Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow

Two orthogonal components of velocity and associated Reynolds stresses have been measured in a square-sectioned, 90 degree bend of 2.3 radius ratio using laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. The boundary layers at the bend inlet were 0.25 and 0.15 of the hydraulic diameter and resulted in secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity respectively. Comparison with fully-developed inlet flow shows that the boundary layer thickness is important to the flow development (mainly in the first half of the bend), particularly so when it is reduced to 0.15 of the hydraulic diameter. Turbulent flow in an identical duct with a radius ratio of 7.0 gives rise to smaller secondary velocities than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. The detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models. Partially-parabolic techniques are applicable to the flows studied and their reduced storage requirements seem essential if satisfactory numerical accuracy is to be achieved.