In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂_{t_{0}}(Tv)+∇·(Tvv), which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

In the lattice Boltzmann (LB) method, the forcing scheme, which is used to incorporate an external or internal force into the LB equation, plays an important role. It determines whether the force of the system is correctly implemented in an LB model and affects the numerical accuracy. In this paper we aim to clarify a critical issue about the Chapman-Enskog analysis for a class of forcing schemes in the LB method in which the velocity in the equilibrium density distribution function is given by u=∑_{α}e_{α}f_{α}/ρ, while the actual fluid velocity is defined as u[over ̂]=u+δ_{t}F/(2ρ). It is shown that the usual Chapman-Enskog analysis for this class of forcing schemes should be revised so as to derive the actual macroscopic equations recovered from these forcing schemes. Three forcing schemes belonging to the above class are analyzed, among which Wagner's forcing scheme [A. J. Wagner, Phys. Rev. E 74, 056703 (2006)10.1103/PhysRevE.74.056703] is shown to be capable of reproducing the correct macroscopic equations. The theoretical analyses are examined and demonstrated with two numerical tests, including the simulation of Womersley flow and the modeling of flat and circular interfaces by the pseudopotential multiphase LB model.

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Due to piping vibration, fluid pulsation and other environmental disturbances, variations of amplitude and frequency to the raw signals of vortex flowmeter are imposed. It is difficult to extract vortex frequencies which indicate volumetric flowrate from noisy data, especially at low flowrates. Hilbert-Huang transform was adopted to estimate vortex frequency. The noisy raw signal was decomposed into different intrinsic modes by empirical mode decomposition, the time-frequency characteristics of each mode were analyzed, and the vortex frequency was obtained by calculating partial mode's instantaneous frequency. Experimental results show that the proposed method can estimate the vortex frequency with less than 2~ relative error; and in the low flowrate range studied, the denoising ability of Hilbert-Huang transform is markedly better than Fourier based algorithms. These findings reveal that this method is accurate for vortex signal processing and at the same time has strong anti-disturbance ability.

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