Temperature Coefficients of Reactivity

This hydrogen density in e zirconium hydride is as high as in water at room temperature and is appreciably higher than in water at the 300°C used in power reactors. Another advantage of the uranium-zirconium hydride fuel-and-moderator mixture is its high prompt negative temperature coefficient of reactivity, a consequence of the intimate thermal contact between and hydrogen atoms. 

The RCSS and NCSS must provide the capability to control heat generation with moveable poisons and to control heat generation with inherent feedback. The moveable poison control function is accomplished both with a primary and a diverse secondary moveable poison control, while control with inherent feedback requires a negative temperature coefficient of reactivity. The NCSS and the RISS within the RS, also perform the function of heat generation control by maintaining the geometry for insertion of moveable poisons into the core. The NCSS monitors the neutron flux. 

Nominal Reactivity Control Worths The calculation of control rod and reserve shutdown control (RSC) worths under both hot and cold conditions have been performed for both the initial cycle BOG conditions and the equilibrium cycle EOC condition. In addition, the worth of all 30 control rods has been calculated for other times in cycle for both the initial core and an equilibrium reload cycle to determine how the total control rod bank worth is expected to change over the cycle. Other specific rod pattern control worths for hot conditions for the selected withdrawal of groups of three rods each in the outer bank of control rods were analyzed to define the maximum group worth for use in the transients analyzed in Chapter 15. These calculations were only performed for the EOC equilibrium core loading since that cycle condition yields the minimum temperature coefficient of reactivity and the maximum rod group reactivity worth for a rod group withdrawal transient. No reduction in control rod poison worth due to burnup has been assumed in this or other EOC rod worth calculations discussed below, although this effect would be minimal. 

Temperature Coefficient of Reactivity A lOCFRlOO Design Criterion for the... 

BOG conditions and about +3 x 10" / C for EOC conditions over the normal operating temperature range. In the calculation of the total reactor isothermal temperature coefficient of reactivity, the fuel and moderator temperatures up to about 1700 C (3092 F) have been varied isothermally. The inner and outer reflector temperatures on which the reflector contributions to the temperature coefficient calculations are based, are assumed to be in equilibrium with the respective fuel temperatures as discussed later. Table 4.2-12 lists the assumed temperature conditions used to determine the temperature coefficients of reactivity that have been plotted as a function of the active core temperature in Figures 4.2-6 to 4.2-8. A nine neutron group radial diffusion calculational model with cross sections based on the temperatures indicated in Table 4.2-12, was utilized to determine the temperature coefficients of reactivity. 

Figure 4.2-6 shows the calculated temperature coefficient of reactivity for the BOC-IC condition. Curve A is the fuel prompt doppler coefficient due to heatup of the fuel compact matrix as a function of the assumed fuel temperature. Curve B is the active core isothermal temperature coefficient and is the Siam of the doppler coefficient and the moderator temperature coefficient of reactivity which is also strongly negative, due in large measure to the presence of LBP in the BOC condition. The moderator coefficient, not shown in Figure 4.2-6, would be the difference between Curve B and Curve A and would be -4.0 x 10" / C at 800 C (1472 F), for example. Curve C is the total reactor isothermal coefficient and includes the positive contribution of the reflector heatup to the estimated inner and outer reflector temperatures that would result when the fuel reaches the indicated temperature. 

Partial disruption of the core could inhibit the insertion of some control rods under this accident situation, causing a local criticality condition as the core cools down, due to the negative temperature coefficient of reactivity of the fuel. Modifications were made to supplement a number of control rods with a facility to inject boron beads from storage hoppers above the core into in-core thimbles. This secondary shutdown system is automatically triggered by differential pressure sensors the beads can be recovered from the thimbles and returned to the hoppers in the event of a spurious operation. 

The Doppler effect in thermal reactors (13, 14) has been developed to the point where calculations are considered to be highly reliable. The reliability has not yet been established for fast reactors. Authors have typically attached uncertainties of 50% to their calculated Doppler temperature coefficients of reactivity (6, 12k, 121). However, we believe that, with improvements in the theory of recent years, the theoretical methods are actually substantially more accurate than 50%, and the main remaining errors lie in the experimental data for resonance parameters and calculation of the group fluxes and adjoints. It is the main purpose of this chapter to present a derivation and discussion of the currently available theoretical techniques for fast reactors. ... 

The first serious attempt to calculate the Doppler effect for a fast reactor was by Goertzel and Feshbach (4, 12j, 15), who developed a technique that is basically equivalent to that presented here for the high end of the Doppler effect energy region. Their work was directed toward obtaining an estimate for the effect in EBR-1, which exhibited what at that time was an unexplainable instability, which was at least in part due to the existence of a prompt positive temperature coefficient of reactivity (16). Since this reactor was fueled with fully enriched uranium, it was conceivable that the positive coefficient was due to Doppler broadening of... 

The most recent and apparently also the most accurate experiments to date are those of G. J. Fischer et al. 12c, 21). They quote an accuracy of +0.02 inhours for all measurements. The reactivity changes in the U experiments varied from -0.156 to -0.327 inhours, depending upon the sample size and the reactor spectrum. The measurements for Pu and U are, of course, less accurate, as the magnitude of the reactivity changes were only 0.02 to 0.06 inhours, and the corrections for expansion are of the same magnitude. The corrected measurements for the fissionable isotopes correspond to small positive temperature coefficients of reactivity, as expected theoretically. ... 

The development of the theory for calculation of Doppler temperature coefficients of reactivity involves many physical quantities and thus requires the introduction of many mathematical symbols and formulas. We present first the basic physical formulas and then a summary of the definition of the symbols utilized throughout. 

III. DEFINITION OF THE DOPPLER TEMPERATURE COEFFICIENT OF REACTIVITY FOR ONE ISOTOPE... 

We define the Doppler temperature coefficient of reactivity for a single isotope to be the fractional temperature derivative of the multiplication constant when the temperature of that isotope is changed and all other temperatures held constant. With this definition for a single isotope, the total reactivity change when all temperatures change an infinitesimal amount is... 

These features combined with a negative temperature coefficient of reactivity, large heat capacity of the graphite and die large design margins make the reactor safety extremely difficult to challenge. 

Core reactivity is controlled by means of chemical poison dissolved in the coolant, burnable poison rods and control rod assemblies. Soluble boron and burnable poison rods are utilized for shutdown and fuel bumup reactivity control. Control rod assemblies (37 clusters) are used for power regulation and hot shutdown. The core consists of 3 regions with enrichments of 2.4%, 2,67 % and 3. 0%, It has a negative temperature coefficient of reactivity. The core has a fuel cycle of 12 to 16 months with a discharge bumup of 30,000 MWd/tU. 

Burnable poison (Gd203) is used to partly compensate the fuel bum up reactivity, and soluble boron is utilized for reactor shutdown only. This results in a negative temperature coefficient of reactivity over the complete core life. 

From the safety standpoint, the thermal capacity and strong negative temperature coefficient of reactivity also work to passively mitigate reactivity and loss of coolant accidents. Nevertheless, a safety-related reactor trip and safety features monitoring systems are included... 

On the one hand, this is achieved by the fact that there is a temperature span of approx. 700 C between the maximum permissible fuel element temperature of 1600°C and the maximum operating temperamre of the fuel elements. This temperature span ensures that the reactor core shuts itself down via the negative temperature coefficients of reactivity, even after accident-incurred introduction of any existing surplus reactivity. 

Load change can be followed-up automatically by negative coolant temperature coefficient of reactivity. 

Temperature coefficients of reactivity were measured for the system, both with and without a iiressure ve L Total reactivity of the core was determined, bodi with and without a pressure vessel... 

Negative temperature coefficient of reactivity, which inherently shuts down the core above normal operating temperatures... 

Temperature coefficient of reactivity -17.5 pcm/K —14.6 pcm/K -4.3 pcm/K blanket salt positive void coefficient -2.4 pcm/K recent indications maybe positive -6.7 pcm/K... 

The negative temperature coefficient of reactivity causes a decrease of neutron production in the reactor with increasing temperatures. It thus guarantees an inherent safety mechanism in the system. 

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