Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-12-01
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| Series: | Energies |
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| Online Access: | http://www.mdpi.com/1996-1073/9/12/1028 |
| _version_ | 1811302335791497216 |
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| author | Federico Di Rocco Dan Gabriel Cacuci |
| author_facet | Federico Di Rocco Dan Gabriel Cacuci |
| author_sort | Federico Di Rocco |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T07:26:11Z |
| format | Article |
| id | doaj.art-dac5a2c2a4f44c02837b3183779d3311 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-04-13T07:26:11Z |
| publishDate | 2016-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-dac5a2c2a4f44c02837b3183779d33112022-12-22T02:56:28ZengMDPI AGEnergies1996-10732016-12-01912102810.3390/en9121028en9121028Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted UncertaintiesFederico Di Rocco0Dan Gabriel Cacuci1Department of Astronautic, Electric and Energy Engineering (DIAEE), “Sapienza”—University of Rome, 00185 Roma, ItalyCenter for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USANuclear 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.http://www.mdpi.com/1996-1073/9/12/1028cooling toweradjoint sensitivity analysisadjoint cooling tower model solution verificationdata assimilationmodel calibrationbest-estimate predictionsreduced predicted uncertainties |
| spellingShingle | Federico Di Rocco Dan Gabriel Cacuci Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties Energies cooling tower adjoint sensitivity analysis adjoint cooling tower model solution verification data assimilation model calibration best-estimate predictions reduced predicted uncertainties |
| title | Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties |
| title_full | Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties |
| title_fullStr | Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties |
| title_full_unstemmed | Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties |
| title_short | Predictive Modeling of a Buoyancy-Operated Cooling Tower under Unsaturated Conditions: Adjoint Sensitivity Model and Optimal Best-Estimate Results with Reduced Predicted Uncertainties |
| title_sort | predictive modeling of a buoyancy operated cooling tower under unsaturated conditions adjoint sensitivity model and optimal best estimate results with reduced predicted uncertainties |
| topic | cooling tower adjoint sensitivity analysis adjoint cooling tower model solution verification data assimilation model calibration best-estimate predictions reduced predicted uncertainties |
| url | http://www.mdpi.com/1996-1073/9/12/1028 |
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