Transition delay by surface heating: a zonal analysis for axisymmetric bodies

Abstract

It has long been known from linear stability theory that heating a surface immersed in water flow tends to stabilize the boundary layer on the surface, suggesting that there may be a corresponding delay in transition. Experiments confirm the suggestion, but based on intermittency data on a heated body of revolution (Lauchle & Gurney 1984) it has been inferred that incremental changes in transition Reynolds number diminish as the overheat increases. The parameter chosen to locate transition in the analysis leading to this conclusion corresponds to the point where the intermittency is 0.5. However, intermittency distributions in the transition zone on an axisymmetric body may contain what have been called 'subtransitions' (Narasimha 1984). Taking this possibility into account, we formulate here a model for the variation of intermittency with flow Reynolds number at a fixed station on the body, as in the experiments. The rate at which turbulent spots merge with each other is shown to determine the location of subtransition. The transition onset Reynolds number (corresponding to the location where intermittency begins to depart from zero), inferred from the data on the basis of this model, shows a continuing increase with the temperature overheat, a trend in closer agreement with stability theory; but the axisymmetric body geometry results in a very short transition zone, countering in part the benefits of transition delay.