Analysis on a Kinetic Theoretical Model of the Straight-Curved Pipe Conveying Fluid

Abstract

A kinetic theoretical model for the straight-curved pipe conveying fluid was proposed and studied in this paper. Firstly, the new equations of static equilibrium and motion about equilibrium position were derived by applying perturbation method to the motion equations of the curved pipe conveying fluid. Then, the kinetic equations of the straight pipe were derived by ignoring the terms containing the curvature of the curved pipe in these equations. Subsequently, considering different factors, four segmental kinetic theoretical models of the straight-curved pipe were built. Lastly, based on the present theoretical models and finite element method, the static deformations and natural frequencies of the pipes with three typical boundary conditions were simulated. The simulation results show that the applicability of these kinetic theoretical models is closely related to the boundary conditions: 1) For the pipes with any one of three boundary conditions, the geometrical non-linearity and the nonlinear force caused by the deformation of straight pipe segment, have a great effect on the static deformation of the pipes, while they have little effect on the natural frequencies of the pipes. 2) When the natural frequencies of the pinned-pinned pipe or the pinned-sliding bearing-pinned pipe are solved, the static deformation of the pipes must be considered.3) When the natural frequencies of the pinned-pinned-pinned pipe are solved, the static deformation of the pipe can be ignored.

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

“…In addition, it was found that the steady combined force could have a great impact on the vibration characteristics of the curved-shaped pipe. As pointed out by Wen et al [40], the nonlinear force caused by the deformation of the straight pipe segment, static deformation and geometrical non-linearity of the pipe could have a considerable influence on the dynamics of the straight-curved combination pipe. Unfortunately, this effect was not taken into account in the study of Koo and Yoo [36], and only the static axial force caused by static deformation of the pipe was contained in the Dai et al's model [38].…”

“…Thus, it is worth to explore the dynamics of the straight-curved combination fluid-conveying pipe. Indeed, a few researchers have studied this kind of pipe [34][35][36][37][38][39][40][41][42][43]. In 1990, a linear analytical model that include the Poisson coupling was proposed by Lesmez et al [34] to perform the modal analysis of vibrations in liquid-filled piping system.…”

“…Unfortunately, this effect was not taken into account in the study of Koo and Yoo [36], and only the static axial force caused by static deformation of the pipe was contained in the Dai et al's model [38]. Thus, a modified four segmental kinetic theoretical model was established by Wen et al [40] to explore the nonlinear static deformation and the linear stability of the straight-curved pipe conveying fluid. Their numerical results indicated that the effect of the static deformation of the pipe on the natural frequencies of the pinned-pinned pipe or the pinned-sliding bearing-pinned pipe was pronounced, while for pinned-pinned pipe, this effect could be ignored.…”

“…It should be pointed out that the model developed in the present work has four advantages compared with those models mentioned in the Ref. [31][32][33][34][35][36][37][38][39][40]: (i) it can determine the extremely large-amplitude vibrations of the soft straight-curved combination pipes conveying fluid; (ii) it can be applied to the straight-curved combination pipes with arbitrary initially shapes, such as L-, Z-, U-, J-shaped pipes, etc. ; (iii) it can be applied to any boundary conditions, such as pinned-pinned, clamped-free, pinned-pinned-free and so on; (iv) it can handle not only the self-excited vibrations but also the forced oscillations.…”

Conductance Study on The Effect of Torsion of Drilling Pipe on The Inside Pattern Fluid Flow

“…Doll and Mote Jr [15] presented dynamical curved and twisted pipes to conclusion proved to be comparable. Wen and Yang [16] and Morad [17] investigated the pipe included in a direct section associated to a curved section. The conservatory of the pipe axis was suitably accounted for and natural frequencies of the system which they found to be slightly responsive to fluid flow velocity variations.…”