# Analytical Reconstruction of Failure of a Shell and Tube Heat Exchanger

## Abstract

Heat exchanger tubes are supported at intermediate points by support plates. Flow-induced vibration of tube can cause it to impact or rub against a support plate or against adjacent tubes and can result in tube fretting wear. Fretting wear damage assessment procedure has been presented. This procedure is implemented by studying classical heat exchanger cases of premature failures. The authors expect this study to be useful for estimating the fretting wear damage of heat exchanger tubes. The study shows that based on fretting wear volume rate the life of heat exchanger tube can be predicted.

## Keywords

Flow-induced vibration Heat exchanger tube Fretting wear Vortex shedding Finite element simulation## List of symbols

- \( \rho \)
Fluid density

- \( v \)
Free stream velocity

- \( {\text{f}}_{n} \)
Reduced frequency

*D*Tube diameter

- \( C_{\text{L}} \)
Lift coefficient, dimensionless

- \( \omega_{\text{s}} \)
Circular vortex shedding frequency, radian/s

- \( F_{\text{L}} \)
Lift force (force perpendicular to the mean flow) per unit length of tube

- \( \rho V \)
Mass flux

- \( S_{\text{FF}} \)
Power spectral density

- \( \emptyset_{i} \)
Phase angle

*N*Number of harmonics contributing to the total force

- \( L_{\text{e}} \)
Element length

*M*Mass matrix

*C*Linear damping matrix

- \( C_{\text{NL}} \)
Non-linear damping matrix

*K*Linear stiffness matrix

- \( K_{\text{NL}} \)
Non-linear stiffness matrix

- \( R_{t + \Delta t} \)
External force vector at time \( t + \Delta t \)

- \( \ddot{U}_{t + \Delta t} ,\dot{U}_{t + \Delta t} ,\;U_{t + \Delta t} \)
Acceleration, velocity, and displacement vectors at time \( t + \Delta t \), respectively

*f*Contact force

- \( K_{\text{NL}} \)
Support stiffness

*U*Displacement between tube and support

- \( C_{\text{NL}} \)
Non-linear damping coefficient

- \( V\left( t \right) \)
Worn volume after time

*T*,*k*Specific wear coefficient,

- \( F_{\text{N}} \)
Normal contact force between tube and support

- \( L\left( t \right) \)
Sliding distance after time

*T*- \( \dot{V} \)
Fretting wear damage volume rate

- \( K_{\text{W}} \)
Specific wear coefficient

- \( W_{\text{N}} \)
Normal work rate

*L*Support thickness

- \( d_{\text{W}} \)
Tube wall wear depth

- TEMA
Tubular Exchanger Manufacturer Association

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