**4.2 Re-Entrant fuel Channels**

130 Nuclear Reactors

considered, steam from high and intermediate turbines are extracted and sent to a series of open and closed feed-water heat exchangers. The steam is used to increase the temperature

The design of a fuel channel for SCWRs is an arduous undertaking due to high operating temperatures, which require materials that withstand temperatures as high as 625°C under normal operating conditions. In contrast, current materials, which withstand such design temperatures, have high absorption cross-sections for thermal neutrons. Consequently, a fuel-channel design must address the limitations due to material options to allow for maximum performance using available materials. AECL has proposed several fuel-channel designs for SCWRs. These fuel-channel designs can be classified into two categories: directflow and re-entrant channel concepts, which will be described in Sections 4.1 and 4.2. It should be noted that a re-entrant fuel-channel concept was developed by Russian scientists and was utilized at Unit 1 of the Beloyarskaya NPP in the 1960s (Saltanov et al., 2009).

The High Efficiency fuel Channel (HEC) consists of a pressure tube, a ceramic insulator, a liner tube, and fuel bundles. Figure 5 shows a 3-D view of HEC. The outer surface of the pressure tube is exposed to a moderator. The moderator could be a liquid moderator such as heavy-water or a solid moderator. The purpose of using an insulator is to reduce the operating temperature of the pressure tube and heat losses from the coolant to the moderator. Low operating temperatures of the pressure tube would allow for the use of available materials such as Zr-2.5%Nb, which has low absorption cross-sections for thermal

Fig. 5. High efficiency fuel channel (based on Chow and Khartabil, 2008).

of the feed-water.

**4. Fuel channel designs** 

**4.1 High-Efficiency fuel Channel** 

neutrons (Chow and Khartabil, 2008).

There are several Re-Entrant fuel Channel (REC) designs. As shown in Fig. 6, the first design consists of a pressure tube and a flow tube which are separated by a gap. The coolant flows along the gap between the pressure tube and the flow tube. Then, at the end of the fuel channel, the coolant flows inside the flow tube where a bundle string is placed. The outer surface of the pressure tube is in contact with the moderator. The use of this fuel-channel design is possible only if the liquid moderator is pressurized to reduce heat loss.

Since the heat loss from the aforementioned fuel channel is significantly high, this design has been modified in the form of the fuel channels shown in Figs. 7 and 8. The second design (see Fig. 7) consists of a calandria tube, a pressure tube, and a flow tube. The gap between the pressure tube and the calandria tube is filled with an inert gas, which provides thermal insulation, reducing the heat losses from the 'hot' pressure tube to the moderator. As shown in Fig. 7, the outer surface of the calandria tube is exposed to a liquid moderator.

Unlike the HEC design, forces due to fuelling/refuelling are not exerted directly on the ceramic in the third design shown in Fig. 8, ensuring that the mechanical integrity of the ceramic insulator is maintained. In addition, the ceramic insulator acts as a thermal barrier, which in turn results in relatively lower operating temperatures of the pressure tube while reducing the heat loss from the coolant to the moderator. Such low operating temperatures allow for the use of Zr-2.5%Nb, which has low absorption cross-sections for thermal neutrons, as the material of the pressure tube. Therefore, lower heat losses, a better protection of the ceramic insulator, and the possibility of using Zr-2.5%Nb as the material of the pressure tube are several advantages of this fuel channel.

Fig. 6. Re-entrant fuel channel (based on Chow and Khartabil, 2008).

Thermal Aspects of Conventional and Alternative Fuels

conductivity fuels are UC and UN.

**Theoretical** 

**Heat of** 

**Thermal** 

2 Frost(1963)

3 Cox and Cronenberg (1977) 4 Lundberg and Hobbins (1992) 5 at nitrogen pressure ≥ 0.25 MPa 6 Leitnaker & Godfrey (1967)

10 Faced-Centered Cubic (FCC)

7 UN(s)=U(l)+0.5N2(g), Gingerich (1969) 8 UN(s)=U(g)+0.5N2(g), Gingerich (1969) 9at 1000°C, Bowman et al.(1965;1966)

**Linear Expansion** 

in SuperCritical Water-Cooled Reactor (SCWR) Applications 133

on ceramic fuels. The ceramic fuels examined in this chapter are UO2, MOX, ThO2, UC, UN, UO2–SiC, UO2–C, and UO2–BeO. Further, these ceramic fuels can be classified into three categories: 1) low thermal-conductivity fuels, 2) enhanced thermal-conductivity fuels, and 3) high thermal-conductivity fuels. Low thermal-conductivity fuels are UO2, MOX, and ThO2. Enhanced thermal-conductivity fuels are UO2-SiC, UO2–C, and UO2–BeO; and high thermal-

**Property Unit UO2 MOX ThO2 UC UN** 

**Molecular Mass** amu 270.3 271.2 264 250.04 252.03

**density** kg/m3 10960 11,074 10,000 136302 14420

**Heat Capacity** J/kgK 235 240 235 2036 190

**Vaporization** kJ/kg 1530 1498 - 2120 <sup>11447</sup>

**Conductivity** W/mK 8.7 7.8 9.7 21.2 14.6

**Coefficient** 1/K 9.75×10‒<sup>6</sup> 9.43×10‒<sup>6</sup> 8.99×10‒6 10.1×10‒6 7.52×10‒<sup>6</sup>

**Crystal Structure** - FCC10 FCC FCC FCC FCC

In addition to the melting point of a fuel, the thermal conductivity of the fuel is a critical property that affects the operating temperature of the fuel under specific conditions. UO2 has been used as the fuel of choice in BWRs, PWRs, and CANDU reactors. The thermal conductivity of UO2 is between 2 and 3 W/m K within the operating temperature range of SCWRs. On the other hand, fuels such as UC and UN have significantly higher thermal conductivities compared to that of UO2 as shown in Fig. 9 (Cox and Cronenberg, 1977; Frost et al., 1963; IAEA, 2008; Ishimoto et al., 1995; Leitnaker and Godfrey, 1967; Khan et al., 2010, Kirillov et al., 2007; Lundberg and Hobbins, 1992; Solomon et al., 2005). Thus, under the same operating conditions, the fuel centerline temperature of high thermal conductivity

25073 2520 25324

2850±305

33258

**Melting Point** °C 2847±30 2750 3227±150

Table 2. Basic properties of selected fuels at 0.1 MPa and 25°C.

fuels should be lower than that of UO2 fuel.

Fig. 7. Re-entrant fuel channel with gaseous insulator.

Fig. 8. Re-entrant fuel channel with ceramic insulator.

#### **5. Nuclear fuels**

Nuclear fuels can be classified into two main categories; metallic fuels and ceramic fuels. The most common metallic fuels include uranium, plutonium, and thorium (Kirillov et al., 2007). The advantage of metallic fuels is their high thermal conductivity; however, they suffer from low melting points and also that the fuel undergoes phase change. The three phases in a metallic uranium fuel includes α-, β-, and γ-phase. A phase changes to another phase as a function of temperature, resulting in a volume change in the fuel. In addition, metallic fuels undergo oxidation when exposed to air or water. For use in high-temperature applications, a potential fuel must have a high melting point, high thermal conductivity, and good irradiation and mechanical stability (Ma, 1983). These requirements eliminate various nuclear fuels categorized under the metallic fuels mainly due to their low melting points and high irradiation creep and swelling rates (Ma, 1983). On the other hand, ceramic fuels have promising properties, which make these fuels suitable candidates for SCWR applications. Table 2 provides basic properties of selected fuels at 0.1 MPa and 25°C (Chirkin, 1968; IAEA, 2008; Frost, 1963; Cox and Cronenberg, 1977; Leitnaker and Godfrey, 1967; Lundberg and Hobbins, 1992).

In general, ceramic fuels have good dimensional and radiation stability and are chemically compatible with most coolants and sheath materials. Consequently, this section focuses only

Nuclear fuels can be classified into two main categories; metallic fuels and ceramic fuels. The most common metallic fuels include uranium, plutonium, and thorium (Kirillov et al., 2007). The advantage of metallic fuels is their high thermal conductivity; however, they suffer from low melting points and also that the fuel undergoes phase change. The three phases in a metallic uranium fuel includes α-, β-, and γ-phase. A phase changes to another phase as a function of temperature, resulting in a volume change in the fuel. In addition, metallic fuels undergo oxidation when exposed to air or water. For use in high-temperature applications, a potential fuel must have a high melting point, high thermal conductivity, and good irradiation and mechanical stability (Ma, 1983). These requirements eliminate various nuclear fuels categorized under the metallic fuels mainly due to their low melting points and high irradiation creep and swelling rates (Ma, 1983). On the other hand, ceramic fuels have promising properties, which make these fuels suitable candidates for SCWR applications. Table 2 provides basic properties of selected fuels at 0.1 MPa and 25°C (Chirkin, 1968; IAEA, 2008; Frost, 1963; Cox and Cronenberg, 1977; Leitnaker and Godfrey,

In general, ceramic fuels have good dimensional and radiation stability and are chemically compatible with most coolants and sheath materials. Consequently, this section focuses only

Fig. 7. Re-entrant fuel channel with gaseous insulator.

Fig. 8. Re-entrant fuel channel with ceramic insulator.

**5. Nuclear fuels** 

1967; Lundberg and Hobbins, 1992).

on ceramic fuels. The ceramic fuels examined in this chapter are UO2, MOX, ThO2, UC, UN, UO2–SiC, UO2–C, and UO2–BeO. Further, these ceramic fuels can be classified into three categories: 1) low thermal-conductivity fuels, 2) enhanced thermal-conductivity fuels, and 3) high thermal-conductivity fuels. Low thermal-conductivity fuels are UO2, MOX, and ThO2. Enhanced thermal-conductivity fuels are UO2-SiC, UO2–C, and UO2–BeO; and high thermalconductivity fuels are UC and UN.


Table 2. Basic properties of selected fuels at 0.1 MPa and 25°C.

In addition to the melting point of a fuel, the thermal conductivity of the fuel is a critical property that affects the operating temperature of the fuel under specific conditions. UO2 has been used as the fuel of choice in BWRs, PWRs, and CANDU reactors. The thermal conductivity of UO2 is between 2 and 3 W/m K within the operating temperature range of SCWRs. On the other hand, fuels such as UC and UN have significantly higher thermal conductivities compared to that of UO2 as shown in Fig. 9 (Cox and Cronenberg, 1977; Frost et al., 1963; IAEA, 2008; Ishimoto et al., 1995; Leitnaker and Godfrey, 1967; Khan et al., 2010, Kirillov et al., 2007; Lundberg and Hobbins, 1992; Solomon et al., 2005). Thus, under the same operating conditions, the fuel centerline temperature of high thermal conductivity fuels should be lower than that of UO2 fuel.

7 UN(s)=U(l)+0.5N2(g), Gingerich (1969)

<sup>2</sup> Frost(1963)

<sup>3</sup> Cox and Cronenberg (1977)

<sup>4</sup> Lundberg and Hobbins (1992)

<sup>5</sup> at nitrogen pressure ≥ 0.25 MPa 6 Leitnaker & Godfrey (1967)

<sup>8</sup> UN(s)=U(g)+0.5N2(g), Gingerich (1969) 9at 1000°C, Bowman et al.(1965;1966)

<sup>10</sup> Faced-Centered Cubic (FCC)

Thermal Aspects of Conventional and Alternative Fuels

UO2 fuel.

**5.1.2 ThO2**

Tsoulfanidis, 1999).

indicates temperature in Kelvin.

in SuperCritical Water-Cooled Reactor (SCWR) Applications 135

properties of MOX fuel compared with those of UO2 fuel. Nonetheless, the thermophysical

Most thermophysical properties of UO2 and MOX (3 – 5 % PuO2) have similar trends. For instance, thermal conductivities of UO2 and MOX fuels decrease as the temperature increases up to 1700°C (see Fig. 9). The most significant differences between these two fuels have been summarized in Table 2. Firstly, MOX fuel has a lower melting temperature, lower heat of fusion, and lower thermal conductivity than UO2 fuel. For the same power, MOX fuel has a higher stored energy which results in a higher fuel centerline temperature compared with UO2 fuel. Secondly, the density of MOX fuel is slightly higher than that of

The thermal conductivity of the fuel is of importance in the calculation of the fuel centerline temperature. The thermal conductivities of MOX and UO2 decrease as functions of temperature up to temperatures around 1527 – 1727°C, and then it increases as the temperature increases (see Fig. 9). In general, the thermal conductivity of MOX fuel is slightly lower than that of UO2. In other words, addition of small amounts of PuO2 decreases the thermal conductivity of the mixed oxide fuel. However, the thermal conductivity of MOX does not decrease significantly when the PuO2 content of the fuel is between 3 and 15%. But, the thermal conductivity of MOX fuel decreases as the concentration of PuO2 increases beyond 15%. As a result, the concentration of PuO2 in commercial MOX fuels is kept below 5% (Carbajo et al., 2001). Carbajo et al. (2001) recommended the following correlation shown as Eq. (2) for the calculation of the thermal conductivity of 95% TD MOX fuel. This correlation is valid for temperatures between 427 and 2827°C, *x* less than 0.05, and PuO2 concentrations between 3 and 15%. In Eq. (2), *T*

> -3 -3 5/2 <sup>6400</sup> ( ) exp , 2

*<sup>1</sup> <sup>T</sup> k T,x = <sup>+</sup> x= -O / M*

Currently, there is an interest in using thorium based fuels in nuclear reactors. Thorium is widely distributed in nature and is approximately three times as abundant as uranium. However, ThO2 does not have any fissile elements to fission with thermal neutrons. Consequently, ThO2 must be used in combination with a "driver" fuel (e.g., UO2 or UC), which has 235U as its initial fissile elements. The presence of a "driver" fuel such as UO2 in a nuclear-reactor core results in the production of enough neutrons, which in turn start the thorium cycle. In this cycle, 232Th is converted into 233Th, which decays to 233Pa. The latter element eventually results in the formation of 233U, which is a fissile element (Cochran and

In regards to PT reactors, there are two possibilities when ThO2 is used. One option is to place ThO2 and a "driver" fuel in different fuel channels. The separation between ThO2 fuel and the "driver" fuel allows ThO2 fuel to stay longer inside the core. The second option is to

*A x = x+* ( ) 2.58 0.035 (mK/W) ( ) -0.715 0.286 (m/K) *, C x = x+*

(10 ) (10 )

Where *x* is a function of oxygen to heavy metal ration and


*A+C T T* (2)

properties of MOX fuel should be selected when a study of the fuel is undertaken.

Fig. 9. Thermal conductivities of several fuels.

#### **5.1 Low Thermal-Conductivity Fuels: UO2, MOX, and ThO2**

#### **5.1.1 UO2 and MOX**

As a ceramic fuel, Uranium Dioxide (UO2) is a hard and brittle material due to its ionic or covalent interatomic bonding. In spite of that, the uranium dioxide fuel is currently used in PWRs, BWRs, and CANDU reactors because of its properties. Firstly, oxygen has a very low thermal-neutron absorption cross-section, which does not result in a serious loss of neutrons. Secondly, UO2 is chemically stable and does not react with water within the operating temperatures of these reactors. Thirdly, UO2 is structurally very stable. Additionally, the crystal structure of the UO2 fuel retains most of fission products even at high burn-up (Cochran and Tsoulfanidis, 1999). Moreover, UO2 has a high melting point; however, its thermal conductivity is very low, minimizing the possibility of using UO2 as a fuel of choice for SCWRs. The thermal conductivity of 95% Theoretical Density (TD) UO2 can be calculated using the Frank correlation, shown as Eq. (1) (Carbajo et al., 2001). This correlation is valid for temperatures in the range of 25 to 2847°C.

$$k\_{\rm{uo}\_2}(T) = \frac{100}{7.5408 + 17.692 \left(10^{-3} T\right) + 3.6142 \left(10^{-3} T\right)^2} + \frac{6400}{\left(10^{-3} T\right)^{5/2}} \exp^{-16.35/\left(10^{-3} T\right)}\tag{1}$$

Mixed Oxide (MOX) fuel refers to nuclear fuels consisting of UO2 and plutonium dioxide (PuO2). MOX fuel was initially designed for use in Liquid-Metal Fast Breeder Reactors (LMFBRs) and in LWRs when reprocessing and recycling of the used fuel is adopted (Cochran and Tsoulfanidis, 1999). The uranium dioxide content of MOX may be natural, enriched, or depleted uranium, depending on the application of MOX fuel. In general, MOX fuel contains between 3 and 5% PuO2 blended with 95 – 97 % natural or depleted uranium dioxide (Carbajo et al., 2001). The small fraction of PuO2 slightly changes the thermophysical properties of MOX fuel compared with those of UO2 fuel. Nonetheless, the thermophysical properties of MOX fuel should be selected when a study of the fuel is undertaken.

Most thermophysical properties of UO2 and MOX (3 – 5 % PuO2) have similar trends. For instance, thermal conductivities of UO2 and MOX fuels decrease as the temperature increases up to 1700°C (see Fig. 9). The most significant differences between these two fuels have been summarized in Table 2. Firstly, MOX fuel has a lower melting temperature, lower heat of fusion, and lower thermal conductivity than UO2 fuel. For the same power, MOX fuel has a higher stored energy which results in a higher fuel centerline temperature compared with UO2 fuel. Secondly, the density of MOX fuel is slightly higher than that of UO2 fuel.

The thermal conductivity of the fuel is of importance in the calculation of the fuel centerline temperature. The thermal conductivities of MOX and UO2 decrease as functions of temperature up to temperatures around 1527 – 1727°C, and then it increases as the temperature increases (see Fig. 9). In general, the thermal conductivity of MOX fuel is slightly lower than that of UO2. In other words, addition of small amounts of PuO2 decreases the thermal conductivity of the mixed oxide fuel. However, the thermal conductivity of MOX does not decrease significantly when the PuO2 content of the fuel is between 3 and 15%. But, the thermal conductivity of MOX fuel decreases as the concentration of PuO2 increases beyond 15%. As a result, the concentration of PuO2 in commercial MOX fuels is kept below 5% (Carbajo et al., 2001). Carbajo et al. (2001) recommended the following correlation shown as Eq. (2) for the calculation of the thermal conductivity of 95% TD MOX fuel. This correlation is valid for temperatures between 427 and 2827°C, *x* less than 0.05, and PuO2 concentrations between 3 and 15%. In Eq. (2), *T* indicates temperature in Kelvin.

$$k(T, \mathbf{x}) = \frac{1}{A + \text{C}(10^{-3}T)} + \frac{6400}{\text{(10}^3 T)^{5/2}} \exp^{-16.35/(10^{-3}T)}, \quad \mathbf{x} = \mathbf{2} \text{ - O } / M \tag{2}$$

Where *x* is a function of oxygen to heavy metal ration and

$$A(\mathbf{x}) = 2.58\mathbf{x} + 0.035 \quad \text{(mK/W)}, \quad C(\mathbf{x}) = -0.715\mathbf{x} + 0.286 \quad \text{(m/K)}$$

#### **5.1.2 ThO2**

134 Nuclear Reactors

As a ceramic fuel, Uranium Dioxide (UO2) is a hard and brittle material due to its ionic or covalent interatomic bonding. In spite of that, the uranium dioxide fuel is currently used in PWRs, BWRs, and CANDU reactors because of its properties. Firstly, oxygen has a very low thermal-neutron absorption cross-section, which does not result in a serious loss of neutrons. Secondly, UO2 is chemically stable and does not react with water within the operating temperatures of these reactors. Thirdly, UO2 is structurally very stable. Additionally, the crystal structure of the UO2 fuel retains most of fission products even at high burn-up (Cochran and Tsoulfanidis, 1999). Moreover, UO2 has a high melting point; however, its thermal conductivity is very low, minimizing the possibility of using UO2 as a fuel of choice for SCWRs. The thermal conductivity of 95% Theoretical Density (TD) UO2 can be calculated using the Frank correlation, shown as Eq. (1) (Carbajo et al., 2001). This


Mixed Oxide (MOX) fuel refers to nuclear fuels consisting of UO2 and plutonium dioxide (PuO2). MOX fuel was initially designed for use in Liquid-Metal Fast Breeder Reactors (LMFBRs) and in LWRs when reprocessing and recycling of the used fuel is adopted (Cochran and Tsoulfanidis, 1999). The uranium dioxide content of MOX may be natural, enriched, or depleted uranium, depending on the application of MOX fuel. In general, MOX fuel contains between 3 and 5% PuO2 blended with 95 – 97 % natural or depleted uranium dioxide (Carbajo et al., 2001). The small fraction of PuO2 slightly changes the thermophysical


*T TT* (1)

Fig. 9. Thermal conductivities of several fuels.

**5.1.1 UO2 and MOX** 

2

**5.1 Low Thermal-Conductivity Fuels: UO2, MOX, and ThO2** 

correlation is valid for temperatures in the range of 25 to 2847°C.

Currently, there is an interest in using thorium based fuels in nuclear reactors. Thorium is widely distributed in nature and is approximately three times as abundant as uranium. However, ThO2 does not have any fissile elements to fission with thermal neutrons. Consequently, ThO2 must be used in combination with a "driver" fuel (e.g., UO2 or UC), which has 235U as its initial fissile elements. The presence of a "driver" fuel such as UO2 in a nuclear-reactor core results in the production of enough neutrons, which in turn start the thorium cycle. In this cycle, 232Th is converted into 233Th, which decays to 233Pa. The latter element eventually results in the formation of 233U, which is a fissile element (Cochran and Tsoulfanidis, 1999).

In regards to PT reactors, there are two possibilities when ThO2 is used. One option is to place ThO2 and a "driver" fuel in different fuel channels. The separation between ThO2 fuel and the "driver" fuel allows ThO2 fuel to stay longer inside the core. The second option is to

Thermal Aspects of Conventional and Alternative Fuels

*T* is in degrees Kelvin.

temperatures.

in SuperCritical Water-Cooled Reactor (SCWR) Applications 137

4 2 12 3

In addition to Eqs. (6) and (8), Kirillov et al. (2007) have recommended another correlation, shown as Eqs. (9) and (10), for the calculation of the thermal conductivity of UC in W/m K. In the current study, Eq. (21) have been used to determine the thermal conductivity of UC for the calculation of the UC fuel centerline temperature at SCWR conditions, because this equation provides the lowest thermal conductivity values for a wide temperature range, leading to a conservative calculation of the fuel centerline temperature. In Eqs. (9) and (10),

Frost (1963) developed a correlation shown as Eq. (11), which can be used to determine the diametric increase of UC fuel as a function of time-averaged fuel centerline temperature. According to Eq. (11), UC fuel undergoes significant swelling for temperatures above 1000°C. In Eq. (11), *R*D and *T* are percent diametric increase per atom % burn-up and timeaveraged fuel centerline temperature in K, respectively. In addition, as shown in Fig. 10, Harrison (1969) provided the volumetric swelling of UC as a function of burn-up for various

Fig. 10. Volumetric swelling of UC as function of temperature and burn-up.



= 10 5.75 10 +1.25 10 ( -273.15) *<sup>T</sup>* (5)

<sup>182</sup> *k T* = 100 2.04 10 +2.836 10 ( - 843.15) (6)

= 10 5.7 10 +1.82 10 ( -1123.15) *<sup>T</sup>* (7)

18 2 *k T* = 100 1.95 10 +3.57 10 ( -1123.15) (8)

4 26

enclose ThO2 and the "driver" in same fuel bundles, which are placed inside the fuel channels throughout the reactor core. This option requires the enrichment of the "driver" fuel since it has to be irradiated as long as ThO2 fuel stays inside the core (IAEA, 2005). Nevertheless, the current study considers the thermal aspects of one single fuel channel, which consists of ThO2 fuel bundles (i.e., first Option). However, this assumption does not suggest that the whole core is composed of fuel channels containing ThO2.

The use of thorium based fuels in nuclear reactors requires information on the thermophysical properties of these fuels, especially thermal conductivity. Jain et al. (2006) conducted experiments on thorium dioxide (ThO2). In their analysis, the thermal conductivity values were calculated based on Eq. (3), which requires the measured values of the density, thermal diffusivity, and specific heat of ThO2. These properties were measured for temperatures between 100 and 1500°C (Jain et al., 2006). In the current study, the correlation developed by Jain et al. (2006), which is shown as Eq. (4), has been used.

$$k = a\rho c\_p \tag{3}$$

$$k\_{\rm ThO\_2} = \frac{1}{0.0327 + 1.603 \times 10^{-4} \, T} \tag{4}$$

#### **5.2 High Thermal-Conductivity Fuels: UC and UN**

#### **5.2.1 UC**

From a heat transfer point of view, there is an interest on carbides of uranium as nuclear fuels due to their high thermal conductivities and high melting points. Carbides of uranium usable for nuclear fuels are Uranium Carbide (UC) and Uranium Dicarbide (UC2). For instance, UC has been proposed as the fuel of choice for a SCWR concept in Russia (Pioro and Duffey, 2007). Uranium sesquicarbide (U2C3) is another carbide of uranium; however, it cannot be manufactured through casting or compaction of a powder. However, UC2 may transform to U2C3 at high temperatures and under stress (Frost, 1963).

UC, which has a Faced-Centered Cubic (FCC) crystal structure similar to those of UN and NaCl, has a high melting point approximately 2507°C and a high thermal conductivity, above 19 W/m K at all temperatures up to the melting point. UC has a density of 13630 kg/ m3, which is lower than that of UN but higher than those of UO2. It should be noted that the density of hypo-stoichiometric UC is slightly higher than that of stoichiometric UC, which is listed in Table 2. Coninck et al. (1975) reported densities between 13730 and 13820 kg/m3 at 25°C for hypo-stoichiometric UC. Moreover, UC has a higher uranium atom density compared to UO2 but lower than that of UN. The uranium atom densities of UC and UN are 1.34 and 1.4 times that of UO2, respectively.

For hypo-stoichiometric UC, the thermal diffusivity *α*, in m2/s, and thermal conductivity *k*, in W/m K, correlations are valid for a temperature range of 570 and 2000°C. In Eqs. (5) and (6), *T* is in degrees Kelvin (Coninck et al., 1975). For stoichiometric UC, Coninck et al. (1975) provided two correlations, shown as Eqs. (7) and (8), which can be used to determine the mean values of the thermal diffusivity and thermal conductivity of stoichiometric UC for a temperature range between 850 and 2250°C, in m2/s and W/m K, respectively.

enclose ThO2 and the "driver" in same fuel bundles, which are placed inside the fuel channels throughout the reactor core. This option requires the enrichment of the "driver" fuel since it has to be irradiated as long as ThO2 fuel stays inside the core (IAEA, 2005). Nevertheless, the current study considers the thermal aspects of one single fuel channel, which consists of ThO2 fuel bundles (i.e., first Option). However, this assumption does not

The use of thorium based fuels in nuclear reactors requires information on the thermophysical properties of these fuels, especially thermal conductivity. Jain et al. (2006) conducted experiments on thorium dioxide (ThO2). In their analysis, the thermal conductivity values were calculated based on Eq. (3), which requires the measured values of the density, thermal diffusivity, and specific heat of ThO2. These properties were measured for temperatures between 100 and 1500°C (Jain et al., 2006). In the current study, the

*<sup>p</sup> k = α ρc* (3)

*T* (4)

correlation developed by Jain et al. (2006), which is shown as Eq. (4), has been used.

ThO2 -4 <sup>1</sup> <sup>=</sup>

From a heat transfer point of view, there is an interest on carbides of uranium as nuclear fuels due to their high thermal conductivities and high melting points. Carbides of uranium usable for nuclear fuels are Uranium Carbide (UC) and Uranium Dicarbide (UC2). For instance, UC has been proposed as the fuel of choice for a SCWR concept in Russia (Pioro and Duffey, 2007). Uranium sesquicarbide (U2C3) is another carbide of uranium; however, it cannot be manufactured through casting or compaction of a powder. However, UC2 may

UC, which has a Faced-Centered Cubic (FCC) crystal structure similar to those of UN and NaCl, has a high melting point approximately 2507°C and a high thermal conductivity, above 19 W/m K at all temperatures up to the melting point. UC has a density of 13630 kg/ m3, which is lower than that of UN but higher than those of UO2. It should be noted that the density of hypo-stoichiometric UC is slightly higher than that of stoichiometric UC, which is listed in Table 2. Coninck et al. (1975) reported densities between 13730 and 13820 kg/m3 at 25°C for hypo-stoichiometric UC. Moreover, UC has a higher uranium atom density compared to UO2 but lower than that of UN. The uranium atom densities of UC and UN are

For hypo-stoichiometric UC, the thermal diffusivity *α*, in m2/s, and thermal conductivity *k*, in W/m K, correlations are valid for a temperature range of 570 and 2000°C. In Eqs. (5) and (6), *T* is in degrees Kelvin (Coninck et al., 1975). For stoichiometric UC, Coninck et al. (1975) provided two correlations, shown as Eqs. (7) and (8), which can be used to determine the mean values of the thermal diffusivity and thermal conductivity of stoichiometric UC for a

temperature range between 850 and 2250°C, in m2/s and W/m K, respectively.

0.0327+1.603×10

suggest that the whole core is composed of fuel channels containing ThO2.

*k*

transform to U2C3 at high temperatures and under stress (Frost, 1963).

**5.2 High Thermal-Conductivity Fuels: UC and UN** 

1.34 and 1.4 times that of UO2, respectively.

**5.2.1 UC** 

$$\alpha = 10^{-4} \cdot \left[ 5.75 \cdot 10^{-2} + 1.25 \cdot 10^{-6} (T \cdot 273.15) \right] \tag{5}$$

$$k = 100 \cdot \left[ 2.04 \cdot 10^{-1} + 2.836 \cdot 10^{-8} (T - 843.15)^2 \right] \tag{6}$$

$$\alpha = 10^{-4} \cdot \left[ 5.7 \cdot 10^{-2} + 1.82 \cdot 10^{-12} (T \cdot 1123.15)^3 \right] \tag{7}$$

$$k = 100 \cdot \left[ 1.95 \cdot 10^{-1} \text{+3.57} \cdot 10^{-8} \text{(T-1123.15)}^2 \right] \tag{8}$$

In addition to Eqs. (6) and (8), Kirillov et al. (2007) have recommended another correlation, shown as Eqs. (9) and (10), for the calculation of the thermal conductivity of UC in W/m K. In the current study, Eq. (21) have been used to determine the thermal conductivity of UC for the calculation of the UC fuel centerline temperature at SCWR conditions, because this equation provides the lowest thermal conductivity values for a wide temperature range, leading to a conservative calculation of the fuel centerline temperature. In Eqs. (9) and (10), *T* is in degrees Kelvin.

$$k = 21.7 \text{ - } 3.04 \cdot 10^{-3} \text{ (T - 273.15)} + 3.61 \cdot 10^{-6} \text{ (T - 273.15)}^2, \quad 323 \text{ < T \le 973 K} \tag{9}$$

$$k = 20.2 + 1.48 \times 10^{-3} \text{(T-273.15)}, \quad 973 \text{$$

Frost (1963) developed a correlation shown as Eq. (11), which can be used to determine the diametric increase of UC fuel as a function of time-averaged fuel centerline temperature. According to Eq. (11), UC fuel undergoes significant swelling for temperatures above 1000°C. In Eq. (11), *R*D and *T* are percent diametric increase per atom % burn-up and timeaveraged fuel centerline temperature in K, respectively. In addition, as shown in Fig. 10, Harrison (1969) provided the volumetric swelling of UC as a function of burn-up for various temperatures.

Fig. 10. Volumetric swelling of UC as function of temperature and burn-up.

Thermal Aspects of Conventional and Alternative Fuels

ΔV

in SuperCritical Water-Cooled Reactor (SCWR) Applications 139

2.36

1 *CLT <sup>B</sup> <sup>T</sup> <sup>ρ</sup>*


Fig. 11. Percent volumetric swelling of UN as function of burn-up and temperature.

Currently, there is a high interest in developing high thermal-conductivity fuels, and improving the thermal conductivity of low thermal-conductivity fuels such as UO2. High thermal conductivities result in lower fuel centerline temperatures and limit the release of gaseous fission products (Hollenbach and Ott, 2010). As shown previously, UO2 has a very low thermal conductivity at high temperatures compared to other fuels such as UC and UN. However, there is a possibility to increase the thermal conductivity of UO2. This increase in the thermal conductivity of UO2 can be performed either by adding a continuous solid phase or long, thin fibbers of a high thermal-conductivity material (Hollenbach and Ott,

A high thermal-conductivity material must have a low thermal-neutron absorption crosssection, assuming that the fuel will be used in a thermal-spectrum nuclear reactor (Hollenbach and Ott, 2010). In addition, it must have a high melting point and be chemically compatible with the fuel, the cladding, and the coolant. The need to meet these requirements narrows the potential materials to silicon carbide (SiC), beryllium oxide (BeO), and graphite (C). The following sections provide some information about UO2 fuel composed of the

The thermal conductivity of UO2 fuel can be improved by incorporating silicon carbide (SiC) into the matrix of the fuel. SiC has a high melting point approximately at 2800°C, high thermal conductivity (78 W/m K at 727°C), high corrosion resistance even at high temperatures, low

**5.3 Composite fuels with enhanced thermal-conductivity** 

aforementioned high thermal-conductivity materials.

2010; Solomon et al., 2005).

**5.3.1 UO2 - SiC** 

%TD

(14)

0.82

$$R\_{\rm p} = 0.6 + 0.77 \left(\frac{9 \cdot T}{5000} \cdot 1\right) \tag{11}$$

#### **5.2.2 UN**

Uranium mononitride or uranium nitride (UN), which is a ceramic fuel, can be produced by the carbothermic reduction of uranium dioxide plus carbon in nitrogen. This process produces UN with densities in the range of 65 to 90% of TD (Shoup and Grace, 1977). UN has a high melting point, high thermal conductivity, and high radiation stability. These properties enhance the safety of operation and allow the fuel to achieve high burn-ups (IAEA, 2008). In addition, UN has the highest fissile atom density, which is approximately 1.4 times that of UO2 and greater than those of other examined fuels. In other words, when UN is used as a fuel, a smaller volume of fuel is required, which leads to a smaller core. In contrast, one disadvantage of the UN fuel is that under some conditions it decomposes to liquid uranium and gaseous nitrogen (IAEA, 2008), which in turn results in the formation of cracks in the fuel. These cracks increase the chance of the release of gaseous fission products. In addition, the formation of cracks in nuclear fuels has adverse effects on their mechanical and thermophysical properties.

Hayes et al. (1990a) developed a correlation shown as Eq. (12), which calculates the thermal conductivity of UN, in W/m K. This correlation, which is a function of both temperature and percent porosity, can be applied when porosity changes between 0 and 20% for temperatures in the range of 25°C and 1650°C (Hayes et al., 1990a). The standard deviation of the Hayes et al. correlation is ±2.3%.

$$k = 1.864 \exp(-2.14 \text{ P}) \, T^{0.361} \tag{12}$$

Irradiation swelling, growth, and creep are the primary effects of irradiation on a nuclear fuel. Irradiation swelling results in volumetric instability of the fuel at high temperatures while irradiation growth causes dimensional instability of the fuel at temperatures lower than 2/3 of the melting point of the fuel (Ma, 1983). In addition to dimensional and volumetric instability, a continuous and plastic deformation of the fuel due to creep may adversely affect its mechanical properties. Thus, it is required to study the behaviour of the fuel under irradiation specifically the irradiation-induced swelling, irradiation-induced growth and irradiation-induced creep of the fuel.

Ross et al. (1990) developed a correlation for the prediction of percent volumetric swelling of UN fuel. This correlation is shown as Eq. (13), where *T*avg is the volume average fuel temperature in K, *B* is the fuel burn-up in MW day/M g(U), and *ρ*%TD is the percent theoretical density of the fuel (e.g., *ρ*%TD equals to 0.95 for a fuel with 5% porosity). In addition to this correlation, the volumetric swelling of UN can be calculated based on fuel centerline temperature using Eq. (14) (Ross et al., 1990). The uncertainty associated with Eq. (14) is ±25% for burn-ups above 10,000 MW day/Mg (U) while at lower burn-ups the uncertainty increases to ±60% (Ross et al., 1990). Figure 11 shows the volume expansion of 95% TD UN based on Eq. (14).

$$
\Delta \text{V/V(\%)} = 4.7 \cdot 10^{-11} \, T\_{\text{avg}}^{312} \left( \frac{B}{9008.1} \right)^{0.83} \rho\_{\text{\*} \text{m}}^{0.5} \tag{13}
$$

<sup>9</sup> = 0.6 + 0.77 - 1

*<sup>T</sup> <sup>R</sup>*

Uranium mononitride or uranium nitride (UN), which is a ceramic fuel, can be produced by the carbothermic reduction of uranium dioxide plus carbon in nitrogen. This process produces UN with densities in the range of 65 to 90% of TD (Shoup and Grace, 1977). UN has a high melting point, high thermal conductivity, and high radiation stability. These properties enhance the safety of operation and allow the fuel to achieve high burn-ups (IAEA, 2008). In addition, UN has the highest fissile atom density, which is approximately 1.4 times that of UO2 and greater than those of other examined fuels. In other words, when UN is used as a fuel, a smaller volume of fuel is required, which leads to a smaller core. In contrast, one disadvantage of the UN fuel is that under some conditions it decomposes to liquid uranium and gaseous nitrogen (IAEA, 2008), which in turn results in the formation of cracks in the fuel. These cracks increase the chance of the release of gaseous fission products. In addition, the formation of cracks in nuclear fuels has adverse effects on their mechanical

Hayes et al. (1990a) developed a correlation shown as Eq. (12), which calculates the thermal conductivity of UN, in W/m K. This correlation, which is a function of both temperature and percent porosity, can be applied when porosity changes between 0 and 20% for temperatures in the range of 25°C and 1650°C (Hayes et al., 1990a). The standard deviation

Irradiation swelling, growth, and creep are the primary effects of irradiation on a nuclear fuel. Irradiation swelling results in volumetric instability of the fuel at high temperatures while irradiation growth causes dimensional instability of the fuel at temperatures lower than 2/3 of the melting point of the fuel (Ma, 1983). In addition to dimensional and volumetric instability, a continuous and plastic deformation of the fuel due to creep may adversely affect its mechanical properties. Thus, it is required to study the behaviour of the fuel under irradiation specifically the irradiation-induced swelling, irradiation-induced

Ross et al. (1990) developed a correlation for the prediction of percent volumetric swelling of UN fuel. This correlation is shown as Eq. (13), where *T*avg is the volume average fuel temperature in K, *B* is the fuel burn-up in MW day/M g(U), and *ρ*%TD is the percent theoretical density of the fuel (e.g., *ρ*%TD equals to 0.95 for a fuel with 5% porosity). In addition to this correlation, the volumetric swelling of UN can be calculated based on fuel centerline temperature using Eq. (14) (Ross et al., 1990). The uncertainty associated with Eq. (14) is ±25% for burn-ups above 10,000 MW day/Mg (U) while at lower burn-ups the uncertainty increases to ±60% (Ross et al., 1990). Figure 11 shows the volume expansion of

3.12


avg %TD

1 *<sup>B</sup> <sup>T</sup> <sup>ρ</sup>*

0.83

(13)

0.361 *k* = 1.864 exp(-2.14 ) *P T* (12)

5000

(11)

D

**5.2.2 UN** 

and thermophysical properties.

of the Hayes et al. correlation is ±2.3%.

growth and irradiation-induced creep of the fuel.

ΔV

95% TD UN based on Eq. (14).

$$
\Delta \text{V/V(\%)} = 1.16 \cdot 10^{-8} \, T\_{\text{<1T}}^{236} \left( \frac{B}{9008.1} \right)^{0.82} \rho\_{\text{\textdegree m}}^{0.5} \tag{14}
$$

Fig. 11. Percent volumetric swelling of UN as function of burn-up and temperature.

### **5.3 Composite fuels with enhanced thermal-conductivity**

Currently, there is a high interest in developing high thermal-conductivity fuels, and improving the thermal conductivity of low thermal-conductivity fuels such as UO2. High thermal conductivities result in lower fuel centerline temperatures and limit the release of gaseous fission products (Hollenbach and Ott, 2010). As shown previously, UO2 has a very low thermal conductivity at high temperatures compared to other fuels such as UC and UN. However, there is a possibility to increase the thermal conductivity of UO2. This increase in the thermal conductivity of UO2 can be performed either by adding a continuous solid phase or long, thin fibbers of a high thermal-conductivity material (Hollenbach and Ott, 2010; Solomon et al., 2005).

A high thermal-conductivity material must have a low thermal-neutron absorption crosssection, assuming that the fuel will be used in a thermal-spectrum nuclear reactor (Hollenbach and Ott, 2010). In addition, it must have a high melting point and be chemically compatible with the fuel, the cladding, and the coolant. The need to meet these requirements narrows the potential materials to silicon carbide (SiC), beryllium oxide (BeO), and graphite (C). The following sections provide some information about UO2 fuel composed of the aforementioned high thermal-conductivity materials.

#### **5.3.1 UO2 - SiC**

The thermal conductivity of UO2 fuel can be improved by incorporating silicon carbide (SiC) into the matrix of the fuel. SiC has a high melting point approximately at 2800°C, high thermal conductivity (78 W/m K at 727°C), high corrosion resistance even at high temperatures, low

Thermal Aspects of Conventional and Alternative Fuels

UO2–BeO fuel with 13.6 wt% of BeO has been examined.

**6. Fuel centerline temperature calculations** 

UO2 (Solomon et al., 2005).

step shown in Fig. 12.

11 It might be as high as 850°C.

in SuperCritical Water-Cooled Reactor (SCWR) Applications 141

alloys. In addition to its chemical compatibility, BeO is insoluble with UO2 at temperatures up to 2160°C. As a result, BeO remains as a continuous second solid phase in the UO2 fuel matrix while being in good contact with UO2 molecules at the grain boundaries. BeO has desirable thermochemical and neutronic properties, which have resulted in the use of BeO in aerospace, electrical and nuclear applications. For example, BeO has been used as the moderator and the reflector in some nuclear reactors. However, the major concern with beryllium is its toxicity. But, the requirements for safe handling of BeO are similar to those of UO2. Therefore, the toxicity of BeO is not a limiting factor in the use of this material with

Similar to other enhanced thermal-conductivity fuels, the thermal conductivity of UO2 can be increased by introducing a continuous phase of BeO at the grain boundaries. The effects of the present of such second solid phase on the thermal conductivity of UO2 is significant such that only 10% by volume of BeO would improve the thermal conductivity of the composite fuel by 50% compared to that of UO2 with 95% TD. For the purpose of this study,

In order to calculate the fuel centerline temperature, steady-state one-dimensional heattransfer analysis was conducted. The MATLAB and NIST REFPROP software were used for programming and retrieving thermophysical properties of a light-water coolant, respectively. First, the heated length of the fuel channel was divided into small segments of one-millimeter lengths. Second, the temperature profile of the coolant was calculated. Third, sheath-outer and inner surface temperatures were calculated. Fourth, the heat transfer through the gap between the sheath and the fuel was determined and used to calculate the outer surface temperature of the fuel. Finally, the temperature of the fuel in the radial and axial directions was calculated. It should be noted that the radius of the fuel pellet was divided into 20 segments. The results will be presented for fuel-sheath gap widths of zero, 20 *μ*m and 36 *μ*m. Moreover, the fuel centerline temperature profiles have been calculated based on a no-gap condition in order to determine the effect of gap conductance on the fuel centerline temperature. Figure 12 illustrates the methodology based on which fuel centerline temperature was calculated. The following section provides more information about each

As shown in Fig. 12, the convective heat transfer between the sheath and the coolant is the only heat transfer mode which has been taken directly into consideration. In radiative heat transfer, energy is transferred in the form of electromagnetic waves. Unlike convection and conduction heat transfer modes in which the rate of heat transfer is linearly proportional to temperature differences, a radiative heat transfer depends on the difference between absolute temperatures to the fourth power. The sheath temperature is high11 at SCWR

In the case of the sheath and the coolant, the radiative heat transfer has been taken into consideration in the Nusselt number correlation, which has been used to calculate the HTC. In general, the Nusselt number correlations are empirical equations, which are developed

conditions; therefore, it is necessary to take into account the radiative heat transfer.

thermal neutron absorption, and dimensional stability (Khan et al., 2010). Therefore, when used with UO2, SiC can address the problem of low thermal conductivity of UO2 fuel.

Calculation of the thermal conductivity of UO2 plus SiC the fuel falls under the theories of composites. Generally, theories contemplating the thermal conductivity of composites are classified into two categories. One category assumes that inclusions are randomly distributed in a homogeneous mixture. The effective thermal conductivities of the composites, based on the aforementioned principle, are formulated by Maxwell. The other category, which is based on the work performed by Rayleigh, assumes that particles are distributed in a regular manner within the matrix.

Khan et al. (2010) provided the thermal conductivity of UO2–SiC fuel as a function of temperature and weight percent of SiC. Khan et al. (2010) assumed that the thin coat of SiC covered UO2 particles and determined the thermal conductivity of the composite fuel for three cases. The results of the study conducted by Khan et al. (2010) indicate that the continuity of SiC layer leads to a relatively significant increase in thermal conductivity. However, the discontinuity of SiC resulted in little improvement in the ETC of the fuel. Thus, the addition of a continuous solid phase of SiC to UO2 fuel increases the effective thermal conductivity of the fuel. In the present study, UO2–SiC fuel with 12wt% SiC with an overall 97 percent TD has been examined and its thermal conductivity has been calculated using Eq. (15).

$$k\_{\rm eff} = 9.59 \cdot 10^{-9} \, T^3 + 4.29 \cdot 10^{-5} \, T^2 - 6.87 \cdot 10^{-2} \, T + 4.68 \cdot 10 \tag{15}$$

#### **5.3.2 UO2-C**

Hollenbach and Ott (2010) studied the effects of the addition of graphite fibbers on thermal conductivity of UO2 fuel. Theoretically, the thermal conductivity of graphite varies along different crystallographic planes. For instance, the thermal conductivity of perfect graphite along basal planes is more than 2000 W/m K (Hollenbach and Ott, 2010). On the other hand, it is less than 10 W/m K in the direction perpendicular to the basal planes. Hollenbach and Ott (2010) performed computer analyses in order to determine the effectiveness of adding long, thin fibbers of high thermal-conductivity materials to low thermal-conductivity materials to determine the effective thermal conductivity. In their studies, the high thermalconductivity material had a thermal conductivity of 2000 W/m K along the axis, and a thermal conductivity of 10 W/m K radially, similar to perfect graphite. The low thermalconductivity material had properties similar to UO2 (e.g., with 95% TD at ~1100°C) with a thermal conductivity of 3 W/m K.

Hollenbach and Ott (2010) examined the effective thermal conductivity of the composite for various volume percentages of the high thermal-conductivity material, varying from 0 to 3%. The results show if the amount of the high thermal-conductivity material increases to 2 % by volume, the effective thermal conductivity of the composite reaches the range of high thermal-conductivity fuels, such as UC and UN.

#### **5.3.3 UO2–BeO**

Beryllium Oxide (BeO) is a metallic oxide with a very high thermal conductivity. BeO is chemically compatible with water, UO2, and most sheath materials including zirconium

thermal neutron absorption, and dimensional stability (Khan et al., 2010). Therefore, when

Calculation of the thermal conductivity of UO2 plus SiC the fuel falls under the theories of composites. Generally, theories contemplating the thermal conductivity of composites are classified into two categories. One category assumes that inclusions are randomly distributed in a homogeneous mixture. The effective thermal conductivities of the composites, based on the aforementioned principle, are formulated by Maxwell. The other category, which is based on the work performed by Rayleigh, assumes that particles are

Khan et al. (2010) provided the thermal conductivity of UO2–SiC fuel as a function of temperature and weight percent of SiC. Khan et al. (2010) assumed that the thin coat of SiC covered UO2 particles and determined the thermal conductivity of the composite fuel for three cases. The results of the study conducted by Khan et al. (2010) indicate that the continuity of SiC layer leads to a relatively significant increase in thermal conductivity. However, the discontinuity of SiC resulted in little improvement in the ETC of the fuel. Thus, the addition of a continuous solid phase of SiC to UO2 fuel increases the effective thermal conductivity of the fuel. In the present study, UO2–SiC fuel with 12wt% SiC with an overall 97 percent TD has

Hollenbach and Ott (2010) studied the effects of the addition of graphite fibbers on thermal conductivity of UO2 fuel. Theoretically, the thermal conductivity of graphite varies along different crystallographic planes. For instance, the thermal conductivity of perfect graphite along basal planes is more than 2000 W/m K (Hollenbach and Ott, 2010). On the other hand, it is less than 10 W/m K in the direction perpendicular to the basal planes. Hollenbach and Ott (2010) performed computer analyses in order to determine the effectiveness of adding long, thin fibbers of high thermal-conductivity materials to low thermal-conductivity materials to determine the effective thermal conductivity. In their studies, the high thermalconductivity material had a thermal conductivity of 2000 W/m K along the axis, and a thermal conductivity of 10 W/m K radially, similar to perfect graphite. The low thermalconductivity material had properties similar to UO2 (e.g., with 95% TD at ~1100°C) with a

Hollenbach and Ott (2010) examined the effective thermal conductivity of the composite for various volume percentages of the high thermal-conductivity material, varying from 0 to 3%. The results show if the amount of the high thermal-conductivity material increases to 2 % by volume, the effective thermal conductivity of the composite reaches the range of high

Beryllium Oxide (BeO) is a metallic oxide with a very high thermal conductivity. BeO is chemically compatible with water, UO2, and most sheath materials including zirconium


been examined and its thermal conductivity has been calculated using Eq. (15).

used with UO2, SiC can address the problem of low thermal conductivity of UO2 fuel.

distributed in a regular manner within the matrix.

**5.3.2 UO2-C** 

**5.3.3 UO2–BeO** 

thermal conductivity of 3 W/m K.

thermal-conductivity fuels, such as UC and UN.

alloys. In addition to its chemical compatibility, BeO is insoluble with UO2 at temperatures up to 2160°C. As a result, BeO remains as a continuous second solid phase in the UO2 fuel matrix while being in good contact with UO2 molecules at the grain boundaries. BeO has desirable thermochemical and neutronic properties, which have resulted in the use of BeO in aerospace, electrical and nuclear applications. For example, BeO has been used as the moderator and the reflector in some nuclear reactors. However, the major concern with beryllium is its toxicity. But, the requirements for safe handling of BeO are similar to those of UO2. Therefore, the toxicity of BeO is not a limiting factor in the use of this material with UO2 (Solomon et al., 2005).

Similar to other enhanced thermal-conductivity fuels, the thermal conductivity of UO2 can be increased by introducing a continuous phase of BeO at the grain boundaries. The effects of the present of such second solid phase on the thermal conductivity of UO2 is significant such that only 10% by volume of BeO would improve the thermal conductivity of the composite fuel by 50% compared to that of UO2 with 95% TD. For the purpose of this study, UO2–BeO fuel with 13.6 wt% of BeO has been examined.
