Abstract
：A linear theoretical model is established for the dynamics of a hanging vertical cantilevered pipe which is subjected concurrently to internal and reverse external axial flows. Such pipe systems may have instability by flutter (amplified oscillations) or static divergence (buckling). The pipe system under consideration is a slender flexible cantilevered pipe hanging concentrically within an inflexible external pipe of larger diameter. From the clamped end to the free end, fluid is injected through the annular passage between the external pipe and the cantilevered pipe. When exiting the annular passage, the fluid discharges in the counter direction along the cantilevered pipe. The inflexible external pipe has a variable length and it can cover a portion of the length of the cantilevered pipe. This pipe system has been applied in the solution mining and in the salt cavern underground energy storage industry. The planar motion equation of the system is solved by means of a Galerkin method, and Euler–Bernoulli beam eigenfunctions are used as comparison functions. Calculations are conducted to quantify the effects of different confinement conditions (i.e., the radial confinement degree of the annular passage and the confined-flow length) on the cantilevered pipe stability, for a long leaching-tubing-like system. For a long system, an increase in the radial confinement degree of the annular passage and the confined-flow length gives rise to a series of flutter and divergence. Additionally, the effect of the cantilevered pipe length is studied. Increasing the cantilevered pipe length results in an increase of the critical flow velocity while a decrease of the associated critical frequency. For a long enough system, the critical frequency almost disappears.
Highlights
This paper focuses on the pipe paper focuses on the pipe model shown in Figure 1a, and the motivation is desired to potentially model shown in Figure and thecantilever motivation is desired to to potentially improve design of slender improve the design 1a, of slender pipes in order avoid issues cause the by flow-induced cantilever pipes in order to avoid issues cause by flow-induced vibration
A few researchers haveconsideration been done the oninconveying-fluid pipes lies in the undeflected centerline of the internal cantilever pipe, while the z-axis lies along the lateral subjected simultaneously to both internal and external axial flows
It should be pointed out that after the external flow exits from the outside annular passage, fluid is conveyed upwards as the internal flow in the cantilever pipe
Summary
In [5], Hannoyer et al investigated the dynamics and stability of both clamped–clamped cylindrical tubular beams conveying fluid, which simultaneously are subjected to independent axial external flows. They studied the dynamics of cantilevered pipes fitted with a tapered nozzle at the free end. In [8], Païdoussis et al developed a theoretical model to study the vibration of a hanging tubular cantilever which was centrally inside a cylindrical container, with fluid flowing within the cantilever, and discharging from the free end. They developed a theoretical model and carried out corresponding experiments.
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