Extrapolating channel flow data to high Reynolds number conditions

Authors: Vinuesa, R., Dressler, K, Nagib, H.M.
Document Type: Article
Pubstate: Accepted
Journal: 63rd Annual Meeting of the American Physical Society, Division of Fluid Dynamics. 21 November 2010, Long Beach, CA, USA.
Year: 2010


Channel and pipe flows require relatively larger Reynolds numbers (Re) than boundary layers to achieve “high-Re conditions” for wallbounded flows. Unlike the pipe case, where the Superpipe results far exceed such conditions, even the highest Re channel experiments have not reached such a state. Because of the extremely large channel facility required to achieve these high-Re conditions with good spatial resolution for the measurements, DNS may present the best hope. Available experimental and DNS results, and new data from a channel with variable aspect ratio, are used to estimate the high-Re von K´arm´an coefficient and the Re required to achieve it. Wall shear stress measurements with oil film interferometry were obtained over the range 7, 500 < Rem < 30, 000 in channel flows for aspect ratios varying from 18 to 48. The results show that the relationship between Reynolds number and skin-friction coefficient depends on the channel aspect ratio well beyond the traditional values of 8 to 12 generally believed to ensure two-dimensionality. The results indicate that an increase by a factor of about four or five in the current Re capabilities of DNS is required to approach the asymptotic von K´arm´an coefficient for the channel, which likely is even lower than our recent estimates of 0.37.