HW20-22page2 - increase in the moderator/coolant(c 135Xe...

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10-15 where r == Ax / A[ ~ 0.724. Take the logarithm of both sides and solve for tmax to get the desired result, namely 1 { [ X(O) ] } tmax = -:>;~ In r 1 + (1 -r)I(O)' (P10.6) Now consider under what conditions there is a rise in 135Xe following the shut- down. Since >'1 > >'x, we see that in Eq. (PIO.6) the argument of the logarithm must be < 1 to make tmax > 0, i.e., X(O) 1 1 + (1 -r)- < - 1(0) r which, upon rearrangement gives the condition X(O) 1 ( >.[ """j(O) < -;.- = ~ ~ 1,38./ Thus to get a rise in the 135Xe following a shutdown, the initial X(O) and 1(0) concentrations must be such that 23. In a fast reactor, does 135Xe produce feedback? Why? Solution: The absorption cross section of 135Xe for fast neutrons is not large, and hence the presence of 135Xe produces negligible feedback. 24. Many phenomena produce reactivity feedback. Within orders of magnitude, over what time interval would you expect the following reactivity feedback causes to take effect? (a) temperature increase in the fuel, (b) temperature
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Unformatted text preview: increase in the moderator/coolant, (c) 135Xe increase, (d) fuel burnup, (e) boiling in the core, and (f) increased coolant flow through the core. Solution: (a) Fuel Temperature: Since the fission fragments transfer their initial ki-netic energy to thermal energy of the fuel matrix within 10-12 s (see Sec-tion 6.6), the fuel temperature responds to changes in the fission rate or power and produces feedback within a very small fraction of a second. (b) Moderator/Coolant Temperature: The thermal energy deposited in the fuel material takes time to be conducted to the fuel rod surface, the time depending on the diameter of rods, properties of the fuel-clad inter-face, and the conductivities of the fuel and cladding. Typically, it take several to tens of seconds for the moderator/coolant to change its temper-ature and produce feedback. July 24, 2002...
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