Nombre de Knudsen

Résumé

Le nombre de Knudsen, généralement noté (\mathrm{Kn}), est un nombre adimensionnel permettant de déterminer le régime d'écoulement (en termes de continuité du milieu et non en termes de turbulence) d'un fluide. Ce nombre porte le nom de Martin Knudsen, physicien et océanographe danois. Il s'exprime par\mathrm{Kn}=\frac{\ell^}{L^}où \ell^* est le libre parcours moyen et L^* une longueur caractéristique du problème vue sous l'angle de la mécanique des fluides. Cette dernière longueur peut être définie par L^* = \frac{X}{\left\Vert \nabla X \right\Vert},où X étant n'importe quelle grandeur : température, pression, etc. On peut souvent en donner une estimation a priori : c'est une grandeur caractéristique du domaine d'étude comme la taille du domaine ouvert à l'écoulement dans un problème de milieu poreux ou de microfluidique ou le rayon de courbure de paroi en aérodynamique.

Source officielle

https://fr.wikipedia.org/wiki/Nombre_de_Knudsen

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Cours associés (9)

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Séances de cours associées

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A novel tethered-sphere add-on to enhance grid turbulence

Peter Monkewitz, Richard Vonlanthen

The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C (p) than the same bare grid without the spheres. At the same time, the Reynolds number Re-lambda based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid's simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Re-lambda range of 50-100.

Springer-Verlag2011

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Plasma rotation and momentum transport studies at JET

An experimental study in plasma rotation and momentum transport was carried out at JET. The toroidal rotation profile was found to scale approximately with that of the ion temperature. However, significant deviations from this were found in high density ELMy H-mode discharges, which had broader rotation profiles. A rotation database analysis showed the variation of the dimensionless Mach number with respect to the plasma scenario. For predominantly NBI heated discharges the Mach number was found to be in the range of 0.3-0.45. Larger Mach numbers were observed in type I ELMy H-modes, while scenarios exhibiting type III ELMs or L-mode had lower Mach numbers. Advanced scenarios often showed a significant increase in the central Mach number when an internal transport barrier formed. A detailed study was done to investigate the Prandtl number, P-r, defined as the ratio between momentum and ion heat diffusivity. Generally the Prandtl number was found to be significantly below unity, e. g. 0.18 < P-r < 0.35. Although it is often predicted that momentum and heat diffusivity are equal in ITG dominated plasma, also for high density ELMy H-mode discharges with temperature profiles close and above the ITG threshold, the Prandtl number was P-r similar to 0.3.

2006

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An assessment of ion temperature measurements in the boundary of the Alcator C-Mod tokamak and implications for ion fluid heat flux limiters

Christian Gabriel Theiler

The ion temperature is not frequently measured in the boundary of magnetic fusion devices. Comparisons among different ion temperature techniques and simulations are even rarer. Here we present a comparison of ion temperature measurements in the boundary of the Alcator C-Mod tokamak from three different diagnostics: charge exchange recombination spectroscopy (CXRS), an ion sensitive probe (ISP), and a retarding field analyzer (RFA). Comparison between CXRS and the ISP along with close examination of the ISP measurements reveals that the ISP is space charge limited. It is thus unable to measure ion temperature in the high density (>10^19 m−3) boundary plasma of C-Mod with its present geometry. Comparison of ion temperatures measured by CXRS and the RFA shows fair agreement. Ion and electron parallel heat flow is analyzed with a simple 1D fluid code. The code takes divertor measurements as input and results are compared to the measured ratios of upstream ion to electron temperature, as inferred respectively by CXRS and a Langmuir probe. The analysis reveals the limits of the fluid model at high Knudsen number. The upstream temperature ratio is under predicted by a factor of 2. Heat flux limiters (kinetic corrections) to the fluid model are necessary to match experimental data. The values required are found to be close to those reported in kinetic simulations. The 1D code is benchmarked against the 2D plasma fluid code UEDGE with good agreement.

2013

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