X. Neutron and Power Distribution

Transcription

1 X. Neutron and Power Distribution X.1. Distribution of the Neutron Flux in the Reactor In order for the power generated by the fission reactions to be maintained at a constant level, the fission rate must remain steady over the course of time. This means that the number of thermal neutrons that cause fission in one generation must be the same as those that cause fission in the next generation, and the next, and so on. Thus, the total number of neutrons in the reactor must remain constant. In point of fact, the Σ f φ = fissions/s product must remain constant, but let us assume that factor Σ f varies somewhat. In this module we will discuss the distribution of the neutron population. DISTRIBUTION OF THE NEUTRON FLUX IN THE REACTOR The thermal neutron flux is the quantity determined by the fission rate per cm 3 Σ f φ and thus, the power generated in the fuel. Due to the fact that the flux is different at each point of the reactor, its distribution or form is of utmost importance, since it will determine the distribution of power generated in the core. In general, the thermal neutron flux achieves its maximum value in the center of the reactor and falls to zero at the contour of the reactor, since no thermal neutrons are produced in this area. The distribution of the neutron flux depends greatly on the form of the reactor and since most reactors are cylindrical, we will discuss this form. Let's consider the flux distribution in two directions: Axial and Radial from the center of the reactor (Figure 1).

2 Figure 1 The form of the flux along the axes is provided in the following expressions: Axial: (10-1) Along the contour of the core (Figure 2), it is given that Z = H/2 and Z = -H/2, thus, it is given that π/2 = 0, therefore: φ Z = 0 The distribution of the flux along the radius has a similar form. It is not exactly a cosine, but it is, nevertheless, fairly correct to express it as: (10-2)

3 Figure 2 Along the contour (Figure 3), it is given that r = R. Therefore: φ r = 0 Figure 3 One of the physical conditions is that φ must not drop abruptly to zero along the geometric contours, but that it do so at a given distance (d) (Figure 4).

4 (Figure 4 Combining both distributions, we find the flux as related to (z,r) at any given point in the reactor. (10-3) X.2. Implications of the Non-Uniform Distribution of Flux 1. As the neutron flux has a maximum value at the center of the reactor and drops to zero in the contours, the maximum power generated by the fuel will be produced in the center of the reactor and very little power will be generated in the fuel located in the outer areas. 2. The total power produced in the reactor will depend on the average thermal flux. Due to the type of distribution produced in a cylindrical reactor, the average flux is only 27.5% of the maximum flux.

5 3. The only way to increase the total power generated by the reactor is by increasing the average flux. If we maintain the same flux distribution, the only way to augment the average flux is by increasing the maximum flux (Figure 5). Figure 5 Nevertheless, this situation would increase the heat generated by the fuel in the center of the reactor and might not be acceptable due to the limits of the fuel and the heat extraction capacity of the system. Conclusion: Total power is limited due to the low ratio between average flux and maximum flux. There are ways of increasing the average flux without augmenting the maximum flux. In this way we can generate more power with the same size of core. Hence the great interest demonstrated in flattening the distribution of flux, and there are different ways of doing this.

6 Case I: Reflector Effect Figure 6 a: flux without reflector b: flux with reflector a) A flattening of the thermal flux in the core is achieved, or, that is to say, the average flux/maximum flux ratio is increased. As seen in the figure above, the "hump" in the flux distribution is due to the leakage of fast neutrons into the reflector, where they are thermalized. Since the reflector contains no fuel to absorb the thermal neutrons, it behaves as (is equivalent to) a source of thermal neutrons. b) Due to the increased flux in the contours of the core, there is better utilization of fuel in the outer areas of the reactor, which contributes greatly to the total of generated power. Thanks to the benefits analyzed, the use of the reflector is widespread. Case 2: Flattening Flux With Absorbers In this case, control rods are inserted in the central area of the core, depressing the thermal flux and thus flattening flux distribution.

7 Figure 7 a: flux without reflector b: flux with control rods in The control rods soak up part of the excess reactivity, which is found in the core and which is detrimental to the k eff. Case 3: Flattening of Flux Due to Zone Refuelling Zone refuelling means that fuel in the central channels is left for a longer period of time than the fuel in the outer channels so as to achieve a high burn level. Thus the central fuel elements generate relatively fewer neutrons than the outer elements. Example for the effect of flux flattening on a natural uranium core. The expression for the power in a natural uranium core = relates power expressed in MW(t) to the mass of natural uranium (expressed in ton), and the average thermal flux, expressed as (neutrons cm -2 s -1 ). It may be observed from the formula that there are enormous economic benefits to be gained from increasing the average flux without increasing the maximum flux. For the Atucha I PP the average flux is 53% of maximum power. Without any flattening, average φ/maximum φ = 27%, or in other words, with approximately the same investment, we would produce only half of the installed capacity.

8 X.3. Power Peaking Factor The thermal hydraulic design of the reactor core is done for the maximum power (not only for the average power), thus it is better to use a new quantity Power Peaking Factor which is defined as: PPF = (maximum power density) / (average power density) Table 1 shows the power peaking factor for different reactor geometries. Geometry PPF Infinite Slab 1.57 Rectangular Parallelepiped 3.88 Infinite Cylinder 2.32 Finite Cylinder 3.64 Sphere 3.29 Table 1