SUBCRITICAL CONTROL BLADE CALIBRATION

An assembly which includes fissionable material may function n one of two fashions: if k_eff is less than 1, the assembly is known as a subcritical assembly; if k_eff is 1 or greater, it is a reactor. Control rods move neutron absorbing material into, and out of, the core region, changing the configuration from one mode to the other.

We are interested in evaluating the effect of the control rods on the multiplication of the core when in a subcritical mode. To achieve this, consider the core with all rods in. A neutron source is placed (and kept) in, or adjacent to, the core. As a result of fissions induced in the fuel, there is a multiplication of the source neutrons. A neutron detector located in, or adjacent to the core, will respond to the total neutron population (composed of both primary (source) and fission neutrons).

If S neutrons/s from the source impinge on the detector in the absence of fuel, then when fuel is introduced both source and fission neutrons will influence the detector. This sum can be computed by noting that at the end of one generation the neutrons produced will be Sk_eff; after two generations, Sk_eff²; etc. The k_eff is the effective multiplication factor for the subcritical configuration under consideration.

The steady state multiplication for the assembly is thus the ratio of the events contributed by all generations divided by those due only to the first generation:

M = {S + S k_eff+ S k_eff² +S k_eff³+......} /S

Which becomes: M = 1 / {1 - k_eff}

Provided: k_eff < 1

If changes are made to the assembly geometry or composition, k_eff changes, and the multiplication changes.

Note that the multiplication may be defined in terms of the response of the detector:

• With no fuel in place, C_o counts are recorded per unit time,
• With fuel in place C counts are recorded per unit time.

Then, the multiplication is: M = C/C_o and C = S / {1 - k_eff}

With the core in a shutdown condition, withdrawing a blade (control or regulating) removes neutron absorbing material from the core. As a result, the reading of neutron detecting channels will change. The change is difficult to predict, as it is dependent upon many factors:

• Location of source,
• Location of detector,
• Which blade is moved,
• How much the blade is moved, and
• Where, vertically, the motion is effective.

However, the change in count rate recorded at the detector is readily obtained. By moving the blade out of the core in discrete steps, the count rate (C_n) may be recorded at each of the n steps. Note that C_o cannot be measured unless the core is unloaded.

Two possibilities for presenting the data exist. First, if the C_n values are plotted versus rod position, one notes that the shape will be the same as a plot of C_n/C_o values, since C_o is a constant. This plot will show the relative effect of rod position on change of multiplication due to motion of the rod.

On the other hand, absolute values can be found by dividing (C_n -C_n-1) /C_n-1 which is the same as dividing the change in multiplication from (n1) to (n) by that at (n1). This of course describes the fractional change in multiplication due to movement of the rod.

With the source in the core source holder, and an operator at the console:

1. Withdraw Control Blade #3 three inches per step.
2. Take several one-minute counts or one count for at least five minutes at each interval.
3. Take a one-minute count at each step after the count rate stabilizes.
4. Withdraw the remaining Control Blades.
5. Withdraw the Regulating Blade to within 3 inches of the estimated core critical position (ECP) based upon previous log entries.
6. Take several one-minute counts.
7. Remove the neutron source and observe the count rate.
8. Take several successive one-minute counts.

If time permits:

• Bring the reactor exactly critical at a low power (1 watt or less) and remove the source.
• Bring the reactor critical at 50 watts and remove the source.

1. Present three curves for the control blade.
2. One curve should present the counts versus rod position (shape of the variation in multiplication).
3. The second curve should show the fractional change in multiplication versus rod position.
4. The third curve should show the reactivity of the blade versus position.

Discuss the results:

1. Explain the shapes of the curves.
2. Assume that the effective multiplication of the core with all blades in is 0.892. What is the rod worth, expressed as % del k_eff/k_eff for each blade?
3. Explain why the count data changes while close to critical.
4. Explain your count data observations when removing and re-inserting the source while near critical (is the decrease linear or exponential, and why), and while critical at a low power and a high power.
5. From an engineering standpoint, why are reactivity curves helpful?