Flow Transitions for Flow Through a Pipe With a Twisted Tape Insert

Abstract

Insertion of twisted tape in a pipe provides heat transfer augmentation due to swirl formation inside the pipe. Understanding of the transitions of such a swirling flow is an important fluid flow problem. This problem has been studied numerically for H/D = 8.0 and 700 ≤ Re ≤ 1400, where H is the pitch of the twisted tape, D is the diameter of the pipe, and Re is the Reynolds number based on the pipe diameter. The results obtained with large eddy simulations (LES) of such a flow are used in the present work to explore the transitions in the flow through a pipe with twisted tape insert. It is observed that the flow is steady laminar for Re ≤ 700 and changes to periodic laminar flow for 700 ≤ Re ≤ 1126. During this flow regime, the flow occurs with sinusoidal variation of streamwise velocity which exhibit single frequency in the flow. For 1126 ≤ Re ≤ 1263, the flow behavior is quasi-periodic in nature and the time series of streamwise velocity shows two incommensurate frequencies namely primary and secondary frequencies with harmonics in the form of linear combination of primary and secondary frequencies. Further, for 1263 ≤ Re ≤ 1400, the flow transits to chaotic behavior. These transitions have been obtained through a bifurcation analysis of instantaneous streamwise velocity signals captured at a point where maximum fluctuations are likely to occur. It is noticed that the Hopf bifurcation occurs three times as flow changes from steady laminar to chaotic flow. It is further observed through the vorticity contours that, at low Reynolds number, the rate of vorticity generation is low and this vorticity is transported by mere diffusion. Beyond critical Reynolds number, the vorticity pumped from boundary layer into the shear layer is high and diffusion is not sufficient to transport the vorticity and hence the convection of vorticity sets in. This causes the vorticity shedding in the flow, and hence, the fluctuations in the velocity. These results should help to improve the understanding of transitions in the flow through a pipe with twisted tape insert.