Gradient de pression

Résumé

Le gradient de pression est la quantité utilisée en mécanique pour représenter la variation de la pression dans un fluide. Le gradient de pression est une grandeur vectorielle normalement exprimée dans le système international d'unités en pascals par mètre (Pa/m). Les gradients de pression jouent un rôle important en aérodynamique et hydrodynamique, théories appliquées dans divers domaines scientifiques et techniques comprenant l'aéronautique, la géophysique, l'astronomie et la biophysique. En sciences de l'atmosphère (météorologie, climatologie et domaines connexes), le gradient de pression (typiquement de l'atmosphère terrestre) est la grandeur physique qui décrit en quelle direction et selon quelle proportion la pression change le plus rapidement autour d'un endroit particulier. En géologie du pétrole et dans les sciences pétrochimiques relatives aux puits de pétrole, et plus précisément en hydrostatique, le gradient vertical de pression dans une colonne de fluide à l'intérieur d'

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High-confinement mode (H-mode) is a promising reference scenario for ITER. But we are still facing major issues because of instabilities. They expel periodically some of the energy, which can damage the device. These instabilities are called the edge localized modes (ELM) and are not yet fully theoretically understood. The present work is a study on the profiles evolution in between ELMs and on the ELM effects. This may help to have a better understanding of the conditions before the ELM. We use the simulations as theoretical tool. For the purpose of the simulations, we build an H-mode χ e profile according to a standard L-mode one that we truncate at the edge to create a transport barrier. This gives a good agreement with the experimental data. Several scaling laws were successfully used. The first one is the energy confinement time scaling which was used for the thermal diffusivity to scale the temperature profile. A scaling between the core and pedestal energies was found recently. It was used to compute the pedestal χ e to scale the temperature pedestal, which was successful. Finally, we used a scaling for transport barriers which links the density gradient length to that of the temperature to compute the density in the pedestal. It was already found to be good in TCV electron internal transport barriers and in ASDEX Upgrade H-mode pedestals. Looking at the MHD stability parameters, it was found that for our reference case, ELMs are not likely to be triggered by the time evolution of the pressure gradient and the current density profiles in our model, as these are only varying significantly during the first millisecond after the crash, and are almost constant during the long remaining time until the next crash. Studying different cases, we investigate the behavior of the plasma when replacing the edge heating by central one to observe the influence of the heating profile, but no significant difference was found, neither in the MHD stability parameters. Further we change the particle diffusion coefficient to compare the dynamic behavior of the density. Slowing down the density dynamic behavior also slows down the pressure one, this can be seen on the MHD stability parameters. We also vary the ELM period to compare to the change due to the variation of the particle diffusivity. It was found that there may be a sort of relation between the particle diffusivity and the ELM period at least for the density, since both cases change the density recovery time with respect to the ELM period. A last case considered is doubling the radial ELM interaction range. This is done in order to observe the difference to the reference simulation that takes the density top of pedestal as ELM range, and to compare the spatial range influenced by the MHD activity and the one by the transport improvement. It was found that the MHD stability parameters in the pedestal exhibit a different behavior with the pressure gradient starting to increase very fast.

2011

Chargement

Bio Simulation of Brain Ventricle Dilation in Normal Pressure Hydrocephalus

Kamal Shahim

Hydrocephalus is a brain disease wherein the ventricles dilate and compress the parenchyma towards the skull. It is primarily characterized by the disruption of the cerebrospinal fluid (CSF) flow within the ventricular system. Normal pressure hydrocephalus (NPH) is a form of hydrocephalus for which the enlargement of ventricles occurs although the intracranial pressure (ICP) remains close to normal. The pressure gradient between the source of CSF production in the ventricles and the absorption sites is reported to be very low (∼1 mm Hg), i.e. within the experimental errors. The mechanism of NPH evolution is still obscure and its distinction from the other causes of dementia such as Alzheimer and neurodegenerative diseases is difficult. The present work contributes to a better understanding of the NPH mechanism in terms of CSF disturbances and/or parenchyma defects. To this end, imaging techniques such as Magnetic resonance imaging (MRI), Diffusion tensor imaging (DTI) and Magnetic resonance elastography (MRE) are used together with a finite element (FE) model. As a final step, NPH onset and evolution are clarified via a theoretical model for healthy and NPH brains assuming a spherical geometry. The proposed mechanism is further analyzed in a realistic 3D model of the brain parenchyma. Geometries of ventricular system and skull are obtained from MRI images of a human brain. DTI data are used to establish the fiber tracts direction as well as the local frame of anisotropic elasticity and permeability. The brain parenchyma is considered as a poro-elastic material where the tissue displacement and CSF flow are modeled using the Biot's theory. A link between the CSF diffusion and CSF permeability in brain parenchyma is established and the importance of space dependent CSF content and transverse isotropic (TI) permeability is highlighted in case of low pressure gradient hydrocephalus. Calculations are carried out to simulate the ventricular dilation using FE softwares such as MATLAB® and COMSOL®. The numerical results show that consideration of space dependent CSF content and TI permeability leads to a much more realistic model for NPH in terms of CSF velocity and CSF content. Anisotropic MRE experiment is conducted over selected slices of a healthy human brain. The experimental results are statistically refined and further used to assess the healthy brain stiffness as well as the degree of anisotropy in elasticity. Moreover, the constitutive behavior of the white matter is modeled as a composite material containing fiber tracts surrounded by a matrix; with the assumption of a low fiber-matrix bonding and fiber tract undulation. A non-linear elastic model is proposed in order to take into account the load transfer from white matter matrix to fiber tracts when these are fully stretched. The unknown value of the elastic coefficients in a sick brain is determined by using inverse modeling, i.e. by adjusting these coefficients so that the right ventricle dilation is obtained. It is demonstrated that NPH development can be associated with a degradation of the brain parenchyma elastic stiffness in NPH patients. It is shown that during NPH development, a load transfer from the white matter matrix (cell bodies and interstitial fluid) to fiber tracts takes place, initiating elastic anisotropy in white matter tissues at rather large strains. An analytical approach is developed to seek the underlying NPH mechanism in a simplified model of brain. Without further refinement in the constitutive equation or adding complexity to the material behavior, the Biot's formulation is regarded as the basis. However, an absorption term is added to the Biot's model to consider the possible transparenchymal CSF resorption. The ventricle stability concept is introduced and is further utilized to investigate the equilibrium positions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and the healthy and NPH equilibrium positions are found to be dependent in particular on the CSF seepage through the ventricle wall and the absorption and permeability coefficients of the brain parenchyma. Although very simple, the proposed analytical model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions. Incorporating the stability concept in a more realistic geometry of brain (3D), the respective equilibrium positions are recaptured using the parameter values provided by the analytical spherical model. The disruption of ventricle surface during the NPH development increases CSF seepage and consequently the medium permeability. A dilation dependent permeability is moreover incorporated in a 3D model of the brain. The results emphasize the importance of strain dependent permeability which favors the ventricle equilibrations in more realistic geometries of brain. Future works might consider the time dependent deformation (creep effects and stress induced remodeling) of ventricles and the incorporation of anisotropic permeability and elasticity in the 3D model. The geometry should be extended to the full ventricular system including the subarachnoid spaces (SAS).

EPFL2011

Chargement

Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers

Peter Monkewitz

The paper presents an in depth assessment of different similarity laws for the mean velocity profile in zero pressure gradient (ZPG) turbulent boundary layers (TBL's) in comparison with mostly experimental and few computational data. The emphasis is on the descriptions which are complete in the sense that a full representation of the mean velocity profile, its streamwise evolution and all integral parameters, including the friction factor and the shape factor, are provided as a function of Reynolds number. The first such complete description is the classical two-layer theory with its characteristic logarithmic mean velocity profile in the region where the two layers overlap, henceforth referred to as the "log law." The main alternative scalings which have been proposed over the last decade have led to power law descriptions of the turbulent mean velocity profile. Since the different descriptions were calibrated with different data sets, the controversy over the relative merits of the different approaches has lingered on. The purpose of the present paper is to measure the principal competing theories against the same vast data set of more than 300 mean velocity profiles from more than twenty different sources. The results confirm the conclusions of numerous authors that the log law provides a fully self-consistent and accurate description of all the mean quantities and demonstrates conclusively that the same cannot be achieved by the competing power law theories. Along the way, it is also argued that the traditional description of the outer velocity profile in terms of a wall-normal coordinate normalized to unity at a hypothetical boundary layer "edge" delta and a "wake parameter" Pi is not robust with respect to the fit of the outer velicity profile and should therefore not be used in theoretical arguments. (C) 2008 American Institute of Physics.

2008

Chargement

2011

Bio Simulation of Brain Ventricle Dilation in Normal Pressure Hydrocephalus

Kamal Shahim

EPFL2011