Comparison of analytical and variational solutions of steady-state neutron-diffusion problems

Lee, C.E.; Wang, Fan; Bratton, Robert L.

doi:10.1016/0306-4549(84)90075-6

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…It is remarkably direct, in the sense of being free of trial functions, and subsequently not needing any appending of the variational functional with conservational Lagrangian constraints [7]. Moreover, the global accuracy of these eigensolutions is governed solely by the accuracy of determination of the bivariant coefficients which obviously deteriorates with decreasing the nodal size.…”

Section: Discussionmentioning

confidence: 99%

“…A major distinctive feature of the reported adjoint nodal technique from other nodal methods is that its whole reactor solutions (83) satisfy the original group diffusion equation (1) for every mode m, not only at the interfacial positions but everywhere in the nodal volumes. It is remarkably direct, in the sense of being free of trial functions, and subsequently not needing any appending of the variational functional with conservational Lagrangian constraints [7]. Moreover, the global accuracy of these eigensolutions is governed solely by the accuracy of determination of the bivariant coefficients which obviously deteriorates with decreasing the nodal size.…”

Section: Discussionmentioning

confidence: 99%

“…A significant extent of this distortion, however, may be compensated via supplementing the effective differentiation (discretization) with some sort of an opposite (to differentiation) integration operation. This fact perhaps explains why eigensolutions by nodal methods, which involve somewhat more complicated linear systems than FD techniques, have the potential advantages of fewer nodes for equivalent accuracy compared to FD in benchmarks [7]. Moreover, the indicated integration operation may be performed with a variety of weighting functions and could be direct or in functional form; from which stems the variety in nodal schemes.…”

Section: It Variational Analysismentioning

confidence: 99%

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Nodal adjoint method for multigroup diffusion in heterogeneous slab reactors

Haidar

1992

Numerical Methods Partial

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A variational adjoint nodal method is proposed to yield an approximation theory for the eigenvalues of the multigroup neutron diffusion boundary value problem of a heterogeneous quasicritical one-dimensional slab reactor. Semianalytical eigensolutions are constructed for the associated whole-reactor group nodal fluxes. The method appears to be mathematically more consistent, computationally more straightforward, and practically more convenient than alternative nodal or finite element schemes. 0 1992 John Wiley and Sons, Inc.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: It Variational Analysismentioning

confidence: 99%

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Nodal adjoint method for multigroup diffusion in heterogeneous slab reactors

Haidar

1992

Numerical Methods Partial

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Multiplication of neutrons from an external source in cascade subcritical systems with unilateral neutron coupling

Seliverstov¹

1996

At Energy

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The possibility of using suheritical reactors with an external source for burning wastes from nuclear power plants is now being widely discussed. It is suggested that neutrons from a stripping reaction, which form during bombardment of heavy nuclei by a beam of high-energy (-1 GeV) protons from a linear accelerator, be used as the external source. The thermal power of a subcritieal reactor and therefore the potential for burning up wastes depend primarily on the proton current and the multiplication of the source neutrons in the system. Neutron multiplication is determined mainly by the subcriticality of the reactor and its internal properties and arrangement. For the conventional arrangement, consisting of a one-core reactor and a nonmultiplying target, and with an effective neutron multiplication factor -0.95, regarded as the upper limit of criticality which eliminates the possibility of reactivity accidents, source neutron multiplication in the system equals -10-17. With such multiplication, to obtain thermal power of the system of practical interest -2000 MW, the required proton current is -1130 mA, which requires using linear accelerators. The desire to lower the required proton current while rnaintainJllg safety of the system motivated investigations of ways to increase substantially the multiplication in the system while maintaining the presen'bed suberitieality. Specifically, a so-called cascade scheme (or system of coupled blankets) [1, 2] has been proposed. In this scheme the target is essentially a small fast subcritical reactor and the blanket consists of a suberitical thermal reactor with low neutron leakage. Unilateral neutron coupling, in which the fission neutrons of the blanket do not initiate fissions in the target, is provided. In some works it is asserted that such systems will make it poss~le to increase the neutron multiplication by more than a factor of 10 while preserving a fLxed subcriticality and, therefore, safety. This will make it poss~le to switch from linear accelerators to cyclotrons or even electron accelerators, which will greatly simplify the construction of the setup as a whole and decrease its cost. In my opinion, such assertions are much too optimistic. For reasonable parameters of the suberitical state and power, the gain achieved in source neutron multiplication in the cascade arrangements will be very small, it will not make it possible to do away with proton accelerators, and it will hardly compensate the unavoidable complication of the construction and operation of the subcritical reactor. This paper proposes a method and basic results on estimation of the possible multiplication in cascade systems in comparison with the conventional arrangements employing nonmultiplying targets. The method is based on the introduction of the concept of the value of a source neutron and the application of the coupled-core method for calculating cascade systems.Value of a Source Neutron. The distribution of the neutron flux in a suberitical target-blanket system is determined by the solut...

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A conservative variational method for multicomponent concentration time dependent diffusion

Lee

Wilson

1985

Journal of Computational Physics

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Comparison of analytical and variational solutions of steady-state neutron-diffusion problems

Cited by 5 publications

References 4 publications

Nodal adjoint method for multigroup diffusion in heterogeneous slab reactors

Nodal adjoint method for multigroup diffusion in heterogeneous slab reactors

Multiplication of neutrons from an external source in cascade subcritical systems with unilateral neutron coupling

A conservative variational method for multicomponent concentration time dependent diffusion

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