Predictive Modeling of a Buoyancy-Operated Cooling Tower Under Saturated Conditions—I: Adjoint Sensitivity Model

A cooling tower discharges waste heat produced by an industrial plant to the external environment. The amount of thermal energy discharged into the environment can be determined by measurements of quantities representing the external conditions, such as outlet air temperature, outlet water temperature, and outlet air relative humidity, in conjunction with computational models that simulate numerically the cooling tower’s behavior. Variations in the model’s parameters (e.g., material properties, model correlations, boundary conditions) cause variations in the model’s response. The functional derivatives of the model response with respect to the model parameters (called “sensitivities”) are needed to quantify such response variations changes. In this work, the comprehensive adjoint sensitivity analysis methodology for nonlinear systems is applied to compute the cooling tower’s response sensitivities to all of its model parameters. These sensitivities are used in this work for (1) ranking the model parameters according to the magnitude of their contribution to response uncertainties; (2) propagating the uncertainties in the model’s parameters to quantify the uncertainties in the model’s responses. In an accompanying work, these sensitivities are subsequently used for predictive modeling, combining computational and experimental information, including the respective uncertainties, to obtain optimally predicted best-estimate nominal values for the model’s parameters and responses, with reduced predicted uncertainties.