Numerical solution of the unsteady Euler equations for airfoils using approximate boundary conditions |
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Authors: | Gao Chao Luo Shijun Liu Feng |
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Institution: | (1) Department of Airraft Engineering, Northwestern Polytechnical University, 710072 Xi'an, China;(2) Department of Mechanical and Aerospace Engineering, University of California, 92697-3975 Irvine, CA, USA |
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Abstract: | This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary rectilinear grids.
Boundary conditions on the surface of an airfoil are implemented by using their first-order expansions on the mean chord line.
The method is not restricted to flows with small disturbances since there are no restrictions on the mean angle of attack
of the airfoil. The mathematical formulation and the numerical implementation of the wall boundary conditions in a fully implicit
time-accurate finite-volume Euler scheme are described. Unsteady transonic flows about an oscillating NACA 0012 airfoil are
calculated. Computational results compare well with Euler solutions by the full boundary conditions on a body-fitted curvilinear
grid and published experimental data. This study establishes the feasibility for computing unsteady fluid-structure interaction
problems, where the use of a stationary rectilinear grid offers substantial advantages in saving computer time and program
design since it does not require the generation and implementation of time-dependent body-fitted grids. |
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Keywords: | unsteady flow Euler equations Cartesian grid numerical method approximate boundary conditions |
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