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Computational fluid dynamics (CFD) is a computer-based analysis of the dynamics of fluid flow, and it is widely used in chemical and process engineering applications. However, computation usually becomes a herculean task when calibration of the CFD models with experimental data or sensitivity analysis of the output relative to the inputs is required. This is due to the simulation process being highly computationally intensive, often requiring a large number of simulation runs, with a single simulation run taking hours or days to be completed. Hence, in this research project, the kriging meta-modelling method was coupled with expected improvement (EI) global optimisation approach to address the CFD model calibration challenge. In addition, a kriging meta-model based sensitivity analysis technique was implemented to study the model parameter input-output relationship. A novel EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chi-square distribution, where existing normal distribution-based EI measures are not applicable. This novel EI measure suggested the values of CFD model parameters to simulate with, hence minimising SSE and improving the match between simulation and experiments. To test the proposed methodology, a non-CFD numerical simulation case of the semi-batch reactor was considered as a case study which confirmed a saving in computational time, and an improvement of the simulation model with the actual plant data. The usefulness of the developed method has been subsequently demonstrated through a CFD case study of a single-phase flow in both a straight type and convergent-divergent type annular jet pump, where both a single turbulent model parameter, C_μ and two turbulent model parameters, C_μ and C_2ε where considered for calibration. Sensitivity analysis was subsequently based on C_μ as the input parameter. In calibration using both single and two model parameters, a significant improvement in the agreement with experimental data was obtained. The novel method gave a significant reduction in simulation computational time as compared to traditional CFD. A new correlation was proposed relating C_μ to the flow ratio, which could serve as a guide for future simulations. The meta-model based calibration aids exploration of different parameter combinations which would have been computationally challenging using CFD. In addition, computational time was significantly reduced with kriging-assisted sensitivity analysis studies which explored effect of different C_μ values on the output, the pressure coefficient. The numerical simulation case of the semi-batch reactor was also used as a basis of comparison between the previous EI measure and the newly proposed EI measure, which overall revealed that the latter gave a significant improvement at fewer number of simulation runs as compared to the former. The research studies carried out has hence been able to propose and successfully demonstrate the use of a novel methodology for faster calibration and sensitivity analysis studies of computational fluid dynamics simulations. This is essential in the design, analysis and optimisation of chemical and process engineering systems. |
