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Unsteady thin airfoil theory revisited for a general deforming airfoil

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Abstract

The unsteady thin airfoil theory of von Karman and Sears is extended to analyze the aerodynamic characteristics of a deforming airfoil. The von Karman and Sears approach is employed along with Neumark’s method for the unsteady load distribution. The wake-effect terms are calculated using either the Wagner or Theodorsen function, depending on the desired camberline deformation. The concept of separating the steady and damping terms in the camberline boundary condition is introduced. The influence of transient and sinusoidal airfoil deformations on the airfoil load distribution is examined. The general equations developed for the unsteady lift and load distribution are evaluated analytically for a morphing airfoil, which is defined here by two quadratic curves with arbitrary coefficients. This general camberline is capable of modeling a wide range of practical camberline shapes, including leading and trailing edge flaps. Results of the present model are shown for a variable camber, or morphing, airfoil configuration. The influence of transient and sinusoidal motion on the force coefficients and load distribution is addressed.

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Authors and Affiliations

  1. Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24060, USA

    Christopher O. Johnston & William H. Mason

  2. Department of Aeronautical and Mechanical Design Engineering, Chungju National University, 50 Daehak-Ro, Choongbuk, 380-702, Korea

    Cheolheui Han

Authors
  1. Christopher O. Johnston
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  2. William H. Mason
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  3. Cheolheui Han
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Corresponding author

Correspondence to Cheolheui Han.

Additional information

This paper was recommended for publication in revised form by Associate Editor Do Hyung Lee

Christopher O. Johnston is currently2 an Aerospace Engineer in the Aerothermodynamics Branch at NASA Langley Research Center. He received his B.S., M.S., and Ph.D. at Virginia Tech, which is where the present work was performed.

Cheolheui Han received a B.S. degree in Mechanical Engineering from Hanyang University in 1993. He received his M.S. and Ph.D. degrees from Hanyang University in 1998 and 2003, respectively. Then, he worked as a visiting post-doctoral researcher at the Dept. of Aerospace and Ocean Engineering at Virginia Tech, USA. Dr. Han is currently an Assistant Professor at the Department of Aeronautical and Mechanical Design Engineering.

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Johnston, C.O., Mason, W.H. & Han, C. Unsteady thin airfoil theory revisited for a general deforming airfoil. J Mech Sci Technol 24, 2451–2460 (2010). https://doi.org/10.1007/s12206-010-0920-4

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  • DOI: https://doi.org/10.1007/s12206-010-0920-4

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