Multi-group Model

Multi-group Model Calculate group-averaged: Or for, we need group-averaged Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model • Group-averaged parameters? • ENDF. • Integrate term by term over groups and equate to equation of multi-group model. Units! Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model • Define group flux  Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model  Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model ENDF High G, few mesh points. Flux Poison, burnup (or better consumption), temperature, control rod position, etc… Small G, more mesh points. Flux Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model • What could we make life a little easier?! • No upscattering • set group G to include neutrons up to ~1 eV. • No group skipping when scattering down (directly coupled). Your choice of how to tackle in-scattering. HW 27 How can we pledge this? What about H? Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model Criticality Not all sources, only fission. Not only sinks Iterations. No upscatter Redundant when no upscatter. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model No upscatter Iterations. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model No upscatter Directly coupled Iterations. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model Multi-group  one-group Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model Substituting all of the above into yields which is the one-group diffusion equation. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model Project 3 Work out the multi-group to two-group collapsing and investigate criticality. Write down the appropriate matrices. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning 135Xe 106 b Saturates Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning 149Sm 105 b Continuously accumulates Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Not anticipated! Reactor shut down! Time scale: Hours and days. 135Xe 106 b 149Sm 105 b Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning HW 28 Negative reactivity due to poison buildup. It is proportional to the amount of poison. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning small • Initial conditions? • Clean Core Startup. • Shutdown (later). Assume no spacial dependence. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning HW 29 Show that: and Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Now, we know Xe(t) Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Shutdown. After the reactor has been operating for a “long” time. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning HW 30 Show that > 0 ? Height of the peak depends on I() and Xe(), i.e. depends on . Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning Shutdown  Xe   negative  try to add positive reactivity  move control rods out  need to have enough reserve  costly to do that. If, the available excess reactivity can compensate for less than 30 minutes of poison buildup, can’t startup again after ~30 minutes of shutdown, because you can’t achieve criticality. Need to wait long hours for Xe to decay down. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Strategies • If you plan to shut down for “short maintenance”, think about stepback. • Examine different scenarios using a code from • http://www.nuceng.ca/ • Prepare your own report, code, calculations, graphs, comments, conclusions etc….. • Be creative. 20% (8 marks) of the final exam. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Xe Oscillations • (r,t) (spacial dependence)  flux  locally Xe burnup    (reactivity)   flux further   control rods globally in  flux  elsewhere Xe burnup   ….. limited by opposite effect due to increase (decrease) of I in the high (low) flux region. • In large reactors (compared to neutron diffusion length) local flux, power and temperature could reach unacceptable values for certain materials  safety issues. • Think of one sensor and one control rod  feel average flux  apparently OK  more sensors and control rods to locate and deal with local changes. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Poisoning • Permanent Poisons • 149Sm has sizeable but lower cross section than 135Xe. • It does not decay. • Accumulates with time. • Consequences????????? ???? Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh).

Multi-group Model