© 2017 The Korean Society of Rheology and Springer 37
Korea-Australia Rheology Journal, 29(1), 37-49 (February 2017)DOI: 10.1007/s13367-017-0005-3
www.springer.com/13367
pISSN 1226-119X eISSN 2093-7660
Numerical analysis of the heat transfer and fluid flow
in the butt-fusion welding process
Jae Hyun Yoo1, Sunwoong Choi
2, Jaewook Nam
3, Kyung Hyun Ahn
1 and Ju Seok Oh
2,*1Institute of Chemical Process, School of Chemical and Biological Engineering, Seoul National University,
Seoul 08826, Republic of Korea2Department of Advanced Materials, Hannam University, Daejeon 34430, Republic of Korea
3Department of Chemical Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea
(Received August 15, 2016; final revision received November 2, 2016; accepted November 22, 2016)
Butt-fusion welding is an effective process for welding polymeric pipes. The process can be simplified intotwo stages. In heat soak stage, the pipe is heated using a hot plate contacted with one end of the pipe. Injointing stage, a pair of heated pipes is compressed against one another so that the melt regions becomewelded. In previous works, the jointing stage that is highly related to the welding quality was neglected.However, in this study, a finite element simulation is conducted including the jointing stage. The heat andmomentum transfer are considered altogether. A new numerical scheme to describe the melt flow and pipedeformation for the butt-fusion welding process is introduced. High density polyethylene (HDPE) is usedfor the material. Flow via thermal expansion of the heat soak stage, and squeezing and fountain flow of thejointing stage are well reproduced. It is also observed that curling beads are formed and encounter the pipebody. The unique contribution of this study is its capability of directly observing the flow behaviors thatoccur during the jointing stage and relating them to welding quality.
Keywords: butt-fusion welding, finite element method, computational fluid dynamics, heat transfer, polymer
processing
1. Introduction
Polymeric pipes are used extensively for the transpor-
tation of water and gas supplies. They have many advan-
tages over metal pipes such as low weight, inexpensive
construction cost, and especially high corrosion resistance
(EL-Bagory et al., 2014; Leskovics et al., 2006; Wood,
1993). Polymeric pipes are easily welded using a butt-
fusion welding process (EL-Bagory et al., 2014; Leskov-
ics et al., 2006; Shillitoe et al., 1990; Wood, 1993). Butt-
fusion welding is a popular and effective process for weld-
ing polymeric pipes. It consists of five stages.
Figure 1 represents schematic sketches of each of these
five stages of butt-fusion welding on a 2D axisymmetric
domain. The first stage is a bead-up stage, and the second
stage is a heat soak stage. In both stages one end of the
polymeric pipe is contacted with a hot plate, and the heat
is transferred from the hot plate to the pipe. In reality the
pipe end is rough and not precisely flat, so perfect
mechanical contact may not occur. The bead-up stage is a
preparatory heating process used to guarantee a perfect
mechanical contact before the heat soak stage, which is
the actual heating process. In the bead-up stage, as the
pipe is heated, a melt layer is created at the end of the
pipe. The pipe is simultaneously compressed against the
hot plate causing the melt layer to squeeze out at the inner
and outer pipe wall, thereby ensuring complete contact
between the pipe and the hot plate. Then, a heat soak stage
follows, in which the pipe is not compressed as is during
the bead-up stage. Instead, the pipe is held just to flush
with the hot plate surface. As time passes, even the pipe
region which was not in contact with the hot plate
becomes a melt state. The length of the melt layer from
the hot plate is called melt depth. The heat soak stage is
continued until a melt depth to perform enough welding is
secured. Thermal expansion occurs, and the expanded
melt layer flows out at both inner and outer pipe walls. As
soon as the heat soak stage is over, the hot plate is
removed. There is a moment during this time in which the
heated pipe surface is exposed to the air and cooled. This
third stage is called the dwell stage. The jointing stage fol-
lows during which the melt regions of each pipe are ori-
ented towards each other and the pipes are compressed
against one another so that the melt regions become
welded. A melt layer squeezes out as a result of the com-
pression, and the shape of squeezed-out melt layer is dif-
ferent from those of the heat soak and bead-up stages.
Because there is no heat source, the pipe undergoes cool-
ing, and the melt region solidifies during the jointing
stage. For additional cooling to room temperature, a cool-
ing stage follows (Benkreira et al., 1991; Shillitoe et al.,
1990; Wood, 1993, 1996).
Polymeric pipes are welded through the butt-fusion*Corresponding author; E-mail: [email protected]
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
38 Korea-Australia Rheology J., 29(1), 2017
welding process. One problem is that welded pipes show
weaker mechanical properties than pipes without welding.
It is important to resolve this weakness to improve the
welding quality. Some approaches to solve this problem
include empirical optimization of operating conditions
such as hot plate temperature, compression pressure, and
process time (Barber and Atkinson, 1972, 1974; Colaluca
et al., 1983; deCourcy and Atkinson, 1977). These exper-
imental approaches are meaningful and reliable, but they
require fundamental understanding of how to achieve sys-
tematic and efficient process design. Systematic under-
standing on the thermal and flow behaviors of the melt
region is needed for good process design. However, using
only experimental approaches it is difficult to obtain
enough information, because observing thermal and flow
behaviors is not easy in such a narrow melt layer. In this
respect, some researchers conducted numerical study.
Wood (1993, 1996) investigated the thermal behavior of
this process excluding the flow behavior by considering
butt-fusion welding process as a heat transfer problem
consisting of conduction from a hot plate and convective
cooling in the air. However, in addition to heat transfer,
there is also momentum transfer from the thermal expan-
sion and squeezed-out flow of the melt layer, which is
very important to the welding quality. Heat and momen-
tum transfer even affect one another consistently. To con-
duct a realistic simulation, the heat and momentum transfer
must be considered altogether. By solving the momentum
transfer, the pipe deformation can be described too. There
are some preceding works that consider both heat and
momentum transfer, but they deal only with the heat soak
and bead-up stages, neglecting the jointing stage (Benk-
reira et al., 1991; Riahi et al., 2011; Shillitoe et al., 1990).
In some cases, a lubrication approximation is used to sim-
plify the momentum transfer (Benkreira et al., 1991). The
residual stress generated during the process has also been
investigated (Chang and Teng, 2004).
There is a huge demand for robust welding with increas-
ing application of polymeric pipes. With this trend, it is
necessary to understand the underlying physics and to
improve the process. However, there exist only a few
studies that discuss the flow behavior generated in the pro-
cess, even though it is highly related to the welding qual-
ity. Additionally, most studies concentrate only on the
heating processes, including the bead-up and heat soak
stages. However, the actual welding occurs during the
jointing stage, so the jointing stage must be considered to
determine the welding quality. Therefore, it is essential to
Fig. 1. (Color online) Schematic sketches of the five stages of the butt-fusion welding on a 2D axisymmetric domain; (a) bead-up, (b)
heat soak, (c) dwell, (d) jointing, and (e) cooling. The left vertical dotted line is rotational axis. As rotating along the axis, the pipes
are depicted on a 3D domain. The horizontal dotted line in (d) and (e) is the imaginary interface between the pipes.
Numerical analysis of the heat transfer and fluid flow in the butt-fusion welding process
Korea-Australia Rheology J., 29(1), 2017 39
investigate the thermal and flow behaviors simultaneously
that occur during the jointing stage to understand and
improve the process. In this study, we consider heat and
momentum transfer altogether, and investigate not only
the heating stage, but also the jointing stage. A new numer-
ical scheme to describe the melt flow and pipe deforma-
tion for the butt-fusion welding process is introduced in
Sec. 2. The temperature dependence of the material prop-
erties of the pipe is also considered. Thermal and flow
behaviors can be observed directly, which are hardly
achievable in experiments, and systematic process analy-
sis can be performed based on these observations. There
are some previous works in which welding quality is
related to temperature or process time (Bousmina et al.,
1998; Ezekoye et al., 1988; Kim and Wool, 1983; Qiu and
Bousmina, 1999; Wool et al., 1989), but the flow behavior
was not mainly discussed with the respect to welding
quality. The unique contribution of this study is its capa-
bility of directly observing the flow behavior that occurs
during the jointing stage and relating them to the welding
quality. Observations and the subsequent analysis are
described in Sec. 3.
2. Modeling and Simulations
The butt fusion welding process consists of several
stages. However, the bead-up time is very short compared
with the heat soak time, and perfect contact of the entire
surface of the pipe end can be assumed in the numerical
simulation. Thus, the bead-up stage is neglected in this
study. Meanwhile, the hot plate is removed after the heat
soak stage before proceeding to the following stages.
During this time the heated end is exposed to the air for
a moment, which is the dwell stage. In practice, this stage
should be minimized in order to optimize welding quality.
In this study, which represents an ideal situation, the dwell
stage is omitted. In addition, there exists no meaningful
flow behavior in the cooling stage, so the cooling stage is
also neglected in this study. As a result, the entire butt-
fusion welding process can be simplified into two stages:
heat soak stage and jointing stage.
The heat soak stage is a heating process in which heat
is conducted from a hot plate, and flow caused by thermal
expansion occurs. The jointing stage is a cooling process
during which the hot plate is removed, and flow by com-
pression occurs. In both stages, heat and momentum trans-
fer coexists. Thus, heat and momentum conservation equations
should be solved altogether in both stages. The differences
between the two stages are the initial and boundary con-
ditions. A 2D axisymmetric simulation is conducted.
2.1. Governing equationsHeat and momentum conservation equations are solved
in a Lagrangian framework (Mao and Khayat, 1995), and
they are decoupled. First, the heat conservation equation is
solved in the entire pipe domain. A temperature distribu-
tion is obtained. A region that reaches a temperature above
the melting point of the pipe material is defined as the
melt region. We solve the momentum conservation equa-
tion only in the melt region, and a velocity field is obtained.
Eq. (1) represents the heat conservation equation. T is
the temperature, DT/Dt is the material time derivative, ρ is
the density, and k is the thermal conductivity. The effec-
tive heat capacity, Ceff which includes an effect of latent
heat, is used to compensate the phase transition from solid
to melt (Bergheau and Fortunier, 2008; Lewis et al., 2004).
As the butt-fusion welding process is very slow, viscous
heating is negligible. In addition, a term representing com-
pressibility effect is also neglected in the heat conserva-
tion equation due to a low thermal expansion coefficient
of the polymer melts (Kennedy, 1995; Lide et al., 2010).
. (1)
The momentum conservation equation is solved in the
melt domain. Equation (2) represents the momentum con-
servation equation. σ is the stress tensor of the fluid, p is
the pressure, τ is the deviatoric stress tensor, and u is the
fluid velocity field. In this process, the Reynolds number,
which is the ratio of inertial force to viscous force, is very
low (due to high melt viscosity and slow process), and the
inertial term in the momentum conservation equation can
be neglected.
. (2)
In the heat soak stage, the density change dominates the
flow behavior depending on the temperature, which is
thermal expansion flow. If the material density is not con-
stant, then the fluid is compressible and the continuity
equation for the compressible fluid is used as represented
by Eq. (3) in the heat soak stage. In addition, the stress for
the compressible fluid is considered as defined by Eq. (4).
, (3)
. (4)
However, in the jointing stage, the flow by the com-
pression is dominant, and the amount of flow induced by
density change is negligible. Accordingly, the fluid is
assumed to be incompressible, and the continuity equation
for incompressible fluid represented by Eq. (5) is used in
the jointing stage, instead of Eq. (3). In addition, since the
fluid was assumed to be incompressible, the constitutive
equation was simply defined by Eq. (6), instead of Eq. (4).
, (5)
. (6)
ρCeff
DT
Dt------- = ∇ k∇T( )⋅
∇ σ⋅ = 0, σ = p– I + τ
Dρ
Dt------- + ρ∇ u⋅ = 0
τ = 2η D1
3--- ∇ u⋅( )I–⎝ ⎠
⎛ ⎞
∇ u⋅ = 0
τ = 2ηD
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
40 Korea-Australia Rheology J., 29(1), 2017
2.2. Heat soak stage modelingIn heat soak stage, the pipe is initially at room tempera-
ture. A hot plate is located at one end of the pipe, which
is at z = H, and the temperature of that surface is the same
as the temperature of the hot plate. For an industrial heat
soak time scale, axial directional heat transfer into the pipe
from the hot plate is limited. The pipe domain is defined
up to a certain distance from the hot plate, where it
remains at room temperature during the process, and the
axial position of that surface is defined as z = 0. The inner
and outer walls of the pipe are free surface boundaries that
are exposed to the air, and cooling by natural convection
occurs. Equation (7) represents these initial and boundary
conditions for the heat transfer. tsoak is the heat soak time,
and n is the surface outward normal vector from the fluid.
Troom is the room temperature (20oC), and Th is the hot
plate temperature. h is the heat transfer coefficient. The
boundary conditions for heat transfer on a 2D axisymmet-
ric pipe domain in the heat soak stage are represented in
Fig. 2a. Ri is the inner radius, and Ro is the outer radius of
the pipe.
@ tsoak = 0; T = Troom,
@ z = H; T = Th, (7)
@ z = 0; T = Troom,
@ free surface; .
A melt region is defined in the pipe domain, and only
that region is used in solving the momentum conservation
equation. Phase interface between the solid and melt
regions is the isothermal line of the melting point. When
a hot plate is located above the pipe domain, phase inter-
face divides the pipe domain horizontally. Once the region
above the phase interface exhibits a temperature above the
melting point, the region is defined as the melt domain.
The bold solid line in Fig. 2b represents the melt domain.
Density changes during the heating process, and then a
flow by thermal expansion is followed. In this study, ther-
mal expansion of the solid part is not considered. Accord-
ingly, we assume no density change of the solid part, and
the solid density is assumed to be a constant, which is the
value at the melting point of the material. As the melt
region expands, the pipe is mechanically pushed back axi-
ally from the hot plate while not holding the pipe in place.
In this case, the pipe can lose the contact with a hot plate.
To avoid this, a break pressure is imposed at the end of the
pipe that does not contact the hot plate. The break pressure
is a pressure that supports the pipe to prevent push-back
from the hot plate. It is equivalent that the rigid body
translational velocity of the solid part is defined to be zero.
Since the solid part is stationary, zero velocity is imposed
on the phase interface between solid and melt. In this pro-
cess, the hot plate is designed to have low affinity with the
melt, because a clear removal of the pipe from the hot
plate is required in the following stages. The polymer melt
sometimes slips on a plate that has low affinity with the
n k∇T–( )⋅– = h– T Troom–( )
Fig. 2. (Color online) Boundary conditions (a) for the heat transfer and (b) for the momentum transfer in the heat soak stage. The
numerical (a) pipe domain and (b) melt domain are represented by the bold solid line. The left vertical dotted line is rotational axis.
Numerical analysis of the heat transfer and fluid flow in the butt-fusion welding process
Korea-Australia Rheology J., 29(1), 2017 41
melt (Hatzikiriakos, 2012; Wilhelm, 2011). In actual exper-
iments, slip occurs substantially throughout the process.
Therefore, the perfect slip boundary condition is imposed
on a pipe end contacting the hot plate to describe sub-
stantial slip on the plate. A force balance related to surface
tension is imposed on the free surface boundaries. Imple-
mentation of the slip and surface tension to the free sur-
face is explained well in (Kistler and Scriven, 1984; Silliman
and Scriven, 1980). Equation (8) represents these bound-
ary conditions for the momentum transfer. t is the surface
tangential vector, κ is the mean curvature of the free sur-
face boundary, and γ is the surface tension of the melt. The
boundary conditions for momentum transfer on a 2D
axisymmetric melt domain in the heat soak stage are rep-
resented in Fig. 2b.
@ z = H; nt: σ = 0, n·u = 0,
@ phase interface; u = 0, (8)
@ free surface; n·σ = κγn.
2.3. Jointing stage modelingDuring the jointing stage, the hot plate is removed, and
is replaced with second pipe to be welded. The surface at
which a second pipe is located is called the pipe-faced sur-
face in this study. The pipes are compressed, and the melt
squeezes out evenly over the inner or outer radius of the
pipe on the pipe-faced surface. Contact is not guaranteed
at the surface where developed pressure is not sufficient
on the pipe-faced surface. It can be observed in experi-
ments that some regions squeezed out over the radius on
the pipe-faced surface are torn away from the other pipe,
failing to contact in the middle of the jointing stage (see
Fig. 13). In this study we assume that the entire region
squeezed out over the radius on the pipe-faced surface
does not contact the other pipe, and that surface of failed
contact is defined as the free surface boundary (located at
Ri > r or r > Ro, z = H). The other region on the pipe-faced
surface is the boundary at which there is contact with the
other pipe, and this surface becomes the interface between
the pipes (located at , z = H). The interface is the
mirror plane, since a pair of pipes is symmetric with
respect to that interface, so the interface is defined as the
symmetric boundary.
The initial temperature distribution in the jointing stage
is the same as that at the end of the heat soak stage. In the
jointing stage, the pipes are compressed against one another
rather than simply imposing a break pressure and the
interface between the pipes becomes welded end of the
pipe. The end of the pipe opposite to that of the welded
end moves toward the symmetric boundary due to the
compression of the pipe. The movement of the pipe is
described by the rigid body translational velocity V of the
solid part, and it moves exclusively with an axial compo-
nent. The axial position of this pipe end opposite to the
welded end is define as z = Hend, and is obtained by the
summation of VΔt to Hend in the preceding time step. Δt is
the discretized time size used in the computation. Further-
more, the surface (z = Hend) is kept at room temperature.
No heat flux occurs at the symmetric boundary out of the
pipe-faced surface. The free surface boundaries, which are
Ri r Ro≤ ≤
Fig. 3. (Color online) Boundary conditions (a) for the heat transfer and (b) for the momentum transfer in the jointing stage. The numer-
ical (a) pipe domain and (b) melt domain are represented by the bold solid line. The left vertical dotted line is rotational axis.
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
42 Korea-Australia Rheology J., 29(1), 2017
the inner and outer walls of the pipe and the entire region
squeezed out over the radius on the pipe-faced surface,
experience natural convection by the air. Equation (9) rep-
resents these initial and boundary conditions for the heat
transfer. tjointing is the jointing time, and Tfinal is the tem-
perature distribution at the end of the heat soak stage. The
boundary conditions for heat transfer on a 2D axisymmet-
ric pipe domain in the jointing stage are represented in
Fig. 3a.
@ tjointing = 0; T = Tfinal,
@ , z = H; , (9)
@ z = Hend ; T = Troom,
@ free surface; .
A melt region is defined in the pipe domain as is done
in the heat soak stage. The bold solid line in Fig. 3b rep-
resents a numerical melt domain.
The pipes are compressed by making the pipe ends that
is opposite to the welding region pushed against each
other with using a welding machine. The pipe end is dis-
placed axially with uniform distance at any radial position
of the pipe end surface. Welding machine measures the
total force to require the pipe moved, and the total force
is divided by surface area to estimate average compression
pressure. This compression pressure, not a moving veloc-
ity or displacement of the pipe, is given for operating con-
ditions, because the velocity or displacement is hard to
measure. As only the melt domain is used in solving the
momentum conservation equation, boundary condition to
describe the uniform pipe movement at any radial position
should be imposed at the phase interface between the solid
and melt, although solid part is actually pushed by the
welding machine. If the traction boundary condition that
imposes the desired compression pressure on the phase
interface is used, the pipe end cannot be displaced uni-
formly due to the curvature of interface. Radial center of
the pipe may be displaced more than other regions. The
movement of a pipe can be described either by the impos-
ing velocity V at the phase interface. Thus, we impose
velocity V at the phase interface as a boundary condition
to guarantee uniform displacement of pipe end, and check
the average compression pressure acting on the melt
region. The average compression pressure acting on the
melt region can be estimated by integrating the total nor-
mal stress on the symmetric surface, S, as represented by
Eq. (10) (Farjoud et al., 2011; Matsoukas and Mitsoulis,
2003).
. (10)
If the estimated average compression pressure does not
match the specific value that we want to apply to the pipe
in the butt-fusion welding process, then we change V. This
procedure is iterated until the value matches within a cer-
tain limit (the tolerance is 10% of the specific value that
we want to apply). A symmetric boundary condition is
imposed on the interface between the pipes. A force bal-
ance related to surface tension is imposed on the free sur-
face boundaries, which are the inner and outer walls of the
melt domain and the entire region squeezed out over the
radius on the pipe-faced surface. Equation (11) represents
these boundary conditions for the momentum transfer. The
boundary conditions for momentum transfer on a 2D
axisymmetric melt domain in the jointing stage are rep-
resented in Fig. 3b.
@ , z = H; nt: σ = 0, n·u = 0,
@ phase interface; u = (0, V ), (11)
@ free surface; n·σ = κγ n.
2.4. Galerkin/finite element methodHeat and momentum conservation equations are solved
in a Lagrangian framework (Mao and Khayat, 1995), and
they are decoupled. First, the heat conservation equation is
solved in the entire pipe domain. The mesh created on the
pipe domain is called pipe mesh in this study. A tempera-
ture distribution on the pipe mesh is obtained. A region
that reaches a temperature above the melting point of the
pipe material is defined as the melt region. The other
region representing the lower temperature is a solid part,
which is assumed to move with a rigid body translational
motion. A new mesh is created on the melt region, and
this new mesh describing the melt region is called the melt
mesh in this study. We solve the momentum conservation
equation only in the melt region, and a velocity field is
obtained. Then, each nodal position of the pipe mesh is
moved with the corresponding fluid velocity vector inter-
polated from the velocity field on the melt mesh. In this
way, the pipe mesh is deformed and the pipe deformation
can be described. During the deformation, triangular mesh
can be distorted. Because a squeezing of the domain
occurs, triangular mesh is typically stretched horizontally
and compressed vertically. In addition, as melt is emerged
out to the inner and outer wall of the pipe, free surface
regions that are exposed to the air are grown and more ele-
ments are required to cover that surface. To guarantee a
good quality of the mesh and compliment elements to
cover the free surface regions, re-mesh is followed in the
deformed pipe domain to obtain accurate numerical solu-
tions. However, as information such as temperature of the
preceding time step is interpolated in deformed mesh, the
numerical accuracy can be compromised. By repeating
this procedure, time marching proceeds. Figure 4 rep-
resents a flow chart of the numerical scheme described.
In this study, positions of nodal points of the mesh are
Ri r Ro≤ ≤ n k∇T–( )⋅– = 0
n k∇T–( )⋅– = h– T Troom–( )
p
p = nn∫∫ :σdS
s------------------------–
Ri r Ro≤ ≤
Numerical analysis of the heat transfer and fluid flow in the butt-fusion welding process
Korea-Australia Rheology J., 29(1), 2017 43
moved with a fluid velocity in every time step in a Lagrang-
ian manner. Thus, nodal points naturally follows the mate-
rial: . X is the position vector of nodal point. In this
situation, as just considering the partial time derivative of
density on the moving mesh following the material, mate-
rial derivative can be considered: .
f is a variable that can be a scalar or any tensor field.
, (12)
. (13)
The governing equations with appropriate boundary con-
ditions to consider each stage are solved by using Galerkin
finite element method with triangular elements. First, the
heat conservation equation is solved in the entire pipe
domain. The weighted residual Eq. (12) is obtained, as
multiplying the governing Eq. (1) by test function ψ T and
integrating over the flow domain Ω bounded by Γ. Implicit
Euler method is used in temporal discretization. n indi-
cates the current time step. Subscripts T represents tem-
perature. Quadratic basis function ψ T is used to describe
the temperature in Eq. (13). is the unknowns repre-
senting the temperature at the nodal points. Material prop-
erties are approximated to the value in the temperature at
the n−1 time step. is the solution vector. As the
temperature is represented in terms of basis functions, the
system of differential equations is reduced to a set of alge-
braic equations, that describes the evolution of
temperature at the nodal points.
, (14)
, (15)
, (16)
, . (17)
The momentum conservation Eq. (2) and continuity Eq.
(3) in heat soak stage or continuity Eq. (4) in jointing
stage are solved only in the melt region. The weighted
residual Eqs. (14) and (15) in heat soak stage or weighted
residual Eqs. (14) and (16) in jointing stage are obtained,
as multiplying governing equations by test function ψm or
φ c and integrating over the flow domain Ω bounded by Γ.
Subscripts m and c represent momentum and continuity.
Quadratic basis function ψm is used to describe fluid veloc-
ity and pressure is done with linear basis function φ c.
and are the unknowns for fluid velocity and pressure at
the nodal points. is the solution vector. As all
variables are represented in terms of basis functions, the
system of differential equations is reduced to a set of alge-
braic equations, R(U) = 0 that describe the evolution of
fluid velocity and pressure at the nodal points.
, (18)
. (19)
The resulting weighted residual equations are
non-linear equations to solve momentum conservation
equation due to the viscosity dependence on the shear rate,
which is solved by using Newton’s method with Eqs. (18)
and (19). k indicates the current Newton’s step, and
is the Jacobian matrix. The tolerance on the
second norm of the residual R and δUk is set to 10−6.
3. Results and Discussion
3.1. Material propertiesIn this study, HDPE was used for the pipe material. The
melting point, Tm was 135oC. The effective heat capacity,
Ceff, thermal conductivity, k of HDPE were defined as a
function of temperature (Woo et al., 1995). The density ρ
is defined by the state equation relating the pressure and
temperature. However, pressure dependence of the density
∂X∂t------- = u
Df
Dt------ =
∂f∂t---- + u
∂X∂t-------–
⎝ ⎠⎛ ⎞ ∇f =
∂f∂t----⋅
Ri
T = ρ
Ω
∫ Ceff
TnT
n 1––
Δt-------------------ψi
TdΩ + k
Ω
∫ ∇ψi
T ∇T n⋅ dΩ
− ○∫ Γψ i
Tn k∇T n⋅( )dΓ = 0
Tn = Tjψj
T
Tj
U = Tj
n
[ ]†
R U( ) = 0
Ri
m = ∇
Ω
∫ ψi
mσ⋅ dΩ ○∫ Γ
– ψ i
mn σ⋅( )dΓ = 0
Ri
c =
ρn
ρn 1–
–
Δt-------------------
Ω
∫ φi
cdΩ + ρ
n
Ω
∫ ∇ u⋅( )φi
cdΩ = 0
Ri
c = ∇ u⋅( )
Ω
∫ φi
cdΩ = 0
u = ujψj
mp = pjφj
c
uj
pj
U uj
n, pj
n[ ]
†
–
J δUk⋅ = R– Uk 1–( )
Uk = Uk 1– + δUk
R U( ) = 0
J = ∂R/∂U
Fig. 4. Flow chart of the numerical scheme used in this study.
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
44 Korea-Australia Rheology J., 29(1), 2017
is negligible in 0.1 MPa order scale (Lide, 2010), which is
usually developed in the butt-fusion welding. We only
considered the density is a function of temperature (Woo
et al., 1995). As mentioned in Sec. 2.2., the density of the
solid was assumed to be a constant, which is the value at
the melting point of the material. The density of the melt
is defined in Eq. (20) as a function of temperature.
. (20)
The viscosity was measured, and the details for the mea-
surement are described later. We used h = 43W/moC (Wood,
1993). We defined the surface tension, γ, to be 0.03 N/m,
rferring to various literature (Demarquette et al., 2000;
Hybart and White, 1960; Wei, 2009).
The Carreau-Yasuda model was used in this study, in
which the viscosity varies as a function of shear rate, dif-
fering from that of a Newtonian fluid. The Arrhenius rela-
tionship was used for temperature dependence. The viscosity
is defined by Eq. (21). is the infinite shear viscosity,
is the zero shear viscosity, is the shear rate, which
was estimated by the second invariant of the rate of the
deformation tensor, and Ta is the absolute temperature.
,
, (21)
.
The viscosity was measured with PE 4710 grade (The
Dow Chemical Company, USA). A frequency sweep test
was performed with ARS Rheometer M-200 (Advanced
Rheology Solutions, Korea) over a frequency range from
0.1 rad/s to 10 rad/s at different temperatures (180oC,
200oC, and 230oC). The viscosity curve was fitted to the
measured data using a least square regression method,
from which the model parameters were obtained. The
relaxation time, λ, was 7.11 s, and the power index, n, was
0.26. The pre-exponential factor, a, and the exponential
factor, b, were 314 Pa·s and 2,050 K, respectively. The
pre-exponential factor for the infinite shear viscosity, ,
was 0.1, and that for the zero shear viscosity, , was 4.
3.2. Operating conditionsAs the butt-fusion welding proceeded, the pipe domain
was deformed from its initial state. Figure 5 shows the ini-
tial pipe domain and its dimensions before the butt-fusion
process (tsoak = 0 s). W is the pipe thickness. Meshes also
experienced deformation in shape and size as the numer-
ical domain became deformed. The number of triangular
elements used in the initial pipe domain was about 150,000.
Industrially well-defined operating conditions were used
in this study. The average compression pressure, , in the
jointing stage had a certain profile represented by Eq.
(22), where Pmax is the maximum value of the average
compression pressure over time, and tloading is the time
required for the pressure to reach its maximum.
; , (22)
; .
In the heat soak stage, the hot plate temperature, Th was
230oC, and the heat soak stage continued for 240 s. In the
jointing stage, we used tloading = 10 s and Pmax = 150,000
Pa. The discretized time size used in the computation, Δt
was 1 s in heat soak stage, and 0.1 s in jointing stage.
3.3. Heat soak stageFigure 6 shows the temperature contour and pipe shape
with respect to process time. As heat was conducted from
the hot plate, the temperature began to increase from the
ρ = 1
1.14 0.0009T+----------------------------------- T 135 C
o≥( )
η∞
η0 γ·
η η∞–
η0 η∞–---------------- = 1 λγ·( )
2+[ ]
n 1–
2----------
η∞ = μ∞a exp b/Ta( )
η0 = μ0a exp b/Ta( )
μ∞
μ0
p
0 tjointing< tloading≤ p = tjointingtloading-------------Pmax
tloading tjointing< p = Pmax
Fig. 5. Initial pipe domain and its dimension used in this study.
Fig. 6. (Color online) Temperature contour and pipe shape in the
heat soak stage with respect to time; (a) tsoak = 1 s, (b) tsoak = 120
s, and (c) tsoak = 240 s.
Numerical analysis of the heat transfer and fluid flow in the butt-fusion welding process
Korea-Australia Rheology J., 29(1), 2017 45
region near the hot plate. Because of the cooling from nat-
ural convection at the inner and outer walls of the pipe, the
edges showed lower temperature than the center. Figure 7
shows the changes in melt depth over time. As the region
of which temperature was above the melting point increased
over time, the melt depth also increased.
As the temperature increased, the density became lower
in the melt region. Figure 8 shows the velocity magnitude
contour and stream lines in the heat soak stage. The vol-
ume expanded, and induced thermal expansion flow. A
hot plate blocked the melt layer from flowing in the direc-
tion to the hot plate, and only the inner and outer walls of
the pipe allowed for the expanded melt layer to flow out
as seen in Fig. 8. Accordingly, the melt formed swollen
beads at the inner and outer walls of the pipe (close to the
hot plate). This flow behavior was observed throughout
the entire heat soak stage. Bead formation with respect to
time is depicted in Fig. 6. More swollen beads were
formed near the hot plate because the temperature change
was larger in that region.
Figure 9 shows the pipe shape after completion of the
heat soak stage in experiment. In experiment, the outer
radius, Ro is 112.5 mm, and the inner radius, Ri is 92.05
mm. The pipe thickness, W is 20.45 mm. The pipe material
is HDPE (PE100, Piping Engineering & Materials Korea,
Korea). Hot plate temperature, Th was 230oC during the
bead-up and heat soak stage. The compression pressure
against the hot plate was 150,000 Pa in bead-up stage, and
the bead-up stage continued for 30 s. The heat soak stage
continued for 205 s. The swollen bead formation was also
observed in actual experiment. However, the melt was
detached from the hot plate at the edge during the heat
soak stage, unlike numerical results. A purely viscous mate-
rial becomes pinned to the plate when it is forced to move
to the plate. We defined the melt to be purely viscous
using the Carreau-Yasuda model, so it is natural for the
melt to be pinned in this case. To describe the detachment
of the melt region, the elasticity of the material needs to
be considered. The different pipe shape between experi-
ments and simulation is a limitation since the elasticity of
the melt was neglected in this study. Meanwhile, it can be
observed in experiments that the detachment of the melt is
enhanced at the outer radius compared to the inner radius.
The elasticity of the material is enhanced when the tem-
perature is lower. The bead at the outer radius is exposed
to external air, but the bead at the inner radius is exposed
to air which is kept at a relatively higher temperature due
to the closed inner volume of the pipe. Thus, the lower
temperature at the outer radius enhances the detachment
of the melt more than at the inner radius.
3.4. Jointing stageFigure 10 shows temperature contour and pipe shape
with respect to time in the jointing stage. In this study vis-
cous force is dominated rather than surface tension due to
Fig. 7. The melt depth over time in the heat soak stage. The melt
depth varies along the radial position. Represented melt depth
was measured at the center of the domain.
Fig. 8. (Color online) Velocity magnitude contour and stream lines (the solid lines with arrows) in the melt region in the heat soak
stage at tsoak = 120 s.
Fig. 9. (a) Global shape and (b) cross section of the pipe cut in
a plane which is perpendicular to the theta direction at the end
of the heat soak stage in an experiment.
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
46 Korea-Australia Rheology J., 29(1), 2017
the high viscosity of material. Surface tension does not
affect significantly the shape of boundary, but it helps the
curvature of free surface to be smoothed. Unlike the heat
soak stage, cooling keeps on proceeding as there’s no heat
source in the jointing stage. Radial and axial flow velocity
contours at tjointing = 8.8 s are represented in Fig. 11. The
axial flow heading to the symmetric boundary could be
observed. At the same time, diverging radial flow occurred
from the center towards the edges. In addition, stronger
radial flow was generated close to the symmetric surface.
In addition, the viscosity was lower due to the higher tem-
perature near the symmetric boundary, which enhanced
the flow velocity in that region. In this manner, squeezing
flow occurred in the melt region during the jointing stage.
Figure 12 represents the velocity magnitude contour and
stream lines in the melt region with respect to time. As
seen in Fig. 12, the fountain flow can be observed through-
out the jointing stage. Thus, there were mixed flows includ-
ing both squeezing flow and fountain flow. Some re-
searchers have previously used lubrication approximation
to describe the momentum transfer in narrow melt regions
during the butt-fusion welding process (Benkreira et al.,
1991). However, this approach cannot capture the mixed
complex flow behaviors. The squeezing and fountain flow
deformed the external boundaries of the melt domain,
which actually determined the shape of the bead. The
squeezed out melt formed bead curling to the pipe body,
as experienced by the fountain flow.
As the curling of the bead intensified over time, the bead
encountered the pipe body (see Fig. 10e). After encoun-
tering the pipe body, the bead curling was blocked by the
presence of the pipe body. In addition, the bead cooled
quickly, since the temperature of the pipe body was low.
This blocking and cooling restricted the flow and defor-
mation of the melt. After the bead encountered pipe body,
Fig. 10. (Color online) Temperature contour and pipe shape in the jointing stage with respect to time; (a) tjointing = 0.1 s, (b) tjointing = 2 s,
(c) tjointing = 4 s, (d) tjointing = 6 s, and (e) tjointing = 8.8 s.
Fig. 11. (Color online) (a) Radial and (b) axial flow velocity con-
tours in the melt region in the jointing stage at tjointing = 8.8 s.
Fig. 12. (Color online) Velocity magnitude contour and stream
lines (the solid lines with arrows) in the melt region in the joint-
ing stage with respect to time; (a) tjointing = 0.1 s, (b) tjointing = 5 s,
and (c) tjointing = 8.8 s.
Numerical analysis of the heat transfer and fluid flow in the butt-fusion welding process
Korea-Australia Rheology J., 29(1), 2017 47
the compression of the pipe did not cause significant flow
any more, and numerical simulation terminated at the
moment when the bead encountered the pipe body for this
reason.
Figure 13 shows the pipe shape of an experiment in the
middle of jointing stage, before the bead encounters the
pipe body. And Fig. 14 shows the pipe shape at the end of
the jointing stage. The pipe dimensions and operating con-
ditions of the bead-up and heat soak stages in experiments
are described in Sec. 3.3. After completing the heat soak
stage, the dwell stage continued for 10 s. Maximum com-
pression pressure, Pmax was 150,000 Pa. The jointing stage
lasted for some minute until the melt solidifies, even after
the fluid flow was terminated. The formation of curling
beads and encountering of the pipe body were also
observed in experiment. As seen in Fig. 13, the pipe shape
looks analogous to numerical results. At the moment for
the bead to encounter the pipe body the simulation termi-
nates, however the experiment continues unlike simulation.
Although there is no significant flow any more, radial
diverging flow around the symmetric surface still contin-
ued due to the high temperature in that region, which
induced horizontal stretching of the interface between the
pipes, forming the pipe shape at the end of the jointing
stage as shown in Fig. 14.
3.5. Effect to the orientation of polymerIt is well known that shear flow induces to orient the
polymer toward the direction of flow (Huang et al., 2010;
Islam and Archer, 2001; Lin et al., 1988; Padding and Bri-
els, 2003; Rotella et al., 2014). The squeezing flow incor-
porates the shear flow significantly, and occurs throughout
the whole jointing stage. In this regard, orientation of the
polymer can be tilted in some degree toward the flow
direction in the welding region. The welding region is not
limited to the interface between the pipes, but also includes
the entire region subjected to melting during the process.
Figure 15 shows the stream lines and shear rate contour in
the jointing stage. The shear rate was estimated from the
second invariant of the rate of deformation tensor. The
stream lines represent the trajectory of the velocity field,
and the tangential direction of the stream line indicates the
flow direction. The polymer was originally oriented axi-
ally during pipe extrusion in manufacturing (Leskovics et
al., 2006). However, as represented by the stream lines in
Fig. 15, the flow was induced radially due to squeezing,
and it may help the polymer orientation to be tilted toward
radial direction in a degree. The shear rate determines how
strongly the polymer is affected in that region. An extent
of the polymer orientation was enhanced at the region of
higher shear rate (Huang et al., 2010; Islam and Archer,
2001; Padding and Briels, 2003). A surface morphology
of polymer and appearance of fracture that suggest the
alignment in the welding region have been observed in the
industries. This indicates shear rate developed in the pro-
cess can affect the polymer orientation in a certain level,
even if they are not perfectly oriented. The shear rate was
not high at the interface between the pipes compared to
Fig. 13. (a) Global shape and (b) cross section of the pipe cut in
a plane which is perpendicular to the theta direction in the mid-
dle of the jointing stage in an experiment. This figure is at
tjointing = 5 s. The dotted line is the imaginary interface between
the pipes.
Fig. 14. (a) Global shape and (b) cross section of the pipe cut in
a plane which is perpendicular to the theta direction at the end
of the jointing stage in an experiment. The dotted line is the
imaginary interface between the pipes.
Fig. 15. (Color online) Stream lines (the solid lines with arrows) and shear rate contour in the melt region in the jointing stage at
tjointing = 8.8 s.
Jae Hyun Yoo, Sunwoong Choi, Jaewook Nam, Kyung Hyun Ahn and Ju Seok Oh
48 Korea-Australia Rheology J., 29(1), 2017
other regions, which means that the orientation at the
interface was not enhanced over the other regions, and it
was also observed in experiments that the orientation was
not significantly induced around the interface (Leskovics
et al., 2006).
The welding quality is usually determined by testing the
toughness of the welded pipe using a tensile test that axi-
ally elongates the welded pipes. The toughness is mea-
sured by the amount of energy per unit volume that a
material can absorb before fracture. Strong toughness is an
indicator of good welding quality. When testing the tough-
ness of welded pipes, a test specimen was made with the
welding region included. It is well known that the tough-
ness becomes lower, as the polymer orientation is deviated
from the parallel direction of applied strength. As axial
directional strength is applied to the specimen in a tensile
test, it can be suggested that the deviated orientation of
polymer from the axial direction leads to a weak tough-
ness of the welded pipes. As the pipe without a welding
region maintains axial orientation which is originated from
manufacturing, it is expected to exhibit higher toughness
than welded pipe. Lower toughness of the welded pipes
was well observed in experiments (EL-Bagory et al., 2014;
Leskovics et al., 2006). In such experiments, the fracture
was generated in the vicinity of the interface, not exactly
at the interface where two pipes meet (EL-Bagory et al.,
2014). This proves that the interface is not the weakest
zone, because the orientation is not significantly affected
around the interface. Rather, the vicinity of the interface
seems to be the weakest zone in terms of that higher shear
rate appears and fracture is located.
It is necessary to minimize effect to tilt the orientation of
the polymer in order to compensate weak toughness in the
welding region. For this purpose, an operator may main-
tain the compression pressure or hot plate temperature at
lower values in order to decrease the shear rate. However,
this may be risky, as it may reduce polymer diffusion. An
alternative solution is to change the flow direction to
induce preferred orientation. The flow occurs parallel to
the interface between the pipes, because it is a symmetric
boundary. A change of the interface shape, for instance
zigzag or wavy patterns on the interface, may cause the
partially axial flow and reduce radial flow, thereby remain-
ing axial orientation of the polymer. Further study is
required to identify an optimal surface shape. In most pre-
vious works, the welding quality was discussed only with
respect to the interface between the pipes (Bousmina et
al., 1998; Ezekoye et al., 1998; Kim and Wool, 1983; Qiu
and Bousmina, 1999; Wool et al., 1989). The problem in
this case is that the mechanical properties are weak not
only at the interface, but also in the region adjacent to the
interface. This is a result of squeezing flow and polymer
orientation as described above. We could not observe
polymer orientation directly, and the orientation is inferred
from the shear rate information. But, it is a unique con-
tribution of this study to observe the flow behaviors in
jointing stage and to relate them with welding quality.
4. Conclusion
There is a huge demand for robust welding with increas-
ing application of polymeric pipes. With this trend, it is
necessary to understand the underlying physics and to
improve the butt-fusion welding that is an effective pro-
cess for welding polymeric pipes. The entire butt-fusion
welding process can be simplified into two stages: The
heat soak stage and the jointing stage. In heat soak stage,
as the heat was conducted from the hot plate, the melt
depth increased. At the same time, heating induced ther-
mal expansion flow. It made the melt layer flow out at
inner and outer walls of the pipe, and swollen bead was
formed. In jointing stage, mixed flow behaviors consisting
of squeezing and fountain flows were observed. The melt
layer squeezed out over the radius of the pipe and it
formed the curling bead. The flow was radially induced as
a result of squeezing, so the polymer orientation can be
tilted in some degree toward the radial direction. It can be
suggested that the tilted orientation of polymer in the
welding region led to a weak toughness of the welded
pipes. It is necessary to minimize the effect to the orien-
tation of the polymer in order to compensate weak tough-
ness in the welding region. A change in the interface shape,
for instance zigzag or wavy patterns on the interface, may
cause the partially axial flow and reduce radial flow,
thereby remaining axial orientation the polymer.
There are some limitations of this study. We did not con-
sider the elasticity of the material. In addition, the numer-
ical simulation was terminated at the moment when the
beads encounter the pipe body. However, a new numerical
scheme to describe the melt flow and pipe deformation for
the butt-fusion welding process could be successfully
introduced in this study. The unique contribution of this
study is its capability of directly observing the flow behav-
iors that occur during the jointing stage and relating them
to welding quality.
Acknowledgment
This work was supported by the Korea Institute of
Energy Technology Evaluation and Planning (grant num-
ber 20131510200400); and Hannam University for grant-
ing research fund (2015).
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