Abstract
A simulation of flows' behavior, in other words, computational fluid dynamics (CFD) simulation of flows, requires a large source of computational power to resolve the behavior of all turbulent fluctuations (i.e., eddies) in a highly turbulent and complex case. As a solution, one can simulate only the mean quantities, discard the simulation of turbulent fluctuations, and decrease the computational demand. This method is better known as RANS (Reynolds-averaged Navier-Stokes) simulations. Even though the turbulent fluctuations are not simulated in RANS, the effect of them on mean quantities should be taken into account by RANS models.
The RANS models try to predict this effect by physics-based mathematical equations, and they have been developed during the last half-century. Specifically in the industrial applications of CFD, the RANS simulations are quite popular because of their robustness and computational speed whereas it is well known that RANS models have shortcomings in capturing various physics existing in turbulent flows. The growth of available high-fidelity data (e.g., data obtained by direct numerical simulations and large-eddy simulations) and recent developments in machine-learning methods encouraged us to investigate the potential of data-driven techniques to amend the shortcomings of the RANS models.
In addition to the openly available high-fidelity data, we used an in-house pseudo-spectral solver to run large-eddy simulations of roughness-induced secondary flow in the atmospheric boundary layer where we also systematically investigated the effect of convective thermal stratification on the secondary flows. Our results showed that convective thermal heating can weaken the roughness-induced secondary flows and replace them with new and stronger buoyant secondary flows, rotating in the opposite direction.
In a comprehensive investigation, we compared 8 propagation techniques for the propagation of Reynolds stress tensor (RST) and Reynolds force vector (RFV) data into RANS equations, where we introduced frozen propagation methods for the Reynolds force vectors. Our comparison showed that our new RFV frozen propagation techniques resulted in a lower propagation error than the RST frozen propagation methods. Therefore, we compared their potential in a training process. We used Pope's decomposition of RST where the unknown coefficients of the decomposition were determined either by a sparse linear regression (so-called white-box configuration) or by a multi-layer perception (so-called gray-box configuration). For using the RFV data, we introduced a vector-based neural network (VBNN) which was derived from Pope's decomposition. The results showed that using RFV data does not necessarily improve the performance of data-driven models even though it had a lower propagation error.
While training a data-driven RANS model, generalizability and consistency with \textit{a posteriori} results were the most critical challenges. Therefore, we combined CFD-driven optimization and progressive augmentation techniques to modify the k- SST model for two of its popular shortcomings: the prediction of Prandtl's second kind of secondary flow, and the correct prediction of the recirculation zone in the presence of strong adverse pressure gradients. The new corrections were augmented progressively for the specific shortcomings while preserving the successful performance of the k- SST in the law-of-the-wall prediction. The results showed improvement in the prediction of velocity components and friction coefficients in both training and testing cases.
In conclusion, this thesis presents a journey of data-driven development of turbulence modeling from generating high-fidelity data to reliable progressive models. We tried to investigate each step with curiosity about multiple methods and possibilities to ensure that we were on the right track toward a successful data-driven RANS model. Our final findings (i.e., progressive augmented models) showed great potential in this way, which will hopefully inspire further investigations to find even better turbulence models.
The RANS models try to predict this effect by physics-based mathematical equations, and they have been developed during the last half-century. Specifically in the industrial applications of CFD, the RANS simulations are quite popular because of their robustness and computational speed whereas it is well known that RANS models have shortcomings in capturing various physics existing in turbulent flows. The growth of available high-fidelity data (e.g., data obtained by direct numerical simulations and large-eddy simulations) and recent developments in machine-learning methods encouraged us to investigate the potential of data-driven techniques to amend the shortcomings of the RANS models.
In addition to the openly available high-fidelity data, we used an in-house pseudo-spectral solver to run large-eddy simulations of roughness-induced secondary flow in the atmospheric boundary layer where we also systematically investigated the effect of convective thermal stratification on the secondary flows. Our results showed that convective thermal heating can weaken the roughness-induced secondary flows and replace them with new and stronger buoyant secondary flows, rotating in the opposite direction.
In a comprehensive investigation, we compared 8 propagation techniques for the propagation of Reynolds stress tensor (RST) and Reynolds force vector (RFV) data into RANS equations, where we introduced frozen propagation methods for the Reynolds force vectors. Our comparison showed that our new RFV frozen propagation techniques resulted in a lower propagation error than the RST frozen propagation methods. Therefore, we compared their potential in a training process. We used Pope's decomposition of RST where the unknown coefficients of the decomposition were determined either by a sparse linear regression (so-called white-box configuration) or by a multi-layer perception (so-called gray-box configuration). For using the RFV data, we introduced a vector-based neural network (VBNN) which was derived from Pope's decomposition. The results showed that using RFV data does not necessarily improve the performance of data-driven models even though it had a lower propagation error.
While training a data-driven RANS model, generalizability and consistency with \textit{a posteriori} results were the most critical challenges. Therefore, we combined CFD-driven optimization and progressive augmentation techniques to modify the k- SST model for two of its popular shortcomings: the prediction of Prandtl's second kind of secondary flow, and the correct prediction of the recirculation zone in the presence of strong adverse pressure gradients. The new corrections were augmented progressively for the specific shortcomings while preserving the successful performance of the k- SST in the law-of-the-wall prediction. The results showed improvement in the prediction of velocity components and friction coefficients in both training and testing cases.
In conclusion, this thesis presents a journey of data-driven development of turbulence modeling from generating high-fidelity data to reliable progressive models. We tried to investigate each step with curiosity about multiple methods and possibilities to ensure that we were on the right track toward a successful data-driven RANS model. Our final findings (i.e., progressive augmented models) showed great potential in this way, which will hopefully inspire further investigations to find even better turbulence models.
| Original language | English |
|---|
| Publisher | Aarhus University |
|---|---|
| Publication status | Published - Feb 2024 |