Alkali Metal Loop Heat Pipe Development for Solar Dynamic

48th International Conference on Environmental Systems ICES-2018-159 8-12 July 2018, Albuquerque, New Mexico

Copyright © 2018 Abengoa

Alkali Metal Loop Heat Pipe Development for Solar Dynamic Energy Conversion

Sonia Fereres1 and Sonia De La Rosa2 Abengoa, Sevilla, 41014, Spain

Bastien Bonnafous3 ESA/ESTEC, Noordwijk, The Netherlands

Mikaël Mohaupt4 Euro Heat Pipes, Rue de l’Industrie 24, B-1400 Nivelles, Belgium

Benjamin Lagier5 and Raphaël Mari6 Airbus Defence and Space SAS,31 Rue des Cosmonautes, 31400 Toulouse, France

Cristina Guraya7 and Cristina Jiménez8 Tecnalia, Mikeletegi Pasealekua 2, 20009 San Sebastian, Spain

Future space exploration missions and outposts on the Moon and Mars would benefit from compact, efficient, high temperature energy conversion devices such as nuclear and solar reactors. In the case of solar dynamic systems, extending operation beyond the hours of solar exposure can be achieved by incorporating Thermal Energy Storage (TES) if the concentrated radiation can be decoupled from the power conversion unit and stored. Conventional heat pipes have been previously developed for this purpose in terrestrial solar receivers and dish-Stirling systems, but the low pumping capacity provided by the capillary structure limits their operational range to horizontal configurations and short distances. Here a high temperature Loop Heat Pipe (LHP) is investigated to transport the concentrated solar radiation from a parabolic dish´s focal point to alternative locations. LHP can perform well at high power, transporting heat over large distances and in different orientations. However, the large power transport (> 10 kW) and high temperature (> 600ºC) requirements of dish-Stirling systems are above current state-of-the-art LHP technology, making this a challenge in terms of materials, fluids, and design. A trade-off study is performed taking into account system requirements, performance and cost, developing a numerical model to determine the most promising solution for a future prototype. The working fluids options at these temperatures are limited to liquid metals: mainly sodium, potassium, and cesium. Although sodium might seem like the most promising working fluid candidate, potassium is anticipated to work better within the system requirements. This paper will show through analysis that, in contrast to conventional LHP where working fluids have negligible thermal conductivity, when using a highly conductive liquid metal the parasitic heat fluxes might be extremely important. This is a novel problem, indicating that design parameter optimization has to be performed differently to ensure proper operation.

1 Senior Thermal Engineer, Aerospace Dept., Abengoa Innovación, Energía Solar 1, Sevilla 41014, Spain. 2 Head of Dept., Aerospace Dept., Abengoa Innovación, Av. Madrid 50, Alcala de Henares 28802, Spain. 3 Thermal Engineer, Thermal Division, ESA/ESTEC, Keplerlaan 1, PO Box 299 - 2200 AG Noordwijk, Netherlands 4 Design Engineer, Rue de l’Industrie, 24 B-1400 Nivelles Belgium 5 Fluid &Thermal Engineer, Mechanical Design Office, Av. Cosmonautes 42, Toulouse 31402, France 6 Fluid &Thermal Engineer, Mechanical Design Office, Av. Cosmonautes 42, Toulouse 31402, France 7 Project Manager, Aeronautic & Space Area, Industry & Transport Division, Mikeletegi Pasealekua 2, San Sebastian 20009, Spain. 8 Project Manager, Aeronautic & Space Area, Industry & Transport Division, Mikeletegi Pasealekua 2, San Sebastian 20009, Spain

International Conference on Environmental Systems

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I. Introduction PACE nuclear and solar power systems designed for future exploration missions and human habitats on the Moon and Mars require the development of high temperature energy conversion devices for propulsion, power

generation, and energy infraestructure. Nuclear power can serve as a compact durable energy source that can operate long-term. Solar dynamic power conversion reactors using Stirling or Brayton engines are viable alternatives, especially if they include energy storage, allowing continuos operation regardless of the incoming solar radiation. Efficient methods to transfer high heat fluxes at high temperatures for these nuclear or solar devices has traditionally been addressed by conventional high temperature heat pipes (HP). However, loop heat pipes have several advantages over conventional heat pipes: improved tolerance for noncondensable gases, a more flexible piping design, and the possibility of ground testing in any orientation1. Here, the development of a high temperature Loop Heat Pipe (LHP) for solar dynamic energy conversion is analyzed.

Solar dynamic energy conversion systems focus and collect the solar radiation on a solar receiver and transfer this thermal energy to a power conversion unit, which is located at a certain distance from the receiver. Extending the operation beyond the hours of solar exposure can be achieved by incorporating Thermal Energy Storage (TES), if the concentrated radiation can be decoupled from the power conversion unit and stored. Conventional heat pipes have been previously developed for this purpose in terrestrial solar receivers and dish-Stirling systems 2, but the low pumping capacity provided by the capillary structure limits their operational range to horizontal configurations and short distances. Power conversion units (PCU) are usually Stirling or Brayton engines, but more recently thermionic converters or alkali metal thermoelectric converters (AMTEC) are also being investigated3. These PCU requirements are shared among nuclear or bimodal space fission power and/or propulsion systems. Thus, these applications would also benefit from high temperature LHP developments. Transporting the concentrated solar radiation effectively from the solar receiver to alternative locations by means of a LHP can bring the following benefits: 1) decouple the solar receiver from the power conversion unit, allowing its relocation in more favorable position, thereby lightening structural loads and reducing frame costs; 2) increase the competitiveness of the solar dynamic system for continuos operation when the sun is not shining by allowing the incorporation of TES, hybridization and cogeneration designs without negatively impacting the structure; 3) using a latent heat device allows to absorb higher, uneven temperature distributions, providing a more uniform heat input for the engine/PCU, which will translate in higher engine efficiency.

Heat pipes are effective thermal devices to passively transport large amounts of heat over a given distance with the lowest temperature gradient. For temperatures above 450ºC (723 K), liquid metals are the only working fluid option. Although the literature concerning high temperature /liquid metal heat pipes is vast and has found recent renewed interest in concentrated solar power plants 2, there are limited reports regarding high temperature, liquid metal LHP. Several decades ago, a high temperature LHP using cesium as the working fluid was fabricated and tested at 850 K1. This LHP had a titanium envelope, and a titanium aluminide wick, reporting a power transport capability of 600 W. More recently, a loop-type HP using sodium as the working fluid and a stainless steel casing was designed, fabricated and tested to transport 1 kW at 1000 K from a solar receiver to an AMTEC power conversion unit located 0.5 m away3. A capillary pumped loop (CPL) using sodium as the working fluid was also designed and tested in a parabolic dish/AMTEC solar thermal power system4, but little information was given regarding the CPL´s performance and operation. To the best of the authors´ knowledge, there are no further reported studies focusing on liquid metal LHP.

The objective of this study is to evaluate the solar dynamic system requirements and technologies trade-offs, with the aim of designing a high temperature loop heat pipe (HT LHP) capable of transporting a large amount of heat (> 10 kW) at temperatures above 650ºC, as a first step in the design of a proof-of concept.

II. Requirements Specification A parabolic dish tracks the sun moving along two axes, concentrating and reflecting the radiation at its focal point

situated above the center of the dish where the heat engine is located. The LHP shall transport the heat collected at the solar receiver (located at the parabolic dish´s focal point) to an alternative location, delivering it to the PCU/engine or TES system. This new location is ideally a non-mobile part of the dish structure. It can be the rear of the dish, the ground or on the pedestal mount structure. For the proof-of-concept, we will focus on transferring the heat to the rear of the dish, as other solutions can be derived subsequently. Thus, the minimum required length would be the parabolic dish´s focal distance (f, as shown in Figure 1).

S


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The focal distance, solar beam spot, and flux distribution are intrinsically related to the dish reflector geometry and optics. In general terms, for wider acceptance angles, the receiver can be located at greater distances from the dish collector surface. Typical receiver intercept sections are circular spots with diameter dimensions around 150 mm to 225 mm.

The peak fluxes can easily be in excess of 80-90 W/cm2, depending on the dish geometry. These peak fluxes are located at the center for a standard flat 2-D distribution of the mirror facets. However, the dish optics can be optimized to change the flux distribution if needed. Using a similar geometry to that of the EuroDish5, for parabolic dishes in the 6-8

m diameter range, a focal distance of 3-3.5m is needed for solar spots with heat fluxes above 60W/cm2.

Table 1 – Main HT LHP Requirements # Description Value Comments 1 Power transport capability 10kW to 30kW A solar dish-Stirling with ~30 kWth has a typical dish

diameter 6-11 m 2 Operating temperature range 650- 1000°C Lower T will lead to inefficiencies at Stirling and HT LHP

level 3 Hot source surface R20cm interface Based on focal cavity dimensions, a disk shape with a

diameter of 180 mm is recommended. 4 Gravity head 3 to 5m Value for remote PCU/engine position at focal cavity 5 Power density on evaporator

side >30 W/cm² Typical ~60 W/cm2 with peaks up to 150 W/cm²

6 Cold source surface TBD Function of TES and Stirling design 7 Start-up conditions TBD Include start-up heaters 8 Total heat, Q > 10 kW Function of TES and Stirling design 9 Cold source temperature 650-800°C Stirling I/F temperature; TES based on NaCl with melting

temperature at 801°C. 10 Material compatibility Lifetime= 20 years Will drive fluid and material choice

The target LHP design requirements can be seen in Table 1. Considering that previous high temperature LHP

designs have only achieved around 1 kW 1, 3, a power transport capability in excess of 10 kW is already beyond the state of the art regarding this technology.

III. Conceptual Design The main mission of the HT LHP is “to carry heat at high temperature (T > 650ºC) to a remote position”. Although

LHP have demonstrated their appropriateness in covering large distances, the high power and flux requirements (wick limitations) of a solar interface has yet to be proven. A LHP has a working fluid, which transfers heat by evaporation and condensation, and an envelope or casing, which provides a leak-tight pressure vessel containing the working fluid. Within the envelope, there are four distinct sections: a) an evaporator, b) a compensation chamber/ reservoir, c) a condenser, and d) separated liquid/vapor transport lines. The capillary structure (wick) in a LHP is only located in the evaporator section, in contrast to conventional HP where the wick covers the whole device length.

The LHP-solar dish/Stirling has the following interfaces (Figure 2): A) Heat source (evaporator interface): solar receiver in a parabolic solar thermal dish. It is characterized by high

heat fluxes, high temperatures and small surface area for the heat exchange within a receiver cavity. An aperture diameter of 180 mm diameter is considered as design basis.

Figure 1. Solar dish-Stirling schematic.


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B) Cold source (condenser interface): a Stirling engine head where the working fluid (helium or hydrogen) is heated through a serpentine or dome type heat exchanger formed by multiple tubes. The heat exchanger surfaces in commercial Stirling engines vary depending on the manufacturer and the heat input type. The condenser shape and size can be further optimized to achieve maximum performance metrics; thus, emphasis will be put on the other elements to ensure that heat can be transported over large distances at high temperatures. If TES is included, the condenser serpentine-type heat exchanger interface will be embedded in a TES material module (sensible heat or latent heat based).Therefore, a simplified heat exchanger shall be sufficient and compatible with both solutions (a Stirling engine head or an intermediate TES interface). For the latter, a second HP/LHP element would transfer the heat from the TES to the PCU/engine head.

C) Distance to be covered (liquid and vapor lines): considering a 7-8 m diameter dish design basis, a focal length of approximately 3-4.5m is required.

IV. Trade-off Evaluation Main elements of the LHP are selected based on a trade-off evaluation, globally focused on:

- The performance with the materials and design selection. - The global material / wick / working fluid compatibility - Overall material, components and system cost

A. Working Fluid Selection The design of the high temperature LHP is driven by the selection of the working fluid. For temperatures above

650ºC, alkali metals like Cs, K, Na, Li have previously been used in high temperature heat pipes 6. Cadmium and zinc might work based merely on their operating temperatures (i.e. Zinc HP can theoretically operate in the 700-1000ºC range), but they have not been extensively used for these applications. Zinc has been evaluated as a high temperature HP working fluid recently in a ceramic envelope HP prototype 7, since it alloys with most metals. Cadmium is discarded as a working fluid because of the inability to find reference performance data and because it is toxic. Mercury is discarded as it is on the lower useful temperature range (250-650ºC) and toxic. Lithium is discarded because it is above the temperature range of interest (1000-1800ºC).

Table 2 – High temperature fluids selected: general data and useful temperature range

Compatible Material Price (€/kg)

Melting point (ºC)

Boiling point at Patm (ºC)

Useful T range (ºC)

Cs Titanium, Niobium, Stainless Steel, Nickel superalloys € 9800 28.4 670.8 450-900

K Stainless steel, Inconel, Titanium alloys (Ti-6Al-4V ) € 900 63.3 774 500-1000

Na Stainless Steel, Nickel, Inconel, Niobium € 225 97.9 892 600-1200

Other options, such as eutectic alkali metal alloys (NaCs, NaK) could be interesting working fluids for HP

applications. They have melting points below ambient temperature, making it easier to manipulate and test under ambient conditions. For example, NaK eutectic (roughly 78% potassium) has a melting point of -12ºC, which is lower than the melting point of either of its constituents (sodium melts at 98 ºC and potassium at 62 ºC). However, NaK is a non-azeotropic mixture, meaning that the composition of the liquid phase and the vapor phase are not the same in saturated mixtures. Consequently, the liquid composition changes during boiling.The vapor in a saturated non-azeotropic mixture will have higher fractions of the higher-vapor pressure component (potassium, in the case of NaK) than the liquid, while fractions of the less-volatile component (sodium, in the case of NaK) will be relatively higher than in the vapor phase. Previous tests with NaK heat pipes have demonstrated problems with temperature non-uniformities in the evaporator and condenser interfaces due to its non-azeotropic nature8. Therefore, for this initial

Figure 2. High Temperature LHP Conceptual Design. Evaporator located at the solar receiver and condenser at the heat engine/TES interface.


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proof-of-concept, a single-component working fluid is a preferred option. The preferred working fluids are consequently limited to sodium (Na), potassium (K), or cesium (Cs). Their main operating temperatures and price is shown in Table 2, Figure 3, and Figure 4 show some fluid properties for the temperange of interest.

A figure of merit is usually employed to estimate the suitability of the working fluid as a vapor-liquid transport medium. For classical HP, this figure of merit is based on liquid properties FMl=�� ⁄ , where ρl is the liquid density, σ the surface tension, L the latent heat, and µl the liquid viscosity. For LHP an alternative figure of merit has been proposed 9, based on the assumption that liquid pressure drops may be negligible compared to vapor pressure drops and that there is turbulent flow in the vapor line, FMv� ��

.�� µ� .�� , where ρv is the vapor density, σ the surface

tension, L the latent heat, and µv the vapor viscosity. High merit numbers are desirable. For the fluids in Table 2, FMv for K is slightly higher than for Na at temperatures T< 770ºC, and lower than Na for T>770ºC (Figure 3).

The individual working fluid properties affect the thermal performance of the LHP in the following way:

- Latent heat of vaporization L (Figure 4,a): high values are desirable to transfer large amounts of heat with a minimum mass flow, thus maintaining low pressure drops. Na has a higher L than the other liquid metals; Cs has the worst performance.

- Kinematic viscosity: lower viscosity reduces the pressure drops through the loop allowing larger wick pore sizes for an equivalent heat transfer. Cs is preferred in this case.

- Surface tension and wetting properties (Figure 4, b): higher surface tension will generate a higher pumping head /capillary driving force for a given pore size; thus, fluids with higher surface tension (Na) are desirable.

- Saturation pressure versus temperature slope: a high ��

�� value is desirable because it makes evaporator

temperatures less sensitive to loop pressure drop. In this aspect, cesium has the most favorable saturation curve for temperatures below 900ºC (Figure 4, c).

- Thermal conductivity (λ): on one hand a high thermal conductivity would minimize temperature gradients radially and reduce the possibility of nucleate boiling at the wick/wall interface. In “classical” LHP designs with traditional working fluids, such as water or ammonia, the thermal conductivity of the liquid does not play an important role and is often not considered during the trade-off analysis. However, in this case, since liquid metals are used, their high thermal conductivity is comparable to the wick material’s conductivity and cannot be neglected in the calculations. It seems to influence greatly the parasitic heat flux towards the reservoir. In this sense, it would be desirable to have liquids with the lowest thermal conductivity possible (λCs < λK < λNa).

For the three working fluids that are within our temperature range (Cs, K, Na), sodium has the best properties for “classical” two phase heat transport: higher latent heat of vaporization (minimizing the mass flow rate), higher surface tension ( less constraint on the pore size) and low cost. But sodium has a “flat” saturation curve in the temperature

range of interest (Figure 4 c), requiring large temperature differences for a given hydrostatic ∆P to overcome. It also has a very large thermal conductivity, increasing the amount of heat leaks to the reservoir.

On the other hand, Cs and K, have worse latent heat of vaporization, requiring larger amounts of fluid to transfer the same amount of heat, but they have a better behavior in terms of reducing the overall working temperature (as the saturation curve is steeper in this temperature range) and limiting the parasitic heat fluxes due to their lower thermal conductivity. They will also require smaller wick pores to achieve the same capillary pressure. In particular, Cs has a very high liquid density – almost double that of Na. This means the induced hydrostatic pressure drop is almost doubled (44kPa vs 23 kPa) for 3m. Adding this to the fact that the surface tension of Cs is around a third of the value of Na, the required pore radius will be reduced by a factor of 6 for Cs, possibly reaching practical manufacturing limits. Cs is also very expensive and finally discarded. K does not stand out as having the best properties but rather intermediate values for most, making it a possible compromise. One of the drawbacks of using potassium is that there

Figure 3. Figure of Merit FM v for LHP. Cs, K, and Na over the 500-1200 ºC range.


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is no published material compatibility /corrosion data as the high temperature HP literature has focused on the other fluids (sodium 3, 6, cesium 1, lithium, and even NaK 8).

B. Material Compatibility

The purpose of the LHP envelope is isolating the working fluid from the outside. It must be well sealed, leak-proof, while allowing heat transfer effectively through its walls. It should withstand high temperatures and be compatible with the selected fluid 6. Compatible container structural materials working at high temperatures (T>650ºC) are screened. Typical HP materials such as copper, or aluminium are not appropriate for this temperature range. Based on the operation temperatures and compatibility with the working fluids preselected (sodium or potassium) a number of candidates have been identified and are summarized in Table 3. Other aspects have to be considered such as corrosion and creep, thermo-mechanical fatigue behaviour due to the on/ off behavior of the system, availability, manufacturability, weldability, wettability by the working fluid, cost and lifetime performance.

The two main problems of material incompatibility are corrosion and generation of non-condensable gas. The purity of the working fluid is also of the utmost importance for a satisfactorily lifetime performance, since many failures in liquid metal heat pipes commonly appear due to impurity driven corrosion mechanisms. An assessment of the suitability of a given container material for use with liquid-metals must be based on the knowledge of its total corrosion response. As in many corrosive environments, a simple numerical rate is not an accurate measurement of the susceptibility of a material when reaction with the liquid metal results in more than one of the modes of attacks. Under such circumstances, a measurement reflecting total corrosion damage is much more appropriate for judging the ability of a material to resist corrosion by a particular liquid metal. The two main corrosion mechanisms for liquid metals and structutal alloys are: a) alloy components of the structural material dissolve in the liquid metal and b) intergranular diffusion, leading to early failure under stress. Evaluating available corrosion data for sodium 10, 11, the following conclusions can be made: Sodium/Ni-base alloy corrosion is classical in manner (increasing with both the temperature, the temperature gradient and time), and sodium/stainless steel corrosion presents an anomalous behavior, because the stainless steel surface responds initially

a) Latent Heat b) Surface tension

c) Saturation curve d) Thermal conductivity

Figure 4. Working fluid properties evaluated. Latent Heat, surface tension, saturation curve and thermal conductivity of Cs, K, and Na in the temperature range of 500-1200 ºC.


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to corrosion with microstructural changes hindering further corrosion. This exceptional behaviour results in low, velocity-independent corrosion rates, which make stainless steels attractive materials for alkali metal circuits.

Table 3 – Material compatibility with alkali metals Material Temperature

(ºC) 12 Comments

Stainless steels (304, 316) 600-700 Most common, inexpensive material, but the appropriateness for the upper temperature range limits will have to be evaluated, especially as it might present non-condensable gas generation issues. Best availability of compatible circuit components (e.g. valves)

Superalloys: inconels, Haynes alloys

600-875 Should be evaluated if stainless steels are inadequate. They will have a higher cost, but they will perform better at high temperatures.

Refractory metals (tantalum, niobium and zirconium alloys)

<1200-1900 Highest price point

Ceramics < 2500 Only if ceramic wicks are considered (if metallic powders do not yield the necessary wicking performance characteristics), ceramic casings should be evaluated based on compatibility with the wicks. Difficulty to join them easily and effectively. Porous materials, requiring coatings to prevent gas diffusion into the HP

In terms of mechanical properties, Nickel-base alloys have initially better behaviour at high temperatures compared to stainless steels (SS). Inconel 718 and Hayness 230 have been used with sodium for HP. In both cases the maximum temperatures evaluated have been of 700ºC. The behaviour of these alloys in contact with sodium beyond the 700 ºC is unknown. The mechanical properties (in air) of both nickel alloys (Inconel 718 and Haynes 230) decay drastically at high temperatures. However, they have largely better properties than SS316.

Long duration sodium heat pipe tests were carried out by NASA in the early 2000s13, showing performance without degradation or failure for an extended number of operating hours (Table 4). Some of the conclusions from this study are: 1) improved brazing techniques and ultrasonic inspection of the parts prior to assembly will reduce the risk of failure; 2) the heat pipes were fabricated with sodium-compatible envelopes, but, based on the authors´ know-how, using potassium as the working fluid will experience the same life times as the sodium heat pipes.These life test results collectively have demonstrated the potential for high temperature heat pipes to serve as reliable energy conversion system components for power applications with a long operating lifetime.

Table 4 – Main results from NASA´s long duration sodium HP tests13

C. Wick Characteristics The wick is one of the most important elements in the LHP and its structure is a key factor determining the LHP’s

performance. The capillary wick in a LHP is only located in the evaporator section. The performance of the wick, without other design considerations, is determined essentially by its pore size, porosity, and permeability. Finer pores will provide higher capillary force, while higher porosity will lead to larger permeability. Nevertheless, pores too fine will cause the permeability drop and a sharp increase of the hydraulic resistance. Wicks with very fine pores require very high porosities, reducing the wick’s thermal conductivity and mechanical strength.Considering the loop heat pipe performance requirements, for a 3 m hydrostatic pressure drop using sodium, the wick has to have a target porosity of 60% with pore sizes in the range of 5-12 microns. The resulting permeability should be higher than 4.74 x 10-12 m2.

The material selection for the wick is based on different criteria such as: compatibility with the fluid, working temperatures, thermal conductivity, compatibility with casing material (thermal expansion), manufacturability, wick geometry, and cost.

Ceramics are materials that could satisfy some of the key factors. They are stable at high temperatures well above the operating range, some like aluminium nitride can have high thermal conductivity, oxide ceramics are easy to manufacture and most of them are compatible with the stainless steel casing. Compatibility with sodium of several ceramics such us alumina, silicon nitride, zirconia, silicon carbide, titanium carbide, SiAlON, spinels, aluminium nitride or aluminium oxinitride has been studied. Best results were obtained with high purity alumina, but its thermal

HP envelope wick operation T(ºC) hrs

SS316L sintered porous nickel 650-700 115000 Inco718 stainless steel screen 700 41000

Haynes230 sintered porous nickel 700 20000


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coefficient of expansion could be a disadvantage. Ceramics are also brittle and high porosities reduce their mechanical strength. The wick dimensions make handling and integrating a ceramic wick into the LHP difficult.

Metal wicks seem to be the best candidates due to their compatibility with alkali metals, their high working temperature, their thermal compatibility with the metallic casing and their thermal conductivity. Among possible metals, refractory metals are expensive, mainly used for higher temperatures and their thermal expansion is low. Stainless steel and Nickel are the most suitable candidate materials for the wick fabrication; both materials are commercially available, they are compatible with alkali metals and their integration in the casing is affordable. Nickel can work at higher temperatures than stainless steel and has higher thermal conductivity and lower coefficient of thermal expansion. It is three to four times more expensive than stainless steel and commercial availability grades cover different particle sizes and different particle morphologies, some of them have been widely used. Stainless steel´s main advantages are its low cost, easy welding and the wider commercial offer of powder sizes available; this factor could help in achieving final wick physical properties (porosity and pore size) closer to the specifications.

V. Model Description A nodal resistance network model has been developed to evaluate the performances of a high temperature LHP

evaporator with cylindrical evaporator and integrated reservoir. The model does not consider the condenser side of the circuit and the liquid inlet temperature is an input. Similar LHP modelisation have been previously presented 14 but not applied specifically to alkali metal.

The thermal model is made of four nodes (Figure 5): evaporator saddle (Tsaddle), saturation temperature (Tsat), cavity (Tcav) and liquid line (Tliq). The main heat conduction is though Cvap which is the effective evaporation conductance. Cbody and Cwick are parasitic heat flux conductances toward cavity from Tsaddle and Tsat, respectively. Heat (Pin) is directly applied to the saddle (radiative heating in this case) and extracted by exiting vapor through vaporization (latent heat) and by subcooled liquid entering cavity (specific heat). The complete model couples these four thermal nodes with a circuit pressure drop calculation. Tsat and Tcav are on the saturation curve but at two different pressure levels and hence at two different temperatures.. The subcooling need of the

evaporator is the thermal gradient between Tcav and Tliq required to cancel parasitic heat flux from body and wick conduction (Pleaks). An iterative solving method is used to solve the system, which is nonlinear due to physical properties variation and pressure drop.

Working with alkali metal around 700 °C with a high pressure drop requires the following modifications compared to classical low temperature models:

• More resilient solving method to cope with a very low �� ⁄ value which makes evaporator temperatures very sensitive to small pressure variations

• �� ⁄ needs to be evaluated at both evaporation and cavity side due to possible large temperature gradient (+100°C) between Tsat and Tcav.

The maximum allowable loop pressure head is determined by the capillary pumping capacity of the porous wick (∆Pc, max) provided by the size of its pores (Dpore), the fluid surface tension (σ) and contact angle (θ) with the capillary material.

∆��,�� !"#�$

%&'() (1)

The pressure losses generated by the fluid flow (∆P) through the different items of the loop (wick, condenser, liquid return from the condenser, vapor flow from the evaporator to condenser, vapor channels inside the evaporator (grooves), and the gravitational head) must be lower than the maximum capillary pumping pressure:

∆��,�� ≥ +��,-.�/01 + +��/34/��/01 + +��-0�1051. + +�6/�7 + +�8.--�15 + +�8.��/9: (2)

Figure 5. Model nodal network schematic.

Tsaddle

Tsat

Tcav

Pin

Pevap= L vap

Pleaks = Cp (Tcav - T liq )

Cvap

Cbody

T liq

Cwick

T liq

Tcav

;<=>?@

AB CD

Tsat E;<FFD

E;EG

Te

mpe

ratu

re


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∆Pvapor line, ∆Pliquid line, ∆Pcondenser depend on the fluid

density and kinematic viscosity, ∆Pwick depends on the wick permeability (K) and the fluid’s kinematic viscosity, and ∆Pgravity depends on the hydrostatic height between the evaporator and the condenser and liquid and vapor density (ρl, ρv). The following reference values were used in these initial calculations: liquid line and vapor line tubes are 3 m long and have a diameter of 10 mm each; the overall distance to cover (hydrostatic height) is 3m, and the condenser has a total length to evacuate heat of 0.2 m. Considering such large distances to overcome, the hydrostatic pressure drop is the main parameter driving the maximum pore radius for a wick capable of producing the required capillary pressure.

The parameters used for the baseline calculations are shown in Table 5. The manufacturing limit Dpore

2/K = 150 is taken to be a conservative, achievable limit based on experience. This ratio is typically Dpore

2/K ~ 100 for very optimized wicks. The wick or saddle should be grooved and a collector added to drive the created vapor from the wick center to the vapor tubing. These geometries should be carefully chosen to avoid high pressure losses.

VI. Results and Discussion

A. Wick design sensitivity study Evaporators of LHP working with high thermally conductive fluids have even more wick design constraints than

classical low temperature LHP. Thermal conduction through the body and wick are increased by the high gradient between the saturation and the cavity temperatures and the high liquid thermal conductivity. This has the potential to severely degrade performances and increase saturation temperature. There are two main parasitic flux sources:

a) Conduction through the evaporator body: this value will depend on the wick and grooves height but is low compared to leaks through the wick

b) Conduction through the metallic wick: a simple expression considering only heat conduction can be used for the wick resistivity:

H6/�7 ��IJ KLMNOPJKQRSMT ULMNO

1LMNO (3)

Where α is the wick porosity, λ the thermal conductivity (VW� > 40 W/m/K,VX > 25 W/m/K, V6/�7 ≈ 4 W/m/K), Swick the surface area calculated for a wick diameter of 180 mm and 5 mm high, and ewick the wick thickness. More complex expressions for the wick resistivity including convective heat transfer can be found15. These leaks could represent a non-negligible fraction of the input power in the case of thin wick and high circuit pressure drop. These considerations are in line with9, where a detailed non-dimensional analysis of a LHP evaporator wick was presented. They showed a radial heat leak by conduction across the wick is proportional to the effective thermal conductivity as long as the Péclet number is low. The Péclet number represents the relative magnitude of the convective to conductive heat transfer and can be calculated as:

�Y ��B Z&,QRSMT

K)QQ 1LMNO⁄ (4)

where [B is the fluid mass flow rate, ewick the wick thickness. For a classical 50W LHP using ammonia can have a Pe ~1.7 (ewick=3mm, Dwick=28mm), whilst a 20 kW LHP such as the design under consideration using potassium has Pe~0.26 (ewick= 30mm, Dwick =180mm). Thus, in this LHP, for Pe <1, the heat conduction dominates over the heat convection (contrary to classical small LHP using NH3).

Reducing wick parasitic flux (lower Cwick) for a given fluid can be achieved with different drawbacks: • Decrease wick porosity → Decrease wick permeability and increase wick pressure drop • Increase wick thickness → Increase wick pressure drop • Lower V\�4/�, by working at higher temperature → Material limitation

Table 5. Evaporator wick, grooves and collector parameters (assuming rectangular cross sections)

Wick Diameter Dwick = 180 mm Thickness e = 5 - 30 mm Thermal conductivity

λ = 4 W/K

Pore diameter Dpore = 12.5 µm Permeability K = 1.04x10-12 m2 Manufacturing limit

Dpore2/K = 150

Porosity 50% Grooves Side a = 2.5 mm

Pitch b = 6 mm Length L = Dwick/2 Number of grooves (subchannels)

Nb = 30

Collector Length L = π Dwick/2 Number Nb = 2 side a = 10 mm


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The sensitivity to the wick thickness is evaluated. The results are shown in Figure 6 with parasitic heat flux through

the wick plotted against inlet liquid temperature. This suggests that a very thick wick (e > 30 mm) is required, both with Na and K, to reduce the parasitic flux. Wick porosity could also be decreased ideally but the wick characteristics may vary (i.e. permeability) and generate more pressure drop. This is a peculiarity of this HT LHP project. Generally, in standard LHP with traditional working fluids (H2O, NH3) higher porosity values and thinner wicks are required to provide better performance characteristics. However, here, because of the fluid properties, the design solution seems to suggest to go to “worse” performing wicks in order to achieve tolerable temperatures (T < 850ºC). This appears to be a novel approach to optimize wick characteristics. Using potassium instead of sodium enables lower saturation temperature for a given input power but with higher circuit pressure drop induced by a higher mass flow rate.

Figure 6. Sensitivity study to parasitic flux varying with wick thickness for 15 kW heat input Sodium and

potassium are compared assuming 50% porosity, Dpore2/K=150, Dpore = 12.5 µm

From a performance point of view, higher working temperatures allows transporting larger heat input power.

However, to comply with metallic casing material limits, the vapor temperature should be kept under certain values. For example, based on corrosion data for stainless steels it is not reasonable to think the wall temperature can be above 700ºC for extended operation, even though some heat pipe studies claim it can be used up to 800ºC 4. Higher temperature nickel alloys can maybe withstand up to 800ºC, although reported performance data is limited to 750-770ºC because above these values the mechanical properties experience a dramatic decrease.

Reducing Tsat is only favorable to material behavior (Figure 7). There are three ways of proceeding: 1) reduce the subcooling need by increasing wick thickness, 2) reduce circuit pressure drop, and 3) increase dP/dT value (increase the working temperature). Increasing the wick thickness will reduce the wick parasitic heat flux due to the conduction into the wick and will reduce the cavity temperature Tcav and the saturation temperature Tsat. However, increasing wick thickness indefinitely is not sufficient to bring Tsat closer to Tcav due to the dP/dT value imposed by the fluid. The generated gradient is mainly produced by hydrostatic pressure head (3 m) which is a fixed parameter in our case.

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Figure 7. Tsat vs. Tliq for various wick thicknesses for Na and K. 15 kW input power, Dpore = 12.5µm,

K = 1.04x10-12 m2, D2/K = 150, Porosity = 50%.

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Following the same approach as before, the sensitivity of the evaporator temperature level to input power is evaluated for potassium in Figure 8 with improved circuit and wick caracteristics. At low power, the pressure drop induced by flow resistivity is rather low but the hydrostic pressure remains and generates a thermal gradient between Tcav and Tsat and thus a parasitic heat flux. The saturation level tends to stabilize at high power. However, the 30 kW case presented here exceeds the wick maximum capillary pumping capacity even with improved wick and circuit parameters.

B. Design trade-off All design choices are interconnected: fluid, casing material, wick, and system performances. The modeling results

indicate that for the required temperature range to use a metallic casing (T< 800ºC), sodium does not present optimum characteristics. However, other options for lower temperatures (such as using potassium) present other disadvantages.

In terms of TRL, there is very little reported research done with LHP at high temperatures. Besides 1, 3, additional references using alkali metal two-phase transport are for conventional HP rather than LHP. Most of the corrosion studies and life tests correspond to sodium. Considering this fact, the TRL for sodium seems higher than for cesium and certainly higher than for potassium. The literature with potassium for HP is almost non-existent.

The analysis shows that, in contrast to conventional low temperature LHP where working fluids have negligible thermal conductivity, when using a liquid metal, the parasitic heat fluxes might be extremely important. This is a novel problem and it indicates that wick parameter optimization has to be performed differently, perhaps in the lines of hindering thermal transport (thicker wicks, lower conductivity liquids) to ensure proper operation.

In terms of cost, higher temperature metals (Inconel, Haynes) are significantly more expensive than stainless steel. However, the higher temperature working fluid (sodium) is much cheaper and will require less amount to fill a similar performing potassium heat pipe (1.9 kg vs. 4 kg).

Performance limitations will be determined by minimum wick pore diameter achievable in practice (raw materials, manufacturing process) and the homogeneity of the wick over its entire length. Considering potential LHP for solar dishes around 8 m diameter (a focal length between 3.5- 5 m), simple calculations were made to ensure that the design choice is not impossible for longer distance solutions. For potassium to overcome 5 m (Table 6), a 3.5 µm pore diameter will be required only to overcome the hydrostatic pressure drop without considering any other pressure losses.

Table 6. Minimum wick pore diameter & thickness to overcome hydrostatic pressure with different fluids

(50% porosity, permeability is obtained through Dpore2/K =150)

3 m 5 m K: 30 mm thick wick Dpore = 5 µm Dpore = 3.5 µm Na: 60 mm thick wick Dpore = 8 µm Dpore = 6.2 µm

From the trade-off analysis it seems that there is no obvious winning solution. • Na works better at higher temperatures, with larger pore diameters, but requires more expensive alloys for a

compatible casing. There is corrosion and life test data available, and the filling ratio is not excessive (<2 kg). • K is better suited for lower temperatures and can use a stainless steel casing, but it will require a higher filling

ratio (~4 kg), thicker ducts too, and will not be able to use the upper range power. High performing wicks, with smaller pores are required. Perhaps a smaller dish system is better suited for this solution.

Figure 8. Sensitivity study to input power for potassium for a 30 mm

wick with improved capacity. (Dpore = 8.5 µm, K = 1.45x10-12 m2, D2/K = 50, Porosity = 50%, Dvap line = 25mm, collector side = 15 mm)

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VII. Conclusion Sodium seems to be the best option for its large heat of vaporization and its large surface tension (high capillary

pumping capacity). However, the flatness of its saturation curve at temperatures of 600-750°C is a major drawback for the use of stainless steel material.

Thus, two alternatives are proposed: a) A stainless steel LHP filled with potassium working at lower temperature and lower maximal power, and b) an inconel (or another Nickel alloy) LHP filled with sodium and working in the an upper temperature range 750-800°C. The potassium solution requires high performance wicks (smaller pore diameter with adequate permeability) and calls for a large filling ratio (2-4 kg). It will not be able to achieve 30 kW, but it may perform better at the lower temperature/lower power range.

This analysis shows that, in contrast to conventional LHP where working fluids have negligible thermal conductivity, when using a liquid metal the parasitic heat fluxes might be extremely important. This is a novel problem and it indicates that wick parameter optimization has to be performed differently to ensure proper operation. Additional temperature constraints to use metallic envelope casing materials, slightly change the classical LHP performance requirements, where having a high figure of merit is not sufficient. Due to the large parasitic flux, the LHP under design has a high subcooling requirement. Approaches to reduce the subcooling should be explored.

Acknowledgments The authors would like to thank the contributions of Xabier Azpiroz and Emmanuel Dehombreux, who actively

contributed to the work and discussions performed during this trade-off analysis.

References 1 Anderson, W. G., Bland, J. J., Fershtater, Y., Goncharov, K. A., Nikitkin, M., and Juhasz, A. “High temperature loop heat pipes”. Intersociety Energy Conversion Engineering Conference, Orlando, Florida, 1995. 2Andraka, C. E.; Rawlinson, K. S.; Siegel, N. P., “Technical Feasibility of Storage on Large Dish Stirling Systems”, Sandia National Laboratories, SAND2012-8353, 2012. 3Boo, J. H.; Kim, S. M.; Kang, Y. H. “An Experimental Study on a Sodium Loop-type Heat Pipe for Thermal Transport from a High-temperature Solar Receiver”, Energy Procedia 2015, 69, 608-617. 4Wu, S.Y.; and Xiao, L., “A parabolic dish/AMTEC solar thermal power system and its performance evaluation”, Applied Energy Vol. 87, 2010, pp. 452–462. 5Reinalter, W.; Ulmer, S.; Heller, P. . R. T.; Gineste, J.M.; Ferriere, A.; and Nepveu, F, “Detailed Performance Analysis of a 10kW Dish⁄Stirling System”, J. Sol. Energy Eng Vol. 130, No.1, 2007, 011013-011013-6. 6Reay, D.; McGlen, R.; Kew, Heat Pipes: Theory, Design and Applications, Butterworth-Heinemann, 2006. 7Meisel, P.; Jobst, M.; Lippmann, W.; Hurtado, A., “Design and manufacture of ceramic heat pipes for high”, Applied Thermal Engineering Vol.75, 2015, pp. 692-699. 8Tarau, C.; Walker, K. L.; Anderson, W. G., “High temperature variable conductance heat pipes for radioisotope stirling systems”, Space, Propulsion and Energy Sciences International Forum (SPEIF), Huntsville, AL, 2009. 9Mishknis, D.; OChterbeck, J. M.; Sodtke, C.; Ku, J.; Butler, D., “Non-dimensional analysis and scaling issues in loop heat pipes”, 41st AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2003; 2003-AIAA 2341. 10Romano, J.; and Klamut, C. J.” Corrosion and deposition of steels and nickel-base alloys in liquid sodium”, In Advances in Corrosion Science and Technology; Plenum press: New York, 1973. 11Thorley, W.; and Tyzack, C.,“Alkali Metal Coolants”, IAEA, Vienna, 1967. 12El-Genk, M. S.; Tournier, J.-M., “A review of refractory metal alloys and mechanically alloyed-oxide dispersion strengthened steels for space nuclear power systems”, Journal of Nuclear Materials Vol. 340, 2005, pp. 93-112. 13Rosenfeld, J. H.; Ernst, D. E.; Lindemuth, J. E.; Sanzi, J. L.; Geng, S. M.; and Zuo, J. “An Overview of Long Duration Sodium Heat Pipe Tests”; NASA, 2004. 14Vlassov, V. V.; Riehl, R. R., “Mathematical model of a loop heat pipe with cylindrical evaporator and integrated reservoir”, Applied Thermal Engineering Vol. 28, 2008, pp. 942-954. 15Launay, S., Sartre, V., and Bonjour, J., “Analytical Model for Characterization of Loop Heat Pipes”, Journal of Thermophysics and Heat Transfer Vol. 22, No. 4, 2008, pp. 623-631.

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Alkali Metal Loop Heat Pipe Development for Solar Dynamic