# The Fluids Structure Instability Engineering Essay

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## 2.1 Introduction

The purpose of this chapter is to provide a review of the past research related to the fluid-structure instability, flow-induced vibrations, vortex induce vibration and LES modeling. The review is organized chronologically so as to offer approaching to how research hard works have laid the base for subsequent studies, including the present research effort. The review is fairly detailed so that the present research effort can be properly modified to add to the present body of literature as well as to justify the scope and direction of present research effort.

## 2.2 Fluids-Structure Instability (FSI)

Fluid-structure-interaction (FSI) problems are a common concern in nuclear engineering. Because vibration can cause fatigue and fracture, nuclear power plant designers and operators forever seek to avoid large amplitude flow induced vibration. The immersion of a solid body in a turbulent flow induces distortions that are connected to strong kinematic and dynamic instability. The fluid dynamic forces, due to the fluid-structure interaction, can be analyzed in terms of mean and instantaneous components.

"The interactive phenomena between fluid and body motion represent one of the most difficult problems in the field of fluid dynamics" said Murakami et al. (1998). B. Sreejith et al. (2003) conducted an investigation on a new finite element formulation for the fully coupled pipe dynamic theory. The wave equation is formulated in terms of velocity. The objective of this study is to find the behavior of liquid filled pipelines to valve closure excitation. The work carried out by this author by using finite element formulation to verify through a valve closure excitation experiment for simple pipeline geometry. Then the formulation was applied to a secondary sodium pipeline of a fast breeder reactor to determine the effect of FSI on structural velocities. They found out that, numerical study for the structural velocities reduce drastically if FSI effects are considered in the analysis when the fluid filled pipelines subjected to fluid transients like valve closure excitation.

Researchers face challenges unique to their method of solving this FSI problem through analytical, numerical or experimental means. Current analytical and numerical techniques model fluid flow using simplifying assumptions, typically based on time-averaged equations, which do not provide instantaneous values. Experimental solutions can be time-consuming and expensive. It can also be difficult to isolate the vibrations induced by pressure fluctuations alone. Because of these challenges, accurately quantifying the vibrations induced by pressure fluctuations alone has not yet been accomplished.

The accuracy of computational fluid dynamics in simulating the cross-flow around a steam generator and the feasibility of a full scale coupled CFD/FEA fluid-structure-interaction (FSI) analysis is examined through successive validations was investigated by K. Kuehlert et al. (2008). The study focuses on the simulation of flows through tube banks, and flow-induced vibration of an individual tube and a hydrofoil. The feasibility and potential of accurate predictions of fluid-structure-interaction phenomena are demonstrated through a series of studies with increasing complexity towards a fully coupled FSI simulation. M. T. Pittard (2003) have been studied the development of a numerical, fluid-structure interaction (FSI) model that will help define the relationship between pipe wall vibration and the physical characteristics of turbulent flow. The study presents an FSI approach based on Large Eddy Simulation (LES) flow models that compute the instantaneous fluctuations in turbulent flow for internal flow. The results based on the LES models indicate that these fluctuations contribute to the pipe vibration. The result of his study shows that, when the flow rate increased, the diameter of pipe will decrease. The author concludes that, a strong relationship between pipe vibration and flow rate exists.

With respect to fluid-structure-interaction problems it can be concluded from the tube bundle study that the LES turbulence model is preferable for an accurate representation of the flow and turbulence. Eisinger et al. (1995), who created a numerical model of FSI in tube arrays by coupling a finite element solver to Chen's (1983) unsteady flow theory, showing agreement with experimental displacement data. Kim and No (2004) tackled CFD modeling of realistic 4Ã-4 and 5Ã-5 fuel rod channels, including spacer grids using Large-Eddy Simulation (LES), showing the power spectrum of the flow. This was followed by a detailed, fundamental validation of CFD for calculating the forces on a tube in high Reynolds number cross-flow using LES by Kim and Mohan (2005). Full fluid-structure-interaction of single tubes at high Reynolds number using DES was tackled for offshore oil production spars by Oakley et al. (2005) and by Schowalter et al. (2006).

## 2.3 Flow-Induced Vibration (FIV)

Flow induced vibrations are widely recognized as a major concern in the design of tubular heat exchanger. While some tube failures occur due to the fatigue or thinning and splitting at mid-span as a result of tube-to-tube clashing, most failures are due to fretting wear at the tube supports. Almost all heat exchangers have to deal with this problem during their operation. The phenomenon has been studied since the 1970s and the database of experimental studies on flow-induced vibration is constantly updated with new findings and improved design criteria for heat exchangers.

During the past 30 years, considerable investigations have been carried out and reported in the open literature to explain the phenomenon of flow-induced vibration failure, some design guidelines have also been proposed. Excellent reviews are given by Paidoussis (1983), Weaver and Fiztpatrick (1988), Moretti (1993), Blevins (1994), Price (1995), and Pettigrew and Taylor (2003a, b). It is generally accepted that there are four vibration excitation mechanisms in flow-induced vibrations (FIV) of tube bundles. They are fluidelastic instability,vortex shedding excitation, turbulence buffeting and acoustic excitation. Fluidelastic instability is the most important mechanism. It is the result of fluid-structure interaction and reflects the unsteady nature of the interstitial flow in the tube bundle. A number of theoretical models have been used to analyse the fluidelastic instability (Price, 1995). Among the possible FIV mechanisms in SG tube bundles, the so-called fluidelastic instability, a self-excited vibration mechanism, is the most important safety issue in the design and operation of SGs because it may cause severe tube failures in a very short time. Fluidelastic instability is not a problem for tube bundles in axial flow but the most important FIV mechanism for tube bundles in cross-flow (Pettigrew et al., 1991, 1998).

Nuclear component means steam generators, heat exchangers, condensers, piping systems and reactor internals. Vibration problems often occur locally in areas where excessive flow velocities exist, such as inlet regions and around sealing strips in heat exchangers. Pettigrew et al. (1978) was presents approach and technique to the analysis of heat exchanger and steam generator designs from a flow-induced vibration point of view. Work was done in support of the CANDU reactor system; it is equally applicable to other reactor systems and to other industries where tube and shell heat exchange components are used. It is concluded that most flow-induced vibration problems may be avoided by proper analysis at the design stage. In 1991, (Pettigrew et al.) update the investigation in the related areas of thermal-hydraulic analysis, flow-induced vibration and mechanical damage prediction. Detailed three-dimensional thermal-hydraulic analyses are required to obtain flow velocity distribution in components. Recent development work to predict flow velocity distribution around sealing strips and in the U-bend tube region of steam generators is described. The authors concluded that most flow-induced vibration problems can be avoided by thorough analyses at the design stage. This requires thermal-hydraulics modeling, a good understanding of vibration excitation and damping mechanisms and techniques to predict fatigue and fretting-wear damage.

The fluid structure interaction shows a significant dependence on the Reynolds number. Mittal and Kumar (2001) investigated vortex induced vibration of a light circular cylinder placed in uniform flow at Reynolds number in the range of 103-104 flows at lower Reynolds number are associated with organized wakes while disorganized wakes are observed at higher Reynolds number. In certain cases, competition is observed between various modes of vortex shedding. The authors also observed lock-in while in some other cases soft-lock-in is observed. Mittal and Tezduyar (1992) reported their result for a computational study of flows past an oscillating cylinder using the finite-element method. For a cylinder restricted to cross-flow vortex induced vibration, they were able to observe the phenomena of lock-in and hysteresis. The Reynolds numbers for their computations are in range 290-300. They also explain the cause of hysteresis through numerical experiment and conclude that it is consequence of lock-in.

Fluid-elastic instability has been recognized as a major cause of failure in shell-and-tube-type heat exchangers due to tube repairs and plant downtime. This in turn causes significant economic losses in the heat exchanger, power and nuclear industries. This mechanism occurs once the flow rate exceeds a threshold velocity at which the tubes become self-excited and the vibration amplitudes rise rapidly with an increase in flow velocity. From a mechanistic view, the flow field around an array of flexible tubes will cause the tube to be displaced from its initial position and the flow field will change when the fluid forces acting on the tubes. The damping force of the tube that tries to restore it back to its equilibrium position opposes this change in fluid force. Thus, the results between the energy input by the fluid force and the energy expended in damping. The vibration will die when the energy in damping more than energy input in the fluid. A schematic of this mechanism is shown in Figure 2.0

Figure 2.0: Mechanism of fluid-elastic instability in a tube array (D. Mitra et al. (2009)

Since this phenomenon was identified in the early 1970's, a large amount of work has been carried out to understand the phenomenon through systematic experiments and physical modeling. Most of the early experimental research in this field relied on sectional scale models of tube arrays subjected to single-phase fluids such as air or water, using relatively inexpensive flow loops and wind tunnels. A study on flow-induced vibration in heat exchanger tubes was first was made by Roberts (1966) who observed the instability in a row of flexibly mounted tubes. He observed that the tubes vibrated with large amplitude beyond a critical velocity of the fluid flow. The instability was attributed to the time lag between the tube displacement and the fluid force. This was later verified by the experiments of Connors (1970), which were conducted in an array of tubes suspended by piano wires subjected to cross flow of water. Nonetheless, the impact of Connors' work is so great that most of the research out to date use Connnors' criterion to correlate the experimental results of the instability.

A particular complicating issue with flow-induced vibration in tube bundles is that past experience of design and operation is not necessarily a guide for future performance. Small changes in flow rates, or mechanical design, can lead to conditions that result in the dramatic failure of a unit. Pettigrew and Taylor (2003) were developed guidelines to prevent tube failures due to excessive flow induced vibration in shell-and-tube heat exchangers. The purpose of study is to summarize their design guidelines for flow-induced vibration of heat exchangers. The requirements applicable to each step are outlined in this paper. It is divided in two parts: Part 1 covers flow calculations, dynamic parameters and fluid elastic instability, and Part 2 covers forced vibration excitation mechanisms, vibration response prediction, fretting-wear damage assessment, and acceptance criteria. Kassera and Strohmeier (1997) applied the finite-volume method to simulate the flow-induced vibration of full flexible tube bundles, with different turbulence models for the turbulent nature of the flow. Sadaoka et al. (1998) numerically studied the occurrence of fluid elastic instability for 3Ã-3 square cylinder arrays. Schroder and Gelbe (1999) simulated the flow-induced vibration of tube bundles with the CFD program, STAR-CD, in combination with a coupled solver for the differential equations of parallel vibrating cylinders. Still, cylinder structures and turbulent flows have not been described in great detail due to the immense consumption of computation time. Ichioka et al. (1997) simulated the fluid elastic vibrations of two cylinders, and cylinders in a row by applying a finite-difference-scheme on a body-fitted moving grid. Their simulation was restricted to low-Reynolds numbers.

Research on fluid-elastic instability in two phase flow has been lacking compared to single-phase flow. Experimental difficulties and uncertainties in measurement of experimental parameters are the main deterrents in such experiments. In addition, two phase flow introduces two new parameters; namely the void fraction and the flow regime both of which affect the instability and are absent in single phase flow. Most of the work in two-phase flows has been carried out for air-water flows, the justification being that an air-water flow system is fundamentally no different than steam-water flow. However, issues related to compressibility of the fluid system and the differences in fluid properties such as density and viscosity make this justification weak. Several researchers (Pettigrew et al., 1995, Feenstra et al., 1995, 2002) have reported some data obtained from tests carried out with liquid-vapor Freon. However, very few tests have been carried out for steam-water mixtures, which are most representative of flows in practical heat exchanger equipment. Pettigrew et al. (1985, 1989) reported on some comprehensive experimental work carried out with air-water flow for studying fluid-elastic instability pertaining to nuclear applications. A detailed discussion of this method is available in Pettigrew et al. (1985). The authors noted that since the spectral peak narrowed at the onset of instability giving the appearance of reduced damping, the damping measurements were carried out at a point halfway between the instability points. They also saw an effect of the P/D ratio on the slope of the instability curve indicated by the value of the constant, K. Another conclusion reached by the researchers was that in the intermittent flow regimes at void fractions higher than about 80%, instability was achieved at lower values of critical velocity than what would be predicted using the Connors' criterion distorting the general trend of the instability curve, and thereby suggesting that operation of heat exchangers in such flow regimes is highly undesirable.

Instability was clearly seen in most of the steam-water experiments. The authors presented a new theory for correlating the instability data based on equating the energy of the fluid to that of the tube oscillation. Nakamura, Fujita, et al. (1995) conducted steam-water experiments at extreme pressures and temperatures of 7 MPa and 284°C respectively. The correlation seems to provide a satisfactory stability boundary that works for the authors' data and also those of some other experimenters. Nakamura et al., Hirota et al., Mureithi et al., (2002) has completed a series of tests providing some much needed data on damping and fluid-elastic instability in steam-water two-phase flow. Tests were carried out on an inline array and an array inclined at (300) to the direction of the flow. In their work, the authors used homogenous properties to calculate the flow parameters such as density, velocity and void fraction. Their tests indicated the damping ratio of the tubes in the drag direction to be almost double of that in the lift direction, which also supported their observation of fluid-elastic instability being achieved earlier in the lift direction. Their results also indicated that the critical reduced velocity decreased with an increase in system pressure of the steam-water mixture. However, the critical reduced velocity did not change significantly with void fraction.

Lately the significant progress in numerical simulation, the complex flow, which has not been investigated easily by experiments, may be simulated in more detail for analysis of flow-induced vibration in the immersed structure.

## 2.4 Vortex Induce Vibration (VIV)

Vortex-induced vibrations (VIV) of elastically mounted obstacles are of interest in a broad range of areas of engineering practice. These include, among others, the design of risers and conductor tubes in oil-drilling platforms, civil structures such as bridges and chimney stacks and marine structures in the ocean. In addition to their great practical relevance VIV problems are also important from a fundamental standpoint due to the enormous richness of their underlying vorticity dynamics. For these reasons a large and continuously expanding body of literature is dedicated to the study of VIV; see the recent review by Williamson & Govardhan (2004).

The flow past a single elastically mounted two-dimensional cylinder has served as the generic VIV model problem and has been widely studied both numerically and experimentally. As pointed out in the recent review of Williamson & Govardhan (2004), however, even this relatively simple system exhibits enormous complexity, and several aspects of its fundamental physics are still the subject of vigorous scientific debate and intense research. The complexity of VIV dynamics should thus be expected to increase considerably when two or more elastically mounted cylinders are arranged in close proximity to each other and allowed to vibrate freely as a coupled system. Even though early literature on VIV of two-cylinder configurations dates back to almost a century ago. The early work done by Pannell, Grifiths & Coales (1915) on airplane wires and Biermann & Herrnstein (1933) on airplane twin struts to support the wings. This problem has not been studied nearly as extensively as its single-cylinder counterpart. Yet understanding the VIV dynamics of multi-cylinder configurations is essential for the safety and reliability of various marine structures, where the suppression or minimization of flow induced structural vibrations is a critical design requirement (Griffin & Ramberg 1982).

The most recent ones, has been for the most part on the cylinder response (amplitude) and to a lesser extent on the forces exciting the VIV. No experiments aimed at identifying the flow patterns associated with the modes and characteristics of the vibrations have been reported to date. Yet and as pointed out by Sumner, Price & Paidoussis (2000), flow visualization and identification of the flow patterns are critical prerequisites for understanding the fluid mechanics of multi-cylinder arrangements. Sumner et al. (2000) made this comment in relation to fixed cylinders, but the need for systematically studying the flow patterns should be even more pressing when the cylinders are free to vibrate, and the complexity of the problem increases dramatically.

Numerical simulations can provide the necessary physical insights, but to the best of our knowledge only two numerical studies have been reported to date focusing on VIV of two-cylinder configurations (Mittal & Kumar 2001; Jester & Kallinderis 2004). Mittal & Kumar (2001) carried out two-dimensional simulations for two elastically mounted cylinders in tandem for Re = 100 and L/D = 5.5. Jester & Kallinderis (2004) simulated two dimensional free vibrations for the tandem configuration for Re = 1000 and L/D = 5. For such spacings (L/D â‰ˆ 5) the flow will fall into the wake interference region as classified by Zdravkovich & Pridden (1977). Therefore, the upstream cylinder behaves as an isolated single cylinder, while the downstream cylinder experiences large, flow-induced vibration over a wide range of flow velocities. D. Rocchi, A. Zasso (2002) investigated vortex shedding from a circular cylinder in a smooth and wired configuration: Comparison between 3D LES simulation and experimental analysis. They analyzed particular device, consisting of two wires, having a diameter smaller than that of the cylinder, helically wrapped around the cylinder itself. The efficacy of this solution has been investigated, in this paper, both by experimental tests and by numerical simulations. Experimental tests have been carried out in a water channel located at Politecnico di Milano and have produced data for a velocity range that covers Reynolds numbers from 2X104 to 4X104. Numerical simulations, performed by using a commercial CFD code (FLUENT) with a large eddy simulation (LES) approach, have been feasible only for the lowest values of the Reynolds number, due to the large computational power required for these kinds of applications.

The available experimental observations are at significantly higher Reynolds number. The results will show, however, that important aspects of the VIV dynamics observed in the experiments are also reproduced numerically at lower Re. This finding is not surprising given the large body of previous numerical work with a single, freely vibrating cylinder, which has shown that low Re simulations can capture and adequately explain a wide range of VIV phenomena (Williamson & Govardhan 2004). Furthermore, given the current state of understanding of two-cylinder VIV especially in the proximity wake interference region simulations at low Reynolds number should be a useful first step towards elucidating the mechanisms responsible for excitation of cylinders to large amplitudes (Mittal & Kumar 2001).

## 2.5 Large Eddy Simulation

Most of the research currently taking place in the field of CFD concerns the study of turbulent flows.  Almost any naturally occurring flow is turbulent, and hence it is important to be able to model turbulent flows accurately.  To that end, many models have been put forth to provide accurate solutions to these flows.  Large Eddy Simulation is simply one of these models. It was first used by Joseph Smagorinsky to simulate atmospheric air currents, and its primary use at that time was for meteorological calculations and predictions. During the 1980s and 1990s LES became widely used in the field of engineering. LES requires less computational effort than direct numerical simulation (DNS) but more effort than those methods that solve the Reynolds-averaged Navier-Stokes equations (RANS). The main advantage of LES over computationally cheaper RANS approaches is the increased level of detail it can deliver. While RANS methods provide averaged results, LES is able to predict instantaneous flow characteristics and resolve turbulent flow structures. LES also offers significantly more accurate results over RANS for flows involving flow separation or acoustic prediction. To incorporate turbulence dispersion physics, improve velocity field prediction, and reduce empiricism associated with RANS modeling, one may choose to instead resolve all of the turbulent features and scales. The simply entails use of the un-averaged Navier-Strokes equations and is generally termed Direct Numerical Simulations (DNS), for which the resulting flow can be three -dimensional and unsteady. The DNS approach can be used for laminar, transitional and turbulent flows. However, its computational cost can become excessive even at modest Reynolds number. Therefore, intermediate approaches which a significant portion of the turbulent scales have become popular for engineering simulations. The most common of these is the Large Eddy Simulations (LES) approach.

Numerical tools for a deeper understanding of the device fluid dynamics, allowing for a design linked to the physics of the phenomenon and for a numerical optimization through parametric studies, avoiding expensive and time-consuming experimental campaigns. Numerical simulations, performed by using a commercial CFD code (FLUENT) with a large eddy simulation (LES) approach, have been feasible only for the lowest values of the Reynolds number, due to the large computational power required for these kinds of applications. Simulations have been performed for 2D and a 3D configuration and have been compared with experimental results (Rocchi and Zasso , 2002). Eisinger et al. (1995) puts more efforts at full 3D simulation of flow-induced tube motion include, created a numerical model of FSI in tube arrays by coupling a finite element solver to Chen's (1983) unsteady flow theory, showing agreement with experimental displacement data. Kim and No (2004) tackled CFD modeling of realistic 4Ã-4 and 5Ã-5 fuel rod channels, including spacer grids using Large Eddy Simulation (LES), showing the power spectrum of the flow. This was followed by a detailed, fundamental validation of CFD for calculating the forces on a tube in high Reynolds number cross-flow using LES by Kim and Mohan (2005). Matthew (2003) presents an FSI approach based on Large Eddy Simulation (LES) flow models for internal flow, which do compute the instantaneous fluctuations in turbulent flow.

LES technique is used to solve the partial differential equations governing turbulent fluid flow. Liang and Papadakis (2007) used to study vortex shedding characteristics inside a staggered tube array consisting six rows with intermediate spacing at the subcritical Reynolds number of 8600 (based on gap velocity). Fully three-dimensional LES calculations over a number of rows in a staggered tube bundle with intermediate tube spacing are reported in this paper. The predictions are validated against detailed mean and r.m.s velocity measurement as well as correlation for the length of recirculation zones. (Hassan and Ibrahim, 1997; Barsamian and Hassan, 1997; Bouris and Bergeles, 1999; Hassan and Barsamian, 1999) use the first simulation of 2D. However, the problem of two dimensional LES calculations is that important mechanism, such as vortex stretching cannot be reproduced. 3D LES simulations were performed by Rollet-Miet et al. (1999) and Benhmadouche and Laurence (2003) using finite element and finite volume method respectively. In both paper, an elemental 'cell' were simulate assuming periodicity streamwise and cross stream direction and improve prediction compares to RANS approach for mean and turbulence were reported. They also observed that the subgrid-scale model, whether the standard Smargorinsky with constant coefficient of dynamic version had little effect on the result.

In the heat exchanger tube bundles, the vortex structure cannot be clearly observed and a lot of valuable information cannot be obtained by experimental technique because of the complicated flow characteristic. Numerical simulations is suggested because it able to capture the instantaneous three dimensional vortex structures and other instantaneous fluid dynamic parameters, such as drag, lift, pressure, velocity and Reynolds stress. Successful numerical investigations of flow around tube bundles had been carried out by Bouris and Bergeles (1999), Watterson et al. (1999), Beale and Spalding (1999), Sweeney and Meskell (2003), Schneider and Farge (2005), Lam et al. (2006) and Paul et al. (2008) using different numerical methods. For turbulent flow, large eddy simulation (LES) has become a very popular and reliable numerical method, with which the complex turbulent flow characteristics can be captured accurately.

In this present study, attentions is focused on flow induce vibration in heat exchanger using fluid structure interaction for external flow based on vibration. In this case, 3D modeling is considered using LES simulation based on Smargorinsky Lily model. The next chapter discuss about research methodology.