PCGA: Polynomial collocation genetic algorithm for singular Poisson-Boltzmann equation arising in thermal explosions.

Heat generation as a result of the exothermic reaction reaches the environment mainly due to the conduction through the walls of the vessel. The balance between the heat generated and the heat conducted away, resulting in the explosion is described by the Frank-Kamenetzkii (FK) parameter ρ. The critical value of FK for which the explosion occurs depends upon the shape of the vessel, which requires the solution of governing singular nonlinear Poisson-Boltzmann equation. Owing to the exponential nonlinearity and singularity the analytical exact solution for the non-integer k values does not exist. This work focuses on implementing the polynomial collocation by exploiting the global optimization features of the genetic algorithm to solve the Poisson-Boltzmann equation for integer and non-integer shape factors (k). The governing equation was converted into coupled nonlinear algebraic equations and an objective function was formulated. The method was examined for six different configurations of the control parameters of GA to find the best set of parameters. The solution for temperature distribution is obtained for cylindrical (k = 1), parallelepiped (k = 0.438, 0.694), and an arbitrary shape (k = 0.5) respectively. The solution obtained from Polynomial Collocation Genetic Algorithm (PCGA) remained in good agreement with the corresponding analytical results for k = 1, with the minimum absolute error of 10 - 10 . The critical values of the FK are obtained as 1.5 , 1.4 , a n d 1.7 for shape factor k = 0.438 , 0.5 , a n d 0.694 respectively with the convergence of the order of 10 - 6 t o 10 - 5 . The obtained solution is fairly stable over appropriate independent runs with the variation in the fitness value ranging from 10 - 05 t o 10 - 03 . Further simulations were performed to validate the results through statistical error indices. The diminutive errors of the order of 10 - 6 confirm reliable optimum solution, accuracy, and stability.

Determination of age specific ¹³¹I S-factor values for thyroid using anthropomorphic phantom in Geant4 simulations.

Using anthropomorphic phantom in Geant4, determination of ß- and γ-absorbed fractions and energy absorbed per event due to (131)I activity in thyroid of individuals of various age groups and geometrical models, have been carried out. In the case of (131)I ß-particles, the values of the absorbed fraction increased from 0.88 to 0.97 with fetus age. The maximum difference in absorbed energy per decay for soft tissue and water is 7.2% for γ-rays and 0.4% for ß-particles. The new mathematical MIRD embedded in Geant4 (MEG) and two-lobe ellipsoidal models developed in this work have 4.3% and 2.9% lower value of S-factor as compared with the ORNL data.

Kinetic study of fission product activity released inside containment under loss of coolant transients in a typical MTR system.

Based on continuous release of fission product (FP) activity from fuel to the coolant and then to the containment, a kinetic model is developed for source term after a LOCA in a typical MTR type system. The time dependent source, re-suspension rate, decay of fission products, leakage, deposition on surfaces, and re-circulation of air through filters are employed with a partial prompt source plus a time varying source. Releases of different FP activities are simulated for various release rates.

Simulation of corrosion product activity for nonlinearly rising corrosion on inner surfaces of primary coolant pipes of a typical PWR under flow rate transients.

For nonlinear accelerating corrosion, calculation of activated corrosion products on inner surfaces of primary coolant pipes have been done in a typical pressurized water reactor (PWR) under flow rate perturbations. Computer program CPAIR-P (Corrosion Product Activity In Reactors) (Deeba et al., 1999) has been modified to accommodate for time-dependent corrosion rates. Results, for (24)Na, (56)Mn, (59)Fe, (58)Co, (60)Co and (99)Mo, show that the specific activity in primary loop approaches equilibrium value under normal operating conditions fairly rapidly. Predominant corrosion product activity during operation is due to (56)Mn, and cobalt isotopes dominate the activity after shutdown of reactor. Flow rate perturbations and different types of rising corrosion rates were introduced in the system and effects on saturation activity were studied. For a linear decrease in flow rate and a constant corrosion rate, the total coolant activity and activity on pipe scale approaches higher saturation values when compared to normal condition values. With a nonlinearly accelerating corrosion, the behavior of specific activity changes considerably. The flow rate perturbations on specific activity for pipe scale results in a new saturation value which depends on both the changes in flow rate (Delta w) and equilibrium corrosion rate (C(s)) values. However, the time taken to reach the saturation activity depends on the slope of corrosion rate. For a slow pump coastdown, the activity does not show an initial drop when flow rate starts decreasing. It monotonically rises and follows the slope of corrosion rate. The peak value and decay of activity after scram are strong functions of flow rate and removal efficiencies.