Hydrodynamic stability

Résumé

In fluid dynamics, hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find out if a given flow is stable or unstable, and if so, how these instabilities will cause the development of turbulence. The foundations of hydrodynamic stability, both theoretical and experimental, were laid most notably by Helmholtz, Kelvin, Rayleigh and Reynolds during the nineteenth century. These foundations have given many useful tools to study hydrodynamic stability. These include Reynolds number, the Euler equations, and the Navier–Stokes equations. When studying flow stability it is useful to understand more simplistic systems, e.g. incompressible and inviscid fluids which can then be developed further onto more complex flows. Since the 1980s, more computational methods are being used to model and analyse the more complex flows. Stable and unstable flows To disting

Source officielle

https://en.wikipedia.org/wiki/Hydrodynamic_stability

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Cours associés (11)

This course focuses on the physical mechanisms at the origin of the transition of a flow from laminar to turbulent using the hydrodynamic instability theory.

The students understand and apply the physics of fluids, electromagnetism, and special relativity.

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Matlab, and a commercial software is used for more complex problems.

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Séances de cours associées (24)

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Impact of water activity on the mineralogy of hydrated cement

Luis Guillermo Baquerizo Ibarra

Cement hydrates and their chemically bound water content are sensitive to changes in relative humidity (RH) and temperature. This may cause specific solid volume changes affecting dimensional properties of hydrated cement paste such as shrinkage, swelling and expansion, and therefore impact the performance and the transport properties of cementitious materials. The present thesis studies the impact of drying conditions on the structure and thermodynamic properties of crystalline cement hydrates in different hydration states (i.e. varying molar water contents). The cement hydrates studied include the most important AFm and AFt phases present in different types of cements. A novel multi method approach, including XRD, TGA, DSC, sorption balance measurements, sorption calorimetry and the hydrate pair ¿ humidity buffer method, was used to derive physico-chemical boundary conditions and the thermodynamic properties of the studied hydrated phases. The stability and hydration states of AFm phases depend on the anion content and the exposure conditions. Some phases such as monosulfoaluminate and hydroxy-AFm are very sensitive to different relative humidities. On the other hand monocarboaluminate and strätlingite present very good volume stability with varying RH. Ettringite shows a strong hysteresis during desorption/adsorption, and the thermodynamic properties associated with its decomposition and reformation were determined. The experimental results were included into a thermodynamic model capable of predicting the response of cementitious systems considering the ¿true¿ crystal water content on the final phase assemblage in two different scenarios: i) during hydration, even at conditions where the amount of water added was insufficient for complete hydration, and ii) during drying and re-wetting processes in already hydrated systems. Our work hence opens the possibility to model the response of various cement materials exposed to different climatic conditions and to engineer cementitious systems with respect to minimizing volume changes in the course of drying, which may positively impact properties like drying shrinkage and total porosity.

EPFL2015

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It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Prandtl number, Pr. Here, we study stratified shear flow restricted to two dimensions at finite Reynolds number, continuously forced to have a constant background density gradient and a hyperbolic tangent shear profile, corresponding to the 'Drazin model' base flow. Bifurcation diagrams are produced for fluids with Pr = 0.7 (typical for air), 3 and 7 (typical for water). For Pr = 3 and 7, steady billow-like solutions are found to exist for strongly stable stratification of Ri(m) beyond 1/2. Interestingly, these solutions are not a direct product of a Kelvin-Helmholtz instability, having half the wavelength of the linear instability, and arising through a superharmonic bifurcation. These short-wavelength states can be tracked down to at least Pr approximate to 2.3 and act as instigators of complex dynamics, even in strongly stratified flows. Direct numerical simulations of forced and unforced two-dimensional flows are performed, which support the results of the bifurcation analyses. Perturbations are observed to grow approximately exponentially from random initial conditions where no modal instability is predicted by a linear stability analysis.

2021

Chargement

Dark goo: bulk viscosity as an alternative to dark energy

Jean-Sébastien Gagnon, Julien Lesgourgues

We present a simple (microscopic) model in which bulk viscosity plays a role in explaining the present acceleration of the universe. The effect of bulk viscosity on the Friedmann equations is to turn the pressure into an "effective" pressure containing the bulk viscosity. For a sufficiently large bulk viscosity, the effective pressure becomes negative and could mimic a dark energy equation of state. Our microscopic model includes self-interacting spin-zero particles (for which the bulk viscosity is known) that are added to the usual energy content of the universe. We study both background equations and linear perturbations in this model. We show that a dark energy behavior is obtained for reasonable values of the two parameters of the model (i.e. the mass and coupling of the spin-zero particles) and that linear perturbations are well-behaved. There is no apparent fine tuning involved. We also discuss the conditions under which hydrodynamics holds, in particular that the spin-zero particles must be in local equilibrium today for viscous effects to be important.

2011

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Impact of water activity on the mineralogy of hydrated cement

Luis Guillermo Baquerizo Ibarra

EPFL2015