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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

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

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

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

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

Review of Subcritical Source-Driven Noise Analysis Measurements

Description: Subcritical source-driven noise measurements are simultaneous Rossia and randomly pulsed neutron measurements that provide measured quantities that can be related to the subcritical neutron multiplication factor. In fact, subcritical source-driven noise measurements should be performed in lieu of Rossia measurements because of the additional information that is obtained from noise measurements such as the spectral ratio and the coherence functions. The basic understanding of source-driven noise analysis measurements can be developed from a point reactor kinetics model to demonstrate how the measured quantities relate to the subcritical neutron multiplication factor.
Date: November 1, 1999
Creator: Valentine, T.E.
Partner: UNT Libraries Government Documents Department

The equivalent, fundamental-mode source

Description: In 1960, Hansen analyzed the problem of assembling fissionable material in the presence of a weak neutron source. Using point kinetics, he derived the weak source condition and analyzed the consequences of delayed initiation during ramp reactivity additions. Although not clearly stated in Hansen`s work, the neutron source strength that appears in the weak source condition actually corresponds to the equivalent, fundamental-mode source. In this work, they describe the concept of an equivalent, fundamental-mode source and they derive a deterministic expression for a factor, g*, that converts any arbitrary source distribution to an equivalent, fundamental-mode source. They also demonstrate a simplified method for calculating g* in subcritical systems. And finally, they present a new experimental method that can be employed to measure the equivalent, fundamental-mode source strength in a multiplying assembly. They demonstrate the method on the zero-power, XIX-1 assembly at the Fast Critical Assembly (FCA) Facility, Japan Atomic Energy Research Institute (JAERI).
Date: December 24, 1996
Creator: Spriggs, G.D.; Busch, R.D.; Sakurai, Takeshi & Okajima, Shigeaki
Partner: UNT Libraries Government Documents Department

The use of active learning strategies in the instruction of Reactor Physics concepts

Description: Each of the Active Learning strategies employed to teach Reactor Physics material has been or promises to be instructionally successful. The Cooperative Group strategy has demonstrated a statistically significant increase in student performance on the unit exam in teaching conceptually difficult, transport and diffusion theory material. However, this result was achieved at the expense of a modest increase in class time. The Tutorial CBI programs have enabled learning equally as well as classroom lectures without the direct intervention of an instructor. Thus, the Tutorials have been successful as homework assignments, releasing classroom time for other instruction. However, the time required for development of these tools was large, on the order of two hundred hours per hour of instruction. The initial introduction of the Case-Based strategy was roughly as effective as the traditional classroom instruction. Case-Based learning could well, after important modifications, perform better than traditional instruction. A larger percentage of the students prefer active learning strategies than prefer traditional lecture presentations. Student preferences for the active strategies were particularly strong when they believed that the strategies helped them learn the material better than they would have by using a lecture format. In some cases, students also preferred the active strategies because they were different from traditional instruction, a change of pace. Some students preferred lectures to CBI instruction, primarily because the CBI did not afford them the opportunity to question the instructor during the presentation.
Date: January 1, 2000
Creator: Robinson, Michael A.
Partner: UNT Libraries Government Documents Department