Challenges and Fundamentals of Modeling Heat Pipes'Startup from a Frozen State

Mohamed El-Genk and Jean-Michel TournierInstitute for Space and Nuclear Power Studies, Department of Chemical and Nuclear Engineering

The University of New Mexico, Albuquerque, NM 87131(505) 277 - 5442, Fax: -2814, email: mgenk@unm.edu

Abstract. Alkali metal heat pipes are being used in a variety of space nuclear power applications, including cooling ofnuclear reactors and heat rejection radiators. Candidate working fluids for these heat pipes, in an order of increasingoperation temperature, are potassium (700-950 K), sodium (800-1100 K), and lithium (1100 K-1600 K), which arefrozen at startup conditions. The startup of alkali metal heat pipes from a frozen state poses a number of complexissues and challenges, some of which are reviewed and discussed in this paper. In addition, the selection of theworking fluid, wick and wall materials, and the operation limits of the heat pipes are briefly reviewed, including thesonic limit and the change in the vapor flow regimes during the startup from a frozen state. The successive processesoccurring during the startup of a radiatively-cooled sodium heat pipe are also presented and discussed.

INTRODUCTIONAlkali metal heat pipes are being considered for thermal energy transport in many high temperature, high powerdensity, space and terrestrial power and energy systems. Many space nuclear power system concepts developedand/or proposed during the past two decades have used alkali metal heat pipes for removing the heat generated byfission in the nuclear reactor to an energy conversion subsystem external to the core, behind a shadow radiationshield (Ranken, 1982; Houts et al., 1998). Alkali metal heat pipes are also used to transport the unconverted heatfrom the cold side of the energy converters to the heat rejection radiator. The conversion subsystems considered inthese systems include Stirling engine (Angelo and Buden, 1985; Schmitz et al., 1994), Thermoelectric (Ranken,1982; Josloff et al., 1994), Brayton engine (Shepard et al., 1994), in-core Thermionic (Merrigan and Trujillo, 1992;Determan and Hagelston, 1992; Mills et al., 1994), and out-of-core Thermionic (Begg et al., 1992). In thesesystems, alkali metal heat pipes have also been proposed for use in the heat rejection radiator at 700-973 K.

Besides offering passive heat removal at high heat fluxes, alkali metal heat pipes provide high redundancy, becauseof the absence of any failure propagation among heat pipes. Other advantages of alkali-metal heat pipes for use inspace nuclear power systems include: passive and continuous decay heat removal after reactor shutdown; selfcontainment, very low working fluid inventory (typically < 40 g/m of heat pipe length) and, hence, light weight;isothermal operation and very high power throughput (up to 16 and 30 kW/cm2 with sodium and lithium heat pipesat 1200 K and 1600 K, respectively). Heat pipes also provide simplicity in the design and flexibility in theintegration to the different energy conversion systems (Begg et al., 1992; Schmitz et al., 1994).

The utilization of alkali-metal heat pipes in space power applications, however, requires proper selections of theworking fluid, wick design and material, and wall material, based on considerations of chemical compatibility, creepstrength and reliable performance in nuclear radiation environment, for the projected operation life of the system(> 7 years). In addition, since candidate working fluids have relatively high melting points (336.4 K, 370.9 K and453.7 K, for potassium, sodium, and lithium, respectively), they are frozen at the startup of the nuclear powersystem, after reaching an operation orbit. Reid et al. (1991) have provided a comprehensive review of alkali metalheat pipe work performed until 1991, covering both modeling and experimental investigations of the startup from afrozen state. One criterion for the selection of the working fluid for alkali metal heat pipes is the range of operationtemperature: potassium for 700-950 K, sodium for 800-1100 K, and lithium for 1100-1600 K. It is desirable tooperate these heat pipes at an internal vapor pressure between 10 and 100 kPa and at or close to the temperature atwhich the Figure-of-Merit (FOM) of the working fluid is maximum (Figure 3). Another selection criterion is lowneutron activation and generation of non-condensable gases.

CP608, Space Technology and Applications International Forum-STAIF 2002, edited by M.S. El-Genk© 2002 American Institute of Physics 0-7354-0052-0/027$ 19.00

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This paper reviews and discusses the operation limits of heat pipes, and the processes occurring during the startup ofalkali metal heat pipes from a frozen state, as well as the challenges of simulating the startup. In addition, thechange in the prevailing vapor flow regime during the startup, the selection of the working fluid, wick, and wallmaterials, and the generation of non-condensable gases by neutron activation are briefly reviewed. The successiveprocesses occurring during the startup of a radiatively-cooled sodium heat pipe are presented and discussed. In acompanion paper in these proceedings, the modeling capabilities of the Heat Pipe Transient Analysis Model forsimulating the frozen startup of alkali metal heat pipes are summarized, and examples of startup predictions andcomparison with experimental measurements are presented and discussed (Tournier and El-Genk, 2002).

WORKING FLUIDSFigure 1 shows a schematic of a liquidmetal heat pipe. The liquid metal workingfluids potassium (K), sodium (Na), andlithium (Li) span the operationtemperature range from '-TOO K to 1600 K.Commensurate with the melting andboiling temperatures of these workingfluids, the vapor pressures PK > PNa > Puand the operation temperaturesTK < TNa < Tu> The saturation vapor pressures of K, Na and Li are compared in Figure 2, along with that of water asa reference. Operation pressure in alkali metal heat pipes is typically between 10 and 100 kPa, to ensure subsonicvapor velocities during normal operation, without over-pressurizing the pipe container, as discussed later in thispaper. To speed up the startup process from a frozen state, the heat pipes may be loaded with a small amount ofnon-condensable gas. These gases speed up the transition of the heat pipe operation from the very inefficientmolecular and transition vapor flow regimes to the continuum or viscous flow regime. On the other hand, whenalkali metal heat pipes are being used in a neutron environment, such as in-core or near a nuclear reactor, inert gasesare generated within the heat pipes by neutron activation and could degrade their performance. These gasesaccumulate at the end of the condenser, continuously reducing its effective length for heat rejection, and, hence thepower throughput of the heat pipe.

FIGURE 1. A Schematic of a Simplified Design of an Alkali Metal Heat Pipe.

10°

« io6Q^ 40

| io2

I 10°C o

•g 10"2

co| io-4

& ID'6Critical pointMelting pointMaximum FOM

1014

^ 1013

I io12

1010

10O0

i? 108

200 400 600 800 1000 1200 1400 1600 1800Temperature (K)

FIGURE 2. Vapor Pressure of Some Heat Pipe working Fluids.

10'

! Lithiiim

SxDditim

Water•D

A

Melting pointCritical pointMaximum FOM

200 400 600 800 1000 1200 1400 1600 1800Temperature (K)

FIGURE 3. Figure of Merit of Some Heat Pipe Working Fluids.

During startup from a frozen state, the vapor in alkali metal heat pipes does not transition to the viscous (or thecontinuum) flow regime until the heat pipe temperature is relatively high (Tournier and El-Genk, 2002). For a heatpipe having a vapor core diameter of 20 mm, Li vapor is in the free-molecule flow regime up to 800 K (or vaporpressure < 1.4 Pa), in the transition flow regime between 800 K and 1025 K, and in the viscous regime above 1025K (> 185 Pa). These transition temperatures are 550 K (0.74 Pa) and 700 K (89 Pa) for sodium and 460 K (0.34 Pa)and 580 K (41 Pa) for potassium (Figure 2). During the startup from a frozen state, all three flow regimes may co-exist in the vapor core along the heat pipe, depending on the location of the thaw front of the working fluid, and theheating and cooling rates of the evaporator and condenser. A successful startup scenario is the one in which theheat rejection from the condenser section of the heat pipe remains nil until the heat pipe is fully thawed, the capillaryand entrainment limits are avoided both by design and by the initial value of and the incremental increases in the

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heating rate, the transition from the free-molecule to the continuum vapor flow regime is speeded up, and the lengthof the condenser is sufficient to account for the accumulation of non-condensable gases and the excess liquid.

Ideally, when alkali metal heat pipes are used in the heat rejection radiator of a nuclear reactor power system, inwhich the reactor core is also cooled by alkali metal heat pipes, covering the radiator with an insulation blanket untilthe heat pipes are fully thawed is highly recommended. As indicated earlier, the initial presence of non-condensablegases, by design, speeds up the startup process as it increases the initial total pressure in the vapor region of the heatpipe. After the heat pipe is fully thawed and reaches its operation temperature, the non-condensable gases willtypically accumulate at the end of the condenser, which could be accounted for in the design. However, some ofthese gases and those generated by neutron activation in a nuclear reactor partially accumulate at the surface of thewick in the condenser section, adding a thermal resistance to condensation of vapor and to the heat rejection,decreasing the operation power throughput, and/or increasing the heat pipe temperature, when operating at aconstant thermal power input.

The alkali metals increase in volume as they thaw and the liquid temperature increases to the operation temperature,but their viscosity, latent heat of vaporization, and surface tension all decrease with temperature. Table 1 liststypical values of theses properties at the fluid's melting point and a typical operating temperature, and the associateddecreases in percentage. The changes in the physical properties of the working fluids with temperature also affecttheir FOM, and hence the peak power throughput for design consideration (Figure 3).

TABLE 1. Some Physical Properties of Candidate Alkali-Metal Working Fluids for Heat Pipes.Property\working fluid

Liquid density (kg/mj):@ Melting point(Melting point)@ Operation Temperature(Operating temperature)Liquid viscosity (kg/m.s):@ Melting point@ Operation TemperatureLatent heat of vaporization (kJ/kg):@ Melting point@ Operation TemperatureSurface tension (N/m):@ Melting point@ Operation Temperature

PotassiumValue

829.3(336.4 K)

719.(800 K)

5.3 x10"4

1.6x10"4

2,230.2,050.

0.1090.0784

Change

-13.3%

-70.0%

-8.1%

-28.1%

SodiumValue

928.2(370.9 K)

778.(1000K)

6.9 x10"4

1.8x10"4

4,540.4,060.

0.1980.135

Change

-16.2%

-73.9%

-10.6%

-31.8%

LithiumValue

516.9(453.7 K)

420.(1400K)

6.0 x10"4

1.8x10"4

22,550.20,100.

0.4010.250

Change

-18.7%

-70.0%

-10.9%

-37.7%

WICK AND STRUCTURAL MATERIALSTypical materials for the wick and the wall of alkali metal heat pipes, in an order of increasing temperature anddensity, are titanium and titanium alloys, stainless steel, superalloys, refractory metals (Nb, Mo, Ta and W) andrefractory alloys (Nb-lZr, PWC-11, TZM, T-lll, Astar-811C, Mo-Re, W-R) (Table 2). The service temperature ofthese various materials is determined based on considerations of the high-temperature creep strength; fabricability;changes in mechanical properties in irradiation environment; chemical compatibility with working fluid and nuclearfuel (UO2, UC, or UN), when relevant; static and dynamic tensile behavior; fracture toughness and weldability; andthe ductile-to-brittle (DTB) transition temperature. For example, molybdenum (Mo) and tungsten (W) are brittlebelow ~ 400 K and 600 K, respectively, but could be alloyed with rhenium to decrease the DTB transitiontemperature.

A failure of an alkali metal heat pipe, without an excessive over pressure or temperature, is generally caused by thetransport of the wall and the wick materials by dissolution in alkali-metal liquid from the evaporator, and depositionin the condenser section. Other mechanisms, which govern the corrosion of refractory metals and their alloys inalkali metals, are reactions with impurities, particularly non-metallic contaminants such as oxygen, carbon, nitrogenand silicon (Reid et al., 1991; King and El-Genk, 2001). Corrosive failures could also result from the reaction oftrace impurities with the heat pipe wall materials to form mobile compounds, which are soluble in alkali metalworking fluids. Many of these corrosion mechanisms could be alleviated by the proper selection of structuralmaterials and the working fluid, ensuring their high-purity, and using appropriate cleaning and filling techniques ofthe heat pipe during fabrication and loading of the working fluid.

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TABLE 2. Structural Materials for Alkali Metal Heat Pipes.

Type ofmaterial

Titanium

Steel alloys

Superalloys

Niobium &alloys

Molybdenum&alloys

Tantalum &alloys

Tungsten &alloysCarbon

Temperature(K)

775 - 875

875 - 900

900 1150

Up to 1500

Up to 1800

Up to 2200

Up to 2200

Up to 3000

DemonstratedCompatibility

K

Na, K, Hg

Na, KNa, K, NaK

Na

Li, Na, KLi, Na, K, NaK

Li, NaLi, Na, K

Li

Li, Na, K,NaK, Hg, Cs

Li

Needs liner

MaterialTitaniumSS-304SS-316

Inconel 750XHastelloy X

Haynes-25NiobiumNb-1%ZrPWC-1 1C-103

MolybdenumMo-TZM

Mo-44.5%ReTantalum

T-111Astar811CTungstenW-4%ReCarbon

Composition(elements > 1%)

TiFe-19Cr-(8-12)Ni-2MnFe-17Cr-(10-14)Ni-2Mn

73Ni-15.5Cr-7Fe-2.5Ti-1Nb49Ni-22Cr-15.8Fe-9Mo

50Co-20Cr-1 5W-1 ONi-3Fe-1.5Mn

NbNb-1Zr

Nb-1Zr-0.1CNb-10Hf-1Ti-0.5Zr

Mo (brittle below ~ 400 K)Mo-0.5Ti-0.1Zr

Mo-44.5ReTa

Ta-8W-2HfTa-8W-1 Re-0.7Hf-0.025CW (brittle below - 600 K)

W-4ReC

Meltingpoint (K)

19411699165816661523

1602

275026802680262328962896302332903250

3695

3923

Density(9/cm3)

4.517.927.9

8.258.2

8.578.588.608.8610.2810.1613.516.616.7

19.2518.352.25

Tests conducted during the SPAR and SP-100 programs (Ranken, 1982; Angelo and Buden, 1985) demonstratedgood compatibility of refractory metals with alkali metals, provided that oxygen content is kept very low, less than1-10 ppm (Reid et al., 1991; King and El-Genk, 2001). Niobium and tantalum are particularly susceptible tooxygen driven attacks, even in Na containing < 1-10 ppm O2. Using refractory alloys containing traces of oxygengetters such as Zr or Hf could alleviate this concern. Examples are the niobium alloys: Nb-l%Zr, PWC-11 and C-103 (Table 2). Pure molybdenum and tungsten do not appear to be as susceptible to oxygen-assisted alkali metalattack, like tantalum and niobium, but suffer from high DBT temperatures (W more so than Mo). This concerncould be addressed by alloying these metals with other refractory metals, such as the molybdenum alloys TZM andMo-Re, which offer improved strength and ductility over pure Mo. Mo-13Re has excellent high-temperature creepstrength, low-temperature ductility for launch conditions and excellent compatibility with lithium (> 11,000 hrstesting at 1500 K) and UO2 fuel (Angelo and Buden, 1985). Similarly, TZM and Na have excellent compatibility(tested for 53,000 hrs at 1390 K) (Table 3).

LIFETIME TESTS AND IN-CORE USE OF HEAT PIPESLifetime tests reported for high-temperature heat pipes using different combinations of working fluids and wallmaterials are listed in Table 3. The longest lifetime demonstrated to date is for a short lithium heat pipe fabricatedfrom low-carbon, arc-cast Mo and operated for 25,400 hrs at 1700 K with a thermal power transport of - 1 kW(Ranken, 1982). The heat pipe experienced extensive grain growth, to the point that the grain diameter was severaltimes larger than the 1.0 mm thick wall. The lithium working fluid leaked when the unit was fastened up in a latheto remachine the support system (Ranken, 1982). Other lifetime issues which affect the operation of alkali metalheat pipes are the changes in the surface tension and the wetting characteristics of the working fluid by impurities,and the change in wick hydraulic characteristics, such as reduced permeability and/or increased average pore size.Many of these issues can be alleviated or eliminated through impurity control, the use of good filling and bake-outprocedures, in-situ cleanup by hot and cold trapping during fabrication and prior to filling the heat pipe with theworking fluid, and active gettering of oxygen using zirconium or hafnium.

The potential use of in-core alkali metal heat pipes has been demonstrated in a number of reactor experiments. Atotal of 29 heat pipes have been irradiated to high, fast neutron fluences with no reported failures (Determan andHagelston, 1992; Houts et al., 1998). Nineteen SS/Na heat pipes and eight SS/K heat pipes have been tested in theEBR-II core in both gravity-assisted and gravity-opposed positions, with no failures, at temperatures of 900 - 1100K, power throughput of 0.5 to 5 kW, and fast neutron fluence of 0.27 - 10 x 1022 n/cm2. These values of the neutronfluence are about an order of magnitude higher than those typically encountered in space nuclear reactors operatingcontinuously for 7 - 10 years.

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Individual testing periods of these heat pipes, in-core, varied from 1,100 to 23,000 hours, for a total cumulative testtime of 137,000 hours. As indicated earlier, neutron activation of alkali metal working fluid causes generation andaccumulation of non-condensable gases in the heat pipes, affecting their operation over time. For example, 6Li,with an abundance of 7.4 at% and 1.0 at% in natural and depleted lithium, respectively, absorbs neutrons to producetritium and helium gases. The reaction cross-section is 945 barns for thermal neutrons (< 0.1 eV) and 0.12 barns forfast 100-keV neutrons. Also, the common potassium isotope39^ absorbs thermal neutrons with a cross-section of1.94 b, generating hydrogen and argon gases.

TABLE 3. Demonstrated Operation Life (Merrigan, 1985; Angelo and Buden, 1985; Houts et al., 1998).

FluidLithiumLithiumLithiumLithiumLithium

SodiumSodiumSodium

PotassiumPotassiumPotassium

Mercury

MaterialW-26Re

TZMNb-1Zr

Mo-13%Remolybdenum

Mo-TZMmolybdenum

300-series SS

Nb-1%Zr300-series SS

titanium

300-series SS

Temperature (K)18751775177515001700

13901400920

1350920800

600

Time (hours) Failure10,00010,500 Weld cracking9,000

1 1 ,40025,400 Large grain formation, Li impurities

53,00045,00023,000

10,0005,3005,000

10,000

OPERATION LIMITSThis section reviews the operation limits and emphasizes those particularly pertinent to alkali metal heat pipes.Alkali metal heat pipes can operate over a broad range of temperature, depending on the type of the working fluidselected (Table 1 and Figures 2 and 3). The choice of type and design of the wick is critical in raising some of theoperation limits such as the wicking limit and entrainment limit. The best wick design, heat pipe diameter, andworking fluid are those which maximize the useful area of the operation envelope (or domain) by raising theoperation limits of the heat pipe, over the temperature range of interest. The heat pipe operation limits (Figure 4) are:viscous, sonic, wicking or capillary, entrainment, boiling, and heat rejection. The latter, also shown in Figure 4,moves up or down, with increasing or decreasing the heat rejection capability of the heat pipe condenser.

Entrainmentlimit

Vapor phase

Temperature

FIGURE 4. Operation Limits of Heat Pipe. FIGURE 5. Illustration of Capillary Pumping at Liquid-Vapor Interface.

The viscous limit arises when operating at low temperature near the melting point of the alkali metal working fluid,whereas the high liquid pressure losses in the wick, due to the high viscosity of the working fluid, hinder the liquidcirculation back to the evaporator section of the heat pipe. Avoiding this limit requires operating the heat pipe at arelatively low input power until its temperature is high enough for the viscosity of the working fluid to decrease, andhence, the liquid pressure losses in the wick to decrease.

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The capillary (or wicking) limit arises when the net capillary pressure head developing at the liquid-vapor interfacein the evaporator section is less than the combined pressure losses of the liquid in the porous wick and of the vaporflow. The capillary pressure head increases proportionally to the surface tension of the liquid and inverselyproportionally to the radius of curvature of the liquid-vapor meniscus in the surface pores of the wick structure, Rc(Figure 5). The maximum capillary pressure head is reached when Rc equals the effective pore radius of the wickstructure, Rp. Thus, the capillary limit in a heat pipe wick, neglecting the effect of acceleration forces (such asgravity), can be calculated as (Figure 5):

^0v*ev' \ A ncd , A n , A r> s^\

PThe total pressure losses of the liquid in the porous wick along the heat pipe are given by:

L ^ _ _ _

A^L=Tr^|vLm(z)Jz = -^vL= VL . (2)KAW J KAW KAW hfg (Tev)

The pressure drop in the vapor region is negligible compared to that of the liquid in the porous wick (APy « APL ),

and the wick is usually flooded at the condenser end, due to the accumulation of excess liquid (APC^ = 0). Thussubstituting Equation (2) into Equation (1) gives the power throughput at the capillary limit as:

(3)

The first term on the right hand side is solely a function of the geometry and permeability of the porous wick. Thesecond term, ML, known also as the Figure-Of-Merit (FOM), is solely a function of the physical properties of theworking fluid (Figure 3). As shown in Figure 3, FOM initially increases with temperature, as the liquid viscositydecreases faster than the liquid surface tension and the latent heat of the working fluid with temperature, reaching amaximum value when the decrease in the latter balances that in the former. Beyond the maximum FOM, furtherincrease in the liquid temperature causes both the surface tension and latent heat of vaporization to decrease fasterthat the liquid viscosity, decreasing the FOM. The capillary limit can be raised through increasing the capillarypressure head, and at the same time decreasing the liquid flow pressure losses in the wick. The former is achievedby decreasing the effective pore size of the wick structure, while the latter is obtained through the use of longitudinalgrooves on the inside of the wall, an annular wick geometry with a small (~ 0.4 mm) liquid gap between the walland the wick, or arteries in the vapor space (Ivanovskii et al., 1982; Merrigan, 1985; Reid et al., 1999; Glass et al.,1999b). While arteries increase the complexity of the design and the fabrication cost, they could significantlyincrease the power throughput of alkali metal heat pipes. A homogeneous wick, made of a wrapped wire-screenedmesh, or a ceramic or metallic powder, is commonly used in heat pipes. The main limitation of such a wick in alkalimetal heat pipes is the relatively large liquid pressure losses.

The entrainment limit is typically encountered during the startup, when the vapor velocity at the exit of theevaporator section is chocked or sonic. The induced shear stress at the surface of the wick would not only slowdown the flow of the liquid back to the evaporator section, but also cause the break up and entrainment of tiny liquiddroplets in the vapor flow toward the condenser. The resulting reduction in replenishing the wick with liquid in theevaporator section could result in its dryout. The entrainment limit could be raised through employing a wick with asmaller pore size at the liquid-vapor interface, and/or increasing the cross-sectional area for the vapor flow, thusreducing the vapor velocity at the exit of the evaporator section.

The boiling limit in a heat pipe is reached when the liquid superheat at the wall/wick interface exceeds that forincipient nucleation of the working fluid. The formation and growth of vapor bubbles at the wall/wick interface mayblock the liquid flow returning from the condenser to the evaporator section, eventually resulting in a dryout of thewick in the latter. It is worth noting, however, that for an alkali-metal heat pipe, such a limit is typicallyencountered at a very high wall temperature.

Another operation limit, often overlooked, is imposed by the heat removal or rejection in the condenser section. Inspace nuclear power applications, the condenser section of the radiator heat pipes is cooled by radiation into outerspace. Therefore, the heat removal rate is proportional to the effective surface area of the condenser, its surfaceemissivity, and temperature raised to the fourth power. Metallic surfaces typically have low emissivities, and must

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be treated with a coating or a paint to improve the heat rejection rate. This limit may also be encountered late in life,due to the generation of non-condensable gases in in-core heat pipes by neutron activation, reducing the effectivelength of the condenser section. The net result is a reduction in the useful area of the operation envelope or domain,and in the operation power throughput of in-core liquid metal heat pipes.

STARTUP OF ALKALI METAL HEAT PIPES FROM A FROZEN STATEThe performance of an alkali metal heat pipe depends not only on the type of wick and working fluid used, but alsoon the thermal conditions during the startup, as many laboratory experiments have shown (Table 4). Most of thefabrication and testing of alkali metal heat pipes for space nuclear reactor power systems in the United States havebeen performed at the Los Alamos National Laboratory (Deverall et al., 1970; Ranken, 1982; Merrigan, 1985; Reidet al., 1991). The results of the startup from a frozen state and shutdown transient tests preformed at LANL havecontributed greatly to the understanding of the various processes occurring during the startup of alkali metal heatpipes from a frozen state. These tests have shown that when the capillary limit, the entrainment limit, or the boilinglimit is encountered, the wick structure in the evaporator dries out, resulting in a rapid excursion in temperature.

The startup of alkali metal heat pipes from a frozenstate generally involves very high vapor velocities,particularly at low temperatures near the meltingpoint of the working fluid. At this condition, thevapor in the heat pipe is either in the free-molecule orthe transition flow regime. In most cases, the soniclimit is reached and supersonic vapor velocitiesdevelop along the condenser at relatively lowtemperatures, because of the extremely low vaporpressure and density. In liquid-metal heat pipes athigh operating temperatures, the power throughput atthe sonic limit is several kW/cm2, but < 1.0 mW/cm2

near the melting point of the working fluid (Figure6).

Sonic limitMelting pointMaximum FOM

200 1400400 600 800 1000 1200Temperature at Evaporator Exit (K)

FIGURE 6. Power Throughput at the Sonic Limit in Alkali MetalHeat Pipes, as Function of Evaporator Exit Temperature.

At the sonic limit, the vapor flow is sonic at the exit of the evaporator section, and the corresponding powerthroughput is proportional to the vapor cross-sectional flow area and the vapor pressure of the fluid, and inverselyproportional to the square root of the vapor temperature. When the vapor flow is choked, the power throughputbecomes independent of the condenser heat rejection rate. When in the free-molecule flow regime, the vaporpressure is so low that the vapor velocity becomes supersonic in the condenser section (Deverall et al., 1970;Ivanovskii et al., 1982). To avoid the sonic limit during the startup of alkali metal heat pipes from a frozen state, theinput power to the evaporator section must be initially very low and increase progressively in small increments, andthe heat rejection from the condenser is nil. However, such a safe startup scenario would take several hours beforereaching the operating temperature (Table 4); the duration of the startup is primarily a function of the heat rejectionrate at the condenser, early in the startup transient.

Three types of startup failures of alkali metal heat pipes, all related to reaching the sonic limit, have been observedexperimentally (Deverall et al., 1970; Ivanovskii et al., 1982; Merrigan, 1985). When the heat pipe temperature islow and the condenser heat rejection rate is high, the vapor flow chokes at the evaporator exit. In this case, theresulting limited thermal energy transport rate to the condenser section is insufficient to raise its temperature abovethe fusion temperature of the working fluid, and the vapor freezes onto the condenser wick. Eventually, the workingfluid in the evaporator section is depleted and the wick in the evaporator section dries out. The second type ofstartup failure of high-temperature heat pipes, caused by reaching the sonic limit, could occur at moderate condenserheat rejection rates. When increasing the evaporator input power or temperature cannot raise the temperature of thecondenser, due to the sonic-limited heat transport rate to the condenser, the heat rejection in the condenser generatessupersonic vapor velocities along the condenser, sweeping the liquid out of the wick structure (entrainment limit),eventually causing a dryout of the evaporator wick.

The third type of startup failure of alkali-metal heat pipes, caused by reaching the sonic limit, could occur whenoperating at moderate heat input and rejection rates. The combination of low temperature and moderate heat

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TABLE 4. Recent Frozen Startup and Performance Tests of High-Temperature Heat Pipes for Space Applications.

Reference Heat pipe design Test Test resultsReid et al.

(2001)SS/Na heat pipe (Lev = 43 cm, Lcd = 77cm, D = 2.54 cm). SS-304L annular,multi-layer screen wick (60, 100 and400-mesh, f?p < 47 jim).

Distillation-filled heat pipe with145 g of Na. Wet in at 875 K for50 hrs. Four cartridge heaterssurrounding evaporator section.Horizontal test in vacuumchamber. Test with unoxidizedmetal surface.

Frozen startup to 850 K (Q^ = 600W) in 2 hr (except 10 cm-long poolof excess Na). Fully thawed at rev =650 K. Qev limited by viscous limit(rev < 750 K), then by radiation(Tev>750 K). Normal operation at900 K ((3^ = 800 W)._________

Van Dyke etal. (2001)

Mo/Li heat pipe (Lev = 45 cm, Lcd = 100cm, D = 1.27 cm), with a crescentannular wick (7 layers of 400-meshsintered Mo screen).

Six cartridge heaterssurrounding evaporator section,delivering up to 9.2 kW. Heatrejection by radiation to theenvironment.

Reached 1300 K is reached.Reached 1219 K after 115 min.Fast startup transient: heat pipereached isothermal operation at1447 K after 55 min. Nine cyclesperformed successfully_____

Glass et al.(1999a)

Mo-41 Re/Li heat pipe for leading edge(Lev = 6.4 cm, Lcd = 85 cm). Wick madeof 4 layers of 400-mesh Mo-5Rescreen, and 1 artery (3 layers of 400-mesh Mo-5Re). Heat pipe embeddedin C-C composite. D-shaped section.

Filled with 4.5 g of Li. Wet in at1250 K for 42 hrs. Tested inhorizontal and vertical positionsin vacuum. Heated using quartzlamps. Condenser insulatedwith 2"-thick ceramic board.

Frozen startup to 1500 K in 1 hr.Tested to 1622 K (160 W/cm2 radialflux, 3.3 kW power throughput).Lithium pool formed at the end ofthe condenser.

Glass et al.(1999b)

Nb-1%Zr/K heat pipe (Lev= 10 cm, Lcd =87 cm). Annular wick with ~ 0.5-mmgap, made of 3 layers of 100-mesh Nb-1%Zr screen (ftp = 13 jim).

Wet in at -850 K for 50 hrs.Tested in horizontal position invacuum. Evaporator heated byinduction coils. Condensersurrounded by a cooling shroud.

Steady calorimetry, followed by afast frozen startup, to 840 K in 25min (7 W/cm2 radial flux). 23 cm-long, liquid pool formed at end ofcondenser. Carried 600 W at 950 K.

Reid et al.(1999)

Mo/Li heat pipe (Lev = 30 cm, Led = 147cm, D = 1.9 cm). Annular wick with ~0.4-mm gap, made of 7 layers of 400-mesh Mo-41 %Re screen (Rp = 19 jim).Use 20 Hf getter foils at evaporator end.

Filled with 30 g of Li. Heat pipeinserted in an evacuatedtransparent quartz tube. Testedat various inclinations. Heatedevaporator using induction coils.

Slow startup: Li thawed after 140min, reached steady state 4 hoursinto the transient (1540 K, Qcd = 4kW). A 8.3 cm-long liquid poolformed at end of condenser.

Dickinson etal. (1998)

Three SS-304/K heat pipes flown onSpace Shuttle STS-77 (Lev= 8.9 cm, Lcd= 52.1 cm, D = 2.3 cm). Three wickstested: homogeneous wick (11 layers of100-mesh); annular wick with ~ 0.5-mmgap; and arterial wick with 2 arteries.

Filled with 46 g (homogeneous),61.5 g (annular), and 19.2 g(arterial wick) of K. Tested inmicrogravity. Heaters fixed toheat pipes using SS jackets.

Frozen startup to 900 K in 90 min(with 14 cm-long liquid pool at endof condenser). Frozen startup withpreheated condenser acceleratedthe startup. Nine startup/ shutdowncycles performed for each pipe.

Juhasz et al.(1995)

Potassium heat pipe with Nb-1%Zr liner(64 jim thick) and integral C-C pressureshell and radiation fins (emissivity =0.85, L = 91.4 cm, D = 2.5 cm). Wickmade of 4 layers of 400-mesh Mo-5Re,and one artery (3 layers of 400-meshMo-5Re). Heat pipe embedded in C-Ccomposite._______________

Three potassium fill-soak cyclesat 875 K. Filled with 13.5 g of Kon 4th cycle. Tested in vacuumchamber. Radiatively heatedusing electrical heater. CooledCondenser using a watercalorimeter.

Slow startup (11 hrs) from frozenstate to steady-state operation at680 K (Qcd = 300 W, limited byheater power of 700 W). Potassiumcompletely melted at 2.8 hr into thestartup transient. Measured aradiation fin thermal efficiency of80%.

Jang(1995) SS/K heat pipe (Lev= 13.9 cm, Lcd =30.5 cm, D = 2.54 cm). Homogeneouswick made of 40-mesh SS screen.

Filled with 26 g of K.Evaporator heated by radiatingheaters surrounded by heatshield. Condenser radiates tocooling shroud (black painted).Tested in vacuum chamber.

Potassium thawed after 22 min,reached steady state after 50 mininto transient (800 K, Qcd = 285 W).Faster startup transients at higherinput power (to 1100 K, Qcd = 1 kW,in 17 min), till capillary limit wasreached.

Faghri et al.(1991)

SS-304L/Na heat pipe (Lev= 5.3 cm, La= 61.7 cm, Led = 29.2 cm, D = 2.7 cm).Homogeneous wick made of 2 layers of100-mesh SS screen (f?p = 70 jim).

Filled with 30 g of Na, insulatedwith heat shield and cooled bywater calorimeters. Evaporatorelectrically heated. Tested invacuum.

Na thawed after 95 min, reachedsteady state 3 hours into transient(730 K, Qcd = 120W). Part ofcondenser still inactive (last 10 cm).

Ponnappanetal. (1990)

Argon-loaded, SS-304L/Na heat pipewith long adiabatic zone (Lev= 37.5 cm,La = 74.5 cm, Lcd = 91 cm, D = 2.7 cm).Uses reservoir wick at evaporator end.Double-wall artery heat pipe ensuresentrainment-free adiabatic section.

Overfilled with 93.4 g of Na.Evaporator heated by electricheaters. Insulated heat pipewith heat shields andsurrounded it by a coolingshroud. Tested in vacuum.

Active zone is isothermal, whileinactive gas slug is cooler.Evaporator isothermal after 20 min,the thaw front reached thebeginning of condenser 14 min later,then steady state 49 min later.___

Trujillo et al.(1990)

Demonstration of SS/Na membraneheat pipe (L = 1 m). Evaporator 0.9mm-thick SS-304 tube (D = 5 cm) andfusion welded to a 127 mm-thick SScondenser metal foil (rectangular, 8 cm-wide). Homogeneous slab wick.____

Wet in at 975 K for 48 hrs.Tested in vacuum. Evaporatorinduction heated. Condenserradiates to chamber. Heat pipewas rolled, to a diameter ofabout 20 cm, and frozen.

Slow startup to 1000 K (Qcd = 3 kW).No startup anomalies observed. Asmelting/vapor fronts propagatedalong the heat pipe, the membranedeployed smoothly under the effectof internal pressure.________

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rejection rate in the condenser chokes the vapor flow in the heat pipe. A moderate heat input to the evaporatorcauses the evaporator temperature to rise rapidly, because the thermal energy transport rate by the vapor to thecondenser is limited by the sonic flow. Eventually the vapor pressure in the evaporator becomes so large to hinderthe liquid return to the evaporator (capillary limit), resulting in a dry out of the evaporator wick.

The aforementioned details help better understand the various limitations and hence, help developing the properscenario for achieving a successful startup of alkali metal heat pipes from a frozen state. A successful startup ofalkali metal heat pipes can be achieved (Table 4), even when the heat transfer rate to the condenser is choked (soniclimited), if the heat rejection rate of the condenser is low or nil. In the case of heat rejection heat pipe radiators, thecondenser is self-regulated and heats up gradually, because the heat rejection is proportional to the surfacetemperature raised to the fourth power. With radiatively-cooled condensers, the startup of alkali-metal heat pipes inground experiments has always been successful (see Table 4). The next section describes a typical, successfulstartup of a sodium heat pipe from a frozen state, with a radiatively-cooled condenser.

SUCCESSFUL STARTUP OF A SODIUM HEAT PIPE FROM A FROZEN STATESimulating the startup of alkali-metal heat pipes from a frozen state requires incorporating the contributions of anumber of complex physical processes. In addition, an efficient and fast numerical solution must be developed tosolve the highly non-linear, multi-phase problem. The numerical solution must be able to track, preferably at orfaster than real time, the following: (a) the radial and axial propagation of the melting front in the wick; (b) the free-molecule, transition and continuum flow regimes in the vapor, and their propagation towards the end of thecondenser; (c) the volume expansion of working fluid upon melting and heating above the melting point; (d) theevaporation of liquid, resolidification of vapor onto the frozen wick of the heat pipe downstream, the condensationof vapor and the entrainment of liquid by the vapor flow; (e) accumulation of excess liquid and non-condensablegases, if any, at the end of the condenser section; and (f) potential partial dry out of the evaporator wick. Thereported models for simulating the startup of alkali metal heat pipes from a frozen state are reviewed in a companionpaper in these proceedings (Tournier and El-Genk, 2002).

The experimental work of Faghri et al. (1991) and the modeling results of their experiment using the Heat PipeTransient Analysis Model (HPTAM) developed at the University of New Mexico's Institute for Space and NuclearPower Studies (Tournier and El-Genk, 1996) demonstrate the various processes taking place successively during thestartup of a radiatively-cooled, SS-304L/sodium heat pipe from a frozen state. The effective lengths of theevaporator, adiabatic and condenser sections were 5.3 cm, 61.7 cm and 29.2 cm, respectively. The circumferentialwick of the heat pipe was made up of two wraps of 100-inch"1 mesh SS screen, having a wire diameter of 114 |im,effective pore radius of 70 jim, and porosity of 0.70. The heat pipe, with a sodium charge of 30 grams, was tested ina vacuum chamber at an ambient temperature of 290 K. The measured surface emissivity of the condenser was0.645. The transition temperatures to continuum, transition and free-molecule flow regimes, corresponding toKnudsen numbers of 0.01 and 1 for the vapor core diameter of 21 mm, are 686 K and 540 K, respectively.

Initially, the working fluid in the wick was frozen at a uniform temperature of 290 K. The startup was initiated byincreasing the input power to the evaporator section from zero to 119 W with an exponential period of 50 s. Afterabout 2 minutes into the transient, the working fluid at the evaporator wall melted, and the melting front propagatedradially inward (Figure 7a). Although sublimation of the Na working fluid in the evaporator and solidification at thesolid-vapor interface in the condenser occurred, these processes transported only negligible amounts of the workingfluid, owing to the very low vapor pressure. Complete melting of the working fluid in the evaporator occurred veryrapidly, in less than a minute. After the working fluid in the evaporator was completely melted, evaporation of theworking fluid occurred at the L-V interface, while the vapor flow was still rarefied or free molecular. Asevaporation continued, the vapor accumulation in the evaporator increased, transitioning the vapor to the transitionflow regime (Figure 7b). After about 8 minutes into the transient, the continuum flow was established along theevaporator section, at which time the vapor temperature reached roughly the transition temperature of 686 K. Vaporflow was choked at the evaporator exit, and the remaining length of the heat pipe was still in the free-molecule flowregime (Figure 7c).

After the working fluid in the evaporator wick was fully thawed, the melting and the continuum vapor flow frontspropagated axially toward the condenser (Figure 7d). It took these fronts about 50 additional minutes to traverse the

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thermal insulation

61.7 cm-long adiabatic section, at an average velocity of about 1.2 cm/minute. During this period, most of the heatinput was utilized in the vaporization of the working fluid in the evaporator section, and the heat pipe length can bedivided into several sequential zones (Figure 7d). In region (I), the evaporator, the vapor was in the continuum flowregime and evaporation occurred uniformly along the L-V interface, increasing the vapor velocity linearly along theevaporator. In region (II) within the adiabatic section, the vapor was also in the continuum flow regime, with onlyminimal condensation occurring at the L-V interface. The vapor flow accelerates, however, due to the slowdecreases in vapor temperature and density. In region (III), also in the adiabatic section of the heat pipe, the vaporpressure and temperature decrease rapidly due to axial conduction to the condenser, and the vapor is in the transitionflow regime. The continuum vapor flow front continued moving forward toward the condenser, as the condensationof vapor raised the wick and wall temperatures in this region (Figure 6d). In region (IV), also in the adiabaticsection, where vapor is in the transition flowregime, the vapor velocity became slightlysupersonic over a short distance, at a Machnumber between 1 and 1.1. Finally, in region(V), resolidification of vapor occurred at thesolid-vapor interface. However, only aminimal working fluid mass was involved inthis process, since the axial vapor mass flowrate at the melting front was very small. Thevapor axial velocity decreased steadily as theresolidification proceeded along the frozenportion of the heat pipe condenser. While thevapor velocity is subsonic in this region, it isstill significant due to the very small density ofthe rarefied vapor.

t t t t t t.evaporator.. adiabatic (transport) section condenser

(a) Radial melting of the working fluid in evaporator (t = 2 min.)

transition flow regime

t t t t t t 1

(b) Accumulation of vapor in evaporator by evaporation (t = 5 min.)

- continuum flow regime

Once the continuum vapor flow front reachedthe condenser section, the heat pipe beganradiating heat away (Figure 7e), slowing downthe propagation of the melt and the continuumvapor flow fronts. The heat pipe approachedsteady-state operation after the working fluidin the heat pipe is fully thawed, the vaporalong the entire length of the heat pipe is in thecontinuum flow regime, and the heat rejectionrate in the condenser equated the heat inputrate in the evaporator. At steady state, thecondensation rate was uniform along the activelength of the condenser section, and the vaporaxial velocity became subsonic everywhere,with a maximum Mach number of 0.70. Theexcess liquid generated by the decrease indensity of the thawed working fluid forms aliquid pool at the end of the condenser.

t t t t t t 1

(c) Vapor flow reaches continuum regime in evaporator (t = 8 min.)

t t t t t t 1

(d) Propagation of fronts toward the condenser (t = 40 min.)

t t t t t t IUU(e) The active length of condenser rejects heat away (t = 70 min.)

FIGURE 7. Illustration of the Frozen Startup of a Radiatively-Cooled, High-Temperature Heat Pipe.

SUMMARY AND CONCLUSIONSAlkali metal heat pipes are being considered for use in space nuclear power systems to remove the heat generated innuclear reactors to converter subsystems located outside the reactor core, and in lightweight heat rejection radiators.Candidate working fluids, in an order of increasing operation temperature, are potassium (700-950 K), sodium(800-1100 K), and lithium (1100 K-1600 K), which are frozen at startup conditions. The startup of alkali metalheat pipes from a frozen state poses a number of complex issues and challenges, some of which are reviewed anddiscussed in this paper. In addition, the successive processes occurring during the typical startup of a radiatively-cooled, sodium heat pipe are presented and discussed.

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Some of the indicated challenges during the startup of alkali metal heat pipes from a frozen state include coping withthe sonic limit reached early during the startup transient, when the vapor is mostly in the free-molecule and/or thetransition flow regime and the heat pipe temperature is relatively low, near the melting point of the working fluid.As the wall temperature in the evaporator reaches the melting point of the working fluid in the wick, radial thaw ofthe wick in the evaporator begins and is completed within a few minutes. The subsequent evaporation of the liquidmetal in the evaporator changes the vapor in the evaporator section to the transition, then to the continuum flowregime. As the thaw front propagates axially toward the condenser, three vapor flow regimes co-exit along thelength of the heat pipe, continuum flow in the evaporator section, transition flow in the adiabatic section, and free-molecule flow in the condenser section. Eventually, the continuum vapor flow regime fills the entire heat pipe as itis fully thawed and its temperature approaches the steady-state operation temperature. The excess liquid, generatedby the decreasing density of the working fluid at thaw and as the liquid temperature increases, accumulates at theend of the condenser, decreasing its effective length for heat rejection, unless it is accounted for in the heat pipedesign. In summary, besides the proper selection of the wick and wall materials, working fluid and wick design forthe required operation temperature and power throughput, a successful startup and operation of alkali metal heatpipes for 7-10 years is achievable through: (a) proper design; (b) the use of high-purity materials and working fluid;(c) proper cleaning and loading techniques of the heat pipes with the working fluid; and (d) proper control of heatingand cooling rates during the startup from a frozen state.

Results and discussions presented in this paper indicated that the successful startup of alkali metal heat pipes hasbeen demonstrated in laboratory experiments and in-pile tests performed in the EBR II nuclear reactor. A keychallenge, however, is to mitigate the effects of non-condensable gases generated in the heat pipes by neutronactivation and of erosion of the wall materials by dissolution in the working fluid, over time.

NOMENCLATURE

hfsKLLa

LcdLev

iML

mPQ

Wick cross-sectional area (m2)Diameter of vapor space in heat pipe (m)Latent heat of vaporization (J/kg)Permeability of porous wick (m2)Overall length of heat pipe (m)Length of adiabatic section of heat pipe (m)Condenser length of heat pipe (m)Evaporator length of heat pipe (m)Effective length (m), L=La+ (Lev + Lcd)/2Figure of merit (W/m2), ML = ahfg /VL

Liquid mass flow rate in wick (kg/s)Pressure (Pa)Thermal power (W)Radius of curvature of the L-V interface (m)

TzAP

Average pore radius of wick (m)Temperature (K)Axial coordinate along heat pipe (K)Pressure drop or rise (Pa)

Oc Contact angle (radiant), cos 6C = Rp /Rc

VL Kinematic viscosity of liquid (m2/s)a Surface tension of liquid (N/m)Subscript/Superscript

Capillary pressure headCondenser section

ev Evaporator sectionL Liquid phaseV Vapor phase

capcd

ACKNOWLEDGMENTSThis work is sponsored by the Institute for Space and Nuclear Power Studies at the University of New Mexico.

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