Axelle Viré

Lorentz force velocimetry based on time-of-flight measurements

Lorentz force velocimetry (LFV) is a contactless technique for the measurement of liquid metal flowrates. It consists of measuring the force acting upon a magnetic system and arising from the interaction between an external magnetic field and the flow of an electrically conducting fluid. In this study, a new design is proposed so as to make the measurement independent of the fluid’s electrical conductivity. It is made of one or two coils placed around a circular pipe. The forces produced on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated with a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional ...

Modeling and discretization errors in large eddy simulations of hydrodynamic and magnetohydrodynamic channel flows

We assess the performances of three different subgrid scale models in large eddy simulations (LES) of turbulent channel flows. Two regimes are considered: hydrodynamic and magnetohydrodynamic (i.e. in the presence of a uniform wall-normal magnetic field). The simulations are performed using a second-order finite volume (FV) and a pseudo-spectral (PS) method. The LES results are compared with under-resolved results (obtained without model) and direct numerical simulations (DNS). We show that discretization errors affect the FV results in two ways: (1) the flow statistics differ from the spectral estimates in the absence of subgrid model; and (2) the eddy viscosity systematically underestimates the spectral value in the presence of a subgrid model. This is mainly because numerical errors affect the computation of the derivatives, and in particular, they lower the discrete strain rate appearing in the viscous term and the subgrid model. The magnitude of the numerical errors further varies with the mesh resolution and the intensity of the turbulent fluctuations. In this manuscript, a novel formulation of the discrete strain, which was proven successful in homogeneous isotropic turbulence, is used to compute the FV eddy viscosities. Although the average norm of the discrete strain is largely increased using this formulation, the effect on the flow dynamics is marginal. This is explained by analysing the contribution of each term of the discrete kinetic energy balance. It is shown how the underestimation of the discrete viscous dissipation inhibits the effect of the improved discrete strain.

On discretization errors and subgrid scale model implementations in large eddy simulations

We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier-Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.

Large-Eddy Simulations of a Turbulent Magnetohydrodynamic Channel Flow

We consider the channel flow of an electrically conducting fluid subjected to a magnetic field. In this framework, numerical predictions are particularly appealing because liquid metals are difficult to study experimentally. In many industrial processes, the magnetic Reynolds number is low. Hence, the applied magnetic field is not perturbed by the flow (quasi-static approximation) and provides an additional force term in the equations of motion. Moreover, the Lorentz force acting on the flow has globally dissipative and anisotropic effects [1, 2]. In the case of low-intensity wall-normal magnetic fields, the turbulent fluctuations tend to be suppressed at the center of the channel (flattening effect) and confined in the near-wall region, where thin layers of high shear (the Hartmann layers) appear [3]. Direct Numerical Simulations (DNS) of magnetohydrodynamic (MHD) flows require accurate numerical discretizations and are thus limited to moderate Reynolds number flows and simple geometries. In Large-Eddy Simulations (LES), the dynamics of the unresolved scales is taken into account through a subgrid-scale model. The applicability of hydrodynamic models to MHD homogeneous turbulence has been proven successful [4]. Our aim is to evaluate the performances of under-resolved DNS of a MHD channel flow (with and without subgrid model). Finite volume (FV) and spectral (PS) results are compared in terms of first and second order statistics. A particular attention is also given to the contribution of the model to the kinetic energy budget.