RANS Turbulence Model Development using CFD-Driven Machine Learning

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method (Weatheritt and Sandberg, 2016), but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.Comment: Accepted by Journal of Computational Physic

Gradient Information and Regularization for Gene Expression Programming to Develop Data-Driven Physics Closure Models

Learning accurate numerical constants when developing algebraic models is a known challenge for evolutionary algorithms, such as Gene Expression Programming (GEP). This paper introduces the concept of adaptive symbols to the GEP framework by Weatheritt and Sandberg (2016) to develop advanced physics closure models. Adaptive symbols utilize gradient information to learn locally optimal numerical constants during model training, for which we investigate two types of nonlinear optimization algorithms. The second contribution of this work is implementing two regularization techniques to incentivize the development of implementable and interpretable closure models. We apply $L_2$ regularization to ensure small magnitude numerical constants and devise a novel complexity metric that supports the development of low complexity models via custom symbol complexities and multi-objective optimization. This extended framework is employed to four use cases, namely rediscovering Sutherland's viscosity law, developing laminar flame speed combustion models and training two types of fluid dynamics turbulence models. The model prediction accuracy and the convergence speed of training are improved significantly across all of the more and less complex use cases, respectively. The two regularization methods are essential for developing implementable closure models and we demonstrate that the developed turbulence models substantially improve simulations over state-of-the-art models

Bis{1-[(1H-benzotriazol-1-yl)methyl]-2-methyl-1H-imidazole-κN3}dichloridocobalt(II)

In the title mononuclear complex, [CoCl2(C11H11N5)2], the CoII atom is four-coordinated by two ligand N atoms and two Cl atoms in a distorted tetrahedral geometry. In the crystal, molecules are stacked through π–π interactions [centroid–centroid distances = 3.473 (2), 3.807 (3), 3.883 (2) and 3.676 (2) Å], forming a three-dimensional supramolecular network

Photocatalytic Inactivation Effect of Gold-Doped TiO2 (Au/TiO2) Nanocomposites on Human Colon Carcinoma LoVo Cells

The photocatalytic inactivation effecting of gold-doped TiO2 (Au/TiO2) nanocomposites on human colon carcinoma LoVo cells was investigated for the first time. The Au/TiO2 samples containing different amounts of Au (1–4 wt%) were prepared by deposition-precipitation (DP) method. These synthesized Au/TiO2 nanocomposites were characterized by transmission electron microscopy (TEM) and inductively coupled plasma atomic emission spectroscopy. It was found that the photocatalytic inactivation effect of TiO2 nanoparticles on LoVo cancer cells could be greatly improved by the surface modification of Au nanoparticles. Furthermore, the loading amount of Au on the surface of TiO2 nanoparticles affects the photocatalytic inactivation efficiency strongly, and it was found that the most efficient nanocomposites were TiO2 nanoparticles doped with 2 wt% Au. When 50 μg/mL 2 wt% Au/TiO2 nanocomposites were used, all of the LoVo cancer cells were killed under the irradiation of UV light (λmax = 365 nm, Intensity = 1.8 mW/cm2) within 100 minutes. But for 50 μg/mL TiO2 nanoparticles, only 40% cancer cells were killed under the same condition

Transition Modeling for Low Pressure Turbines Using Computational Fluid Dynamics Driven Machine Learning

Existing Reynolds Averaged Navier–Stokes-based transition models do not accurately predict separation induced transition for low pressure turbines. Therefore, in this paper, a novel framework based on computational fluids dynamics (CFD) driven machine learning coupled with multi-expression and multi-objective optimization is explored to develop models which can improve the transition prediction for the T106A low pressure turbine at an isentropic exit Reynolds number of Re2is=100,000. Model formulations are proposed for the transfer and laminar eddy viscosity terms of the laminar kinetic energy transition model using seven non-dimensional pi groups. The multi-objective optimization approach makes use of cost functions based on the suction-side wall-shear stress and the pressure coefficient. A family of solutions is thus developed, whose performance is assessed using Pareto analysis and in terms of physical characteristics of separated-flow transition. Two models are found which bring the wall-shear stress profile in the separated region at least two times closer to the reference high-fidelity data than the baseline transition model. As these models are able to accurately predict the flow coming off the blade trailing edge, they are also able to significantly enhance the wake-mixing prediction over the baseline model. This is the first known study which makes use of ‘CFD-driven’ machine learning to enhance the transition prediction for a non-canonical flow

Improvement of Damping Property and Its Effects on the Vibration Fatigue in Ti6Al4V Titanium Alloy Treated by Warm Laser Shock Peening

In order to increase the vibration life of Ti6Al4V titanium alloy, warm laser shock peening (WLSP) is used to improve the damping properties and thus decrease the vibration stress in this study. Firstly, the Ti6Al4V specimens are treated by WLSP at different treatment temperatures from 200 °C to 350 °C. Then the damping ratios of untreated and WLSPed samples are obtained by impact modal tests, and the improvement of damping properties generated by WLSP is analyzed by the microstructures in Ti6Al4V titanium alloy. Moreover, the finite element simulations are utilized to study the vibration amplitude and stress during the frequency response process. Finally, the vibration fatigue tests are carried out and the fatigue fracture morphology is observed by the scanning electron microscope. The results indicate that the damping ratios of WLSPed specimens increase with the increasing treatment temperatures. This is because elevated temperatures during WLSP can effectively increase the α phase colonies and the interphase boundaries, which can significantly increase the internal friction of materials. Moreover, due to the increasing material damping ratio, the displacement and stresses during vibration were both reduced greatly by 350 °C-WLSP, which can significantly decrease the fatigue crack growth rate and thus improve the vibration fatigue life of Ti6Al4V titanium alloy