Void effects

Notice that oxide is utilised by the reaction at interface B at the same rate as it is formed at >1, so that the void effectively moves through the growing oxide with the distance AB remaining constant. It may be recalled that a truly... 

Langbein209 has derived a corresponding expression for this so-called Void effect which is based on the Lifshitz macroscopic treatment of dispersion forces. 

Bowles KJ, Frimpong S. Voids effects on the interlaminar shear strength of imidirectional graphite-fiber-reinforced composites. J. Comp. Mater. 1992 26 10 1487-509. 

J. H. Kristensen, G. L. Hoatson and R. L. Void, Effects of restricted rotational diffusion on H-2 magic angle spinning nuclear magnetic resonance spectra. J. Chem. Phys., 1999, 110, 4533-4553. 

This defect is met in commercial BWR designs by additional circulation of the coolant around the reactor core, over and above the coolant removed as steam through the turbines. Controllers link the flow rate to the power demand as felt on the turbine, so that the increased coolant input sweeps out the steam bubbles and compensates for the void effect. The RBMK has a similar additional coolant circulation which is necessary, perhaps, for its satisfactory operation with a negative water void coefficient but would exacerbate the disadvantage of a positive coefficient. This again was a feature of the Chernobyl accident. 

Originally, the most wildly used predictive equation was Witczak s equation (Andrei et al. 1999 Witczak 2005), also known as the original Witczak equation. The dynamic modulus was determined with respect to percentage passing through certain sieves, binder viscosity, air voids, effective binder content and loading frequency. 

II. 1 Neutron physical calculations of selected core configurations for burner reactors (CAPRA type) During the determination of the neutronic input data for safety related SAS4A studies systematic deviations in the power distribution for the CAPRA reference core were recognised. The detailed investigations showed that for the more complex types of CAPRA cores more refined calculational treatment is required, i.e. either a fully 3-dimensional diffusion method or even the VARIANT transport method. In the latter case, the considerable influence on control rod worths and on the sodium void effect - especially for configurations with control rods inserted (i.e. not fully withdrawn) - must be studied. 

The combination of analytical methods and of nuclear data used as the basis for the parametric studies in this work was selected so as to be consistent with the safety philosophy, that is, to give reasonable probability of under-predicting Doppler effect and breeding ratio, and of overpredicting sodium void effect. 

This criterion requires that reactor design limit the sodium voiding effect and sets a lower limit on the Doppler effect. Based on Bethe-Tait analyses, the criterion will be satisfied by a negative Doppler effect (TcUcjdT), no weaker than —0.004 with sodium out of the reactor. 

Blockage of a single subassembly by debris or gas entrainment was also analyzed as a credible accident. Damage to the subassembly itself was not of major importance, but rather the sodium voiding effects and eventual local fuel slumping were of principal concern. 

The management of the marked reactivity loss and the optimization of the relative values of the Doppler and sodium void effects appear to be the two major issues to be dealt with so as to ensure the feasibility of Pu burner cores. In this respect, heterogeneous core designs, in which a part of the inert material replacing the fuel in the dilution process is gathered in specific subassemblies, are of particular interest. 

A large number of core design parameters have direct influence on the above mentioned safety targets, but often in contradictory ways therefore the optimization of the core from a global point of view is a very complex matter whose solution requires a sensitivity analysis based on a wide range of parameters including number and location of fuel assemblies, active core height, pin diameter, number and location of GEM s, Pu enrichments and their distribution, possible utilization of burnable poisons and their location, radial profile of the Na void effect, etc.. 

There were also measured reactivity coefficients of main reactor materials samples, the sodium void effect of reactivity, the central control rod mock-up efficiency, Doppler effect at oscillating of neptunium-237 and plutonium-240 samples. The results of the experiments are still being analyzed now. For the central part of the core a negative value of the sodium void effect of reactivity was observed making up 0.04 per 1 kg of sodium. 

In the center of the original core and then in the core with neptunium there were measured by several methods, the ratios of average fission cross-sections for 16 isotopes, including minor actinides, and of capture cross-sections in aurum, neptunium, uranium-238, the central reactivity coefficients with the use of samples, the sodium void effect of reactivity, the efficiency of a mock-up of the central control rod with enriched and natural boron carbide, ad well as the fission reaction rate distributions with height. 

One of the main requirements for advanced core development is ensuring of a zero sodium void effect of reactivity. For compensation of an additional positive component of reactivity arising due to higher burn-up a transition to axial heterogeneous core concept was made. Herewith the inner blanket of depleted uranium dioxide is placed in the central part of the core. A size of this blanket is 2/3 of the core radius. 

The RAPID system has a central 300 mm diameter channel which is normally filled by a small sodium flow. In the event of sodium boiling in the core, the channel fills with sodium vapour providing a neutron streaming path to offset the positive sodium void effect. Positive sodium void reactivity effects present one of the major safety issues in LMRs since they could cause an overheating event to escalate. There has been much attention to ways of reducing the effect, such as the RAPID proposal. 

The results of the calculations are presented In Tablet. Two previously reported basic assemblies having the same fuel loaitogs, foil thicknesses, and spacings as the void ei eriments are usM as l e problems. The void worth Is taken to be the difference between k ff calculated with the dimensions of tte void critical assembly but with the void region filled with full-density core materials, and keff calculated for the base problem. This permits an evaluation of the calculated results in terms of percent of the void effect predicted. 

Calculations carried out by method 3 are shown to predict the void effect very well. 

Measurements of Bucklings and Void Effects in DaO-Moderated, Organic- or HaO-Cooied Lattices of UO2 Rod Ciusters, F. D. Benton and W. E. Graves (duPont-SR)... 

R. A. KARAM, J. E. MARSHALL, and K. D. DANCE, Analysis of Heterogeneity and Sodium-Void Effects in a 2700-Liter Uranium Carbide Fast Core, ZPR-6 Assembly 5, Nucl. Sci. Eng., 43, 5 (1971). 

The large and negative moderator density coefficient at operating power levels is due to the steam void effect. This steam void effect results in the operating advantages listed below. 

Load changing by flow control Because the fuel Doppler reactivity opposes a change in load, the void effect must be and is larger than the fuel Doppler effect to provide load changing capability by flow (or moderator density) control. 

Thermal-hydraulic stability The negative void effect is an important contributor to reactor thermal-hydraulic stability. 

Isothermal temperature coefficient at full power (pcm/°C) Total power coefficient of reactivity (pcm/MWth) at full power, constant inlet temperature Maximum coolant void effect (dollars), including only regions with a nositive coolant reactivity worth... 

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