Chaos Dynamics and Intermittency Studies:

This work was done to study high angle of attack aerodynamics for a NACA 0015 airfoil, by solving the Navier-Stokes equation with statistical disturbance field introduced at the computational inflow of the domain. We used chaos dynamical tools to estimate the Lyapunov exponent, correlation dimension of the flow field at strategic locations. We also used the simulation data to calculate the intermittency factor of the transitional flow at different points in the flow. The following paper is from J. Fluids and Structures: vol. 15, pp 671-690 (2001) by T.K. Sengupta, S. De and K. Gupta:

ABSTRACT: Unsteady flow past a NACA 0015 aerofoil is investigated for moderate Reynolds numbers at high angles of attack by solving the full 2-D Navier-Stokes equations with and without the presence of free-stream turbulence (FST). The investigation focusses on the by-pass mode of transition usually encountered in turbomachinery and wind engineering where the flow field around a bluff-body can experience very high levels of FST. In this study, a 5% level of FST is considered. While FST is all-pervasive, its effects has not been studied at all theoritically. Here, this has been made possible by proposing a new modal for FST based on a moving-average time-series and using it for a long-time computation of the Navier-Stokes equations. The statistics of the modelled FST follows the statistics of a specific wind tunnel. The use of this model in conjuction with higher order upwinding, for the convection term to model the vorticity dynamics, gives the solution a very high degree of accuracy in the by-pass transitional flow regime. The present study is relevant for understanding the implications of reduced order modelling proposed for aeroelastic studies. The numerical results view the solution of the Navier-Stokes equations not only as the output of a dynamical system in the presence of stochastic noise (FST), but which also produces the intermittency factor in and around the aerofoil dominated by differing pressure gradient and unsteady effects. The last attribute is also a novel feature of the present study and is relevant to bluff-body flow fields. The computed flow field shows that the flow acheives a statistical stationarity even though the overall flow is chaotic and aperiodic.