By W. B. Terney, D. C. Wade (auth.), Ernest J. Henley, Jeffery Lewins, Martin Becker (eds.)
The editors are happy to provide to the nuclear com munity our new-look annual overview. In its new glance, with Plenum our new writer, we could desire for a extra speedy pre sentation to our viewers of the contents for his or her consi deration; the contents themselves, even if, are prompted from an identical spirit because the first 9 volumes, reports of vital advancements in either a old and an anticipa tory vein, interspersed with occasional new contributions that appear to the editors to have greater than ephemeral curiosity. during this quantity the articles are consultant of the editorial board coverage of overlaying various pertinent issues from summary concept to perform and contain experiences of either kinds with a spicing of whatever new. Conn's assessment of a conceptual layout of a fusion reactor is well timed in bringing to the eye of the final nuclear group what's maybe popular to these operating in fusion - that functional fusion reactors are going to require a lot skillful and complicated engineering to make the intense hopes of fusion because the inex haustible power resource undergo fruit. Werner's overview of nu merical ideas for fission reactor kinetics, whereas now not precisely backward having a look, is no less than directed to what's now a good tested, nearly traditional box. Fabic's sum mary of the present loss-of-coolant coincidence codes is one realisation of the depth of attempt that permits us to name a mild water reactor 'conventional.
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WADE 54 The nature of the outer region can be determined by examining the value of H at the outer boundary. 10 since W 2 is zero at the outer boundary and must be greater than zero within the region. Therefore, H has a negative value, since leakage is out of the core making x 2 (t f ) negative. Conversely, if the outer region is k , H is positive. Since for the optimal reactor H must ""max have its greatest value, it is concluded that the outer region must be one of k • ""max From the foregoing arguments, the optimal reactor is known to consist of regions of minimum and maximum k , with the outer region required to be k Remarkably, ""max these conclusions are obtainable by inspection.
58. This is accomplished by solving the 2n homogeneous equations numerically, i=l,n separate times, taking ~(t ) = 0 and p. (t ) = o. ,; j=l. •• n. The termo"partitioned" is JH 0 ~J used because the unit initial conditions are applied only to the equations in £. For each i, a row of the nxn (p only) state transition matrix ~ is obtained, where the jth term is P'H(t l ). Once the full matrix! is available, the naw initial conditions are obtained by a matrix inversion, OPTIMAL CONTROL APPLICATIONS IN NUCLEAR REACTOR 33 Then the inhomogeneous set of equations is numerically solved for the k+lth iteratei the entire process is repeated until convergence is obtained.
There is no formal way to determine how many region types there must be or how to arrange them. The number and arrangement depends on the magnitudes of k and k . • The optimal syn""max ""m~n thesis of allowed region types can be determined by postulating arrangements by trial and error until the Pontryagin conditions are satisfied and the Lagrange multiplier, W 2 has the proper sign in each region. Analytic solutions were obtained for two and three region reactors (46) and were examined for a variety of values for k and k .
Advances in Nuclear Science and Technology by W. B. Terney, D. C. Wade (auth.), Ernest J. Henley, Jeffery Lewins, Martin Becker (eds.)