Smooth and rough turbulent boundary layers at high Reynolds number

Abstract

A 2-D turbulent boundary layer experiment with zero pressure gradient (ZPG) has been carried out over a rough and a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 m/s and 20 m/s were set up in order to investigate the effects of the upstream conditions and the Reynolds number on the downstream flow. For a given set of upstream conditions, such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m from the inlet of the wind tunnel to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R θ ≅120,000, for which measurements of the mean velocity are reported. It is shown that by fixing the upstream conditions, the mean deficit profiles collapse with the freestream velocity, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! <![CDATA[% MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGvbWaaSbaaSqaaiabg6HiLcqabaaaaa!3BF0! $$U_{\infty } $$ , but to different curves depending on the upstream conditions and surface roughness. Moreover, the effects of the upstream conditions, the Reynolds number, and roughness are completely removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits scaling, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! <![CDATA[% MathType!MTEF!2!1!+- % feaafeart1ev1aqatCvAUfeBSn0BKvguHDwzZbqefeKCPfgBGuLBPn % 2BKvginnfarmWu51MyVXgatuuDJXwAK1uy0HwmaeHbfv3ySLgzG0uy % 0Hgip5wzaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq % -He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeWaea % aakeaacaWGvbWaaSbaaSqaaiabg6HiLcqabaGcdaWcaaqaaiabes7a % KnaaBaaaleaacqGHxiIkaeqaaaGcbaGaeqiTdqgaaaaa!4079! $$U_{\infty } \frac{{\delta _{ * } }}{\delta }$$ . Consequently, the true asymptotic profile in the turbulent boundary layer is found in ZPG flow regardless of the range of Reynolds number, surface conditions and initial conditions.