Compared to non-cavitating flow, cavitating flow is much complex owing to the numerical difficulties caused by cavity generation and collapse. In this paper, the cavitating flow around a NACA66 hydrofoil is studied numerically with particular emphasis on understanding the cavitation structures and the shedding dynamics. Large Eddy Simulation (LES) was coupled with a homogeneous cavitation model to calculate the pressure, velocity, vapor volume fraction and vorticity around the hydrofoil. The predicted cavitation shedding dynamics behavior, including the cavity growth, break-off and collapse downstream, agrees fairly well with experiment. Some fundamental issues such as the transition of a cavitating flow structure from 2D to 3D associated with cavitation–vortex interaction are discussed using the vorticity transport equation for variable density flow. A simplified one-dimensional model for the present configuration is adopted and calibrated against the LES results to better clarify the physical mechanism for the cavitation induced pressure fluctuations. The results verify the relationship between pressure fluctuations and the cavity shedding process (e.g. the variations of the flow rate and cavity volume) and demonstrate that the cavity volume acceleration is the main source of the pressure fluctuations around the cavitating hydrofoil. This research provides a better understanding of the mechanism driving the cavitation excited pressure pulsations, which will facilitate development of engineering designs to control these vibrations.

► Cavitating flow around a twisted hydrofoil is studied by PANS method. ► Evolution of cavitation patterns are well predicted compared to experiments. ► The reasons for the primary and secondary shedding are discussed. ► The mechanism of cavitating horse-shoe vortex production is illustrated. Cavitating turbulent flow around hydrofoils was simulated using the Partially-Averaged Navier–Stokes (PANS) method and a mass transfer cavitation model with the maximum density ratio ( / ) effect between the liquid and the vapor. The predicted cavity length and thickness of stable cavities as well as the pressure distribution along the suction surface of a NACA66(MOD) hydrofoil compare well with experimental data when using the actual maximum density ratio ( / = 43391) at room temperature. The unsteady cavitation patterns and their evolution around a Delft twisted hydrofoil were then simulated. The numerical results indicate that the cavity volume fluctuates dramatically as the cavitating flow develops with cavity growth, destabilization, and collapse. The predicted three dimensional cavity structures due to the variation of attack angle in the span-wise direction and the shedding cycle as well as its frequency agree fairly well with experimental observations. The distinct side-lobes of the attached cavity and the shedding U-shaped horse-shoe vortex are well captured. Furthermore, it is shown that the shedding horse-shoe vortex includes a primary U-shaped vapor cloud and two secondary U-shaped vapor clouds originating from the primary shedding at the cavity center and the secondary shedding at both cavity sides. The primary shedding is related to the collision of a radially-diverging re-entrant jet and the attached cavity surface, while the secondary shedding is due to the collision of side-entrant jets and the radially-diverging re-entrant jet. The local flow fields show that the interaction between the circulating flow and the shedding vapor cloud may be the main mechanism producing the cavitating horse-shoe vortex. Two side views described by iso-surfaces of the vapor volume fraction for a 10% vapor volume, and a non-dimensional Q-criterion equal to 200 are used to illustrate the formation, roll-up and transport of the shedding horse-shoe vortex. The predicted height of the shedding horse-shoe vortex increases as the vortex moves downstream. It is shown that the shape of the horse-shoe vortex for the non-dimensional Q-criterion is more complicated than that of the 10% vapor fraction iso-surface and is more consistent with the experiments. Further, though the time-averaged lift coefficient predicted by the PANS calculation is about 12% lower than the experimental value, it is better than other predictions based on RANS solvers.

Primary atomization of liquid injected at high speed into still air is investigated to elucidate physical processes by direct numerical simulation. With sufficient grid resolution, ligament and droplet formation can be captured in a physically sound way. Ligament formation is triggered by the liquid jet tip roll-up, and later ligaments are also produced from the disturbed liquid core surface in the upstream. Ligament production direction is affected by gas vortices. Disturbances are fed from the liquid jet tip toward upstream through vortices and droplet re-collision. When the local gas Weber number is O(1), ligaments are created, thus the ligament or droplet scale becomes smaller as the bulk Weber number increases. Observation of droplet formation from a ligament provides insights into the relevance between the actual droplet formation and pinch-off from a slow liquid jet in laboratory experiments. In the spray, the dominant mode is the short-wave mode driven by propagative capillary wave from the ligament tip. An injection nozzle that is necessary for a slow jet is absent for a ligament, thus the long-wave (Rayleigh) mode is basically not seen without the effect of stretch. By the present simulation, a series of physical processes have been revealed. The present result will be extended to LES modeling in the future.

This work reviews methods for time-series analysis for characterization of the dynamics of gas–solid fluidized beds from in-bed pressure measurements for different fluidization regimes. The paper covers analysis in time domain, frequency domain, and in state space. It is a follow-up and an update of a similar review paper written a decade ago. We use the same pressure time-series as used by Johnsson et al. (2000). The paper updates the previous review and includes additional methods for time-series analysis, which have been proposed to investigate dynamics of gas–solid fluidized beds. Results and underlying assumptions of the methods are discussed. Analysis in the time domain is often the simplest approach. The standard deviation of pressure fluctuations is widely used to identify regimes in fluidized beds, but its disadvantage is that it is an indirect measure of the dynamics of the flow. The so-called average cycle time provides information about the relevant time scales of the system, making it an easy-to-calculate alternative to frequency analysis. Autoregressive methods can be used to show an analogy between a fluidized bed and a single or a set of simple mechanical systems acting in parallel. The most common frequency domain method is the power spectrum. We show that – as an alternative to the often used non-parametric methods to estimate the power spectrum – parametric methods can be useful. To capture transient effects on a longer time scale (>1 s), either the transient power spectral density or wavelet analysis can be applied. For the state space analysis, the information given by the Kolmogorov entropy is equivalent to that of the average frequency, obtained in the frequency domain. However, an advantage of certain state space methods, such as attractor comparison, is that they are more sensitive to small changes than frequency domain methods; this feature can be used for, e.g., on-line monitoring. In general, we conclude that, over the past decade, progress has been made in understanding fluidized-bed dynamics by extracting the relevant information from pressure fluctuation data, but the picture is still incomplete.

In the present paper, large eddy simulations combined with the Zwart cavitation model are conducted to simulate the transient cavitating turbulent flow around a Delft Twisted hydrofoil. Numerical results show a reasonable agreement with the available experimental data. A three dimensional Lagrangian technology is developed to provide an alternative method for the analyses in cavitating flow, which is based on Lagrangian viewpoint. With this technology, the track lines of re-entrant and side-entrant jets are straightforwardly displayed and clearly indicate that collisions of the mainstream, the re-entrant jet and the side-entrant jet play an important role in the primary and secondary shedding. The evolution of U-type structures and the interactions between cavitation and vortices are well captured and discussed in detail from the Eulerian viewpoint. The numerical results show that during the stage of attached cavity, the topology of the cavity leaves an important influence on the vortex structure. Once the cavity is cut off, the vortex structure evolution will affect significantly the local cavitating flow. Further analysis demonstrates that the lift acting on U-type structures, which is induced by velocity circulation around U-type structures, significantly affects the formation and the development of U-type structures. Lagrangian Coherent Structures (LCSs) obtained with the three dimensional Lagrangian technology are used to reveal the influence of U-type structures on local flow patterns and it shows that there is a close relationship between the local flow separation and vortex structures. Our work provides an insight into the interactions of cavitation-vortex in the cavitating flow around a twisted hydrofoil and demonstrates the potential of 3D LCSs in the analyses of cavitating flow. Five groups of LCSs are identified and discussed as the sheet/cloud cavitation shedding occurs periodically.

The gelling of waxy crudes and the deposition of wax on the inner walls of subsea crude oil pipelines present a costly problem in the production and transportation of oil. The timely removal of deposited wax is required to address the reduction in flow rate that it causes, as well as to avoid the eventual loss of a pipeline in the event that it becomes completely clogged. In order to understand this problem and address it, significant research has been done on the mechanisms governing wax deposition in pipelines in order to model the process. Furthermore, methods of inhibiting the formation of wax on pipeline walls and of removing accumulated wax have been studied to find the most efficient and cost-effective means of maintaining pipelines prone to wax deposition. This paper seeks to review the current state of research into these areas, highlighting what is so far understood about the mechanisms guiding this wax deposition, and how this knowledge can be applied to modelling and providing solutions to this problem.

► A compressive VOF method is extended to a simple coupled VOF-LS method. ► Surface tension implementation is shown to be critical for capillary dominant flows. ► Bubble growth modelling is significantly improved with the couple VOF-LS method. ► Improvements are most significant when capillary effects are dominant. ► The numerical static contact angle is related to the experimental minimum angle. A simple coupled Volume of Fluid (VOF) with Level Set (LS) method (S-CLSVOF) for improved surface tension implementation is proposed and tested by comparison against a standard VOF solver and experimental observations. A CFD Open source solver library (OpenFOAM®) is used for the VOF method, where the volume fraction is advected algebraically using a compressive scheme. This method has been found not to be suitable for problems with high surface tension effects and it is extended by coupling it with a LS method which is used to calculate the surface tension and the interface curvature. Two test cases; a circular bubble at equilibrium and a free bubble rise, are studied first to examine the accuracy of the S-CLSVOF method. The problem of 3D axi-symmetrical air bubble injection into quiescent water using different volumetric flow rates is then considered to assess the method under challenging capillary dominant conditions. An experimental study has been performed to validate the numerical methods with reference to the geometrical characteristics of the bubble during the full history of formation. The exponential power law controlling the detachment process is investigated. In addition, the influence of the static contact angle imposed at the rigid wall is considered. The results have shown that the coupling code (S-CLSVOF) improves the accuracy of the original VOF method when the surface tension influence is predominant. The two methods provide similar results during the detachment stage of the process due to the large increase of the gas inertia effect. Finally, the static contact angle boundary condition was shown to allow accurate modeling provided that the imposed static contact angle is less than the minimum instantaneous values observed experimentally.

Sheet/cloud cavitation is an important topic that is a very common type of cavitation in turbo-machinery and marine propeller. Up to now we still have limited understanding of the cavitation shedding dynamics and cloud cavity formation and development. The present study used experimental and numerical studies to gain a better understanding of the complex physics involved in this problem. A series of experimental observations around hydrofoils are carried out in the cavitation tunnel of the China Ship Scientific Research Center (CSSRC) to illustrate the spatial–temporal evolution of the cloud cavity in detail. The results demonstrate that U-type flow structures are common in cloud cavities and can be divided into three stages and the closure line in a sheet cavity often has a convex–concave profile. Reentrant flows occur in the convex region with the jet direction normal to the contour edge so the shedding is mainly caused by the converging reentrant flows. Further analysis demonstrated that there was a striking difference with the cavity growth suppressed substantially in the twisted hydrofoil case if compared with straight hydrofoil and the effect of side entrant jets might make the cavity more uniform across the span. Numerical simulations were used to simulate the formation and development of the cloud cavity. The results show that the strong adverse pressure gradient in the stagnation region at the downstream end of the attached cavity forces the re-entrant flows into the vapor structure with a radially-diverging re-entrant jet and a pair of side-entrant jets, which causes the cavity shedding. Further analyzes of the local flow fields show that the interactions between the circulating flow and the shedding vapor cloud may be the main reason for the formation of the U-type cloud cavity structures.

Modeling of bubble-induced turbulence in dispersed gas–liquid multiphase flow is an important but still unresolved issue. Aside from its intrinsic interest, turbulence in this type of flow has a strong impact on other important processes like turbulent dispersion of the bubbles and bubble-coalescence and -breakup and thus is a central part of the overall model. Especially the latter require as input values of turbulent kinetic energy and dissipation, which as shown subsequently are not readily obtained from the most common approach to add a bubble-induced contribution to the effective viscosity. This may be overcome by including source terms in the single phase two-equation turbulence models that describe the bubble effects on the liquid turbulence. However, no consensus on the precise form of these terms has been reached yet. We here report a comparison of different models of this type. Special care has been given to the selection of a rather comprehensive set of reference data allowing to qualify the validity of the different models. Conclusions towards best practice guidelines for modeling bubbly turbulence are drawn and needs for further research identified.

► Drag law for gas–solids flow using particle-resolved simulation of fixed spheres. ► Numerical method PUReIBM based on immersed boundary method with no forcing in fluid. ► PUReIBM is accurate, numerically convergent and consistent with two-fluid theory. ► New drag correlation is proposed that can be used in CFD simulation of fluidized beds. Gas–solid momentum transfer is a fundamental problem that is characterized by the dependence of normalized average fluid–particle force on solid volume fraction and the Reynolds number based on the mean slip velocity Re . In this work we report particle-resolved direct numerical simulation (DNS) results of interphase momentum transfer in flow past fixed random assemblies of monodisperse spheres with finite fluid inertia using a continuum Navier–Stokes solver. This solver is based on a new formulation we refer to as the Particle-resolved Uncontaminated-fluid Reconcilable Immersed Boundary Method (PUReIBM). The principal advantage of this formulation is that the fluid stress at the particle surface is calculated directly from the flow solution (velocity and pressure fields), which when integrated over the surfaces of all particles yields the average fluid–particle force. We demonstrate that PUReIBM is a consistent numerical method to study gas–solid flow because it results in a force density on particle surfaces that is reconcilable with the averaged two-fluid theory. The numerical convergence and accuracy of PUReIBM are established through a comprehensive suite of validation tests. The normalized average fluid–particle force is obtained as a function of solid volume fraction (0.1 ⩽ ⩽ 0.5) and mean flow Reynolds number Re (0.01 ⩽ Re ⩽ 300) for random assemblies of monodisperse spheres. These results extend previously reported results of to a wider range of , Re , and are more accurate than those reported by . Differences between the drag values obtained from PUReIBM and the drag correlation of are as high as 30% for Re in the range 100–300. We take advantage of PUReIBM’s ability to directly calculate the relative contributions of pressure and viscous stress to the total fluid–particle force, which is useful in developing drag correlations. Using a scaling argument, proposed that the viscous contribution is independent of Re but the pressure contribution is linear in Re (for Re > 50). However, from PUReIBM simulations we find that the viscous contribution is not independent of the mean flow Reynolds number, although the pressure contribution does indeed vary linearly with Re in accord with the analysis of . An improved correlation for in terms of and Re is proposed that corrects the existing correlations in Re range 100–300. Since this drag correlation has been inferred from simulations of fixed particle assemblies, it does not include the effect of mobility of the particles. However, the fixed-bed simulation approach is a good approximation for high Stokes number particles, which are encountered in most gas–solid flows. This improved drag correlation can be used in CFD simulations of fluidized beds that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

A vaporization model for multi-component fuel sprays is described. The discrete multi-component (DMC) fuel approach was used to model the properties and composition of gasoline and diesel model fuels. Unsteady vaporization of single and multi-component fuel droplets and sprays was considered for both normal and flash-boiling evaporation conditions. An unsteady internal heat flux model and a model for the determination of the droplet surface temperature were formulated. An approximate solution to the quasi-steady energy equation was used to derive an explicit expression for the heat flux from the surrounding gas to the droplet–gas interface, with inter-diffusion of fuel vapor and the surrounding gas taken into account. The density change of the drop as a function of temperature was also considered. In order to treat phase change under trans-critical conditions, a characteristic length was defined to determine the amount of vaporized fuel as a function of time. The present vaporization models were implemented into a multi-dimensional CFD code and applied to calculate evaporation processes of single and multi-component fuel droplets and sprays for various ambient temperatures and droplet temperatures. Differences between representing model fuels using the single and multi-component fuel descriptions are discussed.

► We use DNS to model the flow around four types of non-spherical particles. ► The results are compared to literature correlations. ► New models are proposed for drag, lift and the two torques for the particles. ► The models fit very well with the simulation results. ► These models can be used in large-scale gas–solid computations. This paper derives and validates a new framework to predict the drag and lift coefficients as well as the torque coefficients for four non-spherical particle shapes in a flow with a wide range of flow and rotational numbers. Correlations are proposed for the drag force, the lift force, the pitching torque, and the torque caused by the rotation of the particle. Each of the correlations depends on number, the dimensionless rotation and the angle of incidence between the particle and the direction of the local fluid velocity. The fit parameters in the correlations for each of the particle shapes are determined by performing a large number of “true” DNS simulations of four different types of particles. The true DNS simulations are carried out with an improved mirroring immersed boundary method. The resulting correlations for the forces and the torques are suitable to be used in Eulerian–Lagrangian simulations, where an accurate prediction of the forces and torques is required to determine the motion of the particles.

This paper reports an experimental investigation on the impact dynamics of droplets (water, decane, ethanol, and tetradecane) onto a flat stainless steel surface, using high-speed microphotography and with a particular interest in the effect of surface roughness on the impact dynamics. Results show that the impacting water droplet spreads on the surface in the form of a rim-bounded lamella and the rim contracts back after reaching the maximum spreading, while this contraction motion is absent for the fuel liquids. With the increase of Weber number (We) and surface roughness, splashing, evidenced by the ejection of secondary droplets, is favored. The droplet spreading, which is characterized by a normalized diameter β, is accelerated with increasing We, while the surface roughness and Ohnesorge number (Oh) tend to slow down the spreading process. Furthermore, the maximum normalized spreading diameter, β , depends primarily on the (We/Oh) and the increase in the surface roughness slightly reduces β . The transition from spreading to splashing is enhanced with increasing We or R or both. An empirical correlation of β as a function of the surface roughness was derived based on the present experimental data. In addition, the transition from spreading to splashing can be represented by a critical (We/Oh) , which was fitted as a function of the surface roughness. All the proposed empirical correlations show good agreement with literature data and are believed to be of importance for the spray/wall interaction modelling.

The objective of this paper is to investigate the hydroelastic response of a flexible NACA66 hydrofoil in cavitating flows by combined experimental and numerical studies. Experimental results are presented for rigid/flexible NACA66 hydrofoils fixed at = 8° for subcavitating ( = 8.0) and cavitating flows ( = 1.4). The high-speed video camera and Laser Doppler Vibrometer are applied to investigate the flow patterns and vibration characteristics. The multiphase flow is modeled with the incompressible and unsteady Reynolds Averaged Navier–Stokes (URANS) equations. The SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that the cavitation has significant effect on the foil deformation and the unsteady characteristics of the hydroelastic response. The bending deformation is enhanced when the cavitation occurred. Meanwhile, the hydroelastic response has also affected the cavitation development and the vortex structure interactions. The cavity shedding frequency and vortex shedding and interacting frequency for the flexible hydrofoil are higher than that for the rigid hydrofoil. Compared to the periodic development of the hydrodynamic coefficients for the rigid hydrofoil, the hydrodynamic load coefficients of the flexible hydrofoil fluctuate more significantly, and the chaotic response of the flexible hydrofoil is mainly attributed to the disturbance caused by the flow-induced flutter and deformation of the foil. The evolution of the transient cavity shape and the corresponding hydrodynamic response can be divided into three stages: During the development of the attached cavity, the partial sheet cavity is formed and develops with the lift and drag coefficients increasing, while the maximum attached cavity formed on the suction side of the flexible hydrofoil is larger than that of the rigid hydrofoil, which is caused by the increase of the effective angle of attack due to the twist deformation. During the vortex structure interaction and cavity shedding process, the hydrodynamic loads for the flexible hydrofoil fluctuate because of the foil deformation, leading to a more complex cavitation pattern. During the residual cavity shedding and partial sheet cavity formation process, the cavities, together with the counter-rotational vortex structures, shed downstream totally and are followed by the formation of partial sheet cavities in next period, which is in advance for the flexible hydrofoil due to the larger effective angle of attack.

The main objective of this study is to present new equations for a flow pattern independent drift flux model based void fraction correlation applicable to gas–liquid two phase flow covering a wide range of fluid combinations and pipe diameters. Two separate sets of equations are proposed for drift flux model parameters namely, the distribution parameter and the drift velocity . These equations for and are defined as a function of several two phase flow variables and are shown to be in agreement with the two phase flow physics. The underlying data base used for the performance verification of the proposed correlation consists of experimentally measured 8255 data points collected from more than 60 sources that consists of air–water, argon–water, natural gas–water, air–kerosene, air–glycerin, argon–acetone, argon–ethanol, argon–alcohol, refrigerants (R11, R12, R22, R134a, R114, R410A, R290 and R1234yf), steam–water and air–oil fluid combinations. It is shown that the proposed correlation successfully predicts the void fraction with desired accuracy for hydraulic pipe diameters in a range of 0.5–305 mm (circular, annular and rectangular pipe geometries), pipe orientations in a range of , liquid viscosity in a range of 0.0001–0.6 Pa-s, system pressure in a range of 0.1–18.1 MPa and two phase Reynolds number in a range of 10 to 5 × 10 . Moreover, the accuracy of the proposed correlation is also compared with some of the existing top performing correlations based on drift flux and separated flow models. Based on this comparison, it is found that the proposed correlation consistently gives better performance over the entire range of the void fraction (0 < < 1) and is recommended to predict void fraction without any reference to flow regime maps.

Enhanced convection, transient conduction, microlayer evaporation, and contact line heat transfer have all been proposed as mechanisms by which bubbles transfer energy during boiling. Models based on these mechanisms contain fitting parameters that are used to fit them to the data, resulting a proliferation of “validated” models. A review of the recent experimental, analytical, and numerical work into single bubble heat transfer is presented to determine the contribution of each of the above mechanisms to the overall heat transfer. Transient conduction and microconvection are found to be the dominant heat transfer mechanisms. Heat transfer through the microlayer and at the three-phase contact line do not contribute more than about 25% of the overall heat transfer.

A robust two-phase flow Large Eddy Simulation (LES) algorithm has been developed and applied to predict the primary breakup of an axisymmetric water jet injected into a surrounding coaxial air flow. The high liquid/gas density and viscosity ratios are known to represent a significant challenge in numerical modelling of the primary breakup process. In the current LES methodology, an extrapolated liquid velocity field was used to minimise discretisation errors, whilst maintaining sharp treatment of fluid properties across the interface. The proposed numerical approach showed excellent robustness and high accuracy in predicting coaxial liquid jet primary breakup. Since strong turbulence structures will develop inside the injector at high Reynolds numbers and affect the subsequent primary breakup, the Rescaling and Recycling Method (R M) was implemented to facilitate generation of appropriate unsteady LES inlet conditions for both phases. The influence of inflowing liquid and gas turbulent structures on the initial interface instability was investigated. It is shown that liquid turbulent eddies play the dominant role in the initial development of liquid jet surface disturbance and distortion for the flow conditions considered. When turbulent inflows were specified by the R M technique, the predicted core breakup lengths at different air/water velocities agreed closely with experimental data.

First, a meshless simulation method is presented for multiphase fluid–particle flows with a two-way coupled Smoothed Particle Hydrodynamics (SPH) for the fluid and the Discrete Element Method (DEM) for the solid phase. The unresolved fluid model, based on the locally averaged Navier Stokes equations, is expected to be considerably faster than fully resolved models. Furthermore, in contrast to similar mesh-based Discrete Particle Models (DPMs), our purely particle-based method enjoys the flexibility that comes from the lack of a prescribed mesh. It is suitable for problems such as free surface flow or flow around complex, moving and/or intermeshed geometries and is applicable to both dilute and dense particle flows. Second, a comprehensive validation procedure for fluid–particle simulations is presented and applied here to the SPH–DEM method, using simulations of single and multiple particle sedimentation in a 3D fluid column and comparison with analytical models. Millimetre-sized particles are used along with three different test fluids: air, water and a water–glycerol solution. The velocity evolution for a single particle compares well (less than 1% error) with the analytical solution as long as the fluid resolution is coarser than two times the particle diameter. Two more complex multiple particle sedimentation problems (sedimentation of a homogeneous porous block and an inhomogeneous Rayleigh Taylor Instability) are also reproduced well for porosities , although care should be taken in the presence of high porosity gradients. Overall the SPH–DEM method successfully reproduces quantitatively the expected behaviour in these test cases, and promises to be a flexible and accurate tool for other, realistic fluid–particle system simulations (for which other problem-relevant test cases have to be added for validation).

► Preferential concentration of inertial particles in turbulent flows is reviewed. ► We describe the tools used to diagnose and analyse preferential concentration. ► We conclude on remaining open questions and on expected future breakthrough. Particle laden flows are of relevant interest in many industrial and natural systems. When the carrier flow is turbulent, a striking feature is the tendency of particles denser than the fluid to inhomogeneously distribute in space, forming clusters and depleted regions. This phenomenon, known as “preferential concentration”, has now been extensively investigated since the 1960s. The commonly invoked turbophoretic effect, responsible for the centrifugation of heavy particles outside the turbulent vortices, has recently got more complex by other additional mechanisms which have been shown to potentially play an important role in segregating the particles (for instance particles with moderate Stokes number have been shown to preferentially stick to low-acceleration points of the carrier flow). As a matter of fact a complete frame for accurately describing and modeling the particle-flow interaction is not yet available and basic questions, as the existence or not of a typical cluster size or of a typical cluster life-time-scale, still remain to be answered. This requires further quantitative investigations of preferential concentration (both from experiments and numerics) as well as dedicated mathematical tools in order to analyze the dispersed phase, its structuring properties and its dynamics (from individual particle level up to clusters level). This review focuses on the description of the techniques available nowadays to investigate the preferential concentration of inertial particles in turbulent flows. We first briefly recall the historical context of the problem followed by a description of usual experimental and numerical configurations classically employed to investigate this phenomenon. Then we present the main mathematical analysis techniques which have been developed and implemented up to now to diagnose and characterize the clustering properties of dispersed particles. We show the advantages, drawbacks and complementarity of the different existing approaches. To finish, we present physical mechanisms which have already been identified as important and discuss the expected breakthrough from future investigations.

Numerical simulations are carried out to describe the dense zone of a spray where very little information is available, either from experimental or theoretical approaches. Interface tracking is ensured by the level set method and the ghost fluid method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. The level set method is coupled with the VOF method for mass conservation. The level set–VOF coupling is validated on 2D and 3D test cases. The level set–ghost fluid method is applied to the Rayleigh instability of a liquid jet. Preliminary results are then presented for 3D simulation of the primary break-up of a turbulent liquid jet with the level set–VOF–ghost fluid method.