29-08-2016, 12:27 PM
FLUID-STRUCTURE-INTERACTION IN PIPE COILS DURING HYDRAULIC TRANSIENTS:
NUMERICAL AND EXPERIMENTAL ANALYSIS
1451386704-FLUIDSTRUCTURS.pdf (Size: 1.28 MB / Downloads: 5)
ABSTRACT
The paper presents the analysis of the effect of Fluid-Structure Interaction (FSI) occurring during hydraulic transients in
pipe coils, in particular the main developments and findings. The research work comprises the development of
mathematical models, their numerical implementation and their validation as compared with experimental evidence. The
aim is to model the behavior of toric pipes during hydraulic transients considering both axial stress waves in the pipe-wall
and fluid conservation principles. Three FSI mechanisms are taken into account: the shear stress generated between the
fluid and the pipe-wall, the axial movement of the pipe induced by its radial deformation and the pipe movement generated
by an imbalance of forces at junctions and boundaries. Hence, Poisson, junction and friction coupling are implemented. To
describe the coil structural behavior two conceptual models are developed: the first representing the coil as a straight pipe
with a moving valve, and the second assuming independent axial deformation in each coil ring. Although the first approach
allows an easier generalization of the method, the second model describes more accurately the FSI problem in the pipe
coil as experimentally observed. The paper novelty is the identification and description of a FSI phenomenon occurring in
coils by means of a four-equation model.
Keywords: hydraulic transients; Fluid-Structure Interaction; friction coupling; junction coupling; Poisson coupling.
1. INTRODUCTION
Among the different damping phenomena affecting water-hammer wave, Fluid-Structure Interaction (FSI) is probably the
most dependent to the specific piping system configuration. Generalization is not presently possible, and the calculations
have to be treated on a case-by-case basis (Locher et al., 2000; Wiggert & Tijsseling, 2001).
Several methodologies can be approached in FSI problems. The most common is the use of the Finite Element Method
(FEM) for the description of the structural motion and the Method of Characteristics (MOC) for the fluid behavior. Despite
classic water-hammer problems have been traditionally solved by MOC, only few authors have attempted FSI coupling by
means of a unique MOC scheme integrating both, the fluid and the structure, to mention some: Wiggert et al. (1987);
Tijsseling & Lavooij (1990); Lavooij & Tijsseling (1991). When a solution of this kind is applied, several problems arise
such us the coupling between the different pipe vibration modes, space and time discretization due to the different wave
celerities within the system, or the correct definition of boundary conditions. To overcome such problems strong
assumptions must be added and the model becomes convoluted, making the MOC approach unattractive and not easy to
deal with when several vibrating modes are considered.
On the other side, Ferras et al. (2014) carried out a stress-strain analysis of toric pipes for inner pressure loads in the
context of hydraulic transients. The basic pipe-wall degrees of freedom were analyzed and strain equations were derived
for the predominant pipe-wall displacements, which were identified to be in the axial and circumferential directions. As a
result, the FSI problem in toric pipes is reduced to these two vibrating modes and bending, shear and torsional pipe
movements can be neglected.
The present research aims at the solution of the FSI generated in coil systems during hydraulic transients by means of the
implementation of a four-equation model (two-mode model) in a unique MOC scheme. Hence, classic water-hammer
equations are combined with Timoshenko beam equations for the axial pipe-wall loading. The different coupling
mechanisms (i.e. Poisson, friction and junction coupling) are analyzed in order to determine the most suitable assumptions
for the description of the coil structural behavior.
2. EXPERIMENTAL DATA COLLECTION
The experimental set up (Figure 1), assembled at Instituto Superior Técnico (Lisbon, Portugal), is composed of a copper
pipe of nominal diameter D = 0.02 m, pipe-wall thickness e = 0.001 m and pipe length L = 105 m. The torus radius is
R = 0.45 m and 36 rings compose the entire coil. Strain gauges were installed in the middle section of the pipe in order to
carry out strain measurements in the axial and in the circumferential directions for different positions of the cross-section.
Young's modulus of elasticity and Poisson ratio of the copper material were experimentally determined by measuring stress-strain states over a straight pipe sample for the experimental range of pressures. The obtained values were
Young's modulus of elasticity E = 105 GPa and Poisson ratio n = 0.33.