The upstream scale of flow development in curved circular pipes

Abstract

For steady airflows at moderate Dean number (100 [les ] κ [les ] 500) axial- and transversevelocity profiles were delineated by anemometry in the entry region of curved circular pipes, having curvature ratios R/a of 4.66 or 8. Uniform inlet velocity profiles were found to evolve downstream over two inviscid length scales. Axial profiles develop on the lengthscale a, the pipe radius. The upstream influence extends at least 6a into a bend. Within this region axial development is largely inviscid and apparently independent of the radius of curvature R. Secondary currents develop on the scale (aR)½. Their initial growth is consistent with a model of vorticity transport based on streamline curvature, but instead of progressing monotonically to an asymptotic value, this swirl first overshoots, then subsides approximately 2(aR)½ downstream from the inlet. Hawthorne's model of streamline twist appears to account qualitatively for this dampening.