Finite element computation of unsteady viscous transonic flows past stationary airfoils |
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Authors: | S Mittal |
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Affiliation: | (1) Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, UP 208 016, India, IN |
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Abstract: | Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the
Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations.
The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique.
Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the
unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction
between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic
flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively
different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction
between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually
disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase
in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10∘ angle of attack compare well with numerical and experimental results from other researchers |
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