Performance analysis of coated plutonia particle fuel compact for radioisotope heater units

1

PERFORMANCE ANALYSIS OF COATED PLUTONIA PARTICLE FUEL

COMPACT FOR RADIOISOTOPE HEATER UNITS1

Mohamed S. El-Genk2 and Jean-Michel Tournier

Institute for Space and Nuclear Power Studies and Dept. of Chemical and Nuclear Engineering

The University of New Mexico, Albuquerque, NM, U.S.A.

(505) 277–5442, Fax: –2814, Email: [email protected]

Abstract. Coated plutonia particle fuel has been proposed recently for use in Radioisotope

Power Systems (RPSs) and Radioisotope Heater Units (RHUs) for a variety of space

missions requiring power levels from mWs to tens or even hundreds of watts. The 238

PuO2

fuel kernels are coated with a strong layer of ZrC designed to fully retain the helium gas

generated by the radioactive decay of 238

Pu. A recent investigation has concluded that

helium retention in large-grain (> 200 µm) granular and polycrystalline fuel kernels is

possible even at high temperatures (> 1700 K). Results of performance analysis showed that

this fuel form could increase by 2.3 – 2.4 times the thermal power output of a Light Weight

Radioisotope Heater Unit (LWRHU). These figures are for a single-size (500 µm) particles

compact, assuming 10% and 5% helium gas release, respectively, and a fuel temperature of

1723 K, following 10 years of storage. A binary-size (300 and 1200 µm) particles compact

increases the thermal power output of the RHU by an additional 15%.

1.0 INTRODUCTION

Recently, a coated plutonia particle fuel compact was proposed for potential use in advanced

radioisotope heater units (RHUs) and radioisotope power systems (RPSs) (Sholtis et al., 1999).

The fuel compact consists of ZrC-coated 238

PuO2 fuel kernels dispersed into a graphite matrix

with a packing density for single size particles of up to 62.5% by volume. This packing density

increases to ~ 73% when two particle sizes with a diameter ratio of 4 are used. The 238

PuO2 fuel

kernels are covered with a 5-µm thick, pyrolytic graphite (PyC) inner coating for protection

during the application of the outer ZrC coating by Chemical Vapor Deposition (CVD). The

CVD process is also used to apply the inner PyC coating. The ZrC, a very strong material that is

ductile at temperatures in excess of 2000 K (Storms, 1962; Ramgopal, 1974), serves as the

primary containment vessel of the plutonia fuel kernel and the helium gas generated by the

radioactive decay of 238

Pu. The thickness of the ZrC coating depends not only on the fuel

temperature, the helium gas release fraction, and the storage time, but also on the plutonia fuel

microstructure. Polycrystalline plutonia kernels fabricated using Sol-Gel ot thermal plasma

processes offer great promise for almost full helium retention, even at high temperatures in

excess of 1700 K (El-Genk and Tournier, 2000). Figure 1a shows a cross-sectional view of a

coated plutonia fuel particle and Figure 1b shows an illustration of a binary-size coated particle

fuel compact (CPFC).

1 Accepted for publication in the Journal of Nuclear Engineering and Design, 2001. 2 Corresponding author.

2

The graphite or carbon-carbon composite matrix of the fuel compact is designed to accommodate

the thermal expansion of the fuel particles and is spongy and structurally weaker than the ZrC

coating. Thus, upon impact on solid surfaces following a launch abort or re-entry accident,

cracking of the coated particles fuel compact (CPFC) is likely to occur through the graphite,

leaving the coated fuel particles intact. The design concept of the CPFC is analogous to that of

the "pomegranate" fruit, in which the holding structure is spongy as well as weak under applied

tensile stress to protect the fruit seeds. In addition, the carbon-based matrix of the compacts is

perfectly compatible with the aeroshell material of radioisotope heater units (Schock, 1980 and

1981).

In addition to their structure strength, the coated plutonia fuel particles offer a promise for

enhanced safety. The fuel kernels are intentionally sized (> 300 µm) to prevent any adverse

radiological effects. They are non-respirable, non-inhalable, and if ingested, would simply be

excreted with no radiological effects (Hoover, 1999). In addition, this coated fuel form offers

excellent design flexibility as the CPFC could be made into different shapes and sizes to provide

thermal power from milli-watts to tens or even hundreds of watts.

1.1 Potential Applications

The CPFC can be made into heating tapes, buttons, or paints as RHUs or miniaturized RPSs for

satellites, spacecraft, and planetary exploration probes. For example, a button-like CPFC heat

source could be used with miniaturized thermoelectrics (TEs) to provide electrical power in the

mWe range for more than 10 years. The heat rejected by the TE couples could be used for

thermal management of the space probes, thus achieving 100% energy utilization. Larger size

CPFC in the form of pellets or disks could be used in higher power RHUs as well as in RPSs to

produce power in the range from one to tens or even hundreds of watts.

One could envision fabricating thin CPFC wafers the size of an Oreo cookie or smaller in which

a thin layer of Fine-Weave Pierced Fabric (FWPF, a carbon-carbon weave used in re-entry

aeroshells) is used on both sides of the fuel compact for thermal protection. These “cookies” like

CPFCs could be attached to surfaces more readily than the more bulky, present-day LWRHUs.

Figure 2a shows an example of a miniaturized CPFC-RHU for thermal management of

electronics circuit boards. The CPFC fuel, used in conjunction with low-temperature

thermoelectric couples (Caillat et al. 2000), could be used in milliwatt CPFC-RPSs. These RPSs

provide both thermal and electric power for circuit boards, as shown in Figure 2b.

The proposed CPFC design offers four basic barriers to prevent potential release of the fuel and

the helium gas. The first barrier is the large-grain or polycrystalline plutonia fuel matrix; the

second is the multi-layer coating of the plutonia fuel particles; the third barrier is the fuel

compact matrix; and the fourth barrier is the FWPF aeroshell (Figures 1 and 2).

High performance, reliable, low mass, and long operation lifetime (5-10 years) RHUs and RPSs

are required for several new NASA missions planned over the next few years. Examples include

the Saturn Rings Observer, Solar probe, Europa Lander, Cryobot and Hydrobot, and the Titan

Explorer missions which call for electrical power requirements in the 20 to 200 watts range and 6

3

to 10 years mission duration. CPFC-RPSs could meet these power requirements and present

several advantages such as scalability, reliability, and retention of helium gas. Modular CPFC-

RHUs could be developed for a variety of thermal and electrical applications up to 20 W thermal

or electric, that are 30-50% lighter than current LWRHUs (Schock, 1981; Johnson, 1997). The

CPFC-RHUs could be used either by themselves, or in conjunction with low-temperature

thermoelectric (TE) converters having an efficiency of 4-6%, currently under development at the

Jet Propulsion Laboratory, to provide up to 150 mWe at power densities > 100 mWe/kg (Figure

2b).

The CPFC-RHUs are easily scalable to meet mission power requirements ranging from a few

watts to hundreds of watts, or even a few kilowatts. They could be coupled with advanced, 18%

efficient vapor anode, multi-tube Alkali-Metal Thermal-to-Electric Converter (AMTEC) cells

(Figure 2c). Higher efficiencies and specific powers could be obtained by cascading the

AMTEC cells with segmented thermoelectrics (TE) (Caillat et al., 2000) for the bottom cycle

(Figure 2c). For example, a CPFC-RPS which cascades an 18%-efficient AMTEC cells (El-

Genk and King, 2000) operating between 1100 K and 650 K, with a 9%-efficient segmented TE

converter (Caillat et al., 2000) operating between 650 K and 350 K, would have an effective

conversion efficiency of about 25%. The CPFC-RHUs could also be used in conjunction with

high temperature segmented TE (η ~ 15%) (Caillat et al., 2000), Stirling engine units (η ~ 23–

30%) (Mason, 2000), or even a He-Xe Brayton engine (η ~ 23–28%) (El-Genk, 2000),

depending on the electric power and mass requirements for the power system. CPFC-RPSs with

higher energy conversion efficiency are quite attractive because they require a smaller amount of 238

PuO2 fuel.

The coated plutonia particle fuel form is also ideal for use in scientific probes requiring both

thermal and electric powers and in which the appropriate type and shape of the RHU can be

fabricated to optimize the design, operation, and the functionality of the probe. Some of the

space missions that employ planetary probes for in-situ analysis of surface materials require that

the He gas be fully retained in order to avoid contaminating the environment and skewing the

sensitive measurements. Such an option and design flexibility are not attainable using the

current LWRHU (Schock, 1981; Johnson, 1997) and General Purpose Heat Source (GPHS)

designs (Schock, 1980).

The coated fuel particles could also be compacted into a brick form for high power CPFC-RHUs

that could be lighter than current GPHSs (Schock, 1980). In current LWRHUs, the refractory

cladding of the plutonia fuel pellets is kept at relatively high temperatures (> 1173 K) to ensure

sufficient ductility when impacting solid surfaces. In addition to being very heavy, these

claddings (platinum-30%rhodium in LWRHUs and iridium in GPHSs) must be kept well below

their melting temperatures and those of any eutectics that could form in a solid propellant fire.

These temperatures are maintained with the aid of multi-layered, low conductivity, PyC

insulation sleeves (Figure 3). Conversely, the CPFC has no temperature constraint: the

zirconium carbide coating forms an eutectic with carbon at the very high temperature of 3123 K

(Storms, 1962). Thus, most of the internal thermal insulation sleeves and the refractory cladding

in the LWRHU (Figure 3) could be replaced with CPFC. This would result in higher thermal

power, at lower or same mass, or in smaller size and lower mass, for the same thermal power.

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1.2 Objectives

During FY 99, an exploratory effort sponsored by the Department of Energy was initiated to

investigate the potential of the coated plutonia particles fuel form for RHUs and address

fabrication and performance issues. The specific tasks investigated were to:

(a) Review the fabrication technology of coated plutonia fuel particles;

(b) Review the release mechanisms of helium gas in small grain (7-40 µm) granular plutonia

pellets in GPHSs and LWRHUs, and examine the applicability of these mechanisms to the

He release from large grain (> 200 µm) and polycrystalline fuel kernels (El-Genk and

Tournier, 2000);

(c) Review the spectrum of credible launch and re-entry accident environments that the coated

particle fuel could potentially experience. Based on this review, design and functional

requirements for coated particle fuel were established (Sholtis, 2001);

(d) Develop a design and performance model of coated fuel particles to investigate the impact

of using single-size and binary-size CPFC on the thermal power output of a RHU. Also

quantify the effects on the RHU thermal power of the helium gas release fraction, fuel

temperature, and storage time before launch; and

(e) Identify future research and testing needs to confirm the coated particle fuel’s potential

operation and safety promise.

This paper provides a summary of the work done under this joint exploratory research effort and

presents and discusses in details results on the performance of the CPFC-RHU.

2.0 NOMENCLATURE

a Average fuel grain radius (m)

b Coefficient (Equation (11)), 2105121.1

−×=b (m3/kg)

D Gas mass diffusion coefficient in fuel matrix (m2/s)

D’ Effective gas diffusion coefficient in fuel, D’ = D/a2 (s

-1)

Df Diameter of fuel kernel (m)

Dg Average diameter of fuel grain (m)

Dp Outer diameter of coated fuel particle (m)

F Fraction of helium gas released from the fuel matrix that exerts pressure on outer coating

F* Release-to-birth rate ratio of radioisotope

M Molecular weight (kg/mole)

n Number of moles (moles)

Na Avogadro number (Na = 6.0225 x 1023

atoms/mole)

No Pu-238 atom density of as-fabricated plutonia fuel kernel (atoms/kg)

P Pressure (Pa)

q Thermal power (Wth)

q ′′′ Volumetric thermal power (Wth / m3)

Rg Perfect gas constant (Rg = 8.3143 J / mole.K)

Rinner Inner radius of ZrC coating (m)

ℜ Dimensionless stress factor of a spherical shell

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Sp Geometrical surface area of as-fabricated fuel kernel (m2)

SR Effective gas release area in fuel kernel (m2)

T Temperature (K)

t Time (s)

tPyC Thickness of pyrolytic carbon inner layer (m)

tZrC Thickness of ZrC coating (m)

T1/2 Radioactive decay half life (s)

VOL Volume (m3)

YZrC Yield strength of ZrC (Pa)

Greek

α Fraction of coarse spheres in a binary mixture at maximum packing

β Maximum packing volume fraction of 2-size spheres in compact

γ Open grain boundary porosity

εf As-fabricated porosity of fuel kernel openfε Amount of open porosity in fuel kernel

εPyC As-fabricated porosity of pyrolytic carbon layer

λ Radioactive decay constant (s-1

) η Thermal-to-electric conversion efficiency ρ Density (kg / m

3)

σT Maximum tangential tensile stress in ZrC coating layer (Pa)

Ψ Thermal power ratio, LWRHURHUCPFC qq /−

Subscript/Superscript

f PuO2 fuel

He Helium gas

max Maximum

Pu Plutonium

TD Theoretical density

1 Coarse particles in a binary mixture fuel-compact

2 Fine particles in a binary mixture fuel-compact

3.0 FABRICATION TECHNIQUES AND FUEL MICROSTRUCTURE

There are two basic microstructures of the fuel kernels (Figure 4): granular and polycrystalline.

No data were found on the fabrication of granular or polycrystalline 238

PuO2 fuel kernels using

the binderless agglomeration or the Sol-Gel techniques. The data on the fabrication of

monocrystalline fuel kernels using thermal plasma processes are also nil (Silver, 1999).

Granular UO2 and mixed-oxide fuel kernels with small grain sizes (7-40 µm) have been

successfully fabricated on a large scale using the binderless agglomeration process (Burnett et

al., 1963; Ford and Shennan, 1972; Allen et al., 1977). This process, however, has not been used

6

to fabricate large grain (100-300 µm) plutonia fuel kernels. Polycrystalline UO2 and mixed-

oxide fuel kernels have been successfully fabricated on a bench scale using Sol-Gel and plasma

processes (Haas et al., 1967; Huschka and Vygen, 1977; Förthmann and Blass, 1977). Granular

fuel kernels fabricated using binderless agglomeration or similar processes consist of a number

of polycrystalline grains, typically 7-40 µm in average diameter (Figure 4a). Common grain

boundaries and tiny voids at the triple interface between fuel grains develop during the sintering

of the oxide fuel kernels at high pressure and temperature. The as-fabricated porosity in the fuel

matrix and at the triple interface of the grains is controlled during sintering. Typical as-

fabricated porosity in oxide fuel kernels ranges from 5 to 15% (Figure 4a). The produced fuel

kernels are highly spherical, and virtually mono-size particles with diameters ranging from 200

to 1000 µm (Burnett et al., 1963; Ford and Shennan, 1972; Allen et al., 1977).

Polycrystalline UO2 and mixed-oxide fuel kernels, having diameters as large as 1200 µm, have

been fabricated using Sol-Gel techniques (Haas et al., 1967; Huschka and Vygen, 1977;

Förthmann and Blass, 1977). These techniques do not require milling or grinding (as during the

fabrication of granular fuel by powder metallurgy), thus generate very little, if any, radioactive

dust or aerosols. Liquid waste, however, may be produced in the Sol-Gel processes, depending

on the efficiency of recycling the chemicals and the fabrication procedures used. The gelled fuel

microspheres, of an almost perfect sphericity, are sintered to the desired density and

stoichiometry by heating to high temperature in air or in an oxidizing atmosphere. The sintered

fuel kernels typically have a polycrystalline structure with tiny, intragranular voids (< 1 µm in

diameter) (Figure 4b). As with granular fuel, the as-fabricated porosity in the Sol-Gel, oxide fuel

kernels (5-20%) is controlled during sintering.

4.0 HELIUM GAS RELEASE

With respect to the helium gas release from 238

PuO2 fuel kernels, the polycrystalline structure

(Figure 4b) may be regarded as a single grain of the kernel diameter, with the as-fabricated

intragranular porosity made of tiny pores. In granular fuel kernels, however, the average size of

the helium gas release unit equals that of the fuel grain, significantly increasing the helium gas

release fraction at high temperature (> 1100 K) (Mueller et al., 1974; Peterson et al., 1984).

Experimental results of helium release from granular 238

PuO2 pellets (7-40 µm grain size) have

indicated that transient heating increases the release rate. However, the He release fraction was

the same as that measured during isothermal steady-state experiments performed at the same fuel

temperature of up to 2023 K (Peterson and Starzynski, 1982; Peterson et al., 1984; Mueller et al.,

1974). The reported data on helium gas release from granular 238

PuO2 fuel pellets were for 7-50

µm grain sizes and storage times of a few months to ~ 8 years. The reported results showed that

He release below 900 K was nil. However, at higher temperatures, increasing the grain size

decreased the He release fraction. During a simulated re-entry heating pulse in which the peak

fuel temperature reached 1723 K, the measured release fraction from granular RHU 238

PuO2 fuel

pellets was as much as 88%. The identified helium release mechanisms in these small grain,

RHU 238

PuO2 fuel pellets and test samples were in agreement with the release mechanisms

discussed later and with the equivalent-sphere model for fission gas release (Olander, 1976).

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According to the equivalent-sphere model (Olander, 1976), the fractional release, F*, of the

radioactive fission gases that attained steady-state concentrations in the fuel, equals the release-

to-birth rate ratio, BR && / , and can be expressed as (El-Genk and Tournier, 2000):

2/1)(

1)(/* TT

Ta

TDD

VOL

SBRF

f

R γ

λλ∝

′∝×

≈≡ && . (1)

This equation shows that F* is inversely proportional to the average fuel grain radius, a, but

directly proportional to the square root of the half-life, T1/2. As the half-life increases, F*

approaches the release fraction of non-radioactive species (Figure 5). Thus, for the same fuel

material and microstructure, temperature, T, and grain size, F* increases exponentially with the

half-life of the gas species, approaching an asymptote corresponding to the release fraction of

non-radioactive gases, such as helium in granular 238

PuO2 fuel. The effective diffusion

coefficient, D' (s-1

) = D/a2, which increases exponentially with the fuel temperature, accounts for

the increases in both the gas mass diffusion coefficient, D (m2/s), and the effective release area,

SR (m2). This release area is a function of temperature and includes any developed cracks in the

fuel matrix and open porosity at the grain boundaries.

Neglecting the contribution of the as-fabricated open porosity in the fuel, the normalized surface

area for helium gas release from granular plutonia fuel kernels can be expressed as (El-Genk and

Tournier, 2000):

g

f

p

R

D

D

S

Sγγ +−=

)1( . (2)

The coefficient γ (0 < γ < 1.0) depends on the effective surface area available for He gas release

from the fuel matrix, SR.

4.1 Helium Gas Release Mechanisms

Below ~ 900 K, He release occurs by atomic diffusion from the fuel matrix, and SR equals the

geometrical surface area of the as-fabricated fuel kernel (i.e. γ = 0). Between 900 K and 1150

K, 0 < γ < 1 and SR in granular fuel increases slowly with temperature, due to the formation and

the coalescence of grain boundary bubbles. Above ~1150 K, SR increases rapidly with

temperature as γ approaches unity, due to the formation of open porosity at the grain boundaries.

At ~1450 K, SR reaches its maximum value ( γ = 1.0), as the formation of the open porosity at the

grain boundaries is complete. Above this temperature, He gas release in granular fuel is no

longer limited by the surface area available for release, SR, but rather by the atomic and volume

diffusion of the gas in the fuel grains.

Therefore, for the same fuel temperature and kernel diameter, increasing the grain size from 10

µm to 200 µm could reduce the He gas release in plutonia fuel at high temperatures (>1450 K)

by more than one order of magnitude (El-Genk and Tournier, 2000). As indicated earlier, a

polycrystalline fuel kernel may be regarded as a single grain with a size equal to the diameter of

the kernel. Thus, the effective surface area for the He gas release in large grain (> 200 µm) or

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polycrystalline fuel is essentially equal to the geometrical surface area of the kernel. This

surface area is significantly smaller than the effective area available for the He gas release in

small-grain fuel at temperatures > 900 K.

4.2 Estimates of Helium Gas Release

Gas release data have been reported for UO2 fuel particles irradiated at isothermal conditions in a

fission reactor by Friskney et al. (1977 and 1979). These authors investigated the effects of grain

size, radioactive decay constant, fuel burnup (up to 6.4 at. %), and fuel temperature (up to 2023

K) on the release-to-birth rate ratio of various noble fission gases and volatile isotopes. The UO2

fuel particles used included small-grain (average grain size of 10 µm) and large-grain (effective

grain size of 300-600 µm) spheres and were irradiated up to a 6.4 at. % burnup. In addition,

monocrystal right cylinders of natural (0.72 wt. % 235

U) stoichiometric UO2 were irradiated at

the same conditions in the experiments. The released amounts of various fission gaseous species

were measured by γ-spectroscopy, after correcting for their respective radioactive decay. The

release rates of noble fission gases and volatile fission products were calculated based on these

measurements, while their birth rates by fission and radioactive decay were calculated using

computer codes (Friskney and Turnbull, 1979).

Results showed that when irradiated at 1723 K and up to 4.0 at.% burnup, the small-grain fuel

particles (7-40 µm) released essentially all fission gases and volatile products (~ 70–80%

release), whereas only ~ 7% were released from the large-grain (~ 300-600 µm) fuel particles. It

is worth noting that the release fraction from the small-grain UO2 particles is in agreement with

the experimental data generated at LANL for GPHS and LWRHU granular plutonia pellets

(Mueller et al., 1974; Land, 1980; Peterson and Starzynski, 1982; Peterson et al., 1984). The

data showing the effect of half-life on the release fraction of noble fission gases and volatile

products from various UO2 fuel samples at 1723 K is presented in Figure 5 (El-Genk and

Tournier, 2000). According to Equation (1), the release-to-birth rate ratio is proportional to the

square root of the half-life, for the relatively short-lived isotopes that reach equilibrium early in

time. Such dependence of the release-to-birth rate ratio on the half-life is evident in Figure 5; the

gas release data exhibited an exponential increase with half-life, reaching asymptotic values at

large half-lives. These asymptotic values are representative of the release fractions of stable,

noble fission gases in granular UO2 fuel, and should equal that of helium in plutonia fuel

particles of the same average grain sizes at the same fuel temperature.

Based on these experimental data and the above argument, helium gas release from small-grain

(7-40 µm) plutonia fuel at 1723 K is expected to be ~ 70–80%. However, for large-grain (> 300

µm) and polycrystalline fuel microspheres, when heated up to 1723 K, the helium gas release

could be more than an order of magnitude lower (< 7%) (Figure 5). The gas release data for UO2

particles (Friskney et al., 1977 and 1979) showed that, at 1042 K, less than 1% of the noble

fission gases and volatile fission products were released from the large-grain fuel particles. A

similar release fraction would be expected for helium in plutonia fuel particles having large grain

sizes (> 200 µm). Even lower helium release fractions are expected in polycrystalline fuel

kernels. Therefore, the helium gas release in coated, large-grain or polycrystalline 238

PuO2 fuel

kernels at the nominal operating temperature in a RHU (~ 800 K) would be practically nil. The

release of He from large-grain (> 200 µm) 238

PuO2 fuel kernels at > 1723 K, however, could be ~

9

7%, decreasing to ~ 0.8% at 1042 K. In polycrystalline plutonia fuel kernels fabricated using

Sol-Gel processes, the helium release fraction could be even lower than the estimates for the

large-grain 238

PuO2 kernels (< 7% at 1723 K and < 0.8% at 1042 K).

5.0 PERFORMANCE MODEL OF COATED PARTICLE FUEL

A performance and stress analysis model of coated 238

PuO2 fuel kernels was developed to

calculate the required thickness of ZrC coating to fully retain the He gas as a function of fuel

temperature, release fraction, and storage time of CPFC before launch. At 1723 K, the model

assumes conservatively that the fuel kernel is constrained solely by the ZrC coating. No credit

was taken in the model for the strength of PyC inner coating or the constraint by the graphite

matrix in the CPFC. The induced tangential tensile stress in the ZrC coating is calculated using

the spherical shell model (Kaae, 1966). This model is applicable to the coated plutonia fuel

particles since the thickness of the ZrC coating is much smaller than the diameter of the fuel

kernel.

5.1 Particles Packing and Plutonia Volume Fraction in Fuel Compact

For fuel kernel diameters Df1 and Df2, as-fabricated fuel volume porosities εf1 and εf2, and coated

particles’ diameters Dp1 and Dp2, respectively, the maximum packing volume fraction of the 2-

size particles in the compact, β, and the corresponding fraction of the coarse particles (Dp1), α,

can be calculated as:

)1/(03127.0625.0 21 −×+= pp DDβ for 1 < Dp1/Dp2 < 6.5 ,

02.1/0.281

91.0/0.239

21

21

−×

−×=

pp

pp

DD

DDβ for 6.5 < Dp1/Dp2 < 19.1 , (3)

and

)8.4(log

)/(log247.00.1

10

2110 pp DD×−=α for 1 < Dp1/Dp2 < 4.8 ,

)8.4(log)1.19(log

)8.4(log)/(log033.00.753

1010

102110

−

−×−= pp DD

α for 4.8 < Dp1/Dp2 < 19.1 . (4)

As shown in Figure 6, β increases linearly with Dp1/Dp2, up to 6.5, then increases slowly beyond

this value. Therefore, for a CPFC of a total of N spherical coated particles, of which αN are

coarse (subscript 1) and (1-α)N are fine (subscript 2), the total volume of plutonia (238

PuO2) fuel

in the compact can be calculated as:

2211 )1()1()1( ffffTDf VOLNVOLNVOL ×−−+×−= εαεα . (5)

The total volume of the coated particles in the compact is given by:

10

compactppspheres VOLVOLNVOLNVOL ×=×−+×= βαα 21 )1( . (6)

The volume fraction of the 238

PuO2 fuel in the compact is then given by:

.)1(

)1)(1()1(

32

31

322

311

pp

ffff

spheres

TDf

compact

TDf

DD

DD

VOL

VOL

VOL

VOL

×−+×

×−−+×−×==

αα

εαεαββ (7)

Note that Equation (7) developed for a binary mixture also applies to mono-size particles when

substituting α = 1, as:

3

3)1(

625.0)1(

p

ff

p

ff

compact

TDf

D

D

VOL

VOL

VOL

VOL ×−×=

×−×=

εεβ . (8)

Figure 7 shows the effect of as-fabricated fuel porosity and ZrC coating thickness on the volume

fraction of plutonia in the base case, single-size CPFC. The plutonia loading in the CPFC

decreases as either the as-fabricated fuel porosity or tZrC increases. The fuel loading in Figure 7

is used next to calculate the thermal source strength of the CPFC in which the ZrC coating

thickness is determined from the stress analysis shell model (Section 5.3).

5.2 Helium Gas Pressure in Fuel Kernel

To determine the thickness of the ZrC coating needed to accommodate the internal pressure of

the helium gas released from the plutonia fuel matrix, the helium gas pressure inside the particle

must be calculated. Since the decay of a 238

Pu atom produces one alpha particle (4He atom), the

instantaneous moles of helium gas generated in a coated 238

PuO2 particle can be calculated as:

)1()1(

6)(

2383t

a

oTDfff

He eN

NDtn λρεπ −−×

×−×= . (9)

At low temperatures (< 900–1000 K), most of the helium gas generated by radioactive decay of 238

Pu in the coated fuel particles will be retained within the fuel matrix. Therefore, only the

released fraction, F, will exert pressure on the PyC and ZrC coatings. The density of the released

helium gas depends on F and the available volume within the ZrC-coated fuel particle, VOLHe,

and can be calculated as:

He

HeHeHe

VOL

MnF ××=ρ . (10)

Since the perfect gas law underpredicts the gas pressure at the high densities encountered in

coated plutonia particles, the following equation, developed based on the work of Rowlinson

(1964) and Ronchi (1981), was used to determine the helium gas pressure in the present study:

11

bM

TRP

Heb

He

gHe

e 1−×=

ρ . (11)

This equation reduces to the perfect gas law at low densities.

The helium gas pressure in the coated fuel particles, obtained by Equation (11), is used next to

determine the appropriate thickness of the ZrC coating. The latter is then used to calculate the

thermal power density of the CPFC.

5.3 Stress Model

The stress model calculates the thickness of ZrC coating required to withstand the helium gas

pressure in the coated plutonia particles. The specific thermal power of the CPFC is then

calculated as a function of storage time prior to launch, operation time after launch, and the fuel

temperature.

The inner pyrolytic carbon (PyC) layer in the coated particle fuel is a low-temperature isotropic

(LTI) layer deposited by Chemical-Vapor-Deposition at temperature > 1673 K (Kaae, 1971). It

is 5-µm thick and has a density < 1.7 g/cm3 (or a volume porosity > 25%). The zirconium

carbide coating is deposited typically near 1773 K (Ogawa et al., 1981), and its thickness is taken

to be at least 10 µm. Since the operating fuel temperature in a CPFC-RHU is expected to be

< 1000 K (at which most of the helium gas generated will be retained within the fuel matrix), the

most stringent condition will occur during a potential re-entry heat pulse following a launch

abort (Schock, 1981), after a relatively long storage time. A long storage time (10 to 20 years)

translates into a large helium inventory in the fuel. Reaching a fuel temperature of up to 1723 K

during a re-entry accident (Schock, 1981) results in a higher release fraction of helium from the

fuel matrix (see Section 4.0). Therefore, it is advantageous to deposit the PyC and ZrC coatings

onto the fuel kernels at the maximum possible temperature of ~ 1723 K. It just so happens that

CVD of PyC and ZrC coatings at 1700–1800 K produces preferred mechanical properties (Kaae,

1971; Ogawa et al., 1981).

As the PyC and ZrC coatings are deposited onto the plutonia fuel kernel near 1723 K, they are in

contact with the fuel kernel and thermally unconstrained. After the coated fuel particle cools

down, the fuel kernel shrinks faster than the PyC and ZrC coatings (PuO2 has higher thermal

expansion coefficient than PyC and ZrC). The shrinking of the fuel kernel produces a void space

within the coated fuel particle that is large compared to the as-fabricated open porosity in the fuel

kernel. The present stress model does not take credit for this void volume, and is therefore

conservative at temperature < 1723 K. The model assumes that the helium gas released from the

fuel matrix occupies a volume that is comprised of the as-fabricated open porosities in the fuel

kernel and the PyC layer (which is relatively small). The volume available in the coated fuel

particle to accommodate the released helium gas is then given as:

−

+×+×= 1

21

6

33

f

PyCPyC

openf

fHe

D

tDVOL εε

π . (12)

12

The PyC layer is assumed in the model to be 25% porous (εPyC = 0.25), which is also

conservative, considering that PyC with a porosity as high as 50% has been used successfully in

TRISO-coated fuel particles. The as-fabricated open and closed porosities in the plutonia fuel

kernel depend on the fuel density achieved during the sintering process, and are assumed to

follow that of commercial UO2 fuel pellets (Gontar et al., 1997). The as-fabricated porosity in

the fuel pellets is typically between 5% and 20%. As shown in Figure 8, a dense fuel pellet with

95% TD has essentially no open porosity. The entire 5% porosity appears as tiny voids within

the fuel grains. Most of these intragranular voids are < 1 µm in size (Gontar et al., 1997). On

the other hand, most of the as-fabricated porosity in a 85% TD fuel pellet is mostly present at the

grain boundaries as an open porosity (~ 13% open porosity).

In this work, the as-fabricated open porosity in the plutonia fuel is assumed to follow the dashed

straight line in Figure 8, expressed mathematically as:

03.0067.1 −×= fopenf εε . (13)

The helium gas released from the plutonia fuel matrix exerts pressure onto the PyC inner layer

and the ZrC coatings. In this study, it is assumed that the ZrC layer alone must withstand the

pressure of the released helium gas within the coated plutonia particles. The induced, maximum

tangential stress in the ZrC layer is calculated using a two-dimensional spherical shell model

(Prados and Scott, 1966; Kaae, 1966) as:

HeT P×ℜ=σ , (14)

where the dimensionless stress factor, ℜ , is related to the thickness of the ZrC coating as:

112

223/1

−

−ℜ+ℜ

=inner

ZrC

R

t . (15)

The thickness of the ZrC coating must be greater than the failure threshold value given by

Equation (15). The design thickness of the ZrC coating is that in which the maximum tangential

stress does not exceed 80% of the yield strength of the ZrC material (i.e.

ZrCHeT YP ×≤×ℜ= 80.0σ ) at the fuel temperature.

The experimental data of the yield strength of ZrC (Ramgopal, 1974; Dobranich, 1990) plotted in

Figure 9 show that the yield stress decreases exponentially with temperature. Since no data exist

above 2073 K, a yield stress of zero was assumed at the ZrC melting temperature of 3800 K

(Storms, 1962). The yield stress data are correlated as:

[ ]55.1591017.2exp10657.4)( TPaYZrC ××−××= −

. (16)

At the predicted maximum fuel temperature during a re-entry accident of 1723 K (Schock,

1981), zirconium carbide has a very high yield strength of 475 MPa.

13

6.0 PERFORMANCE RESULTS OF CPFC-RHU

The CPFC-RHU’s performance results presented in this section are for a storage time of up to 20

years, and a fuel temperature of 1723 K (Schock, 1981). At such temperature, the He gas

fractional release from large-grain (> 200 µm) and polycrystalline Sol-Gel fuel kernels could be

less that 10% (El-Genk and Tournier, 2000). Nonetheless, parametric calculations were

performed for release fractions of 1.0, 0.10 and 0.05.

Figure 10a shows the calculated ZrC coating thickness to withstand the helium gas pressure at

1723 K, assuming full release (F = 1.0). Figure 10b presents the ratio of the thermal power of

the CPFC-RHU to that of LWRHU (Figure 3), when replacing the fuel pellet (0.287 cm3) and the

Pt-alloy clad (0.370 cm3) in the latter (Table 1) with 500-µm single-size CPFC (Design I). Note

that the upper envelop of the curves in Figure 10b corresponds to the maximum thermal power of

the CPFC-RHU. The plateaux at small storage times before launch correspond to the specified

minimum ZrC coating thickness of 10 µm.

6.1 CPFC Thermal Source Strength and Specific Power

In the present study, the composition of the PuO2 fuel is assumed identical to that of the pellet in

Light Weight Radioisotope Heater Units (Johnson, 1997). The plutonia fuel contains 80.05 at.% 238

Pu, has a theoretical density =TDfρ 11,460. kg/m

3 (Johnson, 1997), a Beginning-Of-Life

(BOL) activity of 448 GBq/g (12.1 Ci/g), and a specific thermal power of 0.40 W/g. For 238

Pu,

the decay constant, 110105048.2 −−×= sλ , the molar weight, PuM = 238.24 g/mole, and the

atom density in the as-fabricated plutonia fuel, atoms/kg10784.124238 ×=oN . The specific

thermal source strength of this fuel decreases with storage time according to the relation:

40.0)/gW( thteq

λ−×= . (17)

The other isotopes present in the plutonia fuel (239

Pu and 240

Pu) also undergo alpha decay, but

their half-lives of 24,131 years and 6,569 years, respectively, are much longer than that of 238

Pu

(87.75 years). Therefore, they contribute insignificantly to the specific thermal power of the

plutonia fuel. In a typical LWRHU, the plutonia fuel pellet has an as-fabricated porosity of 15%

and a thermal power density at Beginning Of Life (BOL) of LWRHUq ′′′ = 3.9 W/cm3. For

comparison, a fuel compact using base-case coated fuel particles (Figure 1) with same as-

fabricated fuel porosity (εf = 0.15) and tZrC = 30 µm provides 1.65 W/cm3 at BOL, or 42% of

LWRHUq ′′′ (Figure 7). This lower thermal power density of the CPFC is a disadvantage which can

be more than compensated by increasing the CPFC volume within the aeroshell of the current

LWRHU, and hopefully at no or little mass penalty. As shown in Figures 7 and 10, the volume

fraction and specific thermal power of the CPFC decreases with increasing fuel kernel porosity

and increasing ZrC coating thickness. The specific thermal power of CPFC depends on the

storage time of the RHU prior to launch and the maximum fuel temperature that could be

achieved during a re-entry accident.

14

6.2 Thermal Analysis of CPFC-RHU

In the current LWRHU (Figure 3), the Pt-30%Rh cladding occupies a 29% larger volume than

the fuel pellet itself (Table 1; Tate, 1982). Thus, replacing both the fuel pellet and the cladding

in Figure 3 with CPFC provides more than a two-fold increase (a factor of 2.29) in the RHU

thermal power. As shown in Figure 10b, for this design option I, the CPFC-RHU thermal power

is 80% that of the LWRHU, assuming full He release after a 10-year storage.

The three PyC insulation sleeves in the current LWRHU occupy a relatively large volume

(Figure 3 and Table 1). They are designed to maintain the Pt-alloy temperature below its

eutectic point (Sholtis et al., 1999) during an accidental re- entry heat pulse (Pt-30%Rh forms an

eutectic with carbon at 2033 K). A portion of the insulation sleeves could be replaced with

CPFC (Figure 11), without risking overheating the CPFC. To confirm this statement, a thermal

analysis of the CPFC-RHU is performed to calculate the temperature of the CPFC during a re-

entry heating pulse.

To estimate the maximum temperature of the CPFC during a re-entry heating pulse (Figure 12a),

a one-dimensional, transient thermal model of the RHU was developed. This model was

benchmarked against the LWRHU thermal response results reported by Schock (1981) during

the worst-case re-entry accident (inertial angle of –4.85o). This author used a comprehensive 3-

D transient model to simulate the LWRHU thermal response during re-entry. The present

thermal model simulates transient heat flow in a radial section along the mid-plane of the RHU.

The radial heat flow occurs by conduction and radiation. In the LWRHU, the plutonia fuel pellet

(19% porous) is assumed to be in perfect contact with the Pt-30%Rh clad, which has an

emissivity of 0.53. The Pt-Rh cladding is surrounded by three PyC insulation sleeves (of 25%

porosity), separated by thin radiation gaps, and a thick aeroshell consisting of Fine Weave

Pierced Fabric (FWPF, 90% porous) (Schock, 1980 and 1981). The heat capacities, thermal

conductivities and radiative emissivities of these various layers are calculated as functions of

temperature.

In addition to conduction and radiation heat transfers, contact resistances between the various

layers are accounted for. The LWRHU is designed with radial gaps between the fuel capsule, the

three PyC insulation sleeves and the FWPF aeroshell, to facilitate assembly and increase the

thermal resistance between the fuel capsule and the aeroshell. However, during a side-on, stable

re-entry, all LWRHU components are in contact along their stagnation line, due to aerodynamic

forces (Schock, 1981). The present analysis assumes a total circumferential contact of 30o

between all adjacent components. The contact resistance between the PyC sleeves is taken equal

to 11.4 K / (W/cm2), and 5.7 K / (W/cm

2) between the aeroshell and the third PyC sleeve

(Schock, 1981). Thermal analyses performed by Schock (1981) have shown that the effect of

helium gas conduction in the LWRHU during re-entry was negligible. This is because the pre-

activated vent of the LWRHU fuel capsule steadily releases the helium gas during re-entry. In

addition, the relatively high porosity of the FWPF aeroshell does not allow the helium gas to

accumulate inside the LWRHU aeroshell.

The transient heat balance equation is solved in each radial layer simultaneously, subject to a

zero heat flux at the fuel pellet centerline, and a time-dependent temperature at the aeroshell

15

outer surface. The latter is obtained from Schock’s results (1981). The model’s predictions in

Figure 12b of the thermal response of the LWRHU during the worst-case re-entry accident

(inertial angle of –4.85o) agreed reasonably well with those reported by Schock (1981). The

present 1-D transient model reproduced the 3-D results of Schock (1981) to within + 30 K over

the full 300 s re-entry transient, and the Pt-30%Rh cladding maximum temperature (1726 K)

within 3 K and 5 s (at 270 s), see Figures 12b and 13.

The present thermal model was then used to predict the temperatures in designs I and II of

CPFC-RHUs during both normal operation and a re-entry heating pulse (Figure 12a). The

surface emissivity of the CPFC graphite matrix was taken equal to 1.0. During re-entry heating,

the aeroshell surface temperature was assumed the same as for the LWRHU. This assumption is

justified because: (a) the overall thermal masses of the LWRHU (35.7 J/K), the Design I,

CPFC-RHU (36.0 J/K) and the Design II, CPFC-RHU (36.7 J/K) are almost identical; and (b) the

FWPF aeroshell is the largest component in the RHUs (it weights 23 g compared to the overall

RHUs mass of ~ 40 g each). The aeroshell contributes 63% to the overall thermal mass of each

RHU, and its temperature is mostly controlled by aero-ablation, and is not affected by the

components design inside the RHUs. The present analysis showed that in the CPFC-RHU

design I, the maximum temperature of CPFC is 1688 K after 278 s into the re-entry transient

(Figure 13). The calculated initial (operating) fuel temperature in the CPFC-RHU is 709 K, or

100 K lower than in the LWRHU (Figure 13). When the inner PyC insulation was removed and

replaced with CPFC (Design II, Figure 11), the calculated initial CPFC temperature is slightly

higher (735 K), and a maximum CPFC temperature of 1734 K is reached after 255 s into the re-

entry transient (see Figure 13). The CPFC temperature of 1723 K is used in the subsequent

stress analyses of the CPFC-RHU.

6.3 Effect of Helium Release on CPFC-RHU Performance

In the present study, when the inner PyC insulation sleeve in the LWRHU is also replaced with

CPFC (Design II, Figure 11), the thermal power of the CPFC-RHU is 1.83 times that of Design

I, in which only the fuel pellet and the Pt-30%Rh clad in the LWRHU (Figure 3) are replaced

with CPFC. The total volume enclosed by the inner insulation sleeve is 1.20 cm3, which

amounts to 12% of cavity between the Pt-30%Rh clad and the aeroshell (Table 1). Results show

that a Design II CPFC-RHU designed for a peak fuel temperature of 1723 K and storage time

before launch of 10 years, assuming full He release, provides 46% more thermal power than the

LWRHU, at only 95% of the total mass. Using a binary-size CPFC with 300 and 1200 µm

diameter fuel kernels increases the thermal power of the CPFC-RHU by an additional 15% to 1.7

times that of the LWRHU, at essentially the same total mass of the LWRHU (~ 40 g).

To investigate the effect of He gas release on the performance of the CPFC-RHU, calculation are

performed for F = 0.1 and F = 0.05. The predicted CPFC-RHU thermal power relative to that of

the LWRHU is delineated in Figure 14 for F = 0.1 and a fuel temperature of 1723 K. In a CPFC

with 11% as-fabricated fuel porosity and Df = 500 µm, a 11-µm ZrC coating is needed to

withstand the pressure of the released He after 10 years of storage. When the fuel pellet and the

Pt-30%Rh clad in the LWRHU are replaced with a single-size CPFC, the RHU provides 25%

more thermal power than the LWRHU (Figure 14), a 56% increase over the CPFC-RHU

assuming full He release (F = 1.0).

16

When the inner insulation sleeve in the LWRHU is also replaced with single-size CPFC (Design

II in Figure 11), an RHU stored for 10 years would provide 2.3 times the thermal power of a

LWRHU. Using binary-size (300 and 1200 µm fuel kernel diameters) CPFC increases the

thermal power of the CPFC-RHU by an additional 15%, to 2.6 times that of the LWRHU (Figure

14), at essentially the same total mass (~ 40 g).

The effect of He release fraction on the performance of Design II CPFC-RHU is best illustrated

in Figure 15. In this RHU design, the fuel pellet, Pt-30%Rh clad and inner PyC insulation sleeve

in the LWRHU are replaced with a single-size CPFC. After a storage time of 10 years, a

decrease in He release from 100% to 10% increases the fuel loading in the CPFC-RHU and

hence the thermal power by 56%. However, a decrease in the He release from 10% to 5% results

in only ~ 5% increase in the CPFC-RHU’s thermal power (Figure 15). These results suggest that

He release in excess of 10% strongly impacts the thermal power density of the CPFC-RHU, but

has little impact below 10%.

The results, summarized in Table 2, demonstrate the potential of the CPFC-RHU for achieving

specific thermal powers as high as 60 Wth/kg, or 2.3 times that of LWRHU. When a binary-size

CPFC of 300 and 1200 µm particles is used, the thermal power of the CPFC-RHU increases by

an additional 15% to ~ 2.6 W (Table 2), at essentially the same total mass as the LWRHU (~ 40

g). These calculations are conducted at a CPFC temperature of 1723 K and 11% as-fabricated

fuel porosity, assuming a 10% He gas release from the fuel kernel. The calculated thickness of

the ZrC coating to withstand the internal He gas pressure at these conditions is 10, 11, and 24 µm

for 300, 500, and 1200 µm diameter fuel kernel, respectively. As indicated earlier, using large

grain (> 200 µm) or polycrystalline 238

PuO2 fuel kernels could reduce the He release fraction at

1723 K to below 7% (El-Genk and Tournier, 2000). When the assumed He release fraction is

only 5%, the calculated thermal power of the single-size, Design II, CPFC-RHU is 2.4 Wth,

increasing to 2.76 Wth for the binary-size CPFC-RHU. Such good performance, together with

the potential for enhanced safety and design flexibility, make the CPFC an attractive fuel form.

6.4 Specific Thermal Power of CPFC

Figures 16 and 17 demonstrate the effects of fuel temperature and kernel diameter on the specific

thermal power and thermal power density of single-size CPFC, respectively. Initially, the CPFC

specific thermal power increases rapidly with the kernel diameter, reaching an asymptote at

about 500 µm. Beyond this value, the specific thermal power increases slowly with increasing

fuel kernel diameter, as the volume contribution of the inner PyC layer (5 µm thick) becomes

vanishingly small. At small fuel kernel diameter, the specified, minimum design thickness of

ZrC coating (10 µm) is greater than that needed to withstand the internal pressure of helium

released, resulting in a relatively low CPFC specific power. When the needed ZrC coating

thickness is beyond 10 µm, it increases proportionally with the fuel kernel diameter (see

Equations (14) and (15)).

Figures 16 and 17 show the CPFC performance results for three different operating conditions.

The first conditions are a maximum temperature of 1723 K (which may occur during a re-entry

into the atmosphere following a launch abort accident) and full helium gas release after 10-year

storage. This CPFC uses plutonia fuel of 25% as-fabricated porosity and has a relatively low

17

specific thermal power of 0.23 Wth/g (power density = 1.25 Wth/cm3), or 57% that of a typical

LWRHU fuel pellet. The second conditions are a maximum temperature of 1723 K and 10%

helium gas release after 10-year storage. As shown in Figures 16 and 17, a CPFC of plutonia

fuel with 11% as-fabricated porosity achieves a specific thermal power of 0.303 Wth/g (power

density = 2.0 Wth/cm3). Finally, the third conditions for the single-size CPFC are a maximum

fuel temperature of 1000 K, 5% helium gas release after 10-year storage, and single-size plutonia

particles with 5% as-fabricated fuel porosity. This CPFC uses a 10 µm-thick ZrC coating and

can achieve a specific thermal power as high as 0.325 Wth/g (power density = 2.3 Wth/cm3).

7.0 FUTURE RESEARCH NEEDS

The previous results showed that CPFC-RHUs could provide significantly higher thermal power

than a LWRHU, with no increase in total mass. Several technical issues remain, however, that

are worthy of further investigations. The first is related to demonstrating the fabrication

technology of large grain (> 200 µm) and polycrystalline 238

PuO2 fuel kernels (300-1200 µm in

diameter) using either state-of-the art Sol-Gel and/or thermal plasma processes. The potential,

and the cost of production, decontamination, and of mastering each of these technologies need to

be investigated and compared. This is a priority that supersedes any of the following issues.

Given that the outcome of the first issue is positive, the second issue in order of priority would

be to confirm the potential of the fuel kernels for retaining helium gas. The retention of the He

gas generated in the 238

PuO2 fuel kernels depends strongly on the fuel microstructure (El-Genk

and Tournier, 2000). Almost full He release is expected in small grain (7-40 µm) fuel kernels at

1723 K, making them a poor selection for the CPFC-RHUs. Large-grain or polycrystalline 238

PuO2 fuel kernels, which are the primary choice for CPFC-RHUs, could retain as much as 93-

95% of the He gas generated in the fuel matrix at temperatures in excess of 1700 K. The small,

needed thickness of the ZrC coating would increase the fuel loading and, hence, the thermal

output of the CPFC-RHU, well in excess of that of the current state-of-the-art LWRHU.

Therefore, future experimental investigations to confirm the He gas release estimates in the

present paper are recommended. These investigations should involve both coated and uncoated,

large-grain (> 200 µm) and polycrystalline, 238

PuO2 fuel kernels (El-Genk and Tournier, 2000).

Experiments could also be performed to investigate the effects of storage time, fuel temperature,

and heating mode (steady-state and ramped heating transient) on both the release rate and release

fraction of He from uncoated and coated fuel particles. These experiments may also investigate

potential failure modes and the threshold temperature for a ZrC coating failure, if any.

The third issue in order of priority is to confirm that coating 238

PuO2 fuel kernels on a large scale

is possible. The coating of UO2 and mixed-oxide fuel kernels with PyC and ZrC has been

demonstrated successfully for many years for commercial, high temperature gas cooled reactors

(HTGRs) with SiC outer coating and recently with ZrC coating for operation at higher

temperature and fuel burnup (Minato et al., 1997). Owing to the relatively shorter half-life of 238

Pu (86 years), however, the alpha particles released by the radioactive decay of 238

Pu could

affect the quality of the coating in two ways. The heat dissipated in the decay process and the

bombardment of the deposited coating by the emitted alpha particles could affect the quality of

the PyC and ZrC coatings during the CVD processes.

18

The positive outcome of the aforementioned issues would suggest addressing the fourth and final

issue, which is related to the fabrication and strength of the CPFC. The later is related to the

fracture strength of the CPFC upon impacting solid surfaces. Both fracture and impact tests

involving CPFC and detailed stress analysis are recommended. The results could guide future

development of the graphite matrix of the CPFC, which can protect the coated fuel particles

during handling, re-entry heating, as well as during impact on solid surfaces. As indicated

earlier, the graphite matrix should be structurally strong and of low density to accommodate

thermal expansion of the coated fuel particles during a re-entry heating pulse. It has also to

fracture upon impact with solid surfaces in order to protect the coated fuel kernels, "the

pomegranate concept." Ultimately, mechanical, thermal, and aeroablation testing of the coated

particle fuel in simulated accident environments will subsequently be needed.

8.0 SUMMARY AND CONCLUSIONS

The potential of coated 238

PuO2 fuel particles compact for future use in advanced RHUs and

RPSs is investigated. A stress and design model of the coated plutonia fuel particle was

developed and used to investigate the performance of both single-size and binary-size CPFC-

RHUs as a function of the helium gas release fraction, for a 10-year storage before launch and

fuel temperature up to 1723 K. This fuel temperature corresponds to the predicted peak value

during an accidental re-entry heating pulse.

Results indicated that large grain (> 200 µm) or polycrystalline 238

PuO2 fuel kernels would retain

most of the helium gas generated by the radioactive decay of 238

Pu. Recent estimates of the He

gas release from large-grain and polycrystalline 238

PuO2 fuel kernels showed that He release in

large-grain (> 200 µm) 238

PuO2 fuel kernels at 1723 K could be less than 7% and even lower in

polycrystalline fuel kernels. At fuel temperatures < 1000 K, the He release will be nil. Large-

grain fuel kernels could be fabricated using binderless agglomeration or similar processes, while

the polycrystalline fuel kernels could be fabricated using Sol-Gel or thermal plasma processes.

Although these processes have successfully been used in the fabrication of UO2 and mixed-oxide

fuel kernels, they have not been demonstrated for the fabrication of 238

PuO2 fuel kernels. In

addition, using CVD techniques to apply the PyC and ZrC coatings on plutonia kernels is yet to

be demonstrated.

Performance analyses of a conservatively designed CPFC-RHU indicate that its thermal power

could be 2.3 and 2.4 times that of the LWRHU, at essentially the same total mass. The CPFC-

RHU uses the same Fine-Weave Pierced Fabric (FWPF) aeroshell, and two of the three inner

PyC insulation sleeves of the LWRHU. These performance figures of the CPFC-RHU are for a

single-size (500 µm) coated 238

PuO2 fuel particle compact, 11% and 7% as-fabricated fuel

porosity, and 10% and 5% helium gas release, respectively. In the CPFC-RHU, the fuel pellet

and its refractory cladding and the inner PyC insulation sleeve in the LWRHU are replaced with

CPFC. Using a binary-size (300 and 1200 µm) CPFC increases the thermal power of the CPFC-

RHUs by an additional 15%.

19

The CPFC is a promising fuel form for use in advanced RHUs and RPSs. In addition to

enhancing the thermal power output, it offers enhanced safety and unique design flexibility,

since it could be fabricated in different sizes and shapes. CPFC-RHUs and RPSs could meet the

thermal and electric power needs for future spacecraft and planetary exploration in the range

from a few milli-watts to tens and even hundreds of watts, for more than ten years. Several

issues for future research, given in order of priority and order of conduct, are recommended:

(a) Investigate and demonstrate the fabrication techniques of large-grain (> 200 µm) and

polycrystalline plutonia fuel kernels and the application of the PyC and ZrC coatings using

CVD processes;

(b) Perform helium gas release tests from large grain and polycrystalline fuel kernels, both

coated and uncoated, to confirm the recent estimates of the He gas release (El-Genk and

Tournier, 2000); and

(c) Fabricate CPFC-RHUs and perform fracture impact tests and analysis to provide data to

benchmark models. These data and analysis results could also be used to guide the

development and the selection of the most appropriate graphite matrix material for CPFCs.

Ultimately, mechanical, thermal, and aero-ablation testing of coated particle fuel in

simulated accident environments will subsequently be needed.

9.0 ACKNOWLEDGMENTS

This research was funded by Sandia National Laboratories (SNL), Kirtland Air Force Base,

Albuquerque, NM, under contracts No. BE-2543, to the University of New Mexico’s Institute for

Space and Nuclear Power Studies, and BE-2544, to Sholtis Engineering & Safety Consulting,

Tijeras, NM. The opinions expressed in this paper are solely those of the authors.

20

LIST OF FIGURES

Figure 1a. A cross-sectional view of a coated plutonia fuel kernel.

Figure 1b. Binary-size, coated plutonia particles fuel compact (CPFC).

Figure 2a. A miniaturized CPFC-RHU for supplying thermal power to circuit boards on board

of spacecraft.

Figure 2b. Milliwatt CPFC-RPS and RHU for supplying both thermal and electric power to

circuit boards on board of spacecraft.

Figure 2c. Conceptual design of a high-efficiency (~ 25%) CPFC-RPS for space exploration

missions.

Figure 3. Current LWRHU (Johnson, 1997).

Figure 4. Microstructures of plutonia fuel kernels.

Figure 5. Release fraction of noble gases and volatile fission products in UO2 fuel particles,

versus half-life (El-Genk and Tournier, 2000).

Figure 6. Volume fraction of two-size spheres in CPFC as a function of coarse-to-fine

diameter ratio (data from McGeary, 1961).

Figure 7. Effect of fuel porosity and thickness of ZrC coating on volume fraction of plutonia

in CPFC.

Figure 8. As-fabricated open and closed porosities in UO2 fuel pellets after sintering (Gontar

et al., 1997).

Figure 9. Yield stress of zirconium carbide as a function of temperature (Ramgopal, 1974;

Dobranich, 1990).

Figure 10a. Calculated ZrC coating thickness for full helium retention in CPFC.

Figure 10b. Ratio of thermal power of CPFC-RHU (Design I) and LWRHU.

Figure 11. Proposed CPFC-RHU (Design II).

21

Figure 12a. Measured helium release rate and temperature during simulated re-entry heating

pulse of 8-year-old LWRHU 027 (Peterson and Starzynski, 1982).

Figure 12b. Calculated temperatures in LWRHU during nominal operation and side-on re-

entry heating pulse (-4.85o inertial angle).

Figure 13. Calculated fuel temperatures in CPFC-RHU designs I and II during nominal

operation and side-on re-entry heating pulse, and comparison with calculated Pt-

30%Rh cladding temperature in LWRHU.

Figure 14. Comparison of CPFC-RHU thermal power with that of LWRHU assuming 10%

helium gas release.

Figure 15. Effect of helium gas release on thermal power of CPFC-RHU for Tf = 1723 K in

design II, in which single-size CPFC replaces LWRHU fuel pellet, Pt-alloy clad and

inner PyC insulation sleeve.

Figure 16. Effects of fuel temperature, He gas release fraction and fuel kernel diameter on the

specific thermal power of CPFC, after 10 years of storage.


thermal power density of CPFC, after 10 years of storage.

LIST OF TABLES

Table 1. Volumes and mass breakdown of various components of a LWRHU (Tate, 1982;

Figure 3).

Table 2. Thermal power estimates of CPFC-RHU designed for a peak fuel temperature of

1723 K after 10 years of storage.

22

PyrolyticCarbon (PyC)

5 µm thick

ZrC coating

(thickness

> 10 µm)

300-1200 µm

Large-grain

(> 200 µm) orpolycrystalline

238PuO2

PyrolyticCarbon (PyC)

5 µm thick

ZrC coating

(thickness

> 10 µm)

300-1200 µm

Large-grain

(> 200 µm) orpolycrystalline

238PuO2

Figure 1a. A cross-sectional view of a coated plutonia fuel kernel.

Coarse-size

coated particles

Small-size

coated particles

Graphite matrix

Figure 1b. Binary-size, coated plutonia particles fuel compact (CPFC).

23

Circuit board

AeroshellCPFC heat

source

Heat pipe shellThermal

insulation

Metal support plate

Circuit board

AeroshellCPFC heat

source

Heat pipe shellThermal

insulation

Metal support plate

Figure 2a. A miniaturized CPFC-RHU for supplying thermal power to circuit boards on

board of spacecraft.

Circuit Board

AeroshellCPFC heat

source

TE-Couples Heat pipe

plate

+_

Thermal

Insulation

Circuit Board

AeroshellCPFC heat

source

TE-Couples Heat pipe

plate

+_

Thermal

Insulation

Figure 2b. Milliwatt CPFC-RPS and RHU for supplying both thermal and electric power to

circuit boards on board of spacecraft.

24

AMTEC cells, η = 18%

(Thot = 1100 K, Tcold = 650 K)

Hybrid insulation

(Min-K, Multifoil)

Heat pipe housing and

radiator (~ 350 K)

Segmented TE couples, η = 9%

(Thot = 650 K, Tcold = 350 K)

CPFC heatsource

AMTEC cells, η = 18%

(Thot = 1100 K, Tcold = 650 K)

Hybrid insulation

(Min-K, Multifoil)

Heat pipe housing and

radiator (~ 350 K)

Segmented TE couples, η = 9%

(Thot = 650 K, Tcold = 350 K)

CPFC heatsource

Figure 2c. Conceptual design of a high-efficiency (~ 25%) CPFC-RPS for space exploration

missions.

25

FWPF aeroshell

(H = 32 mm,

D = 26 mm,

t = 4.5 mm)

End cap

(FWPF)

Insulator

plug (PyC)

PyC insulator

sleeves (3)

238PuO2

fuel pellet

(H = 9.4 mm,

D = 6.6 mm)

Insulator

plug (PyC)

Pt-30%Rh

clad

(t = 1 mm)

Pt-30%Rh

shim

Vent

Frit (Pt)

FWPF aeroshell

(H = 32 mm,

D = 26 mm,

t = 4.5 mm)

End cap

(FWPF)

Insulator

plug (PyC)

PyC insulator

sleeves (3)

238PuO2

fuel pellet

(H = 9.4 mm,

D = 6.6 mm)

Insulator

plug (PyC)

Pt-30%Rh

clad

(t = 1 mm)

Pt-30%Rh

shim

Vent

Frit (Pt)

Figure 3. Current LWRHU (Johnson, 1997).

Homogeneouscrystalline

fuel matrix

As-fabricated

tiny voidsAs-fabricated

intergranular

voids

Polycrystalline

fuel grain

with

intragranular

voids

Homogeneouscrystalline

fuel matrix

As-fabricated

tiny voidsAs-fabricated

intergranular

voids

Polycrystalline

fuel grain

with

intragranular

voids

(a) Granular fuel kernel fabricated (b) Polycrystalline fuel kernel fabricated

Using powder-metallurgy using Sol-Gel techniques

Figure 4. Microstructures of plutonia fuel kernels.

26

0.01

0.1

1

10

100

0 1 2 3 4 5 6

7 µm (0.4 at%, 2023 K) 10 µm (4.0 at%, 1723 K) 40 µm (0.4 at%, 2023 K)300-600 µm (4.0 at%, 1723 K) 2500 µm (1.6 at%, 1723 K)

72%

6%T = 1723 K

√T1/2

(years1/2

)

Rele

ase

-to-B

irth

Rate

Ratio (

%)

Figure 5. Release fraction of noble gases and volatile fission products in UO2 fuel particles,

versus half-life (El-Genk and Tournier, 2000).

60

65

70

75

80

85

5 10 15 20

Experiment (McGeary, 1961)Model

62.5% packing limit for one-size spheres

triangular pore path(D

p1/D

p2 = 1/(2√3 - 1)

Spheres' diameter ratio (Dp1

/Dp2

)

Pa

ckin

g V

olu

me

Fra

ctio

n

in C

PF

C,

β (%

)

Figure 6. Volume fraction of two-size spheres in CPFC as a function of coarse-to-fine

diameter ratio (data from McGeary, 1961).

27

0

20

40

60

80

0 50 100 150 200

in particlein CPFC

Df = 500 µm, t

PyC = 5 µm

40%30%

20%10%

εf = 0

Thickness of ZrC Coating, tZrC

(µm)

Fu

el V

olu

me

Fra

ction

(%

)

Figure 7. Effect of fuel porosity and thickness of ZrC coating on volume fraction of

plutonia in CPFC.

0

5

10

15

75 80 85 90 95 1000

5

10

15Data from Gontar et al. (1997)

Density after Sintering (% T.D.)

Op

en

Po

rosity (

%)

Clo

se

Po

rosity (

%)

Figure 8. As-fabricated open and closed porosities in UO2 fuel pellets after sintering (Gontar

et al., 1997).

28

1

10

100

1000

10000

0 1000 2000 3000 4000

Experimental dataExponential fit

20 MPa(2.9 ksi)

256 MPa (37 ksi)

1740 MPa (253 ksi)

Tfus

Temperature, T (K)

Yie

ld S

tre

ss,

YZ

rC (

MP

a)

Figure 9. Yield stress of zirconium carbide as a function of temperature (Ramgopal, 1974;

Dobranich, 1990).

29

0

20

40

60

80

100

0 5 10 15 20

(a)

F = 1.0T

f = 1723 K

4035

3025

20

15

10

εf= 5%

(single-size CPFC,D

f=500 µm, t

PyC=5 µm)

Time to Launch (years)

ZrC

Co

atin

g T

hic

kn

ess,

t ZrC

(µm

)

Figure 10a. Calculated ZrC coating thickness for full helium retention in CPFC.

0.5

1.0

1.5

0 5 10 15 20

(b)

30

40

35

3025201510εf = 5%

F = 1.0T

f = 1723 K


Ψ

Figure 10b. Ratio of thermal power of CPFC-RHU (Design I) and LWRHU.

30

FWPF aeroshell

(H = 32 mm,

D = 26 mm,

t = 4.5 mm)

End cap

(FWPF)

Insulator

plug (PyC)

PyC insulator

sleeves (2)

238PuO2 CPFC

(H = 14.1 mm,

D = 10.4 mm)

Insulator

plug

(PyC)

FWPF aeroshell

(H = 32 mm,

D = 26 mm,

t = 4.5 mm)

End cap

(FWPF)

Insulator

plug (PyC)

PyC insulator

sleeves (2)

238PuO2 CPFC

(H = 14.1 mm,

D = 10.4 mm)

Insulator

plug

(PyC)

Figure 11. Proposed CPFC-RHU (Design II).

31

0

8

16

24

32

0 20 40 60 80 100800

1100

1400

1700

2000

c

b

a

heat pulse(825 K/min)

7.9-year-oldLWRHU(7-12 µm grains)

Time (s)

He

lium

Re

lea

se

Rate

(µ

mo

le /

s)

Me

asu

red

Tem

pe

ratu

re (

K)

Figure 12a. Measured helium release rate and temperature during simulated re-entry heating

pulse of 8-year-old LWRHU 027 (Peterson and Starzynski, 1982).

0

500

1000

1500

2000

2500

3000

0 50 100 150 200 250 300

Tmax

= 1726 K

(270 s)

fuelpelletPt-30Rh

cladding

PyC sleeve 1

PyC sleeve 2

PyC sleeve 3

aeroshell (inner)

Time, t (s)

Te

mp

era

ture

(K

)

Figure 12b. Calculated temperatures in LWRHU during nominal operation and side-on re-

entry heating pulse (-4.85o inertial angle).

32

500

1000

1500

2000

0 50 100 150 200 250 300

Pt-30Rh cladding in LWRHU

CPFC inDesign I

CPFC inDesign II

1688 K

1726 K

1734 K

709 K

735 K810 K

Time, t (s)

Te

mp

era

ture

(K

)

Figure 13. Calculated fuel temperatures in CPFC-RHU designs I and II during nominal

operation and side-on re-entry heating pulse, and comparison with calculated Pt-

30%Rh cladding temperature in LWRHU.

1

2

3

0 5 10 15 20

Single-size CPFC replaces pellet,clad and inner PyC sleeve in LWRHU (Design II)

Single-size CPFC replaces pelletand clad in LWRHU (Design I)

Binary-particle fuel (Dp1

/Dp2

= 4)

in Design II CPFC-RHU

tPyC

=5 µm, F = 0.10, Tf = 1723 K


Ψ

Figure 14. Comparison of CPFC-RHU thermal power with that of LWRHU assuming 10%

helium gas release.

33

1.0

1.5

2.0

2.5

0 5 10 15 20

F = 1.0

F = 0.1

F = 0.05

Single-size CPFC

Df = 500 µm, t

PyC=5 µm, T

f = 1723 K


Ψ

Figure 15. Effect of helium gas release on thermal power of CPFC-RHU for Tf = 1723 K in

design II, in which single-size CPFC replaces LWRHU fuel pellet, Pt-alloy clad and

inner PyC insulation sleeve.

0.20

0.25

0.30

0.35

0 500 1000 1500

tZrC

= 10 µm

1723 K, F = 1.0, εf = 25%

1000 K, F = 0.05, ε

f = 5% (t

ZrC= 10 µm)

1723 K, F = 0.10, εf = 11%

Fuel Kernel Diameter, Df (µm)

Sp

ecific

Th

erm

al P

ow

er

(Wth

/g)


specific thermal power of CPFC, after 10 years of storage.

34

1.0

1.5

2.0

2.5

0 500 1000 1500

tZrC

= 10 µm

1723 K, F = 1.0, εf = 25%

1000 K, F = 0.05, ε

f = 5% (t

ZrC= 10 µm)

1723 K, F = 0.10, εf = 11%

Fuel Kernel Diameter, Df (µm)

Th

erm

al P

ow

er

De

nsity (

Wth

/cm

3)


thermal power density of CPFC, after 10 years of storage.

35

Table 1. Volumes and mass breakdown of various components of a LWRHU (Tate, 1982;

Figure 3).

Region

Density (g/cm3)

Mass

(gram)

Volume (cm3)

Normalized

volume

Cumulated

volume

PuO2 fuel pellet 9.27 2.66 0.287 1 x 1.00

Pt-30Rh cladding 17.6 6.51 0.370 1.29 x 2.29

Inner PyC sleeve

Other PyC sleeves

–

–

–

–

0.537

3.938

1.87

13.72

x 4.16

x 17.88

Total insulation 1.75 7.83 4.475 15.59 –

Inner cavity 17.0 5.132 17.88 –

FWPF aeroshell 1.96 23.0 11.74 – –

LWRHU capsule 40.0 16.87 – –

Table 2. Thermal power estimates of CPFC-RHU designed for a peak fuel temperature of

1723 K after 10 years of storage.

x 1

.83

x 1

.15

x 1.56 x 1.05

Helium gas release fraction, F

CPFC-Type (Design Option)

1.0

0.10

0.05

Single-size a

(Df =500 µm)

ψψψψ = 0.80 (0.83 W)

[21 Wth/kg]

(εf = 25%, tZrC = 36 µm)

ψψψψ = 1.25 (1.30 W)

[33 Wth/kg]

(εf = 11%, tZrC = 11 µm)

ψψψψ = 1.31 (1.36 W)

[34 Wth/kg]

(εf = 7%, tZrC = 10 µm)

Single-size b

(Df =500 µm)

ψψψψ = 1.46 (1.52 W)

[38 Wth/kg]

ψψψψ = 2.29 (2.38 W)

[59 Wth/kg]

ψψψψ = 2.40 (2.50 W)

[62 Wth/kg]

Binary-size b

(Df1 = 1200 µm,

Df2 = 300 µm)

ψψψψ = 1.68 (1.75 W)

[43 Wth/kg]

(tZrC1=86 µm, tZrC2=22 µm)

ψψψψ = 2.63 (2.74 W)

[68 Wth/kg]


ψψψψ = 2.76 (2.87 W)

[71 Wth/kg]


x 1

.83

x 1

.15

x 1.56 x 1.05

Helium gas release fraction, F

CPFC-Type (Design Option)

1.0

0.10

0.05

Single-size a

(Df =500 µm)

ψψψψ = 0.80 (0.83 W)

[21 Wth/kg]

(εf = 25%, tZrC = 36 µm)

ψψψψ = 1.25 (1.30 W)

[33 Wth/kg]

(εf = 11%, tZrC = 11 µm)

ψψψψ = 1.31 (1.36 W)

[34 Wth/kg]

(εf = 7%, tZrC = 10 µm)

Single-size b

(Df =500 µm)

ψψψψ = 1.46 (1.52 W)

[38 Wth/kg]

ψψψψ = 2.29 (2.38 W)

[59 Wth/kg]

ψψψψ = 2.40 (2.50 W)

[62 Wth/kg]

Binary-size b

(Df1 = 1200 µm,

Df2 = 300 µm)

ψψψψ = 1.68 (1.75 W)

[43 Wth/kg]


ψψψψ = 2.63 (2.74 W)

[68 Wth/kg]


ψψψψ = 2.76 (2.87 W)

[71 Wth/kg]


a: Replace LWRHU pellet and Pt-alloy clad with CPFC (Design I).

b: Replace LWRHU pellet, clad and inner insulation sleeve with CPFC (Design II).

Performance analysis of coated plutonia particle fuel compact for radioisotope heater units

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