prob.ii-1 - _. sq":- Iil”. Win13 22.312 Homework set...

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Unformatted text preview: _. sq":- Iil”. Win13 22.312 Homework set #1 Fall 19!]? SnLUImNs: PRflELEM 2—1 Due to the diEerent geometry and arrangement of the pellets within the heel pin. we are faced with two different cases. 1. F llthereactnrs exc r : _. e The [net pellets are cylindrical and are Stacked in the file] pin. Theret'ere we can use the relatiens, straightforwardly derived from eqs. 2-5: (am) 6-5;: _ ' m (mg—5 (2) I: Hate that, with these defirdtiens. D“ is the cuter cladding diameter and the heat flux is evaluated at the outer surface at the cladding. Using the 1talues found in the referenced Tables: AGE. 1132.3 T515 BWR. PWIt m 595.4 524.5 363.4 mean '54.} "32- Whine2 Homework set #1 Fall 1991‘ 22.312 . sis"?- can not he computed as in eq. 1. In fact, by definition (textbook, pg. 22), <q '“P is the power generated per unit volume of the fuel material {both fissile and fertile material}. As in a HTGR the firel particles are niierospheres, the channel is not uniformly loaded with fuel, due to heth voids leFt among the mierespheres and their siliconer graphite layers. oid we start noting that the spheres, having a total diameter of .T to compared to the diameter of the channel (15.? mm}._ whiten _ conditions, the spheres can he assumed to he packed as tightly as pessihle. This leads to a hexagonal closed peeked {HEP} configuration, which can he thought of as a cubic face 3' centered {refs} lattice. Fer this lattice the packing factor. defined as: - To account for the v 1.1 mm are small as _ total - void volume ' l. total volume has the value .1! 2 fr : — E'— E [1:74 to situations like this. where the packing is the result of a Physics studiesI show that icing lhctor should he relaxed by lfi~2fl “In. Using 15% we random disposition, the pee "III-1- -. ohtain: f" .163. With this definition, the total volume oi'the rr . a 2 E D; IV where L is the channel‘s height. d with first. Assuming an inner radius R; of still) the and This volume is not corttpletelig.r fills d _ _ storal shell micEness 5 of [15 tin-l. Elie liaetion of the spheia'mfinemfieflpied by fuel is' 4 3 FILE fr=T3 l —-:-—R']—3=.335- ' EEIRJ+§}J Liar“? I - H Finally. the fidel‘svglurne in the ehannel is: .---I J: =_ S 4 :1 Charles Elect, Eleoteetmjv solid state physics: it short course, What. New 1iI’orlr. 196.1. pg. 2?. {Bardeen emanates}. *' 22.3 Is Homework set #1 Fall was (‘4; “"2- ean be calculated using its definition as ratio of the average heat generation rate to the volume of the fuel which generates this power Referring to a pin of height fl, we can 4' write: ; w ._E a L ._ EDlLfoF Zflefefa ' '. - Using the values «1;: 5=1ST sum and £1.51 5.? mm, the final result is; I cq":=-=1ss_sstwrm-‘ . — which is in the range of the values previoule found; fig; :11”; At the surface of the sphere (and thus, at the surface of the cladding}. fig“?! can be _ obtained from the ratio of the sphere power to the sphere's surface. "t Shore trwcr (gull—Ea tar—P p r 3 - Sphere surface _ 47d}: Using the result above, the sphere power: lsjlfi ngnd the heat flux fiq'fie 11.3 it"llil'll'rn2 At the surface of the channel fiq ' '3’ can he obtained as in case t: From a thermedynamical point efview. the heat fltut of interest is the one calculated at the surface of the cooling channels. Nonetheless. not enough utt‘oonati on is found in the textbook to calculate this quantin ...
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This note was uploaded on 02/02/2012 for the course PHY 4049 taught by Professor Acosta during the Fall '08 term at University of Florida.

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prob.ii-1 - _. sq":- Iil”. Win13 22.312 Homework set...

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