP thrust.

Figure 7 shows the variation of the pitch angle a of the UWGV floating body for different

dimensionless wavelength m and wave height n.

Fig.7 Effect of wavelength and wave height on the pitch angle of the UWGV floating body

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For the same n and an increase in m, the pitch angle of the UWGV decreases in a nearly

linear manner. For the same m, the greater the value of n is, the greater the pitch angle of the

floating body. Therefore, considering the safety of the UWGV, the wave environment with a large

m value and a small n is more favorable. Considering that the WGP layout approaches the middle

part of the ship, when the pitch angle is small, the WGP heaving amplitude caused by the pitch is

small. Therefore, the reduction of the pitch of the UWGV from the perspective of floating body

safety and resistance performance can be employed for the subsequent optimization design, which

will not affect the generation of WGP thrust.

4.4 WGP thrust for different wavelengths and wave heights

The thrust generated by the WGP is an important parameter in the hydrodynamic

performance metrics of the UWGV. The magnitude of WGP thrust in different wave conditions

will directly affect the UWGV navigation velocity, which will affect the working efficiency and

other performance of the UWGV. Figure 8 shows the changing trend of the WGP thrust for

different dimensionless wavelength m and wave height n in a regular wave environment in the

UWGV self-propelled experiment.

As shown in Figure 8 (a), the WGP thrust decreases with an increase in m. According to the

regular wave dispersion relation, the greater the value of m is, the longer the wave period, which

leads to a longer heaving cycle of the WGP foil board with the wave. With a fixed value of n, the

smaller the heaving velocity of the foil board is, the smaller the thrust. As shown in Fig. 8 (b),

with a fixed m, the greater the value of n is, the higher the WGP thrust, which is similar to the

curve trend shown in Figure 8 (a).A linear relationship between WGP thrust and the wave height n

was no longer observed. With an increase in n, the growth rate in thrust decreases. Since the

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heaving amplitude of the WGP has a greater effect on its thrust value, and with an increase in n the

difference between the heaving amplitude WGP and the wave height n increases (referred to

Figure 6 (b)), a deceleration trend of the total rate of increase of the curve is observed. (see Figure

8 (b)). In summary, the wavelength and amplitude of the regular wave have a significant effect on

the WGP thrust. Under the premise of guaranteeing the safety of the UWGV, a small wavelength

and a high wave height are favorable to the generation of WGP thrust; that is, the WGP thrust is

greater in a high state of the sea.

Figure 8 Effect of wavelength and wave height on WGP thrust

4.5 Velocity of UWGV free sailing for different wavelengths and wave heights

In free sailing in head sea, the velocity of the UWGV is the most intuitive parameter for

evaluating its performance. Figure 9 shows the trend of the change in the average velocity V f of

the UWGV in free sailing in head sea for different dimensionless wavelength m and wave height n

in regular waves. With an increase in m of the regular waves, the UWGV velocity increases and

then decreases; at n =0.1 and m = 4.5, the UWGV velocity reaches the maximum of 0.82kn.With a

fixed n, the wavelength that corresponds to the maximum velocity of the UWGV is the optimum

wavelength. Different values of n correspond to different optimal wavelengths, which indicates

that there is not a stable combination of m and n at which the UWGV reaches the optimal velocity.

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With a fixed m, the UWGV velocity also increased and then decreased with an increase in n. The

maximum velocity generally appeared at m ≈５０n in a regular wave. Although the WGP thrust is

high for large values of m or small values of n, the UWGV velocity is not the maximum at this

time. The reason is that in comparison with the optimal situation, the resistance of the UWGV in

the navigation will increase for either a large m or a small n, and the growth rate of the resistance

is higher than that of the WGP thrust.

Figure 9 Effect of wavelength and wave height on UWGV velocity

5 Conclusions

(1) According to the prototype test, when the UWGV is towed in static water, the resistance

of the WGP is approximately 90% of the total resistance. Therefore, enhancing the UWGV

powering performance by reducing the WGP resistance will be a useful method.

(2) The WGP thrust magnitude is primarily determined by the WGP heaving motion that is

transferred from the UWGV floating body, and the pitch motion of the floating body does not

affect the WGP thrust value. Thus, the floating body can be designed to reduce the pitch in the

subsequent optimization, which can improve the stability of the UWGV to improve the efficiency

of the installed equipment on the floating body while ensuring the powering performance.

(3) When the dimensionless wavelength is small or the dimensionless wave height is large in

a regular wave, the WGP can produce more thrust and the total resistance of the UWGV will

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rapidly increase, which causes a decrease in the velocity of the UWGV in free sailing in head sea.

Therefore, a mall wavelength and a large wave height of the regular wave are unfavorable for the

UWGV velocity and security.

(4) The experimental results of this paper provide a technical basis for the development of

long voyage, low-carbon and environment-friendly unmanned water surface robots and provide a

new research direction for additional numerical simulation. In our further work, the experimental

prototype will be theoretically analyzed and optimized, and the corresponding outfield test will be

carried out to verify and enhance its performance.

Acknowledgments

This paper has been supported by NSFC (National Natural Science Foundation of China) funds

(Grant no. 51479039).

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