International Journal of Multiphase Flow最新文献

The occurrence of a steam generator tube rupture (SGTR) accident in a lead-bismuth cooled fast reactor results in the formation of steam bubbles in the liquid lead-bismuth eutectic (LBE). This may degrade heat transfer and power transients in the reactor core due to the migration and accumulation of steam bubbles. To investigate the dynamics of steam bubbles flowing in liquid LBE, it is essential to develop an accurate model for the bubble drag coefficient. In this paper, a three-dimensional numerical model is first established to simulate the injection of high-pressure steam bubbles into a high-temperature LBE molten pool. The model is based on the CLSVOF method. By analyzing the trajectory, velocity, and diameter of bubbles, and combining them with the force equilibrium equation for bubbles, the values of the drag coefficient for bubbles are determined. On this basis, the suitability of current empirical drag models for bubble migration in LBE is evaluated. Finally, the optimal drag coefficient model is selected and further improved. Results reveal that the prediction error of the optimized model for the bubble drag coefficient in liquid LBE is within ±15 %.

The accurate reconstruction of immiscible fluid–fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC), which fits a plane in each mixed-phase computational cell. However, recent work goes beyond PLIC by using two planes or even a paraboloid. To select such planes or paraboloids, complex optimization algorithms as well as carefully crafted heuristics are necessary. Yet, the potential exists for a well-trained machine learning model to efficiently provide broadly applicable solutions to the interface reconstruction problem at lower costs. In this work, the viability of a machine learning approach is demonstrated in the context of a single plane reconstruction. A feed-forward deep neural network is used to predict the normal vector of a PLIC plane given volume fraction and phasic barycenter data in a $3\times 3\times 3$ stencil. The PLIC plane is then translated in its cell to ensure exact volume conservation. Our proposed neural network PLIC reconstruction (PLIC-Net) is equivariant to reflections about the Cartesian planes. Training data is analytically generated with $O\left(10^6\right)$ randomized paraboloid surfaces, which allows for the sampling a broad range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard LVIRA and ELVIRA reconstruction algorithms, and the impact of training data statistics on PLIC-Net’s performance is also explored. It is found that PLIC-Net greatly limits the formation of spurious planes and generates cleaner numerical break-up of the interface. Additionally, the computational cost of PLIC-Net is lower than that of LVIRA and ELVIRA. These results establish that machine learning is a viable approach to Volume of Fluid interface reconstruction and is superior to current reconstruction algorithms for some cases.

Solid–fluid force models are essential to efficiently model multiple industrial apparatuses such as fluidized beds, spouted beds, and slurry transport. They are generally built using strong hypotheses (e.g. fully developed flow and no relative motion between particles) that affect their accuracy. We study the effect of these hypotheses on particle dynamics using the sedimentation of a pair of particles. We develop new induced drag, lift and torque models for pairs of particles based on an artificial neural network (ANN) regression. The fluid force model covers a range of Reynolds numbers of 0.1 to 100 and particle centroid distance of up to 9 particle diameters. The ANN model uses 3475 computational fluid dynamics (CFD) simulation results as the training data set. Using this fluid force model, we develop a reduced-order model (ROM), which includes the virtual mass force, the Meshchersky force, the history force, the lubrication force, and the Magnus force. Using the results of a resolved computational fluid dynamics coupled with a discrete element method (CFD-DEM) model as a reference, we analyze the discrepancies between the ROM and CFD-DEM results for a series of sedimentation cases that cover particle Archimedes number from 20 to 2930 and particle to fluid density ratio of 1.5 to 1000. The errors primarily stem from particle history interactions that are not accounted for by the fully developed flow hypothesis. The importance of this effect on the dynamic of two particles is isolated and it is shown that it is more pronounced in cases with a lower particle-to-fluid density ratio (such as solid–liquid cases). This work underscores the need for more research on these effects to increase the precision of solid–fluid force models for small particle-to-fluid density ratios (1.5).

Shock-driven variable density mixing has been frequently explored through the single-phase Richtmyer–Meshkov instability. Here, such mixing is considered when driven by a multiphase component, the Shock-Driven Multiphase Instability (SDMI). The simple case of a solid particle seeded gas in a cylindrical region surrounded by clean gas is studied. It has been previously shown that the particle-phase can lag behind the gas, diminishing vorticity deposition. In this letter we present theoretical analysis of the vorticity deposition, and a new model predicting the circulation deposition for an SDMI as a function of particle relaxation distance and hydrodynamic mixing strength. The theory is founded on a simplified vorticity equation, advection and multiphase source terms, using simple drag models to predict the particle dynamics, and scaling the results using existing circulation models for the Richtmyer–Meshkov instability in the small particle limit. The model is compared to new high-fidelity experimental data, and previous experiments and simulations, finding good agreement. This model provides the first theoretical prediction of mixing suppression in the SDMI.

In a continuous fluid, the presence of a velocity gradient perpendicular to the flow creates shear stress and shear rate between adjacent layers. The fluid's viscosity can be constant, depending only on temperature (Newtonian fluid), or vary with shear rate (non-Newtonian fluid). However, the viscosity characteristics of shear flows in discrete media, such as vibrated granular materials, remain insufficiently understood. This study experimentally investigated shear flows in vibrated granular media, exploring the relationship between shear stress, shear rate, and the impact of vibration conditions and particle number on granular viscosity. The findings indicate that the viscosity of sheared granular material transitions between dilatant and pseudoplastic non-Newtonian states with increasing vibration strength, shifts from pseudoplastic non-Newtonian fluid to Newtonian fluid with increasing vibration frequency, and remains consistently pseudoplastic non-Newtonian with increasing particle number. Two continuous non-Newtonian fluid models were utilized for comparison with our experimental results. Additionally, ascending curves of granular viscosity against granular temperature reveal gas-like flow characteristics in the sheared granular material, albeit with an abnormal descending viscosity–temperature relationship. These are attributed to volume expansion and oblique collisions in the vibrated granular medium. This study uncovers distinct viscosity properties in a discrete medium under shear flows, markedly different from those in continuous fluids, and highlights potential new applications for granular materials.

This study aims to provide valuable insights into the impact of porous structures on particle dynamics in non-Brownian, non-colloidal suspension flows at very low Reynolds numbers. Two experimental approaches, Particle Image Velocimetry (PIV) with refractive index matching and Optical Flow Tracking Velocimetry (OFTV) were employed to analyze very dilute suspensions over various porous media models. The study considered three different porous structures with permeabilities ranging from 0.7 to 0.9 and three different thicknesses ranging from 0.2 cm to 0.5 cm, while the suspension bulk volume fraction was maintained at 3 %. In the PIV analysis, we observed that decreasing the porous permeability resulted in the maximum velocity location within the free flow region moving closer towards the interface between the flow and the porous media. We further quantified the effect of the porous structure on the suspension by characterizing interface properties, such as dimensionless slip velocity, shear rate, and slip length. These interface properties were found to be influenced by both the thickness and permeability of the porous media. Next, we analyzed particle migration due to the presence of porous structures using OFTV for very dilute suspensions of 1 %, 2 %, and 3 %, considering a porous medium with known physical properties and thickness. The study revealed two local concentration maxima: one within the free flow region on top of the rod arrays used to create the porous structure and a second along the rods' centerline inside the porous media model.

Immiscible flow of oil phase and displacing phase with surfactant can cause emulsification during the oil development. However, it is still unclear how the viscosity of each phase influences the emulsification at the micro level. In this study, we investigated the flow regimes and emulsification of two immiscible fluids in a cross-junction device by using an oil-surfactant system and an oil-surfactant/polymer system. Based on the experimental data, we analyzed the flow regimes and draw flow regime maps of the two systems. Moreover, we established the new scaling laws that include the capillary number, the flow rate ratio, and the viscosity ratio of two phases to predict the droplet diameter or slug length. The findings indicated that there are four flow regimes in the oil-surfactant system, including threading, squeezing, dripping, and jetting regimes. Besides, a new type of flow regime, irregular dripping regime, appears in the oil-surfactant/polymer system. According to the regime maps, the area of dripping regime decreases with the increase of the viscosity of dispersed phase or continuous phase. For both systems, the regression equations with the viscosity ratio have better fitting effect than those without the viscosity ratio. Meanwhile, compared with the effect of viscosity ratio of two phases, the flow rate ratio of two phases has higher influence on droplet diameter and slug length. The experiments present detailed emulsification processes at pore scale and provide new insights for the prediction of emulsion droplets and slugs.

In this paper, we develop a deterministic drag model for stationary spherical particles in a Stokes flow using a cascade of data-driven approaches. The model accounts for the variation in drag experienced by each particle within fixed random arrangements. The developed model is a symbolic expression that offers explainability, ease of implementation, and computational efficiency. Firstly, we generate particle-resolved direct numerical simulation data of the flow past periodic random arrangements of stationary spherical particles with volume fractions between 0.05 and 0.4 using the method of regularized Stokeslets. Secondly, we train graph neural networks (GNs) on the generated data to learn the pairwise influence of neighbouring particles on a reference particle. The GNs are converted to symbolic expressions using genetic programming (GP), unveiling repeated subexpressions. Finally, these subexpressions constitute the foundation of the proposed algebraic model, further refined via non-linear regression. The proposed model can qualitatively mimic the pairwise influences as predicted by the GN and can capture the drag variations with accuracy from 74% and up to 84.7% when compared to the particle-resolved simulations. Due to the interpretability of the proposed model, we are able to explore how neighbour positions alter the drag of a particle in an assembly. The proposed model is a promising tool for studying the dynamics of particle assemblies in Stokes flow.

The objective of this paper is to investigate the multimodal partial shedding dynamics from a multiscale perspective of cloud cavitating flows under two distinct cavity shedding mechanisms, namely the re-entrant jet mechanism and the shock wave propagation mechanism. A two-way Eulerian–Lagrangian coupling algorithm is applied to capture the multiscale vapor topologies from microbubble to large-scale cavities. The large-scale cavity evolution is solved through large eddy simulations (LES) with the volume of fraction (VOF) method in Eulerian frame. The sub-grid microbubbles are tracked in Lagrangian frame based on the discrete bubble model (DBM) method. The predictions agree well with experimental observation of the periodical cavity evolution and microbubble dynamics under both the re-entrant jet mechanism and shock wave mechanism around a NACA66 hydrofoil. The numerical simulation provides detailed analysis of the cavitating turbulent flow on the microbubble behavior with emphasis on the spatial-temporal distribution characteristics of microbubbles. The results show that the number and mean size of microbubbles in the cavitation region increase gradually with the growth of attached sheet cavity, development of re-entrant jet and collapse of largescale cavity for both cavitation patterns. Meanwhile, microbubbles are mainly distributed on the largescale interfaces where have high value of vorticity and turbulent kinetic energy under the effect of re-entrant jet and vortex structures. And the probability density functions (PDFs) of microbubble exhibit gamma distributions with a dominant peak at approximately 50 μm for both shedding mechanisms. However, the shock wave formation and propagation process only occurs in the final stage of cavitating flow under shock wave mechanism causing the condensation of vapor and the decrease of the number and mean size of microbubbles. Moreover, the microbubbles are uniformly distributed along the streamwise and vertical directions behind shock wave front.

Cryogenic refrigerants represented by methane differ significantly in thermophysical properties from working fluids at ambient temperature. Thus, examining their small-scale heat transfer and flow characteristics is essential for designing compact condensers within the cryogenic field. The numerical simulation of methane condensation in minichannels is conducted, and the process of phase-change mass and energy transfer is investigated by programming. Detailed condensation flow field information is obtained, and surface tension and gravity influences are elucidated. Synergy analysis indicates that the synergy near the tube wall still needs to be improved. Heat transfer performance is proved to be dependent on the relative significance of turbulence intensity and condensate film thickness. The tube inclination exerts a more noticeable influence on the condensation heat transfer for large diameters, which is supported by the dominance of gravity in the condensation heat transfer mechanism at larger diameters. At higher vapor quality and mass flux, the heat transfer enhancement governed by surface tension is more significant. The condensate at the bottom is mainly formed by the accumulation of condensate sliding off the tube top driven by gravity as the diameter increases, reducing the heat transfer region. The mass flux augments the frictional pressure drop more noticeably at high vapor quality. The prediction performance of empirical correlations is evaluated, and all the selected correlations underestimate the frictional pressure drop of methane. Moreover, the figure of merit analysis demonstrates that the pressure drop produced by diameter reduction is more substantial than heat transfer enhancement, suggesting the requirement to assess the pressure drop loss in practical applications.