A potential-flow based flight simulator for an underwater glider

Science Arts & Métiers (SAM)

is an open access repository that collects the work of Arts et Métiers Institute of

Technology researchers and makes it freely available over the web where possible.

This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/8991

To cite this version :

Surasak PHOEMSAPTHAWEE, Marc LE BOULLUEC, Jean-Marc LAURENS, François DENISET - A potential-flow based flight simulator for an underwater glider - Journal of Marine Science and Application - Vol. 12, n°1, p.112-121 - 2013

Any correspondence concerning this service should be sent to the repository Administrator : [email protected]

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produce very similar results as expected. This will be the case for most trajectories simulations but in the next section, we will present a case where both approaches yield very different results.

3.2 Helical trajectory

In this section, an examination of the helical trajectory is explored and tested by commanding the glider to dive with positive trim and heel command angles with the intention to change the glider direction. In the example presented here, trim and heel command angles are both equal to 10 degrees. Three different geometries of the stabilizer are considered. The dimensions of the three stabilizers are illustrated in Fig.10.

Fig.10 Dimensions of stabilizers

The glider is expected to turn because of the lateral component of the main wing lift force when the glider is heeling. In the case of a positive heel angle as in these simulations, the glider is then expected to turn to the starboard direction. The obtained trajectories for both approaches are presented in Fig.11. Unlike the sawtooth simulations, the two approaches produce very different results.

According to the numerical results of the simple approach, the glider moves to starboard as expected. The stabilizer size is only of little effect; the three trajectories are almost the same. The glider turns with the steering force generated by the main wing and the stabilizer generates the hydrodynamic moment to adjust the glider orientation to the incident inflow. However, this behavior is not always observed in reality. The glider Sterne (Ahmed-Ali et al. 2003) which was developed at Ensta-Bretagne experienced counter-steering behavior. The first Sterne model was lost during an experiment at sea because of this unexpected behavior. It was suspected that the stabilizer size was responsible for this. The new Sterne model equipped with a larger stabilizer does not present any counter-steering behavior. This is the reason why, in order to confirm the role of the stabilizer, we decided to cover different stabilizer geometries in this study.

Fig.11 Top view of helical trajectory during 1000 seconds for 10° trim and 10° heel command angles; top with potential flow approach, bottom with simple approach

The potential flow results retrieve the experimentally observed counter-steering behavior. The turning equilibrium conditions of the three stabilizers are compared in Table 1. These numerical results confirm that the stabilizer size plays an important role in this behavior. The smallest stabilizer (stabilizer I) causes the glider to turn to the counter-steering direction (the port direction in this case) while the other two do not. When the stabilizer is large enough (stabilizer III), the glider behaves as expected and predicted by the simpler approach. In the case of the intermediate size (stabilizer II), the stabilizer is not large enough to steer the glider properly. When the stabilizer is too small, it cannot produce enough hydrodynamic moment to counteract the counter-steering hydrodynamic moment. The counter-steering hydrodynamic moment is generated by the main wing lift lateral component pointing to starboard (see Fig.12) and the lateral force due to

the body drifting pointing to port. If not sufficiently countered, the moment will make the glider Sterne turn to port because the body drifting drag force center is situated well in front of the wing.

Table 1 Turning equilibrium conditions from the potential flow approach results; the gliding diving with 10° trim and 10° heel command angle

Stabilizer I II III

Turning radius (m) 22 171 39

Turning rate (deg/s) 0.88 -0.11 -0.48 Advance speed (m/s) 0.334 0.339 0.329 Diving speed (m/s) 0.062 0.058 0.056 AOA of stabilizer (deg) 8.85 3.95 2.35 AOA of main wing (deg) 1.68 1.55 1.63 Heel angle (deg) 12.56 9.68 8.51

Trim angle (deg) 7.08 7.51 7.67

Fig.12 Force diagram in steering mechanics

In this case the source of the counter-steering moment was hence generated by the lateral friction force on the drifting body. The simple hydrodynamic model does not have this lateral force because as described in section 2.2, in this simple parametric model, the friction is only applied along the main axis. Once it starts to turn to port, the stabilizer sees a flow from the port direction and its lift points to starboard generating a moment at port helping the glider to find a stable route in the port direction.

With higher accelerations, the added mass tensor could take over this effect. The way the body added mass tensor is taken into account is the same for both models. In such cases, both models would see the same counter steering moment but it does not necessarily imply that they would predict the same trajectory because of the fluid inertia effect on the lifting bodies. In the simple model, the hydrodynamic moment generated by the stabilizer is fully perceived as soon as the glider heels without any delay. In the potential flow simulations, there is a delay between the geometric position and the hydrodynamic response. This delay exists because of the fluid inertia applied by the stabilizer. Because of this delay,

if the stabilizer counteracting moment is not strong enough, the glider could find the time to position itself in the other equilibrium state causing the counter-steering behavior. In principle, it is possible to add such effects and other effects in a parametric model. For instance, we could add the interaction between the glider body and its appendages using a correction factor as suggested by Caldeira and Clarke (1988). Adding some of these parameters would not significantly increase CPU time, but it would rapidly make the parametric model look like a patchwork difficult to control and maintain. Before any additional parameter is included within the parametric model, its importance and effect have to be clearly identified. Furthermore, not all effects are easily replaced by a simple model involving a single parameter. The lateral friction drag for instance depends on the Reynolds number but also on the body geometry. Although the potential flow simulator does not take all the physics into account, it can be used as a numerical towing tank facility to improve the simulator, i.e. the parametric model. Its CPU time is not negligible compared to the simple hydrodynamic code but it consists of a stage between the parametric model and the experimental trials.

4 Computation resource consumption

We now consider the underwater glider equipped with the stabilizer III to simulate a non trivial trajectory. The objective is to simulate a helical diving trajectory followed by a surfacing contra-rotating helical trajectory. As in the previous simulations, the glider is launched with a 0.2 m/s horizontal velocity in the x - positive direction. The heel command b

angle is fixed at 20 degrees. The trim command and the ballast are varied alternatively every 1100 seconds. For the first 1100 seconds, the trim command angle is 10 degrees and the ballast takes the water in for diving. For the next 1100 seconds, the trim command angle is -10 degrees and the ballast drains the water off for surfacing. The total duration of the simulation is 2332 seconds and takes 20000 time steps. This simulation involves about 24 hours of computation time on a standard workstation (CPU 4 cores with 2.66 GHz).

5 Conclusion and perspective

An Euler-Newton equations solver is coupled with a potential flow code to simulate 6-DOF trajectories of underwater gliders. This simulator can be used to study the hydrodynamic behavior of gliders in order to improve the automatic flight control and to optimize the geometry of the glider. A numerical study of the hydrodynamic behavior of an underwater glider has been conducted. All results are compared with a simple parametric simulator. A series of simulations considering sawtooth trajectories was first conducted. In this case both simulators presented very similar trajectories. As expected, the glider velocity varies as a function of the trim angle. To confirm a behavior observed

experimentally, a second series of simulations examining the glider steering was conducted. The potential flow simulator shows that the stabilizer geometry plays an important role in steering control. Inappropriate stabilizer geometry can cause counter-steering behavior that the parametric simulator cannot anticipate. A non trivial case was finally presented to demonstrate the capabilities of the potential flow based glider simulator. Enhancing the parametric model with additional features is easy, but simple models are the best way to determine which physical effect is really important. The potential flow code is a good practical tool to simulate complex trajectory patterns and to verify whether the parametric code predicts the same trajectory. However, further validations utilizing real data and experimental model testing are necessary to increase confidence in the potential simulator before it can be adopted as a template for the parametric model enhancements.

Fig.13 Example of trajectory simulation for a real-time duration of 2332 seconds, of which the CPU time is about 24 hours on a standard PC (the glider appears 10 times bigger than it is) Good quality experimental results will be extremely difficult to obtain. The behavior of the Sterne glider has been obtained from sea trials. The onboard instruments record the velocities, depth, heel and pitch angles. The trajectory is deduced from these data. There is no information concerning the environmental conditions at sea. To conduct a proper experimental investigation at scale 1, we would need a calm pool of water with very large dimensions. Although the glider is only 2 meters long, its gyration radius is about 30 meters. In Fig.13, the glider appears much larger than in reality as stated in the caption. We plan to perform some experimental trials on a reduced size model at the Ifremer tank facility in Brest. Since the scale cannot be too small, we will not be able to conduct anything resembling the case of Fig.13 in the tank. However, a full gyration is not necessary to study the counter-steering behavior. The scale of the experimental model is the key issue since it will be a compromise between several factors including the Reynolds number, manufacture and the observable trajectories in the Ifremer towing tank

facility.

Acknowledgement

This work is partially supported by the Europole Mer (http://www.europolemer.eu).

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Phoemsapthawee Surasak worked on the

development of the maneuvring model for the glider at Ifremer in Brest, France, where he also completed his Ph.D. on the development of a cavitation model. He is now a lecturer in naval hydrodynamics at the IMC in Thailand.

Le Boulluec Marc is a research engineer in

hydrodynamics at Ifremer, Centre de Bretagne, France. His main research fields include dynamics of floating bodies, mooring and flow-lines and marine renewable energy devices.

Laurens Jean-Marc is a senior lecturer in naval

hydrodynamics at Ensta Bretagne, Brest, France. His main research fields include resistance and propulsion, ship and underwater vehicles maneuverability.

Deniset François is an associate professor in naval

hydrodynamics at french naval academy, Brest, France. His main research fields include performance of hydrofoils and marine propulsion systems, fluid-structure interactions and cavitation.