Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size versi

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We present a multi-level algorithm to approximate the inverse of the fluid block in a Navier-Stokes saddle-point matrix where the coarse level is defined as a restriction of the degrees of freedom to those of lower order finite elements. A one-level scheme involving P1 and P2 finite elements is studied in details and several transfer operators are compared by means of two reference problems. Numerical results show that restriction and prolongation operators based on L2 projection lead to faster GMRES convergence of the fluid part, for all the examined combinations of mesh size, time step and Reynolds number.

2013

Hydrocontest: Computational Fluid Dynamics of hydrofoils

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This project is developed within the scope of HydroContest which is an inter-school competition for the design of a racing boat with a high focus on energetic efficiency; the goal is to maximize the speed of the boat under the constraint of a limited power source. Hydrofoils are especially interesting since they offer an important reduction of drag at high speeds while remaining cost efficient. Within the contest, this project aims at delivering a prediction tool for the hydrofoil performance using numerical simulations of the incompressible Navier-Stokes equations approximated by the means of the Finite Element method with suitable stabilization techniques, such as the Variational Multiscale Method; we consider P1 Finite Elements with a second order BDF time discretization scheme. An automated meshing script was developed to handle arbitrary foil geometries and angles of attack. The numerical simulations were conducted using the LifeV Finite Element Library in a parallel setting. Satisfactory results have been obtained using this approach for Reynolds numbers up to 1 million.

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Experimental investigation into localized instabilities of mixed Rayleigh-Bénard-Poiseuille convection

Emeric Grandjean

An experimental study of the stability of the Rayleigh-Bénard-Poiseuille flow was performed in a large transverse aspect ratio channel. The onset for the transverse thermo-convective rolls was determined as a function of the Reynolds number for two different fluids (water: Pr = 6.5 and mineral oil: Pr = 450). Then, the system impulse response was studied and a good agreement with theory was found for the convective/absolute instability transition. Finally the response of the system to localized heating was observed and compared with analytical and numerical results by Martinand, Carrière and Monkewitz (2004 & 2006): experimental thermo-convective global modes are found to correspond to the saturated "steep" variety constructed by Pier, Huerre and Chomaz (2001).

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