In this work, an a priori investigation of a novel family of subgrid scale (SGS) models for the large eddy simulation (LES) is presented. This family of models has the particularity to preserve the Lie-symmetries of the incompressible Navier-Stokes equations. The a priori tests are conducted on the numerical results of a (forced) homogeneous, isotropic and turbulent (HIT) flow which are available in the John Hopkins’ database (JHTDB). In addition to the new family of invariant models, several established subgrid scale models, including scale similarity models, eddy viscosity models and a non linear model are considered for comparison. The accuracy and performance of the models are quantified using the correlation coefficient between the reference subgrid scale tensor and the models. Both box and spectral filters are considered with different filter sizes. The energy dissipation is also evaluated to assess the capability of the models to correctly capture the energy-transfer between the resolved and the unresolved scales. The general invariant model is found to behave similarly to the non linear model of Lund and Novikov, yielding a correlation coefficient of η = 0.8 at small filter widths. Moreover, it closely matches the true subgrid scale dissipation and accounts for backscatter.

This article surveys the formulation and discretization of inertial terms for incompressible two-phase flows with large viscosity and density ratios. The covered topics include progress in the discretization of the momentum equation, with a particular focus on pressure-velocity coupling, together with an algebraic momentum-preserving scheme. The implementation and exploration of approximate momentum conservation based on the integration of auxiliary density equations on a staggered mesh are also discussed. The new algebraic scheme is applied to challenging interfacial flows, such as droplet impacts at high density and viscosity ratios, demonstrating accuracy and stability.

We present a robust, accurate, and computationally efficient numerical strategy for modeling species transfer across immiscible fluid interfaces on Cartesian meshes. The method provides an efficient alternative to the classical one-fluid approach while retaining its algorithmic simplicity and limited computational overhead. The proposed framework relies on a two-phase formulation in cut cells, combining dedicated phase reconstructions with a simple and robust mass-flux approximation to accurately enforce interfacial jump conditions.The method is first assessed against analytical solutions for pure diffusion in both static and moving configurations. Compared with the standard one-fluid model, we demonstrate that appropriate phase reconstructions for the advection and the temporal scheme significantly improve the accuracy of the concentration field, including mean mass fluxes and interfacial concentrations. The approach is then validated on fully coupled three-dimensional simulations of mass transfer on rising bubbles. The computed Sherwood numbers are compared with established numerical results from the literature. While the Sherwood number is shown to be an unreliable indicator of concentration-field accuracy, the proposed schemes provide accurate and robust mass transfer predictions over a wide range of grid resolutions. Overall, the method achieves a substantial gain in accuracy for interfacial mass transfer at a computational cost that is comparable to the classical one-fluid formulations.

Phase change at the interface between a liquid and a gas, commonly referred to as bulk condensation/boiling or interface condensation/boiling, is often overshadowed by wall condensation/boiling. However, interfacial phase change plays a critical role in various industrial applications, including boiling flows in microchannels and boiling liquid metal flows. In this article, we introduce a novel analytical model based on the gradient method. This model accounts for interfacial phase change within multi-field codes. It is validated against both analytical and experimental cases involving bulk boiling, demonstrating excellent agreement. Notably, the mesh convergence aligns with the methods employed in single-fluid codes. Additionally, we propose a hybrid approach that combines the high accuracy of this model with the computational efficiency of dispersed methods.

This paper investigates an approximate block factorization technique for efficiently solving large saddle point systems derived from the discretization of the Navier–Stokes equations. The standard upper triangular approximation is revisited with the addition of a lower block, specifically designed to improve system conditioning and accelerate iterative solver convergence. Numerical experiments highlight the robustness and efficiency of the lower-upper triangular approximation as a preconditioning strategy, particularly in massively parallel environments. The method proves especially effective for simulating multiphase flows with high density and viscosity ratios, complex droplet dynamics, and significant interface deformations.

In this paper, we introduce a compressible formulation for dealing with 2D/3D compressible interfacial flows. It integrates a monolithic solver to achieve robust velocity–pressure coupling, ensuring precision and stability across diverse fluid flow conditions, including incompressible and compressible single-phase and two-phase flows. Validation of the model is conducted through various test scenarios, including Sod’s shock tube problem, isothermal viscous two-phase flows without capillary effects, and the impact of drops on viscous liquid films. The results highlight the ability of the scheme to handle compressible flow situations with capillary effects, which are important in computational fluid dynamics (CFD).

Over the past two decades, numerical modelling of boiling flows in microchannels has gained significant importance across diverse domains encompassing electronics and aerospace devices, where it plays a pivotal role in fostering the creation of compact cooling systems. Furthermore, this research is of critical importance in optimizing the drying process of porous media, especially within the field of nuclear industry applications, particularly in the context of addressing failed fuel rods. Boiling flows in microchannels exhibit marked distinctions from their counterparts in conventional channels. Typically, the bubble diameters in microchannels exceed or closely match the channel dimensions, thereby introducing notable confinement effects as bubbles expand against the channel walls. Therefore, surface tension and wettability effects assume a pronounced role in this scenario and need to be considered. Finally, microchannels typically witness limited occurrences of boiling at their channel walls, with nucleate boiling being less prevalent, as the primary boiling takes place at the interface between bubbles and the liquid. Numerical simulations of boiling flows in microchannels were conducted using the industrial software neptune_cfd. Using the pre-existing Large Interface Model, these simulations employed an interface tracking approach that considers surface tension and wettability effects when modelling vapour bubbles. This paper introduces a novel analytical mass transfer model based on a cut-cell method. Notably, this new model exhibits rapid mesh convergence, with validation studies demonstrating its ability to reach convergence with cells three times larger than the previous model. The validation of this method encompassed a range of 3D scenarios, including the growth of a vapour bubble in an unbounded superheated liquid (the Scriven case) and the buoyant ascent of a bubble within a superheated liquid. Furthermore, this study delves into more intricate scenarios, specifically those characterized by confinement and wettability effects within realistic microchannels.

A single-field representation is derived to describe a multi-species gas flow seeded with perfectly rigid, non-porous and partially inert particles. Indeed, the latter are not involved in heterogeneous reactions with the gas phase (no consumption of the solid by the gas), but they are expected to potentially undergo adsorption and recombination of gaseous radicals on their surface, resulting in the desorption of stable species into the gas. In this work, integral balances are first established at the gas-solid interface, consistent with the local single-phase equations for reactive multi-species gas flow. This allows rigorous derivation of the jump equations that apply at the gas-solid interface in the presence of surface reactions. Then, the description in terms of local single-phase equations, completed by the jump equations at the interface, is recast into a set of equations for the full domain in the sense of distributions. The result extends Kataoka’s formalism (Kataoka, 1986) to reactive gas-solid flow in the presence of both homogeneous and surface reactions.

Computational Fluid Dynamics (CFD) simulations are performed in this work on an experiment where polydisperse steam bubbles are condensed in sub-cooled water.The saturated steam bubbles are injected in subcooled water inside a large vertical pipe and the steam volume fraction, velocity, bubble size distribution and liquid temperature are measured as radial profile at different heights.Six test cases with various pressure, liquid sub-cooling and diameter of the gas injection orifices are simulated.The simulations are largely improved by the introduction of a bubble collapse model in the Interfacial Area Transport Equation (IATE) of Neptune_CFD code.This model allows to consider the phenomena of polydisperse bubbles condensation despite the monodisperse model used in the one-group IATE and gives equivalent results as MUltiple-SIze Group (MUSIG) model with a reduced computational cost.

An accurate modeling of the bubble condensation phenomena in sub-cooled water is developed in this work, using a two-fluid model with one disperse phase and one Interfacial Area Transport Equation (IATE). For this, the aspects of some models are investigated, such as the choice of population balance models, Nusselt closure model and bubble collapse model in IATE. The standard method of moments is formulated using two different bubble size distribution functions among all, namely Dirac and quadratic laws. Therefore, different models for mass and energy interfacial transfers, interfacial forces and source terms of the IATE are developed using both functions. While limited differences are noticeable for the mass and energy transfers obtained by both functions, the results are largely improved using quadratic function for the drag force term and for the IATE source terms. Moreover, the simulations results show that the widely used Ranz-Marshall correlation clearly underestimates the condensation rate. However, this work shows that Chen-Mayinger correlation is relevant to simulate this type of flow, regardless the distribution function. Afterwards, a model is introduced to take into account the effect of bubble collapse by condensation in the IATE. The numerical results obtained using the quadratic function, the collapse model in the IATE and the Chen-Mayinger correlation are comparable to those obtained by the inhomogeneous MUltiple Size Group (iMUSIG) approach, while being less time-consuming.

AbstractAn efficient parallel implementation of the phase field method for quasi-brittle crack simulations able to run on supercomputers with a large number of processes is proposed. This framework uses the finite-element method on 3D structured meshes, and was developed for distributed memory machines using the Message Passing Interface (MPI) for workload distribution and data communication between processes. Parallel assembly is carried out to build the matrices associated with the linear systems of equations. In the proposed context, linear systems derived from displacement and damage discretizations are solved using parallel solvers and preconditioners from the PETSc (Portable, Extensible Toolkit for Scientific Computation) library. All additional operations in this implementation are also efficiently parallelized. Performance analysis shows linear acceleration with an efficiency of $$97\%$$ 97 % for a computation on 6400 processes and over $$80\%$$ 80 % for a computation on 10240 processes. The linear systems involved in the simulations with up to $$10^{10}$$ 10 10 degrees of freedom can be solved in a few seconds. The methodology is applied to quasi-brittle simulations, involving alternate solving of large linear systems and incremental evolution. The applications presented to illustrate the parallel framework involve crack initiation and propagation in strongly heterogeneous materials with a detailed description of the microstructure. Large three-dimensional periodic structures and a realistic geometrical model directly obtained by micro-CT imagery are used.

A statistic-volume averaged two-fluid model, convenient for subchannel and system codes in nuclear industry, is established from RANS equations of Neptune_CFD code and leads to the appearance of subgrid terms. A database of simulations is made on experiments with flow representative of nuclear reactor cores with cylindrical (KIT) and subchannel (PSBT) configurations. The subgrid terms are then compared to the convection terms on the database of 82 test cases. Concerning momentum and energy equations, subgrid terms reach respectively 7.5% and 16% of convection terms. Overall, the comparison shows that dispersion terms are always greater than turbulence terms, but both remain in the same order of magnitude, and are not negligible compared to convection. Moreover, the geometry has an impact on the dispersion terms. This observation suggests that caution should be exercised when using correlation established on a different geometry.

The CFD numerical study of the flash boiling phenomenon of a water film was conducted using an Euler–Euler method, and compared to the experiments on the flashing of a water film. The water film is initially heated at temperatures ranging from 34 to 74 ∘C (frim 1 to 41 ∘C superheat), and the pressure is decreased from 1 bar to 50 mbar during the experiments. This paper shows that the experiments could not be correctly modelled by a simple liquid/bubble model because of the overestimation of the drag force above the water film (in the gas/droplet region). The generalised large interface model (GLIM), however, a multi-regime approach implemented in the version 7.0 of the neptune_cfd software, is able to differentiate the water film, where liquid/bubble interactions are predominant from the gas region where gas/droplet interactions are predominant, and gives nice qualitative results. Finally, this paper shows that the interfacial heat transfer model of Berne for superheated liquids could accurately predict the evolution of the water temperature over time.

This contribution is an experimental and numerical study on the breach of a containment barrier subject to the transient wake of a moving obstacle. In the context of a 100 m3 laboratory with high air exchange rate (8.5 h−1), a passive gaseous contaminant is emitted at a controlled flow rate from the bottom surface of an open cavity (0.8×0.34 m2 wide) swept by a continuous airflow drawn from the lab. Starting from a steady and turbulent airflow situation, a human-sized obstacle passes in front of the cavity and disturbs the established flow. The containment breach is then analyzed by recording time-dependent gas concentrations and velocity components, measured at the cavity open surface, with photoionization detectors and 2D3C PIV, respectively. A penalty method coupled with LES is used to model the experimental setup and predictions are compared to measurements. The numerical model is found to be able to reproduce the contaminant concentrations, air velocities and main POD modes of the flow within experimental inaccuracies. This modeling approach appears to be suitable to study, in-silico, the effect of drafts induced by human motion on aerodynamic barriers. CFD results also show that pollutant leakage is inherently variable, even under stable ventilation conditions. Up to 100% variation of contaminant concentration peaks can be observed, depending on the initial turbulent state of the room.

In the framework of the in-house code Fugu, a fully-coupled solver is developed for massively parallel simulations of three-dimensional incompressible multiphase flows. The linearized momentum and continuity equations arising from the implicit solution of the fluid velocities and pressure are solved simultaneously. The method uses a BiCGStab(2) (Dongarra et al., 1998) iterative solver with an original preconditioner for the velocity block and an approximation of the inverse of the Schur complement. This is achieved by using PFMG or SMG from HYPRE and an efficient sparse matrix–vector multiplication using the CSR storage format. The construction and the tracking of the interface separating the different involved phases is based on a conservative VOF method. Test cases, such as a spherical bubble rising in quiescent liquid and the free fall of a dense sphere, are performed to validate the models, especially in the presence of strong density and viscosity ratios between fluids. Other cases, such as the phase inversion, demonstrate the ability of the new fully-coupled solver to solve two-phase problems with more than 1 billion degrees of freedom with excellent scalability.

Within a flow of a viscous fluid the effects of compression and viscosity are closely coupled with inertia. Discrete mechanics gives a physical sense of these interactions by showing that they exist only in a dynamic vision where the variation of the velocity in time generates the entanglement of the effects of compression and shearing. These two phenomena are described in the form of a Helmholtz–Hodge decomposition by two orthogonal terms within the discrete equation of motion, the first curl-free and the second divergence-free. They can only exchange mechanical energy if the acceleration is nonzero. This entanglement, which occurs at all spatial scales, is a function of longitudinal and transverse celerities. After a presentation of the formal framework, simple examples allow to understand the temporal shifts of direct and induced flows in accordance with the causality principle.