RAPID ESTIMATION OF N-FACTORS FOR TRANSITION PREDICTION

摘要

Accurate prediction of transition from laminar to turbulent flow is not only needed for drag estimation, but is also important in predicting scale effects when extrapolating wind tunnel data to full scale. One of the methods commonly used for estimating the most likely position of this transition is based on stability theory. Linear stability theory is used to calculate the spatial evolution of all possible instability waves. If any wave exceeds some maximum amplification the ensuing nonlinear behaviour is assumed to cause a rapid breakdown to turbulence. From a correlation of calculated amplification factors with a large amount of experimental data a value of critical amplification has been found to be roughly e~n, where n is 9. This so called "e-to-n" approach has been used for many years and although not precise it is still one of the best tools available for the purpose of estimating the location of transition. The process of calculating all the eigensolutions needed, especially in three-dimensional boundary layers, can be quite time consuming and the estimation of the transition turns out to be too expensive for routine design purposes. Here we demonstrate an approximate way of calculating eigensolutions that can be used to speed up the prediction process significantly. Approximate eigenvalues are obtained from a set of pre-computed tables covering the required range of pressure gradients, Reynolds numbers and frequencies.