**5.1 Results**

In heat exchangers, the analysis of a complex influence of perforated bottoms on the jacket connected to them, as well as a distribution of stresses in the jacket, pipes and perforated bottoms is essential. The substitutive stress that decides basically about strains occurring in steel structures was calculated according to the Huber-Misses hypothesis. The calculations of the heat exchanger were conducted on the assumption of high strains in the structural elements.

The Finite Element Method - ANSYS 12.0 - was used for the numerical calculations. The results of the numerical calculations have been presented in the form of maps of stresses and strains. The results shown in Figs. 5-12 concern the heat exchanger in which the thickness of

Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 175

Fig. 6. Distribution of reduced stresses in the heat exchanger [MPa] – case1.

Fig. 7. Total strains in pipes and perforated bottoms [mm] – case 1.

the perforated plate was decreased up to 50mm, whereas Figs.13-20 depict the results for the plate thickness equal to 30mm.

The ANSYS code used in the calculations shows the results in the form of maps for stresses or strains, respectively. The maps are colored. Individual colors correspond to specific numerical values (see the legend). While analyzing Figs. 5 and 6, we have observed that the maximum stresses σmax=198MPa and the maximum strains εmax=(0.56-0.72)mm occur in the jacket collar and they are marked in red. Figure 7 presents strains in the heating cartridge pipes. It was expected that highest strains would occur in the central part along the pipe length. The numerical calculations confirmed the earlier assumptions of Umax=0.21mm. The pipes in this region show a tendency to deflection along the geometrical axis of the heat exchanger.

A detailed discussion of the results shown in Figs. 5-20 is to be found in the section entitled "Analysis of the results".

Fig. 5. Total strains in the heat exchanger [mm] – case 1.

the perforated plate was decreased up to 50mm, whereas Figs.13-20 depict the results for the

The ANSYS code used in the calculations shows the results in the form of maps for stresses or strains, respectively. The maps are colored. Individual colors correspond to specific numerical values (see the legend). While analyzing Figs. 5 and 6, we have observed that the maximum stresses σmax=198MPa and the maximum strains εmax=(0.56-0.72)mm occur in the jacket collar and they are marked in red. Figure 7 presents strains in the heating cartridge pipes. It was expected that highest strains would occur in the central part along the pipe length. The numerical calculations confirmed the earlier assumptions of Umax=0.21mm. The pipes in this region show a tendency to deflection along the geometrical axis of the heat

A detailed discussion of the results shown in Figs. 5-20 is to be found in the section entitled

plate thickness equal to 30mm.

exchanger.

"Analysis of the results".

Fig. 5. Total strains in the heat exchanger [mm] – case 1.

Fig. 6. Distribution of reduced stresses in the heat exchanger [MPa] – case1.

Fig. 7. Total strains in pipes and perforated bottoms [mm] – case 1.

Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 177

Fig. 10. Distribution of reduced stresses in perforated bottoms [MPa] – case 1.

Fig. 11. Total strains in pipes mounted in the center of the perforated plate; magnified

deformation of pipes [mm] – case 1.

Fig. 8. Distribition of reduced stresses in pipes and perforated bottoms [MPa] – case 1.

Fig. 9. Total strains in perforated bottoms [mm] – case 1.

Fig. 8. Distribition of reduced stresses in pipes and perforated bottoms [MPa] – case 1.

Fig. 9. Total strains in perforated bottoms [mm] – case 1.

Fig. 10. Distribution of reduced stresses in perforated bottoms [MPa] – case 1.

Fig. 11. Total strains in pipes mounted in the center of the perforated plate; magnified deformation of pipes [mm] – case 1.

Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 179

Fig. 14. Distribution of reduced stresses in the heat exchanger [MPa] – case 2.

Fig. 15. Total strains in pipes and perforated bottoms [mm] – case 2.

Fig. 12.Total strains in pipes subject to the maximual strain; magnified deformation of pipes [mm] – case 1.

Fig. 13. Total strains in the heat exchanger [mm] – case 2.

Fig. 12.Total strains in pipes subject to the maximual strain; magnified deformation of pipes

Fig. 13. Total strains in the heat exchanger [mm] – case 2.

[mm] – case 1.

Fig. 14. Distribution of reduced stresses in the heat exchanger [MPa] – case 2.

Fig. 15. Total strains in pipes and perforated bottoms [mm] – case 2.

Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 181

Fig. 18. Distributions of reduced stresses in perforated bottoms [MPa] – case 2.

Fig. 19. Total strains in pipes mounted in the center of the perforated plate; magnified

deformation of pipes [mm] – case 2.

Fig. 16. Distribition of reduced stresses in pipes and perforated bottoms [MPa] – case 2.

Fig. 17. Total strains in perforated bottoms [mm] – case 2.

Fig. 16. Distribition of reduced stresses in pipes and perforated bottoms [MPa] – case 2.

Fig. 17. Total strains in perforated bottoms [mm] – case 2.

Fig. 18. Distributions of reduced stresses in perforated bottoms [MPa] – case 2.

Fig. 19. Total strains in pipes mounted in the center of the perforated plate; magnified deformation of pipes [mm] – case 2.

Numerical Analysis of the Structural Stability of Heat Exchangers – The FEM Approach 183

Fig. 22. Strain path in the pipe along its length [mm] – an example (the pipe is mounted in

A shell-solid model of the heat exchanger - a water heater - was subjected to the numerical calculations. The author's task was to conduct a possibly full analysis of stresses and strains occurring in structural elements of the heat exchanger, especially under extreme conditions that appear during, e.g., emergency operation. The calculations were carried out for altered thickness of the plate (in the first case by 15%, in the second one by 50%). This change was dictated by economic reasons. On the basis of the calculation results and the analysis of distributions of stresses and strains, one can conclude that the perforated bottom (the perforated plate) is not the place where stresses concentrate. In the first case, the reduced stresses in the bottom were equal to approx. 30 MPa (Fig.10), and in the second case they increased to approx. 50 MPa (Fig.18). The analysis of local zones of stresses in the whole heat exchanger has allowed us to find out that the maximal stresses in both cases appeared in the connections between the collar with the jacket and they were equal to, respectively, 198MPa, and in the second case they increased by approx. 10%. As opposed to the values of stresses, the total strains differ considerably. The maximal strains occurring in the heat exchanger were of the magnitude of 0.07 mm in the first case (Fig.5), whereas in the second case they increased up to 4.45 mm (Fig.13). Some exemplary maps of strains in the selected

2. in the outer part of the perforated plate, in the place where the maximal deflection is

the position farthest from the geometrical axis of the heat exchanger).

1. in the central part of the perforated plate (Fig. 11 and Fig.19),

anticipated (Fig.12 and Fig. 20) have been presented in the paper.

**6. Analysis of the results** 

pipes mounted, correspondingly:

Fig. 20. Total strains in pipes subject to the maximal strain; magnified deformation of pipes [mm] – case 2.

Fig. 21. Strain path in the pipe along its length [mm] - an example (the pipe is mounted in the position closest to the geometrical axis of the heat exchanger).

Fig. 22. Strain path in the pipe along its length [mm] – an example (the pipe is mounted in the position farthest from the geometrical axis of the heat exchanger).
