Emmanuel Lévêque’s research while affiliated with École Centrale de Lyon and other places

The development and application of a compressible hybrid lattice Boltzmann method to high Mach number supercritical and dense gas flows are presented. Dense gases, especially in Organic Rankine Cycle turbines, exhibit nonclassical phenomena that offer the possibility of enhancing turbine efficiency by reducing friction drag and boundary layer separation. The proposed numerical framework addresses the limitations of conventional lattice Boltzmann method in handling highly compressible flows by integrating a finite-volume scheme for the total energy alongside a nonideal gas equation of state supplemented by a transport coefficient model. Validations are performed using a shock tube and a three-dimensional Taylor–Green vortex flow. The capability to capture nonclassical shock behaviors and compressible turbulence is demonstrated. Our study gives the first analysis of a turbulent Taylor–Green vortex flow in a dense Bethe–Zel'dovich–Thompson gas and provides comparisons with perfect gas flow at equivalent Mach numbers. The results highlight differences associated with dense gas effects and contribute to a broader understanding of nonideal fluid dynamics in engineering applications.

In mixed-phase clouds, graupel forms by riming, a process whereby ice crystals and supercooled water droplets settling through a turbulent flow collide and aggregate. We consider here the early stage of the collision process of small ice crystals with water droplets and determine numerically the geometric collision kernel in turbulent flows (therefore neglecting all interactions between the particles and assuming a collision efficiency equal to unity), over a range of energy dissipation rate 1–250 cm ² s ⁻³ relevant to cloud microphysics. We take into account the effect of small, but nonzero fluid inertia, which is essential since it favors a biased orientation of the crystals with their broad side down. Since water droplets and ice crystals have different masses and shapes, they generally settle with different velocities. Turbulence does not play any significant role on the collision kernel when the difference between the settling velocities of the two sets of particles is larger than a few millimeters per second. The situation is completely different when the settling speeds of droplets and crystals are comparable, in which case turbulence is the main cause of collisions. Our results are compatible with those of recent experiments according to which turbulence does not clearly increase the growth rate of tethered graupel in a flow transporting water droplets.

Simulating plasmas in the Hall-magnetohydrodynamics (Hall-MHD) regime represents a valuable approach for the investigation of complex nonlinear dynamics developing in astrophysical frameworks and fusion machines. The Hall electric field is computationally very challenging as it involves the integration of an additional term, proportional to $\boldsymbol {\nabla } \times ((\boldsymbol {\nabla }\times \boldsymbol {B})\times \boldsymbol {B})$ , in Faraday's induction law. The latter feeds back on the magnetic field B at small scales (between the ion and electron inertial scales), requiring very high resolutions in both space and time to properly describe its dynamics. The computational advantage provided by the kinetic lattice Boltzmann (LB) approach is exploited here to develop a new code, the fast lattice-Boltzmann algorithm for MHD experiments ( flame ). The flame code integrates the plasma dynamics in lattice units coupling two kinetic schemes, one for the fluid protons (including the Lorentz force), the other to solve the induction equation describing the evolution of the magnetic field. Here, the newly developed algorithm is tested against an analytical wave-solution of the dissipative Hall-MHD equations, pointing out its stability and second-order convergence, over a wide range of the control parameters. Spectral properties of the simulated plasma are finally compared with those obtained from numerical solutions from the well-established pseudo-spectral code ghost . Furthermore, the LB simulations we present, varying the Hall parameter, highlight the transition from the MHD to the Hall-MHD regime, in excellent agreement with the magnetic field spectra measured in the solar wind.

Aims. A linear scaling of the mixed third-order moment of the magnetohydrodynamic (MHD) fluctuations is used to estimate the energy transfer rate of the turbulent cascade in the expanding solar wind. Methods. In 1976, the Helios 2 spacecraft measured three samples of fast solar wind originating from the same coronal hole, at different distances from the Sun. Along with the adjacent slow solar wind streams, these intervals represent a unique database for studying the radial evolution of turbulence in samples of undisturbed solar wind. A set of direct numerical simulations of the MHD equations performed with the Lattice-Boltzmann code FLAME was also used for interpretation. Results. We show that the turbulence energy transfer rate decays approximately as a power law of the distance and that both the amplitude and decay law correspond to the observed radial temperature profile in the fast wind case. Results from MHD numerical simulations of decaying MHD turbulence show a similar trend for the total dissipation, suggesting an interpretation of the observed dynamics in terms of decaying turbulence and that multi-spacecraft studies of the solar wind radial evolution may help clarify the nature of the evolution of the turbulent fluctuations in the ecliptic solar wind.

The linear scaling of the mixed third-order moment of the magnetohydrodynamic fluctuations is used to estimate the energy transfer rate of the turbulent cascade in the expanding solar wind. In 1976 the Helios 2 spacecraft measured three samples of fast solar wind originating from the same coronal hole, at different distance from the sun. Along with the adjacent slow solar wind streams, these represent a unique database for studying the radial evolution of turbulence in samples of undisturbed solar wind. A set of direct numerical simulations of the MHD equations performed with the Lattice-Boltzmann code FLAME is also used for interpretation. We show that the turbulence energy transfer rate decays approximately as a power law of the distance, and that both the amplitude and decay law correspond to the observed radial temperature profile in the fast wind case. Results from magnetohydrodynamic numerical simulations of decaying magnetohydrodynamic turbulence show a similar trend for the total dissipation, suggesting an interpretation of the observed dynamics in terms of decaying turbulence, and that multi-spacecraft studies of the solar wind radial evolution may help clarifying the nature of the evolution of the turbulent fluctuations in the ecliptic solar wind.

Simulating plasmas in the Hall-MagnetoHydroDynamics (Hall-MHD) regime represents a valuable {approach for the investigation of} complex non-linear dynamics developing in astrophysical {frameworks} and {fusion machines}. Taking into account the Hall electric field is {computationally very challenging as} it involves {the integration of} an additional term, proportional to \bNabla \times ((\bNabla\times\mathbf{B})\times \mathbf{B}) in the Faraday's induction {law}. {The latter feeds back on} the magnetic field $\mathbf{B}$ at small scales (between the ion and electron inertial scales), {requiring} very high resolution{s} in both space and time {in order to properly describe its dynamics.} The computational {advantage provided by the} kinetic Lattice Boltzmann (LB) approach is {exploited here to develop a new} code, the \textbf{\textsc{F}}ast \textbf{\textsc{L}}attice-Boltzmann \textbf{\textsc{A}}lgorithm for \textbf{\textsc{M}}hd \textbf{\textsc{E}}xperiments (\textsc{flame}). The \textsc{flame} code integrates the plasma dynamics in lattice units coupling two kinetic schemes, one for the fluid protons (including the Lorentz force), the other to solve the induction equation describing the evolution of the magnetic field. Here, the newly developed algorithm is tested against an analytical wave-solution of the dissipative Hall-MHD equations, pointing out its stability and second-order convergence, over a wide range of the control parameters. Spectral properties of the simulated plasma are finally compared with those obtained from numerical solutions from the well-established pseudo-spectral code \textsc{ghost}. Furthermore, the LB simulations we present, varying the Hall parameter, highlightthe transition from the MHD to the Hall-MHD regime, in excellent agreement with the magnetic field spectra measured in the solar wind.

Collisions, resulting in aggregation of ice crystals in clouds, is an important step in the formation of snow aggregates. Here, we study the collision process by simulating spheroidshaped particles settling in turbulent flows, and by determining the probability of collision. We focus on plate-like ice crystals (oblate ellipsoids), subject to gravity, to the Stokes force and torque generated by the surrounding fluid. We also take into account the contributions to the drag and torque due to fluid inertia, which are essential to understand the tendency of crystals to settle with their largest dimension oriented horizontally. We determine the collision rate between identical crystals, of diameter 300 μm , with aspect ratios in the range 0.005 ≤ β ≤ 0.05, and over a range of energy dissipation per unit mass, ε , 1 cm ² /s ³ ≤ ε ≤ 250cm ² /s ³ . For all values of β studied, the collision rate increases with the turbulence intensity. The dependence on β is more subtle. Increasing β at low turbulence intensity ( ≲ . 16 cm ² /s ³ ) diminishes the collision rate, but increases it at higher ε ≈ 250cm ² /s ³ . The observed behaviors can be understood as resulting from three main physical effects. First, the velocity gradients in a turbulent flow tend to bring particles together. In addition, differential settling plays a role at small ε when the particles are thin enough ( β small), whereas the prevalence of particle inertia at higher ε leads to a strong enhancement of the collision rate.

Owing to its efficiency and aptitude for a massive parallelization, the lattice Boltzmann method generally outperforms conventional solvers in terms of execution time in weakly-compressible flows. However, the authorized time-step (being inversely proportional to the speed of sound) becomes prohibitively small in the incompressible limit, so that the performance advantage over continuum-based solvers vanishes. A remedy to increase the time-step is provided by artificially tailoring the speed of sound throughout the simulation, so as to reach a fixed target Mach number much larger than the actual one. While achieving considerable speed-ups in certain flow configurations, such adaptive time-stepping comes with the flaw that the continuities of mass density and pressure cannot be fulfilled conjointly when the speed of sound is varied. Therefore, a trade-off is needed. By leaving the mass density unchanged, the conservation of mass is preserved but the pressure presents a discontinuity in the momentum equation. In contrast, a power-law rescaling of the mass density allows us to ensure the continuity of the pressure term in the momentum equation (per unit mass) but leaves the mass density locally discontinuous. This algorithm, which requires a rescaling operation of the mass density, will be called “adaptive time-stepping with correction” in the article. Interestingly, we found that this second trade-off is generally preferable. In the case of a thermal plume, whose movement is governed by the balance of buoyancy and drag forces, the correction of the mass density (to ensure the continuity of the pressure force) has a beneficial impact on the resolved velocity field. In a pulsatile channel flow (Womersley's flow) driven by an external body force, no difference was observed between the two versions of adaptive time-stepping. On the other hand, if the pulsatile flow is established by inlet and outlet pressure conditions, the results obtained with a continuous pressure force agree much better with the analytical solution. Finally, by using adaptive time-stepping in a channel entrance flow, it was shown that the correction is compulsory for the Poiseuille flow to develop. The expected compressibility error due to the discontinuity in the mass density remains small to negligible, and the convergence rate is not notably affected compared to a simulation with a constant time step.

Lattice-Boltzmann simulations of corner separation flow in a compressor cascade are presented. The lattice Boltzmann approach is rather new in the context of turbomachinery and the configuration is known to be particularly challenging for turbulence modelling. The present methodology is characterized by a quasi-autonomous meshing strategy and a limited computational cost (a net ratio of 5 compared to a previous finite-volume compressible Navier-Stokes simulation). The simulation of the reference case (4° incidence) shows a good agreement with the experimental data concerning the wall pressure distribution or the distribution of losses. A good description is also obtained when incidence angle is increased to 7°, with a span-wise development of the separation. Subsequently, the methodology is used to investigate the sensitivity of the flow to the end-wall boundary-layer thickness. A thinner boundary-layer results in a smaller corner separation, but not a complete elimination. Finally, the ingredients of the wall modelling are analysed in details. On the one hand, the curvature correction term promotes transition to turbulence on the blade suction side and avoids a spurious separation. On the other hand, the addition of the pressure-gradient correction term allows a wider and more realistic corner separation.