In recent years, phase-field-based models for multiphase flows have gained significant popularity, particularly within the lattice Boltzmann (LB) community. These models typically use two lattice Boltzmann equations (LBEs), one for interface tracking and the other for solving hydrodynamic properties. However, for the purposes of this paper, we focus only on the LB model for hydrodynamics. Our goal is to undertake a comparative investigation into the differences between three classical hydrodynamic LB models proposed by Lee et al. [1], Liang et al. [2] and Fakhari et al. [3]. The interfacetracking equation used in this study is based on the conservative phase-field model. We provide a detailed derivation of the governing equations in each model using the Chapman-Enskog analysis. Additionally, three discretization methods for the interaction forces are introduced, and a modified method for the gradient term is proposed based on the nonequilibrium distribution method. The accuracy of three LB models in combination with four discretization methods is examined in this study. Based on the results, it appears that different combinations of models and methods are appropriate for different types of problems. However, some suggestions for the selection of hydrodynamic models and discrete methods for the gradient term are provided in this paper.

A parameter identification method which merges experimentally monitored signals and physics-based simulation data is proposed, targeting the identification tasks in shaft seals which are challenging due to the high-dimensional parameter space. Features were extracted from the monitored acoustic emission signals following a proposed cross-timescale analysis routine, and the simulation data were augmented using Kriging surrogate model to obtain a dataset with stratified fidelity. Then, a transferable architecture of convolutional neural network modified for periodical data was proposed, with which part of the parameters trained by simulation data were reserved when training model using acoustic emission data acquired in experiments. Cross validation shows that transfer learning can effectively improve the performance, provided data augmentation and proper transfer mode. In conclusion, the study provides an effective parameter identification method which merges the simulation data which carry the physical knowledge and the experiment data which carry directly monitored results.

In hydrodynamic lubrication problems, the presence of step structures on the surface can cause discontinuities in the film thickness. This article proposes two models for solving the two-dimensional Reynolds equation with film thickness discontinuity using the finite difference method (FDM). In model I, the film thickness variable is defined at the center of the mesh grids, allowing the Reynolds equation to be reformulated in a weak form that eliminates the singularity of film thickness discontinuity and satisfies the flow continuity condition at the film thickness discontinuity region. By considering the step boundary on the surface as the interface, model II is constructed based on the immersed interface method, turning the hydrodynamic lubrication problem into a classical interface problem. The jump conditions across the interface are derived in accordance with the continuous flow requirement. A phase-field function is adopted to describe the interface on the uniform rectangular mesh grids. Numerical experiments are conducted to assess the accuracy and capabilities of the two proposed models for analyzing a step-dimple-textured sealing. The results demonstrate that both modified FDM models can effectively address the thickness discontinuity issue. Model II achieves second-order accuracy for the pressure distribution when dealing with curved interfaces based on Cartesian grids, whereas model I demonstrates first-order accuracy. Both the proposed models exhibit superior accuracy compared to the traditional second-order central FDM when dealing with curved interfaces. Moreover, the performance of model II is further assessed by simulating lubrication problems with complex groove shapes, and the results indicate its flexibility in addressing thickness discontinuity problems with complex curve interface.

The monitoring of abnormal states of dry gas seals is a critical but challenging task for equipment reliability. This paper proposes an end-face groove structure oriented to the condition monitoring of dry gas seals. In addition to hydrodynamic grooves on the end face of the mating ring, seven special monitoring grooves are manufactured on the other side of the dual end face. These monitoring grooves can induce characteristics of end-face contact that can be detected by an acoustic emission sensor, where the primary characteristic is the seven times the motor speed frequency(7-TMSF). Simulations are conducted using a dynamic model to help establish the monitoring method.