The reactor outlet coolant temperature of LWRs is around 300 °C and the temper­ature elevation from inlet to outlet is at most several tens of degrees. Thus, the power distribution is designed to be axially flat in LWRs. On the other hand, the reactor outlet coolant temperature is 950 °C and the temperature elevation from inlet to outlet is about 550 °C in the HTTR. Thus, special core design methods are necessary so that the fuel temperature at the core bottom where coolant temperature is high does not exceed the limit.

[1] Optimization of power distribution [33, 34]

If the power distribution is not optimized, the fuel temperature exceed the limit at the core bottom as shown in Fig. 4.21. The fuel temperature at the core bottom must be reduced by flattening the axial temperature distribution. The power distribution for flattening the axial temperature distribution is analyti­cally obtained.

Tf (z) — Tin + Tcl (z) + Tcm (z) (4*15)

where

Tin : Core inlet coolant temperature (° C)

Tcl : Elevation of gas temperaturefrom core inlet to axial potion Z (° C)

Tcl(z)=ajp(z)dz (4.16)

P(z) indicates the axial power distribution and a is a factor which depends on coolant flow rate and coolant heat capacity. The heat capacity is regarded as constant.

Tcm : Temperature elevation from surface of graphite

sleeve to inner surface of fuel compact (°C) (4.17)

Tcm (z) — bP(z

Here, b is a factor which depends on fuel rod geometry and thermal conduc­tivity. Although the thermal conductivity changes with temperature, it is regarded as constant.

Equation (4.18) is obtained by substituting Eqs. (4.16) and (4.20) into Eq. (4.16).

N і Radial fuel region • — Burnable poison

Fig. 4.23 Uranium enrichments of each fuel block in core

Tf(z)=Tin+aJp(z)dz+bP(z) (4.18)

By differentiating this equation under the condition Tf(z) = constant, which means axially flat distribution of fuel temperature, the following relation is obtained.

aP(Z )dz = —bdp(z) (4.19)

By solving this relation, the power distribution for achieving the axially flat distribution of fuel temperature is an exponential function.

(4.20)

C is an integration constant and determined to make Tci of Eq. (4.16) the elevation of the coolant temperature in the core. Figure 4.21 shows the expo­nential power distribution for axially flattening the fuel temperature distribution of the HTTR. Such an optimized power distribution is achieved by making the uranium enrichment relatively high at the core top and relatively low at the core bottom. The fuel temperature distribution among the fuel columns is also flattened by making the uranium enrichment relatively high at the core periph­eral region and relatively low at the core center region. The uranium enrichment division obtained by those adjustments is shown in Fig. 4.23. The number of enrichment divisions is 12. The minimum and maximum values are 3.4 wt% and 9.9 wt%, respectively. The core average enrichment is 5.9 wt%. The power

Fig. 4.24 Adjustment of keff for making control rod insertion shallow

Burnup day

distribution after the optimization is shown in Fig. 4.21. Due to shallow insertion of the control rods and other factors, the power distribution is not an exact exponential function at the core top.