Abstract
Fast reactor design requires the simultaneous application of mechanical and thermal-hydraulics analysis methods. We reviewed some aspects of mechanical analysis in Chapter 8; we will discuss mechanical design further in Chapter 12. Chapters 9 and 10 will deal with thermal-hydraulics analysis. In the present chapter we will investigate methods of determining temperature distributions within fuel pins. We will then extend these methods to assembly and core-wide temperature distributions in Chapter 10. While the actual analysis of fuel pin thermal performance depends strongly on the material, the mathematics and concepts associated with determining temperature distributions within fuel pins is essentially independent of the material in a fast reactor. Throughout this chapter, the discussions of correlations and closure relationships necessary to complete the mathematical analyses, and to introduce important concepts, are generally based on oxide fuel with notes where other fuel types show different behavior.
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Notes
- 1.
Neglect of neutronics spatial self-shielding is an excellent assumption for fast reactors. The spatial variation of the heat source is complicated by restructuring of the fuel, however, as in Eq. (9.9).
- 2.
This is an acceptable approximation in most cases, since the radial temperature gradient is much greater than the gradient in the axial direction.
- 3.
Alternatively, Eq. (9.2) can be obtained by defining; \(\theta = \int_{T_s }^{T\left( r \right)} {k\;dT}\) so that \({{d\theta } \mathord{\left/ {\vphantom {{d\theta } {dr}}} \right. \kern-\nulldelimiterspace} {dr}} = k{{dT} \mathord{\left/ {\vphantom {{dT} {dr}}} \right. \kern-\nulldelimiterspace} {dr}}\). Equation (9.1) can then be written as \({{d^2 \theta } \mathord{\left/ {\vphantom {{d^2 \theta } {dr^2 }}} \right. \kern-\nulldelimiterspace} {dr^2 }} + \left( {{1 \mathord{\left/ {\vphantom {1 r}} \right. \kern-\nulldelimiterspace} r}} \right)\left( {{{d\theta } \mathord{\left/ {\vphantom {{d\theta } {dr}}} \right. \kern-\nulldelimiterspace} {dr}}} \right) + Q = 0\). The solution of this equation is \({{\theta \left( r \right) = - Qr^2 } \mathord{\left/ {\vphantom {{\theta \left( r \right) = - Qr^2 } 4}} \right. \kern-\nulldelimiterspace} 4} + C\ln r\).
- 4.
Laboratory measurements indicate that the thermal conductivity of mixed oxide fuel varies with the oxygen-to-metal (O/M) ratio. Equation (9.6) and Fig. 9.2 correspond to a stoichiometric O/M ratio of 2.00. The precise effect of O/M ratio on fuel conductivity and temperature during actual reactor operation, however, is still in question.
- 5.
See Chapter 11 for a discussion of the thermal properties of these fuels.
- 6.
Additional details in the solution are given in Ref. [3].
- 7.
Throughout the literature the word “gap” is used for the width or thickness of the gap in addition to referring to the region between the fuel and the cladding.
- 8.
- 9.
See Section 10.4 for a discussion of overpower and hot channel factors.
- 10.
- 11.
A boomerang has a dog-leg shape. If the reader is still uncertain about this shape, he can ask anyone who plays golf, for there are always several dog-leg holes on a golf course.
- 12.
This can be observed from Fig. 10.4 in Chapter 10.
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Waltar, A., Todd, D. (2012). Fuel Pin Thermal Performance. In: Waltar, A., Todd, D., Tsvetkov, P. (eds) Fast Spectrum Reactors. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9572-8_9
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