Ezzeddine Hadj-Taïeb

Propagation of strain waves in cylindrical helical springs

This paper discusses the vibrations of a coil, which is excited axially, in helical compression springs. The mathematical formula is composed of a system of four hyperbolic partial differential equations of first order with unknown variables, which are angular and axial deformations and velocities. The numerical resolution is based on the conservative finite difference scheme of Lax-Wendroff. The impedance method is applied to calculate the frequency spectrum. The spring is excited by a sinusoidal axial velocity at its end. The results obtained by using this method are used to analyze the evolution in time of deformations and velocities in different sections. These results clearly show the effect of the interaction between the slow axial waves and the fast angular waves. Indeed, the amplification was more important for the axial strain than for the rotational one that was caused by the effect of coupling Poisson. In addition to this, the resonance phenomenon and other phenomena related to wave propagations such as wave reflections and beat are analyzed.

Iterative Methods for Steady State Looped Network Analysis

The aim of this paper is to numerically study the steady state of water flows in looped networks. This study will be performed by the use of Hardy Cross Method and Newton-Raphson algorithm. The comparison of the numerically obtained results by these two methods to those obtained by the use the commercial software Pipe Flow Expert has shown a good concordance between them. The numerical analysis has shown that the convergence of Newton-Raphson method is more rapid than that of the classic Hardy Cross Method.

Effect of Water Hammer in Relatively Long Inclined Pipelines

Consideration is given in this paper to the numerical solution of transient flows in relatively long pipeline provoked by the water hammer phenomenon. Equations which describe these one-dimensional flows in a cylindrical pipe, of linear elastic behavior according to the Hooke’s law, are solved in the time domain by the method of characteristics using linear integration. The obtained results due to a rapid closure valve at the downstream end of a long pipeline show that the gravity lift may have an important effect on the maximum pressures, which may become very important near the valve and provoke the failure of the pipe especially in presence of defect. The safety factor, computed at equidistant sections of the pipe, determines the distance between the supplying reservoir and the defect from which the failure may happen.

Transient Flow Analysis through Centrifugal Pumps

A theoretical study has been carried out on the transient flow through a centrifugal pump during the starting period. The problem is governed by two hyperbolic partial differential equations which the continuity and the motion equations. The mathematical model is solved numerically by using the method of characteristics with specified time intervals. The comparison between the obtained numerical results and those obtained by experiment has shown a good concordance. In this study, the effect of the starting time, the impeller diameter, the number and the height of blades on the pressure increase were analyzed. The numerical results have shown that the pressure increase is inversely proportional to the starting time. However, during the starting period, these results have shown that the number of blades has no significant effect on this pressure increase.

Multi-leaks Detection and Sizing in Viscoelastic Pipeline System

This paper presents a technique for detecting and locating several leaks in a single viscoelastic pipe by means of transient analysis. The system studied is a reservoir-pipe-valve one. The viscoelastic behavior of the pipe wall material is modeled by a generalized Kelvin-Voigt model. To determine the leak location the mathematical formulation has been solved by the characteristics method. The method uses transient pressure waves initiated by the sudden closure of a downstream shut-off valve. The computed results describe the influence of the multi-leaks on pressure time-history and the effect of leaks locations on the pressure signal behavior. The results show that the method of characteristics is for great importance to model and simulate the affect of multi-leaks on transient pressure. Sensitivity of the proposed method on the location of the leak is determined in the case: two or three leaks. The effects of Young’s modulus are also investigated.

Numerical Study of Anti-ram of Hydraulic Lines by an Additional Viscoelastic Pipe

The purpose of this paper is to study numerically the effect of adding a short viscoelastic pipe in series with a main quasi-rigid pipe on water hammer phenomenon. The model takes into account the viscoelastic behaviour of the added pipe. The governing equations of such phenomenon are two coupled, non linear, hyperbolic, partial equations. The fluid pressure and velocity are considered as two principal dependant variables. The problem has been solved by the non linear method of characteristics. The obtained results show that the deformability of the additional pipe reduces the celerity of pressure waves and significantly alleviates the pressure fluctuations.