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Cooling towers discharge waste heat from an industrial process into the atmosphere, and are essential for the functioning of large energy-producing plants, including nuclear reactors. Using a numerical simulation model of the cooling tower together with measurements of outlet air relative humidity, outlet air and water temperatures enables the quantification of the rate of thermal energy dissipation removed from the respective process. The computed quantities depend on many model parameters including correlations, boundary conditions, material properties, etc. Changes in these model parameters will induce changes in the computed quantities of interest (called “model responses”). These changes are quantified by the functional derivatives (called “sensitivities”) 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 needed 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 predictive modeling, including assimilation of experimental measurements and calibration of model parameters to produce optimal predicted quantities (both model parameters and responses) with reduced predicted uncertainties.


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Cacuci, D. G., & Fang, R. (2016). Predictive modeling of a paradigm mechanical cooling tower: I. Adjoint sensitivity model. Energies, 9(9), 718. doi:10.3390/en9090718