Chapter 12

Strength Analysis of a Plate Heat

Exchanger with Two Design-By-Analysis
Methods

Zhenning Liu, Huifang Li, and Caifu Qian

Abstract Plate heat exchangers are widely used equipment in engineering. As the
structure of the equipment is complicated, it is hard to perform accurate design with
the traditional method or so-called design-by-rules. In this paper, two design-by-
analysis methods, namely Elastic Stress Analysis Method and Limit-load Analysis
Method were used to perform stress assessment of a plate heat exchanger. Results
show that the plate heat exchanger meets the strength requirements according to
ASME VIII-2. It is also found that if applying Elastic Stress Analysis Method, a lot
of SCLs should be specified on components of the plate heat exchanger and stresses
have to be categorized according to their effects on the strength failure of the equip-
ment. If applying Limit-load Analysis Method, the materials are assumed to be ideal
elastic-plastic, and no Stress Classification Lines (SCLs) and stress categorization are
needed. Strength assessment is simply to find convergent solutions for the maximum
loading. So if the equipment is complicate in structure like the plate heat exchanger,
it is suggested to apply Limit-load Analysis Method to perform strength assessment.

Keywords Plate heat exchanger · Finite element analysis · Strength assessment ·

Design-by-analysis

12.1 Introduction

Heat exchangers are devices that transfer heat from hot fluid to cold fluid to meet
specific process requirements or to recover energy. Based on the structures, heat
exchangers can be divided into shell-and-tube heat exchangers, plate heat exchangers,
etc. Plate heat exchangers are composed of multiple plates that have different corru-
gations to enhance the heat transfer between the two fluids [1]. Plate heat exchangers
have higher heat transfer coefficient than shell-and-tube heat exchangers [2] and
are considered to be the ideal equipment for liquid-liquid heat exchange and vapor-
liquid exchange. A lot of studies were addressed on the performance of plate heat

Z. Liu (B) · H. Li · C. Qian

Beijing University of Chemical Technology, Beijing 100029, China
e-mail: 1758609342@qq.com

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 143
J. Xu and K. M. Pandey (eds.), Mechanical Engineering and Materials,
Mechanisms and Machine Science 100,
https://doi.org/10.1007/978-3-030-68303-0_12
144 Z. Liu et al.

exchangers. Shokouhmand and Hasanpour [3] found that reducing the uneven distri-
bution can improve the thermal efficiency of the plate heat exchangers. Corrugation
has a great influence on the heat transfer efficiency of plate heat exchangers. Islam-
oglu and Parmaksizoglu [4] found that increasing in the height of the corrugation
leads to an increase in the coefficient of friction and a reducing in heat transfer effi-
ciency. Grijspeerdt et al. [5] used CFD (Computational Fluid Dynamics) software to
build optimized corrugated model of plate heat exchanger. Galeazzo et al. [6] used
CFD to perform simulation calculations and found that turbulence in the flat flow
channel is only partially generated, and the main state is laminar. The flow state of
non-Newtonian fluid in the plate heat exchanger was also studied by Femandes et al.
[7]. The sequence of chemical reactions also has a certain impact on fluid flow [8].
Barbaryan et al. [9] used numerical analysis methods to design low fluid pressure
safety valves. Nagaraju et al. [10, 11] studied the flow state of magnetic fluid in pipes.
Under the combined action of the plate-side pressure, shell-side pressure and
temperature field, a possible failure mode of the heat exchangers is cracking owing
to insufficient structural strength [12]. So it is needed to perform strength assessment
for the heat exchangers. Yang Xirong simulated the stress distribution on U-shaped
heat exchangers [13]. Hoseinzadeh et al. [14] conducted life fatigue analysis on heat
exchangers in power plants. Fen Xiao [15] performed stress analysis on fixed tube-
plate heat exchangers. Regarding the influences of the working environment on the
heat exchangers, Gagliardia [16] studied the plate heat exchangers working in the
river and found that its failure reason was related to the upstream water treatment
process.
As the structure of plate heat exchangers is complicated, it is hard to perform
accurate design with the traditional method or so-called design-by rules. So in this
paper, finite element method was used to perform stress analysis for a plate heat
exchanger under different load cases. Two methods, namely stress category method
and limit analysis method, are applied based on ASME VIII-2 to perform strength
assessment of the heat exchanger.

12.2 Finite Element Modelling

12.2.1 Geometry and Grid Models of the Plate Heat

Exchanger

The basic design parameters of the plate heat exchanger are listed in Table 12.1. As
shown in Fig. 12.1 for the structure, the heat exchanger is composed of curved plate,
pipes, shell, supports, etc.
Solid186 with the software ANSYS was used to mesh the plate heat exchanger.
The total number of grids is 1526053. The mesh quality was checked in terms of
skewness, and the average value was 0.14, meaning that the mesh quality is good.
12 Strength Analysis of a Plate Heat Exchanger … 145

Table 12.1 Design

Parameter/Unit Plate-side Shell-side
parameters
Design pressure (MPa) 0.1 0.4
Design temperature (°C) 170 50
Working pressure (MPa) 0.01 0.3
Medium Air Water
Corrosion allowance (mm) 0 0
Material S30408 S30408

Fig. 12.1 Geometric model

of the plate heat exchanger

12.2.2 Load and Constraint Conditions

Design pressures, dead load, seismic load, external nozzle load, and equivalent nozzle
force are considered in this study. Among them, seismic load is assumed to be static
with the acceleration being equal to 0.2 times of the gravitational acceleration. Each
nozzle is acted by the equivalent nozzle force with magnitude being calculated by
the Eq. (12.1):

di2
pe = p (12.1)
do2 − di2

where p is the pressure on the inner wall of nozzles.

On the air inlet and outlet nozzles of the equipment, there are also external loads
with the magnitudes listed in Table 12.2.
In this study, two load cases are specified for static strength assessment as listed
in Table 12.3 for the included pressures.
As shown in Fig. 12.2, in case 1, only the plate-side surface of the heat exchanger
was loaded with the pressure of 0.1 MPa. The equivalent force applied on the air
outlet and inlet nozzles is 2.5 MPa. Fixed constraint was imposed on the supporters.
146 Z. Liu et al.

Table 12.2 External loads on nozzles

Force (N) Moment (N·m)
Fx Fy Fz Mx My Mz
Air inlet nozzle −66,100 18,800 −32,600 −23,100 79,200 −5000
Air outlet nozzle 5000 50,700 20,200 35,000 13,700 −25,200

Table 12.3 Pressures in load

Static load cases
cases for static strength
assessment Case 1 Case 2
Plate-side pressure(MPa) 0.1 0
Shell-side pressure(MPa) 0 0.4

Fig. 12.2 Loads and

constraints in case 1

As shown in Fig. 12.3, in case 2, only the shell-side surface of the heat exchanger
was loaded with the pressure of 0.4 MPa. The equivalent force applied to the water
outlet and inlet nozzles is 3.765 MPa. Fixed constraint was imposed on the supporters.

12.3 Strength Assessment Based on Elastic Stress Analysis

Method

Elastic Stress Analysis Method assumes the material of the equipment is linear elastic.
Stresses on the equipment will be classified into different categories in terms of
Mises equivalent stress. Different categories of stresses will be limited with different
allowable values according to their effects on the possible strength failure of the
equipment. The allowable stress S for S30408 at the design temperature is 134.2 MPa.
The Mises equivalent stress distributions at the plate heat exchanger under
different working cases were shown in Figs. 12.4–12.5.
12 Strength Analysis of a Plate Heat Exchanger … 147

Fig. 12.3 Loads and

constraints in case 2

Fig. 12.4 Mises equivalent

stress distribution under load
case 1

The Mises equivalent stress in case 1 is 154.55 MPa which is located at the
connection zone between the square-circle transition shell and connecting plate. The
maximum Mises equivalent stress in case 2 is 189.15 MPa which is located at the
T-shaped ribs.
According to Elastic Stress Analysis Method, Mises equivalent stresses should be
categorized into General Primary Membrane Equivalent Stress (Pm ), Local Primary
Membrane Equivalent Stress (PL ), Primary Membrane (General or Local) Plus
Primary Bending Equivalent Stress (PL + Pb ) and Primary Membrane (General
or Local) Plus Primary Bending Equivalent Stress Plus secondary Equivalent Stress
(PL + Pb + Q). For calculating the equivalent stresses, the total stress shall be
148 Z. Liu et al.

Fig. 12.5 Mises equivalent

stress distribution under load
case 2

linearized on a stress component basis to produce membrane and bending stresses.

Membrane and bending stresses are developed on cross sections through the thickness
of a component. Therefore, Stress Classification Lines (SCLs) should be specified
orienting normal to contour lines of the stress component of highest magnitude.
In this study, SCLs or paths are specified at components of the equipment. As
an example, Fig. 12.6 shows the paths at the connection zone between the square-
circle transition shell and air inlet nozzle under load case 1. Table 12.4 lists stress
categorization and assessment for each path. It should be noted, like at the small end
of a conic shell, the local primary membrane equivalent stress PL at the round end
of square-circle transition shell is limited by 1.1 S.

Fig. 12.6 Paths at the

connection zone between the
square-circle transition shell
and air inlet nozzle under
load case 1
12 Strength Analysis of a Plate Heat Exchanger … 149

Table 12.4 Stress categorization and assessment at the connection zone between the square-circle
transition shell and air inlet nozzle under load case 1
Paths Stress category Calculated stress, MPa Allowable stress, MPa Assessment results
Path 8 Pm 19.20 134.2 Pass
Path 5 PL 43.60 147.6 Pass
PL + Pb + Q 58.29 402.6 Pass

Similarly, as an example, Fig. 12.7 shows the paths at the connection zone between
the curved plate and water inlet nozzle under load case 2. Table 12.5 lists stress
categorization and assessment for each path.
It turns out that all types of Mises equivalent stresses in the whole equipment are
less than the corresponding allowable values according to ASME VIII-2, meaning
the plate heat exchanger meets the strength requirements based on Elastic Stress
Analysis Method.

Fig. 12.7 Paths at the

connection zone between the
curved plate and water inlet
nozzle under load case 2

Table 12.5 Stress categorization and assessment at the connection zone between the curved plate
and water inlet nozzle under load case 2
Paths Stress category Calculated stress, MPa Allowable stress, MPa Assessment results
Path 4 Pm 21.76 134.2 Pass
Path 1 PL 12.61 147.6 Pass
PL + Pb + Q 88.92 402.6 Pass
Path 2 PL 24.17 147.6 Pass
PL + Pb + Q 111.32 402.6 Pass
Path 3 PL 23.68 147.6 Pass
PL + Pb + Q 110.8 402.6 Pass
150 Z. Liu et al.

12.4 Strength Assessment Based on Limit-Load Analysis

Method

When the maximum stress reaches the yields limit, the actual structure usually does
not lose its load-carrying capability immediately. With the increase of the load, the
stress in the high stress zone first reaches the yield limit, and the material enters
the yield state. Then the stress will be redistributed and the range of plastic zone
will be expanded. The ultimate load refers to the load corresponding to the plastic
state when the component changes from elastic state to plastic state under the action
of external load. When the ultimate load is reached, the component will enter the
instability state. The results of the Limit-load Analysis Method are closer to the real
failure conditions.
The ideal elastic-plastic material mode is adopted in the Limit-load Analysis
Method as shown in Fig. 12.8 for the material used in the plate heat exchanger
studied here.
For the plate heat exchanger studied here, two load cases are specified in the limit-
load analysis. The first is only applying pressure on the plate-side and finding the
maximum pressure by performing limit-load analysis. The second is only applying
pressure on the shell-side and finding the maximum pressure by performing limit-load
analysis.
Dead load, seismic load, external nozzle load, equivalent nozzle force and
constraints for the limit-load analysis are the same as those for stress category anal-
ysis discussed above. Gravity acceleration, seismic load, and external nozzle load do
not change with time.
Limit-load analysis is a non-linear analysis, so load-steps and sub-steps are
required. Based on the limit-load analysis theory, the limit load, i.e. the maximum

Fig. 12.8 Ideal elastic-plastic stress-strain curve

12 Strength Analysis of a Plate Heat Exchanger … 151

pressure is the one corresponding to the last sub-step before the calculation becomes
divergent. In this study, 1 load-step and 100 sub-steps are set for the computation.
About 48hrs are required to finish a computation to get the limit load.
For the first load case where the pressure only acts on the plate-side, it is found that
the calculation becomes divergence after the 68th sub-step. Figure 12.9 shows the
load-displacement relationship corresponding to each sub-step before divergence.
When the deformation is not large, the displacement increment of each sub-step is
stable. But the slope of the curve gradually decreases to zero, which means that the
structure could generate a very large displacement increment under a very small load
increment. From the last step results before divergence, it is found the maximum
pressure or the limit pressure is 0.53 MPa. If taking 1.5 as the safety factor, the
allowable pressure is 0.35 MPa, much larger than the design pressure (0.1 MPa)
on the plate-side, meaning the strength on this side meets the strength requirement.
Figure 12.10 shows the von Mises distribution under the maximum pressure on the
plate-side. It is clear that the yielding zone is at air outlet nozzle connecting area.
For the second load case where the pressure only acts on the shell-side, it is found
that the calculation becomes divergence after the 66th sub-step. Figure 12.11 shows
the load-displacement relationship corresponding to each sub-step before divergence
and it turns out the maximum pressure or the limit pressure is 2.25 MPa. If taking
1.5 as the safety factor, the allowable pressure is 1.5 MPa, much larger than the
design pressure (0.4 MPa) on the shell-side, meaning the strength on this side meets
the strength requirement. Figure 12.12 shows the von Mises distribution under the
maximum pressure on the shell-side. It is found that the yielding zone is at water
outlet nozzle connecting area.
As all allowable pressures are larger than the corresponding design pressures, the
plate heat exchanger meets the strength requirements based on Limit-load Analysis
Method according to ASME VIII-2.

Fig. 12.9
Load-displacement
relationship when only
plate-side pressure was
applied
152 Z. Liu et al.

Fig. 12.10 von Mises

distribution under the
maximum pressure on the
plate-side

Fig. 12.11
Load-displacement
relationship when only
shell-side pressure was
applied

12.5 Conclusions

In order to make accurate and effective strength design of plate heat exchangers,
finite element analysis was conducted to evaluate the static strength of a plate
heat exchanger under the different load cases. Two design-by-analysis methods,
namely Elastic Stress Analysis Method and Limit-load Analysis Method were used
to perform stress assessment. Results show that the plate heat exchanger meets the
strength requirements according to ASME VIII-2. It is also found that if applying
Elastic Stress Analysis Method, a lot of SCLs should be specified on components of
the plate heat exchanger and the stresses have to be categorized according to their
effects on the strength failure of the equipment, which significantly complicates the
computation and strength assessment. If applying Limit-load Analysis Method, the
12 Strength Analysis of a Plate Heat Exchanger … 153

Fig. 12.12 von Mises

distribution under the
maximum pressure on the
shell-side

materials are assumed to be ideal elastic-plastic, which is conservative since real

materials are of strain-hardening and can still undertake some more loadings after
yielding. In addition, no SCLs and stress categorization are needed and the strength
assessment is simply to find convergent solutions for the maximum loading. So if
the equipment is complicate in structure like the plate heat exchanger, it is suggested
to apply Limit-load Analysis Method to perform strength assessment.

References

1. Numan, A., Mohd, I., Sayyed, H.: Study and analysis of plate type heat exchanger. Invertis J.
Renew. Energy 7(3), 137–141 (2017)
2. Pelliccione, A.S., SantAnna, R., Siqueira, M.H.S., Ribeiro, A.F., Ramos, J.E., Silva, O.P.,
Pimentel, M.F.: Failure analysis of a titanium plate heat exchanger–Mechanical fatigue. Eng.
Fail. Anal. 105, 1172–1188 (2019)
3. Shokouhmand, H., Hasanpour, M.: Effect of flow maldistribution on the optimal design of plate
heat exchanger using constrained multi objective genetic algorithm. Case Stud. Thermal Eng.
18, 100570 (2020)
4. Islamoglu, Y., Parmaksizoglu, C.: The effect of channel height on the enhanced heat transfer
characteristics in a corrugated heat exchanger channel. Appl. Therm. Eng. 23(8), 979–987
(2003)
5. Grijspeerdt, K., Hazarika, B., Vucinic, D.: Application of computational fluid dynamics to
model the hydrodynamics of plate heat exchangers for milk processing. J. Food Eng. 57(3),
237–242 (2003)
6. Galeazzo, F.C.C., Miura, R.Y., Gut, J.A.W., Tadini, C.C.: Experimental and numerical heat
transfer in a plate heat exchanger. Chem. Eng. Sci. 61(21), 7133–7138 (2006)
7. Femandes, C.S., Dias, R., Nobrega, J.M., et al.: Simulation of stirred yoghurt processing in
plate exchangers. J. Food Eng. 69(3), 281–290 (2005)
8. Science - Applied Physical Science; Research Data from Department of Mathematics Update
Understanding of Applied Physical Science (Order of chemical reaction and convective
154 Z. Liu et al.

boundary condition effects on micropolar fluid flow over a stretching sheet). J. Technol. Sci.
(2018)
9. Heat and Fluid Flow; Study Results from University of Pretoria in the Area of Heat and
Fluid Flow Reported (Developing a low-fluid pressure safety valve design through a numerical
analysis approach). Mathematics Week (2020)
10. Nagaraju, G., Garvandha, M.: Magnetohydrodynamic viscous fluid flow and heat transfer in a
circular pipe under an externally applied constant suction. Heliyon 5(2) (2019)
11. Murthy, J.V.R., Nagaraju, G., Sai, K.S.: Numerical solution for MHD flow of Micro polar
fluid between two concentric rotating cylinders with porous lining. Int. J. Nonlinear Sci. 13(2),
183–193 (2012)
12. Xu, L., Qian, C.F., Liu, J.Y., Liu, Z.S.: Thermal stress analysis of tube sheet of floating head
heat exchanger. Pressure Vessel 32(6), 55–60 (2015). (In Chinese)
13. Yang, X.R., Wang, Z.W., Meng, X.Y.: U-tube heat exchanger tube sheet and tube stress
calculation and fatigue analysis. Contemporary Chem. Ind. 48(04), 855–858 (2019). (In
Chinese)
14. Hoseinzadeh, S., Heyns, P.S.: Thermo-structural fatigue and lifetime analysis of a heat
exchanger as a feedwater heater in power plant. Eng. Fail. Anal. 113, 104548 (2020)
15. Xiao, F., Chen, Z.W.: Stress analysis and fatigue analysis of fixed tube-plate heat exchanger.
Chem. Equip. Pipel. 47(5), 5–7 (2010). (In Chinese)
16. Gagliardi, A., Lanzutti, A., Simonato, M., Furlanetto, R., Magnan, M., Andreatta, F., Fedrizzi.
L.: Failure analysis of a plate heat exchanger used in a blast chiller. Eng. Failure Anal. 92,
289–300 (2018)