A unified simplified multiphase lattice Boltzmann method (USMLBM) is constructed in this work for simulating complex multiphase ferrofluid flows with large density and viscosity ratios. In USMLBM, the Navier–Stokes equations, the Poisson equation of the magnetic potential, and the phase-field equation are utilized as the ferrohydrodynamics behavior modeling and interface tracking algorithm. Solutions of the macroscopic governing equations are reconstructed with the lattice Boltzmann framework and resolved in a predictor–corrector scheme. Various benchmark tests demonstrate the efficiency and accuracy of USMLBM in simulating multiphase ferrofluid flows. We further adopt USMLBM to analyze in detail the mechanisms of bubble merging inside a ferrofluid under a uniform external magnetic field. The numerical results indicate that the bubbles tend to move toward each other and further merge together, even for a large initial separation between the bubbles. Due to complex interaction between the bubbles and the ferrofluid during the magnetophoretic acceleration process, the nonlinear effect on bubble merging is observed when the initial separation increases. Moreover, at a larger initial separation, the shape of bubbles seems to be not sensitive to the initial separation.

With the rapid development of data-driven methods in recent years, deep neural networks have attracted significant attention for aerodynamic predictions and design optimizations. Among these methods, the multi-fidelity deep neural network (MFDNN), which can combine high-fidelity (HF) and low-fidelity (LF) data, has gained popularity. This paper systematically investigates the performances of employing MFDNN models in predicting aerodynamic coefficients and in performing aerodynamic shape optimizations (ASOs), especially the impact of using various HF/LF data ratios for training models. The results of the prediction accuracy of the aerodynamic coefficients of airfoils show that the less HF data used, the more advantages can be achieved by the MFDNN models than the single-fidelity models. The well-trained MFDNN models are then employed in an ASO problem of airfoil in the subsonic regime, and it is found that a higher HF/LF data ratio does not definitely result in a better performance in the ASO. As the insufficiency in the prediction accuracy of the optimal shapes appears when employing the non-updated MFDNN models, an update strategy is developed by tightly integrating the MFDNN models with the particle swarm optimization algorithm. To further reduce the time costs for updating models, a dual-threshold update strategy is then introduced, which can half the counts of evaluating HF data.

In this work, a comprehensive numerical study of the magnetic field-induced dynamic self-assembly process of multiple bubbles inside the ferrofluid is presented. For multiple bubbles inside the ferrofluid, the magnetic attraction force between bubbles is usually greater and lasts longer than the magnetic repulsion force, resulting in self-assembly movement. This process can be influenced by a number of factors, such as surface tension, inertia force, and initial position, and their specific mechanisms have not been fully understood. Particularly, what roles the magnetic field strength, the surface tension coefficient, and the initial position play are our major interest. Results show that higher magnetic field strength is unfavorable for improving self-assembly efficiency as it leads to stronger magnetic interactions, including attraction and repulsion. In contrast, an increase in the surface tension coefficient can enhance the effect of attraction and weaken the effect of repulsion. Further analysis of the influence of the initial position shows that the magnetic repulsive force can be enhanced by increasing the horizontal gap, which causes a reversing motion along the magnetic field direction. However, an increase in the vertical gap has a nonlinear effect on the efficiency of the self-assembly process, and there is a critical distance below which the self-assembly process could be accelerated with the increase in the vertical gap.

In this paper, the Navier-Stokes equations coupled with a Lagrangian discrete phase model are described to simulate the air-particle flows over the S809 airfoil of the Phase VI blade, the NH6MW25 airfoil of a 6 MW wind turbine blade and the NACA0012 airfoil. The simulation results demonstrate that, in an attached flow, the slight performance degradation is caused by the boundary layer momentum loss. After flow separation, the performance degradation becomes significant and is dominated by a more extensive separation due to particles, since the aerodynamic coefficient increments and the moving distance of separation point present similar variation trends with increasing angle of attack. Unlike the NACA0012 airfoil, a most particle-sensitive angle of attack is found in the light stall region for a wind turbine airfoil, at which the lift decrement and the drag increment reach their peak values. For the S809 airfoil, the most sensitive angle of attack is about 3° higher than that for the maximum lift-to-drag ratio. Hence, the aerodynamic performance of a wind turbine is very susceptible to particles. Based on the most sensitive angles of attack, the more sensitive scope of angles of attack of a blade airfoil and the more sensitive range of rotor tip speed ratios are predicted sequentially. The present study clarifies the principles for the performance degradation of a wind turbine airfoil due to particles and the conclusions are useful for the wind turbine design reducing the particle influences.