(320b) Structure of Poiseuille-Couette Flow in an Infinite Channel with Direct Numerical Simulations

Super hydrophobic surfaces (i.e., those with contact angle larger than 150 degrees) have been found to produce not only fluid slip in microchannel flows but also to induce considerable drag reduction for laminar flows [1]. Furthermore, applications of such surfaces for drag reduction in turbulent flows are also under consideration [2]. Previous works by Rothstein and his coworkers [3,4] have indicated  that turbulent drag reduction may be obtained by using super hydrophobic surfaces appropriately. Another study by Spencer et al. [5] has pointed out that a specified fluid slip at the wall leads to a decrease of turbulent intensities and of turbulent kinetic energy production as well as a decrease in drag force at the channel wall. The present simulation study would give further information on how specified slip velocity at the wall affects near-wall flow structures.

A Poiseuille-Couette flow is simulated in an infinite channel in order to impose a streamwise slip boundary condition on one of the channel walls, based on the movement of the walls in this kind of flow. The pressure gradient is kept unchanged, and the top wall moves in the flow direction, while the bottom one is kept moving in the opposite direction compared to the top wall. A computational box size of 8πh x 2h x 2πh (with a resolution of 512 x 129 x 256) in x,y and z directions, respectively, with periodic boundary conditions is used to simulate this Poiseuille-Couette flow (h is half of the channel height, and is 300 in viscous wall units).  The relative velocity between the two walls were set to be 1, 2 and 4 in viscous wall units, which are calculated based on the shear stress at the wall, and the density and viscosity of fluid under study. Due to the Galilean invariance of the Navier-Stokes equation, subtracting the mean velocity at the bottom wall would give us a corresponding case in which the bottom wall is stationary, while the top wall moves in the positive streamwise direction with a velocity equal to the relative velocity between the two walls. This is a way to simulate a super hydrophobic surface at the top wall of the channel. Our results show that the presence of streamwise wall slip modifies turbulence at the near wall region to get closer to the limiting state of the Lumley triangle (one component sate) and to satisfy both two-component limit and axisymmetry at large and small scales. Earlier analytical work has proved [6] that this would lead to a significant suppression of small scale turbulence and rapid laminarization close to the wall, leading to drag reduction. Correlation coefficients and analysis of the turbulence structure close to the wall will also be discussed.

References

[1] Ou, J., and J. P. Rothstein, Phys. Fluids 17(10), Art. No. 103606 (2005).

[2] Fukagata, K., Kasagi, N., and P. Koumoutsakos, Phys. Fluids 18(5), Art. No. 051703 (2006).

[3] J. P. Rothstein, Annu. Rev. Fluid Mech. 42, 89-109 (2010).

[4] M. B. Martell, J. P. Rothstein, and J. B. Perot, Phys. Fluids 22(6), Art. No. 065102 (2010).

[5] N. B. Spencer, L. L. Lee, R. N. Parthasarathy, and D. V. Papavassiliou, The Canadian Journal of Chemical Engineering  87(1), 38-46,(2009).

[6] J. Jovanovic and R. Hillerbrand, Thermal Science 9, 3 (2005).