Effects of Various Shaped Roughness Elements in Two-Dimensional High Reynolds Number Turbulent Boundary Layers

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Virginia Tech


Modeling the effects of surface roughness is an area of concern in many practical engineering applications. Many current roughness models to this point have involved the use of empirical 'constants' and equivalent sand grain roughness. These underdeveloped concepts have little direct relationship to realistic roughness and cannot predict accurately and consistently the flow characteristics for different roughness shapes. In order to aid in the development of turbulence models, the present research is centered around the experimental investigation of seven various shaped single roughness elements and their effects on turbulence quantities in a two-dimensional turbulent boundary layer.

The elements under scrutiny are as follows: cone, cone with spatial variations equal to the smallest sublayer structure length scale, cone with spatial variations equal to 2.5 times the smallest sublayer structure length scale, Gaussian-shaped element, hemisphere, cube aligned perpendicular to the flow (cube at 90°), and a cube rotated 45° relative to the flow. The roughness element heights, k+, non-dimensionalized by the friction velocity (U_tau) of the approaching turbulent boundary layer, are 145, 145, 145, 145, 80, 98, and 98 respectively. Analysis of a three-dimensional fetch of the same Gaussian-shaped elements described previously was also undertaken. In order to analyze the complex flow fields, detailed measurements were obtained using a fine-measurement-volume (50 micron diameter) three-velocity component laser-Doppler velocimetry (LDV) system.

The data reveals the formation of a horseshoe vortex in front of the element, which induces the downwash of higher momentum fluid toward the wall. This 'sweep' motion not only creates high Reynolds stresses (v^2, w^2, -uv) downstream of the element, but also leads to higher skin-friction drag. Triple products were also found to be very significant near the height of the element. These parameters are important in regards to the contribution of the production and diffusion of the turbulent kinetic energy in the flow. The 'peakiness' of the roughness element was found to have a direct correlation to the production of circulation, whereas the spatial smoothing does not have an immense effect on this parameter. The peaked elements were found to have a similar trend in the decay of circulation in the streamwise direction. These elements tend to show a decay proportional to (x/d)^-1.12, whereas the cube elements and the hemisphere do not have a common trend.

A model equation is proposed for a drag correlation common to all roughness elements. This equation takes into account the viscous drag and pressure drag terms in the calculation of the actual drag due to the roughness elements presence in the boundary layer. The size, shape, frontal and wetted surface areas of the roughness elements are related to one another via this model equation. Flow drawings related to each element are presented which gives rise to a deeper understanding of the physics of the flow associated with each roughness element.



Isolated roughness elements, Distributed roughness, Near-wall flow structure, Drag correlation, Subsonic, Turbulent boundary layer, Turbulent kinetic energy, Laser-Doppler Velocimetry, Circulation decay