Sensitivity and Uncertainty Analysis of Counter-Flow Mechanical Draft Cooling Towers—II: Predictive Modeling

Abstract

Based on the adjoint sensitivity models for the saturated case of the counter-flow cooling tower developed in the accompanying Part I, this work computed and analyzed the sensitivities, with respect to all of the 52 model parameters, of the following responses (i.e., model outputs of interest): the outlet air temperature, outlet water temperature, outlet water mass flow rate, and outlet air relative humidity. The sensitivity results indicate that, in general, all these response of interest are mostly sensitive to the boundary-related parameters (e.g., , , , , , and ) and also somewhat sensitive to those parameters (e.g., , , , , , , and ) that directly relate to the heat and mass transfer terms in the cooling tower model. The rankings of these parameters depend on the respective model responses. With the sensitivities known, the propagation of the uncertainties in the model parameters to the uncertainties in the model outputs are readily obtained. The uncertainties associated with the model outputs were reduced by applying the “predictive modeling for coupled multiphysics systems” (PM_CMPS) methodology. For a typical case studied in this work, the uncertainties associated with the model outputs of the outlet air temperature, outlet water temperature, and outlet air relative humidity, are reduced by 22%, 38%, and 68%, respectively. Moreover, the PM_CMPS methodology also generated optimal best-estimate nominal values for the model parameters and model responses. It also improved (i.e., reduced) the uncertainties associated with model parameters through the process of model calibration, as shown in the paper. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.

Keywords:

• Adjoint sensitivity analysis
• data assimilation
• model calibration

Acknowledgments

This work has been partially sponsored by the U.S. Department of Energy (J. J. Peltz, program manager) with the University of South Carolina.