Numerical analysis of the heat transfer and fluid flow in the ...Numerical analysis of the heat...

© 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



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.



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.



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≤ ≤



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.



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.



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.



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.



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


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.


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.



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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