Solar energy harvesting on-board small satellites

Small satellites are receiving increased recognition in the space domain due to their reduced associated launch costs and shorter lead time when compared to larger satellites. However, this advantage is often at the expense of mission capabilities, such as available electrical power and propulsion. A possible solution is to shift from the conventional solar photovoltaic and battery configuration to a micro-Organic Rankine Cycle (ORC) and thermal energy storage system that uses the waste energy from a solar thermal propulsion system. However, limited literature is available on micro-ORC systems, which are capable of producing a few hundred Watts of electrical power. This paper describes the proposed system layout and model of the integrated micro-ORC system, for various working fluids such as Toluene, Hexamethyldisiloxane (MM), and Octamethylcyclotetrasiloxane (D4). Toluene has been identified as a promising working fluid candidate resulting in a power generation system volume fraction of 18% for a 215 kg Low Earth Orbit satellite. The micro-ORC system is capable of producing 200 W of electrical power. The design provides high specific energies of at least 500 Wh/kg but, has a low shared specific power of 10 W/kg. A preliminary design of the micro-turbine provides a conservative total-to-static efficiency of 57%. © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).


Introduction
The increase of electrical power consumption required by small satellites boosted the need for on-board power sources that have high energy and power densities. This increase is especially important for future planned interplanetary missions proposed by NASA. Future missions are estimated to need power densities in the range of 150 and 250W/kg [1] and specific energies greater than 250 Wh/kg [2]. Conventionally, small satellite power systems consist of photovoltaic technologies which have a specific power from around 20W/kg to 100W/kg [3,4]. Power systems can also include an on-board energy storage device, with advanced lithiumpolymer or -ion batteries being the most commonly used. These batteries have specific energies between 150 and 250 Wh/kg [5]. These systems may not be suitable for future missions. Therefore, alternative power systems should be investigated. A possible alternative system that has the potential to offer high power densities is the micro-organic Rankine Cycle (ORC) system [6]. Here micro refers to power levels in the range of 100e500W.
Power systems are not the only crucial sub-system for satellites. To further extend the capabilities of small satellites for future missions, a propulsion system is also required. Solar thermal propulsion (STP) has been identified as a possible cost-effective solution [7]. STP is a system that generates thrust by using concentrated solar radiation to heat a propellant to temperatures of more than 1500K, such to increase the performance over conventional propulsion systems. Coupling an STP system with a micro-ORC system, as shown in Fig. 1, could improve the system efficiency to develop small high-performance satellites by harvesting the energy from the STP receiver to co-generate electrical power and propulsion [6]. The waste heat could also be used for on-board thermal control. The major challenge with integrating an ORC with an STP system for space applications is the different operating temperatures. The STP requires propellant temperatures above 1500K to achieve high performance. In contrast, the ORC has a maximum operating temperature of approximately 600K, depending on the working fluid and its corresponding thermal stability limit. Available literature reports the thermal stability limit for MM to be 300 + C [8] and as high as 400 + C for cyclic siloxanes [9,10] and Toluene [11]. Therefore, this work also investigates the feasibility of using a hightemperature receiver as a hot source for a micro-ORC system.
The idea of using an ORC for power generation in space dates back to the 1960s [12,13]. ORC systems with power capacities on the order of 1e30 kW, were proposed to power the International Space Station. These systems are attractive for space applications as they can have a higher resistance to degradation in the space environment compared to photovoltaic systems [12,13]. In general, Rankine cycles can have better thermal efficiencies than Brayton and Stirling cycles for space applications at a cost of larger radiators [14]. At micro-scales, Rankine cycles can also have better thermal efficiency and higher power density versus Brayton cycles [15]. Rankine cycles can therefore lead to lighter designs which are of utmost importance for small satellites. The advantages of using a micro-ORC power generation system in space instead of a conventional steam Rankine cycle are lower turbine rotational speeds, larger turbine designs, lower freezing temperatures and the organic fluid can act as lubricant [10,12,16]. These advantages reduce the system maintenance required for ORC systems to once per year, for current terrestrial applications [17]. This could be extended to a few years to meet the operational life time of a small satellite. Drawbacks of a micro-ORC system include a lack of space heritage and reduction in reliability due to the ORC system having more moving parts than the PV-battery system, as well as potential transient inertial effects during start-up and shutdown, leakages, cooling of components, micro-gravity operation, and large radiators [10,18,19] Working fluid at the low electrical power output considered in this paper ultrahigh rotational speeds of more than 500krpm are possible even when using organic working fluids [6].
Research on micro-ORC systems, from a few Watts to 2 kW, has focused on solar thermal and waste energy power generation in portable electronic devices, miniature robotics, automotive industry, and remote off-grid applications [20e23]. However, little is known on the topic of micro-ORC systems, especially for small satellite applications, and investigations have often neglected the sizing of the components such as the turbine and heat exchangers [13]. Therefore, an investigation into the feasibility of generating power by harvesting energy from a solar thermal propulsion receiver on-board a small satellite is required. The satellite is assumed to be in Low Earth Orbit (LEO) at an altitude of 700 km above the Earth, to simulate a mission with low daylight to eclipse ratio. This study focuses on a micro-ORC system that meets the manufacturing and operational constraints while still conforming to the performance requirements. The feasibility is conducted by using a system design methodology comprising a thermodynamic analysis of the micro-ORC system with no pressure drops, where then the heat exchangers are sized and the micro-ORC is reanalysed with the calculated pressure drops. The design approach is combined to a genetic algorithm for the optimal exploration of the design space to minimise the total system volume while meeting the thermal energy storage capacity requirement. A meanline model is used to determine the turbine efficiency of the optimal configuration.

System description
A schematic of the proposed system is shown in Fig. 2a. Fig. 2b shows the related thermodynamic cycle in the temperatureentropy diagram of the micro-ORC system. For this study, only superheated regenerative ORC configurations are investigated. The power generation system can be split up into three major parts: 1) the optical system, 2) the high-temperature receiver, and 3) the ORC system. The propulsion system is not analysed in this study.
The optical system consists of a primary mirror, a flat plate secondary mirror and fibre optic cables, as shown in Fig. 3. A parabolic dish was chosen, as the primary concentrator, which concentrates solar radiation onto the secondary mirror, because it can achieve higher concentration ratios than both spherical mirrors and Fresnel lenses or mirrors, which suffer from spherical or chromatic aberration [24]. A non-concentrating flat plate secondary mirror was included as it increases the ease of optical fibre placement and reduces the length of the optical fibre cables required between the concentrator and the receiver, therefore making the design more compact [25]. A flat plate mirror is also simpler and easier to manufacture over improving the performance compared to concentrating secondary mirrors. The optical fibre bundle is made up of a number of individual cables. The diameter of the bundle can be determined based on the number of rings as defined by Fig. 3. The core represents the central optical fibre cable. Fibre optic cables have been included in the design instead of directly focusing solar radiation onto the receiver to reduce the pointing accuracy required and decouple the concentrator and receiver position. This is also a requirement from the propulsion side such that the concentrator position does not constrain the satellite manoeuvring direction. Additionally, they provide the system with the potential to reduce the overall mass by replacing a single large mirror with multiple smaller ones [25]. Disadvantages of the selected optical configuration include decreased end-to-end power efficiency, increased complexity and storage integration challenges.
The solar radiation collected by the receiver superheats the working fluid that is passed through the working fluid tubing coiled inside the insulation of the receiver, illustrated in Fig. 4a, This acts as the evaporator of the micro-ORC system. Near-and far-term high-temperature materials that are suitable to function as receivers for STP applications are silicon and boron respectively [26]. Silicon has been selected as the receiver material and heat source for this work since it is cheaper, more abundant, and a more mature (near-term) material compared to Boron. The receiver is assumed to be cylindrical and is made up of a silicon phase change material (PCM), a boron nitride container, and uses carbon bonded carbon fibre (CBCF) as the insulation material. The receiver also includes a rhenium coating for oxidation protection. The aperture diameter of the receiver is designed to accommodate all the optical fibre bundles entering the receiver, which are part of the optical system. By using a PCM the receiver is able to act as a latent heat energy storage system [26]. Advantages of using a latent heat storage system are relatively constant operating temperatures and high energy storage density, which are attractive qualities for ORC systems and small satellites. The thermal energy stored is crucial to ensure continuous electrical power generation during eclipse periods, therefore not limiting the operations of the small satellite during orbit. Challenges include thermal stresses, radiation losses, and containment of the phase change material. The inclusion of a heat transfer loop between the high-temperature receiver and working fluid was discarded. This was because it would decrease the system efficiency due to the addition of another pump, as well as increase the complexity and therefore reduce the system's reliability. This work, therefore, investigates the possibility of directly embedding the working fluid tubing inside the receiver's insulation, such that the maximum temperature exposed to the working fluid tubing is 20K less than the thermal stability limit of the fluid. The temperature is controlled by placing the working fluid tubing inside the insulation material away from the outer container wall. The distance is calculated based off the receiver's maximum expected temperature, which is equivalent to the melting temperature of the PCM.
The condenser radiates heat to space to condense the working fluid. It is made up of several circular channels, a honeycomb support structure, and two thin flat sheets of aluminium on the top and bottom, referred to as fins, as shown in Fig. 4b. A regenerator is included before the condenser to improve the efficiency of the ORC system. It also reduces the heat transfer surface area of the receiver and condenser at the expense of increased complexity and mass as well as reduced reliability. The regenerator is assumed to be a crossflow plate-fin heat exchanger (HX) with rectangular channels, depicted in Fig. 4c, due to its compactness, lightweight, and ability to operate at high temperatures. The hot vapour exiting the turbine enters the cross-flow plate-fin HX on the hot side and the cold liquid fluid from the pump enters on the cold side, which is perpendicular to the hot flow. A radial inflow turbine is coupled to a generator to provide on-board electrical power. The selection of this turbine was mainly due to its high power density, comparatively higher efficiency for low power output capacity, and compactness, which are critical aspects for small satellite subsystems.

Model description
In this section, the modelling of the system is described, and the sizing method of each component shown in Fig. 2a is discussed. This provides insight into the volume and mass distribution of the system, which is important for satellite design and to determine feasibility.

Optical system
A critical design aspect of the optical system is the volume required to store the system on-board the satellite during launch, referred to as the stowed volume. Determining the stowed volume of the optical system is difficult without a full design of the concentrating and deployment system. Three concentrator designs are considered in this study: i) a rigid-fixed concentrator, ii) a rigiddeployable concentrator and iii) an inflatable-deployable concentrator design. The total volume of a rigid-fixed design is taken as the volume of a cylinder with the diameter equal to the primary concentrator and the height equal to the distance between the primary dish and secondary mirror plus the thickness of the secondary mirror. The stowed volume of the optical system is assumed to be a percentage of the rigid-fixed design volume with the same primary dish diameter. Parabolic dish designs for the three cases were taken from Refs. [27] and the stowed volume fraction of each system was determined to be 100% for the fixed-rigid design, 25% for the deployable-rigid design and 1% for the inflatable design. An inflatable design was used in the optimisation and the concentrator and support areal densities are assumed to be 1 and 1.5 kg/m 2 respectively [25,26]. The effect of selecting a non-inflatable design type is discussed in Section 5.2 by conducting a one-at-a-time sensitivity analysis on varying the stowed volume fraction input and concentrator areal density.
The total input power of the optical system, _ Q in , is determined using Equation (1) [28], where the solar flux, S, is assumed to be 1350W/m 2 , b f is the shadow factor (fraction of area of the primary mirror covered by the secondary mirror's shadow), and A op which is the area of the primary mirror times the number of concentrators. The optical efficiency, h op , combines the efficiency of the optical fibre (transmission (90%), Fresnel efficiency (96.5%) and bundle packaging factor) and the primary dish and secondary mirror (reflectivity of the mirrors (90%) and intercept factors (96%)) [29]. The bundle packaging factor, BPF, is defined as the number of optical fibres, N f , times the area of the one fibre, A f divided by the bundle area, A b ,

Receiver
A one-dimensional steady-state radial analysis using a temperature-dependent thermal conductivity and shell thickness method [30] is used to determine the radiation losses through the insulation of the receiver as well as the position of the working fluid tubing (Fig. 4a). The radiation loss through the aperture and the absorption losses of the receiver are also included. From the conservation of energy, an estimated discharge time can be computed during an eclipse if there is adequate energy storage, Equation 3 where m pcm is the mass of the PCM, L is the latent heat of the PCM, _ Q o is the thermal power required for the ORC system, and _ Q loss account for the radiation and absorption losses. The receiver is assumed to act as a lumped-capacity thermal mass with no temperature distribution; this is only valid for low Biot numbers (≪ 1) [31]. Therefore this results in a preliminary analysis that requires future in-depth analysis to more accurately determine the coupled convective heat transfer between the PCM, insulation, and the working fluid, as well as the solar flux input. Furthermore, analytical and experimental investigations into the thermal cycling and expansion of the PCM and long exposure between the PCM and its container are required. The expansion of silicon during freezing was not considered in this study. However, it has been found that by reducing the fill factor of the PCM by 80%, the container damage due to the expansion can be mitigated [26]. The volume and mass of the receiver are found based on its described geometry depicted in Fig. 4a, assuming that the length of the inner cavity of the receiver is 80% of the total length of the phase change material.

ORC modelling
Fig . 5 shows the flowchart of the design method implemented in determining the ORC sizing. First, a steady-state thermodynamic analysis of the ORC system has been carried out using an in-house Matlab code based on the work of [32], assuming no pressure drops through the heat exchangers (HXs). Fluid thermophysical properties are determined by integrating the code with the software library Fluidprop [33]. If the constraints are met, then the HXs are sized and pressure loss calculated as presented in Fig. 5. Thereafter, if the results are within the constraints an updated thermodynamic analysis is conducted incorporating the HX pressure losses. The constraints that result in an infeasible design are described in Section 4.2. Each HX has been discretised to evaluate the onedimensional local heat transfer coefficient and pressure drop in the single-phase and two-phase flow regions using the models and methods described in Table 1. The mass and volume of the HXs are found based on the geometries described in Fig. 4. Thin-walled pressure vessel and plate fin thickness [34] calculations are performed to ensure structural integrity of the HXs. A safety factor of 2 and 4 [35] are used for the aluminium condenser channel and boron nitride evaporator tubing based on the yield stress and maximum expected pressure. The minimum condenser channel is set to 1 mm in this paper due to machinability and deployability concerns. The regenerator is assumed to be manufactured out of Inconel 617 with its temperature dependant allowable yield stress provided by Ref. [36].
In the evaporator, the high operating wall temperatures could result in low/high-quality critical heat flux (CHF) regimes. The CHF quality is determined using the method proposed by Ref. [45]. If the CHF quality is low, boiling is split into Inverted Annular Flow Boiling (IAFB) and Dispersed Flow Film Boiling (DFFB) regimes. Dryout at high qualities will result in DFFB being present after saturated boiling flow. Both of these flow types, can considerably reduce the heat transfer coefficient and thus increase the evaporator tubing length required for sufficient heat transfer. The radial inflow turbine geometry was analysed based on a meanline model similar to that proposed in Ref. [32]. It is assumed that the change in kinetic energy is negligible between the turbine inlet and outlet, that the flow in the stator is isentropic, and the deviation angle at both stator and rotor exit is null. Although, in reality these assumptions may affect the results, it is assumed the changes generated by these effects can be neglected for simplicity of the model as the trend should be correct [32]. A conservative value has been taken for the mass and volume of the turbine by assuming it is a solid disk with a diameter equivalent to the stator and the length equal to the axial length of the turbine. The turbine is assumed to be manufactured out of titanium due to manufacturability and high operating temperatures.
The remaining components of the system that require sizing are the pump, generator, and plumbing. The plumbing consists of circular tubing connecting the ORC components to each other. Each section of tubing has a length equivalent to three times the largest characteristic length of the component it provides an outlet for. The tubing material is assumed to be titanium and aluminium for vapour and liquid flows respectively, such that the tubing can withstand the high temperatures and is compatible with the working fluids analysed such as Toluene. Wall thickness is determined based on hoop stresses assuming a safety factor of 3 on the operating pressure [35]. A survey was conducted on available micro-pumps and generators suitable for a 200 W micro-ORC. The result of the micro-pump study shows that the volume of the micro-pump remained similar for different differential pressure. Therefore, for simplicity the pump volume and mass are equal to the maximum values found from the survey rounded up to 0.001m 3 and 1.5 kg respectively to be more conservative. Linear relationships were derived to relate the mass (M g ¼ a _ W net þ b) and volume of the generator to the net power output _ W net , where the coefficients a, b, c, and d are defined as 1.8 kg/kW, 2.718 kg, 2 Â 10 À6 m 3 /W, and 7 Â 10 À5 m 3 .

System model validation
Validations on determining the size and performance of the micro-ORC system have been conducted and presented in Table 3. Most components are validated with given data in terms of mass which can be equated to volume based on geometry and density. All component validations fall within the acceptable threshold of 5%, except for the volume of the optical system and the overall heat transfer and conductance of the regenerator.
The rigid volume of the concentrator was found to have a large deviation of 17% due to the lack of data on the design of the 0.5 m dish from Ref. [27] as well as the assumption that this study assumes the rigid volume of the optical system is equivalent to a cylinder. This deviation is assumed acceptable for this analysis as it provides a more conservative approach taken in this work, especially as the pressurisation system required to inflate the optical system is not modelled. The regenerator model was validated against the commercially available ASPEN Exchanger Design and Rating [52] software. Both the hot and cold side of the regenerator were assumed to use Toluene as the working fluid, 5 bar pressure, 10 kg/s mass flow rate, 20 layers, and a fin height of 8.9 mm. The hot Table 1 Models and methods implemented to determine the heat transfer coefficient and pressure drop in the heat exchangers.

Component Flow type Method/Model Reference
Regenerator Single-phase a The plate-fin rating model and ε-NTU method are used with frictional factors and Nusselt numbers provided in Table 2 for rectangular channels. [37] Evaporator Single phase a Frictional factors and Nusselt numbers used are provided in Table 2 for circular channels. Two-phase b,c (saturated) Universal method used to predict saturated flow boiling heat transfer coefficient and two-phase frictional pressure drop for mini-channels. [38e40] IAFB and DFFB Empirical correlations [41,42] Condenser Single phase a Frictional factors and Nusselt numbers used are provided in Table 2 for circular channels. Two-phase b,c (saturated) Universal method used to predict saturated flow condensing heat transfer coefficient and two-phase frictional pressure drop for mini-channels. [43,44] a Only the frictional effects are considered for single phase flow pressure drop calculations. b Accelerational pressure drop is negative for condensing flow and positive for positive for boiling flow. c Gravitational pressure drop is neglected in two-phase flow due to operation in micro-gravity. a Constants Kð∞Þ, fRe, and C in the apparent friction factor can be found in [47]. b The Gnielinski equation [50] can be used to determine the Nusselt number for rectangular ducts as it gives an error 9% for rectangular ducts with all four sides heated [47]. and cold side temperatures were 200 + C and 150 + Crespectively. The hot side length, fin thickness, and fin frequency were 0.418 m, 0.2 mm and 787 fins/m, whereas the cold side was 0.485 m, 0.41 mm and 236 fins/m. A maximum percentage error of 10.5% for the overall heat transfer and conductance (UA value) was found.
Higher tolerance for these values is acceptable with deviations as high as 30% experienced in literature. Table 4 provides the sample size, the mean absolute error (MAE) and the percentage of results predicted within 30% and 50% of the experimental results, q and z respectively. The predicted results are obtained using the correlation derived by Refs. [40,44] for saturated boiling and condensing frictional pressure drop respectively, and the experimental data points are from Ref. [53] for boiling flow and [54] for condensing flow. For the saturated two-phase flow heat transfer coefficient, predicted values are obtained using [39,43] for boiling and condensing flow, respectively. Experimental data are provided by Ref. [55] for boiling flow and [56] for condensing flow. Based on the results, the use of the saturated boiling and condensing heat transfer correlations is deemed adequate as the predicted results fall mostly within 30% of the experimental. The frictional pressure gradient has a larger deviation, however, mostly the large discrepancies occur at low values (less than 5 kPa/m) and therefore deemed adequate for this preliminary analysis.

Design methodology
The focus of the paper is on the feasibility of micro-ORCs for space applications. An optimisation using a genetic algorithm to minimise the micro-ORC system volume is described in this section. Before the system is analysed and sized, it is necessary to ensure suitable heat transfer correlations are used. A concern for the proposed system, is the possibility of the working fluid in the evaporator to operate in the IAFB and DFFB regimes, as mentioned in Section 3.3. Therefore, an investigation into the boiling flow regime of the evaporator is warranted due to the high operating temperatures expected in the receiver. Finally, a set of suitable turbine loss models are discussed and validated so that the turbine performance of the optimal design can be estimated. Fig. 6 provides a flowchart summarising the three main investigations conducted in this work.

Critical heat flux analysis
To the authors' knowledge, no ORC optimisation study has included the effects of boiling flow in the IAFB and DFFB regimes. A number of IAFB and DFFB empirical correlations provided in Ref. [41,42] are analysed to determine the most suitable correlations for this study. This analysis includes comparing the empirical correlations with experimental data based using R134a [57] and water [58,59]. A local sensitivity analysis, using the one-at-a-time (OAT) technique was also conducted on the two-phase boiling heat transfer coefficient to minimise this uncertainty, due to a lack of experimental validation of the correlations and working fluid considered in this study. This sensitivity analysis was conducted on various operating pressures (1, 10, and 20 bar), tube diameters (1, 2, 3, and 6 mm), surface wall temperatures (500, 550, and 650 K) and mass flow rates (1, 5, and 10 g/s), that are expected to occur during the optimisation study, with the baseline parameters underlined. The working fluid was taken as Toluene and the maximum (bulk) temperature was constrained to 10K above its saturation temperature. The effect of various heat transfer coefficients on the system was also investigated by assuming constant heat transfer coefficient values in the system model. The results are provided in Section 5.1. The selected IAFB and DFFB empirical correlations were then used in the evaporator model in the optimisation study (discussed in the next section) to determine the heat transfer coefficient if these flow regimes were experienced.

System optimisation
An investigation into the feasibility of a micro-ORC system in terms of volume has been conducted. Reducing the volume and mass are both crucial for small satellite subsystems. However, these variables are proportional to each other and therefore only one variable needs to be considered in the optimisation. System volume was selected as a more appropriate optimisation variable due to the physical concerns regarding integration inside the launch vehicle, especially of large components such as the concentrators. Only superheated configurations with regeneration are analysed, as illustrated in Fig. 2b. The analysis is performed using a singleobjective genetic algorithm (GA) implemented in MATLAB [60] based on the system architecture shown in Fig. 2a. The optimisation process is shown in Fig. 7. Genetic algorithms are common methods used in ORC optimisation studies [61] due to their robustness, however at the expense of higher computational time when compared to other methods such as the direct search and variable metric method.
For this study, the optimisation minimises the objective function, FðxÞ, with respect to the design variables, x, defined in Equation (4), where m 1 is the system volume fraction (m 1 ¼ V sys =V sc ) and U is the penalty term. The total volume of the ORC system, V sys , is the summation of the volume of the evaporator, regenerator,   condenser, pump, plumbing, and turbine. An additional margin of 20% has been included to account for miscellaneous components such as support structures, interfaces, and control hardware. The total volume of the satellite is denoted by V sc and is determined based on the allowable payload volume inside the standard Evolved Expendable Launch Vehicles (EELV) Secondary Payload Adapter (ESPA). The micro-ORC system is constrained to produce 200 W of electrical power output. The parabolic penalty method has been used to increase the search domain by relaxing specific system constraints into a penalty term and reduce the risk of non-convex solutions by squaring each term in the objective function [62]. The penalty term is defined as the summation of penalty parameters, P i , The parameter c represents the system constraint that has been relaxed such that the solution is not discarded during the iteration process of the optimisation. In this case, a penalty is given if the fluid velocity in the HXs (regenerator, evaporator, and condenser) falls outside the limits for liquid (0:5 u f 5), vapour (1 u v min½60 175r À0:43 v ), and two-phase (1 u tp 183r À0:5 m ) flow [63]. Penalties are also given if the mass velocity, Reynolds number (liquid-only, superficial liquid, and superficial vapour), and reduced pressure falls outside the range of validity of the two-phase flow correlations used in the condenser [43] and evaporator [38] models. c min and c max represent the upper and lower feasible bounds of these parameters.
Constraints that result in infeasible solutions that are not passed through the iteration process are provided in Table 5 along with the fixed parameters used in the optimisation. Table 6 defines the 14 design variables, x, used and their corresponding upper and lower limits.
The upper value of the maximum pressure was set to 5% less than the critical pressure of the working fluid and the lower value was set to 1 bar, to explore a broad design space. In terrestrial applications, the minimum cycle pressure of the working fluid has to be greater than atmospheric pressure to avoid air leakage into the system. This is not a concern in this design due to vacuum ambient conditions. However, the lower limit of the minimum cycle pressure was restricted to 0.1 bar to ensure the condenser pressure losses could be overcome. Fin geometry ranges are limited to common values used in plate-fin heat exchanger designs [37]. The length of hot and cold sides of the regenerator was constrained for spacial constraints and to minimise the aspect ratios for structural concerns. A minimum of 2 hot layers was set because the hot channels form the outer part of the regenerator, as shown in Fig. 4c. Further improvement in the regenerator design could be to design the cold layers on the outside to minimise heat loss and extend the length of the hot and cold sides. The diameter of the condenser was limited to the validity range of the condensing heat transfer correlations [43,44]. The minimum number of concentrators was set as 2 for redundancy. The lower bound of the number of fibre rings, as described by Fig. 3, was set to 2 because one ring does not meet the power input requirement. A wide range of receiver geometries was also evaluated to meet the thermal energy storage requirement, to ensure continuous power generation during eclipse periods. The Table 5 Optimisation constraints and system model parameters.

Constraints
Model parameters Rotor blade height: b > 0:2 mm * Stator inlet to outlet radius ratio: r 0 r 1 ¼ 1:3 y Regenerator thickness to height ratio:   Regenerator fin height mm 0.2e8 x 4 Regenerator fin thickness mm 0.1e1 x 5 Regenerator fin frequency fin/m 100e1000 x 6 Regenerator length of hot side mm 1e100 x 7 Regenerator length of cold side mm 1e100 x 8 Number of hot layers 2e200 x 9 Condenser diameter mm 0.2e6 x 10 Number of concentrators 2e20 x 11 Number of rings (fibre bundle) 2e10 x 12 Receiver thickness mm 1e100 x 13 Receiver length mm 1e100 x 14 Receiver insulation thickness mm 1e500 insulation range ensures the working fluid does not exceed its thermal stability limit. It is expected that the MM and MDM scenarios will therefore require larger insulation thickness to meet the thermal stability constraint. For a specific satellite mission, the temperature of the outer layer of the insulation can be constrained to the required spacecraft environment for better thermal control, however, this is not considered in this study. The optimisation was run for six working fluids Toluene, MM, MDM, D4, D5, and D6, based on the results of [6] as well as the work of [10], to identify the most suitable working fluid for small satellite applications. Working fluids are constrained to fluids that correspond to a Fire Protection Association (NPFA) 704 health rating of less than 4 to minimise the integration risks of a small satellite with the primary payload on-board the launch vehicle. Flammability is less of concern in space due to the absence of oxygen reducing the risk of a fire. However, the flammability of the fluid increases handling costs and launch risks.
The optimisation population size was set to 140, and the termination criterion was set as either a convergence criterion of 10 À10 or a maximum number of generations of 1000. These values were selected as a compromise between computational speed and accuracy. An initial mutation rate of 0.02 and a crossover probability of 0.7 were used.

Turbine performance estimation
The turbine efficiency decreases with size. The major reason for this decrease is because the relative aerodynamic losses increase for smaller designs, such as the relative clearance between the blade and shroud gets larger which increases the losses. Generally, during the preliminary design phase, turbine losses are determined using loss model correlations. However, these empirical loss correlations have been developed for large-scale turbines using nonorganic fluids and their accuracy for the problem at hand is debatable. There is a lack of experimental testing of micro-radial inflow turbines (micro-RIT), which are necessary to characterise and quantify the associated turbine losses.
To determine an estimation of the losses and provide more realistic preliminary results, this work extends the research conducted by Ref. [64] and uses a set of loss models that were found to be acceptable for small-scale applications (with rotor diameters of 30 mm). These loss models show satisfactory agreement within 5% of the total-to-static efficiency compared with CFD results and 14% compared to experimental data [64]. In this case, we are interested to maximise the total-to-static efficiency, h TS , given by Equation (6), where, h TT is the total-to-total efficiency, v is the absolute velocity, w is the relative velocity and T is the static temperature. The subscripts 2 and 3 refer to the rotor inlet and outlet section. DW is is the Eulerian work obtained from the isentropic calculation performed in Stodola [65]. The loss coefficient of the stator, z N , was computed by resorting to the Glassman model complemented by a firstprinciple loss model for the mixing losses [66]. The rotor loss coefficient z R , can be calculated using Equation (8) and is made up of tip clearance, Dh tc , secondary flow, Dh sf , skin friction, Dh fric , and incidence losses, Dh inc , A large concern with small scale turbomachinery is the tipleakage loss due the relatively high tip gap to blade span ratio resulting from manufacturing and safety constraints. Here, the associated loss is calculated according to Equation (9) [67], where tc is the tip clearance and b 2 is the rotor inlet blade height. Equation (10) [67e69] determines the losses inside the blade passage such as secondary flow loss and skin friction loss, where, r c is the radius of curvature and Z is the number of rotor blades. The average velocity w is defined as w ¼ 0:5½w 2 þ0:5ðw 3;sh þw 3;hb Þ [70], the modified friction coefficient, c' f ;c is determined by the correlation proposed by Ref. [71] shown in Equation (11) to account for the effects of curvature in the turbine. The friction coefficient, c f ;c is determined using Equation (12) [72] and the Fanning friction factor f is calculated as f ¼ 16=Re av if laminar flow and the Colebrook-White correlation if turbulent flow [73], The incidence losses can be determined using Equation (13) [74] and the losses caused by the rotor outlet kinetic energy referred to as the exit losses is given by Equation (14) [64], Dh ee ¼ 0:5v 2 3 : The predictive capability of the loss model for small-scale applications was verified by a test case example. The turbine design used as the test case is the ORCHID mini-turbine [66] that uses MM as the working fluid; additional inputs are given in Table 7. Results are compared with the Baines model [75] using the STODOLA software [65]. For simplicity, the average velocity in Equation (10) is taken as the average of the inlet and outlet of the rotor. The results of the verification analysis performed on the ORCHID turbine are shown in Table 8. The total-to-static efficiency using the empirical loss models defined in this study is found to be within 3% of the model described by Baines and 6.5% of the CFD results. The implemented model is shown to provide a conservative value of the total-to-static efficiency. Table 7 provides the input values used to determine the turbine efficiency of a micro-turbine design. The turbine efficiency is varied from 45 to 65% in a OAT sensitivity analysis to determine the impact of turbine efficiency on the system feasibility. Table 9 provides the indexing of the existing IAFB and DFFB correlations used in the CHF analysis. The table also provides the results of the empirical correlations compared with experimental data, to identify which empirical correlations are the most suitable.

Critical heat flux results
The results indicate that the correlations that perform the closest with the experimental data in terms of MAE, q, and z are the models proposed by Breen and Westwater (Index 3), and Bromley based on either using the vapour (Index 1) or vapour film temperature (Index 2) for the IAFB regime. The closest performing DFFB correlations are the Bishop (Index 9), Tong (Index 13), and Slaughterbeck (Index 14) correlations.
The Bishop (Index 9) DFFB correlation was selected for use in the optimisation study because it is the best performing correlation against the experimental data, illustrated in Table 9. Although, the Breen and Westwater (Index 3) correlation provides the most comparable values with the experimental data, the Bromley (Index 2) correlation was selected for use in the optimisation study. Fig. 8a indicates that for the operating conditions expected in this optimisation study the Bromley (Index 2) and Breen and Westwater (Index 3) correlations provide similar heat transfer coefficients, thus making it acceptable to select the Bromley (Index 2) correlation. By using the Bromley correlation we reduce the dependency of the film boiling heat transfer coefficient on the surface tension, which was uncertain for D5, D6 and MDM siloxanes under investigation. It was found that the diameter has the most significant influence on the DFFB heat transfer coefficient and that most IAFB correlations are not affected by the mass flow rate, as shown in Fig. 8. During this sensitivity analysis, the radiation heat transfer coefficient accounted for a maximum of 6% of the total heat transfer coefficient for both the Bromley and the Bishop correlations, assuming a wall and liquid emissivity of 0.95 and 0.6 respectively.
The results in Table 10, showing the effect of heat transfer coefficients on the ORC system, indicate as expected an increase in evaporator length and volume with decreasing heat transfer coefficient. However, the ORC volume and thermal efficiency are not significantly affected, and therefore the use of the selected IAFB and DFFB correlations in the optimisation is assumed to be satisfactory for the purposes of determining a preliminary design of the proposed system. The small effect on the ORC volume is also due to the rest of the ORC system components, such as the concentrator, condenser and regenerator, remaining the same for this analysis. Table 11 shows the design input parameters for the optimal solutions of all the working fluid scenarios that can meet the discharge time required to operate continuously during the eclipse period. The results illustrate that the length of the cold side of the regenerator reaches the upper bound of the given range. Extending the upper limit of the cold side length, results in an increase in regenerator geometry and thermal efficiency of the system by 1e2%. If the design requires a higher discharge time then a larger receiver is needed. At discharge time requirements of more than three times that specified in this optimisation, a larger optical system is also needed to meet the energy input required to obtain the thermal storage capacity.

System optimisation results
The volume and mass of all the components for the various working fluids are provided in Fig. 9. The critical component of the system is the concentrator has it has the largest stowed volume and mass, for the Toluene case they occupy 11.5% and 13.25% of the total allowable spacecraft volume and mass respectively.
Inflatable concentrators are necessary for the feasibility of micro-ORC systems as deployable rigid concentrators significantly exceed the spacecraft volume for the input power requirement, as depicted in Fig. 10a. For example, the concentrator stowed volume fraction increases from 11.5% to 57.5% when changing the concentrator storage volume from 1% to 5%. Additionally, changing the design from inflatable to rigid the concentrator mass fraction increases from 13.25% to 31.04%. Fig. 10b illustrates the mass saving potential of inflatable designs, although this sensitivity analysis does not include the mass of the pressurisation system needed to inflate the optical system.
The receiver and condenser are the next largest components. These components, together with the generator, make up the Table 8 Verification of the total-to-static efficiency of the implemented loss model of the ORCHID turbine.
heaviest components of the system. Toluene is shown to be the optimal working fluid for reducing the size of the system for a specific energy storage capacity and requires a stowed volume fraction of 18%. This is due to its higher thermal efficiency. However, this advantage is at the expense of faster rotor rotational speeds and smaller rotor blade heights, refer to Table 13. These high speeds, together with the high operating temperature and long lifetime required, eliminate the use of standard ball bearings [80]. Alternative existing high-speed bearings include hydrodynamic, hydrostatic, foil, and magnetic bearings. In the field of micro-gas turbines, foil and hydrostatic (specifically hydroinertia) gas bearings have been identified as possible candidates [81]. Molecular complexity [82] defines the slope of the saturation curve in the T-s plane and is a function of the molecular structure. It increases with number and mass of atoms that form the molecule. All fluids analysed in the optimisation have high molecular complexity and result in dry expansion, which is beneficial in extending the life of the turbine. Fig. 11 illustrates the relationship between molecular complexity and rotor blade height and rotational speed. Fluids with relatively higher molecular complexity require lower enthalpy drops. The size parameter of the turbine is inversely proportional to the enthalpy drop across the turbine and therefore turbine geometry increases with molecular complexity. Rotational speed is proportional to the enthalpy drop and therefore decreases with increasing molecular complexity [6,83]. The thermal efficiency reduces with increasing complexity as the optimal solutions resulted in a decrease in pressure ratio. This is a result of lower critical pressure which reduces the design space, as the upper limit of the maximum cycle pressure is constrained to 0.95p cr . Fig. 11 also shows the potential inverse relationship between shared power density and molecular complexity. This is due to the decrease in thermal efficiency and thus decrease in electrical power output with increasing fluid molecular complexity. Toluene and linear siloxanes with relatively lower molecular complexity have higher shared power densities which is more advantageous for small satellites, with blade heights larger than the manufacturing limit. Fluids with lower molecular complexities would result in rotor geometries that are not feasible at the power level and operating temperature considered in this study.
A proportional linear relationship can be derived from the optimal solutions system volume and mass with respect to molecular complexity, as shown in Fig. 12. The linear trends have an rsquared fit of 0.90 and 0.81 for the system mass and volume respectively. This proportional relationship is mainly due to the decrease of thermal efficiency, which increases the power input required for the same design constraints. The increase in power input needed means that a larger optical system is required which has the most significant effect of the proposed system. For the application considered in this study, fluids with high molecular complexity are required to meet the manufacturing limit of microturbines. However, out of the working fluids considered in this study, fluids with relatively lower molecular complexity are desired to maximise thermal efficiency and therefore minimise the system mass and volume. Table 13 illustrates that the system using the Toluene working fluid has a total specific power of 3.6W/kg, which does not compete  with solar photovoltaic systems. For example, the SMART-1 mission has an end of life specific density of 24 W/kg (mass includes the solar panels, the Power Control and Distribution Unit and Battery Management Electronics systems). When coupling the micro-ORC system to an STP system the shared specific power is improved to 10.3W/kg assuming that the mass of the concentrator and receiver are part of the propulsion system (shared specific power excludes the receiver and concentrator mass but includes the margin). Despite the low specific power, the advantage to this system comes with the high-temperature thermal energy storage as it provides around 500 Wh/kg of specific energy that could be beneficial in future missions. By using boron instead of silicon, as the PCM, the specific energy could be increased up to 1280 Wh/kg. More efficient and lightweight concentrators, condensers, regenerators, and generators could increase the power density of the system. Designing micro-turbines is a challenging task due to supersonic flow in the stator, fast rotational speeds and small blade heights. One of the largest unknown parameters is the turbine efficiency of small-scale turbines that utilise organic working fluids. The next section investigates the preliminary total-to-static efficiency of the micro-turbine design using Toluene as a working fluid. Only the Toluene design is evaluated because it is the most suitable working fluid for small satellites due to its low system volume and mass. It also has the smallest turbine size and therefore is the most interesting design to investigate regarding total-to-static efficiency.

Sensitivity analysis on turbine efficiency
For the micro-turbine design a total-to-static efficiency of 57.38% was found assuming a tip clearance of 75 mm [81] and a surface roughness of 0.05 mm [64]. The fluid was found to operate in the turbulent region with the Reynolds number equal to 1.753 Â 10 5 and 1.346 Â 10 5 for the stator and rotor respectively. This is because the high vapour density and low viscosity of Toluene alleviate the effects of the small blade height. The turbine efficiency used in the optimisation, refer to Table 5, is too high. Therefore, a sensitivity analysis with respect to turbine efficiency is needed to determine the impact of this parameter on the system. Reducing the turbine efficiency, from 65% to 45%, decreases the thermal efficiency of the system by 30.3% and therefore, the electrical power output by 5.16% with respect to reference value (65% turbine Fig. 9. Optimal solution (a) volume and (b) mass fraction of all the system components relative to the total volume and mass of the satellite.  Table 12 provides the stowed volume fraction and areal density inputs for each concentrator type. efficiency). This, in turn, reduces the shared power density by 18.6%, as shown in Fig. 13. The micro-ORC system mass and volume fraction with respect to satellite mass and volume is 24.6% and 18.4% for the 45% turbine efficiency case and 23.2% and 17.5% for the 65% case. Therefore, these turbine efficiencies are feasible if a system mass and volume fraction of less than 25% and 20% respectively are acceptable, however, this depends on the satellite mission.
Additionally, in small-scale turbine designs, heat loss increases with reducing size [81], which would significantly affect the efficiency of the turbine. Heat loss has not been accounted for in this study. However, it is advised that it should be considered in future work along with investigating the possibility of using thermal control from the high-temperature receiver.

Conclusions
The study focused on the feasibility of micro-ORC systems for power generation on-board small satellites that use waste energy from a solar thermal propulsion system. An optimisation was performed on six working fluids, accounting for system design, satellite mission, and fluid constraints. From the results, it has been found that Toluene is the optimal fluid in terms of minimising the   volume for a given discharge time. However, the turbine rotor has a small blade height (0.27 mm) and fast rotational speed (772krpm), which makes the attainment of high turbine efficiency challenging. Low turbine efficiencies are expected for micro-turbines mainly due to the large tip clearance of 75 mm, with an total-to-static efficiency of 57.38% obtained for the optimal Toluene solution. The optical system is the largest and heaviest component of the system, promoting the use of inflatable technology. It was found that the critical heat flux is necessary to determine the flow regime inside the evaporator when high-temperature phase change materials are used to better predict the heat transfer and therefore accurately determine the length and volume of the evaporator. However, the heat transfer coefficient of the evaporator has a negligible effect on the complete system volume. Various post CHF empirical equations were evaluated, and the Breen and Westwater and the Bishop correlations were found to provide the closest results to experimental data and mid-range results during the sensitivity analysis. However, the Bromley correlation was adopted instead of the Breen and Westwater because both correlations provide similar heat transfer coefficients under the expected operating conditions but the Bromley reduces the dependency of film boiling heat transfer coefficient on the surface tension. Recommended future work is to conduct experimental testing and in-depth modelling of the evaporator-receiver coupling to predict the heat transfer better and characterise the off-design and transient effects of the system. Investigation into the performance of micro-turbines is also recommended. The results indicate that micro-ORC systems are feasible on-board small satellites in terms of size and energy storage, and are attractive to missions requiring high specific energies. However, they have low shared specific powers on the order of 10W/kg when coupled to a solar thermal propulsion system. The proposed micro-ORC system would therefore result in a heavier electrical power system for small satellites compared to current state-of-the-art power systems.
CRediT authorship contribution statement

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.