Hydrodynamic analyses of typical underwater gliders*

CHEN Ya-jun （陳亞君）， CHEN Hong-xun （陳紅勛）， MA Zheng （馬崢）

1. Shanghai Institute of Applied Mathematics and Mechanics， Shanghai University， Shanghai 200072， China，E-mail： yjchen@shu.edu.cn

2. China Ship Scientific Research Center， Wuxi 214082， China

Hydrodynamic analyses of typical underwater gliders*

CHEN Ya-jun （陳亞君）1， CHEN Hong-xun （陳紅勛）1， MA Zheng （馬崢）2

1. Shanghai Institute of Applied Mathematics and Mechanics， Shanghai University， Shanghai 200072， China，E-mail： yjchen@shu.edu.cn

2. China Ship Scientific Research Center， Wuxi 214082， China

The underwater glider changes its weight and the weight distribution through the battery use， to move up and down and forward in the sea. It enjoys many advantages such as a long endurance， and a long operational range with its unique device. The performance of the underwater glider can not evaluated only by the drag， the energy consumption is also one of the key factors. In this paper， the power conversion ratio is proposed according to the transfer efficiency from the gravitational potential energy to the available work， and the performances of three typical underwater gliders are evaluated from multi-angles， such as the drag， the power conversion ratio and the barycenter's offset. So the glide performance and the energy consumption in various motion states can be analyzed. The results of this paper can provide a theoretical basis for further study of underwater gliders.

the underwater glider， the drag， the energy consumption， the power conversion ratio

Introduction

The autonomous underwater glider （AUG）， as a specific autonomous underwater vehicle， has many advantages， including the non-fuel driven mechanism and the long operational duration （months）， so it is widely used in both military and civil areas［1-3］. Since 1989， when the concept was firstly proposed， different kinds of AUGs have been designed， and the three most typical ones are the Slocum （shallow and deep types）， the Spray and the Seaglider. The shallow-type Slocum is designed for missions in the range of 1 300 km and of durations of one month， while the deep-type Slocum can dive to a depth of 1 500 m with a much longer sail distance range up to 4 000 km and a duration of almost 5 months［4］， the Spray can dive to a depth of 1 500 m and its sail range reaches 7 000 km［5］， the Seaglider is designed to cover up to 1500 km of the ocean vertically and 6 000 km horizontally under the remote control over many months［6］. These typical AUGs are shown in Figs.1-4.

Fig.2 Outlook of a Slocum AUG

Fig.3 Outlook of a Spray AUG

Fig.4 Outlook of a Seaglider AUG

The motion characteristics were extensively studied as well as the control behavior of the AUG， largely through carrying out dynamic numerical simulations. A series of studies of the hydrodynamic performance of the AUG were carried out［7-11］. In Ref.［12］，the hydrodynamic performances of the AUG at different velocities and attack angles were predicted by numerical simulations. In Ref.［13］， the maximum horizontal velocity required during the gliding process was analyzed by studying the motion equation in the vertical plane. In Ref.［14］， the different hydrodynamic characteristics corresponding to different gliding layout forms were studied， as well as the different motion performances of the AUG in response to the density of the sea water.

To further improve the endurance and the operational range of the AUG， it is important to increase the gliding efficiency， rather than updating its energy source （the high energy battery）. The former is mainly estimated by two factors： the energy consumption and the operational range. In view of the fact that the kinematic principle of the AUG is quite unique， the hydrodynamic research is important and is related to the accurate prediction of how the lift and drag of the AUG could be changed through the residual buoyancy and the barycenter. In this paper， an evaluation of the performances of the typical gliders is presented. This may provide a theoretical basis for further AUG researches，and help design and optimize the hydrodynamic shape of this special type of autonomous underwater vehicle.

1. Theoretical bases

1.1Force analysis

With the force analysis， the movement mechanism of the AUG can be clarified. A body-fixed （BF）coordinate frame is chosen on the AUG model. The buoyancy of the body is chosen as the origin point，G denotes the body's barycenter，drepresents the horizontal offset between the barycenter and the buoyancy center， andθ，αandξare the corresponding included angles， andD， andN represent the axial force along the axis of the body， and the normal force perpendicular to the body， respectively，M is the torque relative to the origin. The details are shown in Fig.5.

Fig.5 The sketch of force analysis of glider

If the AUG makes a uniform motion only in the X-Zplane， the motion of the AUG can be expressed as

The force balance equation can be written as：

Thus， the conditions for the AUG floating at a constant speed can be expressed as：

1.2Performance assessment

Apart from the traditional evaluation norms， i.e.，the consideration of the drag， the energy consumption is another key factor to be considered for evaluating the performance of the AUG. Especially for the underwater gliders， deriven by a high energy battery， the energy consumption is very important for the long operational duration. To this end， in Ref.［15］， the concept of the power conversion is proposed， and the power conversion is represented by

where fxis the horizontal drag，vxis the horizontal gliding speed，ΔBis the rest of the buoyancy， and vyis the vertical speed. The numerator represents the consumed power used to overcome the drag along the horizontal direction while the denominator represents the output power of the residual buoyancy along the vertical direction. This formula gives the proportion of the horizontal power consumption and the potential output of the residual buoyancy in the vertical direction. The higher the target function is， the greater the power conversion ratio becomes. This formula provides an important index for evaluating the performances of the AUG.

Next， the performances of three typical AUGs are evaluated from multi-angles， including the drag，the power conversion ratio， and the barycenter offset，such that the gliding performance and the energy consumption in various motion states can be analyzed.

2. Numerical simulations

2.1Model

The numerical calculation is implemented by the commercial CFD software， Fluent. In order to make an objective comparison of the performances of these typical AUGs， each AUG model assumes the same geometry size， which is 0.053 m3in volume， and 1.2 m in length （not including the stern rudder）. Besides， the normal cruising speed of the AUG is relatively slow， about 0.6 m/s， which means a small Reynolds number， of ～105， and in addition to the low drag， it ensures the stability of the incoming flow， therefore，the laminar flow model could be adopted.

According to Ref.［6］， the experimental results in the wind tunnel demonstrate that the laminar flow would separate at a point just after the maximum diameter of the body and reattach turbulently near the tail，when the attack angle reaches12o. The glider is placed in the middle of the computational domain at a distance of 2.5 L away from the upstream boundary. Besides， the downstream exit boundary is located at 6.5 L away from the center of the glider， in order to minimize the influence from the boundaries. As the quality of the computational gird is essential for meeting the accurate and stable requirements of the numerical calculation， a grid independence test is performed to find out the optimal number of elements.

Table 1 Grids used for the grid independence test

Table 1 shows the results of the grid independence test performed with the CFD software， wheref andL represent the lift and the drag of Hull01， respectively. From this table， it is obvious that the number of elements of Grid6 and Grid7 are satisfactory in predicting coherent simulation results.

The schemas of the grids of Hull01， Hull02， and Hull03 are shown in Fig.6， Fig.7 and Fig.8， respectively.

Fig.6 Numerical grid of Hull01 （Rogue）

Fig.7 Numerical grid of Hull02 （Slocum）

Fig.8 Numerical grid of Hull03 （Seaglider）

Table 2 Drags of Hull01， Hull02 and Hull03 at different attack angles

Fig.9 Drags of Hull01， Hull02 and Hull03 at different attack angles

2.2Result analyses

At a certain inflow velocity （0.2 m/s）， the drags of Hull01， Hull02 and Hull03 at different attack angles are presented in Table 2. In Fig.9， the curves of drag versus attack angle of all typical gliders are also presented.

From Fig.9， it can be found that， at a certain inflow velocity， the drag of each model increases with the increase of the attack angle. The drags of Hull01 and Hull03 are approximately the same. However， the drag of Hull02 is about two times larger than those of Hull01 and Hull03. In Ref.［16］， the drags of the Seaglider and the Slocum are also compared. The results suggest that the drag of the Slocum is about two times larger than that of the Seaglider. Considering that the stabilizer of Hull02 is higher than those of Hull01 and Hull03， it is necessary to calculate the drag experienced by the stabilizer of Hull02， and the corresponding results are presented in Table 3.

Table 3 Drag experienced by the stabilizer of Hull02

Table 3 presents the proportion of the drag experienced by the stabilizer of Hull02. It can be found that the drag experienced by the stabilizer of Hull02 takes more than 30% of the total drag. When the attack angle is beyond 8o， this proportion reaches over 50%. Therefore， the disadvantage caused by the drag experienced by the Hull02 is limited.

Fig.10 Barycenter offset of Hull01， Hull02 and Hull03 in response to different attack angles

At the same inflow velocity （0.2 m/s）， the barycenter offset-attack angle curves of Hull01， Hull02 and Hull03 in response to different attack angles are shown in Fig.10.

As can be seen from Fig.10， at the same inflow velocity， the barycenter offset of each model increases with the increase of the attack angle. The barycenter offset of the Hull01 is larger than those of Hull02 and Hull03， and the barycenter offset of the Hull02 is slightly greater than that of Hull03.

The energy consumption of Hull03 is the minimal while that of Hull01 is the greatest， hence it can be concluded that， to some extent， the design of Hull01 is unreasonable.

At different inflow velocities （0.2 m/s， 0.3 m/s，0.4 m/s， 0.5 m/s and 0.6 m/s）， the curves of the power conversion ratio of Hull01， Hull02 and Hull03 versus the attack angles are shown in Figs.11-13.

Fig.11 The power conversion ratio of Hull01

Fig.12 The power conversion ratio of Hull02

Fig.13 The power conversion ratio of Hull03

As can be seen from the above three figures， at the same inflow velocity， the power conversion ratio corresponding to each model first increases and then decreases with the increase of the attack angle. As a result， there is a maximum power conversion value. For all three AUGs， when the inflow velocity increases， the attack angles corresponding to the maximum power conversion ratios decrease. At different inflow velocities， the trends of the power conversion ratio are similar. Considering that the usual speed of the AUG is low， generally， 0.25m/s［5］， a velocity of 0.2 m/s can be chosen for further analyses.

When the inflow velocity is 0.2 m/s， the power conversion ratios of Hull01， Hull02 and Hull03 corresponding to different attack angles are shown in Fig.14. The curves of the power conversion ratios of Hull01， Hull02 and Hull03 versus the gliding angles are shown in Fig.15.

Fig.14 The power conversion ratios against different attack angles

Fig.15 The power conversion ratios against different gliding angles

In Fig.14， it can be seen that the attack angles corresponding to the best power conversion rateηof Hull01， Hull02 and Hull03 are 6o，4oand 4o， respectively. When the attack angle is small， Hull02 has the largest power conversion ratio， and Hull03 has the second best， and Hull01 has the smallest. By increasing the attack angle， the power conversion ratio of Hull02 decreases quickly， as a result， the power conversion ratio of Hull02 becomes smaller than that of Hull03 within a certain range. When theattack angle further increases， the power conversion ratio of Hull02 is slightly smaller than that of Hull01.

In view of the power conversion， Hull02 is suitable for a small attack angle gliding while Hull03 has a better performance especially in large attack angle ranges， and it is suitable for a fixed-point gliding.

Figure 15 shows that the glider angles for whichthe best power conversion ratios of Hull01，Hull02 and Hull03 could be achieved are 33o，19oand 28o， respectively. At this point， the corresponding power conversion ratios are 0.623， 0.725 and 0.697， respectively. Also， it should be noted that， at the same inflow velocity， the power conversion ratio of Hull2 is the highest， therefore， the superiority of Hull2 is obvious.

With regard to the power conversion， Hull02 has the best performance， and Hull03 has the next best performance. The performance of Hull01 is the worst. Hull02 is suitable for small-angle gliding while its glide scope is wide. Hull01 and Hull03 are suitable for large-angle gliding with a short gliding scope.

3. Conclusions

In this paper， the performances of three typical AUGs are evaluated from multi-view angles， which include the drag， the power conversion ratio， and the barycenter offset. From the numerical simulation， the following four conclusions can be reached.

（1） In the case of the Rogue， although the drag is low， the power conversion rate is also low， and the barycenter offset is large. They indicate that its corresponding energy consumption is high. Generally speaking，the performance of the Rogue is poor.

（2） For the Slocum， the drag is larger than those of the Rogue and the Seaglider. However， the calculation results show that the disadvantage caused by the drag is limited. The power conversion rate of the Slocum is higher than that of the Seaglider in the cases of small attack angles. Therefore， the Slocum is suitable for small-angle gliding with wild gliding scope.

（3） For the Seaglider， its experienced drag is roughly equal to that of the Rogue while its energy consumption is relative low. From a standpoint of the power conversion， the Seaglider enjoys a better performance， especially in the case of large attack angles，and it is suitable for fixed-point gliding.

（4） Because of the obvious performance advantages of the Slocum， it is reasonable to select the Slocum as the object for further researches. The related research may focus on the leading edge and the wing of the body.

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（November 2， 2014， Revised January 6， 2015）

* Project supported by the National Natural Science Foundation of China （Grant No. 51279184）.

Biography： CHEN Ya-jun （1986-）， Female， Ph. D. Candidate

MA Zheng，

E-mail： Mazh8888@sina.com