摘要:

The elementary solutions of the two-group neutron-transport equation are used to solve critical problems for finite slabs and spheres. The half-range orthogonality properties of the basic eigenvectors are used, along with the fundamentalH-matrix, to reduce the encountered system of singular integral equations to a system of Fredholm-type equations, and these final equations are solved iteratively to yield accurate predictions of the two-group values of the extrapolated endpoint and critical dimensions for a selected set of slabs and spheres.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22582

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

Solutions for collision densities in a slab with an energy- and angle-dependent degenerate scattering kernel are developed. The slab distribution is expanded in a set of regular and singular eigenfunctions and the expansion coefficients are obtained as solutions of a matrix integral equation. From invariance principles, this integral equation depends upon the half-space generalized Milne solution. To obtain this solution one must solve a nonlinear matrix equation for a generalization of the ChandrasekharH-function. Approximate solutions and numerical calculations for the heavy-gas scatterer are presented, including emergent distributions for the slab.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22583

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

Estimated error bounds derived from polynomial calculations have been used to revise the truncation error estimates of published data on gamma-ray penetration in water. It is also shown that more efficient use of moment data is possible to obtain greater accuracy in specific penetration regions and to extend the accuracy of polynomial calculations to greater penetrations. The results also indicate that in addition to the asymptotic power law, data to perhaps 40 mean-free-paths may be needed to make accurate extrapolations to arbitrarily great penetrations.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22584

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

A method of extending moments method calculations for monoenergetic, point isotropic gamma ray sources to depths of approximately 50 mean-free-paths is described. Sample calculations are given for water and aluminum. A method of error analysis recently developed by Spencer suggests that for the range from 10 to∼50 mean-free-paths, the errors associated with the reconstruction of the flux from moments are generally<1%. Comparisons are made between the asymptotic, deep penetration trend of the calculated results and the trend predicted by a theory developed by Fano.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22585

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

A new method of pulsed neutron experimentation is proposed and successfully applied to a beryllium metal system. The present technique utilizes theγ-ray flash from an electron linear accelerator. The employment of an“internal”neutron source, i.e., the (γ,n) reaction in beryllium, which is“softer”than the often used“external”14-MeV neutrons from a generator, improves the state of the art of the die-away technique in beryllium. The reduction of background neutrons makes it possible to measure the decay curve until∼1800µsec after a burst even for a small beryllium assembly of 15×15×15 cm in dimension (B2= 0.101 cm-2), while in earlier experiments the decay curves have been measured only until∼600µsec for such a small beryllium assembly.The present analysis of decay curves indicates that the assumption made by Kothari, who derived the limit of a discrete decay constant for crystalline moderators, is not valid at least for beryllium. On the other hand, Corngold’s limit is consistent with the experimental results.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22586

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

There have been some weak points in the use of modern control theory in xenon shutdown problems. The aim of this paper is to show how Pontryagin’s maximum principle should be applied to these problems. To do this, two special problems have been picked up and solved completely. It is shown that the solution to the energy optimal xenon shutdown problem of Rosztoczy is not a bang-bang control as proposed by Rosztoczy even when the xenon restraint is omitted. The actual optimum control includes a phase with continuously varying control. Further, numerical examples are given to show that the difference in the costs between the optimum control and the control proposed by Rosztoczy is negligible.The other problem considered is the energy optimal xenon shutdown of Lewins et al. It is shown that the solution can be found analytically which gives a slight improvement to their analysis.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22587

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

As part of the liquid-metal fast breeder reactor (LMFBR) safety program, the consequences of a hypothetical molten-fuel release into sodium coolant following fuel pin failure(s) must be evaluated, in order that design constraints can be established to maximize the safety and minimize the economical penalties of such an event. This work represents the first attempt to interpret the voiding rates obtained from an in-pile, fuel-failure experiment in the TREAT reactor in terms of a molten fuel-coolant interaction.Results indicate that it is not only possible to reduce in-pile data to a workable form, but also to obtain representation of loop conditions for simple geometries. The analysis has been successful in reproducing the experimental voiding history in a selected TREAT experiment. It is further shown that the formation of condensate at cold boundaries significantly reduces the amount of energy imparted to the expanding vapor bubble, which in turn limits the extent of the thermal-to-mechanical energy conversion process. It is important to account for this effect when extrapolating in-pile results to reactor conditions.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22588

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

Characteristics of an ideal cascade are analyzed by two differential equations representing the conservation of UF6and235UF6flow. The controlling variables are identified as the cut and the separation factor of centrifuges and of stages as well as feed flow rate. The controlled variables are flow rate and enrichment of stages, especially of the product and waste. The sensitivity of the controlled variables to the controlling variables are analyzed by linearizing the conservation equations, and analytic expressions are obtained. The change in the separative work of the cascade is a sum of changes in the separative work of the constituent centrifuges. When the flow rate is chosen to optimize the separative work of a single centrifuge, the plant separative work is maximum and stationary at the rated feed flow. It has been demonstrated in a few examples that these simple relations for the ideal cascade are useful for the planning, design, and operation of cascade plants.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22589

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

AbstractGast and Candelore have recently pointed out that the standard method of computing confidence limits in Monte Carlo calculations is invalid for iterated-source calculations. This note develops a formula for a confidence-limit correction factor for such calculations, and discusses its use.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22590

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor

摘要:

AbstractA study has been made to evaluate two aspects of the spectral synthesis method as formulated by Lorenzini and Robinson: (1) evaluation of spectral synthesis, relative to group collapsing, in terms of computational time, and accuracy for typical liquid metal fast breeder reactor problems; and (2) the numerical procedures used in solving the equations in two-dimensional geometries.Three trial spectra were used in the spectral synthesis method; the few-group calculations were done with 3, 4, and 8 groups collapsed from a 24-group set. Results were obtained and compared for keff, breeding ratios, fractional power in regions, and power distributions.

ISSN:0029-5639    

DOI:10.13182/NSE73-A22591

出版商:Taylor&Francis    

年代:1973

数据来源: Taylor