DNS of forced mixing layer
Mohammad Javad Maghrebi 1, Ahad Zarghami 11 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran.
Received by the editors April 8, 2008 and, in revised form, February 17, 2009.
The non-dimensional form of Navier-Stokes equations for two dimensional mixing layer flow are solved using direct numerical simulation. The governing equations are discretized in streamwise and cross stream direction using a sixth order compact finite difference scheme and a mapped compact finite difference method, respectively. A tangent mapping of $y =\beta\tan(\pi \zeta/2) is used to relate the physical domain of y to the computational domain of $\zeta$. The third order Runge-Kutta method is used for the time-advancement purpose. The convective outflow boundary condition is employed to create a non-reflective type boundary condition at the outlet. An inviscid (Stuart flow) and a completely viscous solution of the Navier-Stokes equations are used for verification of the numerical simulation. The numerical results show a very good accuracy and agreement with the exact solution of the Navier-Stokes equation. The results of mixing layer simulation also indicate that the time traces of the velocity components are periodic. Results in self-similar coordinate were also investigated which indicate that the time-averaged statistics for velocity, vorticity, turbulence intensities and Reynolds stress distribution tend to collapse on top of each other at the flow downstream locations.
Key words: Mixing layer, compact finite difference, mapped finite difference, self-similarity.
Email: Javad@shahroodut.ac.ir, Ahad.Zarghami@gmail.com