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Rayleigh-Bénard konvektion.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
2012 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Abstract

Consider a  uid being heated from below. The heating leads to an upward convective

force that is counteracted by the viscous forces of the  uid. If the convective

force is large enough in comparison to the viscous forces the  uid will be put in an

unstable state. This means that a small disturbance will give rise to a  ow driven

by a temperature gradient. This  ow is characterised by a pattern of convection

cells. The phenomenon is called Rayleigh-Bénard convection. An example of this

can be seen when heating a pot of oil from below. A part of the contribution to

the formation of these cells is attributed to the variation of surface tension due to

heating. This contribution is of less signicance when the  uid layer is thicker.

In this report the studied  ow eld lies between two plates where the convective

force drives the motion. The in uence of surface tension is eliminated since the

 uid lacks a free surface in this problem. The boundary between stability and instability

is investigated both theoretically, using simplied Navier-Stokes equations,

and by simulation using a DNS-code with the program

Simson(Chevalier et al.,

2007). The simulation also makes it possible to see the shape of the convection cells.

The results is presented in stability diagrams that describe how the stability

boundary is aected by the wavelength, related to the wave number

K, of the

applied disturbance and the dimensionless Rayleigh number,

Ra. The critical value

for the two parameters is found to be

Ra= 1708whenK= 3:12

Finally the similarity between the simplied theory and the more realistic simulation

is discussed.

Place, publisher, year, edition, pages
2012. , 31 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-102770OAI: oai:DiVA.org:kth-102770DiVA: diva2:556472
Uppsok
Technology
Available from: 2012-09-28 Created: 2012-09-25 Last updated: 2012-09-28Bibliographically approved

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