9.154. The first design limitation to be considered is related to the heat flux at which a boiling crisis could occur; for a PWR this is the DNB flux, which can be computed by means of a suitable correlation (§9.103). The DNB flux is expected to decrease as the coolant quality increases, since the larger the vapor content of the fluid, the closer it would be to the conditions at which DNB occurs.[15] The quality increases as the enthalpy of the fluid is increased; hence, the enthalpy rise has an important bearing on the value of the DNB flux. In computing this flux for design purposes, the maximum value of the enthalpy, i. e., the value in the hot channel, must therefore be used.

9.155. Since the enthalpy of the coolant increases as it flows upward through the core, the (computed) DNB flux decreases correspondingly, as depicted in Fig. 9.22. Assuming a sinusoidal axial distribution of the vol­umetric heat source, as in §9.146, the heat flux along the hypothetical hot channel will ideally have the same general distribution, as indicated in the figure. The maximum of this curve, representing the highest possible heat flux in the core for normal operating conditions, is equal to the average core heat flux multiplied by the overall heat flux hot-channel factor. In practice, the axial heat flux will not have a sinusoidal distribution, and this must be taken into consideration by the designer. For the present purpose, however, the ideal axial distribution may be assumed.

9.156. Comparison of the computed DNB heat flux with the hot-channel value at any point along the flow channel gives the departure-from-nucleate — boiling ratio (DNBR) or critical heat flux ratio (CHFR) at that point. The results for the whole channel are shown by the uppermost curve in Fig. 9.22. It is seen that the DNBR passes through a minimum. In the interest of reactor safety, an essential requirement of reactor design at present is that the minimum DNBR shall be greater than 1.3 for the hottest channel at the 118 percent overpower specified for a PWR. This is one of the important constraints in reactor core design. It should be noted that the minimum DNBR does not occur at the point of maximum heat flux but more toward the exit where the enthalpy of the coolant is higher and the DNBR flux is lower (§9.103). Factors that change the axial neutron (and heat) flux distribution, e. g., insertion of control rods, will affect the location of the minimum DNBR.

9.157. The design constraint just considered should provide safety from the onset of DNB under normal operating conditions, allowing for a certain amount of overpower that could arise from the instrumental errors or minor reactivity transients. However, no allowance is made for abnormal situa­tions that might result from excessive overpower or inadvertent decrease in the coolant-flow rate. These matters are aspects of reactor safety con­sidered in Chapter 12.

9.158. A somewhat more sophisticated approach preferred by many PWR designers uses the CHF power ratio as a measure of overpower that can be tolerated before the critical heat flux (CHF) condition is reached at the hot channel. In this method, the CHF correlation curve is recalcu­lated by computer, point by point, as the channel power levels under consideration are changed, thus reflecting shifts in mass-flow rate and other parameters. On a thermal flux, coolant enthalpy coordinate system, a family of curves are then plotted showing the proposed channel flux and corresponding variation of CHF, each at the same power level. The CHF power ratio is defined as the power at which the two curves would be tangent to one another, divided by the design or “rated” power. Since relative displacements of the curves with power level are considered, the margin is more physically meaningful than the DNBR [22].

9.159. The central fuel temperature of a cylindrical fuel rod depends on Qa2, where a is the diameter of the fuel pellet, as may be seen from §9.45 et seq. and Example 9.3. By equation (9.20), this is related to the linear heat rate #L, which is a characteristic property of the fuel material for the specified temperature range. Experiments with uranium dioxide, commonly used as fuel in water-cooled (and moderated) reactors, have shown that melting does not occur until the linear heat rate in the fuel exceeds about 70 kW/m. This is, therefore, the maximum permissible linear heat rate anywhere in the reactor core.

9.160. From equation (9.20), qb is equal to Q(ira2) and the heat flux q/A is equal to Qa2/2b, where b is the outer radius of the clad rod. It follows, therefore, that

If the maximum heat flux in a PWR is about 1.5 x 106 W/m2, and the outer diameter of the clad fuel rod is 0.0095 m, i. e., b = 0.00475 m, the corresponding value of qb is found to be about 45 kW/m. It is apparent that the maximum (hot-channel) heat flux in this reactor is moderate. The average linear heat rate, equal to the maximum divided by the heat flux hot-channel factor 2.5, is about 18 kW/m.

9.161. The zirconium alloy (zircaloy) fuel-rod cladding is subject to failure from a variety of causes, including formation of hydrides, stress corrosion, embrittlement, and interaction with the uranium oxide (§7.172). An increase in the cladding temperature appears to result in an enhanced failure rate. There is little danger in normal operation that the cladding will become hot enough to fail, but under accidental conditions, such as a decrease (or cessation) of the coolant flow, the cladding temperature be­comes a critical parameter (Chapter 12).

9.162. Although the temperatures of the fuel and cladding are not likely to represent design constraints, it is nevertheless a common practice to compute the maximum cladding and central fuel temperatures for normal operation and to include them in the list of specifications. The procedure is based on the principles developed in §9.45 et seq. and §9.143 eq seq., with allowance for the variation of the heat conductivity of the fuel material with temperature. The coolant temperature required for the calculations is derived for the hot channel with the minimum flow rate. As seen in §9.149, the maximum cladding surface temperature occurs beyond the point
of maximum heat flux (or input), and so also does the maximum central fuel temperature, although not at the same point as the maximum cladding temperature. Typical maximum values in a PWR are 350°C for the cladding and 1700 to 1900°C for the fuel. The melting point of the uranium dioxide in the fuel pellets is about 2760°C initially, but it drops to some 2650°C during reactor operation as a result of the accumulation of fission products.