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I
NONLINEAR DYNAMICS OF TUBE ARRAYS IN CROSS FLOW
S. S. Chen, Y. Cal, and S.Zhu
Energy Technology Division
Argonne National Laboratory
Argonne, Illinois 60439, USA.
ABSTRACT
Fluidelastic instability of loosely supported tube arrays was studied analytically and experimentally. This is one of
the important practical problems of autonomous fluid-structure systems with many interesting motions. Both fluid-
damping and fluid-stiffness controlled instabilities were investigated. Depending on the system parameters, the
dynamic response of the tubes includes periodic, quasiperiodic, and chaotic motions. The analytical model is based
on the unsteady flow theory, which can predict the nonlinear dynamics of tube arrays in cross flow. For fluid-
damping controlled instability, analytical results and experimental data agree reasonably well.
1. INTRODUCTION
A group of circular tube submerged in cross flow can be subjected to dynamic instability, typically referred to as fluidelastic
instability. The threshold flow velocity at which tubes begin to undergo large oscillations is called the critical flow velocity (see
Fig. 1). If a system component is operated at a flow velocity above the critical value, severe damage to the components is likely
to occur, often after only a short time of operation. In fact, fluidelastic instability of tube arrays in cross flow has been one of the
main mechanisms causing tube failure in heat exchangers and steam generators [1-3]. Since the early 1970s, extensive studies of
fluidelastic instability have been reported. A significant understanding of the problem now exists. However, at present, it is still
not possible to predict instability phenomena from fundamental principles of fluid dynamics and the theory of elasticity. This
paper is to present an integrated experimental and analytical study with an emphasis to characterize the nonlinear dynamics of
fluidelastic instability of loosely supported tube arrays. It includes:
" The unsteady flow theory of fluidelastic instability of tube arrays.
* Experiment of fluid-damping controlled instability.
" A theory of fluid-damping controlled instability.
* Analysis of fluid-stiffness controlled instability.
Analytical and experimental results show the existence of chaotic, quasiperiodic, and periodic motions when the flow
velocity exceeds the critical flow velocity for loosely supported tube ar s in cross flow.
2. UNSTEADY FLOW THEORY FOR FLUIDELASTIC INSTABILITY OF TUBE ARRAYS
Consider a group of n identical tubes with radius R (= D/2) subjected to cross flow as shown in Fig. 2. The variables
associated with the tube motion in the x and y directions are flexural rigidity El, tube mass per unit length, m, structural damping
coefficient Cs, and displacement uj and vj. The equations of motion for tube j in the x and y directions are [2,41:
EIa +C. +ma- + n PrR2(ajks k a
aZ a t k=1 ( J 11 J2 (1)
+ ajk + jk )+ pU akuk+ajkVk=0
k~l) k=1
Ela2 +C, +ma- + at2 R jk a 2 +jk a (2)
+ jk + P jk +k pU2(Tkuk+PJk)=0
k=t a k=1
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Chen, S. S.; Cai, Y. & Zhu, S. Nonlinear Dynamics of Tube Arrays in Cross Flow, report, April 1, 1994; Argonne, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1313449/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.