Turbulent boundary layer over solid and porous surfaces with small roughness
Kong, Fred Y.
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Experimental studies were conducted to obtain direct measurements of skin friction, mean velocity profiles, axial and normal turbulence intensity profiles, and Reynolds stress profiles in the boundary layer on a large diameter, axisymmetric body with a smooth, solid surface; a sandpaper-roughened, solid surface; a sintered metal, porous surface; a"smooth", perforated titanium surface, a solid, rough Dynapore surface made of diffusion-bonded screening, and a porous, rough Dynapore surface. The roughness values were in the low range (k⁺ = 5-7) just above what is normally considered"hydraulically smooth. 11 Measurements were taken at several axial locations and two different freestream velocities corresponding to dynamic pressures of 12.7 and 17.8 cm. of H₂O, which gives a Re𝓁 range of 2.93 x 10⁶ to 3.38 x 10⁶. For the Law of the Wall, Defect Law, and the turbulence quantities, very good agreement was found between the present results and those from well-established studies for a solid, smooth surface. The sandpaper-roughened, solid wall and solid, rough Dynapore wall tests showed a 20%~30% increment in local skin friction and a slight shift in the log region of the Wall Law, as well as an increase in turbulence quantities over the smooth wall results. These results were in accord with the classical results collected by Clauser for rough, solid surfaces in this range. The effect of porosity can be shown by comparing the sintered metal, porous wall results to the sand-roughened, solid wall results. Although there is a difference in roughness patterns for these two cases, the average k⁺ is in the same range of 5 ~ 7. To check the effect of porosity directly without any interference of different surface roughness patterns, one can compare the results between the 11 smooth 11 perforated titanium wall and the solid, smooth wall, or between the porous Dynapore and solid Dynapore walls. The effect of porosity showed a 30%~40% increment in local skin friction and a marked downward shift of the logarithmic portion of the Wall Law, as well as an increase in turbulence quantities over the smooth wall results. The combined effects of small roughness and porosity could be seen by comparing the results between the sintered metal, porous wall and the smooth, solid wall, or between the porous Dynapore wall and the smooth, solid wall. It was observed that the combined effects of small roughness and porosity are roughly additive. The effect of porosity due to the existence of the penetration of turbulence through the porous surfaces was detected experimentally by a hot-wire underneath the porous walls. All these results demonstrate that a rough, porous wall simply does not influence the boundary layer in the same way as a solid, rough wall. Therefore, turbulent boundary layer models with injection or suction must include both surface roughness and porosity effects.
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