Jérôme Vétel

Asymmetry and transition to turbulence in a smooth axisymmetric constriction

The flow through a smooth axisymmetric constriction (a stenosis in medical applications) of 75% restriction in area is measured using stereoscopic and time-resolved particle image velocimetry (PIV) in the Reynolds number range Re ~ 100–1100. At low Reynolds numbers, steady flow results reveal an asymmetry of the flow downstream of the constriction. The jet emanating from the throat of the nozzle is deflected towards the wall causing the formation of a one-sided recirculation region. The asymmetry results from a Coanda-type wall attachment already observed in symmetric planar sudden expansion flows. When the Reynolds number is increased above the critical value of 400, the separation surface cannot remain attached and an unsteady flow regime begins. Low-frequency axial oscillations of the reattachment point are observed along with a slow swirling motion of the jet. The phenomenon is linked to a periodic discharge of the unstable recirculation region inducing alternating laminar and turbulent flow phases. The resulting flow is highly non-stationary and intermittent. Discrete wavelet transforms are used to discriminate between the large-scale motions of the mean flow and the vortical and turbulent fluctuations. Continuous wavelet transforms reveal the spectral structure of flow disturbances. Temporal measurements of the three velocity components in cross-sections are used with the Taylor hypothesis to qualitatively reconstruct the three-dimensional velocity vector fields, which are validated by comparing with two-dimensional PIV measurements in meridional planes. Visualizations of isosurfaces of the swirling strength criterion allow the identification of the topology of the vortices and highlight the formation and evolution of hairpin-like vortex structures in the flow. Finally, with further increase of the Reynolds number, the flow exhibits less intermittency and becomes stationary for Re ~ 900. Linear stochastic estimation identifies the predominance of vortex rings downstream of the stenosis before breakdown to turbulence.

Anisotropic mesh adaptation on Lagrangian Coherent Structures

The finite-time Lyapunov exponent (FTLE) is extensively used as a criterion to reveal fluid flow structures, including unsteady separation/attachment surfaces and vortices, in laminar and turbulent flows. However, for large and complex problems, flow structure identification demands computational methodologies that are more accurate and effective. With this objective in mind, we propose a new set of ordinary differential equations to compute the flow map, along with its first (gradient) and second order (Hessian) spatial derivatives. We show empirically that the gradient of the flow map computed in this way improves the pointwise accuracy of the FTLE field. Furthermore, the Hessian allows for simple interpolation error estimation of the flow map, and the construction of a continuous optimal and multiscale L^p metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. Typically, the L^1 norm provides meshes best suited to capturing small scale structures, while the L^~ norm provides meshes optimized to capture large scale structures. This means that the mesh density near large scale structures will be greater with the L^~ norm than with the L^1 norm for the same mesh complexity, which is why we chose this technique for this paper. We use it to optimize the mesh in the vicinity of LCS. It is found that Lagrangian Coherent Structures are best revealed with the minimum number of vertices with the L^~ metric.

On the flow separation in the wake of a fixed and a rotating cylinder

The flow past a circular cylinder under diverse conditions is investigated to examine the nature of the different separation mechanisms that can develop. For a fixed cylinder in a uniform, steady, and horizontal stream, the alternating sheddings of vortices, characterizing the Kármán vortex street, occur from two separation points located in the rear cylinder wall. The prediction of the separation positions and profiles is examined in the light of the most recent theory of unsteady separation in two-dimensional flows. It is found that the separation points are fixed in space and located symmetrically about the horizontal axis passing through the center of the cylinder. The unsteady separation profiles are also well-predicted by the theory. If the cylinder rotates on its axis in the anti-clockwise direction, the upper and lower separation points are shifted in the upstream and the downstream direction, respectively, but are no longer attached to the wall and cannot be predicted by the theory. Instead, they are captured as saddle points in the interior of the flow without any connection to on-wall quantities, as suggested by the Moore-Rott-Sears (MRS) principle. The saddle points are detected through a Lagrangian approach as the location of maximum tangential rate of strain on Lagrangian coherent structures identified as the most attracting lines in the vicinity of the cylinder. If, in addition, the uniform stream is unsteady, the Eulerian saddle points, i.e., detected by streamlines, change position in time, but have no direct relation to the true separation points that are defined by Lagrangian saddle points, thus invalidating the MRS principle that is Eulerian by nature. Other separation mechanisms are also described and understood in view of Lagrangian identification tools.

Characterization of a Diffuser Flow by Time-Resolved PIV

Computational fluid dynamics is extensively used in the design methodology of medical devices. However, for such applications, the predictive capabilities of CFD codes are highly dependent upon geometry, which most of the time is extremely complex, and flow conditions. The study concerns a ventricular assist device (VAD) where the exit flow, generated through a diffuser, is of particular importance for blood damage predictions. The difficulty to predict the flow lies in the fact that the Reynolds number range includes the transition Reynolds number of the separated diffuser flow as well as the critical Reynolds number of pipe flows. In order to choose the appropriate CFD methodology in terms of flow hypothesis and turbulence model, an experimental setup of the diffuser was built to run PIV velocity measurements and to analyze the flow pattern with the influence of Reynolds number. The flow is described with mean and variance values of the in-plane velocity components and timeresolved results are used to visualize the development of unsteady phenomena introduced in the diffuser separated region. An optimal filter is also used to remove noise in measured velocity vector fields.

An inverse problem to assess the two-component unsteady wall shear rate

The instantaneous two-dimensional wall shear rate is assessed through an inverse problem using mass transfer data from a threesegment electrodiffusion probe. The method is validated numerically in complex flow conditions involving (i) high amplitude periodic fluctuations on both wall shear rate magnitude and direction and (ii) direct numerical simulation (DNS) data from a turbulent three-dimensional channel flow. The approach is shown to outperform every other post-treatments available for mass transfer sensors, especially regarding its versatility and application range. The impact of the three-segment probe gap size is also examined numerically.

Efficient computation of the finite-time Lyapunov exponent

The finite-time Lyapunov exponent (FTLE) is extensively used as a criterion to reveal fluid flow structures, including unsteady separation/attachment surfaces and vortices, in laminar and turbulent flows. However, for large and complex problems, flow structure identification demands computational methodologies that are more accurate and effective. With this objective in mind, we propose a new set of ordinary differential equations to compute the flow map, along with its first (gradient) and second order (Hessian) spatial derivatives. We show empirically that the gradient of the flow map computed in this way improves the pointwise accuracy of the FTLE field. Furthermore, the Hessian allows for simple interpolation error estimation of the flow map, and the construction of a continuous optimal and multiscale L metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. It is found that Lagrangian Coherent Structures are best revealed with the minimum number of vertices with the L∞ metric.

Analysis of Complex Flows From Experimental Data and Numerical Experiments

Fluid mechanics is considered to be a privileged field in physics because phenomena can be made visible. This is unfortunately not the case in turbulence where diffusion and mixing of passive tracers are enhanced by turbulent transport. Consequently, the analysis of the rich flow physics provided by direct numerical simulations (DNS) and by modern optical diagnostic techniques require advanced post-processing tools to extract fine flow details. In this context, this paper reviews most recent techniques used to reveal coherent structures and their dynamics in turbulent flows. In particular, results obtained with standard Eulerian techniques are compared to those obtained from a more recent Lagrangian technique. Even if this latter technique can provide finer details, it is found that the two methods are complementary. This is illustrated with DNS results and with experimental data including planar measurements as well as time-resolved measurements converted to quasi-instantaneous volumetric data by using the Taylor hypothesis.Copyright