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Unsteady supersonic flow over an oscillatory aerofoil using a second‐order TVD scheme
Author(s) -
Kim JaeSoo
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650170703
Subject(s) - airfoil , mach number , euler equations , transonic , mathematics , inviscid flow , flux limiter , mathematical analysis , geometry , shock (circulatory) , total variation diminishing , physics , aerodynamics , mechanics , medicine
The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second‐order space‐accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0·0 and ± 1·0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co‐ordinates for each time step. The calculations have been done for two angles of attack θ = 5·0° sin (ω t ) and θ = 3·0° + 3·0° sin (ω t ) for the free‐stream Mach numbers 2·0 and 3·0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.