Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, α), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low α. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence ("puffs") analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics are dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero α limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing α) from the decay dominated (quasi steady) threshold to the steady pipe flow level.
Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.
An experimental investigation was carried out on the flapping motion of a turbulent reattaching shear layer downstream of a two-dimensional backward-facing step. The Reynolds number was 2.0 × 104, based on the free-stream velocity and the step height. The aim of this study is to analyze the flapping motion, which is featured unsteadiness of the reattaching shear layer, and its interaction with the recirculation region. High-resolution planar particle image velocimetry was used to measure the separated and reattaching shear layer in a horizontal-vertical plane. The velocity vector fields have shown the reattaching shear layer considerably flaps upwards and downwards as much in scale as approximately one step height from the middle part of recirculation region to the reattachment area. As a result, the recirculation region varies in size and the reattachment point shifts upstream and downstream. By applying singular value decomposition and proper orthogonal decomposition, the flapping motion is decomposed into multiple spatial modes, each of which represents interactions between the reattaching shear layer and recirculation region. In particular, the unsteady movement of the reattachment point is highly correlated with the flapping motion, and so is the maximum reverse flow. As a result, the flapping motion contributes substantial parts of the Reynolds shear stress and turbulent kinetic energy within the shear layer in the latter half of the reattachment length.
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