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Jianfeng ShiJinyang Zheng
1
e-mail: jyzh@zju.edu.cnInstitute of Chemical Machinery and ProcessEquipment,Zhejiang University,Hangzhou,Zhejiang 310027, P. R. China
Weican Guo
Institute of Chemical Machinery and ProcessEquipment,Zhejiang University,Hangzhou,Zhejiang 310027, P. R. China;Zhejiang Inspection Center of Special Equipment,Hangzhou,Zhejiang 310020, P. R. China
Ping Xu
Department of Mechanics,Zhejiang University,Hangzhou,Zhejiang 310027, P. R. China
Yongquan Qin
Institute of Chemical Machinery and ProcessEquipment,Zhejiang University,Hangzhou,Zhejiang 310027, P. R. China
Shangzhi Zuo
China Inspection Center of Special Equipment,Beijing,Beijing 100013, P. R. China
A Model for PredictingTemperature of ElectrofusionJoints for Polyethylene Pipes
With the increasing application of electrofusion (EF) welding in connecting polyethylene(PE) pipes for gas distribution, more effort has been invested to ensure the safety of the pipeline systems. The objective of this paper is to investigate and understand the tem- perature distribution during EF welding. A one-dimensional transient heat-transfer model was proposed, taking the variation in the rate of power input, the phase transitionof PE, and the thermal contact conductance between heating wire and PE into consid-eration. Then, experiments were designed to verify the power input and the temperature.The measured values of the power input were shown to be in good agreement with theanalytical results. Based on ultrasonic test (UT), a new “Eigen-line” method was pre-sented, which overcomes the difﬁculties found in the thermocouples’ temperature mea-surements. The results demonstrate good agreements between prediction and experiment.Finally, based on the presented model, a detailed parametric study was carried out toinvestigate the inﬂuences of the variation in the power input, the physical properties of PE, and the thermal contact conductance between heating wire and surroundingPE.
DOI: 10.1115/1.4000202
Keywords: electrofusion joint, temperature proﬁle, numerical simulation, Eigen-line
1 Introduction
PE has been widely used in gas distribution since it was ini-tially introduced to transport natural gas in the 1960s
1
. Gener-ally, it has lots of advantages such as excellent corrosion resis-tance, ease of installation, and cost-effectiveness. Two types of jointing methods, i.e., butt fusion and electrofusion are commonlyused to connect PE pipelines. Since many of these systems carryfuel gas, failure rates at joints must be very low. Research hasshown that the safety of pipeline system mainly depends on thequality of the welded joints, and that the intensity, the toughness,and the peeling energy after welding largely depend on the mo-lecular entanglement of PE near the fusion interface
2
. The tem-perature and the pressure usually affect the macromolecular diffu-sion at the interface
3,4
. Therefore, it is essential to obtain anunderstanding of the EF jointing of PE pipe systems.Research on predicting temperature proﬁles of the EF joint hasbeen intensively performed in recent years. Shi et al.
5
estab-lished a one-dimensional axisymmetric heat-transfer model. Tosimplify the solving process, the temperature-dependent proper-ties such as speciﬁc heat capacity, density, and thermal conductiv-ity were neglected. Nakashiba and co-workers
6,7
, and Fujikakeet al.
8
investigated the temperature proﬁles with a ﬁnite elementmodel, considering temperature-dependent material properties.However, their studies presented little information on the variationin power input and did not offer an appropriate method to ﬁnd theexact value of the actual input power. As the value of input powerhas a great impact on the temperature ﬁeld, the previously devel-oped models may not address the practical problem.Based on the theory of heat transfer, the present paper estab-lished a one-dimensional transient heat-transfer model. Thismodel comprehensively took the temperature-dependent proper-ties and the power input that changes with the wire temperatureinto consideration. A numerical solution is developed based on theSkeel method
9
. To verify the model, several experiments weredesigned. First, the interface temperature was measured by well-installed thermocouples. Then the total input energy was recordedby the welding machine. Furthermore, the solid-liquid interfacewas detected by an UT machine based on a new Eigen-linemethod. Comparison of the measured temperatures by thermo-couples and analytical results demonstrated that it is very difﬁcultto measure the interface temperature without any bias. The experi-mental results of input power and Eigen-line agree well with the
1
Corresponding author.Contributed by the Pressure Vessel and Piping Division of ASME for publicationin the J
OURNAL OF
P
RESSURE
V
ESSEL
T
ECHNOLOGY
. Manuscript received August 31,2008; ﬁnal manuscript received July 31, 2009; published online October 8, 2009.Assoc. Editor: G. E. Otto Widera.
Journal of Pressure Vessel Technology
DECEMBER 2009, Vol. 131
/ 061403-1Copyright © 2009 by ASME
Downloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use
numerical solution obtained from the established model. Finally,several cases were discussed based on the developed model andsome conclusions were drawn. It should be noted that this studywas examined in a series of EF joints produced by ZhongCaiPipes Co. Ltd.
XinChang, Zhejiang Province, China
. As a rep-resentative selection, the analytical and experimental data pre-sented here are based on EF joints made of material grade PE80,with standard diameter ratio
SDR
11
ratio of outside diameterto the wall thickness is 11
and the diameter is 110 mm
DN110series
.
2 Modeling
2.1 Basic Principles of the EF Welding.
The EF joint of PEpipes is shown in Fig. 1. The EF joint consists of an EF ﬁtting andtwo PE pipes inserted on both sides. The EF ﬁtting is connected toa power supply and heat that is generated in the built-in conduc-tive winding wire by Joule effect, diffuses into the surroundingPE, leading to a progressive melting of the ﬁtting and pipe contactsurfaces. The fusion process lasts for a speciﬁed fusion time
SFT
, which is experimentally measured by joint manufacturersto obtain the best mechanical properties after welding.There are many nonlinear factors in an EF process. First, for aconstant voltage type of power supply, the current always starts ata high value and rapidly declines with increasing wire tempera-ture. Then, as the welding continues, the wire temperature slowlyrises, causing the input power to drop gradually. Furthermore,along with the increasing temperature of contact surface, the PEgradually softens and then is completely melted; with its thermalconductivity, density decreases gradually and heat capacity rises ata high value before melting and then dropping to its srcinal valueafter completely melting. The gap between pipes and ﬁttingslowly closes up and the pressure of the melting zone graduallygoes up because of the heating expansion of PE.
2.2 Basic Assumptions.
The following assumptions aremade.
1
Since there is no temperature gradient in the circumferen-tial direction and little inﬂuence in both ends of fusionzones, the heat transfers only in the radial direction and theheat loss of both sides is neglected.
2
The resistance wire is assumed to be a thin heating zonewith equivalent volume. The thickness of the heating zoneis calculated according to the following formula:
=
n
r
s
2
2
l
c
1
where
n
is the number of wire circles,
r
s
is the cross-sectionradius of the heating wire
m
, and
l
c
is the length of theheating zone
m
.
3
There is a gap between the heating wire and the surround-ing PE. Thus, the thermal contact conductivity is small atﬁrst. As the interface temperature increases, the PE aroundthe heating wire melts and clings to the wire surface, caus-ing the thermal contact conductivity to increase gradually.The thermal contact conductivity of the contact surface isassumed to satisfy the following formula
10,11
:
h
c
=
A
·
T
j
+
B
W m
2
·
K
,
T
j
T
m
C
·
e
T
j
/
T
m
−1
W m
2
·
K
,
T
j
T
m
2
where
T
m
is the melting point of PE
°C
,
T
j
is the tem-perature of the heating wire
°C
, and
A
,
B
, and
C
are takenas 1.664, 800, and 1013, respectively.
4
The heating wire’s resistance satisﬁes the following equa-tion:
R
=
1 +
T
−
T
R
3
where
is the temperature coefﬁcient of the heating wire
°C
−1
,
R
is resistance of the heating wire at calibratedtemperature
, and
T
is the calibrated temperature
°C
.
2.3 Analysis of the Model.
According to the theory of heattransfer
12
, the heat conduction in cylindrical coordinate is con-trolled by Bessel equation. The equation of the one-dimensionalheat-transfer model can be simpliﬁed as
T
t
=
k
C
p
2
T
r
2
+1
r
T
r
,
r
i
r
r
o
4
where
k
,
, and
C
p
are, respectively, the thermal conductivity
W m
−1
°C
−1
, the density
kg m
−3
, and the speciﬁc heat capac-ity
J kg
−1
°C
−1
of PE, and
r
i
and
r
o
are the inner radius of thepipe and the outer radius of the ﬁtting
m
.Thermal boundary conditions were used to describe a linearheat transfer from the pipe and ﬁtting surfaces to the environmentwith a constant temperature. The convection coefﬁcients are
h
1
and
h
2
for pipe bore and ﬁtting outer surface. The ambient tem-perature is
T
0
, and the following equations were obtained:
k
T
r
−
h
1
T
−
T
0
= 0,
r
=
r
i
k
T
r
+
h
2
T
−
T
0
= 0,
r
=
r
o
5
The heat ﬂux is generated by the heating wire and transfers toboth pipe and ﬁtting sidespipe side:
q
1
=
k
T
r
,
r
=
r
c
−
2
6
fitting side:
q
2
= −
k
T
r
,
r
=
r
c
+
2
7
q
=
q
1
+
q
2
8
Fig. 1 Electrofusion joint:
„
a
…
schematic sketch of an EF coupler and
„
b
…
schematic sketchof an EF model
061403-2 /
Vol. 131, DECEMBER 2009
Transactions of the ASME
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As the power input is temperature-dependent, the heat ﬂux canbe calculated from
q
=
U
2
4
r
c
l
c
R
9
where
R
is the temperature-dependent resistance calculated fromEq.
3
,
r
c
is the radius of the heating zone
m
, and
U
is the inputvoltage of electrofusion
V
.According to the second law of thermodynamics, the wire tem-perature must be higher than that of the surrounding PE. As theheat absorbed by the heating wire
copper wire
accounts for lessthan 1% of the total heat energy, it is therefore not included in thismodel
q
=
h
c
T
j
−
T
c
10
where
h
c
is calculated by Eq.
2
and
T
c
is the temperature of PEclose to the heating zone
°C
.Combine Eqs.
3
,
9
, and
10
, and the total heat ﬂux inputcan be expressed as a function of
T
c
q
=
U
2
4
lR
c
R
·
1 +
qh
c
+
T
c
−
T
11
3 Experiments
3.1 Preparations.
The operating and some structural param-eters are listed in Table 1. Figure 2 shows the density and thethermal conductivity of PE within the temperature range of inter-est
13
. The density and thermal conductivity both decline withan increase in temperature. Especially near the melting point of PE, the density rapidly drops and the thermal conductivity ﬂattensout. It should be emphasized that the speciﬁc heat capacity of PEsigniﬁcantly affects the temperature distribution; thus, should becarefully measured. The Perkin Elmer power compensation typeof differential scanning calorimeter
DSC
was used to measurethe heat capacity. The heating rate is 10°C min
−1
. The crystallin-ity
mass percentage of the crystalline phase
of ﬁtting and pipematerials were 51% and 59%, respectively. The DSC result of themaster batch of ﬁttings
Finathene 3802B
was shown in Fig. 3.
3.2 Temperature of Contact Surface.
The pipe surface isscratched to remove the oxide skin before tests. Then, a recess of size 15
3
1 mm
3
is created on the pipe surface at the middleof the heating zone, as shown in Fig. 4. The K-type thermocouplesare used to measure the temperature of the contact surface. Thepipes are carefully inserted into the ﬁtting to prevent the probefrom being pulled out of the groove. The thermocouples are con-nected to Data Logger UCAM-60A automatic temperature acqui-sition system, which can carry on the real-time communicationwith the computer and show the temperature history. The tempera-ture is recorded once per second and the experimental setup isshown in Fig. 5.
3.3 Input Energy.
The input energy is recorded by the weld-ing machine. The welding machine controls the input voltage bychopping the sinusoidal alternating voltage at a speciﬁc time. Themicroprocessor in the welding machine measures the magnitudeand phase of both output voltage and current. Thus, the caloriﬁcvalue during the welding process can be obtained. The welding
Table 1 Experimental welding parameters and joint structure
Parameter ValueWelding voltage,
U
V
39.5Wire resistance at 20°C,
R
0
1.03Radius of the heating zone,
r
c
mm
56Outer radius of ﬁttings,
r
o
mm
69Number of wire circles,
n
41Length of the heating zone,
l
c
mm
40SFT,
t
0
s
190Temperature coefﬁcient of the heating wire,
°C
−1
4.3
10
−3
Cross-section radius of the heating wire,
r
s
mm
0.29Inner radius of pipe,
r
i
mm
45Convection coefﬁcient of pipes,
h
1
W m
−2
20Convection coefﬁcient of ﬁttings,
h
2
W m
−2
35
Fig. 2 Thermal conductivity and density of PEFig. 3 DSC result of the speciﬁc heat capacityFig. 4 Installation of thermocouple
Journal of Pressure Vessel Technology
DECEMBER 2009, Vol. 131
/ 061403-3
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voltage is manually set to nine separated values from 24 V to 48V, and the input energy is recorded once per second for eachvoltage.
3.4 Eigen-Line.
The Eigen-line was ﬁrst discovered when de-tecting “cold welding” in EF joints. Cold welding is a commondefect in EF joints, which is usually caused by insufﬁcient weld-ing time or power input
14,15
. The joints with cold weldingalways appear normal, but their mechanical strength does notreach that of properly welded joints. Bowman and co-workers
16,17
found that the peeling energy and the tensile yield strengthboth increase with the welding time when it is less than SFT. It isvery dangerous to have EF joints with cold welding in service inthe ﬁeld. However, so far there is still no effective nondestructivetesting method to detect cold welding. Based on extensive UTexperiments on EF joints with cold welding, an obscure straightline, which would move away from the heating wire during weld-ing, was found. This obscure line was named the cold weldingEigen-line for the reason that its distance from the heating wirebears an approximate by linear relationship with the welding timeand can be used to characterize the degree of cold welding. Fur-ther researches demonstrated that the cold welding Eigen-line wasactually formed by voids at the solid-liquid interface. Thus, theEigen-line can also be used to detect the position of the solid-liquid interface during welding or the last position of the solid-liquid interface after welding.The experimental setup used in our research is shown in Fig. 6.To obtain the relationship between the position
distance betweenthe Eigen-line and the heating wire
and the welding time, wedesigned two kinds of experiments. In the ﬁrst set, the EF jointswere welded under different welding times. After cooling, cross-section scans were taken by the UT machine. The positions of theEigen-line in cooled joints welded under different welding timeswere obtained. In the second set of experiments, UT scans wereconducted during welding and ultrasonic image videos were re-corded. The moving position of the Eigen-line during welding wasobtained.
4 Results and Discussions
4.1 Model Solutions.
To solve the equation of heat conduc-tion, the authors developed a numerical code by using the Skeelmethod
9
at discrete time steps. The Skeel method is based onthe nonlinear Galerkin/Petrov–Galerkin method, which provides anumerical solution of second-order precision for one-dimensionalparabolic partial differential equations. The element length in ra-dial thickness is set to 0.05 mm in our model
because the maxi-mum temperature gradient during welding reaches 50°C mm
−1
.The variable time step method used in this paper is reported else-where in detail
18
.
4.2 Experimental Veriﬁcations
4.2.1 Input Energy and Power Input
. The comparison of mea-sured and analytical input energy at the time of 30s, 60s and 110swas shown in Fig. 7. The analytical and experimental results arein good agreement. The input energy is approximate by linearrelationship with the input voltage, rather than the square relation,which is deﬁned by Joule’s law. As the input voltage rises, theheat ﬂux from the heating wire also increases. As a result, theincreasing temperature leads to a higher resistance of the heatingwire, which then in turn decreases the input power.Figure 8 compares the power input between experimental dataand analytical results. The resistance of the heating wire is about1.03
at room temperature. According to Joule’s law, if the val-ues of input voltage are 30 V, 39.5 V, and 48 V, the welding powerinput should be 0.874 kW, 1.51 kW. and 2.24 kW
called thenominal power input
, respectively. However, the actual powerinput are about 0.67 kW, 1.16 kW, and 1.61 kW, which are, re-spectively, 76.6%, 76.8%, and 71.8% of the nominal power input.The reason is that the heating wire’s temperature increases rapidlyto over 100°C at the beginning of the welding, causing the weld-
Fig. 5 Automatic temperature measuring setupFig. 6 UT experimental setupFig. 7 Variation in input energy with input voltages
061403-4 /
Vol. 131, DECEMBER 2009
Transactions of the ASME
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ing power to rapidly drop to about 70–80% of the nominal values.The rate of power decline may be different for other types of EF joints, depending on the temperature coefﬁcient of heating wireused.
4.2.2 Interface Temperature
. Plots of the interface contacttemperature between experiments and analysis are shown in Fig.9. As there is a signiﬁcant temperature gradient near the contactsurface
about 50°C mm
−1
according to the analytical results
, asmall installation error of the thermocouple could cause a greatdifference of measured temperature. Furthermore, the temperaturedifferences around the probe can reach to as much as 30°C; thus,the output of the thermocouples should be judged with caution.Despite these uncertainties, we chose this method to monitor theinterface temperature because it has been widely used in the past.None of the analytical curves ﬁt the experimental data fully, butthe maximum relative error is less than 5% for the analyticalresults in some positions
R
=53 mm, for example
and the agree-ment acceptable.
4.2.3 Eigen-Line
. The UT image videos
animation
show thatthe Eigen-line moves away from the heating wire approximate bylinear relationship with the welding time. The distance betweenheating wire and Eigen-line
L
t
mm
can be expressed as
L
t
= 3.78
t
r
− 0.138where
t
r
is the ratio of welding time to SFT
dimensionless
.The cross-section UT images of EF joints under different weld-ing times are shown in Fig. 10. In order to unify the time scale,the welding time is divided by the SFT to get a dimensionlesstime scale. According to DSC results of the ﬁtting material, themelting point is about 126°C. The actual melting point is a littlehigher than that of the DSC experimental result because the actualheating rate is much higher than that of the experiment. The actualmelting point of PE is assumed to range from 128°C to 132°C
19
. The analytical and experimental data are in good agreement
shown in Fig. 11
. It was found that the distance between theboundary of the melting zone
in the ﬁttings
and the heating wireis about 3.7 mm at the end of the EF welding
after 190s
.It has been veriﬁed by many researchers
2
that the mechanicalproperties of fused EF joints are related to the welding time. Asmentioned above, the welding time bears an approximately linearrelationship with the distance between the heating wire and Eigen-line detected by UT machines after welding. So a nondestructivetest
NDT
method for determining the mechanical qualities of EF joints in the ﬁeld is provided here with the following steps. First,calibrate the mechanical properties with the distance between theheating wire and Eigen-line through laboratory experiments.Then, ﬁnd the threshold of the welding time
also the distancebetween the heating wire and Eigen-line
of weakly fused joints.Finally, measure the distance between the heating wire and Eigen-line of speciﬁed samples and compare it with the threshold. If themeasured value was less than the threshold, the joint should beregarded as unacceptable.
4.3 Discussion.
To investigate the inﬂuence of the power de-cline in the EF process, the material properties, and the thermalcontact conductance between the heating wire and PE, the follow-ing cases are discussed. The srcinal model is called “case 0.”Only one condition is changed, in each case, the other parametersin the model remain unchanged.
1
Case I-power decline is neglected.
2
Case II-values of the speciﬁc heat capacity are set to con-stants and neglect the latent enthalpy
3
Case III-values of the thermal conductivity are set to con-stants
4
Case IV-latent enthalpy is set to different values
5
Case V-thermal contact conductance between the heatingwire and PE is neglected
4.3.1 Case I: Inﬂuence of Power Decline
. The input voltagesare assumed to be several constant values, respectively, and thetemperature ﬁelds are calculated. As shown in Fig. 12, the tem-perature of the contact surface in case I is much higher than that incase 0 when the input voltage is the same. Similar ﬁndings arealso reported in literatures
2,14
, which show that the decline of power input occurs in many other types of EF joints and should becarefully considered.
4.3.2 Cases II, III, and IV: Inﬂuence of Material Properties
. Incase II, the speciﬁc heat capacity values are set to2.0 kJ kg
−1
°C
−1
, 2.5 kJ kg
−1
°C
−1
, 3.0 kJ kg
−1
°C
−1
, and3.5 kJ kg
−1
°C
−1
, respectively, and the interface temperatures arecalculated. The value of speciﬁc heat capacity has great inﬂuenceon the analytical results. For example, the temperature of the con-tact surface reduces by about 50°C and the average temperatureacross the joint thickness decreases by about 20°C for each1 kJ kg
−1
°C
−1
rise in speciﬁc heat capacity
see Fig. 13
.In case III, the values of thermal conductivity are set to0.25 W m
−1
°C
−1
, 0.35 W m
−1
°C
−1
, and 0.45 W m
−1
°C
−1
, re-spectively. The results show that in this range, the thermal con-ductivity has only a small inﬂuence on the temperature of the
Fig. 8 Comparison of power over time between experimentaland analytical resultsFig. 9 Comparison between measured temperatures of weld-ing interface and analytical results
Journal of Pressure Vessel Technology
DECEMBER 2009, Vol. 131
/ 061403-5
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