17th Symposium of AER on VVER Reactor Physics and Reactor Safety, September 2007, Yalta, Crimea, Ukraine INNOVATIONS IN MOBY-DICK CODE Šůstek J.,Krýsl V. ŠKODA JS a.s., Orlík 266, Plzeň Czech Republic

During using of the macrocode Moby-Dick has surfaced that structure of the program has some limitations in accuracy of calculations. Many of these limitations originate in extensive using of the low precision representation of the real variables. Increase of precision should allow to remove some non- physical artifacts of calculations, overall increase accuracy of calculations and allow to do types of calculations not possible before.

Our idea was quite simple: replace old representation of real variables, which use single precision, with double precision representation. single precision ~ 7 digits (4 bytes) double precision ~15 digits (8 bytes) Task was not quite easy, we had to rewrite many parts of macrocode. We have used this opportunity to modernize internal structure of macrocode, which now uses memory more effectively.

EFFECTS OF INCREASED PRECISION Generally speaking, effect of increased precision is “smoothing” of results. Tests show that influence on normal calculations, for example core-mesh and pin-wise calculations in 60deg symmetry, is negligible. But when we calculate full- core case, slight asymmetries among symmetrical parts of core for single precision variables can be found, especially in pin-wise model. In the past, we couldn’t average them out, as values of criteria of convergence didn’t allow us to put them more precisely. But as we can use increased precision of criterions, we can completely remedy this situation.

In first example we want to show two examples of this “smoothing”. First case is calculations of the integral and differential reactivity of the control assembly (CA). Calculations were made for EDU NPP, unit 3, cycle 19 for end of the cycle (EOC), reactor at nominal power. Second case is evolution of the power of the reactor when perturbation in the size of the coolant flow occurs. Calculations were made for EDU NPP, unit 3, cycle 28 for beginning of the cycle (BOC), reactor at nominal power. Perturbation is change of the coolant flow, with its increase of 5%.

Fig.1 Calculations of the integral and differential reactivity of the control assembly, single precision

Fig. 2 Calculations of the integral and differential reactivity of the control assembly, double precision

Fig. 3 Evolution of power of the reactor after perturbation of coolant flow, single precision

Fig. 4 Evolution of power of the reactor after perturbation of coolant flow, double precision

In second example we used new precision to compare reactivity coefficients calculated by the perturbation theory (using adjoint fluxes) and by direct calculation. Direct calculation means that we precisely calculate base state (unperturbed) and change value of required quantity, with other parameters of the core unchanged. After that we use difference in reactivities and amount of changed quantity and directly calculate appropriate reactivity coefficient. Concentrations of Xe and Sm are during calculation of the perturbed state as in basic state. Calculations were made for EDU NPP, unit 3, cycle 24, for several moments during the cycle, from which we chose to present state with effective time 2 days. Reactor is at nominal power, and all other parameters are also nominal.

In following pictures we can compare results of both different methods of calculations, for different values of perturbations. Perturbation theory calculations are denoted as “petr”, while direct calculations as “trap”. We must note that using single precision, direct calculations of reactivity coefficients are impossible. Calculations shown include boron reactivity coefficient, moderator density coefficient, (input) moderator temperature coefficient, coolant flow reactivity coefficient and fuel temperature coefficient.

Fig. 5 Boron reactivity coefficient, comparison of the perturbation theory and direct calculation

Fig. 6 Moderator density coefficient, comparison of the perturbation theory and direct calculation

Expected result for all cases is that curves for both types of calculations – direct and using perturbation theory – shall meet in limit for undisturbed state, hopefully with the same angular coefficient. As we can see from results, this condition is met for boron reactivity coefficient and moderator density coefficient. Other coefficients (coolant flow reactivity coefficient, moderator temperature coefficient and fuel temperature coefficient) show discrepancies, albeit fuel temperature coefficient only small. We are currently investigating cause of these discrepancies.

Fig. 7 (input) moderator temperature coefficient, comparison of the perturbation theory and direct calculation

Fig. 8 Coolant flow reactivity coefficient, comparison of the perturbation theory and direct calculation

Fig. 9 Fuel temperature coefficient, comparison of the perturbation theory and direct calculation