Design for a Europa Subsurface Explorer Mission with a Telescopic Subsurface Vehicle

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Abstract
Europa, one of Jupiter’s four large Galilean moons, is a target of prime importance for exploration. This is due to the likely presence of a global subsurface liquid water ocean beneath a water ice crust, raising the possibility that Europa could support simple life. Future mission concepts include a lander deploying a probe to melt through the ice crust (a cryobot), that in turn deploys an Autonomous Underwater Vehicle (AUV/submarine) on entry to the ocean. This study investigates the feasibility of combining the cryobot and submarine elements into a single integrated vehicle (cryosub) in order to make more efficient use of the total probe mass budget. The mission concept, potential science goals, relevant technologies and vehicle operation as a buoyant rover are discussed. A notional probe mass budget is then calculated and mathematical constraints are set out for the single-stage vehicle in both ice and ocean configurations, from which a simple vehicle design is developed. The thermal design of the vehicle with regard to electricity generation from a radioisotope power source is considered. The development of a notional design (mass, dimensions, power requirements etc.) suggests that, within the scope of this study, the single-stage subsurface vehicle concept may be feasible.
Keywords: Europa, cryobot, AUV, single-stage

Nomenclature

θ Folding wheel flexure opening angle
φ Angle in equation 1
G Gravitational Constant
g Gravitational Field Strength
C3 Spacecraft Characteristic Energy
Isp Specific Impulse
R Radius
V Velocity
m Mass
M Total Vehicle Mass
y Length of cryosub compartment
L Total cryosub length
δ Length of sub-compartment in cryosub
Q Power
η Efficiency factor
Pt, Pe Specific Power (thermal, electrical)
κ Thermal conductivity
ρ Density
C Specific heat capacity
µ Dynamic viscosity
h Specific latent heat
T Temperature
t Time
n, d Fit constants in equation 9
Ar, Mr Relative atomic and formula masses
γ Parameter in equation 14 F∗ Buoyancy-corrected weight A Surface Area
E Parameter in equation 19
Z Thermoelectric figure of merit
σ Electrical conductivity
S Seebeck coefficient
w Distance between thermoelectric gener- ator junctions
Nu Nusselt Number Ra Rayleigh Number Pr Prandtl Number
H Heat transfer coefficient

  1. Diameter

β Coefficient of thermal expansion
Subscripts
p at perigee

  1. of Earth

e of Europa
0, f Initial/standard, final
cr, su Cryobot, submarine configurations 1, 2, 3 of compartments 1, 2, 3
s (of power) from Radioisotope Power Source
v Vertical (power)
l Lateral (power)
x (power) lost by convection pu of Plutonium-238 dioxide s, l Solid, liquid states of water m At melting point
h, c Hot, cold thermoelectric junctions
Acronyms
AUV Autonomous Underwater Vehicle MMRTG Multi-Mission Radioisotope Ther-
moelectric Generator
RPS Radioisotope Power Source
Other symbols are introduced where necessary.

Introduction

The existence of a liquid water ocean on Europa beneath its icy crust is consistent with evidence collected by the Galileo space probe. Examples include the detection and analysis of Europa’s magnetic field and the observation of geological features suggestive of subsurface water interacting
with the crust.[1] This ocean has probably existed for much of the solar system’s history[1, 2] and
is likely kept liquid by the tidal heating of Europa; the moon is squeezed and flexed periodically by the force of Jupiter’s gravity during the course of its orbit.[1]
Whether or not Europa is habitable according to the present scientific understanding of life depends upon the availability of water, essential chemical elements and a sufficient energy source;
these conditions must be sustained over a lengthy period of time to allow for the development of life [1, 2].
The existence of liquid water over time having been considered, chemical elements (C,H,N,O,P and S) are likely to have been present on Europa from its formation, in addition to having been delivered by asteroid/cometary impacts[1]. A probable source of energy on Europa that could be utilised by life is chemical energy transferred by redox reactions[1]; oxidants have been shown to be present at the surface of Europa due to radiolytic processing (up to 10cm regolith depth is thought to be bombarded by charged particles trapped within Jupiter’s magnetosphere[1]). Investigating convection mechanisms within
Europa’s crust is therefore of prime importance for future missions to Europa, as such mechanisms constitute the principal means of delivering these surface oxidants to Europa’s ocean. The subsurface ocean is thought to be in contact with a rocky mantle, raising the possibility of
hydrothermal activity driven by the same tidal heating and constituting another energy source.[1]
The exploration of Europa is therefore considered an important facet of future planetary science programs. The 2011 US National Research Council’s Planetary Science Decadal Survey ‘Vision and Voyages for Planetary Science in the Decade 2013-2022’, which advises NASA’s planetary science program based on consultation of the scientific community, states: “because of this ocean’s potential suitability for life, Europa is one of the most important targets in all of
planetary science.”[3]
NASA is currently developing two missions to explore Europa: the Europa Clipper and Europa Lander.[4, 5] The mission investigated in this study would follow these two missions,
delivering a lander to Europa carrying a subsurface vehicle that would melt through Europa’s ice crust to directly explore its ocean, searching for indicators of life as well as gathering data related to Europa’s habitability and geology.
Numerous mission concepts present a two-stage vehicle, comprised of a cryobot that would melt through the ice and a hydrobot (robotic submarine) to explore the ocean.[6, 7]
The possibility of integrating these elements into a single-stage vehicle (cryobot/submarine; cryosub) is investigated in this study. (The term ‘cryosub’ has previously been coined in this context.) Considering the fact that the total mass of the under-ice vehicle will be limited by the capabilities of the launch vehicle and the fuel requirements of the mission, by avoiding the duplication of (e.g.) power sources across two vehicles, the total mass budget for the vehicle could be used more efficiently given a single-stage design. Access to one set of relatively large and capable equipment throughout the mission rather than switching from one set of smaller, less capable infrastructure to another during the course of the mission could also improve the overall vehicle capability.
Current concepts envisage small underwater payloads, limiting the scientific payload for ocean investigations: the ‘submarine payload’ of a Jet Propulsion Laboratory (JPL) cryobot comprises just over one eighth of the total probe mass[8] while B. R¨omgens[7] describes an AUV of length
20cm out of the total probe length of 2m.
Due to the potential improvements in the assignment of the vehicle mass budget described above and the increased volume of the vehicle eventually exploring the ocean, the single-stage cryosub concept could potentially permit a larger and more comprehensive payload of scientific instruments to improve the scientific return of the mission.
Considering the subsurface vehicle power source, the large and long-term thermal power requirements associated with melting through ice renders battery power unsuitable. The challenges of the Europan environment (high radiation flux on Europa’s surface[1, 2], large distance from
the Sun/operating under ice for a lengthy period of time) also rules out solar power; hence the general consensus is in favour of some form of nuclear power.[6, 7]
Some current mission concepts envisage the nuclear-powered cryobot anchoring itself to the underside of the ice crust (the ice-ocean interface), the battery-powered submarine conducting sorties to explore Europa’s ocean before returning to dock with the cryobot and recharge using
nuclear-generated electricity. (For example in M. Hildebrandt et al.[9])
A single-stage cryosub would carry the nuclear power source with it whilst exploring the ocean, permitting constant access to electrical power and hence a greater degree of autonomy and flexibility, as the range of the vehicle in the ocean would not be constrained by battery reserves. Whilst the vehicle would likely still need to dock with some form of communications interface at
the point of entry to the ocean to uplink data and receive instruction from Earth[9], the sortie
duration could be drastically increased, or it could vary from sortie to sortie according to the intentions of the operators on Earth. Note also that in the two-stage vehicle concept the cryobot would need to carry batteries to store generated electricity before recharging a set of submarine batteries; this duplication of batteries could be eliminated in a single-stage architecture, saving mass.
To provide context to the concept of a Europa Subsurface Explorer Mission, notional scientific goals are next discussed, as the single-stage cryosub architecture was motivated primarily as a means of maximising the scientific return of the mission.

Scientific Goals of a Europa Subsurface Explorer Mission

As described earlier, the existence of a subsurface liquid water ocean on Europa raises the possibility of Europa’s habitability, so (likely drawing on data from the Europa Clipper and Lander Missions), the primary goal of a mission exploring the ocean in-situ would be to investigate the extent to which Europa is indeed habitable and to search for indicators of life.
Europa contains multiple environments where bio-indicators could be found, including the ice crust, the ice-ocean interface, the ocean and potentially areas of geothermal activity on the seabed; these areas could potentially all be accessible to a subsurface explorer.
Pending investigations arising from data collected by the Europa Clipper and Lander missions, some scientific questions from the 2013-2022 US NRC Decadal Survey[3] remain relevant to a Europa Subsurface Explorer Mission, including:

    • Does (or did) any life exist beneath the surface of Europa or Enceladus?
    • What is the nature of any biologically relevant energy sources on Europa?

What are the depths below the surface, the thicknesses and the conductivities of the sub- surface oceans of the Galilean satellites?
Following the approach adopted in the Report of the Europa Lander Science Definition Team 2016[2], the notional science to be conducted by the Europa Subsurface Explorer Mission can be split into three goals:

  1. Search for evidence of life, past or present, on Europa.
  2. Investigate the habitability of Europa.
  3. Investigate the properties and dynamics of different environments on Europa.

The 2016 Europa Lander Science Definition Team Report[2] emphasised the need for multiple distinct and verifiable results from a variety of experiments on multiple samples to prove the existence of life, or alternatively Europa’s sterility. An approach for life detection is discussed by the report, including searching for morphological indicators (e.g. imagery of cellular/subcellular structures) and chemical indicators (e.g. enantiomeric excess: organisms on Earth generally use one of the two enantiomers of chiral amino acids; therefore a relative abundance of one
enantiomer is to be expected in the presence of life)[2]. With regard to the second and third notional science goals, bathymetric mapping of the seafloor and ice-ocean interface could be conducted, as well as sampling to determine the structure of the ice and the chemistry of the ice-crust and ocean.[6]
Scientific investigations that could be conducted have been presented in Science Traceability Matrices, such as in[2, 6].

Mission-critical Technology

Cryobots: Overview and Design Considerations

A cryobot, otherwise known as a melt/ice-penetrating/Philberth probe, is a vehicle with a heated tip (melt head) that penetrates through ice sheets under its own gravity, falling through a thin melt-water film produced around the vehicle.[6, 7, 10, 11]
The melt-water film must be reliably maintained around the whole vehicle to prevent it from refreezing and locking the probe in place (stalling it). Given that the melt head thermal power is inversely proportional to the square of the probe’s radius[10], cryobot geometry is generally characterised by a high length:width ratio.[6] Due to this, and especially for cold ice environments
such as Europa, a designated heat source to prevent refreezing may have to be employed, separate to that in the melt head.[6, 12]
Concerning near-surface operation of a cryobot, ice penetration can be challenging given the relatively high porosity of the Europan ice regolith (due to impacts and radiation ‘gardening’).[1]
Given that melting will only occur if pressures greater than the triple-point pressure can be sustained around the vehicle, the porosity of the ice (allowing any melt-water to evaporate and escape) and lack of any significant atmosphere on Europa means that the ice will be sublimated
rather than melted, a much more energy intensive process.[6, 13, 14, 15]
Various methods have been suggested to raise the pressure around the vehicle in the near- surface region, such as deploying flanges or domes from the lander along with the cryobot in order to plug/cap the melt channel[6, 14] and/or mechanical drills to aid the melt head.[14, 15, 16]
The approach considered by this study (potentially supplemented by the above methods) considers the design of the lander. The lander envisaged would be similar to NASA’s current Europa Lander concept[17] with the main body of the lander resting on the surface on a bellypan
rather than held clear by landing legs; the aim would be to use the lander’s weight to compress the regolith and thereby reduce its porosity (see figure 1).
Another issue associated with cryobot design is the ice environment itself, which may contain voids/fissures and impurities. Impurities, if not dispersed, tend to reduce the thermal connection between the vehicle and the ice with a detrimental effect on melting efficiency.[15] Given the high length:width ratio of a tip-standing cryobot, J. Biele et al[13] have observed that “toppling… [is]
almost inevitable in inhomogeneous ice.”
A cryobot could well be designed with a sufficiently low centre of mass to mitigate the toppling risk, but use of SONAR for obstacle detection[14] and various means of steering the probe have been suggested, including (most commonly) differential heating (varying the thermal power transferred to the ice through different areas of the melt head and wider vehicle).[11, 14, 16]
Many cryobot designs utilise water jetting: melt-water is collected at the nose of the vehicle, heated by the nose heat source and expelled from the melt head. This measure increases the ice penetration velocity and also serves to dislodge impurities in the ice.[6] Water jetting also more
actively cools the heat source, reducing the heat load on the melt head and hence the risk of overheating.[6] Turbulence in the melt-water film due to water jetting improves the film’s thermal

Figure 1: Notional Lander Design. Background image from https: // europa. nasa. gov/ resources/ 165/ simulated-view-from-europas-surface-artists-concept
conductivity; melting efficiencies in the region of 95% were predicted by a NASA Innovative Advanced Concepts study[6] based on a model by R. Shreve.[18]
The feasibility of incorporating these thermal control mechanisms in a cryosub vehicle designed for both ice and ocean environments will be discussed later in Section 5.
In terms of communicating with the surface, existing cryobot designs generally envisage the use of RPS-powered radio transceivers released at certain depths in the ice and/or a tether trailed from behind the cryobot, the decision being made according to the vehicle’s mass budget and the properties of the ice.[6, 7, 8, 14] The cryosub design considered in this study uses both
techniques.

Vehicle Density and Implications for the Single-Stage Architecture

A factor critical to the feasibility of the single-stage cryosub concept is the vehicle’s density. As discussed above, minimising the radius and length of a cryobot minimises the power requirements for penetrating the ice and for stall-prevention respectively; hence given the need to carry a
certain payload mass, a high density is beneficial.[14] Increasing vehicle density also increases
the buoyancy-corrected weight of the vehicle, increasing the rate of ice penetration.
However, high density in a single-stage vehicle can prevent the probe from floating/achieving neutral buoyancy when used as a buoyant rover/submarine; NASA’s Tunnelbot concept[14] would
anchor itself to the ice to prevent it sinking, with its nose and science payload projecting into the ocean.
J. Biele et al[13] have suggested that the cryobot deploy some form of ballast on entry to the
ocean, rendering it sufficiently buoyant as to be used as an AUV or (for operations on Earth) recovered for reuse. The alternative is to deploy from the cryobot a large, designated AUV, as with the Teredo Ice Shuttle.[19] This would reduce the overall density of the compound vehicle
(both cryobot and AUV) penetrating the ice, reducing its buoyancy-corrected weight and/or
Figure 2: Cryosub Telescopic Section Deployment. Left: the cryosub enters the ocean, remaining anchored to the ice. Middle: The telescopic hull sections are pulled out by the vehicle’s weight. Right: The submarine configuration cryosub undocks from the ice anchor.
increasing the thermal power requirements due to increased vehicle volume.
The approach investigated in this study is a telescopic vehicle design, with a view to changing the volume and not the mass (i.e. with relatively little implication for scientific payload mass) of the cryosub in order to decrease its average density.
On entry to the ocean, the cryosub is first anchored such that it hangs vertically from the base of the ice. A release mechanism is then engaged, allowing two nested telescopic vehicle hull sections to be pulled clear by gravity, increasing the total volume of the vehicle. The cryobot can then undock from the ice anchor (exposing submarine propulsion equipment); the anchor now serves as a communications relay to the lander at the surface with its high-gain antenna. (See figure 2).
Some of the increased space within the vehicle could be used for dive cells that can be flooded/emptied to alter the buoyancy of the cryosub. In its cryobot configuration, the vehicle is likely to have been designed with a low centre of mass (i.e. with mass concentrated towards the nose of the vehicle). Making the assumption that (as with the DLR Leng and Icefin
AUVs[9, 20]) systems would be housed within individual pressure hulls, the remaining space
within the increased volume, the submarine configuration cryosub allows these hulls to be moved to balance the vehicle about its centre for horizontal operations in Europa’s ocean. (See figure 3.)
The individual pressure hulls of an AUV would most likely out of necessity be connected by some form of umbilical e.g. a wiring harness. Fixing the position of a central pressure hull with respect to the outer hull, the lengths of the umbilical and supplementary support cables can be set such that when the telescopic hulls extend, the pressure hulls are pulled to preset positions relative to the fixed central pressure hull, balancing the vehicle. The support cables would not penetrate the pressure hulls themselves to minimise hull openings, but would prevent the weight of a pressure hull being solely supported by the potentially mission-critical umbilical connection. The vehicle may benefit from being partially pre-pressurised for the transition to submarine configuration; pre-pressurising may also improve the ability of the cryosub to operate at extreme depth.
Motor-driven piston ballast tanks/dive cells (figure 4) are envisaged to avoid the complexity associated with use of compressed air. In the cryobot configuration, these pistons would be fully retracted; during the transition to submarine configuration space is made for the piston to extend
Figure 3: Telescopic Cryosub: Submarine Configuration

Figure 4: Piston Dive Cell
into; i.e. a dive cell volume is created. By retracting the piston again, water can enter the dive cell to increase the vehicle’s average buoyancy. (see figure 4)
Two dive cells are envisaged at the bow and stern of the vehicle, permitting buoyancy and attitude control for the cryosub as a submarine in Europa’s ocean. With the dive cells completely empty, a buoyant ice-ocean interface exploration configuration is enabled, as discussed below.

Buoyant Under-Ice Rover Configuration

Exploration of the ice-ocean interface on Europa is of scientific importance in terms of investigating the chemical and geological environment of Europa, this region also being a site of interest in the search for microorganisms.[21] The exploration of the ice-ocean interface using a submarine
can be challenging due to ocean currents and the high power requirements therefore associated with station-keeping.[22]
The approach to exploring this region currently being investigated by NASA’s Jet Propulsion Laboratory is the Buoyant Rover for Under-Ice Exploration (BRUIE), a two-wheeled vehicle designed to drive along the underside of the ice crust of an ocean world.[21] A prototype has been tested in relevant Earth environments.[22]
Figure 5: Buoyant rover wheel cross-section with ten flexures in folded (left) and unfolded (right) configurations
In light of the concerns above, though not wishing to compromise coverage of the ocean in general and the potentially geothermally active seafloor, the design of a vehicle able to act in both submarine and buoyant rover configurations was considered. With the ability to maintain a positive buoyancy outlined above, a potential design for the rover wheels is discussed below.
To minimise the radius of the vehicle in the cryobot phase and hence reduce the power requirements for melting through Europa’s ice crust at a given velocity (and also to ensure a cylindrical probe geometry in the cryobot configuration), the buoyant rover wheels could be foldable, expanding from a small-radius storage configuration on entering the ocean.
The folding wheel design considered in this study draws inspiration from the wheels of NASA’s Mars Exploration Rovers (MERs) Spirit and Opportunity, which contained spiral flexures between the axle and outer treads to improve the shock absorption of the wheels.[23]
The cryosub wheel would consist of, in closed configuration, overlapping flexures of almost semi-circular cross-section folded around the hull. For deployment, actuators on one or more of the flexures would rotate the flexure outward about the hull-flexure join point, simultaneously pushing the other flexures with it and unfolding the wheel. The deployed configuration would be a circular repeating pattern with each flexure touching the midpoint (or region of) of the adjacent flexure arc (see figure 5). The open geometry of the deployed wheel ensures that it need not be refolded; while operating as a submarine the drag increase would be minimal. Note that the deployed wheel diameter is approximately double the initial vehicle diameter. The folding wheel could provide built-in shock absorption/suspension through retaining a degree of flexibility.
When designing the collapsible wheel, the aim is to maximise the wheel diameter whilst minimising the number of flexures used in order to minimise the mass of the system and the width of the folded wheel (due to cryobot configuration radius constraints). These constraints imply a large opening angle for the flexures.
Considering figure 6, where flexures have negligible width and so are perfect semi-circles, letting the hub/flexure radius r = 1 and using the sine rule twice yields a formula for the opening angle θ (degrees) for a wheel of n segments:
Figure 6: Diagram used for the derivation of the Flexure Opening Angle

(1)

where φ = 360 for n segments. This formula was used for producing figures 5 and 7, using ‘real’ flexures with non-negligible width; note that the flexures do not quite touch.
For simplicity, the wheels could rotate freely, the cryosub being propelled at low speeds in the buoyant rover configuration using its AUV bow and stern manoeuvring thrusters. Ability to operate as a submarine increases the flexibility of the system: should an obstacle be detected such that the wheel diameter provides insufficient clearance, the cryosub can dive under the obstacle before returning to the ice-ocean interface to continue in buoyant rover mode. (See figure 7.)

Cryosub Model

The investigation into the single-stage vehicle concept was motivated primarily by the following aims:
Avoiding component duplication across two vehicles and hence achieving savings within the overall mass budget.
Improving AUV autonomy/capability in Europa’s ocean through providing continual access to the radioisotope power source used for melting through Europa’s ice crust.
These goals were in turn influenced by the aim of improving the science return of a Europa Subsurface Explorer Mission.
In order to investigate the feasibility of the single stage architecture, a simple notional cryosub

Figure 7: Notional image of the cryosub in buoyant rover mode. Background image from https:
// antarcticsun. usap. gov/ science/ images/ seaice_ UnderIceAlgaeSImba. jpg
design was sought through the creation of a mathematical model, the calculations from which are presented in Appendix B. The model balances basic design parameters (dimensions, power source mass etc.) against the following constraints:

  1. Vehicle density to be greater than that of water in the cryobot phase of operations in order to fall by gravity through melt-water beneath the probe.
  2. Vehicle density to be less than that of water in the submarine phase of operations in order to float with a buoyancy reserve.
  3. Ability to penetrate ice of 15km thickness in two years. While an eventual design may well incorporate mechanical drilling/melt-water jetting techniques (see Section 3.1), for simplicity and as a worst case scenario, only passive melting through the ice was considered.
  4. An appropriate balance of ‘vertical power’ (for downward motion through the ice) and ‘lateral power’ (to prevent the refreezing of melt-water surrounding the vehicle walls; in turn to prevent stalling).

The cryosub would use a plutonium-238 dioxide fuelled Radioisotope Power Source (RPS) to provide the necessary thermal and electric power. For the model, two separate RPSs for vertical and lateral power were assumed. (The total plutonium dioxide mass was 30 kg.) An initial
mathematical model using equations from H. Aamot[10] was solved to compare the density of
the vehicle in both cryobot and submarine configurations with the mass of plutonium needed to penetrate through Europa’s ice at the minimum required velocity. (See Appendix B: Model
1) The line colours represent different probe masses and radii (see table 1). The maximum permissible probe mass for the model was 200 kg (see Appendix A).
Figures 8 and 9 demonstrate that by changing the mass and radius of the probe (within a reasonable range), a cryosub design can be achieved that satisfies the cryobot and submarine density constraints.
A potential design consists of a probe of 150 kg mass, 0.15 m radius and 1.5 m length. A probe with these design criteria was considered in greater detail, using a model developed by K.

Figure 8: Graph of Cryobot density against Vertical Power 238PuO2 mass. The line colours are given in table 1. Cryobot densities greater than 1000 kgm−3 are feasible. A 150kg probe with a radius of 0.15m and with 20.2 kg of vertical power 238PuO2 mass has a cryobot density of around 1400 kgm−3.

Line colour Mcr (kg) R (m)
red 100 0.1
pink 100 0.15
grey 150 0.1
green 150 0.15
orange 200 0.1
blue 200 0.15

Table 1: Key to figures 8 and 9

Figure 9: Graph of Submarine density against Vertical Power 238PuO2 mass. The line colours are given in table 1. Submarine densities less than 1000 kgm−3 are feasible. A 150kg probe with a radius of 0.15m and with 20.2 kg of vertical power 238PuO2 mass has a submarine density of around 750 kgm−3.
Schu¨ller and J. Kowalski.[12] (See Appendix B: Model 2) This considers the effects of Europa’s gravity on the vehicle’s motion in the cryobot phase and how convection within the melt-water film surrounding the vehicle affects the proportion of heat from the radioisotope power source that ultimately melts the ice. The total mass of plutonium-238 dioxide required for this probe design was calculated to be approximately 29.6 kg, made up of 20.2 kg for vertical power and
9.4 kg for lateral power. This total mass is similar to the initial estimation of 30 kg. This shows that the design is feasible in terms of the power source and payload.

Cryosub Thermal Control System

The cryosub design considered in this study includes plutonium-238 dioxide-fueled radioisotope thermoelectric generators, the decay heat of the radioisotope providing thermal power for melting through the ice and providing electrical power for the vehicle.
Thermoelectric generators generate electrical power from the temperature difference between a hot surface and a cold surface according to the Seebeck Effect; the electromotive force induced is directly proportional to the temperature difference (i.e. EMF = S∆T where S is the material specific Seebeck coefficient, which is also temperature dependent). In a practical thermoelectric generator, n and p type semiconductors are connected in pairs between plates (that are generally thermal conductors and electrical insulators) such that when a temperature difference is applied
across the plates, a current flows.[24]
The efficiency of a thermoelectric generator depends upon the dimensions, the heat source characteristics, the thermoelectric materials used and the ambient environment with regard to

Figure 10: Notional thermal design layout for operating in ice with melt-water jets.
the rate of heat transfer.[24, 25] Thermoelectric materials should generally have a high Seebeck coefficient and electrical conductivity but a low thermal conductivity in order to maximise the current and voltage of the generator while maintaining a large temperature difference across the
plates.[24]
The single-stage cryosub concept envisages use of the same radioisotope power source both within Europa’s ice crust and its ocean, so the thermal control system built around the RPS must be able to:

    • Provide all necessary thermal and electrical power for the cryosub throughout the mission.

Maintain acceptable temperatures within the vehicle in both the ice and ocean environments.

    • Be compatible with the telescopic cryosub design.

A notional layout of the thermal control system is presented before the results of mathematical models and a Computational Fluid Dynamics (CFD) simulation of the vehicle RPS in the ocean are discussed (see Appendix C).

Notional Thermal Control System

A Jet Propulsion Laboratory (JPL) cryobot concept (T. Cwik et al[16]) envisaged two separate radioisotope power sources (RPSs), the first for penetrating through the ice and the second for electrical power generation. Given the emphasis placed on thermal rather than electrical power for ice-melting ocean world missions, the JPL study raised the possibility of designing
a RPS specifically for a Europa mission rather than using the General Purpose Heat Source (see NASA’s Multi-Mission Radioisotope Thermoelectric Generator (MMRTG) fact sheet[26]), in order to reduce the volume occupied by the RPS. The plutonium dioxide power source is
contained within packaging material as a safety measure;[26] potential new packaging concepts for plutonium dioxide, reducing the RPS volume, are discussed by T. Cwik et al.[16]
A single RPS for both electrical and thermal power is shown in figure 10, a model of the cryosub operating within Europa’s ice crust. In the cryosub model (Section 4 & Appendix B), it was sufficient to split the thermal power required for penetrating the ice into vertical and lateral power; hence two separate RPSs were considered. In reality, rather than distributing plutonium dioxide along the length of the vehicle to provide lateral power, a single RPS may be used with
heat pipes to distribute heat to the vehicle walls, as proposed in NASA’s Tunnelbot concept[14]
and by T. Cwik et al.[16] The vertical heat pipes can use gravity to return the condensed water
to the RPS, so act as thermosyphons. Varying the internal pressure in the heat pipes allows them to be used as a differential heating system for steering the cryosub in the ice.[14]
A RPS designed specifically for the cryosub (rather than one built around the General Purpose Heat Source) is envisaged in this study. Assuming the use of a packaging design aiming to reduce the dimensions of the RPS without decreasing the power, the heat flux entering the thermoelectric generator would be increased. This could require a generator to be built using different thermoelectric materials to those used in the MMRTG in order to keep temperatures within the generator acceptably low. In designing such new thermoelectric materials, the low thermal conductivity constraint on the thermoelectric materials would likely be relaxed (the efficiency of the thermoelectric generator can remain relatively low, the requirement for thermal power being dominant in the ice environment).
Alternatively/additionally, the cryosub RPS may well use less thermal insulation than the MMRTG due to the overwhelming demand for thermal power in the ice and the need for good heat dissipation from the reduced volume/increased heat flux RPS to prevent overheating. During spaceflight, the cryosub is positioned centrally within the lander (see figure 1); the lander could insulate the RPS and/or the RPS could constitute a part of the thermal control system of the lander.
The reservoir in figure 10 holds water for heating to greater temperatures than in the melt- water film surrounding the cryosub. The melt-water inlet/outlet cycle is based on those discussed by B. R¨omgens and W. Zimmerman et al.[7, 11] If both heat pipes and melt-water jets are used,
two separate reservoirs at different pressures may be required: heat pipes operate by boiling water at the heat source for use as a working fluid; furthermore, the heat pipe system would likely be closed. Use of a steam-driven pump for the melt-water jets is suggested by B. R¨omgens,[7]
requiring another low pressure reservoir for steam production using RPS waste heat.
Once within the ocean, the telescopic sections of the vehicle deploy, leaving the reservoir and heat pipes open to the sea. Heat dissipation from the RPS to the ocean water can be achieved by conduction and free/forced convection according to the motion of the cryosub; melt-water pump systems could potentially provide a forced convection mechanism if necessary.

Ocean Thermal Control Models

The thermal design of a cryobot has been investigated generally (e.g. H. Aamot and Schu¨ller & Kowalski[10, 12]) and through the design of a vehicle (e.g. various NASA studies:[11, 14, 16]).
As a cryosub must be able to use a RPS in both Europa’s ice crust and ocean, the performance of a RPS and surrounding thermoelectric generator (of mass, power and dimensions set out in Section 4) was investigated within an ocean environment.
A simple theoretical heat transfer model was produced and solved for the hot- and cold- junction temperatures of the RPS-powered generator, from which the efficiency of the generator could be determined. The same scenario was simulated using Solidworks Flow Simulation, a Computational Fluid Dynamics (CFD) package; the junction temperatures in both cases are compared below. The theoretical model and the solid/fluid properties for the CFD simulation are both presented in Appendix C.
The theoretical model was first solved for a generator with properties similar to the MMRTG. This resulted in a generator hot junction temperature in excess of 2000K, which was considered to be potentially prohibitively high. By increasing the thermal conductivity of the theoretical
generator (as proposed above) to 2 Wm−1K−1 with all other parameters unchanged, hot and cold junction temperatures of approximately 1150K and 350K were attained.
The Solidworks RPS design was kept simple so as to be similar to the theoretical model and to respect the focus of this section of the study (to investigate RPS thermal control on a Europa ocean mission rather than seek a detailed vehicle design). Figure 11 (top) shows a cylindrical plutonium dioxide heat source held concentrically within a cylindrical thermoelectric generator module, with the same dimensions as those assumed for the theoretical model. The rest of the vehicle is in the deployed telescopic/ocean configuration. The new higher value for the generator thermal conductivity was used.
An advantage of the CFD simulation over the theoretical model is the ability to predict the temperature distribution over the hot and cold junction temperatures due to convection (see figure 11); the theoretical model simply assumes uniform junction temperatures. Figure 11 suggests that the junction temperatures predicted by the theoretical model are within an appropriate range, but can differ from the CFD simulation by as much as a few hundred Kelvin. Nevertheless, the simulation demonstrates that the junction temperatures are roughly appropriate for an RPS when increasing the generator thermal conductivity compared to the MMRTG to account for increased heat flux through the generator. (Hot junction temperatures in excess of 1200K have
been used in NASA RPSs.[27])
Figure 12 shows sectional ocean and RPS temperature plots. Temperatures in the convection plume (middle) are not expected to exceed the saturation temperature at the given pressure (greater than 600 K by the Antoine equation). Due to the still relatively low thermal conductivity of the thermoelectric generator, the temperature of the rest of the vehicle does not substantially increase, being roughly comparable to room temperature.

Discussion

The preceding sections have discussed the feasibility of a single-stage cryosub. The ability to change the density of the vehicle was identified as a crucial factor affecting the feasibility of the concept; the cryosub must be able to sink through meltwater in Europa’s ice crust before floating once within the subsurface ocean. Increasing the volume of the vehicle by means of a gravity-driven telescopic hull design was proposed as a means of conducting this density change. Mathematical modelling of the vehicle during the descent through the ice indicated that by modifying the mass and dimensions of the probe, the density constraints described above could be met for a RPS-powered vehicle within a notional mass budget of 200kg. As a worst-case scenario, the model considered a cryosub meeting the constraints using only passive melting through the ice crust, neglecting mechanical/melt-water jetting techniques that may be incorporated in an
eventual mission design.
As the scientific objectives and vehicle specifications of a Europa Subsurface Explorer Mission are yet to be formally decided upon by a space agency and are pending data on Europa from

Figure 11: Solidworks Flow Simulation of the Ocean Thermal Control Scenario. Top: the vehicle model. Left: plutonium dioxide surface temperature plot (Th). Right thermoelectric generator surface temperature plot (Tc). Bottom: Surface temperature plots for both junctions shown with the same temperature scale.

Figure 12: Ocean Thermal Control Simulation continued: Top: RPS temperature section. Middle: ocean temperature section. Bottom: Whole vehicle temperature section. The temperatures of the rest of the vehicle and the surrounding water are unlikely to be problematic.
upcoming missions, the notional design was intentionally conceptual and open-ended. Throughout the mathematical modelling, the cryosub design was considered in terms of cylinders, with complexities such as the shape of the melt head neglected. Similarly, the mass and dimensions of the cryosub were changed without consideration of constraints due to the dimensions of any payloads to be carried by the vehicle.
The practicalities of the mechanical techniques for reducing the density and shifting the centre of mass of the vehicle may well have to be determined by physical experimentation.
Rather than attempting to solve the cryobot phase model around an existing RPS, the model left the RPS mass and dimensions as variables; even at an early stage in the design of a Europa Subsurface Explorer Mission this approach may prove to be impractical.
The cryobot phase mathematical model (section 5) assumed consistent ice properties and therefore a constant ice penetration velocity as it was intended to provide rough vehicle parameters (mass, dimensions and power) to satisfy the density change constraint and various other cryobot phase criteria. As stated in section 3.1, a cryobot must be able to function within heterogeneous ice; a more rigorous design process must factor in the changing thermodynamic properties of the ice with depth, along with ice impurity content and structure.
An objective of the single-stage cryosub concept is the ability to use the cryobot phase RPS on the same vehicle to provide electrical power for the submarine phase of operations. A simple heat transfer model was produced to determine how the RPS of mass and dimensions derived by the cryobot phase model in section 5 would behave within the ocean environment. The model calculated the hot and cold junction temperatures of the thermoelectric generator, which was initially modelled after NASA’s Multi-Mission Radioisotope Thermoelectric Generator (MMRTG).
Assuming the development of a new packaging system for the plutonium-238 dioxide and hence a reduced volume power source, it was found that the low thermal conductivity requirement of the thermoelectric generator material could be relaxed slightly. The thermoelectric generator junction temperature calculated using the theoretical heat transfer model agreed roughly with those found by a Computational Fluid Dynamics (CFD) Simulation of the generator in the ocean environment. (While the theoretical model assumed uniform junction temperatures, the CFD simulation was able to show the temperature distribution across the junctions.) Differences between the junction temperatures predicted by the theoretical model and the CFD simulation may be partially explained by the theoretical model’s use of a correlation (equation (23)) considering only the curved surface area of the generator.
It should be noted that Solidworks Flow Simulation is an add-in to the main Solidworks computer-aided design software; use of a dedicated/stand-alone CFD program may well provide greater accuracy and precision than in the results shown in figures 11 and 12.
The heat transfer modelling was conducted primarily to investigate qualitatively how the properties of a thermoelectric generator could potentially be altered, assuming a low-volume RPS operating in both ice and ocean environments; hence the thermoelectric properties of the generator material were modelled as variables. Consideration of how changing these properties could be realised in terms of the structure and/or chemical composition of semiconductors within the thermoelectric generator is beyond the scope of this study, especially given the relatively simple nature of the heat transfer model, though this could be a topic for further study. It may be more practical however to change the amount of insulation material compared to the MMRTG rather than using different thermoelectric materials in the generator itself.

Conclusion

The aim of this study was to investigate the feasibility of a Europa Subsurface Explorer Mission using a single-stage under-ice vehicle (the cryosub) by producing a relatively simple vehicle design. By avoiding replication of equipment on a multi-stage vehicle and increasing the volume of the vehicle that explores the ocean, the single-stage design may facilitate improvements in the scientific instrument payload carried on such a mission.
As a simple notional design for a single-stage cryosub (layout, mass, power and dimensions) could be produced, it can be concluded that within the scope of this study, a Europa Subsur- face Explorer Mission with a single-stage under-ice vehicle may be feasible. To further investigate the concept and/or produce a more reliable vehicle design, more comprehensive theoretical/computational modelling and physical experimentation will likely be required.

Acknowledgements

The author wishes to thank Mr. P. Lynch of the Colyton Grammar School Physics Department for his helpful feedback on the manuscript.

Appendix A: Probe Mass Budget

In determining an estimate for the subsurface probe mass budget, the SpaceX Falcon Heavy was selected as the notional launch vehicle, in order to demonstrate the feasibility of the mission using a commercial rocket. This necessitates a lengthy multiple-body gravitational assist trajectory through the inner solar system, though the spacecraft could potentially travel on NASA’s
Space Launch System, which is capable of delivering a large payload directly to Jupiter.[28] The
calculations below drew heavily on data from the NASA Europa Study 2012 Report;[1] hence a
Venus-Earth-Earth Gravitational Assist (VEEGA) trajectory was assumed. Data for some other trajectories to Jupiter can be found from NASA’s Trajectory Browser. [29]
Firstly, an estimate for the fuel requirements for injecting the spacecraft onto the interplanetary transfer trajectory from Low Earth Orbit (LEO) were calculated. The Earth Escape Burn was modelled as a two-body problem, considering the spacecraft and Earth only (figure 13), as
per the approach in S. Widnall & J. Peraire. [30]
The spacecraft is in a circular LEO with an altitude of 300km. The launch vehicle upper stage then conducts an engine burn, injecting the spacecraft onto a hyperbolic escape trajectory to eventually leave Earth’s gravitational sphere of influence (dashed circular line in figure 13). This hyperbolic trajectory moves asymptotically towards the dashed straight line, the spacecraft
approaching a hyperbolic excess velocity V∞. The square of V∞ gives the characteristic energy (C3) for that specific hyperbolic trajectory.[31]
Given the altitude of the initial circular orbit Rp (which becomes the perigee (closest point to Earth) radius of the hyperbolic trajectory), the C3 of the trajectory and the standard gravitational parameter for Earth (the product of the gravitational constant G and the Earth’s mass ME), the perigee velocity Vp that must be attained by the spacecraft during the engine burn can be calculated, as that the square of the excess hyperbolic velocity equals the difference
between the squares of the perigee velocity and the escape velocity: [30]

(2)


Figure 13: Earth Escape Burn

Gravitational constant G 6.67 × 10−11Nm2kg−2
Radius of Earth 6.4 × 106m
Mass of Earth ME 6.0 × 1024kg
VEEGA Characteristic Energy C3 1.5 × 107m2kg−2 [1]

Table 2: Constants used in the Earth Escape Burn calculations
The initial velocity of the spacecraft in LEO is given by:

(3)

Thus the velocity change ∆V that must be delivered by the Earth Escape Engine Burn is given by:
∆V = Vp − V0 (4)
For the above parameters, ∆V = 3.87kms−1 (3 significant figures). The fuel requirement for this burn was calculated using the Tsiolkovsky Rocket Equation:

(5)

The specific impulse Isp of the Merlin 1D Vacuum engine for the Falcon Heavy upper stage
is 348s,[32] g0 is the standard gravitational acceleration (9.8ms−2) and m0 and mf are the initial (wet, i.e. with fuel) and final (dry) masses of the spacecraft respectively. The payload to LEO of the Falcon Heavy is reportedly 63800 kg.[32] Subtracting the 4.5 tonne dry mass of the Falcon
Heavy upper stage[32] yields the total interplanetary spacecraft mass budget, approximately 16
tonnes.
A ‘mass margin’ to be kept free within the overall mass budget is usually allocated to account for the possibility of the mass of the spacecraft increasing from its initial value during the design process. This can be calculated by: [1]
Mass Margin = Capability − MEV Prop. − CBE Dry
Capability − MEV Prop.
(6)
MEV Prop. is the Maximum Expected Value for Propellant Mass: the maximum fuel mass needed for the maximum ∆V for the greatest possible spacecraft dry mass. CBE Dry is the Current Best Estimate for the spacecraft dry mass.[1]
A 40% mass margin was used, as per the NASA Europa Study 2012 Report.[1] Using the whole
spacecraft CBE Dry : MEV Prop. and the Lander CBE Dry : Rest of spacecraft CBE Dry ratios for the lander mission in the same report, a notional lander CBE Dry mass of approximately 1200 kg was calculated. Using the ratio of science payload and Radioisotope Power Source
mass to total lander mass for that mission concept,[1] a notional mass budget for the under-
ice vehicle of approximately 200 kg was calculated. For comparison, NASA’s ROSES Scientific Exploration Subsurface Access Mechanism for Europa solicitation also limited the total vehicle mass to 200kg.[33] Similarly, a NASA Jet Propulsion Laboratory cryobot conceptual design had
a total CBE mass of 210.8kg from a 335kg budget.[8]

Appendix B: Cryosub Mathematical Models

Model 1

The cryosub was modelled as a cylinder with three main internal compartments (see figure 14). The first compartment, of mass m1, is modelled to consist solely (by mass) of the 238PuO2 providing the ‘vertical’ power Qv responsible for downward motion through the ice. Qv is equal to the heat source power Qs minus the thermal power loss due to convection within the melt- water layer Qx (which aids stall prevention). Qv = ηQS, where η is an efficiency factor. 238PuO2

Figure 14: Vehicle in Cryobot Configuration

Figure 15: Vehicle in Submarine Configuration: the telescopic hull sections have extended, doubling the length of compartment 2.

Gravitational Acceleration ge 1.3ms−2
Thermal
Conductivity		 ks
kl		 3.5Wm−1K−1
0.6Wm−1K−1
Density ρs
ρl		 927.8kgm−3
1000kgm−3
Specific Heat
Capacity		 Cs
Cl		 1476Jkg−1K−1
4200Jkg−1K−1
Dynamic Viscosity (melt-water) µl 0.0013Nsm−2
Latent Heat of Fusion (ice) hm 333700Jkg−1
Melting Point Tm 273K
Ice Ambient Temperature Ts 175K

Table 3: Properties of the Europa ice environment used in the model. Data from [12].
is assumed to take up 75% of the volume of compartment 1. The length of compartment 1 is given by y1 = 4m1/3ρpuπR2, where the density of plutonium dioxide ρpu is 9600 kg m−3. [34]
The second compartment, of mass m2, would contain Guidance, Navigation and Control and
science equipment in separate internal pressure hulls, but is modelled as a single compartment lined with 238PuO2 to provide the ‘lateral’ power needed for stall prevention, denoted Ql. Note also the sub-compartment of length δ, containing steering/propulsive equipment for the cryosub in the submarine phase. In terms of mass, this sub-compartment is considered part of m2.
The third compartment, of mass m3, consists of communications equipment: 10 RF transmitter pucks (the upper limit assumed by T. Cwik et al[16]) of a similar design to those outlined by B. R¨omgens[7] (cylinders of height 2cm and diameter 20cm). Assuming that the mass of each
puck consists solely of that of a 10cm x 10 cm x 2 cm block of 238PuO2 and adding the mass of a 15km tether of specific mass 0.5 kgkm−1 (as envisaged by NASA’s Innovative Advanced Concepts EUROPA study[6]), m3 was calculated to be 26.7 kg; y3 is 0.2m.
Hence the total mass of the cryosub in the cryobot phase is Mcr = m1 + m2 + m3.
The vehicle moves with velocity V through the ice, has radius R and weight due to gravity (in the cryobot phase) Mcrge where ge is the Europan gravitational field strength.
The sum of the lengths of the compartments y1 + y2 + δ + y3 = Lcr, the total vehicle length in the cryobot phase. Once in the submarine phase (figure 15), the ice communications equipment in compartment 3 will have been jettisoned and the section of compartment 2 with length y2 will have doubled (as described in section 3.2) such that the length of the vehicle will be: Lsu = y1 + 2y2 + δ. The total cryosub mass will be: Msu = m1 + m2 = Mcr -m3.
Physical constants and notional properties for Europa’s ice crust are given in table 3. Following the calculation of the maximum cryosub mass budget (200kg; see Appendix A),
An initial model was used to determine appropriate values of R and Lcr that satisfy two density constraints at the target velocity, given a total plutonium dioxide mass mpu to be split between providing vertical and lateral power. Graphs were produced plotting vehicle density in both cryobot and submarine phases against the mass of 238PuO2 assigned to vertical power (mv = m1).
The density constraints are as follows:
In the cryobot phase, the vehicle must have an average/overall density greater than that of liquid water, so that it will sink through the meltwater pool constantly formed beneath the nose and thus proceed downwards through the ice.

(7)

In the submarine phase, the average vehicle density must be less than that of water for the vehicle to be able to operate as a buoyant rover. (Any dive cells/ballast tanks are assumed to be empty.)

(8)

The graphs used an approximation for Lcr derived empirically by H. Aamot [10] and reported by K. Schuller & J. Kowalski[12]:

(9)

where n and d are fit constants: n = 932 WsK−1m−3 and d = 0.726. L∗ represents the ‘critical refreezing length,’ defined by K. Schuller & J. Kowalski[12] as the distance from the
melt-head beyond which the ice temperature falls below the melting point and refreezing occurs. For simplicity, it was assumed that L∗ = Lcr. (Note that the heat transferred to the ice by the plutonium dioxide in the RF transmitter pucks has been neglected, despite Ql being calculated
to include coverage of compartment 3; hence the error in the above assumption is partly compensated for.) ∆T is the temperature change from the initial ice temperature to the melting point, Tm Ts.
Rearranging equation (9) to make L∗,Lcr the subject and defining yields:

(10)

The velocity of a cryobot is modelled in [10, 6, 12] as:

(11)

where A is the cross-sectional area of the probe, πR2. To relate the heat provided by the plutonium dioxide heat source to Qv in equation (11), an arbitrary (for model 1) efficiency factor was selected to take account of convective losses in the melt-water film between the vehicle and the ice: η = 0.85.
The thermal power of a RPS with plutonium dioxide mass mpu can be defined as:

(12)

where t is the decay time of the radioisotope (years; comprising 3 years ground storage, the interplanetary spaceflight duration and the 2 year melt time (so 11.9 years for this study)), t1/2 is the half-life of plutonium-238 (87.7 years), Pt Pe is the specific thermal power of the radioisotope minus the specific electrical power transferred by the RPS thermoelectric generator
(taken to be 570 and 22.9 Wkg−1 respectively[26, 35]) and Ar is the proportion by mass of the
r
238PuO2 that is plutonium.
For the purposes of the approximation, the total mass of plutonium dioxide was assumed to be 30 kg.
Substituting equations (11) and (12) into equation (10) yields:

(13)

Hence where k and k′ are constants.
Taking δ to be 0.2m and using equation (13), equations (7) and (8) for various values of R
and Mcr were plotted in figures 8 and 9. (See section 4)

Model 2

Following the initial analysis above, the values R = 0.15m and Lcr = 1.5m were selected for the more detailed modelling phase, as the resulting vehicle was judged to be capable of meeting the density constraints with sufficient margin and with plausible values for mv and ml.
Firstly, a more detailed vertical efficiency factor was determined using equations derived by
K. Schuller & J. Kowalski[12] that take into account the fluid- and thermodynamics of the thin
melt-water film surrounding the vehicle, as well as the weight of the vehicle on Europa.
The efficiency factor η is defined as:[12]

(14)

where:

(15)

where in turn αl is the thermal diffusivity of the melt-water, µl is the dynamic viscosity of the melt-water and F∗ is the buoyancy-corrected weight of the probe, defined as F∗ = Mcrge
πR2ρlgeLcr.[12]
Substituting equation (14) into (11) and rearranging yields:

(16)

from which a Qs value of approximately 8900 W was calculated, using the minimum velocity for a two-year descent time. The efficiency factor η was 84.2% to three significant figures. This resulted in a value for mv of around 20.2 kg from equation (12).
Schuller & Kowalski[12] defined the thermal power losses (due to convection in the melt-water
film) from the vertical power heat source as:

(17)

and investigated the critical refreezing length of cryobots using Qx alone for stall prevention, concluding that for a Europa environment a designated lateral power heat source would be needed; otherwise the probe length would be prohibitively small.
Using the vehicle length approximation in equation (9) and substituting Qx for Ql yielded (a slight rearrangement of the formula stated in [12]):

(18)

Replacing the right-hand side of equation (18) with E and considering the designated lateral power (equation (10)) needed to satisfy L∗ = Lcr = 1.5m, Lcr becomes:

(19)

Solving for Ql gave a value of approximately 4100W and hence a ml value of around 9.4 kg; therefore the total mass of plutonium dioxide was 29.6 kg (which is not dissimilar from the mpu value of 30 kg selected for the earlier approximation).

Appendix C: Ocean Thermal Control Model

Theoretical Model

The maximum efficiency of a thermoelectric generator can be expressed as follows: [24]

(20)

where Th and Tc are the hot and cold junction temperatures respectively, T¯ is the mean temperature and Z is the thermoelectric figure of merit, given by E. Kanimba & Z. Tian[24] as:

(21)

where in turn σ and κ are the material’s electrical and thermal conductivities respectively. Equation 21 shows that use of semiconductors with high electrical conductivity but low thermal conductivity is beneficial for thermoelectric generator efficiency; this allows a high current to flow in the semiconductor whilst maintaining a high temperature gradient across the device.[24]
The ocean thermal control model is presented in figure 16. A source of thermal power Qs from the plutonium-238 dioxide enters the thermoelectric generator of width w and surface area A, with hot and cold junction temperatures Th and Tc respectively, giving rise to the temperature difference ∆T1. A proportion of the input thermal power ηQs leaves as electrical power, where the thermoelectric efficiency factor η (0 < η < 1) depends upon the junction temperatures and the thermoelectric figure of merit, Z. The remaining thermal power (1 − η)Qs leaves the cold junction and enters the ambient environment with temperature Ta, thus giving rise to temperature difference ∆T2. Equations 22 and 24 were formed in terms of Th and Tc and plotted to provide an approximate graphical solution (figure 17). As a worst-case scenario for heat rejection, it was assumed that the vehicle is stationary, i.e. with no external fluid flow and hence free rather than forced convection.
The 238PuO2 in a RPS would be surrounded by a protective aeroshell, the thermoelectric generator and insulation material etc.[26] For simplicity, the RPS model in figure 16 amalgamates
these components into a layer of uniform thermal conductivity surrounding the plutonium dioxide that generates electricity with a certain efficiency.
Equation 22 draws on the fact that the thermal power leaving the thermoelectric generator is equal to the thermal power entering the water and being dissipated by convection and conduction (dissipation by radiation is in this case ignored) i.e.:

(22)


Figure 16: Model of the Thermoelectric generator in Europa’s ocean. Thermal power entering the generator is split between electrical power and waste heat leaving the generator.
where N¯u is the average Nusselt number, κl is the thermal conductivity of the water, A is the surface area (in this case of the thermoelectric generator cold junction) and D is the diameter of the vehicle. The dimensionless Nusselt number represents the ratio of convective to conductive heat transfer and is used in equation 22 to determine the heat transfer coefficient, H = N¯uκ , for Newton’s law of cooling: Q = HA∆T . An approximation for the average Nusselt number for steady-state free convection from a horizontal, isothermal cylinder of characteristic diameter D
is given by: [36]

(23)

For equation 24, it was assumed that the thermal power effectively conducted by the thermo- electric generator (were it simply a thermally conductive material) is equal to the thermal power entering the water, allowing Fourier’s law (RHS) for heat conduction to be applied:

(24)

Thus given values for the various physical constants, an approximate solution for the steady- state hot and cold junction temperatures of the thermoelectric generator, can be found by the graphical intersection of equations 22 and 24. From this, the efficiency of the generator η can be calculated,
The radius of the nose plutonium dioxide block was taken to be 0.1m. The length of the cylindrical block was calculated from the plutonium dioxide mass requirement for vertical power (via equation 12); this figure was doubled to take into account packaging surrounding the 238PuO2.

Density ρl 1000 kgm−3
Gravitational acceleration ge 1.31 ms−2
Coefficient of volumetric thermal expansion βl 0.00021 K−1
Specific Heat Capacity Cl 4200 Jkg−1K−1
Viscosity µl 0.00169 Pa s
Thermal Conductivity κl 0.573 Wm−1K−1
Ambient Temperature Ta 273K

Table 4: Notional Thermophysical Constants for the Europa Ocean environment
Using equation 20, a value for Z (9.673 10−4K−1) was calculated given an efficiency of 6% and hot and cold junction temperatures of 530◦C and 200◦C respectively, from data on the NASA Multi-Mission Radioisotope Thermoelectric Generator (MMRTG).[37]
The values used for constants relating to the ocean environment are given in table 4.
The vehicle diameter was that assumed in the second cryosub model (0.3m, see Appendix B). Qs (8900W, as calculated in Appendix B) is used as an approximation for the thermal power entering the system. The initial thermal conductivity of the thermoelectric generator section was calculated from Fourier’s law, based on the MMRTG and taking the distance between the junctions as 0.05m. The surface area of the MMRTG was taken based on the dimensions in
NASA’s Radioisotope Power Systems Reference Book for Mission Designers and Planners[27]:
0.66m height by 0.64m diameter; the diameter was divided by 3 (an approximation) as the figure quoted included the heat rejection fins. The waste heat of the MMRTG (2000W) was used as the thermal power. These were approximate values taken from NASA data.[37, 27]
The initial value of κ calculated was 0.685 Wm−1K−1, using only the curved surface area of the MMRTG as per the correlation in equation 23.
Figure 17 shows equations 22 (blue and green respectively) and 24 plotted using the figure of merit and thermal conductivity calculated from the MMRTG. The y axis represents the hot junction temperature and the x axis the cold junction temperature.
The (curved) surface area of the generator was calculated for a generator module (compartment 1 in the cryosub model) containing a cylindrical RPS fuel block of radius 0.1m (hence surrounded by a 0.05m thick thermoelectric generator). This fuel block was assumed to have
half the density of 238PuO2 to account for packaging material. By equation 8, this implies a submarine-configuration vehicle density of around 820 kgm−3, which satisfies the maximum submarine phase density constraint.
Due to a potentially prohibitively high hot junction temperature for a generator thermal conductivity estimated from the properties of the MMRTG, the thermal conductivity of the
generator module was reduced; the red and black curves on figure 17 represent equations 22 and 24 respectively for κ = 2 Wm−1K−1. However, the value of the power factor σS2 remained constant (see equation 21). It can be seen that hot and cold junction temperatures of approximately
1150K and 350K respectively are attained, and hence a generator efficiency of around 5.7% by equation 20. This is slightly higher than the efficiency in the cryosub model ( 4% from the specific powers assumed for equation 12), so the cryosub modelling in Appendix B is unlikely to have been substantially compromised.

Solidworks CFD Parameters

The vehicle was assumed to be operating at the ice-ocean interface (at a hydrostatic pressure of 1.965 × 107 Pa), with an ambient water temperature of 273.15K.

Figure 17: Graphical Solution of the Ocean Thermal Control Model: Hot junction temperature Th, K against cold junction temperature Tc, K. The intersection of the green and blue lines represents the solution using a generator thermal conductivity estimated from the properties of the MMRTG. The intersection of the red and black lines represents the solution for a generator
thermal conductivity of 2 Wm−1K−1.

Property 238PuO2 TEG∗
Density 9600 kgm−3 [34] 250 kgm−3
Specific Heat Capacity 290 Jkg−1K−1 [38] 1000 Jkg−1K−1
Thermal Conductivity 6.3 Wm−1K−1 [38] 2 Wm−1K−1

Table 5: Properties of user-defined solids for the Solidworks CFD convection simulation. * The Thermoelectric Generator properties (excluding thermal conductivity) were based on those on a data sheet for Microtherm thermal insulation panels[39], which are used in the MMRTG.[40]
The plutonium dioxide and thermoelectric generator cylinders were set as user-defined solids according to the parameters given in table 5.

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Figure references

Figure 1: NASA/JPL-Caltech Accessed 26/02/21 from https://www.jpl.nasa.gov/images/simulated-view-from-europas-surface-artists-concept
Figure 7: Chris Fritsen, National Science Foundation Office of Polar Programs Accessed 26/02/21 from https://antarcticsun.usap.gov/science/2313

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