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problem7 - 2 with the fast flux cutoff specified by E> 1...

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22.314/1.56/2.084/13.14 Fall 2006�� Problem Set V II Due 11 / 02 /0 6 This problem set illustrates applications of beam theory to Zircaloy Follower in a BWR for calculation of curvature caused by Zircaloy growth ; Consult Notes X on Beam Theory. ZIRCALOY FOLLOWER X a) Geometry and Material properties : W Y Consider a BWR reactor core that has cruciform Z shaped control rods. When each control rod is fully withdrawn for power operation, it is replaced in the core by an attached “Zircaloy follower “ to prevent T excessive water hole peaking. The follower is also cruciform shaped and is shown in the adjacent figure. The dimensions are : W L = length in the z-direction = 2.4 m ; W = width or span = 200 mm ; and T = thickness = 7 mm. T The Zircaloy has a Young’s Modulus of 75 GPa and a Poisson’s Ratio of 0.25. The growth strain in the z-direction as a function of fast fluence is given by the following equation : e gz = C 1 N + C 2 N 2 ; (1.1) where : - the z-direction growth strain ( e gz ) is given in percent; - the fast fluence (N) is given in the units of (10 21 fast neutrons per cm
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Unformatted text preview: 2 ) with the fast flux cutoff specified by E > 1 MeV; and -the constants are C 1 = 0.013 and C 2 = 0.0018. b) Notation and Support Information : For points originally on the axial centerline (x = 0; y = 0 ), denote displacements in the x-direction, the y-direction, and the z-direction displacement, respectively, by u, v, and w. 1 At z = 0, the follower is supported so that u, v, and w are all zero and so that no moments are applied. At z = L, the follower is supported so that the z-direction force is zero, so that u and v are zero, and so that no moments are applied. c) Fast Neutron Fluence: After several refueling cycles, a follower has an accumulated fast fluence given by: N = [ x x ][ N z ] ; N ( ) ( ) (1.2) z Where N is the fast fluence expressed in the units of Eq 1.1; where 0.1 x N x = W ; and where (1.3) ( ) 15 1 + x ( z -( L 2 )) N z = . (1.4) ( ) 1.49cos p z L e L e is the extrapolated length of the core ( 2.54 m ) d) Questions : d.1) What is u as a function of z ? d.2) What is the value of w at z = L ? 2...
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