Computational Analysis on the Three-Dimensionality of Turbulent Duct-Flow Subsequent to In-Plane Double Bends

We present a computational study of Prandtl’s secondary flow of the first kind in the presence of turbulence within a 90˚ in-plane double bend fitted between two straight ducts. Most of the previous papers available in the literature demonstrate the gross flow behaviours due to out-of-plane double bends. We, however, focus on capturing the local flow behaviours in an in-plane double bend and the progressive development of the flow downstream of the bend. We capture a pair of Dean vortices located downstream of the double bend. We trace the motion of higher velocity fluid particles within the vortices by in-plane velocity vectors directed from the pipe core towards the bend’s outer side due to an unbalanced centrifugal force of the skewed flow. Our solutions nicely capture the decay of the in-plane flow (or secondary flow) and concurrent re-establishment of primary flow downstream of the bend. For engineering analyses, we introduce a new parameter called enhancement ratio ( \(\varepsilon\) ), a measure of the increase of the fluid velocity while passing through the bend. \(\varepsilon\) decreases with increasing both Reynolds numbers ( \({\text{Re}}\) ) and curvature ratio ( \(\overline{R}_{c}\) ). It is realized that the reduction of \(\varepsilon\) is related to the corresponding fall in non-dimensional pressure loss.