A heat transport benchmark problem for predicting the impact of measurements on experimental facility design

Abstract This work presents the application of the “Predictive Modeling of Coupled Multi-Physics Systems” ( PM_CMPS ) methodology conceived by Cacuci (2014) to a “test-section benchmark” problem in order to quantify the impact of measurements for reducing the uncertainties in the conceptual design of a proposed experimental facility aimed at investigating the thermal-hydraulics characteristics expected in the conceptual design of the G4M reactor ( GEN4ENERGY, 2012 ). This “test-section benchmark” simulates the conditions experienced by the hottest rod within the conceptual design of the facility's test section, modeling the steady-state conduction in a rod heated internally by a cosinus-like heat source, as typically encountered in nuclear reactors, and cooled by forced convection to a surrounding coolant flowing along the rod. The PM_CMPS methodology constructs a prior distribution using all of the available computational and experimental information, by relying on the maximum entropy principle to maximize the impact of all available information and minimize the impact of ignorance. The PM_CMPS methodology then constructs the posterior distribution using Bayes’ theorem, and subsequently evaluates it via saddle-point methods to obtain explicit formulas for the predicted optimal temperature distributions and predicted optimal values for the thermal-hydraulics model parameters that characterized the test-section benchmark. In addition, the PM_CMPS methodology also yields reduced uncertainties for both the model parameters and responses. As a general rule, it is important to measure a quantity consistently with, and more accurately than, the information extant prior to the measurement. For the test-section benchmark, it is shown that the maximum coolant and rod surface temperatures responses are the most important measurable quantities. Using all of the available information, the PM_CMPS formulas yield optimally predicted best-estimate nominal model parameter values and reduced predicted standard deviations for the predicted parameters, such that: (i) the model parameters displaying the largest relative sensitivities and largest relative standard deviations are affected the most; and (ii) the model parameters with zero sensitivities remain unaffected by applying the PM_CMPS methodology. The PM_CMPS formulas also yield optimally predicted best-estimate nominal values for the model responses, along with correspondingly reduced predicted standard deviations. Assimilating within the PM_CMPS methodology an accurate measurement of the benchmark's maximum coolant temperature has the following impacts on the quantity that has been measured (i.e., on the maximum coolant temperature): (i) the nominal value of the predicted maximum coolant temperature is closer to the more “accurate” experimental value; (ii) the originally computed standard deviation is decreased significantly. In addition, the measurement of the maximum coolant temperature impacts not only the quantity being measured, but also impacts the other responses of interest, e.g., the maximum temperature in the rod and the maximum rod surface temperature. In all cases, the predicted standard deviations were decreased substantially, indicating that the predicted values are more accurate than the originally computed ones. The PM_CMPS formulas were also used to predict the impact of the simultaneous assimilation of the maximum coolant and the maximum rod's surface temperature measurements. As expected in view of the fact that the PM_CMPS methodology uses Bayes’ theorem to combine information, the assimilation of two accurate experiments reduces the predicted standard deviations of the maximum rod, rod surface and coolant temperatures even further. The test-section benchmark and methodology presented in this work can serve as a paradigm for quantifying the impact of experimental measurements in the analysis, design and/or operation of other thermal-hydraulics experimental facilities.