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This review is motivated by the fast progress in our understanding of the physics of particle-laden turbulence in the last decade, partly due to the tremendous advances of measurement and simulation capabilities. The focus is on spherical particles in homogeneous and canonical wall-bounded flows. The analysis of recent data indicates that conclusions drawn in zero gravity should not be extrapolated outside of this condition, and that the particle response time alone cannot completely define the dynamics of finite-size particles. Several breakthroughs have been reported, mostly separately, on the dynamics and turbulence modifications of small inertial particles in dilute conditions and of large weakly buoyant spheres. Measurements at higher concentrations, simulations fully resolving smaller particles, and theoretical tools accounting for both phases are needed to bridge this gap and allow for the exploration of the fluid dynamics of suspensions, from laminar rheology and granular media to particulate turbulence.

We propose an analytical model to estimate the interface temperature $\varTheta _{\varGamma }$ and the Nusselt number $Nu$ for an evaporating two-layer Rayleigh–Bénard configuration in statistically stationary conditions. The model is based on three assumptions: (i) the Oberbeck–Boussinesq approximation can be applied to the liquid phase, while the gas thermophysical properties are generic functions of thermodynamic pressure, local temperature and vapour composition, (ii) the Grossmann–Lohse theory for thermal convection can be applied to the liquid and gas layers separately and (iii) the vapour content in the gas can be taken as the mean value at the gas–liquid interface. We validate this setting using direct numerical simulations in a parameter space composed of the Rayleigh number ( $10^6\leq Ra\leq 10^8$ ) and the temperature differential ( $0.05\leq \varepsilon \leq 0.20$ ), which modulates the variation of state variables in the gas layer. To better disentangle the variable property effects on $\varTheta _\varGamma$ and $Nu$ , simulations are performed in two conditions. First, we consider the case of uniform gas properties except for the gas density and gas–liquid diffusion coefficient. Second, we include the variation of specific heat capacity, dynamic viscosity and thermal conductivity using realistic equations of state. Irrespective of the employed setting, the proposed model agrees very well with the numerical simulations over the entire range of $Ra$ – $\varepsilon$ investigated.

We consider suspensions of finite-size neutrally buoyant rigid spherical particles in channel flow and investigate the relevance of different momentum transfer mechanisms and the relation between the local particle dynamics and the bulk flow properties in the highly inertial regime. Interface-resolved simulations are performed in the range of Reynolds numbers $3000 \leq Re \leq 15\ 000$ and solid volume fractions $0 \leq \phi \leq 0.3$ . The Lagrangian particle statistics show that pair interactions are highly inhomogeneous and dependent on the distance from the wall: in their vicinity, the underlying mean shear drives the pair interactions, while a high degree of isotropy, dictated by more frequent collisions, characterizes the core region. Analysis of the momentum balance reveals that while the particle-induced stresses govern the dynamics in dense conditions, $\phi =0.3$ , and moderate Reynolds numbers, $Re , the turbulent stresses take over at higher Reynolds numbers. This behaviour is associated with a reduced particle migration toward the channel core, which decreases the importance of the particle-induced stress and increases the turbulent activity. Our results indicate that Reynolds stresses and the associated velocity fluctuations, characteristics of near-wall turbulence, prevail at high inertia over the resistance to deformation presented by the particles for volume fractions lower than 30 %.

The dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at Rλ ≈ 140, the highest attained up to now. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality.

Emulsions are a major class of multiphase flows, crucial in industrial process (e.g. food and drug production) and ubiquitous in environmental flows (e.g. oil spilling in maritime environment). Already at volume fractions of few precents, the dispersed phase interacts with pre-existing turbulence created at large scale, yet the interaction between phases and the turbulent energy transport across scales is not yet fully understood.In this work, we use Direct Numerical Simulation to study emulsions in homogeneous and isotropic turbulence, where the Volume of Fluid (VoF) method is used to represent the complex features of the liquid-liquid interface.We consider a mixture of two matching-density phases, where we vary volume fraction, viscosity ratio and large-scale Weber number aiming at understanding the turbulence modulation and the observed droplet size distributions. The analysis, based on the spectral scale-by-scale analysis, reveals that energy is consistently transported from large to small scales by the interface, and no inverse cascade is observed. We find that the total surface is directly proportional to the amount of energy transported, and that the energy transfer in the inertial range provides information about the droplet dynamics. We observe the -10/3 and -3/2 scaling on droplet size distributions, suggesting that the dimensional arguments which led to their derivation are verified in HIT conditions and denser conditions. Finally, we discuss the highly intermittent behaviour of the multiphase flow, which can be directly related to the polydisperse nature of the flow.The study provides some significant observations towards a more comprehensive understanding of multiphase turbulence, opening new questions for future studies.

This study discusses turbulent suspension flows of non-Brownian, non-colloidal, neutrally buoyant and rigid spherical particles in a Newtonian fluid over porous media with particles too large to penetrate and move through the porous layer. We consider suspension flows with the solid volume fraction ${{\varPhi _b}}$ ranging from 0 to 0.2, and different wall permeabilities, while porosity is constant at 0.6. Direct numerical simulations with an immersed boundary method are employed to resolve the particles and flow phase, with the volume-averaged Navier–Stokes equations modelling the flow within the porous layer. The results show that in the presence of particles in the free-flow region, the mean velocity and the concentration profiles are altered with increasing porous layer permeability because of the variations in the slip velocity and wall-normal fluctuations at the suspension-porous interface. Furthermore, we show that variations in the stress condition at the interface significantly affect the particle near-wall dynamics and migration toward the channel core, thereby inducing large modulations of the overall flow drag. At the highest volume fraction investigated here, ${{\varPhi _b}}= 0.2$ , the velocity fluctuations and the Reynolds shear stress are found to decrease, and the overall drag increases due to the increase in the particle-induced stresses.

We perform immersed-boundary-method numerical simulations of small amplitude oscillatory shear flow of suspensions of monodisperse noncolloidal rigid spherical particles in non-Newtonian liquids from the dilute to the concentrated regime. We study the influence of suspending liquid inertia and rheology and particle concentration on the computationally measured storage and loss moduli of the suspensions. In particular, the rheology of the suspending liquid is modeled through the inelastic shear-thinning Carreau-Yasuda constitutive equation and the viscoelastic Giesekus and Oldroyd-B constitutive equations. The role of inertia is quantified by the Stokes number, St, whereas the relevance of the non-Newtonian effects of the suspension matrix is measured through the Carreau number, Cu, for the Carreau-Yasuda liquid and the Deborah number, De, for the viscoelastic liquids. In suspensions with a Carreau-Yasuda matrix, both the storage and the loss modulus increase with St and decrease with Cu, yet the order of magnitude of Cu has to be greater than unity for these effects to be visible. In suspensions with a viscoelastic matrix, both the moduli increase with St and have a nonmonotonic trend with De, showing a maximum with no quantitative differences between the results pertaining suspensions with Giesekus and Oldroyd-B constitutive equations.

This study presents direct numerical simulations of turbulent Rayleigh–Bénard convection in non-colloidal suspensions, with special focus on the heat transfer modifications in the flow. Adopting a Rayleigh number of $10^8$ and Prandtl number of 7, parametric investigations of the particle volume fraction $0\leq \varPhi \leq 40\,\%$ and particle diameter $1/20\leq d^*_p\leq 1/10$ with respect to the cavity height, are carried out. The particles are neutrally buoyant, rigid spheres with physical properties that match the fluid phase. Up to $\varPhi =25\,\%$ , the Nusselt number increases weakly but steadily, mainly due to the increased thermal agitation that overcomes the decreased kinetic energy of the flow. Beyond $\varPhi =30\,\%$ , the Nusselt number exhibits a substantial drop, down to approximately 1/3 of the single-phase value. This decrease is attributed to the dense particle layering in the near-wall region, confirmed by the time-averaged local volume fraction. The dense particle layer reduces the convection in the near-wall region and negates the formation of any coherent structures within one particle diameter from the wall. Significant differences between $\varPhi \leq 30\,\%$ and 40 % are observed in all statistical quantities, including heat transfer and turbulent kinetic energy budgets, and two-point correlations. Special attention is also given to the role of particle rotation, which is shown to contribute to maintaining high heat transfer rates in moderate volume fractions. Furthermore, decreasing the particle size promotes the particle layering next to the wall, inducing a similar heat transfer reduction as in the highest particle volume fraction case.

This work presents the GPU acceleration of the open-source code CaNS for very fast massively-parallel simulations of canonical fluid flows. The distinct feature of the many-CPU Navier–Stokes solver in CaNS is its fast direct solver for the second-order finite-difference Poisson equation, based on the method of eigenfunction expansions. The solver implements all the boundary conditions valid for this type of problems in a unified framework. Here, we extend the solver for GPU-accelerated clusters using CUDA Fortran. The porting makes extensive use of CUF kernels and has been greatly simplified by the unified memory feature of CUDA Fortran, which handles the data migration between host (CPU) and device (GPU) without defining new arrays in the source code. The overall implementation has been validated against benchmark data for turbulent channel flow and its performance assessed on a NVIDIA DGX-2 system (16 T V100 32Gb, connected with NVLink via NVSwitch). The wall-clock time per time step of the GPU-accelerated implementation is impressively small when compared to its CPU implementation on state-of-the-art many-CPU clusters, as long as the domain partitioning is sufficiently small that the data resides mostly on the GPUs. The implementation has been made freely available and open source under the terms of an MIT license.

We present the Fluid Transport Accelerated Solver, FluTAS, a scalable GPU code for multiphase flows with thermal effects. The code solves the incompressible Navier-Stokes equation for two-fluid systems, with a direct FFT-based Poisson solver for the pressure equation. The interface between the two fluids is represented with the Volume of Fluid (VoF) method, which is mass conserving and well suited for complex flows thanks to its capacity of handling topological changes. The energy equation is explicitly solved and coupled with the momentum equation through the Boussinesq approximation. The code is conceived in a modular fashion so that different numerical methods can be used independently, the existing routines can be modified, and new ones can be included in a straightforward and sustainable manner. FluTAS is written in modern Fortran and parallelized using hybrid MPI/OpenMP in the CPU-only version and accelerated with OpenACC directives in the GPU implementation. We present different benchmarks to validate the code, and two large-scale simulations of fundamental interest in turbulent multiphase flows: isothermal emulsions in HIT and two-layer Rayleigh-Bénard convection. FluTAS is distributed through a MIT license and arises from a collaborative effort of several scientists, aiming to become a flexible tool to study complex multiphase flows. QC 20220524

The dynamics of microplastics in the ocean can be modeled similarly to natural particles such as sediment grains, marine snow, phyto- and zooplankton. The settling of the particle is important not only for the individual particle motion, but it also affects the encounter rate, which is important for several physical processes such as nutrient uptake, biofouling, the degradation of microplastics and transport of pollutants into the food chain in the marine environment.Some of the factors that determine the collision and accumulation of the particles are the level of turbulence, buoyancy, particle shape and diffusivity. Microplastics are often elongated in shape, whereas phytoplankton often form long chains colonies and filaments, even if these are unicellular, which makes the investigation as nonspherical particles in turbulent flows relevant. The objective of this study is to quantify how turbulence affects collision kernels of the nonspherical settling particles. This work is motivated by recent studies in laminar flows showing how collisions between fiber-like particles are much more frequent than those between spherical particles, even in the presence of turbulence (Slomka, J., Stocker, R., 2020. On the collision of rods in a quiescent fluid, Proceedings of the National Academy of Sciences 117, 3372-3374). To this end, we shall consider particles as elongated spheroids. Given the low-density ratios, close to 1, and the size, order of microns, inertia can be neglected, and the particle velocity is assumed to be equal to the sum of the fluid velocity at the particle position and the settling speed. The settling speed is taken to be the Stokes settling velocity for oblate spheroids, function of the object orientation and aspect ratio; note that this is not parallel to gravity for any general orientation. We report results from simulations of sinking inertia-less elongated spheroids in homogeneous isotropic turbulence (HIT). The velocity field is assumed to be incompressible and to obey the Navier-Stokes and continuity equation. To maintain the turbulent velocity in a statistically steady state, a random forcing field is needed. The elongated spheroids studied here are small compared to the Kolmogorov length scale of the turbulence and have different aspect ratios: 1 (spheres), 2, 5, 10 and 20. We will present results for two different settling velocities – equal to 1 Kolmogorov and 3 times the Kolmogorov velocity, velocity scale of the smallest vortices in the flow. In order to quantify clustering in fully three-dimensional isotropic turbulent flows, the radial pair distribution function (r.d.f.) is used, which provides information about the collision rates when combined with the relative particle velocity at distances of the order of the particle size.We show that the effect of the different collisional relative velocity has a greater impact than the patchiness on the increase of the collision rate. For larger settling velocities, i.e. larger particle sizes, the collision rates of elongated particles increase with the aspect ratio, an increase however smaller than that observed in quiescent flows. Results obtained for the collision of particles of different buoyancy will also be presented.

Using DNS-based Eulerian-Lagrangian simulations, we investigate the dynamics of small gyrotactic swimmers in free-surface turbulence. We consider open channel flow turbulence in which bottom-heavy swimmers are dispersed. Swimmers are characterized by different vertical stability, so that some realign to swim upward with a characteristic time smaller than the Kolmogorov time scale, while others possess a re-orientation time longer than the Kolmogorov time scale. We cover one order of magnitude in the flow Reynolds number, and two orders of magnitude in the stability number, which is a measure of bottom heaviness. We observe that large-scale advection dominates vertical motion when the stability number, scaled on the local Kolmogorov time scale of the flow, is larger than unity: This condition is associated to enhanced migration towards the surface, particularly at low Reynolds number, when swimmers can rise through surface renewal motions that originate directly from the bottom-boundary turbulent bursts. Conversely, small-scale effects become more important when the Kolmogorov-based stability number is below unity: Under this condition, migration towards the surface is hindered, particularly at high Reynolds, when bottom-boundary bursts are less effective in bringing bulk fluid to the surface. In an effort to provide scaling arguments to improve predictions of models for motile micro-organisms in turbulent water bodies, we demonstrate that a Kolmogorov-based stability number around unity represents a threshold beyond which swimmer capability to reach the free surface and form clusters saturates.

Recent experiments report that slowly sheared noncolloidal particle suspensions unexpectedly exhibit rate(ω)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that van der Waals attraction gives rise to this behavior. At volume fractions φ=20-50%, the complex viscosities in both experiments and simulations display power-law reductions in shear, with a φ-dependent exponent maximum at φ=40%, resulting from the interplay between hydrodynamic, collision, and adhesive interactions. Furthermore, this rate dependence is accompanied by diverging particle diffusivities and pronounced cluster formations after repeated oscillations. Previous studies established that suspensions transition from reversible absorbing states to irreversible diffusing states when the oscillation amplitude exceeds a φ-dependent critical value γ0,φc. Here, we show that a second transition to irreversibility occurs below an ω-dependent critical amplitude, γ0,ωc≤γ0,φc, in the presence of weak attractions.

We propose and validate a novel experimental technique to measure two-point statistics of turbulent flows. It consists of spreading rigid fibers in the flow and tracking their position and orientation in time and is therefore named “fiber tracking velocimetry.” By choosing different fiber lengths, i.e., within the inertial or dissipative range of scales, the statistics of turbulence fluctuations at the selected length scale can be probed accurately by simply measuring the fiber velocity at its two ends and projecting it along the transverse-to-fiber direction. By means of fully resolved direct numerical simulations and experiments, we show that these fiber-based transverse velocity increments are statistically equivalent to the (unperturbed) flow transverse velocity increments. Moreover, we show that the turbulent energy-dissipation rate can be accurately measured exploiting sufficiently short fibers. The technique is tested against standard particle tracking velocimetry (PTV) of flow tracers with excellent agreement. Our technique overcomes the well-known problem of PTV to probe two-point statistics reliably because of the fast relative diffusion in turbulence that prevents the mutual distance between particles to remain constant at the length scale of interest. This problem, making it difficult to obtain converged statistics for a fixed separation distance, is even more dramatic for natural flows in open domains. A prominent example is oceanic currents, where drifters (i.e., the tracer-particle counterpart used in field measurements) disperse quickly, but at the same time their number has to be limited to save costs. Inspired by our laboratory experiments, we propose pairs of connected drifters as a viable option to solve the issue., Physical Review X, 11 (3), ISSN:2160-3308

The Scientific Program and Book of Abstracts of the EUROMECH Colloquium 621 "Transport and Fluxes in Dispersed Turbulent Flows", Reykjavik, June 30, July 1-2 2021 (virtual event, due to the COVID-19 pandemic).

A numerical and theoretical study of yield-stress fluid flows in two types of model porous media is presented. We focus on viscoplastic and elastoviscoplastic flows to reveal some differences and similarities between these two classes of flows. Small elastic effects increase the pressure drop and also the size of unyielded regions in the flow which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects. By increasing the yield stress, the difference in the pressure drops between the two classes of flows becomes smaller and smaller for both considered geometries. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and some oscillations in the flow can be observed. Focusing on the regime of very large yield stress effects in the viscoplastic flow, we address in detail the interesting limit of ‘flow/no flow’: yield-stress fluids can resist small imposed pressure gradients and remain quiescent. The critical pressure gradient which should be exceeded to guarantee a continuous flow in the porous media will be reported. Finally, we propose a theoretical framework for studying the ‘yield limit’ in the porous media.

We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$. The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$. The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v^{\prime }$), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.

The flapping states of a flexible fiber fully coupled to a three-dimensional turbulent flow are investigated via state-of-the-art numerical methods. Two distinct flapping regimes are predicted by the phenomenological theory recently proposed by Rosti et al. [Phys. Rev. Lett. 121, 044501, 2018]: the under-damped regime, where the elasticity strongly affects the fiber dynamics, and the over-damped regime, where the elastic effects are strongly inhibited. In both cases we can identify a critical value of the bending rigidity of the fiber by a resonance condition, which further provides a distinction between different flapping behaviors, especially in the under-damped case. We validate the theory by means of direct numerical simulations and find that, both for the over-damped regime and for the under-damped one, fibers are effectively slaved to the turbulent fluctuations and can therefore be used as a proxy to measure various two-point statistics of turbulence. Finally, we show that this holds true also in the case of a passive fiber, without any feedback force on the fluid.

We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.

Self-propelled jumping of two polymeric droplets on superhydrophobic surfaces is investigated by three-dimensional direct numerical simulations. Two identical droplets of a viscoelastic fluid slide, meet and coalesce on a surface with contact angle 180 degrees. The droplets are modelled by the Giesekus constitutive equation, introducing both viscoelasticity and a shear-thinning effects. The Cahn-Hilliard Phase-Field method is used to capture the droplet interface. The simulations capture the spontaneous coalescence and jumping of the droplets. The effect of elasticity and shear-thinning on the coalescence and jumping is investigated at capillary-inertial and viscous regimes. The results reveal that the elasticity of the droplet changes the known capillary-inertial velocity scaling of the Newtonian drops at large Ohnesorge numbers; the resulting viscoelastic droplet jumps from the surface at larger Ohnesorge numbers than a Newtonian drop, when elasticity gives rise to visible shape oscillations of the merged droplet. The numerical results show that polymer chains are stretched during the coalescence and prior to the departure of two drops, and the resulting elastic stresses at the interface induce the jumping of the liquid out of the surface. This study shows that viscoelasticity, typical of many biological and industrial applications, affects the droplet behaviour on superhydrophobic and self-cleaning surfaces.

Much work has been done to understand the settling dynamics of spherical particles in a homogeneous and stratified fluid. However, the effects of shape anisotropy on the settling dynamics of a particle in a stratified fluid are not completely understood. To this end, we perform numerical simulations for settling oblate and prolate spheroids in a stratified fluid. We present the results for the Galileo number, $Ga$ , in the range 80–250 and the Richardson number, $Ri$ , in the range 0–10. We find that both the oblate and prolate spheroids reorient to the edge-wise and partially edge-wise orientations, respectively, as they settle in a stratified fluid completely different from the steady-state broad-side on orientation observed in a homogeneous fluid. We observe that reorientation instabilities emerge when the velocity magnitudes of the spheroids fall below a particular threshold. We also report the enhancement of the drag on the particle from stratification. The torque due to buoyancy effects tries to orient the spheroid in an edge-wise orientation while the hydrodynamic torque tries to orient it to a broad-side on orientation. Below the velocity threshold, the buoyancy torque dominates; resulting in the onset of reorientation instability. Finally, the asymmetry in the distribution of the baroclinic vorticity generation term around the spheroids explains the onset of the reorientation instability.

We perform simulations of suspension of capsules with nucleus in shear flow. Every capsule is modeled as a neo-Hookean hyperelastic membrane enclosing a rigid particle with radius equal to the half capsule radius. The rheology of the suspensions is related to the capsule deformation and orientation when varying the membrane stiffness and capsule volume fraction and compared to the dynamics of capsules without nucleus.

This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In contrast to the classical conservative four-equation model formulation, the adopted set of equations features volume fraction, temperature, velocity and pressure as the primary variables. The model includes the effects of viscosity, surface tension, thermal conductivity and gravity, and has the ability to incorporate complex equations of state. Additionally, a Gibbs free energy relaxation procedure is used to model mass transfer. A key characteristic of the proposed methodology is the use of high performance and scalable solvers for the solution of the Helmholtz equation for the pressure, which drastically reduces the computational cost compared to analogous density-based approaches. We demonstrate the capabilities of the methodology to simulate flows with large density and viscosity ratios through extended verification against a range of different test cases. Finally, the potential of the methodology to tackle challenging phase change flows is demonstrated with the simulation of three-dimensional nucleate boiling.