Abstract
Velocity profiles are extracted from time- and span-averaged direct numerical simulation data, describing the flow over a high-pressure turbine vane linear cascade near engine-scale conditions with reduced inlet disturbance levels. Based on these velocity profiles, local as well as non-local linear stability analysis of the boundary-layer over the suction side of the vane is carried out in order to characterise a linearly unstable region close to the trailing edge. The largest growth rates are found for oblique modes, but those are only slightly more unstable than 2D modes, which describe the locations and frequencies of most unstable modes very well. The frequencies of the most unstable linear modes predict with good accuracy the predominant frequencies found in the direct numerical simulations (DNS) close to the trailing edge.
Highlights
In order to design more efficient high-performance turbines, an improved understanding and prediction of laminar-turbulent boundary-layer (BL) transition is crucial
The basis for the linear stability theory (LST) is provided by the Orr-Sommerfeld equation (OSE), which is derived from the compressible Navier Stokes Equations (NSE) considering a 2D flowfield ([4] provides further detail on the derivation of the OSE)
The temporal LST results are cross-checked with those obtained from a spatial LST approach
Summary
In order to design more efficient high-performance turbines, an improved understanding and prediction of laminar-turbulent boundary-layer (BL) transition is crucial. Disturbance growth rates help to improve empirical laws for predicting transition and can provide characteristic length- and time-scales for turbulence models that are used in design studies. The output of such methods can be used to study active or passive flow control, since the computational effort is low compared to DNS. To perform a linear stability analysis, wall-normal velocity-profiles are extracted from the DNS data, corresponding to a coordinate transformation. In order to obtain consistent and stable results applying the non-local LPSE approach, all velocity profiles are interpolated onto a numerical grid (uniform in the s-direction) and smoothed in the s-direction along the suction-side surface.
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