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Note on the Non-Linear Kinetics of Circulating-Fuel Reactors

Description: The following report analyzes equations of motion for somewhat idealized circulating-fuel reactor that have been previously discussed, specifically the assumptions that the instantaneous power density is constant along the length of the fuel tubes, that the excess radioactivity depends only upon the average fuel temperature, and that the fuel temperature at the inlet is kept constant.
Date: August 15, 1952
Creator: Tamor, Stephen
Partner: UNT Libraries Government Documents Department

Improved criticality convergence via a modified Monte Carlo iteration method

Description: Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights that must sum somehow to maintain the second eigenfunction. Summing negative and positive weights can be done using point detector mechanics, but this sometimes can be quite slow. We show that an approximate cancellation scheme is sufficient to accelerate the convergence to the dominant eigenfunction. A second difficulty is that for some problems the Monte Carlo implementation of the modified power method has some stability problems. We also show that a simple method deals with this in an effective, but ad hoc manner.
Date: January 1, 2009
Creator: Booth, Thomas E & Gubernatis, James E
Partner: UNT Libraries Government Documents Department

Finite difference solution of the time dependent neutron group diffusion equations

Description: In this thesis two unrelated topics of reactor physics are examined: the prompt jump approximation and alternating direction checkerboard methods. In the prompt jump approximation it is assumed that the prompt and delayed neutrons in a nuclear reactor may be described mathematically as being instantaneously in equilibrium with each other. This approximation is applied to the spatially dependent neutron diffusion theory reactor kinetics model. Alternating direction checkerboard methods are a family of finite difference alternating direction methods which may be used to solve the multigroup, multidimension, time-dependent neutron diffusion equations. The reactor mesh grid is not swept line by line or point by point as in implicit or explicit alternating direction methods; instead, the reactor mesh grid may be thought of as a checkerboard in which all the ''red squares'' and '' black squares'' are treated successively. Two members of this family of methods, the ADC and NSADC methods, are at least as good as other alternating direction methods. It has been found that the accuracy of implicit and explicit alternating direction methods can be greatly improved by the application of an exponential transformation. This transformation is incompatible with checkerboard methods. Therefore, a new formulation of the exponential transformation has been developed which is compatible with checkerboard methods and at least as good as the former transformation for other alternating direction methods. (auth)
Date: August 1, 1975
Creator: Hendricks, J.S. & Henry, A.F.
Partner: UNT Libraries Government Documents Department

Application of the FORSS sensitivity code system to fast reactor analysis

Description: The FORSS Sensitivity Analysis Code System is described in terms of its objectives and present capabilities. An example is made of a problem specified by the Processing Methods Testing Subcommittee of the Code Evaluation Working Group, i.e., the determination of integral parameters, sensitivities to cross- section data, methods and data uncertainties, and required cross-section accuracies for an infinite media of ZPR 6/7 core composition. (auth)
Date: October 22, 1975
Creator: Weisbin, C.R.; Oblow, E.M. & Mynatt, F.R.
Partner: UNT Libraries Government Documents Department

Verification and Validation of Corrected Versions of RELAP5 for ATR Reactivity Analyses

Description: Two versions of the RELAP5 computer code, RELAP5/MOD2.5 and RELAP5/MOD3 Version, are used to support safety analyses of the Advanced Test Reactor (ATR). Both versions of RELAP5 contain a point reactor kinetics model that has been used to simulate power excursion transients at the ATR. Errors in the RELAP5 point kinetics model were reported to the RELAP5 code developers in 2007. These errors had the potential to affect reactivity analyses that are part of the ATR’s safety basis. Consequently, corrected versions of RELAP5 were developed for analysis of the ATR. Four reactivity transients were simulated to verify and validate the corrected codes for use in safety evaluations of the ATR. The objectives of this paper are to describe the verification and validation of the point kinetics model for ATR applications and to inform code users of the effects of the errors on representative reactivity analyses.
Date: November 1, 2008
Creator: Davis, Cliff B.
Partner: UNT Libraries Government Documents Department

Monte Carlo verification of point kinetics for safety analysis of nuclear reactors

Description: Monte Carlo neutron transport methods can be used to verify the applicability of point kinetics for safety analysis of nuclear reactors. KENO-NR was used to obtain the transfer function of the Advanced Neutron Source reactor and the time delay between the core power production and the external detectors, a parameter of interest to the safety systems design. The good agreement between the Monte Carlo generated transfer function and the point kinetics transfer function validates that the uncommon ANS geometry does not preclude the use of point kinetics in the frequency range that was investigated. Various features of the power spectral densities also demonstrated the applicability of point kinetics. The time delay was obtained from the cross-power spectral density (CPSD) and is {approximately}15 ms. These analyses show that frequency analysis can be used experimentally to investigate the validity of the use of point kinetics models in critical experiments or zero power testing of reactors.
Date: June 1, 1995
Creator: Valentine, T.E. & Mihalczo, J.T.
Partner: UNT Libraries Government Documents Department

Coupling parameters for partially reflected reactors

Description: For situations in which the standard point kinetic model does not adequately characterize the kinetic behavior of a reflected system, the Avery-Cohn differential equations can be used. However, these equations require that one determine the coupling parameters between the core and the reflector, f{sub cr} and f{sub rc}. The coupling parameter, f{sub cr}, represents the probability that a neutron in the core will leak into the reflector, and the coupling parameter, f{sub rc}, represents the probability that a neutron in the reflector will scatter back into the core. As discussed in Reference 3, these two coupling parameters can be calculated from the multiplication factor of the bare core, k{sub c}, the effective multiplication factor of the integral system, k{sub eff}, and the fraction of system neutrons absorbed in the core region, P{sub ca}. The methodology presented in Ref. 3 was described for a fully reflected system, but it is also applicable to some types of partially reflected systems. In particular, it is applicable to those systems where neutrons leaving any core surface not contiguous to the reflector have a zero probability of entering the reflector. In other words, these surfaces have a view factor of 0 to all reflector surfaces in the system. However, if the view factor between an unreflected core surface and a reflector surface is not zero, then the aforementioned methodology has to be modified. To calculate f{sub cr}, one must include an estimate of the single-pass probability that a neutron escapes from the core to infinity, f{sub ci}. This is accomplished by including a view factor(s) in the calculations that accounts for the fraction of neutrons that are not traveling on a line intersecting some portion of the reflector. This paper illustrates this modification by assuming the partially reflected system shown in Fig. 1c.
Date: July 1, 1995
Creator: Busch, R.D. & Spriggs, G.D.
Partner: UNT Libraries Government Documents Department

Reactor kinetics methods development. Final report

Description: This report is a qualitative summary of research conducted at MIT from 1967 to 1977 in the area of reactor kinetics methods. The objectives of the research were to find methods of integration of various mathematical models of nuclear reactor transients. From the beginning the work was aimed at numerical integration methods. Specific areas of research, discussed in more detail following, included: integration of multigroup diffusion theory models by finite difference and finite element methods; response matrix and nodal methods; coarse-mesh homogenization; and special treatment of boundary conditions.
Date: January 8, 1978
Creator: Hansen, K.F. & Henry, A.F.
Partner: UNT Libraries Government Documents Department

Variational reactivity estimates: new analyses and new results

Description: A modified form of the variational estimate of the reactivity worth ofa perturbation was previously developed to extend the range of applicability of variational perturbation theory for perturbations leading to negative reactivity worths. Recent numerical results challenged the assumptions behind the modified form. In this paper, more results are obtained, leading to the conclusion that sometimes the modified form extends the range ofapplicability of variational perturbation theory for positive reactivity worths as well, and sometimes the standard variational form is more accurate for negative-reactivity perturbations. In addition, this paper proves that using the exact generalized adjoint function would lead to an inaccurate variational reactivity estimate when the error in the first-order estimate is large; the standard generalized adjoint function, an approximation to the exact one, leads to Lore accurate results. This conclusion is also demonstrated numerically. Transport calculations use the PARTISN multi group discrete ordinates code
Date: January 1, 2009
Creator: Favorite, Jeffrey A
Partner: UNT Libraries Government Documents Department

Analysis of Godiva-IV delayed-critical and static super-prompt-critical conditions

Description: Super-prompt-critical burst experiments were conducted on the Godiva-IV assembly at Los Alamos National Laboratory from the 1960s through 2005. Detailed and simplified benchmark models have been constructed for four delayed-critical experiments and for the static phase of a super-prompt-critical burst experiment. In addition, a two-dimensional cylindrical model has been developed for the super-prompt-critical condition. Criticality calculations have been performed for all of those models with four modern nuclear data libraries: ENDFIB-VI, ENDF/8-VII.0, JEFF-3.1 , and JENDL-3.3. Overall, JENDL-3.3 produces the best agreement with the reference values for k{sub eff}.
Date: January 1, 2009
Creator: Mosteller, Russell D & Goda, Joetta M
Partner: UNT Libraries Government Documents Department

The Covariance and Biocovariance of the Stochartic Neutron Field

Description: The use of stochastic neutron field theory (neutron noise) for the measurement of reactor physics parameters goes back to the early work of Serber, Feynmann, and Orndoff. Since then, a large variety of methods and applications has been developed. In the majority of these methods, some form of modified one-point reactor kinetics was used for the interpretation of the measurements. In fact, the high level of sophistication of the instrumentation used was not matched by the theory. In 1965, Bell developed a general theory of the stochastic neutron field, and in 1987, Munoz-Cobo et al enlarged this treatment to include the effect of the detectors in the neutron field. In both instances, the complexity of the theoretical results were beyond the computing capabilities then available thus, the mismatch between experimental and theoretical methods remained in existence because the powerful Monte-Carlo methods then at work, were only applicable to static neutron fields. This problem was eliminated by the development of a time-dependent Monte-Carlo code specially written by T. E. Valentine for the analysis of stochastic measurements that gave them relevance to the results of the general theory. The purpose of this work is to illustrate the derivation of observables of the stochastic neutron filed from its general treatment.
Date: January 1, 1998
Creator: Perez, R.B.
Partner: UNT Libraries Government Documents Department