A two-component lattice Boltzmann method (LBM) with a multiple-relaxation-time (MRT) collision operator is presented to improve the numerical stability of the single relaxation time (SRT) model. The macroscopic and the momentum conservation equations can be retrieved through the Chapman-Enskog (C-E) expansion analysis. The equilibrium moment with the diffusion term is calculated, a diffusion phenomenon is simulated by utilizing the developed model, and the numerical stability is verified. Furthermore, the binary mixture channel model is designed to simulate the sound attenuation phenomenon, and the obtained simulation results are found to be consistent with the analytical solutions. The sound attenuation model is used to study the numerical stability and calculation accuracy of the LBM model. The simulation results show the stability and accuracy of the MRT model and the SRT model under different viscosity conditions. Finally, we study the influence of the error between the macroscopic equation of the MRT model and the standard incompressible Navier–Stokes equation on the calculation accuracy of the model to demonstrate the general applicability of the conclusions drawn by the sound attenuation model in the present study.
Underground water, gas and oil all exist in the fractured or porous strata. Waves that propagate through porous cylinder immersed in infinite fluid are of considerable interest in the estimation of porous parameter, such as an underwater concrete column may present pore characteristics after a long time water immersion. Compared with longitudinal guided wave, circumferential guided wave has its advantages in the ultrasonic nondestructive inspection of porous cylinder. In order to investigate the propagation characteristics of guided waves in a porous cylinder immersed in infinite fluid and analyze the effects of the porous medium parameters on the dispersion characteristic, a model of porous cylinder surrounded by fluid is built. Based on the elastic-dynamic theory and modified liquid-saturated porous theory, the characteristic equation of guided wave is established, and the dispersion curves are obtained numerically. The effects of cylindrical radius and pore parameters on the propagation characteristics of guided waves are discussed; the attenuation characteristics of guided waves are also analyzed; the time domain waveforms of the guided circumferential waves are obtained by numerical inversion, and the influence of porous parameters on waveforms is simulated. It is found that the dispersion curves are similar to that of elastic cylinder in the fluid, there exist multiple mode guided waves and approximate shear velocity of medium for higher modes, and higher order modes are more affected by the radius, but it does not change the tendency of curve. The phase velocity decreases with porosity increasing at the same frequency and the effect of porosity on higher order modes is greater than that on mode 1; due to the dissipation in the medium, the attenuation increases porosity increasing. It can be seen from the transient responses that the wave packets move backward and the displacement amplitude decreases with the porosity increasing. The characteristics of the inversed transient response are in good agreement with theoretical dispersion and attenuation. The results show that the propagation of guided circumferential wave is affected by the pore parameters, especially for porosity, which can provide a theoretical reference for the non-destructive evaluation of the porous cylinder surrounded by infinite fluid.
To study the damage of an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal and flexural modes in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived, each for a pervious and an impervious surface employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influence of porosity on the dispersion curves of guided waves is much more significant than that of thickness, whereas the phase velocity is independent of the static permeability. There is an apparent “mode switching” between the two low-order modes. The characteristics of attenuation are in good agreement with the dispersion curves results. This work can support future studies for optimizing the theory of cylinder or pipeline damage detection.
To study the leakage situation of a liquid-filled pipe in long-term service, a model of a liquid-filled pipe embedded in an infinite porous medium as well as in a finite porous medium is designed. The principal motivation is to perform detailed quantitative analysis of the longitudinal guided wave propagating in a liquid-filled pipe embedded in a saturated porous medium. The problems of pipeline leakage and porosity as well as the media outside the pipe are solved to identify the characteristics of the guided wave in a more practical model. The characteristics of the guided wave are investigated theoretically and numerically, with special emphasis on the influence of porous medium parameters on the dispersion properties. Assuming the pipe is a cylindrical shell buried in an isotropic, homogeneous, and porous medium, the dispersion equations are established based on the elastic-dynamic equations and the modified Biot liquid-saturated porous theory. The characteristics of dispersion, time-domain waveform and attenuation curves varying with porous medium parameters, wrapping layer material, and thickness, are all analyzed. The increase in porosity decreases the partial mode phase velocity in the liquid-filled pipe embedded in the finite porous medium. The characteristics of attenuation are in good agreement with the dispersion curves and the time-domain waveform results.
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