Lattice Boltmzmann Methods (LBM) have been proved to be very effective methods for computational aeroacoustics (CAA), which have been used to capture the dynamics of weak acoustic fluctuations. In this paper, we propose a strategy to reduce the dispersive and disspative errors of the two-dimensional (2D) multi-relaxation-time lattice Boltzmann method (MRT-LBM). By presenting an effective algorithm, we obtain a uniform form of the linearized Navier-Stokes equations corresponding to the MRT-LBM in wave-number space. Using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods, we propose a class of minimization problems to optimize the free-parameters in the MRT-LBM. We obtain this way a dispersion-relation-preserving LBM (DRP-LBM) to circumvent the minimized dispersion error of the MRT-LBM. The dissipation relation precision is also improved. And the stability of the MRT-LBM with the small bulk viscosity is guaranteed. Von Neuman analysis of the linearized MRT-LBM is performed to validate the optimized dispersion/dissipation relations considering monochromatic wave solutions. Meanwhile, dispersion and dissipation errors of the optimized MRT-LBM are quantitatively compared with the original MRT-LBM . Finally, some numerical simulations are carried out to assess the new optimized MRT-LBM schemes.
Computational methods were used to analyse the elasto-hydrodynamic lubrication of a complex rotorbearing system. The methodology employed computational fluid dynamics (CFD), based on the Navier-Stokes equation and a fluid-structure interaction (FSI) technique. A series of models representing the system were built using the CFD-FSI methodology to investigate the interaction between the lubrication of the fluid film, and elastic dynamics of the rotor and journal bearing. All models followed an assumption of isothermal behaviour. The FSI methodology was implemented by setting nodal forces and displacements to equilibrium at the fluid-structure interface, therefore allowing the lubrication of the fluid and the elastic deformation of structures to be solved simultaneously. This is significantly different to the more common techniques-such as the Reynolds equation method-that use an iterative solution to balance the imposed load and the force resulting from the pressure of the fluid film to within a set tolerance. Predictions using the CFD-FSI method were compared with the results of an experimental study and the predictions from an 'in-house' lubrication code based on the Reynolds equation. The dynamic response of the system was investigated with both rigid and flexible bodies for a range of different bearing materials and dynamic unbalanced loads. Cavitation within the fluid film was represented in the CFD-FSI method using a simplified phase change boundary condition. This allowed the transition between the liquid and vapour phases to be derived from the lubricant's properties as a function of pressure. The combination of CFD and FSI was shown to be a useful tool for the investigation of the hydrodynamic and elasto-hydrodynamic lubrications of a rotor-bearing system. The elastic deformation of the bearing and dynamic unbalanced loading of the rotor had significant effects on the position of its locus.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.