Thermal flux calculations

For the thermal flux calculation we used two models of the two-phase media. Thus, we are treating PUR foam a) as a gas containing solid particles with effective radii r in Model A, and... 

FROM TWO-DIMENSIONAL (r,z) -FOUR-GROUP DIFFUSION THEORY CALCULATION j -OF THERMAL FLUX... 

For the HFIR, this ratio is 0.839, and for calculational purposes, the thermal fluxes described in the preceding section were multiplied by this quantity before use in computing reaction rates. 

The Li concentration in atoms per g was converted to ng g natural Li value and the results are presented in Table 2. The six samples were from three canisters, all of which experienced predominantly thermal fluxes. Two of the canisters (containing samples 30006, 30010, 35031 and 35038) were from below the core with an epithermal flux value twice that of the other canister (samples 30114 and 30115) which was positioned at the side of the core. The calculated Li concentrations are generally consistent for all samples apart from specimen 35031 where the result was affected by contamination with " C. The average value for the predicted natural Li concentration in RPV steel, excluding the result for specimen 35031, was 0.3 0.1 ng g ... 

The numerical model we used was originally developed by Gill and Clyne [6] and has been modified to handle multi-layered deposits. It is a 1-dimensional model and consists of two parts thermal profile calculation and stress calculation. By regarding the torch motion as a fluctuation in the heat and mass flux onto a reference point on the substrate and assuming biaxial stress state, the program calculates both the through-thickness thermal profile and stress distribution during thermal spray as functions of time. 

One of the starting points in calculating the thermal history of the early Earth is the observed mismatch between the present-day heat production rate and the rate of heat loss. Today the total thermal flux for the Earth is about 41 TW (Davies, 1998). When this is compared with the present-day radioactive heat production of 20 TW it is clear that the Earth has another source of heat in addition to its radioactive heat. This heat source is thought to be the residue of "old heat" dating from the formation and differentiation of the Earth. 

However, Eq. (3-248) is just Fourier s law, with an effective thermal conductivity k(azUz/48k2). Further, because there is no net convection contribution to the cross-sectionally averaged heat flux calculated with respect to the moving axis z, we see that the convective transport rate down the tube is just that due to the mean velocity U. Both of these results may at first seem surprising. For example, the maximum rate of transport that is due to convection acting alone is the centerline velocity 2 U, and it is not immediately obvious why the actual convective transport rate is slower. In addition, the effective thermal diffusivity is seen in (3-246) to be inversely proportional to the molecular thermal diffusivity k, and this may also seem to be counterintuitive. 

Furthermore, according to water mass conservation equation, porosity does not affect liquid fluxes ratio. Therefore, darcean liquid flow still governs saturation kinetics. As can be seen on table 2, Qm" and Cim" calculations give the same saturation time, whereas in Cim" the saturation phenomenon is accelerated. As for thermal-hydraulics calculations, full saturation of the EB is reached earlier when both the heating source is being activated and liquid dynamics viscosity depends on temperature. Once again, this acceleration is only due to water dynamic viscosity decrease while heating. 

Calculation of thermal radiation flux Calculate thermal radiation flux of the target received according to the following formula ... 

Longitudinally the thermal flux in -the k 1.373 cylindrical reactor (Fig. 4.2.D) drops only by a factor of 2 before again rising in. the top (or bottom) water plus aluminum reflector. The actual longitudinal distribution will be even flatter, than that calculated because the side beryllium reflectors are longer than the reactor proper, and therefore extend into the top and bottom reflector region. 

Lansing, N. F., Thermal Neutron Flux Calculations, ORNL CF-49-11-167, November 16, 1949. 

Fig. 4. Fast, intermediate, and thermal fluxes as function of position for flux-trap reactor. Note that the thermal flux in the water at the center is almost five times higher than the average thermal flux in the active portion. Calculations by Intemuclear Co.

The thermal power is 450 MW. For "° Ag inventory calculation, plutonium fission fraction and thermal flux are assumed to be 60% and 4x lO cm s , respectively. Fractional release from fuel... 

The calculated result of " Ag inventory in GT-HTGR core showed that with higher bumup, higher power density and longer irradiation time, plutonium fission fitiction, thermal flux and irradiation time in GT-HTGR core could be about 70 times larger than that of HTTR. 

The factor, m/ unk> in Eq. (30.38) corrects for thermal neutron flux differences due to the flux gradient at the positions of the monitor and the unknown sample. In cases where the monitor is irradiated before or after the unknown sample, which is often the case with short irradiations, rJ unk corrects for the possible change in flux between the two irradiations. With the exception of this correction factor, the thermal neutron flux does not directly appear in Eq. (30.38) however, the quantity calculated with the flux monitor (the product of all the factors containing m ) is proportional to the thermal flux. Thus, when using this equation, it is commonly understood that the quantity measured with the unknown sample is divided by the thermal neutron flux measured with the monitor. 

Users of the kg method must determine the thermal neutron flux, the ratio of thermal flux to epithermal flux for the irradiation channel used (/), the shape parameter (a), and detection efficiencies for all counting geometries used. Since the calculations for the derivation and the use of these parameters are extensive, a software package is needed. Some new users begin a collaboration with one of the many laboratories using the Icq method and adopt their methods of calculation and their software. Two complete software packages are now readily available to all potential users. The KAYZERO/SOLCOI Software (Van Sluijs et al. 1997), now called KayWin, performs the calculations in the well-understood classical manner. It is widely used... 

Comparisons will be drawn between the experimental results and theoretical calcukitions using few-gioup diffusion theory. Of prime importance is the comparison of the variation of reactivity with temperature and the comparison of die thermal flux traverses. For the few-group calculations the material in a cell was homogenized by transport theory calculatfams and these will be discussed. In addition, the temperatura coefficient measurements will be compared with die results of a few-gmup adjoint theory calculation. 

The (ast-fisslon factor was determined from the ratio of the activities of a depleted and an enriched uranium foil, the resulting value being 1.0214 0.0021. Thebuclcllng was obtained from the critical size of the assemblies and the extrapolation distance. The latter, which was determined by least-squares fitting the flux distribution, was found to be 2.64 0.3 cm. The average buckling was 6.642 x 10 cm . The thermal-diffusion area, calculated from thermal cross sections, was 1,87 cm . The delayed-neutron age to thermal was calculated by O. G. Sullivan using a Monte Carlo moments-method calculation. The value was 15.6 cm . 

Thermal constants were obtained by using an S4 cylindrical cell transport code for the 7090 ffiM computer to calculate the thermal flux distribution in a cell. The cross seettons were Maxwellian averaged. 

For the analysis of these assemblies, the BPG code was used extensively along with a four-group, one-dimensional neutron diffusion code. The thermal flux depression factors were obtained from a one-velocity Monte Carlo program. A resonance integral program was used to calculate epithermal absorption parameters for U-238 and U-235,... 

Thermal-flux distributions. were measured with. bare and cadmium-covered gold and dysprosium foils. Ther- mal fluxes derived from the two detectors agreed, except near the perturbers Where the disagreement i prOached 10% due to spectral effects. Figure 1 shows t tcal flux distributions at 72% D 0. Agreement with theoretical calculations was generally satisfactory. 

The measured fission rates were input to the SAND-II code together with a starting spectrum calculated with the KENO Monte Carlo-code. The SAND-II code produced an adjusted dalcubted spectral shape which agreed vrith the measured data. Table I presents these SAND-II results for the thermal flux, flux of neutrons with energy. 1 and 1 MeV, total flux, and the mean neutron energy. A detailed error analysis was not made, but on the basis of similar Mrilyses, uncertainties in these spectral values are estimated to be 10 to 15% (1 o). 

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