Data-driven turbulence modeling has been considered an effective method for improving the prediction accuracy of Reynolds-averaged Navier–Stokes equations. Related studies aimed to solve the discrepancy of traditional turbulence modeling by acquiring specific patterns from high-fidelity data through machine learning methods, such as artificial neural networks. The present study focuses on the unsmoothness and prediction error problems from the aspect of feature selection and processing. The selection criteria for the input features are summarized, and an effective input set is constructed. The effect of the computation grid on the smoothness is studied. A modified feature decomposition method for the spatial orientation feature of the Reynolds stress is proposed. The improved machine learning framework is then applied to the periodic hill database with notably varying geometries. The results of the modified method show significant enhancement in the prediction accuracy and smoothness, including the shape and size of separation areas and the friction and pressure distributions on the wall, which confirms the validity of the approach.
Implicit large-eddy simulation is employed to simulate the flow in an asymmetric plane diffuser at Re=9000. Flow separation exists near the throat and evolves to large-scale, unsteady separation in the expansion section and the downstream region. An unconventional flow control method, namely, a cylindrical Karman-vortex generator (KVG) with different sizes and locations that induces periodic spanwise vortex shedding, is set upstream of the throat to suppress the flow separation. An appropriately designed KVG can enhance the mixing of the outer flow and the low energy fluid near the wall region by the periodic shedding Karman-vortices, and effectively reduce the separation bubble size. For the present optimal case, the length and height of the separation bubble are decreased 50.4% and 90.9%, respectively. The static pressure recovery coefficient is also increased by about 50%. Moreover, the velocity and total pressure distributions at the end of the expansion section are more uniform with lower fluctuation in the case with KVG installed. An optimal KVG diameter DK is suggested to be 3–4% of the expansion section length LE. The gap ratio to the lower wall G/DK and the length ratio to the throat Lt/DK are suggested to be 2.0–3.0 and 5.0–10.0, respectively.
Field inversion and machine learning are implemented in this study to describe three-dimensional (3-D) separation flow around an axisymmetric hill and augment the Spart-Allmaras (SA) model. The discrete adjoint method is used to solve the field inversion problem, and an artificial neural network is used as the machine learning model. A validation process for field inversion is proposed to adjust the hyperparameters and obtain a physically acceptable solution. The field inversion result shows that the non-equilibrium turbulence effects in the boundary layer upstream of the mean separation line and in the separating shear layer dominate the flow structure in the 3-D separating flow, which agrees with prior physical knowledge. However, the effect of turbulence anisotropy on the mean flow appears to be limited. Two approaches are proposed and implemented in the machine learning stage to overcome the problem of sample imbalance while reducing the computational cost during training. The results are all satisfactory, which proves the effectiveness of the proposed approaches.
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