ISSN 2319-8885 Vol.04,Issue.51, December-2015,

Pages:10951-10954

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Vibration Characteristics of Pipe Conveying Fluid 1 2 AVINASH B KOKARE , DR. PRASHANT M PAWARD 1PG Scholar, SVERI’s College of Engineering, Pandharpur, Maharashtra, India, E-mail: [email protected]. 2Professor, SVERI’s College of Engineering, Pandharpur, Maharashtra, India.

Abstract: The stability of fluid conveying pipe is of practical importance because the induced residual stresses which affected on the vibration characteristics and stability. A finite element (FE) simulation was presented to evaluate velocity and pressure distributions in a single phase fluid flow. This paper deals with the natural frequency of straight pipe made of structural steel, conveying turbulent steady water with different boundary conditions. The structural properties and fluid parameter of pipeline are analyzed, which shows using optimal support and structural properties beneficial to reduce vibration of pipeline.

Keywords: Straight Pipe, Thickness, Pressure, Frequency, COMSOL.

I. INTRODUCTION validity of the proposed treatment. Using TMM, the natural In industry pipes are commonly used for the conveyance frequencies, frequency response functions and instability of of either crude or products. In either case, the pipes are 3D-shaped pipeline systems are analyzed, representing some subjected to different environmental conditions such as fresh results. It is shown that, in the application of TMM to internal and external temperature fluctuations, earthquake the vibration analysis of curved or 3D pipelines conveying ground motion, and pulsating fluid flow. Repeated operational fluid, the steady combined force has to be included, otherwise start-up and shut-down procedures trigger vibrations of these the obtained results may be not reliable. Gale et al. [2] had pipes and propagate internal waves resulting in finite and described and discussed linear eight-equation system for two- irreversible longitudinal extension of the pipe over time. way coupling of single-phase fluid transient and arbitrary Fluid–Structure Interaction (FSI) describes an explicit shaped one-dimensional pipeline movement. The governing coupling between moving fluid and deformable structure, in phenomenon described with this system is also known as which fluid acts on the structure with fluidic force whilst Fluid-Structure Interaction. Standard four-equation model for simultaneously the fluid is acted upon by movement of the axial coupling was improved with additional four structural boundary. The FSI in a fluid-conveying pipeline Timoshenko's beam equations for description of flexural can be induced by sudden opening or closing of a valve, displacements and rotations. Ibrahim [3] has presents two-part sudden start-up or shutdown of a pump, fluid flow ripples and review article an overview of mechanics of pipes conveying mechanical excitation. This phenomenon has been found in a fluid and related problems such as the fluid elastic instability wide range of fields, ranging from hydraulic and pneumatic under conditions of turbulence in nuclear power plants. In the fluid power systems, water supply systems, power production, first part, different types of modeling, dynamic analysis, and petrochemical industry, and even biological vessels. stability regimes of pipes conveying fluid restrained by elastic Structural supports will affect the behavior of a piping system or inelastic barriers are described. The dynamic and stability significantly, changing the system’s natural frequencies. behaviors of pinned-pinned, clamped-clamped, and When an impact is introduced to water in a pipe, there are two cantilevered pipes conveying fluid together with curved and waves traveling at different speeds. A primary wave articulated pipes will be discussed. corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of Karagiozis et al. [4] has presented experimental results on pipe travels fast. the nonlinear dynamics and stability characteristics of thin- walled clamped–clamped circular cylindrical shells in contact Dai et al. [1] has performed the vibration analysis of with flowing fluid. The experiments were conducted with three-dimensional (3D) pipelines conveying fluid is based on three experimental set-ups: one for experiments with the equations of motion, in which the steady combined force elastomer shells in annular air-flow, the second for elastomer is essentially included, a 3D straight pipe element and a shells with internal air-flow, and the last one for aluminum or curved pipe element conveying fluid are formulated by plastic cylindrical shells with internal water-flow. Koo et al. introducing dynamic stiffness matrix in order to apply the [5] has investigated Vibration analysis of a piping system TMM. The natural frequencies of simple pipe systems with conveying fluid is by employing the wave approach. In this straight or circular shape are calculated to demonstrate the paper, the in viscid fluid-dynamic forces acting on a pipe due

Copyright @ 2015 IJSETR. All rights reserved. AVINASH B KOKARE, DR. PRASHANT M PAWARD to internal fluid flow are approximated by the plug-flow Water: Water with following properties is considered for model with the slender-body theory. The straight pipe study. elements conveying fluid are formulated using a dynamic  Viscosity(pa.s)= eta(T[1/K]) stiffness matrix in the frequency domain. Li et al. [6] had  Young’s Modulus(N/mm2)= 200e9[Pa] presented a theoretical study on vibration analysis of pipes  Density (Kg/m3)= 1000 with FSI . Pipelines with high fluid pressure and velocity can be solved by developed method. Several pipeline schemes are discussed to illustrate the application of the method. The proposed method is easier to apply compared to most existing procedures. Influence laws of structural and fluid parameters on FSI of pipe are analyzed. Liu et al. [7] has developed 14- equation model by considering the effects of pipe wall thickness, fluid pressure and velocity, which describes the fluid–structure interaction behaviour of pipelines. The transfer matrix method has been used for numerical modelling of both hydraulic and structural equations. Salman et al. [8] had constricted flow in a thin cylindrical shell with an idealized blunt constriction is modelled using ADINA. Highly disturbed recirculation region is observed at the constriction exit where pressure fluctuations and consequential vessel wall vibrations display broadband spectral content over a range of Fig.2. 2-D model geometry and the mesh. several hundred Hz.

II. FINITE ELEMENT MODELING PROCEDURE The FE analysis was carried out to calculate vibration characteristics of a pipes conveying fluid with different velocities and boundary conditions using a general purpose FE package COMSOL. The numerical analysis was carried out by using Fluid Flow module in COMSOL Multiphysics. Using COMSOL software the modeling of straight pipe and L shaped pipe is done by using Geometry command and Boundary conditions are given to pipe by using the command Fluid Structure Interaction.

A. Geometry Model and Mesh It is applicable to a 1-D, 2-D and 3-D straight pipe , steady- state or transient analysis, Figs.1 to 3 shows the model Fig.3. 3-D model geometry and the mesh. geometry and the mesh of the model. C. Boundary Conditions A no slip boundary condition has assigned for the wall surfaces, where velocity at wall is set to zero. Average velocity applied at inlet zero and outlet is kept at atmospheric pressure. A uniform mass flow and a constant temperature has assigned at the channel inlet.

TABLE I: Boundary Conditions

Fig.1. 1-D model geometry and the mesh.

B. Material Steel: Steel with following properties is considered for study. D. Modal Analysis  Poisson Ratio = 0.33 We used modal analysis to determine the vibration  Young’s Modulus(N/mm2)= 200e9[Pa] characteristics (natural frequencies and mode shapes) of a  Density (Kg/m3)= 7850 pipe conveying fluid. The natural frequencies and mode

International Journal of Scientific Engineering and Technology Research Volume.04, IssueNo.51, December-2015, Pages: 10951-10954 Vibration Characteristics of Pipe Conveying Fluid shapes are important parameters in the design of a structure TABLE III: Natural Frequencies (Hz) of a Clamped- for dynamic loading conditions. For measuring the natural Clamped Pipe frequencies were carried out with different steps:

Pipe Filled by Air:The vibration characteristics measurement was first done on a straight pipe 1m length, 200 mm diameter with cantilever support and fixed support. The natural frequencies were measured by varying the thickness of pipe.

Pipe Filled by Water: The vibration characteristic measurements were performed on straight pipe 1m length and 200mm diameter with cantilever support and fixed support. The natural frequencies were measured by varying the thickness of pipe.

III. RESULTS AND DISCUSSIONS The variations of Natural frequencies of a straight pipe with thickness filled by air & by water for different boundary conditions such as clamped- free & clamped-clamped are shown below in Tables and figure.

A. Pipe Filled by Air Clamped-Free Pipe: TABLE II: Natural Frequencies (Hz) Of A Clamped- Fig.5. variation of natural frequency straight clamped- Free Pipe clamped pipe.

B. Pipe Filled By Water Clamped-free Pipe: Table 3 shows the natural frequencies of a cantilever pipe obtained by finite element analysis, it shows good agreement between these results as shown in Fig.6. We can see that thickness of a pipe causes reduction in the natural frequencies of it. This result is new and important to explain the effect of thickness on the vibration characteristics of a pipe without fluid. TABLE IV: Natural Frequencies (Hz) Of A Clamped- Free Pipe

Fig.4. variation of natural frequency straight clamped- free pipe.

Clamped-Clamped Pipe: Table2 shows the natural frequencies of a clamped-clamped pipe obtained by finite element analysis, it shows good agreement between these results as shown in Figs.4 and 5. We can see that thickness of a pipe causes reduction in the natural frequencies of it. This result is new and important to explain the effect of thickness Fig.6. variation of natural frequency of straight clamped- on the vibration characteristics of a pipe without fluid. free pipe.

International Journal of Scientific Engineering and Technology Research Volume.04, IssueNo.51, December-2015, Pages: 10951-10954 AVINASH B KOKARE, DR. PRASHANT M PAWARD Clamped-Clamped Pipe: Table 4 shows the natural [2]Gale J., Tiselj I., (2006) “Eight equation model for frequencies of a clamped-clamped pipe obtained by finite arbitrary shaped pipe conveying fluid”. In International element analysis, it shows good agreement between these Conference Nuclear Energy for New Europe, Portoro, Sloveni results as shown in Fig.7. We can see that thickness of a pipe pp. 616.1–616.10.3. causes reduction in the natural frequencies of it. This result is [3] Ibrahim R., (2010) “Overview of mechanics of pipes new and important to explain the effect of thickness on the conveying fluids.PartI:Fundamental studies”. ASME J. vibration characteristics of a pipe without fluid. Press.Vessel Technol. 132, 034001-1–034001. [4]Karagiozis K., Païdoussis M., Amabili M.,(2007) “Effect TABLE V: Natural Frequencies (Hz) of a Clamped- of geometry on the stability of cylindrical clamped shells Clamped Pipe subjected to internal fluid flow”Compute Struct.85, 645– 659. [5] Koo G., Park Y., (1998) “Vibration reduction by using periodic support in a piping System” . J. Sound Vib. 210, 53– 68. [6] Li Q., Yang K., Zhang L., Zhang N., (2002) “Frequency domain analysis of fluid–Structure interaction in liquid-filled pipe systems”Int. J. Mech. Sci. 44, 2067–2087. [7] Liu G., Li Y., (2011) “Vibration analysis of liquid-filled pipelines with elastic constraints” J. Sound Vib. 330, 3166– 3181. [8] Salman H., Sert C., Yazicioglu Y., (2013) “Computational analysis of high frequency fluid–structure interactions in constricted flow” Compute, Struct. 122, 145–154. [9] Shen H., Wen J., Yu D., Wen X., (2009) “The Vibration properties of a periodic composite pipe in 3D space” J. Sound Vib. 328, 57–70. [10] Nabeel K. Abid Al-Sahib , Adnan N. Jameel ,Osamah F.Abdulateef “ Investigation into the Vibration Characteristics and Stability of Welded Pipe Conveying Fluid” Volume 4, Number 3, June, 2010 ISSN 1995-6665 Pages 378 – 387.

Fig.7.variation of natural frequency straight clamped- clamped pipe.

IV. CONCLUSION Analysis is used to determine the effect of on the vibration characteristics and stability of a pipe conveying fluid. The main summarized conclusions are:  The natural frequencies of a pipe decreases with increasing thickness of pipe in Clamped-Free boundary conditions.  The natural frequencies of a pipe increases with increasing thickness of pipe in clamped-clamped boundary conditions.  The natural frequencies affected by the thickness of pipe. They are reduces more as the thickness of pipe far from the stationary edge in Clamped-Free and increases in clamped-clamped boundary conditions.

V. REFERENCES [1] Dai H., Wang L., Qian Q., Gan J., (2012) “Vibration analysis of three dimensional pipes conveying fluid with consideration of steady combined force”.pp.2453- 2464,vol.328.

International Journal of Scientific Engineering and Technology Research Volume.04, IssueNo.51, December-2015, Pages: 10951-10954