Höghastighetståg - Är det framtiden?
AbstractConsider a ?uid being heated from below. The heating leads to an upward convectiveforce that is counteracted by the viscous forces of the ?uid. If the convectiveforce is large enough in comparison to the viscous forces the ?uid will be put in anunstable state. This means that a small disturbance will give rise to a ?ow drivenby a temperature gradient. This ?ow is characterised by a pattern of convectioncells. The phenomenon is called Rayleigh-Bénard convection. An example of thiscan be seen when heating a pot of oil from below. A part of the contribution tothe formation of these cells is attributed to the variation of surface tension due toheating. 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 convectiveforce 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 instabilityis investigated both theoretically, using simplied Navier-Stokes equations,and by simulation using a DNS-code with the programSimson(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 stabilityboundary is aected by the wavelength, related to the wave numberK, of theapplied disturbance and the dimensionless Rayleigh number,Ra. The critical valuefor the two parameters is found to beRa= 1708whenK= 3:12Finally the similarity between the simplied theory and the more realistic simulationis discussed.