Trade study of advanced ballast control systems for an extraterrestrial submarine

Ocean Engineering 171 (2019) 1–13

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Trade study of advanced ballast control systems for an extraterrestrial submarine

T

Peter Meyerhofera,∗, Jason Hartwigb a b

Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH, 44106, USA Case Western Reserve University, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Titan Submarine Ballast system Liquid methane Liquid ethane

Saturn's largest moon, Titan, has seas of cryogenic liquid methane and ethane as well as dynamic geology and a cycle of methane evaporation and rain. NASA is evaluating concepts for an extraterrestrial submarine to explore these seas from surface to bottom to shoreline, representing an unprecedented design challenge. The Titan submarine ballast system that controls the vertical ascent and descent must operate autonomously for a minimum of 365 dives in cryogenic seas below 95 K and handle liquid density variations up to 30%. Further complicating the concept is the high solubility of nitrogen gas in the seas, which leads to potential phase change and boiling issues during ballast pressure control. This paper presents a trade study of 7 advanced concepts for an autonomous submarine ballast system for Titan; 4 were down-selected as viable concepts. For each concept, analytical system description and sizing, autonomous concept of operation, parts list, and pros and cons are given. Systems are traded using mass, power, and complexity in control as metrics.

1. Introduction Saturn's giant moon Titan is a remarkable environment, with the only known liquid surface seas outside of Earth (Lorenz and Mitton, 2010; Lorenz and Sotin, 2010; Lorenz, 2013). These seas are composed of liquid methane and liquid ethane with dissolved nitrogen gas from the atmosphere, at a surface temperature of ∼93 K and a pressure of 1.5 bar; the gravity on Titan is 1.35 m/s2. This creates science applications for astrobiology as well as the study of geological cycles similar to those on Earth, but with methane instead of water as the working fluid. A submarine is under study as a means to explore these liquid bodies from atmosphere to seabed to shoreline (Hartwig et al., 2016). The reason for choosing a submarine is the depth estimates of the seas (see section 3.1), at which seabed features are best measured with a submersible, which can also collect sediment samples. The purpose of the submarine ballast system is to control the weight of the craft, and thus density, so that it can rise and sink at will. This involves a balance of the vehicle weight and the weight of the displaced fluid:

ρsea Vsub g = msub g

(1)

In general, a design can work along two different lines: change the mass msub of the vehicle for a fixed vehicle volume, or fix msub within a flexible hull that increases or decreases Vsub as necessary. Terrestrial ∗

submarines change the left side of Equation (1), among other methods, by using diesel fuel to force denser water in or out of the bottom of the tank (Allen, 1961); several control logic schemes for such designs have been developed (Dibitetto, 1995; Hui et al., 2011; Woods et al., 2012; Font and Garcia-Pelaez, 2013). Another design method based on liquid ballast, which controls weight distribution but not total weight, involves shifting fluid between trim tanks at the forward and aft ends of the submarine (Piry, 1959). One means of changing the right side of Equation (1) is by shifting a fluid between an internal storage space and an external storage space that expands when filled. This is the method used by many autonomous submarines on Earth (Davis et al., 2003). A scheme that controls trim and ballast simultaneously is to have a ballast tank on each end of the vehicle, so that filling one more than the other changes the mass balance (Tangirala and Dzielski, 2007). Many of the ballast concepts that function well on Earth cannot be applied to the Titan submarine. Naval submarines (Burcher and Rydill, 1994) commonly flood the main ballast tanks at the beginning of a dive to achieve neutral buoyancy; after using other control methods for fine corrections, such as “hard” tanks that flood and blow down at depth, the main tanks are blown down at the end of the dive. Only in emergencies are the main tanks blown out mid-dive. The flood and blowdown operations are typically done with compressed air. Such vehicles benefit from relatively small density changes with salinity and temperature, but on Titan, the possibility of very large changes (high-

Corresponding author., E-mail address: [email protected] (P. Meyerhofer).

https://doi.org/10.1016/j.oceaneng.2018.10.055 Received 9 June 2018; Received in revised form 21 August 2018; Accepted 24 October 2018 0029-8018/ © 2018 Published by Elsevier Ltd.

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P. Meyerhofer, J. Hartwig

Nomenclature

A C CD Cv d D g J L m n P R Rg Re T t V V˙ v x z

Greek

area (m2) Concentration gradient (mol/m3) Drag coefficient Valve size coefficient Depth (m) Diffusion coefficient (m2/s) Gravitational acceleration (m/s2) Diffusion rate (mol/m2-s) Length (m) mass (kg) number of moles Pressure (MPa) Radius (m) Gas constant (J/kg-K) Reynolds number Temperature (K) Time (s) Volume (m3) Volume flow rate (m3/s) Velocity (m/s) Mole fraction length coordinate (m)

ε ρ μ

Dielectric constant Density (kg/m3) Viscosity (μPa-s)

Subscripts

bal c em eq gb net neu sea sub tank

liquid ballast characteristic length emergency bladder equilibrium gas bottle excess of ballast in tank, above neutral buoyancy neutral buoyancy sea liquid property submarine capacity of ballast tank

Acronyms LNG Scc

methane to high-ethane seas) would require bigger “hard” tanks and offer reason for a different concept entirely. The other benefit terrestrial submarines enjoy is that compressed air may readily be used to push water from the ballast tanks directly. The Titan atmosphere, however, is both near the condensation point and is highly soluble in the seas, which demands modifications for an extraterrestrial submarine. Another terrestrial example (Watson, 1971) is the method of carrying large “shot” weights that may be dropped to allow the sub to rise quickly. This is a common tactic in historic deep submersibles (Forman, 1999), but it requires a support ship at the surface to replace the shot for each dive. This is no difficulty for Earth research expeditions, but the Titan submarine must be completely self-contained; any weight it drops can be used only once as an emergency. One alternative to a submarine with active buoyancy controls is a boat that remains on the surface and acquires data from the depths with a handful of expendable dropsondes (Lorenz et al., 2018). The drawback is that such a design allows the direct study of the seabed at very few locations, while a submarine could explore the whole extent of the depths and seabed along its course.

Liquefied natural gas standard cubic centimeters (cm3 of gas at STP)

for at least one Earth year, totaling 365 dives nominally. One of the biggest challenges in realizing this mission is to design an autonomous, functioning ballast system at cryogenic temperatures. An additional degree of robustness is also necessary because there is no possibility of repairs; Earth submarines, for comparison, have ready access to human maintenance, and room-temperature hardware is much better established than cryogenic hardware. The Phase I submarine was originally intended only for an ethanerich sea. The concept in this paper is intended to be more versatile, able to float or sink at will in any methane-ethane ratio. This allows the submarine to travel between Kraken and Ligeia Mare, with Ligeia being the more methane-rich sea. One of the two ballast tanks for the Phase I submarine is shown in

2. Background Fig. 1 shows a composite image from Cassini of the seas near the north pole of Titan, which are comparable in size to the Great Lakes of North America. The seas are composed primarily of methane and ethane (Cordier et al., 2009), under a mostly-nitrogen atmosphere at ∼93 K and 1.5 bar; Table 1 compares these substances to the water that covers Earth. Kraken Mare and Ligeia Mare are of particular interest because they may be linked by active fluid flow. The tides that might flow through the various regions of the seas (Tokano, 2010), and the possible influence of hypothesized methane rain (Lorenz, 1993), suggest many other dynamic effects to study. NASA is currently developing concepts for a submarine (Oleson et al., 2014) for the seas of Titan is shown in Fig. 2. (It is referred to as the Phase I concept for the remainder of the paper.) The mission plan is to launch in 2038 so that the vehicle arrives on Titan in northern summer to allow for direct-to-Earth communication. Once landed in the seas, the vehicle will dive for 8 h per Earth day, then spent 16 h at the surface communicating to Earth. Such a cycle is expected to continue

Fig. 1. A composite Cassini image of the seas near Titan's North Pole (credit: NASA). 2

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study options considered here. One is upper and lower density bounds of the Titan seas. Based on these bounds, the ballast tank can be sized to allow full operation, and the amount of control resolution determines how quickly the vehicle will rise or sink (based on Reynolds number, and thereby viscosity). Most of the required parts, and the various uncertainties involved in the estimates, are also shared between the concepts.

Table 1 Comparative properties of methane, ethane and water. In the last 3 rows, methane and ethane are based on the Titan atmosphere (1.5 bar and 93 K); water is based on Earth atmosphere (1 bar and 300 K).

Triple Pt (K) Triple Pt (kPa) Critical Pt (K) Critical Pt (MPa) Boiling Pt (K) at 1 bar Liquid Properties Density (kg/m3) Viscosity (μPa-s) Dielectric Constant

Methane

Ethane

Water

91 12 191 4.6 111 450 180 1.67

91 0.0011 306 4.9 184 650 1140 1.93

273 0.61 647 22 373 1000 850 78

3.1. Sea properties The first step toward analyzing the ballast concepts is to determine liquid properties. This is achieved using a 1D thermodynamic equilibrium model where the surface composition (not including nitrogen) ranges from 17 parts methane/3 parts ethane to nearly pure ethane (Hayes, 2016). The Titan Sea was considered to be divided into discrete, static depth layers. At each of these layers the 5 unknowns were pressure, temperature and the mole fractions of methane, ethane, and nitrogen. Five equations are needed to solve for these unknowns: pressure accumulates hydrostatically, mole fractions add to 1, energy is conserved, mixture chemical potential and enthalpy are constant between liquid layers. The general assessment was that sea density changes from the surface value by less than 1% within the depth range modeled. Design ranges are shown in Table 2. To bound properties, assumed mole ratios at the surfaces of Kraken Mare and Ligeia Mare (Hayes, 2016) are 1:19 and 17:3 methane:ethane, respectively. Using the solubility model, this corresponds to a methane:ethane:nitrogen ratio of 5:93:2 and 74:13:13 for Kraken and Ligeia Mare, respectively. Using the thermodynamic equilibrium model to estimate property changes with depth, this corresponds to a density range of 523–643 kg/m3 for Ligeia and Kraken Mare, respectively. The maximum sea pressure estimate in Ligeia is based on a depth measurement from Cassini of about 160 m (Mastrogiuseppe et al., 2014), while Kraken is sufficiently deep that no radar signal returns from the seabed (the pressure estimate assumes 1 km depth). The density bounds that will be used for this study are somewhat wider, at 500–650 kg/m3. The lower bound in intended to guarantee that the submarine can float in any sea composition (the lowest density occurs for pure methane with dissolved nitrogen). This is a density range of 30%; for comparison, for Earth submarines, the range is about 2% between saltwater and freshwater (Talley et al., 2011). Therefore, the ballast system is likely to be the single largest subsystem in the vehicle.

Fig. 2. The Phase I submarine, with the ballast tank labeled.

Fig. 3. To sink, the ballast tank is flooded at the surface by opening bottom valves to allow in sea liquid and top valves to vent gas out. To rise, a high pressure non-condensable gas, either gaseous helium (GHe) or gaseous neon (GNe) is expelled into a space that moves a separator to displace liquid; the separator limited the gas dissolving in the liquid, preserving the fixed supply brought from Earth. This work develops in greater detail an existing submarine ballast concept for the Titan seas (Hartwig et al., 2016; Oleson et al., 2014). In particular, it expands the ballast discussion in (Hartwig et al., 2016) to explore a diverse array of possible control methods, as well as the Phase I baseline. First, it describes concerns that affect all such concepts. These are the sea properties, sizing the ballast tank, hardware specifications, and measurement uncertainty. Seven concepts are presented. For each concept, a model is laid out and analyzed, an approximate operational scheme is given, and the total mass of required parts is estimated. Finally, in the conclusion, the pros and cons of all the concepts are listed, along with a summary of mass and power requirements. An assessment is made of which system is best.

3.2. Tank size and sink rate The second step toward designing the ballast system is to decide the volume of liquid that needs to be expelled, as well as the resolution with which small amounts of liquid can be added or removed. The total weight of the submarine was estimated at 1386 kg, and its total volume was roughly 2 m3. For safety, the vehicle has to float in the lightest sea, methane-nitrogen (∼500 kg/m3), which places the required volume at Vsub = 2.77 m3. The volume threshold for sinking in an ethane-nitrogen sea, ∼650 kg/m3, is Vsub = 2.12 m3 or less. The volume that the tank system must take in to sink is that which covers the surplus of displaced

3. General considerations Several aspects of the ballast design are common to all the trade

Fig. 3. The original proposed ballast system for Phase I. 3

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operate gradually enough that it does not allow more than 90 Pa/s of pressure change. The arrangement of ballast tank volume relative to the submarine body is also important. Because weight distribution is an important factor in the vehicle pitch and roll, the same liquid ballast can be used to cause or mitigate any such variation that is desired. One alternative is to have separate internal, or trim tanks, that shuttle a liquid between several positions inside the submarine, but that would be an additional system. A simple implementation of this method is to have 4 discrete tanks, sharing some of their hardware, at each of the forward and aft, port, and starboard corners. Selectively filling one tank first causes that area of the vehicle to angle down, at which point filling the other tanks would stabilize the attitude.

Table 2 Properties of methane-rich and ethane-rich seas used in the trade study.

Composition ( x CH 4 : x C 2H 6 : xN 2 ratio) Density (kg/m3) Viscosity (μPa-s) Dielectric Constant Depth (m) Max Pressure (MPa)

Ligeia

Kraken

74:13:13 523 200 1.68 200 0.3

5:93:2 643 1000 1.92 500+ 1

mass, or the difference between displaced and actual mass divided by the density as shown in Fig. 4. As a representation of conditions slightly below the sea surface, the pressure (for density calculations) is taken to be 0.2 MPa, with the dissolved nitrogen concentration assumed to be the same as at the surface (pressure of 0.15 MPa). The ballast volume required is greatest for the densest possible composition, pure liquid ethane with dissolved nitrogen, at about 0.65 m3. For Ligeia Mare, with 85% methane, the required ballast volume is about 0.12 m3. These numbers are the total ballast volume between all tanks. Therefore, as a margin of error, and also to compensate for any future increases in submarine weight or displacement, the ballast tanks should be baselined at 1 m3 capacity. Another concern for operation is the submarine sink rate. This determines how tightly the flow through the valves must be controlled. The rate of sinking was calculated from a force balance of gravity and drag, excluding hydrodynamic lift (on the assumption that the submarine is not cruising):

ρsea Vnet g =

1 ρ v 2CD Asub , Vnet = Vbal − Vneu 2 sea

3.3. Uncertainty One important aspect of the operating scheme is the uncertainty within which its parameters can be measured. Current commercial flow meters for LNG (Emerson Process Management, 2015; General Electric, 2016) use ultrasonic measurement and generally have an uncertainty less than 0.5% of the reading; they could likely be miniaturized for the submarine. Cryogenic pressure transducers (Kulite Semiconductor Products, 2014) can have uncertainties well within 1% of full scale. A densimeter is not necessary: before the dive, the chemistry analysis package onboard the submarine can report the composition with negligible error, and the processor can compute mixture density. On the next dive, the control system could then match the vehicle density to this estimate of sea density, with physical checks such as liquid level sensing. The software for this calculation would be REFPROP (Kunz et al., 2007) (with inputs of temperature and pressure, and internal density uncertainty of 0.5% for LNG mixtures) on Earth, but some expedients are required for a vehicle processor. Based on preliminary numerical experiments, a 3-point quadratic fit for sea temperature (91.5, 93, 94.5 K) adds negligible uncertainty to mixture density, and a 4-point table lookup for composition (with linear interpolation) will add up to 1.5% uncertainty to mixture density. Based on a heat transfer calculation through the submarine wall into the Titan Sea, the skin temperature is up to 3 K higher than the sea temperature due to the internal heat source (∼3800 W spread uniformly over the submarine surface). The largest difference occurs when the submarine is stationary, and the convection is natural instead of forced. The processor can use known speed data to iterate heat transfer calculations with fixed properties and estimate, perhaps within 0.5 K, the sea temperature (note that this effect is larger than the one due to silicon diode uncertainty listed in Table 3). The effect of this additional error on the density calculation, given the density gradient of ∼0.3%

(2)

where g = 1.35 m/s2 is the gravity on Titan, the density ρsea is for the liquid mixture and v is the sinking velocity. The value of the drag coefficient is that for a cylinder: CD = 1.2 for Reynolds numbers ρ vL Re = seaμ c (where μ is the viscosity and Lc is the characteristic length) below about 500,000 (Manshadi, 2011). The bottom-facing area of the submarine is about 6.5 m2 in Phase I, but here is scaled up by the factor V 2/3 to Asub = 8.1 m2. This scaling accounts for the increased volume required to float in Ligeia Mare. Also, vehicle length is scaled up by the volume factor V 1/3 to Lc = 1.23 meters. Fig. 5 shows the results obtained from setting Vnet as a parameter and solving for velocity v in each case. Results are shown for ternary seas with methane/ethane mole ratios of 1:19 and 17:3, the Titan composition extremes representing Kraken Mare and Ligeia Mare, respectively. The analogous results for water are included for comparison, showing that both velocity and Reynolds number are lower on Titan than on Earth. The velocities so obtained for rising or sinking are identical for both compositional extremes because they depend only on gravity and geometry, but the Reynolds numbers are much higher for the 85% methane case (mostly due to lower viscosity, see Table 1). Due to the risk of tripping to turbulence near the critical Reynolds number (about 500,000 for a cylinder), which would cause the submarine to rise or sink significantly faster, the desired excess ballast while diving is 0.01 ≤ Vnet ≤ 0.05 m3, corresponding to about 0.1 m/s of depth change. At that rate, the vehicle would rise or sink 360 m in an hour. Therefore, the control resolution of the all concepts should be 0.01 m3 (or 10 L) of liquid. It should be noted that sinking quickly in a methane sea carries a potential risk of the flow around the submarine tripping to turbulence, causing a rapid acceleration and making control more difficult. This is because the turbulence transition could occur at a smaller Reynolds number than 500,000. If the vehicle sinks rapidly, it may hit the bottom with significant force. This can be distinguished by the rate of sea pressure change, which at a rising/sinking speed of 0.14 m/s varies between 95 and 120 Pa/s. A speed of 0.1 m/s, for comparison, creates a pressure change of 68–86 Pa/s. Therefore, the control system should

Fig. 4. Required ballast volume across the range of Titan sea mole fractions. 4

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Fig. 5. Estimates of a) steady-state sinking velocity and b) steady-state sinking Reynolds number of the submarine as a function of excess volume of sea liquid, for both composition extremes.

supported by experience: the gas bottles on spacecraft such as Cassini have held their pressure for many years of operation. The component parts of the concepts below are presented, along with the baseline mass estimates, in Table 4. The parts in the final submarine will be custom-built, but a first-order estimate of the masses can be made by comparison to existing commercial products (not necessarily cryogenic) that reach similar specifications. With respect to reliability, LNG pumps accumulate years of regular service in tank farms and port facilities; vapor return compressors at the same sites are also common; and electric motors can also be designed for submerged cryogenic service (Rush and Hall, 2001). The gas bottles are sized to meet 2 conditions (Lorenz and Mitton, 2010): maximum pressure at 300 K on Earth is 30 MPa; and (Lorenz and Sotin, 2010) after filling the required volume for the density at 93 K and 1 MPa, the bottle pressure at 93 K remains 1.1 MPa. If the gas is helium, the fully charged pressure at 93 K is 9.4 MPa; for neon, it is 7.83 MPa. The isentropic efficiency of hardware such as pumps is assumed to be 80%.

per Kelvin, is 0.15%. In total, the estimated mixture density uncertainty is ∼2%. The instrumentation needed to operate the ballast system in general is shown in Table 3. Inclinometers (TE Connectivity, 2016) can detect whether the submarine is pitching or rolling. The sea liquid level against the submarine side is detected on the surface by diode rakes forward and aft, which both span the vehicle height from top to bottom. While the vehicle is fully submerged, a sonar beacon on the top surface pings the sea surface to give a proxy for depth based on a method used in tanks (Flynn, 2005); if this proxy suddenly or rapidly increases, the submarine may be sinking. Commercial towable sonar units for Earth applications have mass about 20 kg (EdgeTech, 2016), though the unit designed for Titan will likely be significantly lighter due to structural integration. Depth sounding accuracy of 1% of reading is a plausible design goal (Arvelo and Lorenz, 2013). One alternative to the sonar- and pressure-based control scheme described in the concept sections below is the use of temperature and dielectric constant to infer sea density, and thereby estimate the degree of control action required. For reference, the uncertainty in dielectric constant, for the sensor on the Huygens probe, was ∼0.01 (Leese et al., 2012). At the measured temperature and pressure, the absolute dielectric constant corresponds to the nitrogen-methane-ethane composition as shown in Fig. 6, based on (Mitchell et al., 2017) using the solubility model to fix the nitrogen content at each methane/ethane ratio. The approximate mole fraction uncertainty (of methane or ethane) is then ∼0.04, which via REFPROP implies a density uncertainty of 1.5%. This method is available as an alternative to direct composition measurement.

4. Trade study The following section describes each of the seven ballast concept for the extraterrestrial submarine. Immediately, 2 concepts were rejected. The first was a scheme to liquefy nitrogen from the atmosphere into the ballast tank, then pump it out to float, but it was rejected due to high required liquefaction rates and unnecessary complexity. The second rejected concept was to flood the ballast tanks with sea liquid, then float by boiling the liquid; the heat required to do so far exceeds the waste heat available from the power system. In the concepts and operational outlines described below, the parts are labeled with a letter and a number; the letters used are P for pump, V for valve and C for compressor, and the numbers are 1, 2, etc. Note also that all concept drawings are vertically oriented, so that gravity points from top to bottom of the image.

3.4. Shared parts Compared to most LNG applications on Earth, the Titan seas are expected to hold many other hydrocarbons such as benzene as well as solid particulates. Any system that takes sea liquid into the vehicle and puts it through pumps or valves must filter out solid particulates, which would otherwise clog the hardware and possibly cause rapid failure. Such a filter could then be flushed out, for example, with a shot of pressurant gas. One potential complication with gas storage is helium leakage through the bottle over the 8-year duration of the mission, 7 years in transit from Earth, 1 year operating on Titan. Pressure vessels can generally be built and inspected to a helium loss rate of 10−6 scc of helium per second (Ni and Chang, 2010). Over 8 years, that adds up to 250 scc (0.05 g) of helium. For neon gas the equivalent mass is 0.25 g, which is an upper bound since neon should diffuse through the bottle wall less effectively than helium. In summary, the gas bottle should not be compromised by diffusion loss during transit. These estimates are

4.1. Pump system The third concept, which is the simplest ballast concept, uses only valves and a pump as shown in Fig. 7. However, it is limited in its operations compared to other concepts. Its main feature is that the tank sets neutral buoyancy at the surface, then establishes small positive buoyancy so that the vehicle floats if power fails. 4.1.1. Analysis In the following, the change in gas pressure with ullage volume in the tank is treated as ideal and isothermal (so PV is constant) and the total tank volume is assumed to be 1 m3. For nitrogen at Titan conditions, the compressibility factor is Z = 0.96, decreasing to Z = 0.88 near 5

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Adapted for Titan gravity Adapted for Titan gravity Plausible design goals (Arvelo and Lorenz, 2013); Earth unit is ∼20 kg (EdgeTech, 2016) Includes silicon diodes

–

± 0.05° ± 0.05° ± 1% of reading

0.022 K (at 77 K)

± 60 ° ± 60 ° 10–1000 m

0–100% submerged

1.4–500 K Sea temperature; Detect liquid level

Fig. 6. Illustration of the use of a dielectric meter (on the vertical axis) to deduce composition (mole fraction of each component, on the horizontal axis), at 95 K and 0.15 MPa. For example, at ε = 1.8 the mole fractions of methane and ethane are equal.

the saturation pressure (0.462 MPa at 93 K). The atmosphere is assumed to be pure nitrogen because the possible condensation of methane above Titan surface pressure removes only a minor gas component. The greatest operational risk in the pump concept is that the sea density might decrease while the submarine travels submerged. Such an event would result from an increase in methane concentration, and the resulting lack of buoyancy may compromise the mission. This is a concern mainly for the pump concept because without access to the atmosphere, removing liquid ballast draws a partial vacuum in the tank. The opposite change, the sea becoming denser, is safe because the submarine will simply float. The worst case is a transition from the high end of the density range, 650 kg/m3, to the low end, 500 kg/m3. To sink at the high density value, the submarine needs to take on 0.65 m3 of sea ballast. If the atmosphere is vented while taking on liquid, any liquid removal while submerged will risk structural failure as the tank collapses on itself. Therefore, the vent valve should remain closed until the tank pressure reaches 0.45 MPa, just below the saturation pressure. The pumping of 0.65 m3 of liquid ballast does not reach this threshold at any point in a sea temperature range of 91–95 K. The removal of all of this ballast in an emergency should, in principle, restore the tank to 0.15 MPa (without replenishing ullage from the atmosphere). However, any loss would put the empty tank below the surface pressure, risking collapse. It is therefore advisable to cover such uncertainties by building in a source of emergency ballast that allows the submarine to function as a boat even if the pumps fail. The purpose of emergency ballast is to inflate the submarine volume, to make up for the loss in sea density. Because the submarine displaced volume has to remain the same, the balance is ρ1 Vsub = ρ2 (Vsub + Vem) , therefore

Vem =

Silicon diode (Lake Shore Cryogenics, 2016)

Diode rake

Spanning top to bottom surfaces, forward and aft On diode rake

Detect pitch Detect roll Ping the surface to test rising/ sinking Detect liquid level Tilt 1 (TE Connectivity, 2016) Tilt 2 (TE Connectivity, 2016) Top sonar

Inside insulation Inside insulation Top surface

0.5 cm

Comments Uncertainty Range Function Location Measurement

Table 3 Instrumentation list for the ballast system.

P. Meyerhofer, J. Hartwig

ρ − ρ2 dρ Vsub, dρ = 1 1 − dρ ρ1

(3)

where ρ1 andρ2 are the initial/higher and final/lower densities, respectively, and Vem is the added amount of emergency submarine volume required. Using ρ1 = 650 kg/m3 as the top of the density range and ρ2 = 500 kg/m3 as the bottom of the range, the value of dρ is at most 0.23 and Vem is at most 0.83 m3. This is the volume that the single emergency gas and bladder should be able to fill, to cover all plausible requirements.

4.1.2. Operations The operational procedure to dive is: 6

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Table 4 Baseline part mass estimates. Part

Unit Mass

Comments

Ballast tank

26 kg

Valve Pump Compressor Gas Purification Gas bottle

5 kg 9 kg 9 kg 30 kg var

Liquid Cv Gas Cv Bladder Separator

– – var var

2 tanks, made of titanium (Aerospace Specification Metals and Inc, 2016) with safety factor of 2, cylinder with volume 0.5 m3 and length 5 m, thickness 1 mm (for 1 MPa external pressure) Based on commercially available cryogenic valves 1 MPa baseline (Pulsafeeder Engineered Pr, 2016), scaled in proportion to pressure, 80% efficiency Similar to pumps, but baselined at 0.85 MPa (Senco, 2016; Porter Cable, 2016), 80% efficiency See (Meyerhofer and Hartwig, 2017). Includes compressor, heat exchanger and 3 additional valves Spherical geometry, thickness based on ASME standard (American Society of Mechanical Engineers, 2015) with 30 MPa internal pressure in a cylindrical shell, uses yield strength from (Flynn, 2005) with safety factor of 2 Standard method for Cv values (Fisher Controls International, 2005), 50 kPa pressure loss Standard method for Cv values (Fisher Controls International, 2005), 7% pressure loss Spherical, 1 mm stainless steel (∼8000 kg/m3) Planar, 1 mm stainless steel (∼8000 kg/m3).

• Measure the sea composition and use section 3.2 to estimate how • • • • • • •

4.1.3. Parts The largest flow rate that would need to be actively pumped out occurs at depth, to cover possible emergencies. The pump may have to remove 0.1 m3 (neutral 0.05 m3) in 4 min for a total volume flow rate V˙ = 0.000833 m3/s. At this rate, it would take 28 min to empty 0.72 m3 (ethane-rich sea). The total power requirement is 160 W and 139 W per pump for 5% methane or 85% methane sea, respectively. For the liquid valve, an acceptable pressure drop is 50 kPa, which implies a Cv for the liquid valve in each tank of 1.8 in an 85% methane sea or a Cv of 2 in a 5% methane sea. The gas mass let out through the top valve in each tank, based on a volume of 0.5 m3 and nitrogen density, is 2.8 kg. If the whole gas mass is let out in 10 min, then the mass flow rate is 16.8 kg/hour and the required valve size is Cv = 0.9. The emergency bladder would need to have a volume capacity of 0.83 m3 with a minimum bladder and bottle pressure of 1.1 MPa, which requires 4.6 kg of helium. The corresponding bottle volume is 0.126 m3, holding 0.7 kg of residual gas. Such a bladder will only be inflated once. If the emergency bladder fills in 1 min, then the flow rate through the valve is 276 kg/hour and the required Cv value is 5.2. The approximate bottle weight assuming titanium is 75 kg. The bladder mass is about 9.8 kg. Each of the two ballast tanks has 1 pump and 2 valves, while there is one emergency system on the submarine, for a total mass of 180 kg.

much liquid ballast is required for neutral buoyancy. The derived uncertainty of this estimate is less than 1.5% in high-ethane seas, rising to 7.5% in high-methane seas. Activate P1 to start flooding the tank. A flow meter will track the total liquid volume into the tank. At 80% of the estimated required ballast, partly close V1 to slow down the tank flooding; this is well short of the uncertainty limit. Turn off P1 to cease tank flooding when the diode rakes sensors record full submergence. Turn on P1 for 2 min (section 4.1.3) to remove enough liquid to establish slight positive buoyancy. Only open V2 if the tank pressure reaches 0.45 MPa during the previous 2 steps. This threshold is 3.6% less than the nitrogen vapor pressure at 93 K, against 1% measurement uncertainty. With positive buoyancy established, the propulsion system may be used to drive the vehicle down as needed. The submarine will rise by itself if propulsion fails or is turned off. Turn off the propulsion and use the top sonar every minute to verify that the submarine is not sinking. When the submarine has resurfaced, open V2 and pump the liquid out. The atmosphere fills the tank volume as liquid is removed.

The other instructions needed are those to recognize and respond to an emergency loss of buoyancy. The emergency system of choice for the submarine is a cryogenic bladder inflated with a bottle of neon.

4.2. Bladder only

• Sinking is recognized if the external liquid pressure is rising faster • •

The emergency concept for the pump system, a gas-inflated cryogenic bellows to increase the submarine displaced volume, can also be used directly to make the vehicle rise or sink. This fourth ballast concept is illustrated in Fig. 8. The gas used is a non-condensable such as helium or neon.

than 40 Pa/s and the top sonar indicates a rising distance from the surface. The latter should be corrected for the submarine not being level, to send the sonar beam perpendicular to the sea surface. If sinking is recognized after propulsion has been turned off, remove ballast to 0.15 MPa tank pressure or to empty the tank, and abort the dive. If the tank pressure has fallen to 0.15 MPa and the top sonar indicates the submarine is still sinking, inflate the emergency bladder.

4.2.1. Analysis This analysis assumes an ideal, non-condensible gas such as neon or helium as the working fluid in the tank and bladder. The transfer of this

Fig. 7. Conceptual layout of a pump ballast system. There is one such tank on each side of the submarine. This concept requires the tank to be oriented so that P1 is on the bottom. 7

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Fig. 8. Conceptual layout of a bladder-only ballast system. There is a single gas bottle, and one bladder on each side of the submarine.

gas between the two volumes is considered to be isothermal, because the effect of adiabatic heating is to exaggerate any changes in pressure. The isothermal pressure rise as gas is compressed into the bottle may be estimated from the sea/bladder pressure Psea and the change in bladder volume V1 − V2 . The change is gas mass inside the bottle is then:

Δmgb =

(V1 − V2) Psea RT

(4)

•

where R is the gas constant for the working fluid used and T is the sea temperature. Adding this mass difference to the mass already in the gas bottle, which produces pressure P1 according to the ideal gas law, the new isothermal pressure is:

P2 =

RT V − V2 (mgb,1 + Δmgb) = P1 + 1 Ps Vgb Vgb

•

(5)

where Vgb is the volume of the gas bottle. The volume required for this bladder comes from Equation (3) with ρ1 = 650 kg/m3, ρ2 = 500 kg/m3, and Vsub + Vem = 2.77 m3. That means the smallest submarine volume, with the bladders fully contracted, is 2.12 m3 with the total volume of the 2 bladders being about 0.65 m3; all gas is stored in a single bottle. Since the helium density corresponding to 93 K and 1 MPa is 5.1 kg/m3, the amount of gas in the bladder is 3.3 kg.

•

4.2.3. Parts The gas bottle is required to hold 3.3 kg of helium, plus 0.5 kg of residual. The minimum volume required is 0.09 m3, and the bottle mass is about 53.2 kg. With a similar arrangement of 2 gas valves, the mass flow rate per valve is 50 kg/hour, and the required Cv is 0.94. When the vehicle starts a dive, the 2 compressors may take 65 min to take in 3.3 kg of helium, for a flow rate of 0.00042 kg/s. With a final pressure of 9.4 MPa, the required power to each compressor is about 385 W. The mass of each bladder is ∼20 kg. The gas bottle is shared between both sides of the submarine; each side individually has one bladder, one valve and one compressor. The mass of the whole ballast system (both sides and the gas bottle between them) is ∼210 kg. This concept has the specific material requirement of a cryogenic bladder that can reliably cycle hundreds of times. Such a material does not presently exist (Hoggatt, 1968), a major drawback but one that may be surmounted with development and testing.

4.2.2. Operations The submarine should launch and travel to Titan with the bladder fully expanded, so the submarine can float on arrival. The operating procedure for a dive is:

• Before diving, compute a sea density estimate ρ from composition

and temperature measurements (within 0.5%), the submarine mass msub and the maximum submarine volume Vsub from system data. The amount of volume decrease required to achieve neutral buoyancy follows as:

V1 − V2 = Vsub −

msub ρ

volume for slightly positive buoyancy according to Equation (6); from that state, drive down with propulsion. Turn C1 off when the bottle pressure has increased from its initial value P1 to a final value P2 estimated from Equation (5), or when all but the top surface of the submarine is submerged, whichever happens sooner. During the transfer of gas from bladder to bottle, the pressure may spike to a higher value than this, but with effective heat transfer that spike will fade quickly to the isothermal pressure. Open and close V1 as necessary while diving to match the gas pressure and sea pressure to maintain bladder volume. In particular, each dive must operate from lowest depth to highest, sinking and rising monotonically. To return to the surface, open V1; with the sea pressure already matched, the added gas expands the bladder volume. Close V1 when the bladder reaches full volume at 1 MPa gas pressure, and hold that status for the remainder of surface time. To initiate any subsequent dive, turn on C1 to reduce gas pressure in the bladder, then to retract bladder volume. The stopping criterion is the same as on the first dive.

(6)

∙ Turn on C1 to retract the bladder boundaries and reduce vehicle

Fig. 9. Conceptual layout of a pressurant gas system without separators. Each side of the submarine has one gas bottle and 2 tank sections. 8

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amount, if 8 h exceeds the time for dissolved gas to reach equilibrium solubility, or an equivalent fraction of the full soluble amount to 8 h as a fraction of that time. A similar calculation holds over 16 h for the small liquid volume retained at the surface. The approximate time required for equilibrium is based on Fick's first law of diffusion:

4.3. Compressed gas without separator The principal characteristic of ballast concept 4 shown in Fig. 9 is that the submarine carries a bottle of neon or helium with it, and blows down the bottle directly against the liquid surface every time the submarine returns to the surface. Due to the solubility of the pressurant gas in the liquid, a small amount of gas will be dissolved and thus lost during each dive. Therefore, the pressurant gas bottle must be sized to expel liquid at pressure, but also have enough mass to overcome the residual loss over the mission.

teq =

1 2 ⎛ R L ⎜θ − sin θ⎟⎞ ⎜⎛Vliq > 0.5m3) 2 ⎝ ⎠⎝

(7)

•

⎜

⎜

•

(8)

θ dbal = R ⎛1 − cos ⎛ ⎞ ⎞ (Vbal ≤ 0.5m3) or dbal 2 ⎠⎠ ⎝ ⎝ θ = R ⎛1 + cos ⎛ ⎞ ⎞ (Vbal > 0.5m3) ⎝ 2 ⎠⎠ ⎝

3neq dbal DAsurf Ceq

(11)

out due mostly to expansion cooling, is negligible, because that operation is only done occasionally. Gas pressure is treated as ideal and isothermal; this is justified because the compressibility factors are, at 92 K (temperature assumed constant) and 0.15 MPa, Z = 0.9986 for neon and Z = 1.002 for helium. The solubility of gaseous helium in liquid methane (Zimmerli et al., 2010) is:

xHe = P∗ exp( −13.76 + 0.0748T − 0.00137T 2 − 0.015P∗)

(12)

⎟

where the temperature T is in Kelvin and P∗ is the pressure minus the vapor pressure of the solvent (in MPa). The data for helium in ethane below 160 K (Nikitina et al., 1970; Cannon et al., 1968) and neon in methane (Streett et al., 1971) are fitted in this work, and no data for neon in ethane was found. A correlation for mole fraction of helium in liquid ethane below 160 K is:

⎟

(9)

• The volume of ballast liquid taken into all 4 tanks combined ranges •

(10)

• The submarine moves gradually, so that effects of mixing, which would increase the rate of dissolution, are minimal. • The additional solubility loss that occurs during ascent or descent is neglected. • The effect of any change in bottle pressure conditions as gas is let

With the central angle calculated numerically from ballast volume Vliq , the surface area of the liquid body and maximum depth immediately follow:

θ Asurf = 2RL sin ⎛ ⎞ ⎝2⎠

∂C ∂z

The proportionality constant 3 accounts for the spread of dissolved gas in 3 dimensions, which takes longer than in 1 dimension due to lateral effects. Assumptions needed are:

3

1 2 ⎛ R L ⎜θ − sin θ⎟⎞ ⎜⎛Vliq ≤ 0.5m3)orVliq 2 ⎝ ⎠⎝

=1−

=D

where D ≈ 2∗10−9 m /s is the approximate diffusion coefficient of helium in methane at Titan conditions extrapolated from (Sinor, 1965), Ac is the contact area between liquid and gas, and neq is the number of moles of gas dissolved at equilibrium. If the concentration gradient is x nbal Ceq/ dbal , where Ceq = Ne , xNe is the dissolved mole fraction of gas Vbal (neon or helium), Vbal is the amount of liquid in the tank and dbal is the depth of the liquid, then solving for teq gives:

of volume, and a diameter of 0.46 m. Based on length L = 6 meters and radius R = 0.23 meters, the liquid volume based on the smaller central angle θ, which is oriented upward if the tank is more than half full, is

Vliq =

Ac teq

2

4.3.1. Analysis The estimate for amount of gas leaked is based on the small amount of gas that diffuses into the ballast liquid on each dive due to solubility. The loss is accumulated and tracked over the total number of dives. Since the first dive is operated differently and sets up every dive to follow, the losses at that stage are ignored. The assumptions in this model are:

• The ballast tank is described as a cylinder, 6 m long, with 1 m

neq

J=

from 0.25 m3 (70% methane) to 0.72 m3 (ethane), assumed to vary linearly with composition. At the surface, the assumed liquid volume is 0.005 m3 in a recess at the bottom of the tank, with 0.1 m2 surface area and 0.05 m depth. Pure diffusion of the gas occurs through the liquid surface through the dive time of 8 h. The amount of gas lost is the full soluble

xHe = (8.11∗10−7) P∗ exp(0.0419T + 0.00686P∗ − 0.000126TP∗)

(13)

A correlation for mole fraction of neon in liquid methane is:

xNe = (3.99∗10−4) P∗ exp(0.0194T − 0.0395P∗ + 0.000239TP∗)

Fig. 10. Loss percentage of a) neon, and b) helium in both composition extremes, accumulated over many dives. 9

(14)

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For the case of helium in methane-ethane mixtures, the solubility was interpolated linearly between the two binary cases. For neon, the solubility in pure methane was taken as constant for all compositions due to lack of data. The key to guaranteeing that the submarine can surface is that the minimum gas pressure at full blowdown is 1 MPa, sufficiently high for any location in the sea. Given this requirement, Fig. 10 shows the percentage of gas lost for neon and helium in both composition extremes, accumulating over 30 dives. The losses are much greater for neon than for helium, due to higher solubility. Solubility is also the cause of the reversal in loss trend with composition; according to the relations described above, neon is more soluble in methane while helium is more soluble in ethane. Such a difference may result, in part, from the limited solubility data; nonetheless, all estimates are presented here as an order-of-magnitude guide for designing the remainder of the ballast system. Maintaining 1 MPa of neon gas pressure after 30 days of solubility losses requires a mass of neon in the ballast tank of 26.7 kg. Since 5.3 kg of gas have to be replenished every 30 dives (therefore this replenishment mass must be provided 12 times), the total requirement for the whole 365-day mission is to have 90 kg of neon. For helium, a starting gas mass of 5.4 kg is adequate for the entire mission, because the losses are inconsequential. A loss of 0.0007% of the gas to dissolution, repeated 12 times, implies that the ballast tanks lose only half a gram during the entire year of operation.

•

4.3.3. Parts In this concept, the two ballast tanks hold 4 MPa, with a resulting mass of 56 kg between them. The reason for this high pressure is that the ullage is compressed by pumping in liquid to sink; in the most extreme case, a pure ethane sea, the 0.72 m3 of liquid reduces the ullage from the whole tank volume (1 m3) to ¼ of that volume. That leads the pressure to rise by a factor of about 4 from the baseline 1 MPa, which is required to expel the ballast liquid. If neon is the pressurant gas, then each bottle has to release 45 kg (half of the total requirement) while remaining at 1.1 MPa. The minimum volume to meet this requirement is 0.247 m3, with 7.1 kg of residual gas, and the bottle mass is 146 kg. The gas valves for a neon system split are considered to split the gas 2 ways from each bottle. If the full load of 90 kg is assumed to pass through the valve in 5 min, the flow rate is then 270 kg/hour per valve and the Cv is 2.2. If helium is the pressurant gas, then each bottle has to release 2.7 kg (half the total requirement) while remaining at 1.1 MPa. The minimum volume to meet this requirement is 0.074 m3, with 0.4 kg of residual gas, and the bottle mass is 44 kg. Splitting this amount of helium 4 ways, and assuming 5 min to pass the full load of 5.4 kg, yields a mass flow rate of 16.2 kg/hour per valve. The required Cv is 0.3. The liquid valves also split the sea volume into the tanks 4 ways. Taking in 0.72 m3 of liquid in 5 min results in a flow rate of 2.16 m3/ hour per valve, and a Cv of 2.9. The 4 pumps must raise liquid pressure to 4 MPa for this concept instead of 1 MPa. Moving a liquid volume of 0.18 m3 across each pump in a time of 1 h (V˙ = 0.18 m3/hr per pump requires an input power of 185 W per pump. (In fact, the pumping can proceed faster because the peak power only occurs at the end of the process). Each of the two ballast tanks has 1 gas bottle, 4 valves (2 liquid, 2 gas) and 2 pumps. The total mass of both tanks is 664 kg for neon or 362 kg for helium.

4.3.2. Operations Upon arrival to Titan, the ballast tank contains 0.1 MPa of gas and the gas bottle is at 9.4 MPa (for helium) or 7.8 MPa (for neon).

• Follow the sinking instructions for the pump concept. • Drive the submarine down using propulsion from near-neutral buoyancy. Recalculate the sea density every 10 min. • If it is desired to adapt to a higher sea density, then pump in the • •

• •

an isentropic spike, which settles below 1 MPa after equilibrium; in that case, repeat the procedure. The relief valve V3 should be set to open at 4 MPa, the same design limit as the ballast tanks.

excess volume above and beyond that loaded at the surface. This amount should be undershot by 0.5% to account for flow rate uncertainties. If the vehicle orientation is anything other than level and upright when surfacing, the ballast liquid may be covering the gas bottle release valve. It is necessary, then, to blow down one tank of the submarine before other tanks, to make it level and upright. To surface from the first dive, open V2 to pressurize the gas in the ballast tank. When the gas pressure exceeds the outside sea pressure, open V1 to expel liquid from the tank. To prevent the pressurant gas from being expelled alongside the liquid, V1 should be set in a recess on the bottom of the tank; when a liquid level sensor observes when that small volume has begun to empty, close V1 and V2. To surface from subsequent dives, the initial action of the pump would compress the gas in the tank to above sea pressure, so just open V2. The stopping criterion is the same as on the first dive. If, at any point while expelling liquid on subsequent dives, the gas pressure in the tank falls below 1 MPa, open V2 and close it when that pressure reaches 1.05 MPa. Such a threshold may be reached in

4.4. Compressed gas with separator Concept 6 shown in Fig. 11 is a compressed neon gas system but with a physical separator between pressurant and liquid tanks. This concept was baselined for the Phase I submarine in 2014 (Oleson et al., 2014). The advantage of including a mechanical separator between a pressurant gas such as neon and the liquid ballast is that the gas can be recovered into the storage bottle when high pressure is not needed. Therefore, the ballast tank need not store the maximum amount of gas permanently, and may be built to much lower pressure specifications. The trade-off is the need to include a compressor to recover the gas, which adds weight. 4.4.1. Operations The submarine will arrive on Titan with the gas bottle full, the

Fig. 11. Conceptual layout of a non-condensable ballast system with a separator. There are 2 of the units pictured, one on each side of the submarine. 10

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Fig. 12. Conceptual layout of a nitrogen gas ballast system. There is a single gas separation unit, and 2 ballast tank frames, one on each side of the submarine.

Fig. 13. A conceptual layout of the chosen gas purification system, based on (Meyerhofer and Hartwig, 2017).

Table 5 Mass and power estimates of the options in this trade study. Concept

Total Mass (kg)

Maximum Total Power (W)

Complexitya

•

Pump Bladder only Noncondensible, no separator Noncondensible with separator

180 210 664 362 560 600

320 800 740

1 2 2

•

300

3

a

(neon) (helium) (neon) (helium)

4.4.2. Parts For the gas valve that vents to the atmosphere, an operation time of 5 min to fill the entire 0.25 m3 sea volume (per ballast tank) will be adequate. The corresponding vent flow rate is 17 kg/hour, and the required Cv is 0.9. The liquid valves also split the sea volume into the tanks 4 ways. Taking in 0.72 m3 of liquid in 5 min results in a flow rate of 2.16 m3/hour per valve, and the required Cv is 2.9. The required amount of neon gas in each ballast tank is enough to fill 0.5 m3, or 13.2 kg. The minimum volume required for this requirement is

1 is simplest and 3 is most complex.

ballast volume filled with nitrogen, and the separator fully retracted toward the compressor.

• Follow the sinking instructions for the pump concept. • Drive down using propulsion. • To adjust for a lower density, open V1 and V3 (moving

separator) until the flowmeter indicates the desired liquid volume change has been achieved. To surface, fully open V1 and V3 (moving the separator) to blow down the compressed gas and remove ballast liquid, until the separator is as far as possible from the compressor. Record the liquid volume remaining in the onboard processor. To recompress the pressurant gas and retract the separator to the compressor, open V2 and turn on C1 until the gas volume of the tank is at its smallest and matches the surface pressure of 0.15 MPa.

the

Table 6 Overall pros and cons of the options in this trade study. Concept

Pros

Cons

Pump

Very simple; Pumps are familiar equipment No sea interaction; Can cover any density range

Limited composition range per dive

Bladder only

Noncondensible, no separator

Can cover any density range

Noncondensible with separator

Can cover any density range

Bladder materials are not reliable (Hoggatt, 1968); Gas may leak in transit or operation. Expanded vehicle has to be packed for transit Gas may leak in transit; Gas is lost during operation; Weight penalty: tank as pressure vessel and high-pressure pump; Vulnerable to pitching. Gas may leak in transit; Separator failure could contaminate gas bottle; Many parts.

11

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0.0724 m3, with 2.1 kg of residual. The bottle mass is about 42.8 kg. For the gas valve that empties the pressurant tank of neon, an operation time of 5 min is adequate. The flow out of the pressurant bottle is split two ways, for a flow rate per valve of 80 kg/hour, and the required Cv is 0.7. The 4 compressors may take up to 12 h (Oleson et al., 2014) to process 26.3 kg of neon, for a flow rate of 0.00015 kg/s to each compressor. With the associate temperature change assumed transient, the required power to each compressor is about 70 W. If helium is the pressurant chosen, then the required amount of helium gas in each tank is enough to fill 0.5 m3, or 2.55 kg. The minimum volume required for this requirement is 0.0695 m3, with a residual of 0.4 kg. Then the bottle mass is about 41.1 kg. For the gas valve that empties the pressurant tank of helium, the flow out of the pressurant bottle (split two ways, 5 min operating time) is 15 kg/hour per valve. The required Cv is 0.3. In the helium version of the concept, the 4 compressors have the same 12 h to process 5.1 kg, for a flow rate of 30 mg/s per compressor. If the associated temperature change is assumed to be negligible, the required power to each compressor is about 75 W. The mass of each separator is about 1 kg. The whole ballast system has 2 tanks, 2 loaded gas bottles, 12 valves, 4 separators and 4 compressors; the total mass is 560 kg for neon or 600 kg for helium. There is no shared hardware between the tanks on different sides of the submarine.

liquid nitrogen. First, the nitrogen vapor is compressed and adiabatically heated. The liquid is then pumped to its storage pressure. To release this liquid as nitrogen vapor back into the gas side, the liquid is expanded and vaporized. The last part, in particular, may be disturbed by uncertain two-phase effects. In summary, both storage methods are impractical and likely cannot be managed autonomously. The concept is therefore not included in the final comparison below. 5. Conclusion The total mass and power consumption of each concept is shown in Table 5. The power cited is the maximum total power during any stage of operation, out of an estimated available power of 860 W (Oleson et al., 2014). If the submarine were to depend on consumable helium, it would require ∼5 g per day to fill the ballast tank to 1 MPa, and the mass of the tank, using 9.4 MPa, increases by ∼15 kg per dive. Therefore, if the mission consists of ∼30 dives or less, it is preferable to use consumable gas to manage ballast. This is not possible with direct-toEarth communication, which can only be performed with the submarine on the surface, and would require an accompanying orbiter. Table 6 summarizes the overall pros and cons of the concepts described in this paper. The bladder system can bring the vehicle to the surface quickly, but is slow to sink and cryogenic bladder materials have no heritage. The pump system would only need to expand the bladder once, but limits the allowable composition change in any single dive. The pressurant gas systems are easily the heaviest, because the gas bottles need to be built for 30 MPa but can only use less than 10 MPa on Titan; gas blowdowns, however, are well-understood in space vehicles.

4.5. Nitrogen gas system with separator The seventh concept shown in Fig. 12 is another compressed gas system, but using nitrogen gas in place of helium or neon. The most convenient pressurant gas to use in the ballast system would be nitrogen, since it is the dominant component of the Titan atmosphere and can be harvested in-situ. However, it cannot be in direct contact with ballast liquid (especially methane) due to extremely high solubility. Any system that uses it needs to include separation between gas and liquid, and mechanical separation such as bladder or piston/cylinder is a standard method, see Fig. 12. Another component is also needed to purify the Titan atmosphere, by removing the 5% methane component, to prevent such methane from condensing prematurely in the hardware. Such condensation would magnify the uncertainty in vapor pressure, perhaps leading to droplets in parts such as the compressor. Perhaps the greatest difficulty of using pressurant nitrogen is that nitrogen liquefies at 93 K and 0.46 MPa. This creates the risk of 2-phase pressurant storage. The specific gas purification system chosen for the submarine, based on a recent trade study in (Meyerhofer and Hartwig, 2017), is shown in Fig. 13. The atmosphere intake is heated by compression, then returned to 93 K by a heat exchanger with the Titan Sea. The pressure is chosen so that the methane condenses out as the mixture cools, but the nitrogen does not, and passes through to the ballast systems.

Acknowledgements This work was funded through the NASA Innovative Advanced Concepts (NIAC) Phase 2 Titan Submarine Project. The authors would like to thank Eric Lemmon for his assistance with the neon and helium solubility data, as well as Steve Oleson and Anthony Colozza for many discussions on the concepts, and the referees for their comments and suggestions. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.oceaneng.2018.10.055. References Aerospace Specification Metals, Inc. Titanium Ti-6Al-4V (Grade 5), Annealed. [Online] http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MTP641[Cited: August 9, 2016.]. Allen, T.W., February 28, 1961. Automatic Hovering Control System for Submarines. 2972972 US. American Society of Mechanical Engineers, 2015. VIII - rules for construction of pressure vessels, division 2 - alternative rules. In: 2015 ASME Boiler and Presssure Vessel Code. American Society of Mechanical Engineers, New York. Arvelo, J.I., Lorenz, R.D., 2013. Plumbing the depths of Ligeia: considerations for depth sounding in Titan's hydrocarbon seas. J. Acoust. Soc. Am. 134, 4335–4350. Burcher, R., Rydill, L.J., 1994. Concepts in Submarine Design. s.L. Cambridge Univeristy Press. Cannon, W.A., Robson, J.H., English, W.D., 1968. Liquid propellant gas absorption study. Astropower labratory - douglas missile and space systems division. McDonnel Douglas Corporation, Newport Beach, CA DAC-60510-F2. Cordier, D., et al., 2009. An estimate of the chemical composition of Titan's lakes. Astrophys. J. Lett. 707, L128–L131. Davis, R.E., Eriksen, C.C., Jones, C.P., 2003. Autonomous buoyancy-driven underwater vehicles. In: Griffiths, G. (Ed.), Technology and Applications of Autonomous Underwater Vehicles. Taylor and Francis, New York, pp. 37–58. Dibitetto, P.A., 3, 1995. Fuzzy Logic for depth Control of unmanned undersea vehicles. IEEE J. Ocean. Eng. 20, 242–248. EdgeTech, 2016. 4125 Search & Recovery Side Scan Sonar System. [Online]. http:// www.edgetech.com/wp-content/uploads/2014/09/4125-SAR-Brochure-102416.pdf [Cited: November 15, 2016.]. Emerson Process Management, October 2015. Model 3818 liquid ultrasonic flow meter for LNG. [Online]. http://www.emerson.com/resource/blob/44040/

4.5.1. Assessment Many parts of the model are similar to the non-condensible separator. The differences occur on the gas side, where space 2 is limited to 0.46 MPa and space 1 may involve two-phase complications. A version of this system where the nitrogen is a single-phase vapor needs to keep the bottle pressure below saturation, at 0.462 MPa. Otherwise, the nitrogen will partly condense, which makes flow rate and pressure control far more uncertain, a particular concern in an autonomous vehicle. With that condition, it follows the same assumptions as the non-condensible separator model. However, the bottle has to be much larger to make up for the small pressure differential. To store a volume of vapor sufficient to displace 0.5 m3 of sea liquid per bottle, each bottle needs to be more than 1.5 m3 in size (equivalent to 1.4 m in diameter if spherical). The depth is also limited to perhaps 200 m (0.3 MPa in Ligeia or 0.33 MPa is an ethane-rich sea) because the bottle will only release gas through a pressure gradient below the storage pressure limit. The alternative to storing nitrogen vapor is storing compressed 12

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