Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—I: Adjoint Sensitivity Analysis

For counter-flow mechanical draft cooling towers, the air in the fill can reach the point of saturation before leaving the fill section. The heat and mass transfer to the saturated air by evaporative cooling inside the fill are modeled with some assumptions and with over 50 parameters for boundary conditions, cooling tower geometries, heat and mass transfer correlations, water and air thermal properties, etc. Because of the parameter uncertainties and modeling assumptions, the accuracy and reliability of the cooling tower model need to be evaluated by quantifying the uncertainties associated with the model output. First, sensitivities of the model output with respect to all the model parameters need to be analyzed. Based on the cooling tower model, this work developed adjoint sensitivity models for the saturated case to compute efficiently and exactly the sensitivities of the model responses to all model parameters by applying the general adjoint sensitivity analysis methodology for nonlinear systems. The solution of the adjoint sensitivity models are independently verified. With the sensitivities known, the model parameters can be ranked in their importance for contributing to response uncertainties. The propagation of the uncertainties in the model parameters to the uncertainties in the model outputs can be evaluated. By further applying the predictive modeling for coupled multiphysics systems methodology, the cooling tower model for the saturated case can be improved by reducing the model prediction uncertainties through assimilation of experimental measurements and calibration of model parameters.