Engy-4350: Nuclear Reactor Engineering Spring 2019 UMass Lowell; Prof. V. F. de Almeida 04Mar19
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¶Show No. | Now Showing (2:00-3:15pm) | Value | Score |
---|---|---|---|
1 | For a Lifetime | 50 | |
2 | Sudden Insertion Current | 50 | |
- | Total | 100 |
Consider a fission-electric cell, constructed with a thin layer of $^{235}$U, pure metal (mass density 19.1 g/cm$^3$), as shown in the diagram below. The cell is inserted in a nuclear reactor where a constant thermal neutron flux exists where: $\varphi = 10^{14}\,\frac{\text{neutrons}}{\text{cm}^2\,\text{s}}$. Use nuclear data from the NNDC or any other of the nuclear data sites referred to in course notes. Assume the data is for temperature of 20 C.
1.1: Explain why there is an electric current in the external circuit? Be very clear.
1.2: Why is the electric current in the external circuit time-dependent?
1.3: Provide a formula that computes the time-dependent electric current $J(t)$.
1.4: Compute the mean lifetime $\tau$ of the fission-electric cell.
1.5: If the temperature of the cell is 300 C, what is the new current and what is the new lifetime of the cell?
1.6: What needs to be done if this cell is used to measure the constant neutron flux? Explain and give a mathematical answer.
In Problem 1, the reactor is under a start-up condition where a source is suddenly inserted. The source strength is $q_0 = 10^8 \, \frac{\text{neutrons}}{\text{cm}^3\,\text{s} } $ and a negligible amount of neutron density was initially in the reactor at start-up condition. Using a point-reactor model with 6-group delayed-neutron emission precursor species,
2.1: Use the model asymptotic limit of the neutron flux response in the reactor to re-derive the time-dependent electric current on the external circuit of Problem 1.
2.2: Calculate the time needed for the reactor to reach its nominal power condition of $\varphi = 10^{14} \, \frac{\text{neutrons}}{\text{cm}^2\,\text{s} }$.
2.3: If the electric current is measured during this start-up condition, how could you compute the neutron generation time in the reactor?