Effective Multiplication Factor (keff). . keff determines whether the neutron density within a reactor will remain constant or change.. keff and Power. Power is directly proportional to neutron density keff = 1.0000 ? critical (power constant)keff < 1.0000 ? subcritical (power decreasing)keff > 1.0000 ? supercritical (power increasing).
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
1. Nuclear Reactor Kinetics Craig Marianno
2. Effective Multiplication Factor (keff)
3. keff and Power Power is directly proportional to neutron density
keff = 1.0000 ? critical (power constant)
keff < 1.0000 ? subcritical (power decreasing)
keff > 1.0000 ? supercritical (power increasing)
4. k Excess Any difference between a given value for keff and 1.0000 is called the “excess” multiplication factor (?k)
?k = keff - 1.0000 = k excess
5. Reactivity When keff is close to 1.0000, ?k and ? and nearly the same.
Example: keff = 0.98
6. Delayed Neutrons Single most important characteristic for reactor control
Delayed neutrons ? decay of fission products (precursers)
Prompt neutrons ? fission
Fraction of delayed neutrons = ?
Delayed neutrons are more effective than prompt because they are “born” at a somewhat lower energy.
7. Delayed Neutrons
8. Delayed Neutrons
9. Delayed Neutrons While it is true that they are only a small fraction of the total neutron population, they play a vital role in reactor kinetics.
They significantly increase the neutron cycle lifetime!
10. Prompt Critical
11. Prompt Critical
12. Reactivity in Dollars From our previous example:
13. Neutron Lifetime For reactor kinetics, it is important to know the average time elapsing between the release of a neutron in a fission reaction and its loss from the system either by absorption of escape. This is typically called the “prompt neutron lifetime”. This time can be divided into:
1) Slowing Down Time
2) Thermal Neutron Lifetime (Diffusion Time)
14. Neutron Lifetime
15. Neutron Lifetime (infinite medium - prompt only) ?a = total thermal macroscopic absorption cross section
?a = absorption mean free path
v = mean velocity (2200 m s-1)
Note: - finite size reduces average lifetime due to leakage
- ?a for a core includes all materials
16. Effective Neutron Lifetime (delayed neutrons included) ?eff = effective fraction of delayed neutrons
?eff = effective decay constant of precursors
? = reactivity
17. Reactor Kinetics We need to construct an expression for the number of neutrons per second in the reactor during a given “neutron cycle”.
We could use:
18. Reactor Kinetics Solving:
19. Reactor Period To make the previous equation easier, we can define the reactor period (T) as T = l / ?k.
The reactor period represents the length of time required to change the reactor power by a factor of e (2.718). This is why it is sometimes referred to as the “e folding time”.
20. Reactor Kinetics (Prompt Example) Assuming the following, what is the increase in power for a ?k = 0.0025 ($0.357) at the end of 1.0 s?
?a = 13.2 cm
v = 2200 m s-1
21. Reactor Kinetics (Delayed Example) Assuming the following, what is the increase in power for a ? = 0.0025 ($0.357) at the end of 1.0 s?
? = 0.0813 s-1 ?eff = 0.007
v = 2200 m s-1 l = 6.0X10-5 s