Discrete unified gas kinetic scheme for continuum compressible flows.

In this paper, a discrete unified gas kinetic scheme (DUGKS) is proposed for continuum compressible gas flows based on the total energy kinetic model [Guo et al., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704]. The proposed DUGKS can be viewed as a special finite-volume lattice Boltzmann method for the compressible Navier-Stokes equations in the double distribution function formulation, in which the mass and momentum transport are described by the kinetic equation for a density distribution function (g), and the energy transport is described by the other one for an energy distribution function (h). To recover the full compressible Navier-Stokes equations exactly, the corresponding equilibrium distribution functions g^{eq} and h^{eq} are expanded as Hermite polynomials up to third and second orders, respectively. The velocity spaces for the kinetic equations are discretized according to the seventh and fifth Gauss-Hermite quadratures. Consequently, the computational efficiency of the present DUGKS can be much improved in comparison with previous versions using more discrete velocities required by the ninth Gauss-Hermite quadrature.

Diffuse interface model for a single-component liquid-vapor system.

We elucidate the theoretical relationships among fundamental physical concepts that are involved in the diffuse interface modeling for an isothermal single-component liquid-vapor system, which cover both the equation of state (EOS) and the surface tension force. As an example, a flat surface at equilibrium is discussed both theoretically and numerically by using two different approaches. Particularly, the force structure in the transition region is clearly presented, which demonstrates that the capillary contributions due to the density gradients can suppress the mechanical instability of the thermodynamic pressure and lead to constant hydrodynamic pressure (and chemical potential). Then, by comparing with the van der Waals (vdW) EOS for a flat interface at equilibrium, it is shown that applying the double-well approximation can give qualitative predictions for relatively high density ratio (ρ_{l}/ρ_{g}=7.784) and satisfactory results for relatively low density ratio (ρ_{l}/ρ_{g}=1.774). The main cause for this observation is attributed to the nonlinear variation of the generalized coefficient function in the double-well formulation at different density ratios. In addition, for the latter case, we simulate a droplet impact on a hydrophilic wall by using a recently proposed well-balanced discrete unified gas kinetic scheme (WB-DUGKS), which justifies the applicability of the double-well approximation to complex interfacial dynamics in the low-density-ratio limit. Furthermore, the reason for the inconsistency between the coefficients of the mean-field force expressions in the existing literature is explained.

Reactive mixing performance for a nanoparticle precipitation in a swirling vortex flow reactor.

Mixing performance for a consecutive competing reaction system has been investigated in a swirling vortex flow reactor (SVFR). The direct quadrature method of moments combined with the interaction by exchange with the mean (DQMOM-IEM) method was employed to model such reacting flows. This type of reactors is able to generate a strong swirling flow with a great shear gradient in the radial direction. Firstly, mixing at both macroscale and microscale was assessed by mean mixture fraction and its variance, respectively. It is found that macromixing can be rapidly achieved throughout the whole reactor chamber due to its swirling feature. However, micromixing estimated by Bachelor length scale is sensitive to turbulence. Moreover, the additional introduction of ultrasound irradiation can significantly improve the mixing uniformity, namely, free of any stagnant zone presented in the reactor chamber on a macroscale, and little variance deviating from the mean environment value can be observed on a microscale. Secondly, reaction progress variable and the reactant conversion serve as indicators for the occurrence of side reaction. It is found that strong turbulence and a relatively fast micromixing process compared to chemical reaction can greatly reduce the presence of by-product, which will then provide homogenous environment for particle precipitation. Moreover, due to the generation of cavitation bubbles and their subsequent collapse, ultrasound irradiation can further intensify turbulence, creating rather even environment for chemical reactions. Low conversion rate was observed and little by-products were generated consequently. Therefore, it is suggested that the SVFR especially intensified by ultrasound irradiation has the ability to provide efficient mixing performance for the fine-particle synthesis process.

Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models.

A lifting relation connecting the distribution function explicitly with the hydrodynamic variables is necessary for the Boltzmann equation-based mesoscopic approaches in order to correctly initialize a nonuniform hydrodynamic flow. We derive two lifting relations for Guo et al.'s total-energy double-distribution-function (DDF) kinetic model [Z. L. Guo et al., Phys. Rev. E 75, 036704 (2007)1539-375510.1103/PhysRevE.75.036704], one from the Hermite expansion of the conserved and nonconserved moments, and the second from the O(τ) Chapman-Enskog (CE) approximation of the Maxwellian exponential equilibrium. While both forms are consistent to the compressible Navier-Stokes-Fourier system theoretically, we stress that the latter may introduce numerical oscillations under the recently optimized discrete velocity models [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490], namely a 27 discrete velocity model of the seventh-order Gauss-Hermite quadrature (GHQ) accuracy (D3V27A7) for the velocity field combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5) for the total energy. It is shown that the Hermite-expansion-based lifting relation can be alternatively derived from the latter approach using the truncated Hermite-polynomial equilibrium. Additionally, a relationship between the order of CE expansions and the truncated order of Hermite equilibria is developed to determine the minimal order of a Hermite equilibria required to recover any multiple-timescale macroscopic system. Next, three-dimensional compressible Taylor-Green vortex flows with different initial conditions and Ma numbers are simulated to demonstrate the effectiveness and potential issues of these lifting relations. The Hermite-expansion-based lifting relation works well in all cases, while the Chapman-Enskog-expansion-based lifting relation may produce numerical oscillations and a theoretical model is developed to predict such oscillations. Furthermore, the corresponding lifting relations for Qi et al.'s total energy DDF model [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)10.1063/5.0120490] are derived, and additional simulations are performed to illustrate the generality of our approach.

Impacts of evaporation and inundation on near-surface salinity at a coastal wetland park.

Salinization is one of the main causes of conversion between different ecosystems and landuse functions in coastal wetlands. In this paper, we studied the spatiotemporal dynamics of soil moisture and salinity in a reclaimed national wetland park in Guangdong Province, China. We found that diel evaporation affected soil water up to 40 cm deep. Extreme rainfall only increased topsoil moisture with limited leaching effects on soil salinity. Salt accumulation occurred between 40 and 70 cm depth in rainy season, lasting until the end of monitoring period. Whereas the topsoil was salinized between land-surface to 30 cm deep in dry season, which was recovered after rainfall. This result suggested that the force balance between capillarity and gravity created a relative stable saline layer which was not flushed out during inundation. Therefore, considering these site-specific features could lead to the improved understanding of the migration of salinity in the soil profiles.

Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation.

In this paper, two discrete unified gas-kinetic scheme (DUGKS) methods with piecewise-parabolic flux reconstruction are presented for the conservative Allen-Cahn equation (CACE). One includes a temporal derivative of the order parameter in the force term while the other does not include temporal derivative in the force term but results in a modified CACE with additional terms. In the context of DUGKS, the continuum equations recovered from the piecewise-linear and piecewise-parabolic reconstructions for the fluxes at cell faces are subsequently derived. It is proved that the resulting equation with the piecewise-linear reconstruction is a first-order approximation to the discrete velocity kinetic equation due to the presence of the force term and the nonconservation property of the momentum of the collision model. To guarantee second-order accuracy of DUGKS, the piecewise-parabolic reconstruction for numerical flux is proposed. To validate the accuracy of the present DUGKS with the proposed flux evaluation, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zalesak disk and the deformation of a circular interface, have been simulated. Numerical results show that the accuracy of both proposed DUGKS methods is almost comparable and improved compared with the DUGKS with linear flux reconstruction scheme.

Challenges in simulating and modeling the airborne virus transmission: A state-of-the-art review.

Recently, the COVID-19 virus pandemic has led to many studies on the airborne transmission of expiratory droplets. While limited experiments and on-site measurements offer qualitative indication of potential virus spread rates and the level of transmission risk, the quantitative understanding and mechanistic insights also indispensably come from careful theoretical modeling and numerical simulation efforts around which a surge of research papers has emerged. However, due to the highly interdisciplinary nature of the topic, numerical simulations of the airborne spread of expiratory droplets face serious challenges. It is essential to examine the assumptions and simplifications made in the existing modeling and simulations, which will be reviewed carefully here to better advance the fidelity of numerical results when compared to the reality. So far, existing review papers have focused on discussing the simulation results without questioning or comparing the model assumptions. This review paper focuses instead on the details of the model simplifications used in the numerical methods and how to properly incorporate important processes associated with respiratory droplet transmission. Specifically, the critical issues reviewed here include modeling of the respiratory droplet evaporation, droplet size distribution, and time-dependent velocity profile of air exhaled from coughing and sneezing. According to the literature review, another problem in numerical simulations is that the virus decay rate and suspended viable viral dose are often not incorporated; therefore here, empirical relationships for the bioactivity of coronavirus are presented. It is hoped that this paper can assist researchers to significantly improve their model fidelity when simulating respiratory droplet transmission.

Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows.

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

Visualization of the interaction of water aerosol and nanofiber mesh.

Face masks play a critical role in reducing the transmission risk of COVID-19 and other respiratory diseases. Masks made with nanofibers have drawn increasingly more attention because of their higher filtration efficiency, better comfort, and lower pressure drop. However, the interactions and consequences of the nanofibers and microwater droplets remain unclear. In this work, the evolution of fibers made of polymers with different contact angles, diameters, and mesh sizes under water aerosol exposure is systematically visualized. The images show that capillarity is very strong compared with the elasticity of the nanofiber. The nanofibers coalesce irreversibly during the droplet capture stage as well as the subsequent liquid evaporation stage. The fiber coalescence significantly reduces the effective fiber length for capturing aerosols. The nanofiber mesh that undergoes multiple droplet capture/evaporation cycles exhibits a fiber coalescing fraction of 40%-58%. The hydrophobic and orthogonally woven fibers can reduce the capillary forces and decrease the fiber coalescing fraction. This finding is expected to assist the proper design, fabrication, and use of face masks with nanofibers. It also provides direct visual evidence on the necessity to replace face masks frequently, especially in cold environments.

Latest developments in nanofluid flow and heat transfer between parallel surfaces: A critical review.

The enhancement of heat transfer between parallel surfaces, including parallel plates, parallel disks, and two concentric pipes, is vital because of their wide applications ranging from lubrication systems to water purification processes. Various techniques can be utilized to enhance heat transfer in such systems. Adding nanoparticles to the conventional working fluids is an effective solution that could remarkably enhance the heat transfer rate. No published review article focuses on the recent advances in nanofluid flow between parallel surfaces; therefore, the present paper aims to review the latest experimental and numerical studies on the flow and heat transfer of nanofluids (mixtures of nanoparticles and conventional working fluids) in such configurations. For the performance analysis of thermal systems composed of parallel surfaces and operating with nanofluids, it is necessary to know the physical phenomena and parameters that influence the flow and heat transfer characteristics in these systems. Significant results obtained from this review indicate that, in most cases, the heat transfer rate between parallel surfaces is enhanced with an increase in the Rayleigh number, the Reynolds number, the magnetic number, and Brownian motion. On the other hand, an increase in thermophoresis parameter, as well as flow parameters, including the Eckert number, buoyancy ratio, Hartmann number, and Lewis number, leads to heat transfer rate reduction.

Effect of self-assembly on fluorescence in magnetic multiphase flows and its application on the novel detection for COVID-19.

In the present study, the magnetic field induced self-assembly processes of magnetic microparticles in an aqueous liquid (the pure magnetic fluid) and nonmagnetic microparticles in ferrofluid (the inverse magnetic fluid) are experimentally investigated. The microparticles are formed into chain-like microstructures in both the pure magnetic fluid and the inverse magnetic fluid by applying the external magnetic field. The fluorescence parameters of these self-assembled chain-like microstructures are measured and compared to those without the effect of magnetic field. It is found that the fluorescence in the pure magnetic fluid is weakened, because the scattering and illuminating areas are reduced in the microstructures. On the contrary, the fluorescence in the inverse magnetic fluid is enhanced, because more fluorescent nonmagnetic microparticles are enriched and become detectable under the effect of the magnetic dipole force and the magnetic levitational force, and their unnecessary scattering can be absorbed by the surrounding ferrofluid. The average enhancement of the fluorescence area ratio in the inverse magnetic fluid with 3 µm nonmagnetic microparticles reaches 112.92%. The present work shows that the inverse magnetic fluid has advantages such as low cost, no scattering effect, stable fluorescence intensity, and relatively low magnetic resistance. In the end, a prototype design for the novel detection of coronavirus disease 2019 based on the magnetic field induced self-assembly in the inverse magnetic fluid is proposed, which could support the epidemic prevention and control.

Force-amplified, single-sided diffused-interface immersed boundary kernel for correct local velocity gradient computation and accurate no-slip boundary enforcement.

The current diffused-interface immersed boundary method (IBM) with a two-sided force distribution kernel cannot be used to correctly calculate the velocity gradients within the diffused solid-fluid interfaces. This is because the nonzero boundary force distributed to the fluid nodes modifies the momentum equation solved at these locations from the Navier-Stokes equations (NSEs). In this paper, this problem is analytically identified in simple plane channel flow. A single-sided force distribution kernel is used to restrict the boundary force in the solid region and restore NSEs in the fluid region for correct velocity gradient computation. In order to improve the no-slip boundary enforcement in IBM, an extremely simple force amplification technique is proposed. This technique requires no additional computation cost and can significantly reduce the necessary iterations to achieve accurate no-slip boundary enforcement. The single-sided kernel and the force amplification technique are examined in both laminar and turbulent flows. Compared to the standard IBM, the proposed methods not only produce correct velocity gradient results near a solid surface but also reduce numerical errors in the flow velocity and hydrodynamic force and torque results.

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method.

In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

Effects of particle-fluid density ratio on the interactions between the turbulent channel flow and finite-size particles.

A parallel direct-forcing fictitious domain method is employed to perform fully resolved numerical simulations of turbulent channel flow laden with finite-size particles. The effects of the particle-fluid density ratio on the turbulence modulation in the channel flow are investigated at the friction Reynolds number of 180, the particle volume fraction of 0.84%, and the particle-fluid density ratio ranging from 1 to 104.2. The results show that the variation of the flow drag with the particle-fluid density ratio is not monotonic, with a larger flow drag for the density ratio of 10.42, compared to those of unity and 104.2. A significant drag reduction by the particles is observed for large particle-fluid density ratios during the transient stage, but not at the statistically stationary stage. The intensity of particle velocity fluctuations generally decreases with increasing particle inertia, except that the particle streamwise root-mean-square velocity and streamwise-transverse velocity correlation in the near-wall region are largest at the density ratio of the order of 10. The averaged momentum equations are derived with the spatial averaging theorem and are used to analyze the mechanisms for the effects of the particles on the flow drag. The results indicate that the drag-reduction effect due to the decrease in the fluid Reynolds shear stress is counteracted by the drag-enhancement effect due to the increase in the total particle stress or the interphase drag force for the large particle-inertia case. The sum of the total Reynolds stress and particle inner stress contributions to the flow drag is largest at the density ratio of the order of 10, which is the reason for the largest flow drag at this density ratio. The interphase drag force obtained from the averaged momentum equation (the balance theory) is significantly smaller than (but agrees qualitatively with) that from the empirical drag formula based on the phase-averaged slip velocity for large density ratios. For the neutrally buoyant case, the balance theory predicts a positive interphase force on the particles arising from the negative gradient of the particle inner stress, which cannot be predicted by the drag formula based on the phase-averaged slip velocity. In addition, our results show that both particle collision and particle-turbulence interaction play roles in the formation of the inhomogeneous distribution of the particles at the density ratio of the order of 10.

Lattice Boltzmann model capable of mesoscopic vorticity computation.

It is well known that standard lattice Boltzmann (LB) models allow the strain-rate components to be computed mesoscopically (i.e., through the local particle distributions) and as such possess a second-order accuracy in strain rate. This is one of the appealing features of the lattice Boltzmann method (LBM) which is of only second-order accuracy in hydrodynamic velocity itself. However, no known LB model can provide the same quality for vorticity and pressure gradients. In this paper, we design a multiple-relaxation time LB model on a three-dimensional 27-discrete-velocity (D3Q27) lattice. A detailed Chapman-Enskog analysis is presented to illustrate all the necessary constraints in reproducing the isothermal Navier-Stokes equations. The remaining degrees of freedom are carefully analyzed to derive a model that accommodates mesoscopic computation of all the velocity and pressure gradients from the nonequilibrium moments. This way of vorticity calculation naturally ensures a second-order accuracy, which is also proven through an asymptotic analysis. We thus show, with enough degrees of freedom and appropriate modifications, the mesoscopic vorticity computation can be achieved in LBM. The resulting model is then validated in simulations of a three-dimensional decaying Taylor-Green flow, a lid-driven cavity flow, and a uniform flow passing a fixed sphere. Furthermore, it is shown that the mesoscopic vorticity computation can be realized even with single relaxation parameter.

Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows.

The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.

Colloid mobilization by fluid displacement fronts in channels.

Understanding colloid mobilization during transient flow in soil is important for addressing colloid and contaminant transport issues. While theoretical descriptions of colloid detachment exist for saturated systems, corresponding mechanisms of colloid mobilization during drainage and imbibition have not been considered in detail. In this work, theoretical force and torque analyses were performed to examine the interactive effects of adhesion, drag, friction, and surface tension forces on colloid mobilization and to outline conditions corresponding to the mobilization mechanisms such as lifting, sliding, and rolling. Colloid and substrate contact angles were used as variables to determine theoretical criteria for colloid mobilization mechanisms during drainage and imbibition. Experimental mobilization of hydrophilic and hydrophobic microspheres with drainage and imbibition fronts was investigated in hydrophilic and hydrophobic channels using a confocal microscope. Colloid mobilization differed between drainage and imbibition due to different dynamic contact angles and interfacial geometries on the contact line. Experimental results did not fully follow the theoretical criteria in all cases, which was explained with additional factors not included in the theory such as presence of aggregates and trailing films. Theoretical force and torque analyses resulted in similar mobilization predictions and suggested that all mobilization mechanisms contributed to the observed colloid mobilization.

Microstructural evolution of carbon nanotube fibers: deformation and strength mechanism.

A comprehensive investigation of the mechanical behavior and microstructural evolution of carbon nanotube (CNT) continuous fibers under twisting and tension is conducted using coarse-grained molecular dynamics simulations. The tensile strength of CNT fibers with random CNT stacking is found to be higher than that of fibers with regular CNT stacking. The factor dominating the mechanical response of CNT fibers is identified as individual CNT stretching. A simplified twisted CNT fiber model is studied to illustrate the structural evolution mechanisms of CNT fibers under tension. Moreover, it is demonstrated that CNT fibers can be reinforced by enhancing intertube interactions. This study would be helpful not only in the general understanding of the nano- and micro-scale factors affecting CNT fibers' mechanical behavior, but also in the optimal design of CNT fibers' architecture and performance.

Scaling and statistics in three-dimensional compressible turbulence.

The scaling and statistical properties of three-dimensional compressible turbulence are studied using high-resolution numerical simulations and a heuristic model. The two-point statistics of the solenoidal component of the velocity field are found to be not significantly different from those of incompressible turbulence, while the scaling exponents of the velocity structure function for the compressive component become saturated at high orders. Both the simulated flow and the heuristic model reveal the presence of a power-law tail in the probability density function of negative velocity divergence (high compression regime). The power-law exponent is different from that in Burgers turbulence, and this difference is shown to have a major contribution from the pressure effect, which is absent in the Burgers turbulence.

Application of DLVO energy map to evaluate interactions between spherical colloids and rough surfaces.

This study theoretically evaluated interactions between spherical colloids and rough surfaces in three-dimensional space using Derjaguin-Landau-Verwey- Overbeek (DLVO) energy/force map and curve. The rough surfaces were modeled as a flat surface covered by hemispherical protrusions. A modified Derjaguin approach was employed to calculate the interaction energies and forces. Results show that more irreversible attachments in primary minima occur at higher ionic strengths, which theoretically explains the observed hysteresis of colloid attachment and detachment during transients in solution chemistry. Secondary minimum depths can be increased significantly in concave regions (e.g., areas aside of asperities or between asperities) due to sidewall interactions. Through comparing the tangential attractive forces from asperities and the hydrodynamic drag forces in three-dimensional space, we showed that attachment in secondary minima can be located on open collector surfaces of a porous medium. This result challenges the usual belief that the attachment in secondary minima only occurs in stagnation point regions of the porous medium and is absent in shear flow systems such as parallel plate flow chamber and impinging jet apparatus. Despite the argument about the role of secondary minima in colloid attachment remained, our study theoretically justified the existence of attachment in secondary minima in the presence of surface roughness. Further, our study implied that the presence of surface roughness is more favorable for attachment in secondary minima than in primary minima under unfavorable chemical conditions.