Automated Method for Transition Prediction on Wings in Transonic Flows

Abstract

The use of stability analyzers based on the linear stability theory and coupled with the e n method in e owe eld calculationprocedures (viscous/inviscidinteractivemethods,Navier -Stokessolvers )hasbeenimpeded by thatthey require tremendous amounts of information, knowledge, and interaction from the user. A systematic procedure is proposed to obtain a linear stability analyzer suitable for integration in wing performance calculation methods. The proposed transition prediction method relies on the use of a database of stability characteristics of a model three-dimensional compressible boundary layer. A coupling method based on the physical parameters of the mean e ow, such as local Mach number, Reynolds number, and boundary-layer shape factor, allows the extraction from the database of quantities such as the amplie cation rate for a given frequency or the maximum amplie cation frequency of the boundary layer studied. The stability characteristics of the model boundary are precomputed, by the use of the compressible linear stability equations with the classical parallel e ow assumption and without curvature effects. The results obtained with the proposed automated stability analysis method have shown that it provides a qualitatively adequate representation of a transonic three-dimensional e ow stability characteristics: dominant instability type, frequency of maximum amplie cation, and amplie cation rate. Computations of the n factorwereperformed fortheAS409 conicalwingand two Bombardierbusinessaircraftwings. Forthesecases,the automated method n factors are higher than those obtained by a complete eigenvalue calculation. This difference is largely because the model boundary layer used does not provide a completely appropriate representation of the crosse ow velocity proe les. However, it is within the range of variation of the n factor from one case to the other, when the full eigenvalue solution is used. Comparison of the calculated n factors and the experimentally observed location of transition on the Bombardier wings has revealed a spanwise variation of the critical n factor, with both the complete and automated calculation methods. To improve the prediction of transition, a relation between the n factor at transition and a local Reynolds number (varying along the span )is proposed. The proposed automated method provides considerable reductions in both the computational time and the input required from the user, which allows it to be incorporated in the design cycle.