Journal of Failure Analysis and Prevention

, Volume 17, Issue 1, pp 126–135

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

• Gajendra Vasantrao Patil
• M. A. Dharap
• R. I. K. Moorthy
Technical Article---Peer-Reviewed

## 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

## References

1. 1.
R.D. Blevins, Flow-induced vibration (Krieger publishing company, Malabar, 2001)Google Scholar
2. 2.
R.G. Sauve, W.W. Teper, Impact simulation of process equipment tubes and support plates: a numerical algorithm. ASME J. Press. Vessel Technol. 109(1), 70–79 (1987)
3. 3.
M.P. Paidoussis, Flow-induced vibrations in Nuclear reactors and heat exchangers, in Practical experiences with flow induced vibrations, ed. by E. Nausdascher, D. Rockwell (Springer, Berlin, 1980), pp. 1–80
4. 4.
J.F. Eilers, W.M. Small, Tube vibration in a Thermosiphon Reboiler. Chem Eng Progr 69, 57–61 (1973)Google Scholar
5. 5.
M. W. Wambsganss, H. Halle, T. M. Mmulcahy, A report on structural dynamics and fluid flow in shell-and-tube heat exchangers, Summary and overview of a doe/ecut-sponsored research program, Argonee National laboratory (1985)Google Scholar
6. 6.
M.J. Pettigrew, C.E. Taylor, Vibration analysis of shell-and-tube heat exchangers: an Overview-Part2: vibration response, fretting-wear, guidelines. J. Fluids Struct. 18, 485–500 (2003)
7. 7.
R.G. Sauve, M. Tabatabai, G. Moradin, M.J. Kozluk, Ontario Hydro, Application of flow- induced vibration predictive techniques to operating steam generators. In International steam generator and heat exchanger conference; Toronto, ON (Canada), pp. 343–357 (1998)Google Scholar
8. 8.
N.J. Fisher, M.J. Olesen, R.J. Rogers, P.L. Ko, Simulation of tube-to-support dynamic interaction in heat exchange equipment. ASME J. Press. Vessel Technol. 111(1), 378–384 (1989)Google Scholar
9. 9.
M.A. Gajendra Patil, M.A. Dhara, R.I.K. Moorthy, Studies on identification of an efficient and accurate integration scheme for piecewise linear dynamic problems. Int. J. Comput. Methods Eng. Sci. Mech. 1, 1–12 (2016)Google Scholar
10. 10.
K.J. Bathe, E.L. Wilson, Numerical methods in finite element analysis (Prentice Hall, Upper Saddle River, 1978)Google Scholar
11. 11.
R.I.K. Moorthy, A. Kakodkar, H.R. Srirangarajan, S. Suryanarayan, Finite element simulation of chaotic vibrations of a beam with non-linear boundary conditions. Comput. Struct. 49(4), 589–596 (1993)
12. 12.
F. Axisa, J. Antunes, B. Villard, Overview of numerical methods for predicting flow-induced vibration. ASME J. Press. Vessel Technol. 110(1), 6–14 (1988)
13. 13.
K.J. Bathe, S. Gracewski, On nonlinear dynamic analysis using substructuring and mode superposition. Comput. Struct. 13(5–6), 699–707 (1981)
14. 14.
I.F. Stowers, E. Rabinowicz, The mechanisms of fretting wear. ASME-ASLE International lubrication conference, Paper 72-Lub-20 (1973)Google Scholar

© ASM International 2016

## Authors and Affiliations

• Gajendra Vasantrao Patil
• 1
• 2
• M. A. Dharap
• 1
• R. I. K. Moorthy
• 2
1. 1.Veermata Jijabai Technological InstituteMumbaiIndia
2. 2.Pillai college of engineeringNew PanvelIndia