Near-Wall Stress Balance in Front of a Wall-Mounted Cylinder

Abstract

The stress balance in the near-wall flow in front of a cylinder mounted on a flat plate at moderate Reynolds number is investigated by applying highly resolved Large-Eddy Simulation (LES). The flow around wall-mounted bluff bodies is subject of research due to its wide relevance for engineering applications. However, the structure of the vortex system in front of such a bluff body is complex, bears strong velocity and pressure gradients in each spatial direction and has rich dynamics. Furthermore, the vortex system is located close to the investigated flat bottom wall (Dargahi, Exp. Fluids 8(1-2):1–12, 1989; Devenport and Simpson, J. Fluid Mech. 210:23–55, 1990). Thus, classical models for the treatment of the near-wall flow based on the logarithmic law of the wall or a power law cannot be expected to suffice in such kind of flow (Pope 2011). This paper assesses which contributors to the stress balance have significant influence on the balances residual and thus have to be considered by an approach to model the investigated near-wall flow. To do so, the momentum equation in streamwise direction is integrated in wall-normal direction and applied to the results gained from the LES. The evaluation of the stress balance along four selected wall-normal profiles indicates that the significance of each single term depends on where the profile is located. Outside the viscous layer, no term except the viscous stresses can be neglected in general. The amplitude of the pressure gradient as well as horizontal gradients of mean and fluctuating velocity are multiples of the estimated wall shear stress. Wall models not including a spatial approach are therefore most likely to fail in such kind of flow.