TY - GEN
T1 - Görtler Instability on a Variably Swept, Slotted, Natural-Laminar-Flow Airfoil
AU - Groot, Koen J.
AU - Patel, Jay M.
AU - Beyak, Ethan S.
AU - Coder, James G.
AU - Reed, Helen L.
N1 - Funding Information:
This material is based upon work supported by the National Aeronautics and Space Administration (NASA) under cooperative agreement award number NNX17AJ95A. The work was performed under the University Leadership Initiative (ULI) at Texas A&M University as a subcontract to the University of Tennessee, Knoxville Advanced Aerodynamic Design Center for Ultra-Efficient Commercial Vehicles. This research was supported by the U.S. Air Force Research Laboratory/U.S. Air Force Office of Scientific Research (AFOSR) through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of AFOSR or NASA. We acknowledge Mr. Jeppesen Feliciano and Dr. Edward White for close experimental collaborations.
Publisher Copyright:
© 2021, American Institute of Aeronautics and Astronautics Inc.. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.2514/6.2021-2590
DO - 10.2514/6.2021-2590
M3 - Conference contribution
AN - SCOPUS:85126738209
SN - 9781624106101
T3 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
BT - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
PB - American Institute of Aeronautics and Astronautics Inc, AIAA
T2 - AIAA Aviation and Aeronautics Forum and Exposition, AIAA AVIATION Forum 2021
Y2 - 2 August 2021 through 6 August 2021
ER -