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Adjoint Sensitivity Analysis of Extremum-Type Responses in Reactor Safety

D. G. Cacuci, P. J. Maudlin, C. V. Parks

Nuclear Science and Engineering / Volume 83 / Number 1 / Pages 112-135

January 1983

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A recently developed sensitivity theory for nonlinear systems with responses defined at critical points, e.g., maxima, minima, or saddle points, of a function of the system's state variables and parameters is applied to a protected transient with scram on high-power level in the Fast Flux Test Facility. The single-phase segment of the fast reactor safety code MELT-IIIB is used to model this transient. Two responses of practical importance, namely, the maximum fuel temperature in the hot channel and the maximum normalized reactor power level, are considered. For the purposes of sensitivity analysis, a complete characterization of such responses requires consideration of both the numerical value of the response at the maximum, and the location in phase space where the maximum occurs. This is because variations in the system parameters alter not only the value at this maximum but also alter the location of the maximum in phase space. Expressions for the sensitivities of the numerical value of each maximum-type response and expressions for the sensitivities of the phase-space location at which the respective maximum occurs are derived in terms of adjoint functions. The adjoint systems satisfied by each of these adjoint functions are derived and solved. It is shown that the complete sensitivity analysis of each maximum-type response requires (a) the computation of as many adjoint functions as there are nonzero components of the maximum in phase space, and (b) the computation of one additional adjoint function for evaluating the sensitivities of the numerical value of the response. The same computer code can be used to calculate all the required adjoint functions. Once these adjoint functions are available, the sensitivities to all possible variations in the system parameters are obtained by quadratures. The sensitivities obtained by this efficient method are used to predict both changes in the numerical values of these maximum-type responses, and the new phase-space location at which the perturbed maxima occur when the system parameters are varied. These predictions are shown to agree well with direct recalculations using perturbed parameter values.

 
 
 
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