Equilibrium Cycle Research Articles

Choice of operating cycle length to maximize discharge burnup in an LMFBR

The attained discharge burnup of a fuel subassembly in an LMFBR is less than the peak design burnup, on account of mismatch between the chosen operating cycle length and the required residence times of the individual subassemblies to attain the peak design burnup. In this work a discharge burnup loss function is defined and the relationship between loss in discharge burnup and operating cycle length is quantitatively demonstrated by calculation for a typical LMFBR in equilibrium cycle operation.

Studies on syntheses and permeabilities of special polymer membranes, 49. Active transport of ammonium ions through cation exchange membrane

AbstractThe transport of ammonium ions through a cation exchange membrane, made of poly(isobutylene‐alternative co‐maleic anhydride) and poly(vinyl alcohol), was investigated using a diaphragm cell, in which the one side was adjusted to be alkaline and the other side acidic. Ammonium ions could be actively transported from the alkaline side to the acidic side through the membrane owing to the carrier functions caused by dissociation equilibrium cycle of the carboxyl group in the membrane. The active transport of ammonium ions was promoted by H+ ion in the acidic side.

An Economic Model for Fuel Cycle Cost

A simple economic analysis is proposed for light water reactor (LWR) in-core fuel management. Its final objective is the fuel cost. Using the discrete discounting technique with single payment costs, the fuel cost for one equilibrium cycle or a sequence of a number of nonequilibrium cycles may be determined. In this latter case, the costs are projected as groups of costs at the reference time. This technique is simplified by defining new economic factors, time scales, and burnup values. The fuel cost thus obtained is an average cost over the number of cycles considered. This analysis is written as a subroutine FULCOS suitable for absorption by short running computer codes that work the optimization problems for LWRs. 6 refs.

Power-flattening method for boiling water reactor.

A new power-flattening method has been proposed for boiling water reactors (BWRs) which have an axially skewed power distribution caused by the void fraction distribution. In present BWRs, the skewed power distribution is avoided by using shallow control rods and/or axially distributed gadolinia fuel bundles. These means are effective for the axial power shape control, but perturb the self-power-flattening effect due to fuel burnup. The power-flattening method proposed here extensively utilizes this effect in the equilibrium cycle core. Based on this method, a new BWR core design and operating strategy, the WNS core concept, has been realized for reactor operation with no shallow control rod insertion and no fuel bundle shuffling. Studies of the WNS core has shown that the proposed power-flattening method has the potential to improve capacity factors, increase operating thermal margins and simplify reactor operations in comparison with current BWR cores.

Polymorphic equilibria with assortative mating and selection in subdivided populations

Two modes of assortative mating, partial selfing and assorting by phenotypic classes, are studied in a subdivided population. Differential viability is allowed and the selection intensities and assorting tendencies are permitted to vary among the habitats. There exists a symmetric polymorphism; we delimit its level of heterozygosity and stability nature (dependent on the selection intensities and assorting propensities). This complements studies of the fixation states and thereby provides further insight into the global equilibrium structure in subdivided populations. Circumstances are given where the fixation states and symmetric polymorphism comprise the global equilibrium structure. Examples are also given where migration engenders stable polymorphic equilibria and stable polymorphic equilibrium cycles which are absent in single demes without migration.

Regular and chaotic cycling in models of ecological genetics

A model of density-dependent selection is investigated for the cyclical behavior associated with the analogous nonlinear models of population growth. If the population size regulating mechanism reacts too sharply to perturbations in population size, regular and chaotic limit cycles may result. It is established analytically that the population may converge to fixation or an invariant polymorphic gene frequency while the population size undergoes regular or chaotic oscillations. The possibility of joint limit cycles in both the population size and gene frequency is demonstrated and investigated numerically. Such cycles may occur even though one or both fixation equilibria are locally stable. In the context of equilibrium cycles it is found that overdominance in carrying capacity is not necessary for the maintenance of genetic variation in the population. Furthermore, the genetic system appears able to exert a stabilizing influence on the overall system.

Core-State Models for Fuel Management of Equilibrium and Transition Cycles in Pressurized Water Reactors

Fuel management requires that mass, energy, and reactivity balance be satisfied in each reload cycle. Procedures for selection of alternatives, core-state models, and fuel cost calculations have been developed for both equilibrium and transition cycles. Effective cycle lengths and fuel cycle variables--namely, reload batch size, schedule of incore residence for the fuel, feed enrichments, energy sharing cycle by cycle, and discharge burnup and isotopics--are the variables being considered for fuel management planning with a given energy generation plan, fuel design, recycling strategy, and financial assumptions.

Research on a 2700-MW(th) Pebble-Bed Reactor for a Helium-Turbine Power Plant

A favorable distribution of the fuel temperature in combination with a high cooling gas outlet temperature as necessary for a helium-turbine power plant can be achieved in a pebble-bed reactor with “once-through-then-out” fueling without leaving the scope of present feasibility. The equilibrium cycle is reached after a well-balanced and short running-in period. For non-base-load operation, the reactor can be controlled by moving the control rods in the upper void above the pebble bed. Withdrawing the rods causes an increase of the maximum fuel temperature by only 56°C. To avoid replacing of the side reflector during a time of 30 yr, the fast-neutron flux in the reflector can be remarkably lowered by inserting a certain amount of neutron poison into the reflector graphite and by an outer ring of “breeding” fuel elements, respectively.

Optimization of Fuel Assembly Allocation for Boiling Water Reactors

Abstract A direct search algorithm is applied to the optimization of fuel assembly allocation of BWR with particular consideration given to the nuclear model and the treatment of operating constraints. A simple expression is derived for evaluating the stuck rod margin, based on regression analysis of data obtained by three-dimensional full core analysis, and the expression is applied to optimization procedure. The practical applicability of the method is confirmed through trial computations for the second and equilibrium cycles of a medium-sized commercial BWR, with an examination based on various initial guesses and objective functions for radial power peaking.

Optimization of Fuel Assembly Allocation for Boiling Water Reactors

Abstract A direct search algorithm is applied to the optimization of fuel assembly allocation of BWR with particular consideration given to the nuclear model and the treatment of operating constraints. A simple expression is derived for evaluating the stuck rod margin, based on regression analysis of data obtained by three-dimensional full core analysis, and the expression is applied to optimization procedure. The practical applicability of the method is confirmed through trial computations for the second and equilibrium cycles of a medium-sized commercial BWR, with an examination based on various initial guesses and objective functions for radial power peaking.

Studies of core disruptive accidents and licensing aspects of fast breeder reactors

This paper discusses the role of the core disruptive accident (CDA) in the safety evaluations and licensing of Liquid Metal Fast Breeder Reactors (LMFBR). Parametric studies of transient overpower (TOP) accidents based on calculations for SNR-300 using the HOPE computer code are presented. Major uncertainties in TOP analysis are identified and discussed with emphasis on the need for reliable fuel failure criteria. A series of calculations illustrating the possible behavior of the U.S. LMFBR demonstration plant following a loss-of-flow (LOF) accident without scram using the SAS-IIIA computer code are described. It is shown that for a beginning of life (BOL) core and end of equilibrium cycle (EOEC) core, the reactivity effects from sodium voiding and clad motion can lead to further sustained reactivity additions from subsequent fuel motion and FCI driven sodium voiding. In these calculations we have used the fuel enthalpy criterion which predicts clad failure around the core midplane. For the EOEC case these effects can add sufficient reactivity to take the system above prompt-critical (LOF driven TOP) and into hydrodynamic disassembly. For the BOL case the sodium void may not be sufficient to bring the system near sustained prompt-critical. However, clad motion appears to be effective in raising the reactivity to prompt-criticality. These results are based on clad failure dynamics modeling in SAS-IIIA. Further work is needed in the area of fuel-clad behavior under severe transients before definitive conclusions can be drawn regarding the applicability of current clad failure models at high clad temperatures (>1000°C). The potential significance of a new concept in CDA analysis called the “transition phase” is briefly mentioned.

The Breeding Ratio with Correlation to Doubling Time and Fuel Cycle Reactivity Variation

The standard definition of the breeding ratio is subject to some suspicion, since in many cases of practical interest it gives an incorrect measure of the fissile fuel doubling time and erroneous trends of the fuel cycle reactivity variation. The reasons for this behavior are given in this study, along with methods for removing the difficulties. In addition to the standard definition, the method of η weighting due to Ott and the method of reactivity weighting due to Baker and Ross (British definition) are examined. It is shown that the η weighting procedure is not much better than the standard definition, whereas the British definition can be used to give very good results for the doubling time and fuel cycle reactivity variation. The standard for comparison is a detailed explicit fuel cycle analysis of both the startup cycle and equilibrium cycle of an oxide fast reactor. With the methods given it is shown that the important quantities needed from a single fuel cycle analysis can be obtained just from a ...

Optimal fuel replacement in reactivity limited systems

As a step in the development of an optimal fuel replacement scheme for a large pressurized water reactor, it was shown that the operating parameters and constraints for individual fuel subassemblies can be expressed in terms of one time dependent parameter, burnup, as long as the gross neutron flux distribution does not change radically with time. The required constraints on the empirical model are therefore adequately satisfied for the intuitively attractive case of scatter (or Roundelay) refueling. As a result, it was possible to investigate analytically a “quaziequilibriumr” cycle for both direct replacement and shuffle refueling. Whereas direct replacement showed little advantage over the equilibrium cycle, shuffling of the fuel to a more optimum configuration at each fuel replacement cycle indicated potential savings of several hundred thousands of dollars a year for a 1000 MWe pressurized water plant.

Behavior of divalent cations and nucleotides bound to F-actin

1. 1. Nucleotides and divalent cations bound to F-actin were found to be slowly exchanged in the absence of any agitation such as sonic vibration; the half-life time, τ 1 2 , was about 5 h at 37°. 2. 2. The rate of exchange of divalent cation (Ca 2+) was always a little faster than that of nucleotide (ADP); however, the general manner of the exchange of divalent cations was similar to that of nucleotides. 3. 3. The rate of exchange was almost independent of protein concentration. High temperature or high pH increased the rate of exchange. Activation enthalpies for the exchange of ADP and Ca 2+ were both about 25 kcal/mole at neutral pH. 4. 4. The release of divalent cations or nucleotides occurred in divalent-cation- or nucleotide-free solvent. The incorporation of divalent cations and nucleotides into divalent-cation- and nucleotide-free F-actin was examined, and their binding constants were estimated. 5. 5. In the absence of ATP, the rate of exchange was decreased by myosin, H-meromyosin and tropomyosin. A large increase of Ca 2+ and ADP exchange was observed with superprecipitation. 6. 6. The mechanism of exchange or release is discussed on the basis of two models: the cycle of partial destruction of the F-actin structure, and the G-F equilibrium cycle at the peripheral region of F-actin.

Dynamic Equilibrium Cycling in Discontinuously Controlled Electric Process Heating

Open-and closed-loop discontinuously controlled electric process heating and similar electrothermal processes are represented by analog, equation, and block diagram. Dynamic equilibrium cycling and its performance indexes are studied. The error due to process transit delay is corrected by integral feedback or by a new feedforward technique. Temperature differential is reduced by auxiliary feedback from the electric heating apparatus or from a new simple first-derivative transducer. Portions of the dynamic equilibrium cycle can be prolonged by using a new simple second-derivative transducer.

The Equilibrium Cycle in Two-Party Politics

The Equilibrium Cycle in Two-Party Politics

Human Body as an Inconstant Heat Source and Its Relation to Clothes Insulation: Part 2—Experimental Investigation Into Dynamics of the Source

Quantitative measurement on the human in the so-called evaporative, vasomotor, and metabolic control regimes has revealed frequency spectrum of sustained thermal power oscillations with approximate periods of 2, 7, 35 min, and 3 1/2 hr independent of the regime. Step function adjustments take place with a time constant of about 7 min. It is believed that the 3 1/2 hr cycle represents the shortest equilibrium cycle. The hypothesis that it might be possible to measure the resistance of clothing as an ohmic relation among time-averaged equilibrium values, and for a specific mode of operation of the system has now been put in rational context in the time domain. Two equilibrium modes of the human system were explored. The active mode of operation of the system, to which the resistance concept of clothes is most applicable, is as a feedback system in which the extremities are used as error indicators of deviations from a comfort level set point. In response to deviations, the human feeds back a signal to generate an activity level in which only internal work—immediately degraded into heat—is done to maintain the comfort level. This is referred to as the comfort mode of operation of the system. Another “survival” mode of operation of the system is also described.