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Papers by Benjamin LE-CREURER

Chemical Engineering Research and Design, 2023

This study investigates the rheological properties of rye and maize silage digestate from an indu... more This study investigates the rheological properties of rye and maize silage digestate from an industrial digester. In addition to the usual flow mode, oscillatory measurements were performed to highlight the visco-elastic characteristic of the digestate. Regardless of total solid (TS) content and solids size, results showed a shear-thinning behavior with a yield stress of the digestate, which was modelled by a Herschel-Bulkley equation. Furthermore, reducing the solids size by roughly a factor of 10 led to a 35-fold decrease in the viscosity at 20 s−1 for digestate with 8% of TS, which could improve the efficiency of mixing in di- gesters. On the other hand, the apparent viscosity of the digestate increases with in- creasing TS, which corresponded to a rise in cohesive energy. Equations linking rheological parameters and TS were provided. These models can be use in Computational Fluid Dynamics studies for a better modeling of the hydrodynamics within digesters.

Numerical simulation of transitional and turbulent flows requires highly accurate schemes. Such s... more Numerical simulation of transitional and turbulent flows requires highly accurate schemes. Such simulations are usually carried out with spectral methods. However flows with stiff and unsteady gradients such as those occurring in Rayleigh-Taylor (RT) instability require specific techniques: in these cases, one has to resort to transformation of coordinates. Guillard, Malé and Peyret (1992) introduced an adaptive procedure in which a coordinate transform was chosen to minimize the weighted second Sobolev norm of the solution. These results were generalized to the multidomain approach and we have shown that the criterion based on the minimum of the norm may also be used to determine the best location of the subdomain interfaces (Renaud & Gauthier, 1997). This adaption may be carried out dynamically to follow strong gradients.

HAL (Le Centre pour la Communication Scientifique Directe), Aug 24, 2022

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010

We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced f... more We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial con...

Theoretical and Computational Fluid Dynamics, 2008

We numerically simulate a single-mode Rayleigh-Taylor instability between compressible miscible f... more We numerically simulate a single-mode Rayleigh-Taylor instability between compressible miscible fluids with a highly accurate self-adaptive pseudospectral Chebyshev multidomain method in two two-dimensional boxes at small aspect ratios. The simulations are started from rest and pursued until the return toward mechanical equilibrium of the mixing. Four regimes-linear and weakly nonlinear, nonlinear steady bubble rise, return toward equilibrium, and finally a system of acoustic waves-can be identified. We show that this one-dimensional system of stationary acoustic waves is damped by the physical viscosity. This provides a reference solution.

Physica Scripta, 2008

Compressibility effects in buoyant flows are studied on three examples: the classical Rayleigh-Ta... more Compressibility effects in buoyant flows are studied on three examples: the classical Rayleigh-Taylor instability (RTI) for compressible miscible flows, the ablation front instability and the thermal convection of Rayleigh-Bénard. The linear analysis of the classical RTI for viscous flows is performed and the opposite effects of stratification and compressibility on the growth rate are pointed out. Some investigations in the nonlinear regime have also been carried out and show that the trend observed in the linear regime usually holds. On the other hand, a 2D simulation, started from rest and pursued until the return toward mechanical equilibrium of the mixing exhibits a typical compressibility effect, an acoustic wave, damped by the physical viscosity. The ablation front instability is detailed on the 'laser imprint' problem of direct drive irradiation. The linear stability analysis is performed on an unsteady mean flow given by the self-similar solutions of gas dynamics equations with nonlinear heat conduction. Compressibility effects are studied through the Kovásznay modes. It appears that maximum amplitudes are achieved for zero wave number, and complex wave-like structures are observed. Analogy with the large-scale instability, which occurs in compressible thermal convection, is suggested. These results have been obtained with an autoadaptive dynamical multidomain Chebyshev method.

We present a self-adaptive domain decomposition method within the framework of Chebyshev pseudo-s... more We present a self-adaptive domain decomposition method within the framework of Chebyshev pseudo-spectral method. A general distribution of collocation points is given by a set of M subdomains in which a coordinate transform is used. Both the locations of the interfaces and the parameters of the mappings are dynamically adapted by minimizing the H 2 ω norm of the calculated solution. It allows us to handle strong and moving gradients. This numerical method is applied to four problems borrowed from fluid dynamics: (i) a one-dimensional initial boundary value problem (ibvp), the rippled shock wave, governed by Euler's equations and for which the exact solution is known, (ii) a self-similar solution of Euler's equations with nonlinear heat conduction which is solution of a fourth order nonlinear eigenvalue problem, (iii) the stability analysis of the compressible Rayleigh-Taylor flow, governed by the Navier-Stokes equations, which reduces to a generalized linear eigenvalue problem, (iv) finally, a two-dimensional ibvp, the simulation of the Rayleigh-Taylor flow.

Chemical Engineering Research and Design, 2023

This study investigates the rheological properties of rye and maize silage digestate from an indu... more This study investigates the rheological properties of rye and maize silage digestate from an industrial digester. In addition to the usual flow mode, oscillatory measurements were performed to highlight the visco-elastic characteristic of the digestate. Regardless of total solid (TS) content and solids size, results showed a shear-thinning behavior with a yield stress of the digestate, which was modelled by a Herschel-Bulkley equation. Furthermore, reducing the solids size by roughly a factor of 10 led to a 35-fold decrease in the viscosity at 20 s−1 for digestate with 8% of TS, which could improve the efficiency of mixing in di- gesters. On the other hand, the apparent viscosity of the digestate increases with in- creasing TS, which corresponded to a rise in cohesive energy. Equations linking rheological parameters and TS were provided. These models can be use in Computational Fluid Dynamics studies for a better modeling of the hydrodynamics within digesters.

Numerical simulation of transitional and turbulent flows requires highly accurate schemes. Such s... more Numerical simulation of transitional and turbulent flows requires highly accurate schemes. Such simulations are usually carried out with spectral methods. However flows with stiff and unsteady gradients such as those occurring in Rayleigh-Taylor (RT) instability require specific techniques: in these cases, one has to resort to transformation of coordinates. Guillard, Malé and Peyret (1992) introduced an adaptive procedure in which a coordinate transform was chosen to minimize the weighted second Sobolev norm of the solution. These results were generalized to the multidomain approach and we have shown that the criterion based on the minimum of the norm may also be used to determine the best location of the subdomain interfaces (Renaud & Gauthier, 1997). This adaption may be carried out dynamically to follow strong gradients.

HAL (Le Centre pour la Communication Scientifique Directe), Aug 24, 2022

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010

We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced f... more We present a tentative review of compressibility effects in Rayleigh–Taylor instability-induced flows. The linear, nonlinear and turbulent regimes are considered. We first make the classical distinction between the static compressibility or stratification, and the dynamic compressibility owing to the finite speed of sound. We then discuss the quasi-incompressible limits of the Navier–Stokes equations (i.e. the low-Mach number, anelastic and Boussinesq approximations). We also review some results about stratified compressible flows for which instability criteria have been derived rigorously. Two types of modes, convective and acoustic, are possible in these flows. Linear stability results for perfect fluids obtained from an analytical approach, as well as viscous fluid results obtained from numerical approaches, are also reviewed. In the turbulent regime, we introduce Chandrasekhar’s observation that the largest structures in the density fluctuations are determined by the initial con...

Theoretical and Computational Fluid Dynamics, 2008

We numerically simulate a single-mode Rayleigh-Taylor instability between compressible miscible f... more We numerically simulate a single-mode Rayleigh-Taylor instability between compressible miscible fluids with a highly accurate self-adaptive pseudospectral Chebyshev multidomain method in two two-dimensional boxes at small aspect ratios. The simulations are started from rest and pursued until the return toward mechanical equilibrium of the mixing. Four regimes-linear and weakly nonlinear, nonlinear steady bubble rise, return toward equilibrium, and finally a system of acoustic waves-can be identified. We show that this one-dimensional system of stationary acoustic waves is damped by the physical viscosity. This provides a reference solution.

Physica Scripta, 2008

Compressibility effects in buoyant flows are studied on three examples: the classical Rayleigh-Ta... more Compressibility effects in buoyant flows are studied on three examples: the classical Rayleigh-Taylor instability (RTI) for compressible miscible flows, the ablation front instability and the thermal convection of Rayleigh-Bénard. The linear analysis of the classical RTI for viscous flows is performed and the opposite effects of stratification and compressibility on the growth rate are pointed out. Some investigations in the nonlinear regime have also been carried out and show that the trend observed in the linear regime usually holds. On the other hand, a 2D simulation, started from rest and pursued until the return toward mechanical equilibrium of the mixing exhibits a typical compressibility effect, an acoustic wave, damped by the physical viscosity. The ablation front instability is detailed on the 'laser imprint' problem of direct drive irradiation. The linear stability analysis is performed on an unsteady mean flow given by the self-similar solutions of gas dynamics equations with nonlinear heat conduction. Compressibility effects are studied through the Kovásznay modes. It appears that maximum amplitudes are achieved for zero wave number, and complex wave-like structures are observed. Analogy with the large-scale instability, which occurs in compressible thermal convection, is suggested. These results have been obtained with an autoadaptive dynamical multidomain Chebyshev method.

We present a self-adaptive domain decomposition method within the framework of Chebyshev pseudo-s... more We present a self-adaptive domain decomposition method within the framework of Chebyshev pseudo-spectral method. A general distribution of collocation points is given by a set of M subdomains in which a coordinate transform is used. Both the locations of the interfaces and the parameters of the mappings are dynamically adapted by minimizing the H 2 ω norm of the calculated solution. It allows us to handle strong and moving gradients. This numerical method is applied to four problems borrowed from fluid dynamics: (i) a one-dimensional initial boundary value problem (ibvp), the rippled shock wave, governed by Euler's equations and for which the exact solution is known, (ii) a self-similar solution of Euler's equations with nonlinear heat conduction which is solution of a fourth order nonlinear eigenvalue problem, (iii) the stability analysis of the compressible Rayleigh-Taylor flow, governed by the Navier-Stokes equations, which reduces to a generalized linear eigenvalue problem, (iv) finally, a two-dimensional ibvp, the simulation of the Rayleigh-Taylor flow.