Görtler Instability on a Variably Swept, Slotted, Natural-Laminar-Flow Airfoil

Koen J. Groot, Jay M. Patel, Ethan S. Beyak, James G. Coder, Helen L. Reed

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Slotted, natural-laminar-flow airfoils feature a surface with concave curvature, in the slot in particular, which causes Görtler disturbances to be amplified in the boundary layer. By artificially tripping the boundary layer ahead of the slot, previous studies predict a large increase in drag due to the Görtler instability. The present work characterizes the linear instability mechanisms on the bottom surface of the X207.LS airfoil for conditions corresponding to the Klebanoff-Saric wind tunnel to use as reference for experimentation and future non-linear stability studies. The laminar boundary-layer flow is resolved using an infinite-wing, invis-cid pressure distribution provided by MSES in combination with the boundary-layer solver DEKAF. Disturbance amplification factors (N-factors) are computed with Linear Parabolized Stability Equations (LPSE) and both the most amplified, steady and unsteady solutions are identified. Sweep angles from Λ = 0 to 35 are considered and the angle of attack is fixed at a relatively large 2.25, which maximizes the potential for crossflow instability on the bottom side of the airfoil and stabilizes the Tollmien-Schlichting instability. As a consequence, for Λ = 0, large disturbance amplification in the slot can be uniquely attributed to the Görtler mechanism; N-factors in excess of 12 are achieved at the trailing edge of the fore-element of the airfoil. Crossflow-velocity profiles emerge for non-zero sweep, which, upon computing the N-factors with neutral points closest to the slot entrance, have a stabilizing effect on the disturbance amplification in the slot that is monotonic with sweep. At Λ = 35, the most amplified, steady and unsteady disturbances achieve N-factors in excess of 6 and 8, respectively. Upstream of the slot, crossflow disturbances are not significantly amplified (N ≪ 1) for Λ ≤ 20 . At larger sweep, stationary and traveling crossflow disturbances achieve significant, locally maximum N-factors upstream of the slot (up to 3 and 4.5 for Λ = 35, respectively), but the increasingly larger convex curvature of the airfoil leading into the slot quenches most of the linear crossflow growth accumulated upstream. Therefore, upon computing the N-factors with neutral points closest to the attachment line, a relatively small distortion (ΔN = ±2) is recorded with respect to the aforementioned monotonic stabilizing trend with sweep. The N-factors are computed with several approaches, yielding a significant variety of the disturbance shape functions at the slot entrance. The N-factor-envelope variation is found to be relatively mild (ΔN ≤ ±2.1), which is explained by the collapse of the most amplified shape functions at about one-third of the chordwise extent into the slot.

Original languageEnglish (US)
Title of host publicationAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624106101
DOIs
StatePublished - 2021
EventAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021 - Virtual, Online
Duration: Aug 2 2021Aug 6 2021

Publication series

NameAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021

Conference

ConferenceAIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
CityVirtual, Online
Period8/2/218/6/21

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Energy Engineering and Power Technology
  • Nuclear Energy and Engineering

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