MISES Implementation of Modified Abu-Ghannam/Shaw Transition Criterion
نویسنده
چکیده
The ill-posedness arises from the influence of transition on the upstream boundary layer via the potential flow and the viscous displacement effect. When transition begins at xtr, both δ and H first decrease rapidly from their laminar values. The transition region therefore looks like a sink to the potential flow. This effective sink accelerates the upstream potential flow ue(x) towards the transition onset point and drives λ more positive. This therefore simultaneously decreases Rθ and increases RθS , as shown in Figure 1. Although this effect on ue and surface pressure is quite small as far prediction of blade loading is concerned, it is usually strong enough locally so that Rθ and RθS diverge towards the transition location. The result is that the AGS criterion (1) cannot hold at the transition onset point without also being triggered upstream — a direct contradiction. In practice, as the viscous displacement takes effect and Rθ and RθS diverge, transition will jump far downstream in the next iteration of the code. With further iterations, it will propagate upstream, only to jump back downstream again and repeat the cycle. There is no stable overall solution. An intersection of Rθ and RθS might be obtained if a coarse grid is used so that the displacement effect is “lost” inside one grid cell, but this is not guaranteed. Also, relying on inadequate resolution to obtain a solution is a dubious proposition!
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