Wavy Tube Research Articles

Geometric model of a rolling process for multi-wave tubes

From a geometric viewpoint, this work considers the process of wavy tubes cross-rolling at the precision rolling section as meshing of a pair of conjugate surfaces. This work applies coordinate transformation and envelope theory to determine the spatial set of points for contacting surfaces that define the roller. The proposed method can be used to derive the roller surfaces for cross-rolling and parallel rolling of wavy tube manufacture. The envelope theory and the analytical procedure for the proposed method are presented. Numerical examples are presented to demonstrate the application of the method developed in this paper. The advantages, limitations and potential applications of cross-rolling are briefly reported.

Application of spectral elements to viscoelastic creeping flows

The spectral element method is analyzed for the simulation of viscoelastic fluid flows in plane and cylindrical geometries. The implementation of the method and choices of functional spaces is discussed in detail. The method is then applied to the case of the Maxwell- B fluid and compared with the so-called 4×4 SUPG finite element method on the perturbed channel flow problem. Analysis of the rate of convergence of the method is provided as well as thorough discussion on the decomposition of the geometry in spectral elements: the choice is between the h- vs. p-refinement. A comparison with other numerical (e.g. pseudo-spectral) methods is performed for the flow of the Maxwell- B fluid in a wavy tube. In each test case, very good agreement is found.

Practical evaluation of four mixed finite element methods for viscoelastic flow

We apply four stress‐velocity‐pressure algorithms to calculate four benchmark problems, i.e., the flow of a Maxwell fluid around a sphere, through a wavy tube, through an abrupt contraction, and in circular extrusion. For every flow, we use only one mesh, i.e., the same number of velocity nodes and the same boundary conditions for all algorithms. The meshes are neither too coarse nor too refined in order to provide us with a practical evaluation of the methods, i.e., a simple mixed method MIX0, the 4×4 element, and two types of interpolation for elastic‐viscous split stress (EVSS). We also investigate three methods of integration of the constitutive equations: Galerkin, SUPG, and SU. The performance of 4×4 and the high‐order EVSS are about the same. It is shown that the performance of MIX0 can be remarkably stable and accurate with smooth problems or leads to very poor results in more difficult cases. The low‐order EVSS method is accurate, stable, and cheap in computer time. It should be a good candidate for three‐dimensional developments.

Viscous fluid motion in a flat, slightly wavy tube

Viscous fluid motion in a flat, slightly wavy tube