Completely Reflected Systems

As a first example, consider the analysis of a completely reflected cylindrical reactor on the basis of the one-velocity model. A typical 

24 Actual reactor and equivalent side-reflected cylinder. 

To solve this problem we study first a cylindrical reactor with side reflector only which has the same reflector material, the same fuel concentration, and the same core and reflector radii (po and pi, respectively) as the actual system. Such a system I is shown in Fig. 8.24. The only feature of this geometry as yet undetermined is its length (2i). Thus our next objective is to find I such that the two systems shown in Fig. 8.24 are critical with the same fuel concentration. 

One plausible method of obtaining a first guess for I is that of finding the height of a completely bare reactor, III (radius pi), which is critical with the same fuel concentration as that in the core of a critical cylinder reflected on the ends only (reflector material taken the same as that for 

Find I such that system III wili be critical with the same buckling  

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Attenuated total reflectance infrared (ATR-IR) is used to study films, coatings, threads, powders, interfaces, and solutions. (It also serves as the basis for much of the communication systems based on fiber optics.) ATR occurs when radiation enters from a more-dense material (i.e., a material with a higher refractive index) into a material that is less dense (i.e., with a lower refractive index). The fraction of the incident radiation reflected increases when the angle of incidence increases. The incident radiation is reflected at the interface when the angle of incidence is greater than the critical angle. The radiation penetrates a short depth into the interface before complete reflection occurs. This penetration is called the evanescent wave. Its intensity is reduced by the sample which absorbs. 

At Barley Canyon, budworm were placed on trees after all had burst bud. Consequently, most budworm were subjected to tissues that had developed for up to 10 days and which possessed more complete defensive systems. Therefore, the correlation we observed with budburst reflected the length of time the foliage was allowed to mature defensively before the budworm feeding occurred. It did not reflect an escape In time component as the Montana study did where natural populations were studied. 

A polymer s compostability is a function of many factors such as pH, temperature, humidity, microorganisms population, and osmotic pressure. Simulated laboratory conditions as described by ASTM D6400 (//), D5338 (7) and ISO 14855 (6) may be an oversimplification of commercial composting systems which do not completely reflect the conditions in the commercial composting facilities. Therefore, further studies are necessary to assure that laboratory studies can duplicate commercial systems. 

This phenomenon implies, however, the following intriguing possibilities (37) (1) bound state in the continuum and (2) switching of transmission in a periodic system. These are explained very briefly. If we put two noninteracting potentials of the type of Fig. 2b, bound states can exist between the two potential units at the energies which satisfy the condition of complete reflection, Eq. (158). In addition, the following quantization condition is, of course, required ... 

We can therefore use this to construct the transfer function for the LSF problem, where we wish to simulate a completely lossless system by addition of one extra tube and reflection coefficient. We... 

Critical-Mass Measurements on Beryllium-Reflected, Enriched-Uranium, Spherical Systems, by O. Kolar and H, R. Ralston (VCBL-L). A scries of critical mass determinations has been made for spherical beryllium reflected systems. Cores were enriched (93.17S U-235) uranium spheres ranging in mass from 10.6 to 32.6 kg. The corresponding reflector thicknesses were 20.3 to 2.2 cm. All results were nonnalized to a core density of 18.6 g/cc. Some Los Alamos data are included for completeness and have been similarly normalized. These two sets of experiments were found to be in good agreement. The experiments and results arc discussed, together with the fit to the experimental data obtained with the spherical Si, 5-group code in use at UCRL. 

If the core of this reactor were entirely bare, we could use Eq. (6.80) directly to determine the critical fuel concentration. Since the present configuration is completely reflected, we require a modified relation which will take into account the effect of the reflector. We observed in Chap. 1 that the purpose of the reflector is to decrease the neutron escapes from the core and thereby reduce the critical fuel concentration of the system. Clearly, if we were to ignore the reflector altogether, our estimate of the... 

The block geometry considered here is the only rectangular system for which an analytical solution has been obtained. As indicated earlier, the completely reflected geometry is diflicult to treat analytically. Unfortunately this is also true for other more simple configurations such as the block core reflected on four sides, with or without corners (Fig, 8.10). The difficulty in all these cases is that it is not possible to meet... 

Our primary interest in this calculation is the determination of the critical mass of the hot clean reactor and the radial distribution of the fast and thermal flux throughout the core and reflector. An accurate analysis of this system must necessarily take into account the completely reflected cylindrical geometry shown in Fig. 8.216. However, since this would entail a somewhat involved calculation, we will approximate the actual configuration by an equivalent reflected sphere of the same composition. This will reduce our computation appreciably and yet not obscure any of the essential steps in the application of the two-group model. A study of the effect of the corners in the completely reflected cylinder will be deferred until the next section. 

Alternative procedures for determining equivalent systems is given by F. G. Prohammer, A Comparison of One-dimensional Critical Mass Computations for Completely Reflected Reactors, ORNL-2007, Mar. 1, 1956. 

It expresses the ratio of the measured variance to the variance of a completely segregated system. The intensity of segregation as defined in equation (5.10) reflects to some extent gross uniformity on a scale of examination reduced to the scale at which texture or local structure is being examined. 

Task 5, Removing Cost from the Supply Chain, has the longest time line. Normally, it can t be totally complete until systems changes are implemented. Certainly there is opportunity to reduce cost in most cases within the current systems environment. This is reflected by the shorter arrow, which shows a completed initiative in Phase 2. Also a cost reduction initiative may be based on a reconfiguration of physical locations — which usually requires a longer-term transition. 

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