heal.abstract |
In this dissertation, a purely data-driven, equation-free computational framework is proposed for dealing efficiently and effectively with Computational Fluid Dynamics (CFD) large-scale and complex models. The case studies utilized for the framework application are Chemical Vapor Deposition (CVD) reactors, since their CFD models present multiple challenges, such as complex geometries, variety of competing transport phenomena, multiple chemical reaction pathways and nonlinearity. The CFD models are discretized and solved with the commercial code ANSYS Fluent using the Finite Volume Method (FVM). The computational study of such problems is costly because of the studied CFD model size, which is a result of high-fidelity computational grids used and the physicochemical phenomena that occur in a CVD reactor. Therefore, the main purpose of this thesis is to develop and optimize a data-driven computational framework, which is used for the creation of equation-free Reduced Order Models (ROM) of the data obtained from the high-dimensionality models of the CVD reactors. Finally, the computational processing of the ROM is significantly cheaper than the initial studied CVD reactor model and ultimately produces the same high-fidelity results.
The core of the proposed computational framework is specifically the machine learning algorithms of Proper Orthogonal Decomposition (POD) and Artificial Neural Networks (ANN). Since, both algorithms are data-driven, the data collection takes place first, which is the solution of the CFD model several times. The data collection is executed on coarse computational grids with the chemistry removed from the CFD models, to reduce the cost of the procedure. The latter is an assumption that the chemistry does not affect the state of the reactor, because the reactive mixture of CVD processes is dilute. The data collection is a procedure of imposing step changes on a control variable of the process and capturing the trajectory of the dynamic response of the system throughout the change from the initial steady state to the target one. This trajectory is discretized in snapshots of the reactor state for every time increment. Following the data collection, the POD is used to determine the optimal low-dimensionality orthonormal basis that contains most of the spatial dependency information and shows the best accuracy at recreating parts of the data set. Since POD is not able to capture the time dependence, this is achieved by using the same data set and the previously constructed POD basis to train and simulate a Nonlinear Autoregressive Network with exogenous inputs (NARX) for different inputs of the control variable. Therefore, this results to a final ROM that can produce fast approximations of the system states for any given input with extremely low computational cost and great accuracy. Finally, considering that the ROM is built on coarse grid data and without chemistry, its predictions are used as initial estimates after being interpolated using the Nearest Neighbor grid-to-grid interpolation to the fine grid model that includes the chemical reactions. The latter then converges in a small number of iterations and gives the desired high-fidelity solution.
Three different case studies are shown in this work, the first is the aluminum CVD from the precursor DMEAA, the second the copper CVD from copper amidinate and last a CVD reactor that presents solution multiplicity. In the first case study, the CFD model of the reactor is accompanied by a significant computational burden, due to the grid size and the complex reaction kinetics. Thus, by following the framework a ROM is created that, with negligible error on its predictions, accelerates the CFD simulations up to 2.5 times in core hours (core hours = wall clock-time x CPU cores used in parallel processing) and up to 312 times when chemistry is not considered. During the second case study of copper CVD, a novel chemical reaction network is proposed and fitted on existing experimental data, using a ROM to impressively speed up the procedure of fitting the kinetic parameters that carries a high computational burden, since a big part of it is trial and error. The reaction network consists of two temperature activated decomposition volumetric reactions and one surface deposition reaction, the first are proposed in order to explain and capture the decrease of deposition rate at high substrate temperatures, which appears in experimental findings. The two decomposition reactions are a carbodiimide deinsertion and a β-hydrogen abstraction of copper amidinate and their kinetic constants are fitted on the available experimental data. The usage of the ROM shows a 4 times acceleration in core hours with insignificant errors for its predictions, which is crucial for the fitting procedure since the model must be simulated several times. The final case study concerns a CVD reactor with solution multiplicity, which for the same operating conditions has three different states, two stable and observable experimentally, and one unstable that is not observable experimentally. This solution multiplicity increases the computational cost of the CFD study, especially close to the turning points between the stable/unstable state branches of the solution space, since the convergence of the solver “jumps” between the two different stable states. Thus, the framework was implemented and created an equation-free ROM based on data from both stable solution branches, that can capture the solution multiplicity in the studied solution space with less than 2% error, for any input on the controlled variable, thus confirming that the proposed framework can address complex nonlinear systems too. |
en |