ini. J. Pm. Vrs. & Piping 61 (lYY5) Y- 12
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Fatigue evaluation of piping connections
under thermal transients
ICarlos T. DeAquino*
COPESP,
Sdo Pado,
Brazil
Eduardo
Maneschy
COP.ESP/FURNAS,
Sdo Paulo.
Brazil
(Received 16 November 1993;accepted6 December 1993)
Weldolet connectionshave been widely used in the designof Class1 piping
systems in typical PWR nuclear power stations. Under severe thermal
transients,the resultant stressesin suchconnectionscan reach very high levels
and sometimesthe qualifficationof suchconnectionsaccordingto ASME Code
Section III is very difficult. Becauseof that there are situations where it is
necessaryto designa specialfitting in order to obtain a better thermal stress
distribution, reducing the values of stressto acceptablelevels.
The main goal of this paper is to perform a fatigue evaluation of a
connection, using a special fitting, through two different methodologies,as
describedlater in detail. An alternative to employing a standard weldolet will
be investigated and the results calculated using two connections will be
compared.
designed in a way to permit a better distribution
of the stresses, reducing its maximum value to
acceptable levels.
This paper intends to present a fatigue
evaluation of a connection, using the above
mentioned fitting, when subjected to a load
expressed in terms of a step thermal gradient,
varying from 263°C to 40°C.
Two different methodologies are used in this
analysis:
INTRODUCTION
In designing nuclear power plant piping, thermal
transients caused by non-steady operation conditions should be considered. These events may
reduce considerably the lifetime of the pipes,
creating the necessity of using structural elements
designed in such a way as to minimize the acting
thermal stresses.
Typical examples of the usage of such. elements
are the connections between pipes of small and
large diameters, in which a weldolet is usually
used. Nevertheless, in some situations, the
thermal stresses caused by the transients are
greater than the allowable limits; in this case a
special fitting replacing the weldolet is introduced, as can be seen in Fig. 1. Such a fitting is
(i) Determination
of the temperature distribution from the heat transfer equations
for piping, being the stresses calculated
according to ASME III NB-3600.’
(ii) Thermal and stress analyses using axisymmetric elements, according to the rules
presented in ASME III NB-3200.
* Present address:Avenue Prof. Linen Prestes2242,Cidade
Universitaria, Sao Paulo SP 05.508-900,
Brazil.
A similar evaluation has been performed for a
9
10
C. T. DeAquino,
E. Maneschy
subjected to a sudden injection of water at 40°C
through the pipe of smaller diameter.
THERMAL
Fig. 1. Special fitting with a thermal sleeve.
connection using a weldolet. In this case only the
approach according to NB-3200 is considered.
In the case (i), named simplified analysis, the
computer code used is PIPESTRESS while in
the case (ii), the ANSYS program’ was adopted.
OPERATING
MATERIAL
CONDITIONS
PROPERTIES
AND
The connection studied in this paper consisted of
two Class 1 pipes, whose nominal diameters are
sin. and 3 in., both schedule 160, plus the
special fitting, shown in Fig. 1, with a length of
195 mm and angle of 10”.
The material used in this connection was the
austenitic stainless steel SA 376 TP 347, with
design pressure and temperature of 16.5 MPa and
343”C, and normal operating conditions of
13.2 MPa and 263°C. The rates of mass flow are
O-266 kg/s and 1.213 kg/s through 2 in. and 3 in.
pipes, respectively. The material properties at
151°C are:
S,,,= 138 MPa
S, = 145 MPa
Young’s modulus = 190 GPa
Thermal expansion coefficient = 17 X
low6 mm/mm”C
Specific heat = O-5 kJ/kg”C
Thermal conductivity = 17 X lop3 W/mm”C
Density = 7600 kg/m3
The thermal transient specified for this paper
considered the connection initially at a temperature of 263”C, being at a subsequent time
ANALYSIS
In the simplified analysis it has been supposed
that the temperature distribution at the special
fitting could be calculated using a model that
considers the pipes of 2 in. and 3 in. diameters as
directly connected. According to subsection
NB-3650, the temperature distribution at the wall
of the piping, calculated through a dimensional
heat transfer model, is divided into three parts:
uniform, linear and non-linear. Each of these
parts was determined by the PIPESTRESS
program from the transient regime heat transfer
equations, assuming axial symmetry. In order to
get good accuracy, since the method of solution
of the equations is that of finite differences, the
thickness was divided into many elements.
The film coefficient, responsible for the heat
rate flowing through the pipe wall, was
automatically calculated, since the PIPESTRESS
program has internal tables that allow the
determination of the fluid properties (viscosity,
conductivity, specific volume, Reynolds and
Prandtl numbers) from the values of pressure and
temperature at each time. Since the pipe is
isolated the outside walls were considered
adiabatic.
The thermal analysis was performed after the
definition of geometry and material properties,
plus service level conditions and the thermal
transient acting on the pipe.
In the detailed analysis, the special fitting was
represented by thermal isoparametric
solid
elements, with axisymmetry option, identified as
STIFF55 in the element library of the ANSYS
program. The finite element mesh was automatically generated from the definition of keypoints
and line segments, used to limit the areas to be
divided into elements, as can be seen in Figs 2(A)
and 2(B).
The hypothesis of axisymmetry was based on
the work by Cesari,4 in which the author showed
that, provided that the larger diameter pipe was
modelled as a sphere whose radius is three times
the original radius of the piping, this was a
conservative approach.
The boundary conditions for this case took into
account different values of film coefficient, that
had to be furnished to the ANSYS program,
Fatigue evaluation
of piping connections
11
thermal transient, due to the injection of water at
40°C through the 3 in. piping, during 3 min. It was
assumed, for the scope of this analysis, that after
4min the system reached a thermal steady-state
regime.
STRESS ANALYSIS
(B)
Fig. 2. Finite element model: (A) general view; (B) detail.
obtained from expressions defined by Holman5
The boundary conditions were applied to inside
walls, all other surfaces being considered
adiabatic.
Some remarks have to be made on the
calculation of film coefficients for both models.
Although the PIPESTRESS program can compute these values internally, the formulation used
for that is the same as the one presented by
Holman for the detailed model.
A difference between both models is that in
the detailed one the region of interest is divided
into five parts, while in the simplified one only
two film coefficients are used, one for each pipe,
that are the same as the pipe film coefficients
used in the detailed model.
In the thermal analysis, an initial uniform
temperature field of 263°C was supposed, applied
at all nodes of the model. At a time immediately
after the initial, the nodes were subjected to a
The computation of the stresses obtained in the
fatigue analysis considered only the effects due to
the thermal transient, with the effects due to
pressure and bending moments (due to mechanical and thermal loads) not taken into account.
In the simplified model, where the rules of
ASME Code Section III NB-3600 were followed,
the determination of the peak stress, S, (eqn (11)
of NB-3650), was made from the superposition of
the stress contributions of the uniform, linear and
non-linear temperatures, all previously obtained.
In a conservative way, the stress indices adopted
were those related to weldolet, since the values
associated with the special fitting were, up to this
point, unknown.
For the stress analysis of the detailed model,
the bidimensional isoparametric solid element
has been used, with axisymmetry option,
identified as STIF42 in the ANSYS element
library.
The boundary conditions for this case took into
account the continuity of the larger diameter
piping. Because of that, the rightmost nodes of
the model had their thermal displacements
restrained in such a way as to simulate the
situation when a continuity of the pipe exists.
The loads considered for the determination of
stresses were nodal temperatures selected according to a criterion that is briefly discussed
below.
From a section A-B, in Fig. 3, considered as
being critical in the thermal analysis model, the
temperature distribution was analysed for the
times of the six worst temperature gradients
along the section.
RESULTS
In the case of the simplified model, the analysis
performed with PIPESTRESS determined the
stress contributions due to uniform, linear and
non-linear
temperatures at each time and
indicated the maximum value to be used in each
C. T. DeAquino,
E. Maneschy
when a weldolet connection is considered. In this
case, the same procedure used for detailed
thermal stress analysis was adopted. The film
coefficients were those for 2 in. and 3 in. pipes
and the same elements (STIF55 and STIF42)
were selected. The peak stress obtained was
740 MPa and the number of cycles allowable was
350.
Since the mechanical and thermal loads are
partially available for the plant being studied, it
was assumed, conservatively, that the membrane
plus bending stress violated the limit of 3&,, a
maximum allowable value of 3.33 being used for
K, in both analyses.
Table 1 summarizes the most important results
obtained in this study.
Fig. 3. Section used in stress calculations.
CONCLUSION
Table 1. Summary of Results
Results
Maximum stress
(MW
Cycles
Specialfitting
-
Weldolet
Simplified
method
Detailed
method
Detailed
method
930
567
700
740
350
100
of the NB-3650 equations. In this case, only the
peak stress was calculated, which provided a
value of 930MPa. Using fatigue curves from
ASME Section III Appendices for the material
of the connections, the number of cycles N,
corresponding to the lifetime of such a part and
obtained from the input of
s,,, = 3.33 x s,/2
equalled 100 cycles.
For the detailed analysis, the time for a
maximum temperature
gradient across the
thickness was defined and, from that, the peak
stress was obtained only at this time. The
ANSYS program provided the stress at each
node of the section shown in Fig. 3, as well as at
all other nodes, the critical value (567 MPa)
being located at node 854. In this case, following
the same procedure used for the simplified
analysis, the number of cycles N was 700 cycles.
It is interesting to make a similar evaluation
The existence of thermal transients at piping
connections produced high stress levels, resulting
in a reduction of the lifetime of such structural
parts.
An alternative to minimize this problem is to
use a special fitting with thermal sleeves, as
shown in Fig. 1, designed to have a better
temperature
distribution
that will cause a
reduction of the acting stresses. The cases studied
in this paper showed that the fitting provided a
greater lifetime when compared to standard
weldolet.
However, the application of such a fitting
would only be advantageous if the whole analysis
is performed following the rules of ASME
NB-3200.
In spite of increasing the cost, complexity and
time consumed, the results obtained this way
show a more realistic estimation of the lifetime of
the connection.
REFERENCES
1. ASME Boiler and Pressure Vessel Code, Section III,
Division 1, Subsection NB and Appendices, American
Society of Mechanical Engineers,New York, 1989.
2. ANSYS User’s Manual. SwansonAnalysis Inc., Houston,
PA, 1989.
3. PIPESTRESS, version 3.4.02. DST Computer Services
S.A., Geneva, Switzerland, 1991.
4. Cesari, F., Equivalent nozzles in thermomechanical
problems.ht. J. of Pres. Ves. & Piping, (1979)309-17.
5. Holman, J. P., Heat Transfer. McGraw-Hill, SBo Paulo,
Brazil (in Portuguese),1983.