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Publication# Hydrocontest: Computational Fluid Dynamics of hydrofoils

Abstract

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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Related concepts (14)

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.

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).

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Related publications (22)

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum balance equation for the mixture (fluid and sediments).
The model proposed here couples the Navier-Stokes equations, with a
volume-of-fluid (VOF) approach for the tracking of the free surfaces between the liquid
and the air, plus a nonlinear advection equation for the sediments (for the transport, deposition, and resuspension of sediments).
The numerical algorithm relies on a splitting approach to decouple diffusion and advection phenomena such that we are left with a Stokes operator, an advection operator, and deposition/resuspension operators.
For the space discretization, a two-grid method couples a finite element discretization for the resolution of the Stokes problem, and a finer structured grid of small cells for the discretization of the advection operator and the sediment deposition/resuspension operator.
SLIC, redistribution, and decompression algorithms are used for post-processing to limit numerical diffusion and correct the numerical compression of the volume fraction of liquid.
The numerical model is validated through numerical experiments.
We validate and benchmark the model with deposition effects only for some specific experiments, in particular erosion experiments. Then, we validate and benchmark the model in which we introduce resuspension effects. After that, we discuss the limitations of the underlying physical models.
Finally, we consider a one-dimensional diffusion-convection equation and study an error indicator for the design of adaptive algorithms. First, we consider a finite element backward scheme, and then, a splitting scheme that separates the diffusion and the convection parts of the equation.

In the last years, the correlation between air pollution and health issues related to respiratory, cardiovascular and digestive systems has become evident. Today, urban aerosols raise the interest of both scientific community and public opinion. METAS, the Swiss Federal Institute of Metrology, takes part in AeroTox, a European Union’s research project involving the development of a reference aerosol calibration infrastructure - a so-called mixing chamber. In this chamber, pure air and particles are injected on top and the resulting aerosol is sampled at the bottom. The quality of this aerosol is assessed according to its concentration homogeneity: the purpose of this master’s project is to improve it. In addition, two research questions were addressed. How much can the mixing chamber dimensions be reduced without affecting the concentration homogeneity? Dimensions are crucial because the mixing chamber must be transportable. Also, how much can the flow rates be reduced without affecting the concentration homogeneity? Computational Fluid Dynamics (CFD) simulations and experiments were employed. Numerical simulations were performed in COMSOL Multiphysics, implementing a particle tracing and a diluted species model. This allowed to investigate the structure of the flow and the involved mixing mechanisms: diffusion, convection and turbulent dispersion. However, only the diluted species model was successful. The simulated concentration at the outlet is perfectly homogeneous. Experiments were carried out using two particle size distributions: NaCl (size peak at 80 nm) and Polystyrene Latex (PSL, size peak at 900 nm). Empirical data validate simulations and show a concentration homogeneity within 5%. Furthermore, uncertainty on the measurements is of 4.24%: the simulated concentration homogeneity thus lies within the uncertainty of the experimental findings. Moreover, experiments show that salt particles reach a higher concentration homogeneity than PSL particles. Finally, in case of salt particles, experiments prove that the flow rates can be halved and even equalized and the length of the mixing chamber can be reduced to 50% without drastically affecting the concentration homogeneity.

2020This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular implementation of the Reduced Basis Element method. Our contributions include the application to the unsteady three-dimensional Navier--Stokes equations, the introduction of a reduced coupling between subdomains, and the reconstruction of arteries with deformed elementary building blocks. The technique is divided into two main stages: the offline and the online phases. In the offline phase, we define a library of reference building blocks (e.g., tubes and bifurcations) and associate with each of these a set of Reduced Basis functions for velocity and pressure. The set of Reduced Basis functions is obtained by Proper Orthogonal Decomposition of a large number of flow solutions called snapshots; this step is expensive in terms of computational time. In the online phase, the artery of interest is geometrically approximated as a composition of subdomains, which are obtained from the parametrized deformation of the aforementioned building blocks. The local solution in each subdomain is then found as a linear combination of the Reduced Basis functions defined in the corresponding building block. The strategy to couple the local solutions is of utmost importance. In this thesis, we devise a nonconforming method for the coupling of Partial Differential Equations that takes advantage of the definition of a small number of Lagrange multiplier basis functions on the interfaces. We show that this strategy allows us to preserve the h-convergence properties of the discretization method of choice for the primal variable even when a small number of Lagrange multiplier basis functions is employed. Moreover, we test the flexibility of the approach in scenarios in which different discretization algorithms are employed in the subdomains, and we also use it in a fluid-structure interaction benchmark. The introduction of the Lagrange multipliers, however, is associated with stability problems deriving from the saddle-point structure of the global system. In our Reduced Order Model, the stability is recovered by means of supremizers enrichment.
In our numerical simulations, we specifically focus on the effects of the Reduced Basis and geometrical approximations on the quality of the results. We show that the Reduced Order Model performs similarly to the corresponding high-fidelity one in terms of accuracy. Compared to other popular models for cardiovascular simulations (namely 1D models), it also allows us to compute a local reconstruction of the Wall-Shear Stress on the vessel wall. The speedup with respect to the Finite Element method is substantial (at least one order of magnitude), although the current implementation presents bottlenecks that are addressed in depth throughout the thesis.