The eN Method for Transition Prediction. Historical Review of Work at TU Delft

Abstract

A historical review of work at TU Delft on the e N method for transition prediction is presented. The method is shown to be applicable to boundary layers with pressure gradient, suction and separation. Some applications to airfoil design will be discussed. An explanation will be given of the reason for the success of this linear theory to "predict" the position of transition which itself is a highly non-linear phenomenon. It will also be explained why the velocity profile shape factor H is a suitable parameter to characterize stability diagrams for flows with and without suction. Finally a new database method will be presented that is based on the observation that many stability diagrams show a remarkable similarity when properly scaled and shifted. The discussion will be restricted to two-dimensional incompressible flow.

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

“…The (parallel flow) Orr-Sommerfeld equation solution has been corrected for non-parallel mean flow effects by expanding the mean flow in powers of Re −1/2 in the coefficients of the linearized NavierStokes equations (22,23 (24) utilized this non-systematic asymptotic approach by combining the non-parallel effects into the single PSE partial differential equation. In the last two decades the PSE has been used within industry, along with other approaches such as the e N method (7,25), and has been extended to take account of hypersonic flows, nonlinearity and chemical reactions within the boundary-layer flow (26,27). The main advantage of incorporating the nonparallel effects into one partial differential equation is that the algebra required to eliminate secular terms in numerical computations, such as Saric & Nayfeh (23), is removed.…”

Secondary Stability Analysis of Crossflow Vortices using BiGlobal Theory on PIV Base Flows

“…their amplification characteristics and shape, is instrumental in understanding-and ultimately predicting-where laminar-turbulent transition will occur. The classical approach in this regard is the semi-emperical e N -method, 5 which correlates perturbation amplification to the transition location. Malik et al 6,7 established that this method yields a good transition correlation by applying it to the secondary instability, comparing their results to the experiments of Kohama et al 8 Related experiments are elaborated on by Kawakami et al, 9 Bippes & Lerche 10 and Bippes.…”

A two-parameter method for eN transition prediction

“…This issue will also be addressed at a later stage. The original one-parameter database method employed the strong similarity that is present between the Arnal stability diagrams (see work by van Ingen 3,4 and Figs.2 and 3). A further investigation has indicated that such a similarity is also present within a series with the same H at the various combinations of β and f wall .…”