International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 12 (2016) pp7633-7639 © Research India Publications. http://www.ripublication.com 7633 Design of Composite Pipes Conveying Fluid for Improved Stability Characteristics K.Y. Maalawi * , A. M. Abouel-Fotouh * , M. El Bayoumi * , Khaled Ahmed Ali Yehia * * Mechanical Engineering Department, National Research Center, P.O.Box No. 12622, El Buhouth St., Dokki, Cairo, Egypt . Abstract The subject of vibration and stability of thin composite pipes conveying flowing fluids is of a considerable practical interest. Its applications include oil and hydraulic pipelines, heat exchangers, liquid-fuel rocket piping, nuclear reactor cooler channels, etc. The aim of the study is to enhance the pipe overall stability level and avoid the occurrence of flow- induced flutter without increasing its structural mass. For the study, a model has been developed. It simulates performance of unidirectional fibrous composite pipes of the same material type. Pipes are composed of uniform, round tubes of same inner diameter and variable material properties, wall thickness and length. The modules are rigidly connected together, resulting in discrete axial grading pipe. Lower and upper limiting values were imposed on various parameters to avoid unpractical configurations. Analysis has been performed using the transfer matrix technique and the Levenberg- Marquardt algorithm has been adopted to solve the resulting nonlinear equations with its complex roots. Also, efficient updating procedure has been implemented to generate the required frequency branches of the various modes. The obtained results were verified successfully using known classical cases. Results showed a flutter speed percentage gains of up to 26.8% based on flutter speed of baseline pipe design. Useful design charts were developed. Accordingly, the current model proved its capacity to apply piecewise pipe grading in material properties, wall thickness and length to produce lighter composite pipe designs with improved dynamic stability and higher flutter speed. Keywords: Pipe flow, Fluid-structure interaction, Composite materials, Eigen value analysis, Flutter instability. INTRODUCTION The subject of vibration and stability of thin pipes conveying flowing fluids is of a considerable practical interest. Engineering applications include oil and hydraulic pipelines, heat exchangers, liquid-fuel rocket piping, nuclear reactor cooler channels, etc. An advanced text by Paїdoussis [1] gives an excellent review of the several developments made in this research area. A special work by Si-Unget al. [2] considered dynamics of cantilevered pipes conveying fluids and investigated the transfer of flutter instability from one eigen value branch to another. The critical fluid-to-pipe mass ratios were definitely determined for cases with negligible structural damping. Practical models for enhancing static stability characteristics of pipelines constructed from uniform modules were addressed by Maalawi and Ziada [3], where the associated eigen value problem was solved using the transmission matrix technique. Another work by Maalawi and Abouel Fotouh [4] considered the general case of an elastically supported pipe, covering a variety of boundary condition types. Distinct domains of the flutter instability boundaries were presented for different ratios of the fluid-to- pipe mass. The variation of the critical flow velocity with support flexibility was also investigated and discussed. Concerning pipelines made of advanced composites, Zou et al [5] analyzed the vibration produced by flowing fluid in composite pipes. They considered the influence of laminate parameters, thickness of pipe wall and fluid properties in the mathematical formulation. Rabeih et al [6] presented a finite element model for studying the effect of composite material parameters lay-up configuration on the natural vibration of composite pipes conveying fluid with different boundary conditions. In the context of carbon nanotubes, Yoon et al. [7] studied the effect of the flowing fluid on the natural frequencies and mode shapes of the pipe structure. Results showed that the moving fluid could significantly influence resonant frequencies, particularly for nanotubes with larger radius and length. Another work by Yoon et al. [8] presented a continuum elastic model to analyze flutter instability of cantilevered carbon nanotubes transporting fluid. It was shown that such a fluid-induced instability could be eliminated for a moderately stiff surrounding elastic medium within the practical range of flow velocity. Many other cases of pipes conveying fluids were reviewed in Ref. [9], where different types of modeling, dynamic analysis and stability regimes were addressed. A recent paper by Askarian et al. [10] investigated the instability of cantilevered horizontal composite pipe. The coupled bending-torsion equations of motion were derived using Hamilton’s principal and Galerkin method. The effects of coupling parameters and nozzle aspect ratio were considered on the pipe stability margins. Another class of advanced composites named functionally graded materials (FGMs) can be promising in designing flexible pipes conveying fluid. A power-law model was implemented by Sheng and Wang [11]to represent material grading in the direction of the pipe wall thickness. Maalawi [12] presented an exact analytical model for optimizing stability of FGM columns under compression. The material distribution has been tailored along the column axis to avoid the occurrence of buckling instability without mass penalty. The major aim of the present paper is to introduce an exact mathematical approach for selecting pipe configurations having improved resistance against flow-induced instabilities. The formulation is based on the Euler-Bernoulli beam theory as well as the main assumption of plug flow with constant axial velocity. The governing equations are given with all of the parameters expressed in appropriate dimensionless form to make the model independent on a specific pipe configuration.