摘要:

The variational method as applied to the monoenergetic integro-differential Boltzmann equation is investigated. It is shown that rendering the Lagrangian stationary with respect to small changes in the directional flux and adjoint directional flux is equivalent to solving the Boltzmann and adjoint Boltzmann equations. Topics discussed include the use of variational weight functions, the inclusion of boundary terms in the functional, the interpretation of a variational optimum for a nonself-adjoint operator, and the second variation. It is shown that, for the general trial function ensemble and within a special restricted trial function ensemble, the variational method is a saddle point principle. The formalism developed is applied to the angular expansion in polynomials of the directional flux.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26494

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

The monoenergetic integro-differential Boltzmann equation with an arbitrary scattering kernel is transformed to a self-adjoint form and the corresponding Lagrangian written. It is shown that this transformation results in a loss of the continuity (neutron conservation) information contained by the Boltzmann equation. This information is recovered by writing the directional flux as the sum of an even and odd function (in angle) and considering a self-adjoint Lagrangian for only one portion (even or odd) of the directional flux. This procedure is shown to be equivalent to separating the nonself-adjointness from the Boltzmann operator. Further, it is shown that this self-adjoint principle is an extremum principle if the mean number of secondaries per collision is less than one. This self-adjoint formalism is applied to the angular expansion of the directional flux which results in an improved diffusion theory. Numerical results for the linear extrapolation distance and diffusion coefficient are compared with the classical (P−1) diffusion theory.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26495

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

A model is proposed for calculating the scattering of thermal energy neutrons by polyethylene. It is seen that a reasonable fit to the experimental total cross section results. This model is then used to calculate infinite medium spectra and the results compared with calculations using water and perfect gas scattering kernels, with a harder predicted spectrum apparent. The results are compared with experimental data for two amounts of absorption, and agreement between experiment and theory using an appropriate scattering model is observed. The model is then used to calculate reactor quantities for a particular one-dimensional finite lattice. The sensitivity of the flux spectra and criticality to the choice of scattering kernel is presented. The former quantity is more sensitively dependent than the latter.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26496

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

In the case of an infinite reflector, the group diffusion equations are converted to a system of integral equations by a Green's function technique. This system is then Fourier transformed. The transformed Fredholm-type equations have a degenerate kernel, and the solution may be reduced to a system of linear algebraic equations with infinitely many unknowns.The theory is developed for the case of a three-group three-region cylindrical flux trap assembly. An extension of the method to a general multigroup multiregion problem will be considered in a later paper.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26497

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

The material bucklings of twenty-five D2O moderated lattices of natural UO2rod clusters were measured in the Process Development Pile (PDP). The measurements were made in one-region loadings, and should therefore be subject to little systematic error. A number of the lattices employed voided housing tubes around the fuel assemblies. Values of migration areas inferred from measurements of positive periods are also presented.An evaluation of the errors in the buckling measurements indicated that the bucklings should be accurate to about 1%. The migration areas are compared with theoretical values obtained from the Benoist theory, and the agreement is shown to be good.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26498

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

The neutron diffusion length in paraffin has been measured by a static technique in the temperature range from 60°C to 130°C. The neutron transport cross section was abstracted from the measured diffusion length.A semiempirical prescription describing the temperature dependence of the neutron transport cross section in paraffin and polyethylene has been derived. The derivation is based on that of the Radkowsky prescription for water. A calculation of the transport cross section in paraffin and polyethylene has been carried out in the temperature range from 20°C to 125°C.The measured transport cross section in paraffin has been compared with that predicted by the prescription. The values agree within 3%. A 14% difference between the values for paraffin and those for water gives credence to the assumption that calculations of the characteristics of plastic moderated critical assemblies can be improved by the use of the proper prescription.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26499

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

A method for determining Doppler broadening which is rigorous for a Maxwellian gas of resonance absorber atoms has been reduced to computation. Doppler broadened absorption cross sections for low-lying resonances of Er167and Xe135have been computed both by this more accurate method and by theψ-function approximation which is in general use. The more accurate method was found to give a correction, compared with theψ-function method, which was several percent in the case of Xe135and was less than 1 % for Er167. The time required for the more accurate computation was found to be short enough to be practical for those special applications where it is of interest.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26500

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

In order to greatly increase the power density of boiling liquid reactors, more turbulent and effusive boiling of the moderator coolant must ensue. However, this would entail handling very large random reactivity excursions with its attendant dangers.Perhaps, this problem could be circumvented by a novel, hyper-speed control comprised of“rod equivalent”systems of very fast response. This would allow the reactor to approach its stability limit more closely and thereby increase the power density. To realize such systems, this effort is directed toward a different conceptualization of the reactor control problem as opposed to the less than adequate small excursion linearized theory extant. The idea involved in“bang-bang”control is that of ever driving the reactor toward its equilibrium state as rapidly as possible from randomly perturbed states in which it finds itself because of the turbulent moderator.The control problem is formulated in a fashion analogous to the brachistochrone class of problems, but with a stochastic feature due to the random reactivity fluctuations. Using the methods of dynamic programming, a functional equation in the minimum time for the reactor to be driven back to equilibrium is obtained. From this is derived an optimal reactor control policy.A controller computer can then be synthesized which instantaneously senses the perturbed state of the reactor. It then computes the optimal reactivity policy and sends actuating signals to the“rod(s)”system. The responding reactor is then found in its new perturbed state, which is again read, etc. This procedure continually drives the reactor toward the equilibrium state in the sense of minimum time defined above.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26501

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

A charged particle passing through water creates a thermal spike, a region of high temperature along the track. The thermal spike expands explosively, thus producing a pressure wave, and then breaks up because of surface tension into discrete regions of water vapor and hydrogen gas. These vapor-gas microbubbles can act as nucleation centers in superheated or gas supersaturated solutions.Calculations based on this thermal spike model are presented of the total energy and minimum linear energy transfer (LET) required to form nucleation centers of a given size, and the calculations are compared to published data on the radiation nucleation of superheated and supersaturated aqueous solutions. Calculations are also presented of the pressure created by the rapid expansion of the thermal spike, and of the lifetime of the vapor-gas microbubbles under conditions in which they collapse. The calculations cover an LET range of 0.1 to 10 Mev/µor, approximately, from the maximum LET of recoil protons in water to the maximum LET of fission fragments in water. The calculations are carried out for a liquid pressure of one atmosphere and two temperature conditions: the minimum temperature at which vapor nuclei of given size will grow and 0°C. The effect of high pressures and temperatures on the radiation nucleation of vapor bubbles is discussed briefly in terms of the foam limit.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26502

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor

摘要:

Three parallel plate assemblies were tested to investigate the flow induced deflections of the individual plates. Special strain gages imbedded in the edges of the plates were used to measure plate deflections at flow rates up to 190% of the theoretical collapse velocity. The results indicate that the flow induced deflection phenomenon is essentially a magnification of built-in channel spacing perturbations. The deflections assume a sine wave shape along the long axis of the channel, with the greatest deflections occurring at the inlet to the channels. Adjacent plates always move in opposite directions at high flow rates, alternately opening and closing coolant channels. Above the critical velocity, deflections were observed which were sufficient to cause adjacent plates to touch. At about 1.9 times the theoretical collapse velocity, a high frequency flutter of the instrumented plates was observed. Use of an inlet support comb eliminated this flutter.

ISSN:0029-5639    

DOI:10.13182/NSE63-A26503

出版商:Taylor&Francis    

年代:1963

数据来源: Taylor