The motion of an axisymmetric body falling in a tube at moderate Reynolds numbers

This study concerns the rectilinear and periodic paths of an axisymmetric solid body (short-length cylinder and disk of diameter d and thickness h) falling in a vertical tube of diameter D. We investigated experimentally the influence of the confinement ratio (S=d/D<0.8) on the motion of the body, for different aspect ratios (χ=d/h=3, 6 and 10), Reynolds numbers (80<Re<320) and a density ratio between the fluid and the body close to unity. For a given body, the Reynolds number based on its mean vertical velocity is observed to decrease when S increases. The critical Reynolds number for the onset of the periodic motion decreases with S in the case of thin bodies (χ=10), whereas it appears unaffected by S for thicker bodies (χ=3 and 6). The characteristics of the periodic motion are also strongly modified by the confinement ratio. A thick body (χ=3) tends to go back to a rectilinear path when S increases, while a thin body (χ=10) displays oscillations of growing amplitude with S until it touches the tube (at about S=0.5). For a given aspect ratio, however, the amplitudes of the oscillations follow a unique curve for all S, which depends only on the relative distance of the Reynolds number to the threshold of path instability. In parallel, numerical simulations of the wake of a body held fixed in a uniform confined flow were carried out. The simulations allowed us to determine in this configuration the effect of the confinement ratio on the thresholds for wake instability (loss of axial symmetry at Rec₁ and loss of stationarity at Rec₂) and on the maximal velocity Vw in the recirculating region of the stationary axisymmetric wake. The evolution with χ and S of Vw at Rec₁ was used to define a Reynolds number Re*. Remarkably, for a freely moving body, Re* remains almost constant when S varies, regardless of the nature of the path

Wake interaction of two disks falling in tandem

The fluid dynamics video illustrates the interaction of two disks falling in tandem at Reynolds number close to 100. Two fluorescent dyes were used to visualize the wake of each body. We can observe that the trailing body accelerates thanks to the entrainment provided by the wake of the leading body and eventually catches up the leadind body. Then, thick disks (diameter/thickness = 3) lose their initial wakes, separate laterally and fall side by side. On the contrary, the wakes of thinner disks (d/t = 10) merge in a single wake and the bodies continue their fall together adopting a stable Y-configuration.Comment: 2 pages, 2 video

Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo

This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau, 2016) when applied to log-concave probability distributions that are restricted to a convex body $\mathsf{K}$. This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with $\mathsf{K}$. Explicit convergence bounds in total variation norm and in Wasserstein distance of order $1$ are established. In particular, we show that the complexity of this algorithm given a first order oracle is polynomial in the dimension of the state space. Finally, some numerical experiments are presented to compare our method with competing MCMC approaches from the literature

Is scuba sampling a relevant method to study microhabitat in lakes? Examples and comparisons for three European species

We compared fish microhabitat use patterns in the littoral zone of a lake using a new direct method (i.e. Point Abundance Sampling by Scuba, PASS) and the widely used Point Abundance Sampling by Electrofishing technique (PASE). We collected microhabitat data for age 0+ roach (Rutilus rutilus L.), perch (Perca fluviatilis L.), and pike (Esox lucius L.). The two methods yelded different results for fish assemblage structure and microhabitat patterns. Using PASE, fish were mainly found in "shelter habitats" such as shallow waters and dense vegetation. It is likely that this behaviour is caused by the disturbance of the observer stamping around. Using PASS, fish escapement behaviour was rarely observed. Therefore, we concluded that this direct and non-destructive sampling technique is able to provide an accurate microhabitat estimation of a fish community and is assumed to be more suitable than PASE for fish habitat studies

Role of fish communities in particulate organic matter fluxes between salt marshes and coastal marine waters in the Mont Saint-Michel bay.

Among the 90 fishspecies censused in the Mont Saint-Michel Bay (France), 23 colonise and forage in the salt marshes during flood. Therefore, this environmentmay play an important trophic and nursery role for these species. This community is largely dominated by mullets (81% of the biomass), Liza ramada and secondarily L. aurata. But gobies (mainly Pomatoschistus minutus and P. lozanoï) and sea bass (Dicentrarchus labrax) are also present; they represent respectively 11% and 4% of the biomass. During the tide cycles, mullets export from salt marshes about 7% of their body weight (FW) containing a mixture of sediment (43%), organic matter (24%) and water (33%). Gobies and sea bass mainly feed on dwelling macro-invertebrates, and they export respectively 4.5% and 10% of their body weight during a tide cycle. Thus, we estimated that 50 tonnes year−1 of particulate organic matter (dry weight POM) are exported from the 4000 ha of salt marshes to the marine coastal waters. These fish communities appear to be POM transporters and could play a significant role in the global energy budgets of coastal environments such as Mont Saint-Michel Bay. According to the seasons and the years, the energy exported by fish communities is assumed to range between 0 and 10% of the total POM output

The periodic motion of a disk freely falling in a tube

This study is devoted to the rectilinear and periodic paths of an axisymmetric solid body (short-length cylinder and disk of diameter d, thickness h and aspect ratio X= d/h varying between 3 and 10) falling in a vertical tube of diameter D. We investigated the influence of the confinement ratio (S = d/D) on the characteristics of the body motion, for different aspect ratios X and Reynolds numbers (80 < Re < 320), and a density ratio between the fluid and the body close to unity

Interaction of two axisymmetric bodies falling in tandem at moderate Reynolds numbers

This study considers the interaction of two identical solid axisymmetric bodies (of diameter d and thickness h) freely falling in a fluid at rest. We determine the domains of existence of the different interaction behaviour of the two bodies (i.e. attraction, repulsion and indifference) as a function of their initial relative position. We then investigate in detail the case of bodies falling in tandem, for both rectilinear and periodic paths, and the associated attraction behaviour. For all the Reynolds numbers and aspect ratios of the bodies (χ=d/h) investigated, the trailing body catches up with the leading body. We provide a quantitative description of the kinematics leading to the regrouping of the bodies and analyse its relationship with the wake of the leading body. In the case of rectilinear paths, a dynamical model that takes into account the axial evolution of the wake of the leading body is proposed to reproduce the acceleration observed for the trailing body until a vertical separation distance between the bodies of 1.5 diameters. In parallel, direct numerical simulations (DNS) of the flow about two fixed bodies in tandem in an oncoming flow are carried out, providing a good estimation of the motion of the bodies for separation distances larger than 5 diameters. For periodic paths, the kinematics leading to the regrouping of the bodies is slower than for rectilinear paths. However, in this case, the interaction also leads to significant changes in the characteristics of the oscillatory motion and is strongly dependent on the aspect ratio of the bodies. To explain the observed differences, we consider the effect of the transverse inhomogeneity of the wake of the leading body on the oscillatory motion of the trailing disk

Interaction of two axisymmetric bodies falling side by side at moderate Reynolds numbers

We consider the interaction of two identical disks freely falling side by side in a fluid at rest for Reynolds numbers ranging from 100 to 300, corresponding to rectilinear and oscillatory paths. For the three aspect ratios of the disks investigated, we observed that the bodies always repel one another when the horizontal distance between their centres of gravity is less than 4.5 diameters. They never come closer for distances spanning between 4.5 and 6 diameters. Beyond the latter distance, the disks appear indifferent to each other. For both rectilinear and periodic paths, the repulsion effect is weak, leading to an overall horizontal drift lower than 3 % of the vertical displacement. We propose a model for the repulsion coefficient Cr, which decreases with the separation distance between the bodies and is inversely proportional to the aspect ratio of the bodies, Cr thus being stronger for the thicker ones. Furthermore, in the case of the oscillatory paths, we show that the effect of the interaction reduces to the repulsion effect, since the characteristics of the oscillatory motion of each disk appear unaffected by the presence of the companion disk and no synchronization is observed between the paths, nor between the wakes, of the two disks

Chaining of welding and finish turning simulations for austenitic stainless steel components

The chaining of manufacturing processes is a major issue for industrials who want to understand and control the quality of their products in order to ensure their in-service integrity (surface integrity, residual stresses, microstructure, metallurgical changes, distortions,…). Historically, welding and machining are among the most studied processes and dedicated approaches of simulation have been developed to provide reliable and relevant results in an industrial context with safety requirements. As the simulation of these two processes seems to be at an operationnal level, the virtual chaining of both must now be applied with a lifetime prediction prospect. This paper will first present a robust method to simulate multipass welding processes that has been validated through an international round robin. Then the dedicated “hybrid method”, specifically set up to simulate finish turning, will be subsequently applied to the welding simulation so as to reproduce the final state of the pipe manufacturing and its interaction with previous operations. Final residual stress fields will be presented and compared to intermediary results obtained after welding. The influence of each step on the final results will be highlighted regarding surface integrity and finally ongoing validation works and numerical modeling enhancements will be discussed