Abstract
Nuclear and other large-scale energy-producing plants must include systems that guarantee the safe discharge of residual heat from the industrial process into the atmosphere. This function is usually performed by one or several cooling towers. The amount of heat released by a cooling tower into the external environment can be quantified by using a numerical simulation model of the physical processes occurring in the respective tower, augmented by experimentally measured data that accounts for external conditions such as outlet air temperature, outlet water temperature, and outlet air relative humidity. The model’s responses of interest depend on many model parameters including correlations, boundary conditions, and material properties. Changes in these model parameters induce changes in the computed quantities of interest (called “model responses”), which are quantified by the sensitivities (i.e., functional derivatives) of the model responses with respect to the model parameters. These sensitivities are computed in this work by applying the general adjoint sensitivity analysis methodology (ASAM) for nonlinear systems. These sensitivities are subsequently used for: (i) Ranking the parameters in their importance to contributing to response uncertainties; (ii) Propagating the uncertainties (covariances) in these model parameters to quantify the uncertainties (covariances) in the model responses; (iii) Performing model validation and predictive modeling. The comprehensive predictive modeling methodology used in this work, which includes assimilation of experimental measurements and calibration of model parameters, is applied to the cooling tower model under unsaturated conditions. The predicted response uncertainties (standard deviations) thus obtained are smaller than both the computed and the measured standards deviations for the respective responses, even for responses where no experimental data were available.
Highlights
Nuclear and other energy-producing large-scale industrial installations must include systems that guarantee the safe discharge of residual heat from the industrial process into the atmosphere
As detailed in Appendix A, each of these data sets comprises measurements of the following quantities: (i) Outlet air temperature measured with the “Tidbit” sensor; (ii) Outlet air temperature measured with the “Hobo” sensor; (iii) Outlet water temperature; (iv) Outlet air relative humidity
The adjoint sensitivity model yields the adjoint state functions which are used to compute the sensitivities of each model response to all of the 47 model parameters by means of just one adjoint model computation
Summary
Nuclear and other energy-producing large-scale industrial installations must include systems that guarantee the safe discharge of residual heat from the industrial process into the atmosphere. This work is organized as follows: Section 2 presents the mathematical model of a mechanical draft counter-flow cooling tower operating under unsaturated conditions, along with the numerical solution for the quantities (state functions) mentioned above in items (i) through (vi).
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