Elsevier

Computers & Fluids

Volume 174, 30 September 2018, Pages 271-282
Computers & Fluids

Hydrodynamic analysis and optimization of the Titan submarine via the SPH and Finite–Volume methods

https://doi.org/10.1016/j.compfluid.2018.08.014Get rights and content

Highlights

  • A SPH and FVM numerical hydrodynamics analysis of the Titan submarine is presented.

  • Contours of flow variables are shown in the near and far field for several Re and Fr.

  • Preliminary thrust and power values are given for surfaced and submerged conditions.

  • Design recommendations are proposed based on the current submarine hull shape.

  • SPH is successfully applied to simulate 3D fluid flow over complex geometries.

Abstract

This work presents a numerical analysis of the hydrodynamics of a conceptual submarine designed by NASA to operate in the liquid hydrocarbon seas of Titan, the largest Saturnian moon. Operational conditions of the “Titan submarine” include navigation at the free surface as well as deeply submerged. For the former, a numerical flow analysis is conducted using Smoothed Particle Hydrodynamics (SPH), one of the most advanced particle methods with high suitability for the simulation of free-surface flow. The open-source SPH code adopted in this research is benchmarked against results of flow past a boat on Earth from experimental and numerical work of other authors. This validation study corroborates the effectiveness of SPH in modeling flow past marine vehicles. In the deeply-submerged regime, a mesh-based approach is adopted, i.e. the Finite–Volume method (FVM), using well-established commercial software. Preliminary calculations of drag, thrust and power for the Titan submarine are then obtained for both surfaced and submerged conditions. The estimation of the total drag acting on the submarine allows to identify an upper bound for thrust and power requirements for efficient navigation. Results from this study also include flow visualization around the hull and final design recommendations, as well as an assessment of the necessary power requirements for an efficient exploration of Titan’s seas.

Introduction

The Cassini mission has been largely successful for several reasons, including the international collaboration between NASA and ESA on such a large-scale, revolutionary project [1]. The ability to construct elaborate orbital trajectories allowed the satellite to get close-ups of outer solar system phenomena and administer the landing of a separated probe, Huygens, on the farthest planetary object from Earth to date, Titan. Huygens was designed to either land on a dry surface or in a liquid body. The possibility that Titan was covered in a global ocean remained unknown during the launch of the satellite. The probe inevitably landed on a dry surface, proving the moon was not covered in a global ocean. However, the question of whether or not Titan could harbor bodies of liquid on the surface still remained a mystery. In 2006, using radar mapping, Cassini made the discovery of stable, accessible bodies of surface liquid which sustained considerable depths composed of variable concentrations of ethane, methane, and nitrogen, with a surface temperature around 93 K across Titan’s polar regions [2], [3], [4]. Titan has already been investigated for years due to it being the only natural satellite to possess a dense atmosphere [5], but with these recent findings, it is now also the only known planetary object in the solar system other than Earth to harbor such features. Cassini and Huygens unveiled a world that is both strange and familiar to our own [6], with vast equatorial dune fields [7], channel networks that drain from mountains into basins [8], and liquid hydrocarbon seas [3]. Analogous to Earth’s history being tied to its oceans, Titan’s origin and evolution are chronicled within the nature and evolution of its seas. While Cassini has provided a wealth of information regarding the distribution of liquid deposits on Titan [9], [10], [11], it has only provided a basic understanding of its composition and role in Titan’s volatile cycles [6], [12], [13]. Thus, in order to address fundamental questions about the nature of Titan’s seas, in-situ exploration is required.

Since the finding of large, stable bodies of liquid on Titan’s surface, researchers have been working on the design of vehicles capable of landing in these seas and conducting in-situ science. A NASA–ESA Flagship mission, Titan Saturn System Mission (TSSM), included an orbiter, a Montgolfier balloon, and a lander. The orbiter would allow opportunities to observe Saturn, multiple icy moons and the complex interaction between Titan and Saturn’s magnetosphere. The Montgolfier balloon would use an X-band relay link with the orbiter for communications to report findings from its imaging spectrometer, atmospheric and meteorological packages, radar sounder, chemical analyzer and magnetometer. The lander is a battery operated vehicle meant to nominally last for 9 h to conduct in-situ science within the seas [14], [15]; a mission to Jupiter was eventually selected instead. Following the preliminary research of TSSM, a NASA Discovery solicitation study, Titan Mare Explorer (TiME), focused solely on a floating vessel meant to “sail” on the seas of Titan while still being able to return fundamental science [6], [12], [16]. Another NASA funded project introduced a robotic surface vessel equipped with its own on-board real-time navigation and hazard avoidance system, surface and subsurface exploration sensor suite, and autonomous science investigation software system [17].

Continuing the trend of researching and designing marine vessels to explore Titan’s seas, a conceptual design of an autonomous submarine was recently developed for a NASA Innovative Advanced Concept (NIAC) Phase 1 and 2 study [18], as depicted in Fig. 1. The advantage of conducting science with a submarine versus other vehicles seen in previous studies is that a submarine would be capable of submerging to various depths. Additionally, the propulsive capabilities of a submarine would allow for it to traverse much larger distances and potentially enter multiple bodies of liquid instead of simply relying on possible tidal or wind forces as a floating capsule would require. The submarine would still be capable of conducting the typical surface experiments of a floating capsule, such as measuring sea-surface meteorology and exchange; observing shoreline geomorphology, large-scale weather activity and other atmospheric optics; as well as investigating tidal waves and inferring currents. However, conducting submerged science has the potential for a broader range of results from the mission, such as measuring bulk and trace constituents of the seas at different depths and locations; detecting stratified layers, bubbles, and other natural phenomena; analyzing suspended sediment, air-sea exchange and local variations in bulk ethane and methane; and obtaining optical imaging of the seabed.

Stability of the submarine is paramount for the aforementioned experiments to be successfully conducted. One focus of this paper is to optimize the NIAC Phase 1 design to ensure hydrodynamic stability when operating. Furthermore, to meet these science exploration objectives, the submarine must operate autonomously, navigate in the vicinity of the seabed at pressures up to 10 atm, traverse large distances with limited energy, hover at the surface and at any depth within the seas, and withstand different concentration levels of hydrocarbons [18], [19].

One of the current major challenges with the design of the Titan submarine is the calculation of the propulsive power requirements, both at the free surface as well as deeply submerged within the seas. Because of the submarine’s complex geometry, numerical analysis is crucial for an accurate estimation of wave resistance, especially since the top half of the submarine is thin whereas the bottom half is blunt. Future extraterrestrial exploration vehicles that do not communicate using an orbiter will likely follow a similar design as the presence of a phased antenna array is required. This study seeks to understand how fluid resistance behaves on such a unique design when it is partially and fully submerged. Predictions of drag and other fluid forces on the submarine via empirical calculations have been presented in [18] for the simple case of a fully submerged submarine operating under steady-state conditions in pure liquid ethane. However, due to direct-to-Earth communication needs, the submarine is going to be operating in submerged conditions for only 8 h per Earth day, whereas the remaining 16 h will include ascending, descending, and mostly cruising at the free surface. Moreover, the two largest seas that are of particular interest for exploration, Kraken and Ligeia Mare, are not composed of pure ethane but consist roughly of 94% ethane, 5% methane and 1% nitrogen, and 13% ethane, 74% methane and 13% nitrogen, respectively [3]. The amount of propulsion needed to overcome the drag during these operational conditions in seas of varying composition could require design changes and constraints on the power and propulsion system. Operational issues such as speed limits and relocation of sensors need to be determined as well to optimize the hydrodynamics of the vessel. Furthermore, computation of fluid flow around the submarine is essential to observe phenomena such as wave generation and wake patterns. Thus, detailed Computational Fluid Dynamics (CFD) simulations are required to validate preliminary calculations, update concepts of operations based on design limitations, and understand the interaction between the extraterrestrial seas and the submarine at the surface and various depths.

The manuscript is organized as follows: firstly, Section 2 introduces the relevant parameters of the submarine geometry as well as Titan seas. Then, Smoothed Particle Hydrodynamics (SPH) working principles and equations are presented in Section 2.1, together with a validation study showing how SPH is a viable option for simulating navigation of the submarine at the free-surface. Section 2.2 incorporates the numerical set-up for the simulation of deeply submerged navigation via the Finite–Volume method (FVM). Subsequently, Section 3 encompasses numerical results for both SPH and FVM simulations, as well as design considerations for the optimization of the submarine geometry. Finally, some conclusions and future work are drawn in Section 4.

Section snippets

Numerical modeling

The numerical study involves CFD simulations of flow past a rigid body moving with constant speed on the free surface and in deeply-submerged conditions without any heat transfer. A Computer Aided Design (CAD) model of the NIAC Phase 1 submarine has been adopted, with a length overall L=6 m, a beam W=1 m and total height H=2 m. The varying compositions of Kraken and Ligeia Mare result in densities of 644 kg/m3 and 523 kg/m3, and dynamic viscosities of 1014 μPas and 227 μPas at the surface,

Drag, thrust, power

Fig. 7 reports dimensionless results of DualSPHysics simulations for drag coefficient against simulation time, comparing operations in Kraken and Ligeia Mare for a set of Froude numbers given by (0.09, 0.18, 0.26, 0.35), and a hull draft of 0.60 m. The submarine accelerates from rest over 45 s until reaching and maintaining a constant speed for the remainder of the simulation. Thus, the drag coefficient steeply increases to a maximum before decreasing to a steady-state value. Based on the peak

Conclusion and future work

A numerical analysis of the NIAC Phase 1 Titan submarine has been presented in this work. Simulations have been carried out using Smoothed Particle Hydrodynamics code for the free-surface cases and the Finite–Volume method for the deeply-submerged cases. The former has been validated against experimental and numerical work from other authors in the cited literature with good agreement. Numerical results in this research include drag force calculation for navigation at the free surface as well

Acknowledgments

We are grateful for the support of Steve Oleson, COMPASS Concurrent Spacecraft Design Team lead at NASA John H. Glenn Research Center. We would also like to truly thank Mark Stewart for carefully reviewing this paper. Support for this work was provided by NASA through Grant NNX17EA87P from NASA Glenn Research Center.

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