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Critical Mass; Critical Diameter

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Critical Mass; Critical Diameter

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    1. Critical Mass; Critical Diameter

    2. Material Buckling

    3. Critical Dimension

    4. Boundary conditions We need two boundary conditions The is symmetrical about the origin and is finite: Flux drops to zero at the boundary

    5. Solution Apply the first boundary condition Take the the derivative of the continuity equation and set it equal to 0

    6. More Math Since B is real and positive Apply the 2 boundary condition

    7. A little more math The cos term = 0 at odd multiples of ?/2 we want the smallest dimension

    8. Just a little more math Geometric buckling A is an arbitrary constant equal to the maximum flux at the center of the core We can solve for the geometric buckling for other geometries

    9. Other geometries I am not going to do this in class. Geometric buckling for other simple geometries are found in Table 6.2

    10. Strategy There are two types of problems Composition specified Size specified

    11. Size Looking for the right fuel composition Use the right geometry and solve for the Bg Bg=Bm when the reactor is critical Use Bm to find k Use k to find the fuel utilization factor - f

    12. Fuel Utilization In words f = absorbed in the fuel divided by what is absorbed in the fuel and the poisons and everything else

    13. Composition Solve for f Use f to find k and L (diffusion L) Then find material buckling Use material buckling to find geometric buckling Use the right geometry and Bg to get the critical dimension

    14. What else Extrapolated edge Reflected reactors Heterogeneous reactors

    15. Infinite Slab Leakage occurs in the x direction Flux gradient occurs only in the x direction Flux doesnt fall to zero at the edge of the slab

    16. Extrapolation Distance Solve for d At the boundary of the bare core neutrons stream out into space - few scattered back

    17. Solving for d Use neutron current Jx-=0

    18. Finally to solution If you assume that the extrapolation distance is linear then you get the first term if you use a more sophisticated solution you get the 0.71If you assume that the extrapolation distance is linear then you get the first term if you use a more sophisticated solution you get the 0.71

    19. Examples from here to the Exam

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