Navier-Stokes Computations of Transition to Turbulent Flow Around Airfoils


Numerical solutions of the Reynolds-averaged Navier-Stokes equations were obtained with the two-equation K-ε turbulence model. Considering the low-Reynolds-number effect in the closed vicinity of a solid boundary, a stream function and vorticity method was developed to consider both the laminar and turbulent stresses throughout the two-dimensional, incompressible flowfield of any arbitrary geometry. At a low Reynolds number (Re = 30), the initially imposed disturbances around an airfoil are damped out; the flow is laminar. At a moderately high Reynolds number (Re = 1000), instability of laminar flow is obtained by exhibiting cyclic patterns in the stream function and vorticity distributions. Nevertheless, only laminar stress occurs in the entire flowfield. At a higher Reynolds number (Re = 10⁶), turbulent stress, which is about three orders of magnitude larger than the laminar stress, occurs at a certain distance downstream of the leading edge and in the wake region. The location, where the turbulent stress begins to increase is considered as the point of transition.

Meeting Name

Aerospace Technology Conference and Exposition


Mechanical and Aerospace Engineering

Keywords and Phrases

Mathematical Analysis; Aerodynamics

Document Type

Article - Conference proceedings

Document Version


File Type





© 1990 Society of Automotive Engineers, All rights reserved.

Publication Date

01 Jan 1990