Volume 7, Issue 1
DNS of Forced Mixing Layer

M. J. Maghrebi & A. Zarghami

Int. J. Numer. Anal. Mod., 7 (2010), pp. 173-193.

Published online: 2010-07

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  • Abstract

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.

  • Keywords

Mixing layer, compact finite difference, mapped finite difference, self-similarity.

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@Article{IJNAM-7-173, author = {Maghrebi , M. J. and Zarghami , A.}, title = {DNS of Forced Mixing Layer}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {1}, pages = {173--193}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/715.html} }
TY - JOUR T1 - DNS of Forced Mixing Layer AU - Maghrebi , M. J. AU - Zarghami , A. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 173 EP - 193 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/715.html KW - Mixing layer, compact finite difference, mapped finite difference, self-similarity. AB -

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.

M. J. Maghrebi & A. Zarghami. (1970). DNS of Forced Mixing Layer. International Journal of Numerical Analysis and Modeling. 7 (1). 173-193. doi:
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