Abstract
This paper investigates the inflection-point instability that governs the flow disturbance initiated in the entrance region of a pulsating pipe flow. Under such a flow condition, the flow instability grows within a certain phase region in a pulsating cycle, during which the inflection point in the unsteady mean flow lifts away from the viscous effect-dominated region known as the Stokes layer. The characteristic frequency of the instability is found to be in agreement with that predicted by the mixing-layer model. In comparison with those cases not falling in this category, it is further verified that the flow phenomenon will take place only if the inflection point lifts away sufficiently from the Stokes layer.
Highlights
The well-known Reynolds experiment [1] is concerned with the laminar–turbulent transition phenomenon in a pipe flow for which the mean flow is steady
This study confirms a flow regime in pulsating pipe flow that the inviscid flow instability prevails in the entrance region
In comparison with the cases governed by the viscous mechanism, the inviscid flow instability regime is found at lower ReU and higher Rem, such that the inflection point situated outside of the Stokes layer plays an effective role
Summary
The well-known Reynolds experiment [1] is concerned with the laminar–turbulent transition phenomenon in a pipe flow for which the mean flow is steady. An important feature of the laminar–turbulent transition process in a pulsating pipe flow is that the flow disturbance becomes intermittently unstable in every pulsating cycle [2,3,4,5] This intermittent flow behaviour has been found in the fully developed region [6,7,8,9,10,11,12]. The unstable disturbance initially appears as waves of small amplitude within a certain phase region of a pulsating cycle This is typical of flow instability that develops in an unsteady mean flow. It is worthwhile to mention the work of Gad-el-Hak et al [19] on flow instability in a decelerating boundary layer They commented that the inflection point in the decelerating boundary layer velocity profile promoted flow instability at a Reynolds number lower than the critical one corresponding to the steady boundary-layer flow. The experimental data obtained were examined with a mixing-layer model, which is a physical case complied with the inflexion point instability theory
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