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Journal ArticleDOI

A Theory for Fluidelastic Instability of Tube-Support-Plate-Inactive Modes

01 May 1992-Journal of Pressure Vessel Technology-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 114, Iss: 2, pp 139-148

TL;DR: A mathematical model, which incorporates all motion-dependent fluid-forces based on the unsteady flow theory, is presented here to simulate the characteristics of fluidelastic instability of loosely supported tubes in the stable and unstable region associated with TSP-inactive modes.

AbstractFluidelastic instability of loosely supported tubes, vibrating in a tube support plate (TSP)-inactive mode, is suspected to be one of the main causes of tube failures in some operating steam generators and heat exchangers. A mathematical model, which incorporates all motion-dependent fluid-forces based on the unsteady flow theory, is presented here for fluidelastic instability of loosely supported tubes exposed to nonuniform crossflow. In the unstable region associated with a TSP-inactive mode, the tube motion can be described by two linear models: TSP-inactive mode when tubes do not contact with the TSP and TSP-active mode when tubes contact the TSP. A bilinear model, consisting of these linear models, is presented in this paper to simulate the characteristics of fluidelastic instability of loosely supported tubes in the stable and unstable region associated with TSP-inactive modes. The analytical results are compared with published experimental data; they agree reasonably well. The prediction procedure presented for fluidelastic instability response of loosely supported tubes is applicable in the stable regions of TSP-inactive mode. 25 refs., 10 figs., 2 tabs.

Topics: Instability (50%)

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A Theory for Fluidelastic Instability of CONF-910602--2
Tube-Support-Plate InactiveModes DE91 006001
by
Y. Cai, S. S. Chen
Argonne National Laboratory
Argonne, Illinois
S. Chandra
Northeast Utilities Service Company
Hartford, Connecticut
ABSTRACT
Fluidelastic instability of loosely supported tubes, vibrating in a tube support
plate (TSP)-inactive mode, is suspected to be one of the main causes of tube
failures in some operating steam generators and heat exchangers. A
mathematical model, which incorporates all motion-dependent fluid-forces based
on the unsteady flow theory, is presented here for fluidelastic instability of loosely
supported tubes exposed to nonuniform crossflow. In the unstable region
associated with a TSP-inactive mode, the tube motion can be described by two
linear models: TSP-inactive mode when tubes do not contact with the TSP and
TSP-active mode when tubes contact the TSP. A bilinear model, consisting of
these linear models, is presented in this paper to simulate the characteristics of
fluidelastic instability of loosely supported tubes in the stable and unstable region
associated with TSP-inactive modes. The analytical results are compared with
published experimental data; they agree reasonably well. The prediction
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procedure presented for fluidelastic instability response of loosely supported tubes
is applicable in the stable and unstable regions of TSP-inactive mode.
NOMENCLATURE
Ajn Coefficients
ajn,_jn Generalized tube displacement and velocity in the x direction
Bjn Coefficients
bin, t_jn Generalized tube displacement and velocity in the y direction
D ' Tube diameter
E Young's modulus
e Wall thickness of a tube
el, e2 Tube-support gaps
Fi Impact force
f Oscillation frequency
fn Natural frequency of the n-th mode
I Moment of inertia of tube cross section
Kc Equivalent stiffness
knl, kn2 Eigenvalues for tube vibration
Tube length
mj Mass per unit length of the j-th tube
N Number of tubes in an array or row
n Number of modes
P Pitch
R Radius of a tube
Tc Contact time of tube/support

t Time
ts The time when tube strikes TSP
td The time when tube leaves TSP
U Flow velocity
Um Mean flow velocity
Uv Reduced flow velocity (= Urn/lD or U/fD)
uj, flj Displacement and velocity of the j-rh tube in the x direction
Ul, ii I Displacement and velocity of the tube for TSP-inactive mode
u2, 6 2 Displacement and velocity of the tube for TSP-active mode
vi, _j Displacement and velocity of the j-th tube in the y direction
x, y, z Cartesian coordinates
Wr Wear work rate parameters
O_jk, _jk, C_jk, _jk Added mass coefficients
' t !
O_ik,_jk,O'jk,1;jk Fluid damping coefficients
O_jk,_jk,(_jk,_jk Fluid stiffness coefficients
_, _1, _2 Dimensionless coordinates
_j, _j Damping ratio in vacuum
7j Mass ratio (= p_R2/mj) of the j-th tube
_, v Dimensionless distances
co Circular frequency
6Oi, f_j Natural frequency in radian of the j-rh tube in vacuum
_n(Z) Orthonormal function of the n-th mode
_(z) Flow velocity distribution function

t. &
Subscripts
j,k Tube number j,k (j,k = 1 to N)
N Uumber of tubes
n Number of modes
1 For model 1 (TSP-inactive mode)
2 For model 2 (TSP-active mode)
1. INTRODUCTION
Fluidelastic instability associated with a TSP (tube support plate)-inactive
mode for loosely held tubes has been demonstrated in laboratory tests and
observed in a few heat exchangers [1-6]. It is suspected to be one of the main
causes of tube failures in some operating steam generators and heat exchangers.
The phenomenon occurs as a result of design inherent clearances between the
tubes and their' supports, such as baffle plates and anti-vibration bars. When
these tubes are subjected to a cross flow, flow-induced vibration can cause tubes to
impact and rub against their supports and result in tube wear. If tube vibration is
excessive in duration and amplitude, wear can result in sufficient tube wall
. material loss to cause fatigue cracking and/or tube leaks.
In recent years, extensive experimental and analytical studies have been
performed for fluidelastic instability of loosely held tubes and wear. Chen et al. [1]
investigated the fluidelastic behavior of loosely held tubes in laboratory. They
' observed that as the flow velocity is increased to a threshold value, instability in a
TSP-inactive mode may occur. Then for a range of flow velocities larger than the
threshold flow velocity, the tube vibrates predominantly in a TSP-inactive mode

with the response amplitude limited by the clearance between the tube and the
TSP. With a further increase of flow velocity a second threshold, or critical, flow
velocity is reached at which instability in a TSP-active mode begins. In this case,
large amplitude oscillations occur and, in many cases, tubes may impact with
one another.
Additional studies have been published recently to determine the response of
loosely supported tubes under some specific flow conditions [7-16]. References [7]
through [11] described experiments on tubes vibrating in a TSP-inactive mode
including dynamic contact forces between tubes and supports and fretting wear
mechanism. Other studies [12-19] considered computer simulations of the
fluidelastic instability of loosely held tubes using both analytical and numerical
methods. For example, Fisher [13] and Rao [12,15] developed finite element
computer codes to simulate tube vibration and fretting wear, and compared these
results with experimental measurements. Nonlinear analytical methods for
analyzing the fluidelastic instability and impacting behavior of loosely held tubes
were presented by Fricker [14] and Axisa [20]. They used quasi-static or quasi-
steady flow theories, which are applicable in specific parameter ranges. A study
[23] on the basis of the unsteady flow model has also been developed for fluidelastic
instability of tubes in nonuniform flow.
This paper presents an analytical mode] to predict tube response for loosely
held tube arrays in crossflow. An analytical/numerical procedure is described to
predict the critical flow velocity and tube response in rbe instability zone
associated with a TSP-inactive mode. First, fluid coupling effects among tubes
including fluid inertia, fluid damping, and fluid stiffness are described by the
unsteady flow theory. At present, there are very limited data available for these
fluid-force coefficients. In this paper, we use the coefficients presented in Ref. 23
based on the experimental data by Tanaka and his colleagues. Second, as the first

Citations
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Journal ArticleDOI
Abstract: This paper is the second part of the two-part review article presenting an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers were described. The dynamic and stability behaviors of pinnedpinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes were discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations were considered. The first part was closed by conclusions highlighting resolved and nonresolved controversies reported in the literature. The second part will address the problem of fluidelastic instability in single- and twophase flows and fretting wear in process equipment, such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluidelastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting-wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid. DOI: 10.1115/1.4001270

80 citations


Journal ArticleDOI
Abstract: The dynamic response of a loosely supported cylinder, unstable in its first TSP-inactive mode (i.e., when no support is provided by the Tube Support Plate), is investigated experimentally. The test cylinder, modelled by a flexibily mounted rigid tube, was part of an array of rigid cylinders in a rotated triangular array with pitch-to-diameter ratio 1·375 subjected to water cross-flow. Tests were conducted with the flow velocity as the main variable parameter. The effect of other parameters, including cylinder-support gap size, support material properties and the interstitial fluid in the impact zone, was also explored. Distinct bifurcations in the cylinder response were observed as the flow velocity was increased above the threshold for the initial Hopf bifurcation (fluidelastic instability), confirming similar findings from theoretical analyses. Responses with a primarily periodic component, as well as chaotic motions were obtained. Intermittency was found to be the dominant route leading to chaos. The gap size at the support, when coupled with initial cylinder preload, was found to have a profound effect on the resulting cylinder response. Hence, while nearly periodic or borderline chaotic responses occurred for larger gap sizes, generalized chaotic motions were prevalent for the smallest gap sizes tested.

14 citations


01 Jan 2009
Abstract: problem of major interest to researchers and practicing engineers. Tube array vibrations may lead to tube failure due to fretting wear and fatigue. Such failures have resulted in numerous plant shutdowns, which are often very costly. The need for accurate prediction of vibration and wear of heat exchangers in service has placed greater emphasis on the improved modeling of the associated phenomenon of flow-induced vibrations. In this study, the elastodynamic model of the tube array is modeled using the finite element approach, wherein each tube is modeled by a set of finite tube elements. The interaction between tubes in the bundle is represented by fluidelastic coupling forces, which are defined in terms of the multidegree-of-freedom elastodynamic behavior of each tube in the bundle. Explicit expressions of the finite element coefficient matrices are derived. The model admits experimentally identified fluidelastic force coefficients to establish the final form of equations of motion. The nonlinear complex eigenvalue problem is formulated and solved to determine the onset of fluidelastic instability for a given set of operating parameters. DOI: 10.1115/1.3006950

10 citations


Journal ArticleDOI
Abstract: Flow-induced vibrations due to crossflow in the shell side of heat exchangers pose a problem of major interest to researchers and practicing engineers. Tube array vibrations may lead to tube failure due to fretting wear and fatigue. Such failures have resulted in numerous plant shutdowns, which are often very costly. The need for accurate prediction of vibration and wear of heat exchangers in service has placed greater emphasis on the improved modeling of the associated phenomenon of flow-induced vibrations. In this study, the elastodynamic model of the tube array is modeled using the finite element approach, wherein each tube is modeled by a set of finite tube elements. The interaction between tubes in the bundle is represented by fluidelastic coupling forces, which are defined in terms of the multidegree-of-freedom elastodynamic behavior of each tube in the bundle. Explicit expressions of the finite element coefficient matrices are derived. The model admits experimentally identified fluidelastic force coefficients to establish the final form of equations of motion. The nonlinear complex eigenvalue problem is formulated and solved to determine the onset of fluidelastic instability for a given set of operating parameters.

10 citations


03 May 2010
Abstract: The need for accurate prediction of vibration and wear of heat exchangers in service has placed greater emphasis on improved modeling of the associated phenomenon of flow-induced vibrations. It was recognized that modeling of the complex dynamics of fluidelastic forces, that give rise to vibrations of tube bundles, requires a great deal of experimental insight. Accordingly, the prediction of the flow-induced vibration due to unsteady cross-flow can be greatly aided by semi-analytical models, in which some coefficients are determined experimentally. In this paper, the elastodynamic model of the tube array is formulated using the finite element approach, wherein each tube is modeled by a set of finite tube-elements. The interaction between tubes in the bundle is represented by fluidelastic coupling forces, which are defined in terms of the multi-degree-of-freedom elastodynamic behavior of each tube in the bundle. A laboratory test rig with an instrumented square bundle is constructed to measure the fluidelastic coefficients used to tune the developed dynamic model. The test rig admits two different test bundles; namely the inline-square and 45o rotated-square tube arrays. Measurements were conducted to identify the flow-induced dynamic coefficients. The developed scheme was utilized in predicting the onset of flow-induced vibrations, and results were examined in the light of TEMA predictions. The comparison demonstrated that TEMA guidelines are more conservative in the two configurations considered.

2 citations


Cites methods from "A Theory for Fluidelastic Instabili..."

  • ...[10] reported a theoretical investigation of the fluidelastic instability of loosely supported tubes in nonuniform crossflow, wherein the unsteady flow ADVANCES in DYNAMICAL SYSTEMS and CONTROL...

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