Extension of the PSE Code NOLOT for Transition Analysis in Rotating Reference Frames

Abstract

In this paper, spatial linear stability analyses are performed on three flow configurations where rotational effects are present. The first two configurations are the two-dimensional flows along a flat plate and along a curved plate, both with a rotation vector along the spanwise direction. The third configuration is the threedimensional flow over a rotating disk with and without axial inflow. These flows are used as a verification of the extension of the stability analysis code NOLOT to rotating frames. For all these three flows, a perfect matching is observed in comparison with results from the literature for the neutral curves and the eigenfunctions. The present results show that rotation has a considerable effect on the stability of boundary layers. Depending on the intensity and orientation of the rotation vector, stabilization or destabilization of the boundary layer is observed.

Linear stability analysis in rotating frames and its application to fan blade transition prediction

“…Tollmien-Schlichting are found to be hardly modified by rotation while cross-flow waves are destabilised. These findings are in agreement with the work of Dechamps and Hein [11]. The N-factors reached by cross-flow waves are seen to be too low to trigger transition which is rather due to the amplification of Tollmien-Schlichting waves.…”

“…Adding the rotation terms in the linear stability equations is only seen to destabilize the already existing cross-flow waves. The fact that Tollmien-Schlichting instabilities are hardly modified is in agreement with results of Dechamps and Hein [11].…”

“…Moreover, two new validation cases are proposed to validate the implementation of compressible terms. This was motivated by the fact that "only very few test cases combine rotation with compressibility in the litterature" as stated by Dechamps and Hein [11].…”

“…The latter are hardly affected by the rotation. [11], the flow over a fan blade supports cross-flow waves even when rotation is not accounted for. Adding the rotation terms in the linear stability equations is only seen to destabilize the already existing cross-flow waves.…”

“…This paper presents the details for extending the instability analysis program MAMOUT [10] of ONERA to rotating flow (section III). In particular, test cases are provided to validate the implementation of the additional terms appearing in the linear stability equations for compressible flows over arbitrary geometries because, as stated by Dechamps and Hein [11], "only very few test cases combine rotation with compressibility in the literature". The solver MAMOUT is then applied to investigate the effect of the terms associated to rotation in the linear stability equations on the stability of the flow over a fan blade (section IV).…”