The reactor core calculation is carried out by the N-TH coupled core calculation, presented in the list [8] of Sect. 2.1.5, to evaluate properties in normal operation of the reactor. The concept of core design calculation and the calculation model are discussed here.

[1] Heat transfer calculation in single channel model

Figure 2.27 depicts a 1D cylindrical model to describe one fuel rod and its surrounding coolant with an equivalent flow path. It is called the single channel model and it is the basic model used in the core thermal-hydraulic calculation and the plant characteristics calculation. The thermal-hydraulic properties in the core can be calculated on the single channel model where the heat generated from fuel pellets is transferred to coolant which is transported with a temper­ature rise.

The radial heat transfer model is composed of fuel pellet, gap, cladding, and coolant. The radial heat conduction or convection between those components is considered in each axial region and then the axial heat transport by coolant or moderator is examined. The mass and energy conservation equations and the state equation are solved in each axial region in turn from the top of the upward coolant flow. The momentum conservation equation is also solved to evaluate the pressure drop. The axial heat conduction of the fuel pellet is ignored. This

Cladding

Pellet

Convection Model

Fig. 2.27 Single-channel heat transfer calculation model

assumption is valid because the radial temperature gradient is several orders of magnitude larger than the axial one.

The difference between the fuel average temperature and the cladding surface temperature is expressed as

(2.110)

where,

kf: average thermal conductivity of pellet (W/m-K)

hg: gap conductance (W/m — K)

kc: thermal conductivity of cladding (W/m-K)

Q": heat flux from pellet (W/m2)

rf: pellet radius (m)

tc: cladding thickness (m)

jave: pellet average temperature (K)

Ts: cladding surface temperature (K).

The terms inside the RHS square brackets represent the temperature drop in fuel, gap, and cladding, respectively.

The heat transfer from cladding surface to coolant is described by Newtons law of cooling

q"(rc) = hc(Ts-T)

where,

hc: heat transfer coefficient between cladding surface and coolant (W/m2-K) rc: cladding radius (m)

Ts: cladding surface temperature (K)

T: coolant bulk temperature (K).

The heat transfer coefficient hc can be evaluated using the Dittus-Boelter correlation for single-phase flow and the Thom correlation or the Jens-Lottes correlation for nucleate boiling.

Water rods are often implemented into fuel assemblies, especially for BWRs. The heat transfer characteristics of the water rod can also be calculated using the single channel model. Figure 2.28 describes the heat transfer calculation model with two single channels of fuel rod and water rod. The heat from coolant is transferred through the water rod wall into the moderator.

The heat transfer of the water rod is also represented by Newton’s law of cooling. The temperature difference between the coolant in the fuel rod channel and the moderator in the water rod channel is expressed as

where,

T: coolant temperature in fuel rod channel (K)

Tw: moderator temperature in water rod channel (K)

Dw: hydraulic diameter of water rod

hs1: heat transfer coefficient between coolant and outer surface of water rod (W/m2-K)

hs2: heat transfer coefficient between inner surface of water rod and moderator (W/m2-K)

Nf. number of fuel rods per fuel assembly Nw: number of water rods per fuel assembly Q ’ w: linear heat from coolant to water rod (W/m) tws: thickness of water rod (m)

The terms inside of the RHS square brackets represent the heat transfer from the fuel rod channel to the water rod wall and back to the water rod, respec­tively. Temperature drop due to the water rod wall is ignored in this equation. It is also assumed that the water rod wall is an unheated wall, whereas the cladding is a heated wall. Hence, there is no boiling at the outer surface of the water rod although the outer surface of the water rod wall contacts with two phase coolant. It should be subsequently noted that the application condition of heat transfer correlations is not identical for such a water rod wall.

The thermal conductivity of the fuel pellet depends on temperature and in a BWR fuel, for example, it can be given by

q oo л

(2.113)

where Tf? ve and kf are the average temperature (K) and thermal conductivity (W/m-K) of pellet, respectively. The thermal conductivity is actually a function of pellet density, plutonium containing fraction, burnup, etc. as well as tem­perature. Since the fission gas release during irradiation causes pellet swelling and hence it also changes the thermal gap conductance with cladding, the fuel behavior analysis code which includes irradiation experiments is required to precisely evaluate the fuel centerline temperature. However, since the fuel centerline temperature at normal operation is far lower than the fuel melting point, it does not need a highly accurately estimate in the reactor core design. In BWR fuel, the fuel centerline temperature at normal operation is limited to about 1,900 °C to prevent excessive fission gas release rate. The temperature drop in the pellet depends not on pellet radius, but linear power density and fuel thermal conductivity. Hence, the linear power density is restricted at normal operation of LWRs.