Resolvent analysis of separated and attached flows around an airfoil at transitional Reynolds number

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Title: Resolvent analysis of separated and attached flows around an airfoil at transitional Reynolds number
Author(s): Thomareis, N
Papadakis, G
Item Type: Journal Article
Abstract: We analyze the resolvent operator in three flows around a nomi nal NACA-0012 airfoil at Re C = 50 , 000 and 5 o angle of attack. In particular, we study two naturally devel oping flows (around the airfoil with straight and blunt trailing edges) and one t ripped flow. The naturally developing flows exhibit laminar separation, transition and turbulent reattachment, while the tripped flow remains attached in the suction side. For all cases, the time -averaged flow fields are computed from separate DNS simulations. The resolvent analysis can ident ify the areas of maximum receptivity of the flow field as well as the most amplified modes (optimal res ponse). The former was located close to the leading edge, and in the case of naturally develo ping flows, also in the free-stream. The spatial distribution of optimal forcing was dominated b y structures tilted against the mean flow, in agreement with other studies of boundary layer flows. The optimal response of the two naturally developing flows were different. For the NACA-0012 airfoil with straight trailing edge, the response was maximized at the natural frequency of the se parating shear layer, and the shape matched closely with the corresponding DMD mode obtained fr om processing the DNS results. For the blunt airfoil, the receptivity of the separating she ar layer was suppressed in the region of natural frequency, while it was maximized at the frequency o f vortex shedding from the trailing edge. This is attributed to the lock-in mechanism between th e shedding and the separating shear layer observed in the DNS simulations; the lock-in makes the separating shear layer less sensitive to forcing. In the tripped flow, the amplification of the pertu rbations is significantly diminished, and only by restricting the resolvent analysis to a region cl ose to the suction side can we get a dominant frequency that matches with DNS at that region. The dominant resolvent modes were used to get estimations of the velocity spectra based only on the mean flow and the signal of one velocity component at discrete calibration points. Very go od approximation is observed with only one or two points (depending on the flow examined), provided t hat they are located in energetic regions of the flow that contain sufficient spectral content at the relevant frequencies.
Publication Date: 11-Jul-2018
Date of Acceptance: 8-Jun-2018
URI: http://hdl.handle.net/10044/1/61256
ISSN: 2469-990X
Publisher: American Physical Society
Journal / Book Title: Physical Review Fluids
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: FP7 - 317269
Copyright Statement: This paper is embargoed until publication.
Publication Status: Accepted
Embargo Date: publication subject to indefinite embargo
Appears in Collections:Faculty of Engineering
Aeronautics



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