Critical mass calculations

D. S. Selengut, Critical mass calculations for hare hydrogen moderated recuitors by means of transport theory, APEX-121, September, 1952. 

Critical Mass Calculations of a MuItU spectrum Critical Assembly, L. 4. Motm(/br[Pg.91]

DONALD C. COCEIFIELD and DOUGLAS C. HUNT, "The Effects of Spatial Resolution on Critical Mass Calculations," RFP-1133, The Dow Chemical Co., Rocky flats Divisim (May 31, 1968). 

Critical mass calculations were carried out for exposed tube-in-tube fuel assemblies, and for PuAl cylindrical fuel elements. The isotopic discharge concentrations obtained with DCODE were used as input to the HAMMER code to generate multigroup lattice averaged cross sections and to calculate subsequently spherical critical masses of fuel at optimum lattice spacing... 

The minimum critical mass calculations involved arrays of plates, cubes, or square cross-section rods in water. A minimum critical array mass is found by changing the spacing of elements, d, in a particular array until a maximum value of keff is found when keff is plotted versus d. A second element size is then selected for the array and the maximum keff and the associated array element spacing found. The mass and spacing of the minimum critical mass (keff = 1.0) array are obtained by linear interpolation between the masses and spacings at the maximum keff values. 

Results of varyinig the other parameters mentioned above are also presented. For example, in Fig. 2 we see the results of critical mass calculations for a 10 array with several densities of a uniformly distributed water moderator. The dtapes of the curves are similar for the various moderator densities aithough the-crossover points between the regions and the moderator effectiveness vary with moderator density. Another varied parameter was the length-to-diameter ratio of a cyiinder. A full density water-moderated and -reflected 10 array of plutonium metal cylinders, D/L = 4, has a critical mass about 30% less than a comparably moderated and reflected array of spheres with masses ranging from 10 to 300 g. 

The critical-mass calculation for any one of these reactors entails a trial-and-error procedure. One can either assume a size and compute the critical concentration, or vice versa. We will do the latter. The next step then is to evaluate the macroscopic cross sections of the reactor medium for the entire lethargy range, i.e., Sa(i ), /( )i ( )> well as the thermal-group cross sections at the operating temperature of the system. These data may now be applied directly to the computation of the various parameters which appear in the critical equation, i.e., nh, Pth, 17) /) and L. In the first trial calculation it is convenient to assume a value for the fast effect (perhaps c = 1) and check it later. All the necessary data having been collected, B may be computed from the appropri-... 

A pool of PMMA with a diameter of 1 m burns in air. Radiation effects are to be included. In addition to using the properties from Problem 9.1, let XT = 0.25,7f = 1500 K and k = 0.5 nC1. If it is known that the critical mass loss rate for PMMA is 4 g/m2 s, calculate the flux of water (m") needed to extinguish this fire. If instead the oxygen is reduced, at what mass fraction will extinction occur ... 

In this case study, steady-state mass balance models are applied for critical loads calculation for the heavy metals. 

We have made three new calculations following the cooling of proto-neutron stars until the luminosity fell below an observable level. In the first model a soft equation of state (EOS) was used (gravitational critical mass 1.50 MQ). The proto-neutron star was selected by taking a post bounce calculation of the core of a 25 M0 star and removing all the mass but for the inner 1.64 M0. The second model was made with a stiffer EOS using the same core as the first model. The third model was made by... 

In the 1941 paper with Yu. B. Khariton [40], the problem of the critical size of a sample of 235 U in the fission of nuclei by fast neutrons was considered. The calculations showed that, in order to sustain a chain fission reaction by fast neutrons in a sample of 235 U surrounded by a heavy neutron reflector, it is sufficient to have only ten kilograms of pure 235U isotope. Here also a theory is given which allows calculation of the critical mass of... 

The value of critical mass, M., calculated in this way is, however, considerably overestimated by the elementary diffusion theory. The more exact diffusion theory, allowing for the long free path, drops R. by a factor of about 2/3 giving... 

Calculations show that the critical mass of a well tamped spheroid, whose major axis is five times its minor axis, is only 35% larger than the critical mass of a sphere. If such a spheroid 10 cm thick and 50 cm in diameter were sliced in half, each piece would be sub-critical though the total mass, 250 kg, is 12 times the critical mass. The efficiency of such an arrangement would be quite good, since the expansion tends to bring the material more and more nearly into a spherical shape. 

The simplest scheme which might be autocatalytic is indicated in the sketch where the active material is disposed in a hollow shell as indicated in Fig. 8.3a. Suppose that when the firing plug is in place one has just the critical mass for this configuration. If as the reaction proceeds the expansion were to proceed only inward it is easy to see from diffusion theory that v would increase. Of course in actual fact it will proceed outward (tending to decrease v ) as well as inward and the outward expansion would in reality give the dominant effect. However, even if the outward expansion were very small compared to the inward expansion, it has been calculated that this method gives very low efficiency with 12 an efficiency of only about 10 was calculated. 

Characterize the models for HM critical load calculation in terrestrial ecosystems. Highlight the relative importance of various links of biogeochemical food web in mass balance models. 

Physiologic model-physiologically based pharmacokinetic model (PB/PK) A physiologically based model for Gl transit and absorption in humans is presented. The model can be used to study the dependency of the fraction dose absorbed (Fabs) of both neutral and ionizable compounds on the two main physico-chemical input parameters [the intestinal permeability coefficient (Pint) and the solubility in the intestinal fluids (Sint)] as well as the physiological parameters, such as the gastric emptying time and the intestinal transit time. For permeability-limited compounds, the model produces the established sigmoidal dependence between Fabs and Pnt. In case of solubility-limited absorption, the model enables calculation of the critical mass-solubility ratio, which defines the onset of nonlinearity in the response of fraction absorbed to dose. In addition, an analytical equation to calculate the intestinal permeability coefficient based on the compound s membrane affinity and MW was used successfully in combination with the PB-PK model to predict the human fraction dose absorbed of compounds with permeability-limited absorption. Cross-validation demonstrated a root-mean-square prediction error of 7% for passively absorbed compounds. 

In the other case the vapour mass fiaction at the relief device entrance must be estimated taking into account the flushing flow hypothesis. This allows the calculation of the so-called entropy parameter ro, which is required for the determination of the critical mass flow density G. ... 

With the help of the substance property data, which are well known for these common solvents, and the plant data listed above, the mass flow which can be relieved safely by the planned safely valve can be calculated applying the equilibrium model according to Leung. For the sample calculations presented in Table 7-1, a vapour mass fraction of 5 %, an allowable overpressure during relief of 0.2 pset and the simplified model for the determination of the critical mass density have been assumed. 

The critical mass flow density is referenced to the cross-sectional area of the pipe in this case. In order to be able to calculate the friction ctor f for the pipe, the Rey-nolds-number must be known. For the special case of a homogeneous two-phase pipe flow, this can be calculated according to ... 

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