Reactor unperturbed

There are many interesting reports in the literature where computer simulations have been used to examine not only idealized cases but have also been used in an attempt to explain segregation and viscosity effect in unperturbed polymerization reactors (6). Some experimental work has been reported (7, 8). It is obvious, however, that although there is some change in the MWD with conversion in the batch and tubular reactor cases and that broadening of the MWD occurs as a result of imperfect mixing, there is no effective means available for controlling the MWD of the polymer from unperturbed or steady-state reactors. 

A research reactor differs fundamentally from a nuclear power reactor where the desired product is heat. The heat produced by a research reactor is an undesirable by-product and its removal limits the maximum size (and hence neutron flux) of a research reactor core. The latest and most advanced research reactor is the 20 MW FRM-II reactor (Munich, Germany) shown in Fig. 3.1 [5]. It has an unperturbed maximum neutron flux of about 8x10 cm s. The most powerful research reactor is the Institut Laue Langevin (ILL, Grenoble, France), Fig. 3.2, at 57 megawatts (MW) [6] 20 MW research reactors are more common. 

The traditional role of perturbation theory in reactor physics has been to estimate, with a first-order accuracy, the effect of an alteration in the reactor on its reactivity. Lately, application of perturbation theory techniques has increased significantly in both scope and volume. Two general trends characterize these developments (1) improvement of the accuracy of reactivity calculation, and (2) extension of the use of second-order perturbation theory formulations for estimating the effect of a perturbation on integral parameters other than reactivity, and to nuclear systems other than reactors. These trends reflect two special features of perturbation theory. First, it provides exact expressions for the effect of an alteration in the reactor on its reactivity. For small, and especially local alterations, these perturbation expressions are easier and cheaper to apply than other approaches. Second, second-order perturbation theory formulations can be applied with distribution functions pertaining only to the unperturbed system. 

In the normal-mode expansion method, the perturbed distribution is expressed in terms of the normal modes, or eigenfunctions, of the unperturbed reactor (9). This classic approach to perturbation calculations will not be reviewed in this work. 

Consider a reactor with a localized perturbation, shown schematically in Fig. I. Region U is unperturbed. The perturbed region, P, is composed of two subregions C and B. The physical alteration in the system occurs in region C. Region B is a buffer zone beyond its outer boundary the perturbation effect is negligible. 

The first and most well-known feature is the adequacy of the integral methods for calculating space-dependent flux distribution in heterogeneous geometries. This characteristic can be essential for accurate calculations of reactivity worth of small samples in fast systems [see Foell s monograph (2) and its references]. The heterogeneity is due to the perturbing sample as well as to the inherent structure of the unperturbed reactor. 

All first-order approximations (pertaining to integral transport theory) considered are equivalent, in accuracy, either to Pid[x where (j) stands for one of the three approximations, < fl> bd> or ( fd> fo the perturbed flux distribution and stands for either ( fl or ( bd-cf> is a better approximation to compared to better approximation to compared to we conclude that all first-order perturbation expressions in integral transport theory formulations considered in this work are equivalent, in accuracy, to some high-order approximation to Pji>. This higher accuracy can be computed, in integral formulations, using the flux and source-importance functions for the unperturbed reactor. 

The flux (j)yjj is the first-generation flux distribution developed in the perturbed reactor starting from the fission-neutron density distribution in the unperturbed reactor. The calculation of 4)pQ takes into account all the interactions the fission-neutron can undergo up to the first fission event. Thus, p, accounts for perturbations in all nuclear parameters except in the fission cross section. Whereas p (and (/> [,) includes effects of single collision events in the perturbed system, 0pp includes effects of multiple collisions. Consequently we expect that, for many problems, Pid[0fd> ] will be more accurate than Pid[0fl> 0 ]-... 

Both approaches described above need the first-flight kernel for the perturbed reactor (the first approach needs also the unperturbed kernel)— the first approach for the operators of the perturbation expressions whereas the second approach for the calculation of the flux It is possible to avoid the need for the first-flight kernel using p,o[[Pg.215]

Eq. (126) is the differential analog to Eq. (113). It is a fixed-source equation its right-hand side pertains to the unperturbed reactor. 

The integration is over the entire volume of the reactor. In Eq. (A1.4), is the adjoint flux in the unperturbed state, and 4> is the flux in the perturbed reactor with a diffusion coefficient and cross sections of... 

The form of this equation implies a recalculation of the entire reactor problem, the determination of the value of v for criticality being a primary objective. The complex reanalysis required here is not always necessary, however. If the changes introduced into the system are small, it is possible to make use of the knowledge already available about the unperturbed system from the solution of Eq. (13.1). Suppose for each of the primed quantities Q of Eq. (13.6) we take the form... 

A positive power output via the piston implies that the average temperature of the reactor contents in the perturbed case is lower than in the unperturbed case. The difference in total power output of the perturbed and unperturbed case is... 

In the present study we investigate the possibility of enhancing the reactor conversion in the regime of multiple conversions by means of deliberate perturbations of the initial steady state. For all the results reported here, the reactor was initially set to operate at the lowest conversion steady state, and the reactor inlet CO concentration was perturbed by temporarily reducing the CO concentration to a lower value, while maintaining the total flow rate, the reactor pressure, and oxygen concentration essentially unperturbed. Before each pulse, the reactor was cooled down to a temperature well below the hysteresis loop of Fig. 2 and then slowly heated up to a desired temperature to establish the lowest conversion state. 

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