High-density Ratio Research Articles

An improved three-dimensional lattice Boltzmann-volume of fluid (LB-VOF) method for simulation of laminar liquid jet breakup with high density ratio

Lattice Boltzmann method (LBM) has been widely developed in the past decade, while most of the previously presented LBMs are confined to two-phase problems with a low-density ratio. In the present study, we developed the free surface model based on the volume of fluid (VOF) method to a three-dimensional two-phase LBM (LBM-VOF) and utilized this new model to simulate the breakup of a water jet in the air. This problem is characterized by high density and viscosity ratios with the values of about 830 and 58, respectively. Numerical codes are implemented in the open-source library of parallel Lattice Boltzmann solver (PALABOS), and the results are compared and validated against experimental and published numerical outcomes. It is shown this new model could properly confine spurious currents. Afterward, the LBM-VOF model is used to simulate different water jet regimes, including periodic dripping, dripping faucet, and jetting regimes. Furthermore, the dynamics of fluid jet formation and droplet breakup are comprehensively discussed in different ranges of the Weber number (0.063 < We < 6) and three nozzles with different sizes. Results show that the proposed LBM-VOF model is capable of simulating all the three mentioned regimes and their specific characteristics. The proposed model accurately predicts the ranges of critical Weber number (2.4 < We < 2.84) at which the regime transition from periodic dripping to jetting occurs; which is in agreement with the theoretical relation. Moreover, when the dripping to jetting transition occurs, the length of breakup and the frequency of droplet production increased sharply by approximately 3.6 and 3, respectively, while the volume of produced droplets decreased by about 2.4.

An improved MPS method for simulating multiphase flows characterized by high-density ratios and violent deformation of interface

An improved Moving-Particle Semi-Implicit (MPS) method is proposed for multiphase flows with high-density ratios and violent deformation of the interface. First, a particle number density compensation (PNDC) model is developed to remove the ghost particles out of the boundary thoroughly. The model is verified via static pressure simulations. Then, based on previous works (Shakibaeinia et al., 2012; Khayyer et al., 2013; Duan et al., 2017 [1]; Duan et al., 2017 [2]; Sun et al., 2015), the MPS method is extended to a multiphase flow solver. Finally, the improved MPS method is applied to model static pressure, Rayleigh–Taylor instability, sloshing flow, and two-phase dam-break. The comparative analysis with the available experimental datum and other published numerical results proved the applicability and accuracy of the proposed MPS method for simulating multiphase flows with high-density ratios and violent deformation of interface.

Settling dynamics of circular particles in vibrating tanks filled with a yield-stress liquid

The effect of sinusoidal vibration is numerically investigated on the settling dynamics of a heavy particle of circular shape immersed in a viscoplastic fluid obeying the regularized Bingham–Papanastasiou (BP) model. Having modeled the solid particle as a highly viscous Newtonian droplet, we have relied on the finite element method for solving the equations of motion for the particle and the surrounding fluid. Our numerical results could closely recover the theoretical critical Bingham number of 0.0658 for circular particles settling in Bingham materials. Using a very small threshold velocity to decide whether a particle is stuck or unstuck, it is shown that stuck particles can be excited to fall in the BP liquid provided that, for any given frequency, the amplitude is larger than a minimum value. An increase in the size of the particle or its density is predicted to reduce the threshold amplitude. In general, vibration is found to have an accelerating effect on particle settling in the BP liquid although the effect is non-monotonic. The accelerative effect of vibration is attributed to the enlarged size of the yielded zone, while the non-monotonic behavior is attributed to the effect of the sidewalls. At high density ratios, a phase lag is predicted to arise between the particle and the vessel. A comparison between the obtained numerical results with published experimental data for spherical particles suggests that, in settling flows, circular particles can be used as a good paradigm for spherical particles.

A unified forcing scheme for the single relaxation lattice Boltzmann method

The lattice Boltzmann method (LBM) has been successfully used to simulate fluid flow phenomena, which involves incorporating a force term. To the best of the authors' knowledge, no study has extensively investigated the effect of the discretization of the Boltzmann transport equation on the force term. The current study focuses on closing this gap by performing a parametric discretization of the collision and force term. To ensure consistent behavior during the discretization, the moments of both the force term and equilibrium distribution function are compared for the continuous and discrete spaces. The recovered momentum equation using the Chapman-Enskog analysis has an additional term proportional to the square of the external forces. Hence, a novel parametric unified formulation of momentum forcing scheme is proposed to compensate for the additional term. The novel unified forcing scheme is able to improve and predict the error of several previously published forcing schemes. Furthermore. the unified forcing scheme is validated for single- and multi-phase problems. The natural convection in a cavity and the stationary droplet problems are used to benchmark the general proposed discretization and the unified forcing scheme for single-phase and multiphase systems, respectively. The results show that the unified proposed forcing scheme agrees with the reference results of natural convection in a cavity. For multiphase flow, the unified proposed scheme predicts a high-density ratio second after Kupershtokh et al.’s and Shan and Chen’s approaches, which in their turn do not recover the correct momentum equation. The unified proposed approach predicts a slightly larger radius. This indicates that the mean-field potential function should be improved to increase the density ratio and to predict a correct radius while retaining the correct momentum and continuity equations.

Numerical investigation of novel block flow channel on mass transport characteristics and performance of PEMFC

This study develops a three-dimensional numerical model of a proton exchange membrane (PEM) fuel cell (PEMFC) to investigate the mass transport characteristics and performance of PEMFC with novel two-block structures in the cathode channel. The results reveal that the novel two-block structures improve the efficiency of mass transport and the performance of PEMFC. Effects of the arrangement of two-block structures and the operating conditions on the PEMFC performance are investigated. It is found that the block position closer to the outlet of the channel has greater improvement of the PEMFC performance. The PEMFC performance increases firstly with the block structure number and then decreases, and the best number of block structures is 6 for the present study. The block channel has more evident effect when the PEMFC operated under high current density and small stoichiometric ratio, and the block channel is effective in a wide relative humidity (RH) range.

Boundary element method for modeling droplet deformation in secondary atomization

A droplet deformation model based on the combination of an axisymmetric Boundary Element Method (BEM), Viscous Potential Flow (VPF) theory, and a simplified heuristic model for the action of aerodynamic forces is presented. The model predicts droplet distortion and interface shape up to the point of initial droplet break-up. To address liquid viscosity a previously introduced Generalized Viscous Pressure Correction was employed after its extension to 3D axisymmetric cases. Assumed are thin boundary layers within the droplet phase, a high density ratio between the two phases and moderate Reynolds numbers. The model requires at most around 200 flow variables to properly predict droplet deformation and distortion. The overall model produces results comparable to those of the Taylor Analogy Breakup model and its nonlinear version in the vibrational regime. However, it requires a calibration factor of 1.36 for the aerodynamic local pressure, in order to obtain the correct critical Weber number of around 12. In the bag and bag-stamen regimes, the droplet shape and distortion parameters are in good agreement with experimental data. Overall, the results indicate that the present modeling approach might be used as sub-grid model for droplet dynamics in multiphase flow simulation with a highly dispersed liquid phase.

MINDS. The Detection of 13CO2 with JWST-MIRI Indicates Abundant CO2 in a Protoplanetary Disk

We present JWST-MIRI Medium Resolution Spectrometer (MRS) spectra of the protoplanetary disk around the low-mass T Tauri star GW Lup from the MIRI mid-INfrared Disk Survey Guaranteed Time Observations program. Emission from 12CO2, 13CO2, H2O, HCN, C2H2, and OH is identified with 13CO2 being detected for the first time in a protoplanetary disk. We characterize the chemical and physical conditions in the inner few astronomical units of the GW Lup disk using these molecules as probes. The spectral resolution of JWST-MIRI MRS paired with high signal-to-noise data is essential to identify these species and determine their column densities and temperatures. The Q branches of these molecules, including those of hot bands, are particularly sensitive to temperature and column density. We find that the 12CO2 emission in the GW Lup disk is coming from optically thick emission at a temperature of ∼400 K. 13CO2 is optically thinner and based on a lower temperature of ∼325 K, and thus may be tracing deeper into the disk and/or a larger emitting radius than 12CO2. The derived / ratio is orders of magnitude higher than previously derived for GW Lup and other targets based on Spitzer-InfraRed-Spectrograph data. This high column density ratio may be due to an inner cavity with a radius in between the H2O and CO2 snowlines and/or an overall lower disk temperature. This paper demonstrates the unique ability of JWST to probe inner disk structures and chemistry through weak, previously unseen molecular features.

A Generalized Finite Difference Scheme for Multiphase Flow

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square droplet surrounded by a light fluid and a bubble rising in a denser fluid. The scheme is also used to simulate the collision of binary droplets at moderate Reynolds numbers (250–550). The effects of the surface tension and density ratio are explored in this work by considering cases with Weber numbers of 8 and 180 and density ratios of 2:1 and 1000:1. The robustness of the multiphase scheme is highlighted when resolving thin fluid structures arising in both high and low density ratio cases at We = 180.

Micro-nozzle flow and thrust prediction with high-density ratio using DSMC selection limiter

Introduction:A Direct Simulation Monte Carlo (DSMC) solver with a modified collisional routine is used to investigate an argon gas flow through a millimeter-scaled thruster nozzle with high-density ratios.Method:The limiter scheme, denoted as the constant selection limiter (CSL), limits the possible number of selected collisional pairs to a constant value in accordance with the present simulation particles in the cell.Results:Results of the CSL scheme are compared with the experimental and numerical results of a compressible Navier–Stokes solver and discussed in comparison with baseline DSMC simulations. The influence of collision limitation by the CSL is discussed on the stagnation pressure of the thruster and on thrust and specific impulse prediction. The application of the limiter scheme makes the prediction of stagnation pressure challenging in some cases.Discussion:In contrast, thrust and specific impulse are predicted well, and their study remains valid. Investigated mass flow rates are 0.178 mg/s ≤m.≤ 71.360 mg/s, and flow Knudsen numbers below Kn = 0.01 and over Kn = 10 are present. Near atmospheric conditions are reached inside the thruster, generating pressure ratios up to 3,741 along the nozzle. The computational performance of the scheme is also discussed, and speed-up factors up to 0.51 are achieved.

A numerical study of drop evaporation at high density ratios using Front-Tracking method

A numerical study of drop evaporation at high density ratios using Front-Tracking method

Improved boundary conditions for lattice Boltzmann modeling of pool boiling at low temperature

The pseudopotential lattice Boltzmann method (LBM) becomes popular in simulating the boiling heat transfer problems. By using the interaction force determined from an equation of state, the boiling phenomenon can occur spontaneously according to the thermodynamics, which avoids using empirical models for boiling. However, this pseudopotential interaction model also brings additional cause of instability, which becomes severe at high density ratios. Therefore, most of its previous boiling simulations are conducted at high saturated temperatures with low density ratios. Since the instability usually stems from the disturbance at the interfaces, we investigated the scheme of computing the solid pseudopotential for the solid–fluid interaction and proposed using the average surrounding fluid properties as the virtual solid temperature in addition to density. Droplet evaporation and film boiling problems at high saturated temperatures are simulated, and very good agreement is obtained when compared with the available numerical and analytical solutions, respectively. We then applied the pseudopotential LBM model to simulate droplet evaporation and pool boiling at a low reduced temperature of Tr=0.592 with a density ratio of 1000, as demonstrations of the improved numerical stability. Different boiling regimes are observed by varying the superheat imposed at the bottom wall.

Valuing the Natural Capital of Sea Areas Based on Emergy Analysis

Marine natural capital is an important component of natural capital yields goods and service flows benefiting the human being. The emergy analysis method allows one to account for mass, energy and money flows in an ecosystem, providing technical support for assessing its broader value regarding our economic dependence. Thus, we used this method to evaluate the natural capital of the Zhoushan archipelago sea area from 2011 to 2016 and proposed a formula to estimate the marine organism’s transformity. The average total emergy of our study area was 6.93 × 1022 sej and emdollar was about 9.20 billion yuan, which is equivalent to 9.3% of the average regional GDP of 98.5 billion during the same period. The Zhoushan archipelago sea area has high emergy density (ED) and low emergy self-sufficiency ratio (ESR), which shows low input–output efficiency for local use. In addition, the high purchased emergy (PR), high emergy exchange ratio (EER) and low renewable resources emergy ratio (%R) imply an increasing dependence on the outside social and economic inputs. Overall, Zhoushan sea area was in an early but steady state of development. The results can serve as a benchmark for policy making and implementation to achieve local sustainable development. As a tool for emergy-based sea area capital assessment, the model is of great significance for quantifying the ecosystem service value and accounting for marine/land natural capital value.

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 equationof 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.

A hybrid immersed interface and phase-field-based lattice Boltzmann method for multiphase ferrofluid flow

In this study, we developed a hybrid immersed interface and phase-field lattice Boltzmann (LB) method to simulate multiphase ferrofluid flows. The Laplace equation for the magnetic potential with an interface jump condition was numerically solved using a phase-field-based immersed interface method. The phase interface was tracked by the conservative Allen–Cahn equation. One LB equation was used to capture the interfaces between the two immiscible fluids and another to solve for the hydrodynamic properties. The magnetic stress was treated as an interfacial force at the interface, and thus both the magnetic and capillary forces could be formulated in a unified phase-field method framework. Several typical problems, including a circular cylinder in a uniform magnetic field, deformation of a ferrofluid droplet under a uniform magnetic field, two bubbles merging in the ferrofluid, and a ferrofluid droplet suspension under a shear flow to study the rheological characteristics, were simulated to test the accuracy, applicability, and numerical stability of the present model. The numerical examples demonstrated that the present model is able to capture basic phenomenological features in magnetic multiphase flow problems with high density and high viscosity ratios.

Water-Stable Upconverting Coordination Polymer Nanoparticles for Transparent Films and Anticounterfeiting Patterns with Air-Stable Upconversion.

Photon upconversion (UC) based on triplet-triplet annihilation is a very promising phenomenon with potential application in several areas, though, due to the intrinsic mechanism, the achievement of diffusion-limited solid materials with air-stable UC is still a challenge. Herein, we report UC coordination polymer nanoparticles (CPNs) combining sensitizer and emitter molecules especially designed with alkyl spacers that promote the amorphous character. Beyond the characteristic constraints of crystalline MOFs, amorphous CPNs facilitate high dye density and flexible ratio tunability. To show the universality of the approach, two types of UC-CPNs are reported, exhibiting highly photostable UC in two different visible spectral regions. Given their nanoscale, narrow size distribution, and good chemical/colloidal stability in water, the CPNs were also successfully printed as anticounterfeiting patterns and used to make highly transparent and photostable films for luminescent solar concentrators, both showing air-stable UC.

Numerical simulation of bubbly flows by the improved lattice Boltzmann method for incompressible two-phase flows

Bubbly flow problems are simulated to verify the effectiveness of the improved lattice Boltzmann method for incompressible two-phase flows. In this method, it is possible to compute two-phase fluid flows with high density ratios accurately and efficiently compared with the previous method. Firstly, we simulate a stationary bubble to investigate the accuracy of the interfacial tension. As a result, the calculated pressure differences are in good agreement with the theoretical predictions, and the relative errors of the pressure difference are less than 5%. Secondly, we simulate a single bubble rising in a liquid under gravity. It is found that the terminal bubble shapes and Reynolds numbers are in good agreement with available numerical and experimental data. Thirdly, we simulate two bubbles rising in a liquid under gravity for different initial arrangements. It is found that the bubble shapes and transient Reynolds numbers during the coalescence process are generally in agreement with the available numerical results. Finally, we simulate typical slug and churn flows in a square duct. It is found that transition from slug flow to churn flow occurs when the pressure difference between inlet and outlet of the duct is increased. In addition, it is found that square ducts with larger width tend to generate churn flows. These results demonstrate that the present method is applicable to complicated bubbly flow problems.

A consistent adaptive level set framework for incompressible two-phase flows with high density ratios and high Reynolds numbers

We develop a consistent adaptive framework in a multilevel collocated grid layout for simulating two-phase flows with adaptive mesh refinement (AMR). The conservative momentum equations and the mass equation are solved in the present consistent framework. This consistent mass and momentum transport treatment greatly improves the accuracy and robustness for simulating two-phase flows with a high density ratio and high Reynolds number. The interface capturing level set method is coupled with the conservative form of the Navier–Stokes equations, and the multilevel reinitialization technique is applied for mass conservation. This adaptive framework allows us to advance all variables level by level using either the subcycling or the non-subcycling method to decouple the data advancement on each level. The accuracy and robustness of the framework are validated by a variety of canonical two-phase flow problems. We demonstrate that the consistent scheme results in a numerically stable solution in flows with high density ratios (up to 106) and high Reynolds numbers (up to 106), while the inconsistent scheme exhibits nonphysical fluid behaviors in these tests. Furthermore, it is shown that the subcycling and non-subcycling methods provide consistent results and that both of them can accurately resolve the interfaces of the two-phase flows with surface tension effects. Finally, a 3D breaking wave problem is simulated to show the efficiency and significant speedup of the proposed framework using AMR.

A two-particle approach for dry high density-ratio granular collapse

We report on the role of density ratio for granular column collapse experimentally and numerically by demonstrating the fundamental changes using a two-particle approach. The influence of the density ratio for the different profile arrangements on the velocity distribution, interface, and energy transition is described using the Moving Particle Semi-Implicit method (MPS). A constitutive equation utilizing the granular material strength is formulated using the elasto-viscoplastic model under the μ ( I ) rheology framework by replacing the frictional coefficient with the internal friction angle. The dense state of the granular materials results in a linear relationship between the length scale and inertia constant, which makes the shear strength the driving parameter. Experimental data are compared with numerical simulation for granular collapse with varying density profile configurations to validate the method. We found that the density ratio does not influence the velocity and free surface profile. The interface is maintained similarly to a single-phased granular flow except for erosive configurations where a penetrating regime is evident. The rate at which the granular kinetic energy transforms to the potential energy when the lower density material is on top and at the left of the higher granular materials is similar compared to other profile arrangements. The results demonstrated that the density ratio for different profile arrangements could significantly influence the deformation of the granular materials depending on the particle arrangements. The numerical investigation for the granular column collapse agrees well with experimental studies. Collapse mechanisms of varying density ratio configuration. • Flow dynamics and energy evolution in density ratio granular column collapse. • Replacement of the μ (I) rheology model parameters with the material strength parameters. • Effective phase-change for high-density ratio for single and two-phase granular flow. • Relationship between the inertia constant and wave front. • The meshfree particle method, MPS, shows excellent agreement with the experiment.

Probing the influence of inertia, viscosity, and initial offset on the hydrodynamic interaction of droplet pairs in confined shear flow

The collision behavior of droplet pairs subjected to confined shear flows at high density and viscosity ratios remains unexplored and unquantified, and therefore, the critical density and viscosity ratios for the collision mode of droplets under geometric parameters were unknown. Simulations have been performed using a free-energy-based lattice Boltzmann method, with the aim of determining new regimes compared to the previous study. The results demonstrate that the interaction between viscous and inertia forces plays a vital role in the coalescence nature of droplets, their deformation, course of trajectory, as well as their expedition toward the steady state.

A density-based WCSPH numerical scheme for investigation of multiphase flows with intricate interfaces at high density ratios

Numerical investigation of multiphase problems having complex interface at high density ratios is one of the numerical challenges associated with particle scattering and divergence. Fewer problems have been performed using density-based smooth particle hydrodynamics (WCSPH) in order to solve complex joint surface currents, and most of the simulations in this field have been performed using incompressible smooth particle hydrodynamics (ISPH). Solving high density flows by smooth particle hydrodynamics is associated with particle dispersion and divergence. Various methods have been used to eliminate the scattering of particles, such as a repulsive force at the interface or the corrected density re-value, but there is a problem of particle disintegration at interface at higher times. Numerical simulations of SPH multiphase problems with high density ratio present divergence and dispersion of soluble particles over time simulation. However, this problem is solved in the current model so that continuity is preserved and provides a more accurate solution over time simulation. In the present work, in order to simulate multiphase flows with complex surfaces and high density ratios fluids investigation, a new density-based smooth particle hydrodynamic approach has been utilized. To prevent the particles scattering at the interface, an incompatible particle removal method is used. In the present study, a particle displacement optimization scheme for regularization at phase interface is created by implementing a two-stage change algorithm to maintain the regular particle distribution continuously and conservatively. In order to investigate the accuracy of the current numerical scheme, it is firstly compared with two-phase Poiseuille flow with three fluids having diverse values of viscosity, Reynolds-Taylor instability, Single Bubble rising in a fully filled container, merging of two bubbles, and Bubble rising in a partially filled container; then it is compared with analytical and numerical solutions.