Feinberg-Galanin Method of Heterogeneous-reactor Calculation

6 Feinberg-Galanin Method of Heterogeneous-reactor Calculations 

The pre.sent treatment of the heterogeneous method develops the principal concepts obtained in the general theory. The analysis begins with a derivation of the neutron-balance equations. These results are then used to obtain the criticality condition and to demonstrate the basis of the homogenization method used with the unit-cell model. The section is concluded with an application of the method to a reactor with four fuel rods and a numerical example. 

The first of these assumptions is valid if the distance between lumps is much larger than their dimensions. Because of the symmetric configuration of most reactor lattices, this condition tends to be favored and the theory is applicable even in the case of quite large lumps. The second assumption requires that the absorption in the moderator be low and that the diffusion length for the moderator material be small in comparison to the lattice spacing. The third assumption is essentially a computational convenience, and its applicability is determined primarily by the accuracy of the model by which the thermal constant is computed. The last assumption is made to simplify the analysis. A treatment in which resonance absorption is included is given by Galanin.  

With the above assumptions as a model, consider an infinite heterogeneous lattice composed of cylindrical fuel rods of infinite length (i.e., a two-dimensional configuration). Let the radius of these rods be pf and their neutron yield per thermal-neutron absorption be rj. The thermal constant 7a for the fuel lumps is defined as ratio of total net current of thermal 7a = neutrons into the lump to the value of the (10.235) thermal flux at the surface 

On the basis of the diffusion-theory model the thermal-neutron flux at a field point r in the moderator is given by 

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