The technology of nuclear reactor safety reactor physics and control

NUCLEAR ENGINEERING AND DESIGN 6 (1967) 391-394. NORTH-HOLLAND PUBLISHING COMP., AMSTERDAM

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J. T. Thompson and J. G. Beckerley (eds.): The Technology o f Nuclear R e a c t o r Safety - Vol. 1 R e a c t o r P h y s i c s and Control. The M.I.T. P r e s s , C a m b r i d g e , Mass., 1966, 7 2 0 p a g e s , p r i c e : S 2 5 . 0 0 This book is the :First of two v o l u m e s s p o n s o r e d by the AEC designed to b r i n g together in one place and to evaluate, o r g a n i s e and g e n e r a l i s e the twenty y e a r s of e x p e r i e n c e a c c u m u l a t e d in the field of n u c l e a r r e a c t o r safety. The e d i t o r s state quite rightly in the preface that n u c l e a r safety is an e n o r m o u s subject. By its very n a t u r e the subject m a t t e r is diffuse; this situation is not p e c u l i a r to r e a c t o r safety, being often found in applied technology, and would not of itself justify the production of a s p e c i a l text book. In this case, however, the needs of r e a c t o r safety justify exceptional m e a s u r e s in t r y i n g to p r o m o t e the s p r e a d of knowledge. Following the int~coduction, which gives a brief h i s t o r i c a l background and an outline of U.S. safety philosophy, Chapter 2 is devoted to the r e a c t o r core. The f i r s t p a r t of this chapter deals with the r e a c t o r p h y s i c s of core design and of r e a c t i v ity control leading u l t i m a t e l y to a d i s c u s s i o n of t e m p e r a t u r e coefficients, void coefficients, power coefficients, power d i s t r i b u t i o n s and control rod worths. All these a r e the product of steady state r e a c t o r s t u d i e s but they are of fundamental i m p o r t a n c e in the detailed study of m a j o r r e a c t o r faults which a r e the subject of d i s c u s s i o n in subsequent chapters. This chapter may t h e r e f o r e be r e g a r d e d as setting the stage in p r e p a r a t i o n for the main d i s c u s s i o n . The account of static r e a c t o r physics studies is given f r o m the standpoint of a " f o u r - f a c t o r f o r m u l a " for koo and the u s u a l s i m p l e one and two group leakage t e r m s in d e t e r m i n i n g r e a c t i v i t y . Such a t r e a t m e n t wo'ald be r e g a r d e d today as i n adequate for the d e r i v a t i o n of absolute values b e c a u s e of difficulties in the a v e r a g i n g p r o c e s s e s which a r e n e c e s s a r y in any definition of the factors. However, f r o m a conceptual point of view the f o u r - f a c t o r - f o r m u l a has a g r e a t deal to commend it and as the author shows in many i n s t a n c e s the t r e a t m e n t is v e r y useful in obtaining the r e l a tive values of i m p o r t a n t p a r a m e t e r s . No attempt is made in this chapter to p r e s e n t

detailed proofs of the many f o r m u l a e but the large list of r e f e r e n c e s makes this u n n e c e s s a r y . The account is compact, well put together and supported by a large n u m b e r of c l e a r d i a g r a m s and tables. The second p a r t of the chapter deals with the bowing of fuel rods due to t h e r m a l effects. This is a very complex s u b j e c t but the author has dealt adequately with the i m p o r t a n t a s p e c t s of the topic. The m a t h e m a t i c a l example given is a v e r y simple one involving a s y s t e m which has freely supported rod ends. It is stated, however, that other f o r m s of rod fixing can r e a d i l y be a s s u m e d , although it is not added that in the case of one, or two, r i g i d end fixings r e a c t i o n f o r c e s and mom e n t s must be included at the rod ends; these effects being absent f r o m the i l l u s t r a t i v e case presented. It is noted that where the d y n a m i c r e s p o n s e of the rod is c o n s i d e r e d , as might be justified where v e r y rapid t e m p e r a t u r e changes take place, no mention is made of the s e p a r a t e c o n t r i b u t i o n s of fuel and cladding to rod s t i f f n e s s and m a s s d i s tribution. F u r t h e r , it might have been worthwhile to have e x p r e s s e d an opinion on the p r e s e n c e of e n t r a i n e d coolant on the effective m a s s d i s t r i b u tion of the dynamic s y s t e m . P r o b l e m s involving the v i b r a t i o n of a s t r u c t u r e i m m e r s e d in a liquid u s u a l l y entail c o r r e c t i o n , at least, to account for the fact that a portion of the fluid is put in motion. In the thirty pages devoted to Chapter 3, P r o f e s s o r Gyftopoulos (of M.I.T.) has attempted to t r e a t the subject of r e a c t o r d y n a m i c s in a completely g e n e r a l way. The f i r s t section entitled "Nuclear Reactor D y n a m i c s " is an e x t r e m e l y good review of the subject and should be compuls o r y r e a d i n g for those engaged in r e a c t o r safety. It s t a r t s with the b a s i c concepts of t r a n s p o r t theory and develops the u s u a l f o r m s of equations that are capable of computation. It then d i s c u s s e s at some length the l i m i t a t i o n s of the f a m i l i a r s p a c e - i n d e p e n d e n t equations, pointing out the difficulties of defining p r o m p t n e u t r o n lifetime, coefficients of r e a c t i v i t y , the r e l a t i o n s h i p between power level and n e u t r o n density, and their m e a s u r e m e n t , and the d a n g e r s of a s s u m i n g that a p a r t i c u l a r definition r e m a i n s constant during a t r a n sient.

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The next section, on "Analytical techniques u s e d in r e a c t o r safety studies" s t a r t s by looking at a z e r o e n e r g y r e a c t o r in a slow s t a r t - u p but quickly b e c o m e s involved in the s u b j e c t of i n h e r ent shut-down p h e n o m e n a in l a r g e s c a l e t r a n s i e n t s . This t r e a t m e n t tends to be r a t h e r a c a d e m i c and loses a lot by attempting to be e n t i r e ly general. A n u m b e r of the points would b e c o m e m o r e meaningful if they w e r e i l l u s t r a t e d by exa m p l e s but these a r e a s s u m e d to be provided in the other chapters. The subject of s p a c e - d e p e n d ent k i n e t i c s , which is a most i m p o r t a n t aspect of the v e r y l a r g e power r e a c t o r s that a r e now being built, is s u r p r i s i n g l y d i s m i s s e d in a few lines. The last section on " M e a s u r e m e n t of l i n e a r d y n a m i c c h a r a c t e r i s t i c s of n u c l e a r r e a c t o r s y s t e m s " e s t a b l i s h e s the b a s i s of the s i n u s o i d a l oscillation, c r o s s - c o r r e l a t i o n and a u t o - c o r r e l a t i o n methods of m e a s u r e m e n t . It then a t t e m p t s to d i s c u s s the p o s s i b i l i t y of using these techniques - which are e s s e n t i a l l y intended for l i n e a r s y s t e m s - for evaluating n o n - l i n e a r behaviour. The p a r t i c u l a r approach used may be of value to c e r tain types of s y s t e m but its r e l e v a n c e to n u c l e a r r e a c t o r s at other than z e r o - p o w e r conditions is doubtful. The appendices a r e m e r e l y d e s c r i p t i o n s of a n u m b e r of A m e r i c a n computer codes for dealing with z e r o - e n e r g y r e a c t o r k i n e t i c s . The r e f e r e n c e s , although sixty in n u m b e r , l a r g e l y ignore work done outside the USA. Dr. Nordheim has made m a j o r c o n t r i b u t i o n s to the methods of calculating r e s o n a n c e shielding and Doppler coefficients in t h e r m a l r e a c t o r s and in Chapter 4 he has produced an authoritative a c count of the methods of calculation for both fast and t h e r m a l r e a c t o r s . His d i s c u s s i o n of the physical p r i n c i p l e s and the a n a l y t i c a l methods of c a l c u l a t i o n p r o v i d e s a v e r y useful review, the main developments since the review was completed in 1964 being the i n t r o duction of computer p r o g r a m m e s which calculate the r e s o n a n c e shielding n u m e r i c a l l y , and which now s u p p l e m e n t the a n a l y t i c a l methods. The a g r e e m e n t between t h e o r e t i c a l p r e d i c t i o n s and i n t e g r a l m e a s u r e m e n t s is now thought to be l e s s good than was found to be the case at the beginning of 1964 and the r e s o n a n c e p a r a m e t e r s for 239pu and 235U a r e now taken to be m a r k e d l y different f r o m the values Dr. Nordheim quotes but the chapter is n e v e r t h e l e s s an excellent survey. Chapter 5 is c o n c e r n e d in the main with the m a i n t e n a n c e of safety during the time in which a r e a c t o r core is loaded to c r i t i c a l i t y and during s t a r t up to power. It s e e m s s t r a n g e that, although by far the g r e a t e r n u m b e r of r e a c t o r s built, i n -

cluding z e r o - p o w e r r e a c t o r s have been t h e r m a l s y s t e m s , this chapter should be w r i t t e n by a u t h o r s whose e x p e r i e n c e is l a r g e l y with s m a l l fast s y s t e m s . Consequently there is a s t r o n g e m p h a s i s on the l a t t e r type, for which the p r o b l e m s , difficulties and pitfalls are well d e s c r i b e d . However, the p h e n o m e n a p e c u l i a r to t h e r m a l r e a c t o r s a r e dealt with in a few p a r a g r a p h s only, contributed by other authors, and one is left with the i m p r e s sion that much m o r e could have been said which would have been both useful and p e r t i n e n t . After all, apart f r o m a very few s p e c i a l i s e d applications, there is no call for building the Godivalike s m a l l fast r e a c t o r s . The last section on "Nuclear Safety and Fuel Outside R e a c t o r s " was w r i t t e n some six y e a r s ago and it is now c l e a r l y and s e r i o u s l y out of date. The opinion of the authors " . . . that the status of g e n e r a l i n f o r m a t i o n about efficient fuel s t o r a g e and s h i p m e n t is u n s a t i s f a c t o r y , as is the p r e s e n t r a t e of i m p r o v e m e n t " was f i r s t e x p r e s s e d in 1961 or e a r l i e r and, l a r g e l y as a r e s u l t , the situation has changed so that lack of c r i t i c a l i t y data is no longer a p r o b l e m . This section adds nothing to the a l r e a d y published l i t e r a t u r e (upon which it l a r g e l y depends) and, in fact, may be m i s l e a d i n g in that it deals only with a n a r r o w aspect of a broad topic. The r e a d e r wishing to l e a r n about c r i t i c a l i t y control will be b e t t e r advised to consult m o r e r e c e n t works, e.g. the P r o c e e d i n g s of the 1965 IAEA Stockholm Sympos i u m on " C r i t i c a l i t y Control of F i s s i l e Materials". The t r e a t m e n t in Chapter 6 r e l a t i n g to s e n s i n g and control i n s t r u m e n t a t i o n is in g e n e r a l not thorough enough for the s e r i o u s d e s i g n e r or safety a s s e s s o r . It could be used by this type of p e r s o n as a source book for r e f e r e n c e s and poss i b i l i t i e s . In p a r t i c u l a r , pp. 295-299 over s i m plify the a n a l y s i s of f a i l u r e s . A s e r i o u s r e a d e r c o n c e r n e d with safety a n a l y s i s would, for e x a m ple, r e q u i r e to d i s t i n g u i s h in much m o r e detail the d i f f e r e n c e s between u n r e v e a l e d and r e v e a l e d f a i l - d a n g e r o u s faults. In the e a r l y days of r e a c t o r development the p r o b l e m s a s s o c i a t e d with r e a c t i v i t y addition were of g r e a t concern. A n u m b e r of i n v e s t i g a t i o n s were initiated and among these the work of the SPERT team with whom the author of Chapter 7 was associated, played a notable p a r t in developing our c u r r e n t u n d e r s t a n d i n g of r e a c t i v i t y events. As p a r t of the a n a l y s i s of e x p e r i m e n t a l e x c u r s i o n behaviour the development of s i m p l e m a t h e m a t i cal models aided the u n d e r s t a n d i n g of the i m p o r tance of v a r i o u s r e a c t o r p a r a m e t e r s . The author gives an e x c e l l e n t account of the way in which the s i m p l e models were adjusted to give a g r e e m e n t

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with e x p e r i m e n t . However, as pointed out in the chapter, s i m p l e models involving a r b i t r a r y cons t a n t s have significmat l i m i t a t i o n s when a t t e m p t s a r e made to extrapolate to other r e a c t o r s . Thus the chapter is mainly an account of p a r t of the h i s t o r y of r e a c t o r development, and as such p r o vides an excellent r e v i e w of the p r o c e s s by which the u n d e r s t a n d i n g of r e a c t i v i t y e x c u r s i o n behaviour was improved. In Chapter 10 there is an a d m i r a b l e account of the b a s i c p r i n c i p l e s and of topics of p e r e n n i a l i n t e r e s t such as f u n d a m e n t a l p h y s i c s of fast r e a c t o r s and the e x p e r i m e n t a l d e t e r m i n a t i o n of gene r a l r e a c t o r c h a r a c t e r i s t i c s . Many safety p r o b l e m s l e s s s u s c e p t i b l e to complete a n a l y s i s a r e also well p r e s e n t e d . However, to prodace a c o m p r e h e n s i v e account of a rapidly p r o g r e s s i n g field like fast r e a c t o r technology is a f o r m i d a b l e task which cannot be a c c o m p l i s h e d quickly. T h e r e is the danger that in the i n t e r v a l before publication p e r s p e c t i v e s will have changed, cad the r e l a t i v e p r o m i n e n c e given to each topic at the time of p r e p a r a t i o n will no longer r e f l e c t its c u r r e n t i m p o r t a n c e . This chapter is to some extent affected by changing e m p h a s e s of this type. For example, stability is not a m a j o r p r o b l e m in large sod i u m - c o o l e d (though not n e c e s s a r i l y s t e a m - or gas - cooled) r e a c t o r s because of t h e i r p r o m p t n e g a t i v e Doppler effect and r e d u c e d s e n s i t i v i t y to bowing. S i m i l a r l y , r e f i n i n g the B e t h e - T a i t type of a n a l y s i s to include Doppler and vapour p r e s s u r e effects (e.g. Hicks' paper at the 1965 A r gonne Conference) h.'~s shown the d i r e c t r e l e a s e of m e c h a n i c a l ener~7 f r o m a n u c l e a r e x c u r s i o n following meltdown to be much l e s s s e v e r e than was i n i t i a l l y e s t i m a t e d . Of g r e a t e r c u r r e n t i n t e r e s t a r e u n c e r t a i n t i e s in the c o u r s e of events b e c a u s e of h y d r o d y n a m i c i n s t a b i l i t i e s when chann e l boiling begins (e.g. l o s s of flow accidents) and violent i n t e r a c t i o n between hot fuel and sodium analogous to the SPERT ID incident. In the r e v i e w e r ' s opinion i n t e r e s t in the B e t h e - T a i t type of incident should have shifted to the potentially d e s t r u c t i v e power of the heat s t o r e d in the m e l t e d core (Q*) and its adequate s i m u l a t i o n by conventional explosi'ves now that the d i r e c t n u c l e a r "explosion" has been shown to be a r e l a tively low p r e s s u r e ]?rocess c o m p a r e d with TNT. T h e r e a r e also one or two i n s t a n c e s where the r e a d e r might have been given m o r e help in app r e c i a t i n g the size and s i g n i f i c a n c e of n u m e r i c a l v a l u e s . Thus, figure 2-4 (on sodium boiling) is inadequately explained and labelled. In the e x c e l -

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lent s e c t i o n on B e t h e - T a i t methods of a n a l y s i s a typical e x p r e s s i o n for the i m p o r t a n t p a r a m e t e r X, r e l a t i n g r a m p r a t e to r e a c t i v i t y changes due to fuel e n e r g y density, is given. It is not r e a d i l y a p p a r e n t f r o m the text that n e u t r o n lifetime, which o c c u r s in the e x p r e s s i o n , is to be exp r e s s e d in m i c r o s e c o n d s . F u r t h e r m o r e , there is c o n s i d e r a b l e d i s c u s s i o n of energy r e l e a s e s for very large values of X without making it c l e a r that such v a l u e s i m p l y r a m p r a t e s many t i m e s l a r g e r than those given e a r l i e r as typical of collapse u n d e r gravity. The concluding chapter s u f f e r s f r o m the i n evitable fault of works of this kind in that it only contains i n f o r m a t i o n up to the end of 1963 and therefore as is inevitable with an e n c y c l o p a e d i a of this sort, it is a l r e a d y three y e a r s out of date. The portion dealing with a c c i d e n t s draws on published i n f o r m a t i o n and the l e s s o n s and conc l u s i o n s drawn, while sound as far as they go, suffer f r o m a f a m i l i a r difficulty in not t e l l i n g the whole story in many c a s e s where some degree of p e r s o n a l or corporate blame or n e g l e c t may have been involved. This is unfortunate b e c a u s e one of the main o b j e c t - l e s s o n s is that accidents do not usually happen by t h e m s e l v e s - they a r e n e a r l y always a s s i s t e d by a m i s t a k e or o m i s s i o n on the p a r t of a human being. Because the section must r e l y on published data, SL-1, SRE and EBR-1 r e c e i v e a l m o s t half of the total space allotted. As a r e s u l t the l a t t e r p a r t tends to tail off into what looks like m a k e weights in s e c t i o n 5. In dealing with the Windscale accident, it may be noted that the f i r s t sentence a p p e a r s to imply (of c o u r s e e r r o n e o u s l y ) that No. 1 R e a c t o r is s t i l l in being as a r e a c t o r . In g e n e r a l , the e x p e r i e n c e quoted is useful to those who a r e not a l r e a d y f a m i l i a r with the events t h e m s e l v e s , and the c o n c l u s i o n s a r e sound but p e r h a p s unavoidably not always completely exhaustive. Some of the bulky m a t t e r quoted at g r e a t length in two or three c a s e s could have been left to be looked up in r e f e r e n c e s , with only the a c tual outline and l e s s o n s being quoted in the p r e s ent volume. This r e v i e w has been compiled f r o m c o n t r i b u tions r e c e i v e d f r o m n u m e r o u s staff m e m b e r s of the.U.K.A.E.A, whose cooperation I gratefully acknowledge. F . R. FARMER

Safeguards Division U.K.A.E.A. Health and Safety B r a n c h Risley, Warrington, Lancs.