Prediction of the Inner Temperatures in a Duct Based on Outer Thermocouples Measurements
Nuclear power plants (NPP) include connections of branches conveying fluids at different temperatures. Some thermohydraulics phenomena such as stratification may affect the inner wall of the ducts and lead to fatigue damage. They are then defined in a conservative way for fatigue evaluation. In order to improve the definitions of these phenomena EDF plans to install thermocouples rings on the outer surfaces of some ducts. The aim of this article is to define a methodology to derive thermal loadings from outer measurements. To estimate the temperature of the inner skin duct through measurements on the outer surface of the ducts, we propose to use optimal control (with quadratic cost functions) to compare the outer temperatures calculated with a finite element model and the measurements. Different methods are investigated: first, a method based on Nelder-Mead algorithm [3] and second, an advanced method based on gradient computation. The advantage of the latter is to explicitly compute the gradient and a Hessian approximation of the cost function with respect to the water temperatures, which is time saving for computation-wise. To enhance the robustness of the methodology, additional conditions on the regularity of the fluid temperature field are added.