Direct Numerical Simulation Computational Model

In this study, a computational model consisting of a NACA0012 airfoil at zero angle of attack is used. The chord width, C, is 0.1 m, but the sharp trailing edge is truncated and fitted with a round trailing edge. The airfoil is placed in a uniform stream with a velocity Uranging from 30 m/s to 75 m/s. The kinematic viscosity of air, v at 15°C, is taken to be 0.145 x 10-4 m2/s. The corresponding Reynolds number, based on chord width, varies from 2 x 105 to 5 x 105.

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The governing equations are the dimensionless Navier-Stokes equations in two dimensions. Here the length scale is C (chord width), velocity scale is aTO (ambient sound speed), time scale is C/aTO, density scale is p(ambient gas density), pressure and stresses scale is p^a^. These equations (in Cartesian tensor subscript notation) are

U is the free stream velocity, M is the Mach number, and Re is the Reynolds number. Both viscous dissipation and heat conduction are neglected in the energy equation. Away from the airfoil, viscous effects are unimportant. In this part of the computational domain, viscous terms are dropped, that is, the Euler equations replace the Navier-Stokes equations as the governing equations.