OPTIMIZATION OF DISPLACEMENT AND GLIDING PATH AND IMPROVEMENT OF PERFORMANCE FOR AN UNDERWATER THERMAL GLIDER*

YANG Hai, MA Jie

State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, China,

OPTIMIZATION OF DISPLACEMENT AND GLIDING PATH AND IMPROVEMENT OF PERFORMANCE FOR AN UNDERWATER THERMAL GLIDER*

YANG Hai, MA Jie

State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, China,

E-mail: haiyang1121@yahoo.com.cn

(Received March 20, 2010, Revised June 3, 2010)

The underwater thermal glider utilizes ocean thermal energy to change its buoyancy, which enables it to ascend and descend. A Phase Change Material (PCM) as the working fluid inside the thermal engine tubes is sensitive to the surrounding seawater temperature, whose effects are different with the various displacements and gliding angles of the glider. In this paper, the effects of the displacement and the gliding angle on the performance of the thermal engine were studied numerically and experimentally. On this basis, the ways to eliminate the negative effect of a thermocline on the performance of the thermal engine were obtained. The results show that the displacement and gliding angle affect the transition time of the PCM. There exist the threshold values of the displacement and gliding angle for the normal work of thermal engine. There are two means of eliminating the negative effect of a thermocline on the performance of the thermal engine and improving glider performance: one is to increase the displacement, and the other is to decrease the absolute value of the gliding angle. There is also another better way to improve glider performance.

displacement, gliding angle, underwater thermal glider, Phase Change Material (PCM)

1. Introduction

Underwater gliders are highly efficient, buoyancy-driven, winged autonomous underwater vehicles. One type of the glider is battery-powered propulsion, as described by Seaglider[1]and Spray[2]. The other is thermal-powered propulsion, as described by Slocum Thermal[3]. The propulsion of the thermal glider depends on the changing buoyancy of the vehicle with a constant mass. The change of buoyancy is determined by the state of a Phase Change Material (PCM), which is the working fluid inside the thermal engine tubes. The ocean thermocline is a transition layer between the warm surface water layer and the cold deep water layer, in which the temperature gradient is very steep. When the glider passes through the thermocline, the PCM undergoes a phase change and a volume change. The resulting volume change provides an adequate change in buoyancy to propel the glider vertically through the ocean and the hydrodynamic lift on wings converts this vertical velocity into forward motion at the same time. Thus the temperature field around the thermal glider plays a pivotal role in the state of the PCM. However, the paths are different when the thermal glider penetrates through the thermocline with various gliding velocities or gliding angles, and accordingly the temperature field around the thermal glider is changed, thus affecting the thermal engine and glider performance. Further, the steady state gliding velocity is closely related to the net buoyancy, displacement and gliding angle.

Efficiency has been a primary concern in the field of underwater propulsion. Hu[4]studied a pectoral fin rowing propulsion model, and the results showed that a high thrust could be produced in thepower stroke. Shao et al.[5]got inspiration from the caudal fin motion of fish and investigated the flapping wings with different aspect ratios, and the results showed that an increase in aspect ratio could improve the efficiency of the flapping wing. At present, the investigations related to the underwater glider mainly focus on dynamics and motion control. Leonard and Graver[6]derived the feedback control laws based on the model for glider dynamics. Seo et al.[7]developed a simulation program for pitching control using CFD analysis. Kan et al.[8]worked out a simulation program for glider motion using Matlab. Wang et al.[9]designed a linear quadratic regulator for a underwater glider. Ma et al.[10]analyzed the changes of energy of underwater glider when it descends and ascends, and predicted the glider hydrodynamics with various velocities and angles of attack through numerical simulation. Wang et al.[11]constructed a dynamic model of the thermal glider, and designed the thermal engine, the attitude mechanism, and the control devices. However, little attention has been focused on the effects of the displacement and gliding angle on the performance of underwater thermal glider. In addition, Kong et al.[12]studied the phase change process for underwater glider propelled by ocean thermal energy. But there were some drawbacks in that work: firstly, each experiment was performed with constant temperature, while the temperature changes with ocean depth, secondly, the phase transition temperature of hexadecane that was used in the experiments as high as 18oC, while the temperature difference between the hexadecane and the warm surface water is very small and the warm surface water layer is very thin, thus the hexadecane have not enough time to melt and expand during the continuous operation of the thermal glider, thirdly, the thermal glider stayed on the ocean surface for a long time because nearly 83% of hexadecane was still in solid phase, at the same time the glider would drift along at the mercy of strong surface currents and it was difficult for the glider to maintain attitude, thus it wasted the energy expended to control and to change buoyancy, finally, the hexadecane was partly melted for shortening the time of a cycle, it would result in other problems, either an adequate change in buoyancy cannot be provided, or the size of thermal engine tubes is increased but the hydrodynamic performance of the glider is deteriorated.

The purpose of this research is to study the effects and improvement of the displacement and gliding angle on the performance of underwater thermal glider under the condition of temperature variation, and find the ways to improve the performance of underwater thermal glider.

2. Relationship of the steady state gliding velocity, net buoyancy, displacement and gliding angle

Figure 1 shows the forces acting on the glider in the vertical plane during a steady glide. According to the balance of forces, two equations can be obtained as follows[6]:

where m0g is the net buoyancy, D is the drag, L the lift, V the velocity in the vertical plane, θ the pitch angle and defined as positive nose-up, α the angle of attack with its positive direction as from vector V to the vector e1anticlockwise, and ξ (ξ=θ-α) the gliding angle.

Fig.1 Forces acting on the glider during a steady glide

Multiplying Eq.(2) by sinα and subtracting Eq.(1) multiplied by cosα yield

Graver[13]expressed the drag on the glider body as a function of volume and shape, and derived a relation for maximum horizontal speed. In order to determine the coefficient of drag conveniently, by analogy with admiralty coefficient, the drag on the glider is expressed as[14]

where Δ is the displacement of the vehicle. The coefficient CDcan be calculated by using the available data of the existing thermal gliders, which is around 0.8.

Substituting Eq.(4) into Eq.(3) one can give the steady state gliding velocity

Accordingly, the vertical speed can be expressed as

From the Eqs.(5)-(6), it is clear that the steady state gliding velocity and its component are dependent on the net buoyancy, displacement and gliding angle. Under the condition of constant volume change, which is provided by the thermal engine, and the value of net buoyancy remains unchanged in the following discussions.

3. Numerical simulation of the thermal engine

To facilitate heat transfer, the thermal engine comprises tubes that are mounted on the bottom of the hull and immersed in the seawater. In view of the range of seawater temperatures, an n-pentadecane that solidifies at 9.9oC is used as the working fluid inside the thermal engine tubes. The n-pentadecane is a paraffin organic PCM, which is safe, reliable, non-toxic and non-corrosive. During the operation of the glider, the n-pentadecane absorbs heat from seawater or releases heat to seawater through the tubes wall so that it could realize phase change between solid and liquid. Sharma et al.[15]studied the effect of thermophysical properties of heat exchanger material on the performance of latent heat storage system, and the results showed that higher value of thermal conductivity of the heat exchanger container materials did not make significant contribution to the heat transfer. Copper is good heat conductor and its thermal conductivity as high as 401 W·m–1·K–1. Therefore, copper is used as the material of the thermal engine tubes and its thermal resistance is ignored.

3.1 Governing equations

The enthalpy formulation of the heat transfer equation is applied to the thermal engine tubes. For conduction-controlled phase change, the equation of energy conservation can be expressed in one-dimensional cylindrical coordinate as follows:

where t is the time, r the radial coordinate, k the thermal conductivity of the PCM, T the temperature, and H the total volumetric enthalpy. The total volumetric enthalpy is the sum of sensible and latent heats of the PCM[16],

where hmis the latent heat of the PCM, ρ the density of the PCM, subscript s the solid phase and l the liquid phase. The sensible heat h can be written as

where Tmis a reference temperature, and c is the specific heat of the PCM.

As for an isothermal phase change, the local volume fraction of liquid PCM is given by

An alternative form of Eq.(7) can be obtained on splitting the total enthalpy into sensible and latent heat components. Substituting Eqs.(8) and (9) into Eq.(7) yields

where a is the thermal diffusivity.

The discretized form of Eq.(11) is obtained by a fully implicit Finite Volume Method ( FVM), and then solved using a Tri-Diagonal Matrix Algorithm (TDMA).

3.2 Initial and boundary conditions

Initially, the thermal glider stays in the warm surface water. The PCM within the thermal engine tubes and the seawater are in thermal equilibrium. That is, the PCM and the seawater have a same temperature. During operation, the mode of heat transfer between the PCM and the surrounding water is forced convection owing to glider motion.

The boundary conditions associated with the problem can be written as

where Tswis the seawater temperature, hconvthe convective heat transfer coefficient, and R the radius of the tubes.

3.3 Effect of natural convection in the melting process By taking into account the effect of natural convection in the melting process, an effective thermal conductivity for the liquid PCM is used in the conduction equation. For a cylindrical enclosed space, the following correlation is used to predict the natural convection[17]

where keqis the effective thermal conductivity, and Ra is the Rayleigh number.

4. Experimental set-up and test procedure

4.1 Experimental set-up

In the present study, the experiments were designed specifically to meet the conditions explored in the numerical investigation. A schematic of the experimental set-up is shown in Fig.2.

Fig.2 Experimental set-up

The experimental set-up consists of two insulated sections, namely test tank and auxiliary unit. The auxiliary unit is provided with a thermo-regulated bath, an electric heater, a refrigerator and a data logger and temperature controller. The thermo-regulated bath can be programmed to produce a prescribed variation of the water temperature. A temperature variation is prescribed to simulate the real-time temperature around the underwater thermal glider during operation. Three Pt100 temperature transmitters at different locations are used to monitor the water temperature inside the bath. They output 4 mA – 20 mA signals to the data logger for data conversion. Based on these data and the condition required, the temperature controller controls the electric heater and refrigerator by switching the solid state relays on or off, so as to heat or cool the circulating water. To ensure uniform water temperature inside the bath, an electric stirrer is used.

Inside the test tank, there is a test tube filled with PCM. The test tube is a copper tube with an inner diameter of 32 mm, and is 600 mm long with a wall thickness of 1 mm. The PCM chosen for the experiment is n-pentadecane that solidifies at 9.9oC. The top of the copper tube is filled with liquid n-pentadecane of 280 ml, while the bottom of the copper tube is filled with water, and both ends are well insulated. Water cannot dissolve n-pentadecane, and its density is greater than that of n-pentadecane, so the water is always at the bottom of the copper tube and the n-pentadecane is always above water during the solidification and melting processes. A plastic tube with an inner diameter of 6 mm and a length of 2 m is connected with the bottom of the copper tube. During the solidification and melting processes, the shrinkage and expansion of the n-pentadecane can cause the change in water level within the plastic tube. The water level within the plastic tube is measured by level transmitter. The level transmitter outputs 4-20mA signal to the data logger for data conversion.

4.2 Test procedure

In each experiment, a temperature variation was prescribed to simulate the ambient temperature of the underwater thermal glider in operation. Each experiment included a working cycle of the thermal engine. Initially, the vehicle was in stable thermal equilibrium in the warm surface water. During diving, the vehicle gradually descended to cold water, and the PCM solidified and shrinked. The ascent began when the vehicle arrived at the predetermined depth. As the vehicle reached warm water, the PCM melted and expanded. When the vehicle descended to cold water once again, the cycle was completed.

Before the experiment, the water temperature in the test tank should keep constant until the n-pentadecane was in stable thermal equilibrium. Then the experiment was started with established initial conditions. A series of experiments were carried out with different temperature variations, which were caused by the glider’s various displacements and gliding angles.

After the experiment has begun, the water temperature and the water level were recorded oncefor a certain time interval. Using these data the volume fraction of liquid PCM could be calculated, which reflects the operation of the thermal engine. For a certain time interval during solidification or melting process, the volume change of the PCM could be calculated as follows:

where ΔVpcmis the volume change of the PCM for a certain time interval, Δflmthe change in mass fraction of liquid PCM for a certain time interval, and mpcmthe total mass of the PCM. Eq.(15) can be rearranged to the following form:

where A is the cross-sectional area of the plastic tube, and ΔLwateris the change in water level within the plastic tube.

At interval of Δt, Eq.(16) can be written as

Equation (17) can be rearranged to the following form:

For a solidification process, flm0=1, for a melting process, flm

0=0. In addition, the relation between the volume fraction of liquid PCM and the mass fraction of liquid PCM can be derived as follows:

5. Effect of the displacement on the thermal engine

The preset ocean temperature profile is shown in Fig.3. The corresponding depth, thickness and intensity of the thermocline are respectively 64 m, 120 m and 0.10oC·m-1. In addition, the predetermined depth is 1 800 m, and the absolute value of the gliding angle is 39o, while the displacements are 31.6 kg, 53.5 kg and 72.7 kg, respectively.

Fig.3 Ocean temperature profile

Fig.4 Measured temperatures under different displacements

Fig.5 Volume fraction of liquid PCM under different displacements

Figure 4 shows the measured temperatures under different displacements. Figure 5 shows the volumefraction of liquid PCM under different displacements. It shows that the agreements between numerical and experimental values are good. The deviation between numerical and experimental values is mainly caused by a slight change in density of liquid and solid PCM with a temperature variation.

As is shown in Fig.5, with a decrease in the displacement, the time when the volume fraction of liquid PCM becomes less than 1.0 is shorter. That is, the PCM starts the solidification process earlier. And the change rate of the volume fraction of liquid PCM has accelerated slightly. The reason for this is that the vertical speed of the glider increases monotonously with a decrease in the displacement, which is clear from Eq.(6). In this case, the thermal glider can descend to cold water earlier and also ascend to warm water earlier, which is clearly shown in Fig.4. Accordingly, the PCM can start solidification and melting process earlier. Therefore, the transition time in the phase change processes of the working fluid and the gliding cycle become shorter.

Figure 5 further shows that the volume fraction of liquid PCM becomes less than 1.0 at the end of the cycle when the displacement is smaller than a certain value. This value is called the critical displacement here. When the displacement is greater than or equal to the critical displacement, the volume fraction of liquid PCM is 1.0 at the end of the cycle. When the displacement is smaller than the critical displacement, the volume fraction of liquid PCM is less than 1.0 at the end of the cycle, and further reduced with a decrease in the displacement. The reason for this is that the vertical speed of the glider has a large increase and then the PCM has not completely melted when the thermal glider moving to the cold water from the warm water. At this time, the thermal engine will work abnormally. To keep the thermal engine working efficiently, the glider should stay in the warm surface water for a certain period of time before moving to the cold water. With a decrease in the displacement, the thermal glider will stay longer on the surface and be subject to drift with the surface current. It is unfavorable for the thermal glider to penetrate through the ocean currents.

6. Effect of the gliding angle on the thermal engine

The preset ocean temperature profile is shown in Fig.3. Moreover, the predetermined depth is 1 800 m, and the displacement is 53.5 kg, but the absolute values of the gliding angle are 45o, 39o, 36oand 30o, respectively.

Figure 6 shows the measured temperatures at different gliding angles. Figure 7 shows the volume fraction of liquid PCM at different gliding angles. It is shown that the PCM starts the solidification process earlier with an increase in the absolute value of the gliding angle. And the change rate of the volume fraction of liquid PCM has accelerated slightly. The reason for this is that the vertical speed of the glider increases monotonously with an increase in the absolute value of the gliding angle, which is clear from Eq.(6). In this case, the thermal glider can descend to cold water earlier and also ascend to warm water earlier, which is clearly shown in Fig.6. Accordingly, the PCM can start solidification and melting process earlier. Therefore, the transition time in the phase change processes of the working fluid and the gliding cycle become shorter.

Figure 7 further shows that the volume fraction of liquid PCM becomes less than 1.0 at the end of the cycle when the absolute value of the gliding angle is greater than a certain value. This value is called the critical absolute value of the gliding angle here. When the absolute value of the gliding angle is smaller than or equal to the critical absolute value of the gliding angle, the volume fraction of liquid PCM is 1.0 at the end of the cycle. When the absolute value of the gliding angle is greater than the critical absolute value of the gliding angle, the volume fraction of liquid PCM is less than 1.0 at the end of the cycle. The reason for this is that the vertical speed of the glider has a large increase and then the PCM has not completely melted when the thermal glider moving tothe cold water from the warm water. At this time, the thermal engine will work abnormally.

Fig.6 Measure temperatures under different gliding angles

Fig.7 Volume fraction of liquid PCM under different gliding angles

7. Improvement on the performance of the thermal glider

Our recent study[18]showed that there exist the threshold values of the depth and upper thickness of thermocline for the operation of thermal engine. A depth or upper thickness of the thermocline smaller than the corresponding threshold causes the thermal engine to work abnormally. To keep the thermal engine working efficiently, the glider should be kept in warm surface water for a certain period of time before moving through cold water. It is unfavorable for the thermal glider to penetrate the ocean current, which is the main operational constraint of the gliders. Therefore, the operational goal is not only that the thermal engine can work efficiently, but also that the thermal glider can function with a continuous horizontal motion.

From the above analysis, it is clear that a decrease in the displacement or an increase in the absolute value of the gliding angle results in an increase of the vertical speed of the glider. Its effect on thermal engine is equivalent to that of reducing the thermocline depth or thickness. On the other hand, an increase in the displacement or a decrease in the absolute value of the gliding angle results in a decrease of the vertical speed of the glider. Its effect on thermal engine is equivalent to that of increasing the thermocline depth or thickness. Therefore, when the depth and thickness of thermocline are smaller, that is, the warm water layer is thinner, the displacement should be increased in the glider design processes or the absolute value of the gliding angle should be reduced in operational processes so that the negative effects of thermocline could be eliminated. Thus the performance of the thermal engine and then the glider can be improved.

As is shown in Fig.8(a), when the displacement and the absolute value of gliding angle are 53.5 kg and 39o, respectively, the volume fraction of liquid PCM is less than 1.0 at the end of the cycle. The reason for this is that the location of the thermocline is shallow (the corresponding depth, thickness and intensity of thermocline are 54 m, 120 m and 0.10oC·m-1, respectively). By increasing the displacement or decreasing the absolute value of the gliding angle respectively, the volume fraction of liquid PCM equals 1.0 at the end of the cycle and thus the glider performance can be improved.

On the other hand, heat transfer is enhanced by increasing temperature difference. For this reason, the thermal glider should operate at relatively steep gliding angle to rapidly arrive at cold water layer or warm water layer. Based on the above analysis, a better way to improve the performance of the thermal engine and the glider is that the thermal glider operates at relatively shallow gliding angle in the cold water layer or warm water layer but operates at relatively large gliding angle between the cold water layer and the warm water layer. As is shown in Fig.8(b), when the thermal glider operates at 45oin the whole cycle, the thermal engine cannot work continuously and normally. By decreasing the absolute value of the gliding angle from 45oto 35owhen the thermal glider operates at the depth below 1 000 m and above 200 m, and maintaining the absolute value of the gliding angle at 45° when the thermal glider operates at the depth between 200 m and 1 000 m, the thermal engine can work efficiently and the thermal glider can operate continuously. In addition, one can see that the transition time in the phase change processes of the working fluid and the gliding cycle are shorter, thus the glider performance is further improved.

Fig.8 Improvement on the performance of the thermal glider

8. Conclusions

To study the effect of the displacement and the gliding angle on the performance of the underwater thermal glider, a series of numerical and experimental investigations have been carried out. The ways to improve the performance of the thermal engine and the thermal glider have been analyzed. From all the discussions, some meaningful conclusions drawn are as follows:

(1) With a decrease in the displacement, or with an increase in the absolute value of the gliding angle, the transition time in the phase change processes of the working fluid and the gliding cycle become shorter. There exist the threshold values of displacement and gliding angle for the thermal engine’s operation. When the displacement is smaller than the critical displacement, or the absolute value of the gliding angle is greater than the critical absolute value of the gliding angle, the thermal engine will work abnormally. To keep the thermal engine working efficiently, the glider should stay in the warm surfacewater for a certain period of time before its moving into the cold water layer and will be subject to drift with the surface current. It is unfavorable for the thermal glider to penetrate through the ocean current, which is the main operational constraint of the gliders.

(2) A decrease in the displacement or an increase in the absolute value of the gliding angle results in an increase of the vertical speed of the glider. Its effect on thermal engine is equivalent to that of reducing the thermocline depth or thickness. On the other hand, an increase in the displacement or a decrease in the absolute value of the gliding angle results in a decrease of the vertical speed of the glider. Its effect on thermal engine is equivalent to that of increasing the thermocline depth or thickness.

(3) When the location of the thermocline is shallow and it is not conducive to the normal work of the thermal engine, the displacement should be increased in the glider design processes or the absolute value of the gliding angle should be reduced in operational processes so that the negative effects of the thermocline could be eliminated. Thus the performance of the thermal engine and then the glider can be improved.

(4) A better way to improve the performance of the thermal engine and the thermal glider is that the thermal glider operates at relatively small gliding angle in the cold water layer or warm water layer but operates at relatively large gliding angle between the cold water layer and the warm water layer.

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10.1016/S1001-6058(09)60095-0

* Project supported by the Special Research Fund for the Doctoral Program of Higher Education (Grant No. 20090073110012), the National Natural Science Foundation of China (Grant No. 50979058).

Biography: YANG Hai (1981-), Male, Ph. D. Candidate

MA Jie, E-mail: jma@sjtu.edu.cn