Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Liutex identification on hairpin vortex structures in a channel based on msfle and moving-PIV

The spatiotemporal evolution of hairpin vortex structures in a fully developed turbulent boundary layer is investigated qualitatively and quantitatively by using two image methods.In this paper,the moving single-frame and long-exposure(MSFLE)image method is used to intuitively track the evolution process of a hairpin vortex,while the moving particle image velocimetry(moving-PIV)method is applied for obtaining a moving velocity field for quantitative analysis.According to the structural characteristics of the hairpin vortex,an inclined light sheet with an appropriate inclination of 53°is arranged to capture the complete hairpin vortex structure at Re_(θ)=97–194.In addition,the core size and the rotational strength of a hairpin vortex are further defined and quantified by the Liutex vector method.The evolution process of a complete hairpin vortex structure observed by MSFLE shows that the shear along the normal direction leads to an increasing strength of the hairpin vortex,accompanied by a lifting vortex head and a distance decrease between two vortex legs during the dissipation period.By combining moving-PIV with the Liutex identification,the spatiotemporal evolution of four typical regions of a hairpin vortex projecting into a 53°cross-section is obtained.The results show that the process from the generation to the dissipation of a single hairpin vortex can be well characterized and recorded by the Liutex based on the core size and rotational intensity,and the evolution process is consistent with the MSFLE result.According to the statistics of vortex core size and rotation intensity along time,the evolution of the hairpin vortex necks and legs can be described as a process of enhancement followed by dissipation.For the vortex head,its evolution maintains longer attributed to its far-from-wall position,which consists of an absolute enhancement process(stage 1)with an increasing rotation strength and a constant core size,and an absolute dissipation(stage 2)with a decreasing rotation strength and a constant core size.

Experimental study on dynamic mechanism of vortex evolution in a turbulent boundary layer of low Reynolds number

The dynamic mechanism of the vortex generation and evolution process in a fully developed turbulent boundary layer with Reθ=97-194 is experimentally investigated.In this study,a moving single-frame and long-exposure(MSFLE)imaging method and a moving particle image velocimetry/particle tracing velocimetry(M-PIV/PTV)are designed and implemented for measuring the temporal and spatial evolution of vortex cores in both qualitative and quantitative ways,respectively.On the other hand,the Liutex vector,which is a new mathematical definition and identification of the vortex core proposed by Liu’s group,is first applied in the experiment for the structural visualization and quantitative analysis of the local fluid rotation.The results show that an intuitional process of vortex evolution can be clearly observed by tracking the vortex using MSFLE and verify that the roll-up of the shear layer induced by shear instability is the origin of vortex formation in turbulence.Furthermore,a quantitative investigation in terms of the critical vortex core boundary(size)and its accurate rotation strength is carried out based on the Liutex vector field analysis by M-PIV/PTV.According to statistics of the relation between vortex core size and the rotation strength during the whole process,the physical mechanism of vortex generation and evolution in a turbulent boundary layer of low Reynolds number can be summarized as a four-dominant-state course consisting of the“synchronous linear segment(SL)-absolute enhancement segment(AE)-absolute diffusion segment(AD)-skewing dissipation segment(SD)”.

POD analysis on vortical structures in MVG wake by Liutex core line identification

The Liutex core line method, first combined with the snapshot proper orthogonal decomposition (POD), is utilized in a supersonic micro-vortex generator (MVG) wake flow at Ma = 2.5 and Reθ = 5 760 to reveal the physical significance of each POD mode of the flow field. Compared with other scalar-based vortex identification methods, the Liutex core line identification is verified to be the most appropriate approach that is threshold-free and provides full information of a fluid rotation motion. Meanwhile, the Liutex integration is employed to quantitatively track the evolution of the vortices in MVG wake and is applied to the determination of the effective control section of the MVG wake for the optimization study of MVG design. The physical mechanism of each POD mode for multi-scale and multi-frequency vortical structures is investigated by using Liutex core line identification to give some revelations. For the mean mode (mode 0) indicating the time-averaged velocity flowfield of the MVG wake flow, a pair of primary counter-rotating streamwise vortices and another pair of secondary vortices is uniquely identified by two pairs of Liutex core lines with Liutex magnitude. In contrast, mode 1 is featured by a fluctuated roll-up motion of streamwise vortex, and the streamwise component of the MVG wake is demonstrated to be dominant in terms of the total kinetic energy contribution. Meanwhile, a dominant shedding frequency of St = 0.072 is detected from the temporal behavior of mode 2, which has the organized arc-shaped vortex structures shedding from MVG induced by the K-H instability. Additionally, mode 4 subjects to low-frequency oscillations of the wall vortices and thus takes a relatively lower frequency of St = 0.044.