Calibration of Smagorinsky Model to Simulate the Fluid Flow in the Cavity and Compare the Results on Collocated and Staggered Grids

In this article, cavity fluid flow is stimulated in Two-dimension. In order to model the effects of turbulence, large eddy simulation model has been used to include sub-network effects of small eddies, sub-grid Smagorinsky model was used. In this method, Smagorinsky coefficient is a constant value which should be determined by experiment. Suggested values by other researchers are in range 0.065-0.25. In this research, staggered and collocated grids have been used in analyzing lid-driven cavity flow and results were compared for different values of Smagorinsky coefficient. Furthermore, the velocity distribution was evaluated in different parts of the cavity. Comparison of numerical results shows that models presented in this research can stimulate this kind of issues with high accuracy with assigning the Smagorinsky coefficient in range of 0.5-0.7. Also, using the staggered grid in comparison with collocated grid leads to more accurate results. With increase the Reynolds number, horizontal and vertical velocity gradient in wall area increases and decreases in middle area of cavity. Also, staggered and collocated grids in low Reynolds numbers present almost similar results in predicting horizontal and vertical velocity in center of the cavity. But with the increase in Reynolds number, the gained results replaced by the staggered grid are more exact and the gradient of horizontal and vertical velocity in the collocated grid, are less moved by the staggered grid than it was supposed to do.