Parameter optimisation for the improved modelling of industrial-scale gas explosions
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This thesis presents work on improving the predictive capabilities of a numerical model by parameter optimisation. The numerical model is based on computational fluid dynamics (CFD) and predicts the consequences of industrial-scale gas explosions. CFD models are, in general, approximate representations of real phenomena of interest; often, the agreement between model output and relevant experimental data can be improved through optimising parameters in the model. In this work, the parameters considered for optimisation are contained in sub-grid models for turbulence and combustion.
The doctoral project focuses on the gas explosion module of the commercial CFD tool FLACS. Explosion predictions of the tool are utilised in risk management for safer design of industrial facilities handling combustible gases. The challenge of simulating gas explosions with the CFD tool is that the predictions have to be reliable for many different explosion scenarios in extremely different large-scale geometries. This thesis presents an optimisation approach that considers this wide application range of the CFD model.
Four papers constitute the main part of the thesis; they propose a methodology for formulating and solving the optimisation problem (Paper 1, 2 and 4) and present examples of application (Paper 3). Additionally, the thesis comprises scientific contributions that have not been presented in the papers.
Amongst several candidates, suitable model outputs are identified as optimisation targets. The problem has first been formulated as a least-squares problem (Paper 4); this formulation did not appear to be appropriate for improving model predictions in gas explosions. Thus, in Paper 2, a problem formulation is developed that assesses under- and over-predictions as in model validation processes. This validation-based formulation is shown to be closely connected to another formulation in which the solution is the maximum likelihood estimator in the case of log-normally distributed errors in the measurements. It is shown that in contrast to a traditional least-squares problem formulation, the validation-based formulation yields an overall better improvement of the specific model outputs. The thesis presents three methodologies for selecting gas explosion experiments to be included in one optimisation process.
Running simulations is time-consuming. To enable a practical optimisation runtime, the model output is approximated by surrogates, which are fast to evaluate. Surrogates are explicit functions representing parameter-output relations. In Paper 1, surrogates based on neural networks are compared to polynomial response surfaces. Due to the satisfactory overall approximation quality of the neural networks in this application, these are employed as surrogates in subsequent optimisation processes. Furthermore, the smoothness of the surrogates allows for employing gradient-based optimisation routines; the resulting surrogate-based optimisation problem is solved by a trust region method embedded in a multi-start approach that has originally been intended for non-linear least-squares problems. As the developed optimisation problem is not a least-squares problem, the convergence of the routine for this problem with respect to the first order necessary optimality conditions is proven in Paper 2. In the end, to ensure that it is not a blind fit of the optimisation targets, but that characteristic physical phenomena of gas explosions are represented by the model, a comprehensive sanity check of the model is performed after optimisation.
The optimisation approach is used for two purposes: i) to obtain optimal parameter values that lead to reliable predictions for a wide range of applications, and thus can be implemented in the CFD tool; ii) to analyse physical models and detect their strengths and limitations. In this thesis, the second purpose is illustrated by an exemplary analysis of a flame folding model; optimisation for the first purpose is examined in more detail. In particular, the optimisation approach is tested and applied successfully to several versions of the CFD tool FLACS at different stages in the development process: a version released for commercial use and an in-house development version. The applicability of the optimisation approach is shown by testing it on the release version in Paper 2 and Paper 4. The in-house development version comprises models that have been updated recently with parameter values that have been set to an initial ‘best guess’, and thus requires optimisation. The in-house development version comprises updated models in which parameter values have been set to an initial ‘best guess’ and thus requires optimisation. Optimising the development version in Paper 3 improves the predictions significantly.
It is important to note that the optimisation process cannot compensate for models that do not capture the physical mechanisms of gas explosions. Thus, optimisation processes cannot replace further efforts in CFD modelling. However, the optimisation process has proven to be highly useful for supporting modelling efforts (Paper 3); analysing predictions of the optimised model may give information about the model’s predictive capabilities, may suggest updated user guidelines, or may enable a discussion on how to progress within the development of the physical models. Such conclusions for recently updated model systems had been impossible to draw before model parameter optimisation.