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Group cross-sections for fast reactors; Sections efficaces de groupes pour les reacteurs a neutrons rapides; Gruppovye secheniya reaktorov na bystrykh nejtronakh; Secciones eficaces de grupos para reactores rapidos

Abstract

Group cross-sections for fast reactors. A general discussion of the multi-group-diffusion equations is given, and the correct form of the group cross-sections discussed. In particular, it is shown that the average transport cross-section may be written to a certain approximation in terms of an average mean free path. The calculation of this quantity is lengthy because it is not amenable to expression in terms of elemental averages; however, several inequalities are proved which simplify the averaging procedure required. Three further aspects of group cross-sections which are frequently ignored, but may be important in detailed design study, are discussed: (a) The use of the same set of group-averaged cross-sections for all fast reactors is invalid if the spectra in different reactors are dissimilar and if the cross-sections vary rapidly over the group, conditions which frequently hold. An iteration procedure is described by which the correct averages are found; it is then used to determine the sensitivity of reactor calculations to spectral effects. (b) In transport calculations such as S{sub n}, averages must be made over both angle and energy. Since the flux is non-separable in angle and energy, extreme care is necessary to avoid erroneous results. The S{sub n} equation is  More>>
Authors:
Zweifel, P P; [1]  Ball, G L [2] 
  1. University of Michigan, Ann Arbor, MI (United States)
  2. Atomic Power Development Associates, Inc., Detroit, MI (United States)
Publication Date:
Mar 15, 1962
Product Type:
Conference
Report Number:
IAEA-SM-18/65
Resource Relation:
Conference: Seminar on Physics of Fast and Intermediate Reactors, Vienna (Austria), 3-11 Aug 1961; Other Information: 14 refs, 1 fig., 4 tabs; Related Information: In: Physics of Fast and Intermediate Reactors. V. I. Proceedings of the Seminar on the Physics of Fast and Intermediate Reactors. V. I| 500 p.
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; ABSORPTION; CROSS SECTIONS; FAST REACTORS; MEAN FREE PATH; MULTIGROUP THEORY; NEUTRON DIFFUSION EQUATION; NEUTRON SLOWING-DOWN THEORY; NEUTRON SPECTRA; NEUTRONS; RESONANCE INTEGRALS; SENSITIVITY; SPHERICAL HARMONICS METHOD
OSTI ID:
22072705
Research Organizations:
International Atomic Energy Agency, Vienna (Austria)
Country of Origin:
IAEA
Language:
English
Other Identifying Numbers:
Other: ISSN 0074-1884; TRN: XA12S0192032440
Submitting Site:
INIS
Size:
page(s) 189-205
Announcement Date:
Mar 14, 2013

Citation Formats

Zweifel, P P, and Ball, G L. Group cross-sections for fast reactors; Sections efficaces de groupes pour les reacteurs a neutrons rapides; Gruppovye secheniya reaktorov na bystrykh nejtronakh; Secciones eficaces de grupos para reactores rapidos. IAEA: N. p., 1962. Web.
Zweifel, P P, & Ball, G L. Group cross-sections for fast reactors; Sections efficaces de groupes pour les reacteurs a neutrons rapides; Gruppovye secheniya reaktorov na bystrykh nejtronakh; Secciones eficaces de grupos para reactores rapidos. IAEA.
Zweifel, P P, and Ball, G L. 1962. "Group cross-sections for fast reactors; Sections efficaces de groupes pour les reacteurs a neutrons rapides; Gruppovye secheniya reaktorov na bystrykh nejtronakh; Secciones eficaces de grupos para reactores rapidos." IAEA.
@misc{etde_22072705,
title = {Group cross-sections for fast reactors; Sections efficaces de groupes pour les reacteurs a neutrons rapides; Gruppovye secheniya reaktorov na bystrykh nejtronakh; Secciones eficaces de grupos para reactores rapidos}
author = {Zweifel, P P, and Ball, G L}
abstractNote = {Group cross-sections for fast reactors. A general discussion of the multi-group-diffusion equations is given, and the correct form of the group cross-sections discussed. In particular, it is shown that the average transport cross-section may be written to a certain approximation in terms of an average mean free path. The calculation of this quantity is lengthy because it is not amenable to expression in terms of elemental averages; however, several inequalities are proved which simplify the averaging procedure required. Three further aspects of group cross-sections which are frequently ignored, but may be important in detailed design study, are discussed: (a) The use of the same set of group-averaged cross-sections for all fast reactors is invalid if the spectra in different reactors are dissimilar and if the cross-sections vary rapidly over the group, conditions which frequently hold. An iteration procedure is described by which the correct averages are found; it is then used to determine the sensitivity of reactor calculations to spectral effects. (b) In transport calculations such as S{sub n}, averages must be made over both angle and energy. Since the flux is non-separable in angle and energy, extreme care is necessary to avoid erroneous results. The S{sub n} equation is studied in terms of a simple model, and a criterion is derived which may prove useful in determining the importance of angular non-separability in reactor calculations. (c) A consistency relation among group-diffusion coefficients, slowing-down power and absorption cross-sections is derived from neutron-conservation arguments. It is shown that a frequently used definition of group absorption cross-section in terms of effective resonance integrals is not correct, but must be modified according to the type of multi-group scheme being used. (author) [French] Les auteurs procedent a une etude generale des equations de diffusion a plusieurs groupes et de la forme exacte des sections efficaces de groupes. Ils montrent notamment que la section efficace moyenne de transport peut, avec une certaine approximation, s'exprimer en termes de libre parcours moyen. Le calcul de cette quantite prend beaucoup de temps, car elle ne peut se reduire en moyennes elementaires; neanmoins, on a demontre certaines inegalites, qui simplifient la methode de calcul des moyennes qui doit etre utilisee. Les auteurs analysent trois autres aspects des sections efficaces de groupes, que l'on neglige souvent, mais qu'il peut etre important de connaitre pour les etudes de reacteurs. a) Il est injustifie d'utiliser pour tous les reacteurs a neutrons rapides le meme ensemble de sections efficaces dont la moyenne par groupe a ete calculee si les spectres des differents reacteurs sont dissemblables et si les sections efficaces varient rapidement a l'interieur du groupe, comme c'est le cas le plus souvent. Les auteurs decrivent une methode d'iteration qui permet d'obtenir les valeurs moyennes correctes; ils determinent ensuite, a l'aide de cette methode, dans quelle mesure les calculs de reacteurs sont influences par les effets de spectre. b) Dans les calculs de transport (la methode S{sub n}, par exemple), les moyennes doivent etre calculees en tenant compte a la fois de tous les angles et de toutes les energies. Etant donne qu'on ne peut dissocier dans le flux une partie angulaire et une partie energetique, la plus grande attention est necessaire pour eviter les erreurs. Les auteurs etudient l'equation obtenue par la methode S{sub n} sous la forme d'un modele simple, et en tirent un critere qui pourrait aider a determiner l'importance de la non-separabilite angulaire dans les calculs de reacteurs. c) A partir de raisonnements fondes sur la conservation du nombre de neutrons, il est possible d'obtenir une relation consistant entre les coefficients de diffusion de groupe, le pouvoir de ralentissement et les sections efficaces d'absorption. Les auteurs montrent qu'il n'est pas exact de definir, comme c'est souvent le cas, la section efficace de groupe en terme d'integrales de resonance efficace, mais qu'il faut modifier cette definition suivant le type de schema multigroupe utilise. (author) [Spanish] La memoria discute en terminos generales las ecuaciones de difusion de grupos multiples y la forma correcta de las secciones eficaces correspondientes . En particular, demuestra que la seccion eficaz media de transporte puede expresarse con bastante precision en terminos de un promedio de recorridos libres medios. Esta magnitud es dificil de calcular porque no se puede expresar en funcion de promedios elementales ; sin embargo, se demuestran varias desigualdades que simplifican el procedimiento de determinacion de promedios. La memoria discute otros tres aspectos de las secciones eficaces de grupos que con frecuencia se ignoran, pero que pueden ser importantes al estudiar detalladamente un diseno. a) El empleo de los mismos valores medios correspondientes a las secciones eficaces de grupos para todos los reactores rapidos no se justifica si los espectros de los diferentes reactores no son similares y si las secciones eficaces varian rapidamente dentro del grupo, como ocurre a menudo. Los autores describen un metodo de iteracion, que permite obtener valores medios correctos y determinar en que medida los efectos espectrales ejercen influencia sobre los calculos de reactores. b) En los calculos de transporte (metodo S{sub n} por ejemplo), los promedios deben evaluarse en funcion del angulo y de la energia. Como el flujo no es separable en una parte angulo y en una parte energetica, es necesario proceder con sumo cuidado para evitar errores. La ecuacion S{sub n} se estudia sobre la base de un modelo sencillo, y de este estudio se deduce un criterio que puede ser de utilidad al determinar la importancia de la no-separabilida d angular en los calculos de reactores. c) Basandose en los argumentos de conservacion neutronica, se deriva una relacion de compatibilidad entre coeficientes de difusion de grupos, capacidad de moderacion y secciones eficaces de absorcion. Se demuestra que la definicion de las secciones eficaces de absorcion de grupos basada en integrales de resonancia eficaz que se emplea frecuentemente no es correcta, siendo preciso modificarla de acuerdo con el metodo de grupos multiples que se utilice. (author) [Russian] Daetsya obshchij obzor mnogogruppovykh diffuzionnykh uravnenij i rassmatrivaetsya pravil'naya forma gruppovykh poperechnykh sechenij. V chastnosti, pokazano, chto srednee poperechnoe sechenie perenosa mozhet do nekotoroj stepeni priblizitel'no byt' vyrazheno v vide srednej velichiny svobodnogo probega. Podschet takogo kolichestva zanimaet mnogo vremeni, tak kak on ne poddaetsya vyrazheniyu v vide ehlementarnogo usredneniya ; odnako podtverdilis' nekotorye neravnomernosti chto uproshchaet neobkhodimyj metod usredneniya. Rassmatrivayutsya tri sleduyushchikh voprosa gruppovykh poperechnykh sechenij, kotorye chasto ignoriruyutsya, no kotorye mogut imet' znachenie pri detal'nom izuchenii proekta : a) Ispol'zovanie odnoj i toj zhe serii usrednennykh po gruppam sechenij dlya vsekh reaktorov na bystrykh nejtronakh nichego ne daet, esli spektry razlichnykh reaktorov ne odinakovy i esli secheniya bystro izmenyayutsya v gruppe; takoe polozhenie chasto imeet mesto. Daetsya opisanie metoda povtoreniya, posredstvom kotorogo ustanavlivaetsya pravil'noe usrednenie, i ehtot metod ispol'zuetsya dlya opredeleniya vliyaniya spektral'nykh ehffektov na reaktornye raschety. b) Pri raschetakh perenosa, takikh, kak S{sub n} usredneniya dolzhny byt' vypolneny kak po uglu, tak i po ehnergii. Tak kak potok nel'zya razdelit' na 'uglovoj' i 'ehnergeticheskij', neobkhodimo ochen' tshchatel'no izbegat' oshibochnykh rezul'tatov. Uravnenie S{sub n} izuchaetsya v vide prostoj modeli, i poluchaetsya kriterij, kotoryj mozhet okazat'sya poleznym pri opredelenii znacheniya uglovoj nerazdelimosti v reaktornykh raschetakh. c) Na osnove argumentov o sokhranenii nejtronov vyvoditsya postoyannoe otnoshenie mezhdu gruppovymi koehffitsientami diffuzii, umen'sheniem ehnergii i absorbtsiej poperechnykh sechenij. Pokazano, chto chasto ispol'zuemoe opredelenie gruppovogo poperechnogo secheniya absorbtsii v vide integralov ehffektivnogo rezonansa yavlyaetsya nepravil'nym, odnako ono dolzhno byt' izmeneno v sootvetstvii s ispol'zuemym tipom mnogogruppovoj skhemy. (author)}
place = {IAEA}
year = {1962}
month = {Mar}
}