Proceedings of ICMM2005
3rd International Conference on Microchannels and Minichannels
June 13-15, 2005, Toronto, Ontario, Canada
ICMM2005-75143
NUMERICAL STUDY OF THE EFFECT OF INLET CONSTRICTION ON BUBBLE GROWTH
DURING FLOW BOILING IN MICROCHANNELS
Abhijit Mukherjee
[email protected]
Rochester Institute of Technology
76, Lomb Memorial Drive
Rochester, NY 14623
Phone- 585.475.5839, Fax- 585.475.7710
ABSTRACT
Flow boiling through microchannels is characterized by
nucleation of vapor bubbles on the channel walls and their
rapid growth as they fill the entire channel cross-section. In
parallel microchannels connected through a common header,
formation of vapor bubbles often results in flow maldistribution that leads to reversed flow in certain channels. The
reversed flow is detrimental to the heat transfer and leads to
early CHF condition. One way of eliminating the reversed flow
is to incorporate flow restrictions at the channel inlet. In the
present numerical study, a nucleating vapor bubble placed near
the restricted end of a microchannel is numerically simulated.
The complete Navier-Stokes equations along with continuity
and energy equations are solved using the SIMPLER method.
The liquid-vapor interface is captured using the level set
technique. The results show that with no restriction the bubble
moves towards the nearest channel outlet, whereas in the
presence of a restriction, the bubble moves towards the distant
but unrestricted end. It is proposed that channels with
increasing cross-sectional area may be used to promote
unidirectional growth of the vapor plugs and prevent reversed
flow.
INTRODUCTION
Flow boiling in microchannels can result in very high wall
heat transfer coefficient.
However, when the hydraulic
diameter of a channel is decreased, the pressure drop increases
for the same flow velocity. The small cross-sectional area of
the microchannels gets easily filled by nucleating vapor
bubbles and soon the vapor bubbles turn into elongated bubbles
or vapor plugs. The surface area available for vapor addition
into the plug increases directly with increase in length of the
plug. This causes the vapor plug interfaces perpendicular to the
channel axis to accelerate causing high pressure gradients
inside the channels. In parallel microchannels connected with
common headers, random temporal and spatial bubble
nucleation in the channels causes flow mal-distribution. The
Satish G. Kandlikar
[email protected]
Rochester Institute of Technology
76, Lomb Memorial Drive
Rochester, NY 14623
Phone- 585.475.6728, Fax- 585.475.7710
liquid in the inlet header tries to flow into the channels least
blocked by vapor bubbles.
It has been experimentally observed by Balasubramanian
and Kandlikar (2004) that in some of the parallel
microchannels, the upstream interface of the vapor plug moves
towards the inlet. Figure 1 shows high speed images of
reversed flow in parallel channels as obtained by them.
Fig 1 – Reversed flow in parallel microchannels
(Balasubramanian and Kandlikar 2004)
The above phenomenon could occur due to two reasons as
explained in Fig. 2. The rate of vapor generation at the
upstream interface can be more than the rate of liquid supply to
the channel from the inlet header (Fig 2(a)) causing the
interface to move towards the inlet. Otherwise the vapor plug
growth may be too rapid to cause high pressure build up near
the upstream interface pushing the liquid back into the inlet
header (Fig 2(b)).
1
Copyright © 2005 by ASME
Inlet
Liquid
Interface
Inflow
Movement
Vapor Flow
(a)
Inlet
Liquid
Interface
Outflow
Movement
Vapor Flow
(b)
Fig 2 - Schematic representation of liquid flow near
the inlet of microchannel with growing vapor bubble
The first situation can be avoided by ensuring sufficient
inflow of liquid corresponding to the wall heat flux conditions.
The means to avoid the second scenario is being addressed in
this paper.
LITERATURE REVIEW
Kandlikar et al. (2001) experimentally explored different
flow regimes during flow boiling of water in parallel
minichannels. Experiments were carried out with six parallel
channels each with 1 mm hydraulic diameter. The different
flow regimes observed were bubbly flow with nucleate boiling,
bubbly flow, slug flow, annular/slug flow, annular/slug flow
with nucleate boiling and dryout. Large pressure fluctuations
were measured in the channels due to boiling phenomenon. In
some situations, slug growth was found to occur in the direction
counter to bulk flow forcing liquid and vapor back into the inlet
manifold.
Hetsroni et al. (2002) investigated flow instability in
uniformly heated triangular microchannels. The growth and
collapse of vapor fraction were found to cause fluctuations in
pressure drop and decreased the heat transfer coefficient. The
maximum values of pressure fluctuations were found to be in
the order of the pressure drop across the channels.
Peles (2003) studied two-phase boiling in micro heat
exchanger consisting of 16 mm long multiple parallel triangular
microchannels with hydraulic diameter ranging from 50
microns to 200 microns. He observed a ‘rapid bubble flow’
regime where the vapor bubble accelerated inside the channel
after filling up the channel cross-section.
Steinke and Kandlikar (2003) studied flow boiling and
pressure drop in parallel flow microchannels. They measured
wall heat fluxes and pressure drop in six parallel channels each
of hydraulic diameter of 207 microns. A flow reversal was
observed where the vapor interface moved in a direction
counter to the bulk flow of liquid.
Balasubramanian and Kandlikar (2004) studied pressure
drop fluctuations and flow instabilities in a set of six parallel
rectangular minichannels, each with 333 microns hydraulic
diameter. They measured the velocity of the liquid vapor
interface associated with bubble growth. The bubble/slug
growth rate was found to increase with length of the
bubble/slug and was as high as 3.5 m/s.
All the research work mentioned above were primarily
based on experiments. Some researchers have also used
analytical or numerical methods to model bubble growth inside
small dimension channels. Yuan et al. (1999) developed a
model of the growth and collapse of a vapor bubble in a small
channel connecting two liquid reservoirs. The bubble was
assumed to be a sphere from inception until its radius became
nearly equal to the tube radius. Thereafter, the bubble was
modeled as a cylinder inserted between two hemispheres. The
relative velocity between two bubble surface points on the tube
axis of the elongated bubble was found to increase or decrease
linearly with time. The model showed that the dynamics of the
bubble is governed by inertia during most of the bubble
lifetime.
Mukherjee and Kandlikar (2004) numerically simulated a
growing vapor bubble inside a microchannel. The bubble was
placed at the center of the channel surrounded by superheated
liquid. The bubble length was initially found to increase
linearly with time but as the bubble approached the channel
wall, the bubble downstream interface was found to accelerate.
The bubble growth rate was also found to increase with the
incoming liquid superheat.
OBJECTIVES OF THE PRESENT WORK
Bubble/slug expansion inside microchannels leads to rapid
rise in liquid pressure around the bubble interfaces. Under
extreme situations, this pressure rise can possibly cause the
upstream liquid to flow back towards the inlet header. One
possible means to avoid liquid back flow into the inlet header is
to provide the inlet with a restriction. The present work is
carried out to study vapor bubble growth inside a microchannel
with one restricted end.
NOMENCLATURE
specific heat at constant pressure
Cp
D
bubble diameter
g
gravity vector
H
Heaviside function
h
grid spacing
latent heat of evaporation
hfg
k
thermal conductivity
L
length of bubble
length scale
l0
m
mass transfer rate at interface
ms
milliseconds
p
pressure
R
Area ratio between outlets
Re
Reynolds number
r
radius
T
temperature
∆T
temperature difference, Tw-Tsat
t
time
time scale
t0
u
x direction velocity
velocity scale
u0
v
y direction velocity
w
z direction velocity
x
distance in x direction
y
distance in y direction
z
distance in z direction
βT
coefficient of thermal expansion
κ
interfacial curvature
µ
dynamic viscosity
2
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ν
ρ
σ
kinematic viscosity
density
surface tension
time period
level set function
contact angle
τ
φ
ϕ
Subscripts
evp
in
l
sat
v
w
evaporation
inlet
liquid
saturation
vapor
wall
∂
∂x
∂
∂y
x
y
z
∂
Superscripts
*
→
non dimensional quantity
vector quantity
∂z
NUMERICAL MODEL
Computational Domain
Figure 3 shows the typical computational domain. The domain
is 3.96x0.99x0.99 non-dimensional units in size. Cartesian
coordinates are used with uniform grid.
1
--------------> Outlet
0.75
Y
Outlet <-------------0.5
0.25
0
-0.5
-0.25
Z
<----------- Bubble at wall
4
3
0
0.25
2
1
0.5
the pressure correction. A pressure field is extracted from the
given velocity field. At each iteration, the velocities are
corrected using velocity-correction formulas.
The
computations proceed to convergence via a series of continuity
satisfying velocity fields. The algebraic equations are solved
using the line-by-line technique, which uses TDMA (TriDiagonal Matrix Algorithm) as the basic unit. The speed of
convergence of the line-by-line technique is further increased
by supplementing it with the block-correction procedure
[Patankar, 1981]. The multi-grid technique is employed to
solve the pressure equations.
Sussman et al. (1994) developed a level set approach
where the interface was captured implicitly as the zero level set
of a smooth function. The level set function was typically a
smooth function, denoted as φ . This formulation eliminated the
problems of adding/subtracting points to a moving grid and
automatically took care of merging and breaking of the
interface. Furthermore, the level set formulation generalized
easily to three dimensions. The present analysis is done using
this level set technique.
The liquid vapor interface is identified as the zero level set
of a smooth distance function φ . The level set function φ is
negative inside the bubble and positive outside the bubble. The
interface is located by solving the level set equation. A fifth
order WENO (Weighted, Essentially Non-Oscillatory) scheme
is used for left sided and right sided discretization of φ [Fedkiw
et al., 1998]. While φ is initially a distance function, it will not
remain so after solving the level set equation. Maintaining φ as
a distance function is essential for providing the interface with
a width fixed in time. This is achieved by reinitialization of φ .
A modification of Godunov's method is used to determine the
upwind directions. The reinitialization equation is solved in
fictitious time after each fully complete time step. With
h
∆τ =
, ten τ steps are taken with a third order TVD
2u0
(Total Variation Diminishing) Runge Kutta method.
X
0
Fig 3 – Computational Domain
When the vapor bubble grows, the liquid leaves the domain
at x* = 0 and x* = 3.96. To take advantage of symmetry and
reduce computation time, a nucleating cavity is placed on the
bottom wall at the center of the microchannel cross section
equidistant from the walls in the x-y planes. It is shown by
Mukherjee and Kandlikar (2004) that gravity has little effect on
the bubble growth under the given conditions of this study.
r
Thus, all computations are done neglecting gravity ( g = 0).
The number of computational cells in the domain is
320x80x40, i.e. 80 grids are used per 0.99l0. This grid size is
chosen from Mukherjee and Kandlikar (2004) to ensure grid
independence and negligible volume loss. Variable time step is
used which varied typically between 1e-4 to 1e-5.
Method
The complete incompressible Navier-Stokes equations are
solved using the SIMPLER method [Patankar, 1980], which
stands for Semi-Implicit Method for Pressure-Linked Equations
Revised. The continuity equation is turned into an equation for
Governing Equations
Momentum equation r
r
r
∂u r r
ρ ( + u .∇u ) = −∇p + ρg − ρβT (T − Tsat ) g
∂t
r
r
− σκ∇H + ∇.µ∇u + ∇.µ∇u T
(1)
Energy equation ∂T r
+ u.∇T ) = ∇.k∇T for φ > 0
∂t
T = Tsat for φ ≤ 0
ρC p (
Continuity equation r
r m
∇.u = 2 .∇ρ
ρ
(2)
(3)
The curvature of the interface -
κ (φ ) = ∇.(
3
∇φ
)
| ∇φ |
(4)
Copyright © 2005 by ASME
The mass flux of liquid evaporating at the interface r k ∇T
m= l
h fg
(5)
The vapor velocity at the interface due to evaporation –
r
r
k ∇T
m
(6)
uevp =
= l
ρ v ρ v h fg
To prevent instabilities at the interface, the density and
viscosity are defined as -
ρ = ρv + (ρl − ρv )H
(7)
µ = µ v + ( µl − µ v ) H
(8)
Initial Conditions
The bubble is placed at x* = 0.99, y* = 0 and z* = 0, with
0.1l0 radius in the domain shown in Fig. 3. All velocities in the
internal grid points are set to zero. The wall temperatures are
set to 107o C (T* = 1). The vapor inside the bubble is set to
saturation temperature of 100o C (T* = 0). The liquid
temperature inside the domain is set equal to the inlet liquid
temperature. All physical properties are taken at 100o C. The
inlet liquid temperature Tin is set to 102o C. The contact angle
at the walls is specified as 40o which is obtained from the
experimental data of Balasubramanian and Kandlikar (2004).
Boundary Conditions
The boundary conditions are as following –
•
H is the Heaviside function given by -
ux = vx = wx = Tx = 0; φ x = 0
H = 1 if φ ≥ + 1.5h
H = 0 if φ ≤ −1.5h
(9)
•
H = 0.5 + φ /(3h) + sin[2πφ /(3h)] /( 2π ) if | φ | ≤ 1.5h
•
Since the vapor is assumed to remain at saturation temperature,
the thermal conductivity is given by –
where
The level set equation is solved as r r
∂φ
+ (u + uevp ).∇φ = 0
∂t
•
(11)
∂φ
= S (φ0 )(1− | ∇φ |)u0
∂t
S is the sign function which is calculated as S (φ0 ) =
φ0
φ0 2 + h 2
•
(13)
Scaling Factors
The governing equations are made non-dimensional using
a length scale and a time scale. The length scale l0 given by the
channel width is equal to 200 microns. The Reynolds number
is specified as 100 for all cases. Thus for water at 100o C, the
velocity scale u0 is calculated as 0.146 m/s. The corresponding
time scale t0 is 1.373 ms. All non-dimensional quantities
hereafter are indicated with * superscript. The non-dimensional
temperature is defined as
T − Tsat
(14)
T* =
Tw − Tsat
(17)
is the contact angle
At the wall (z* = 0.495):(18)
At the restricted area of the outlet (x* = 0) :u = v = w = 0; T = Tw; φ x = − cosϕ
(12)
φ ( x,0) = φ0 ( x)
ϕ
u = v = w = 0; T = Tw; φ z = − cosϕ
After every time step, the level-set function φ , is reinitialized as
–
(16)
At the walls (y* = 0, y* = 0.99) :u = v = w = 0; T = Tw; φ y = − cos ϕ
(10)
(15)
At the plane of symmetry (z* = 0) :uz = vz = w = Tz = 0; φ z = 0
where h is the grid spacing
k = k l H −1
At the outlets (x* = 0, x* = 3.96) :-
(19)
Since the objective of the simulation is to study reversed
flow, both the channel ends of the microchannel has been
provided with outflow boundary conditions. In this model, no
pressure differential is being maintained across the channel
ends that would otherwise be present in actual experimental
conditions.
Numerical calculations are done with four different area
ratios between the two ends of the microchannel. The restricted
end is always at x* = 0. Four different area ratios are studied
which are R = 1, 0.76, 0.56 and 0.25. The area ratio R is
defined as the ratio between the cross-section areas at x* = 0
and at x* = 3.96.
RESULTS
The numerical calculations start with the bubble nucleating
at x = 0.2 mm for the different area ratios. Since the length of
the channel is 0.8 mm, the bubble is initially at one-third
distance from the restricted end as compared to the unrestricted
end. The bubble grows in time due to evaporation at its
interface and initially the shape of the bubble is spherical.
However, as the bubble grows big enough to almost fill the
channel cross-section, it starts to elongate along the channel
axis. The location of the bubble interfaces along the channel
4
Copyright © 2005 by ASME
axis indicates how far the bubble is from the channel ends.
Figure 4 plots the bubble end locations along the x-axis against
time for different values of area ratios R. As the bubble grows,
one end of the bubble moves towards the unrestricted outlet at x
= 0.8 mm and the distance of that end from x = 0 mm increases
with time. The other end of the bubble tries to move towards
the restricted outlet at x = 0 mm and hence its distance from x =
0 mm may increase, decrease or stay constant with time.
0.00 ms
1
0.5
Y
0.75
0.25
0
-0.5
-0.25
Z
0
0.25
0.5
4
3
2
1
0
X
1
0.05 ms
1
0.76
0.56
0.25
1
0.75
0.7
0.5
0.25
0.6
0
-0.5
-0.25
0.5
Z
0.4
0
0.25
0.5
4
3
2
1
0
X
0.3
0.11 ms
0.2
0.1
0.2
Time(ms)
0.3
0.4
0.5
Y
0.1
0.25
Fig 4 – Comparison of bubble end locations
0
-0.5
-0.25
Z
For the case with area ratio R = 1, the bubble is seen to
grow almost symmetrically in both directions. At around 0.3
ms one bubble end reaches x = 0 whereas the other end is close
to x = 0.4 mm. However, when the restriction is placed at x = 0
mm, the bubble grows more towards the distant outlet (at x =
0.8 mm). As the area ratio decreases, the bubble interfaces
move further away from the x = 0 location. In other words, at
any time say 0.3 ms, the bubble end locations are closer to the
unrestricted outlet for decreasing area ratio, indicating decrease
in reversed flow. The velocity of the bubble interface
(indicated by the slope of the curves) moving towards the x =
0.8 mm location can be seen increasing with time in all cases.
Figure 5 shows the bubble shapes for R = 1.0. The time
corresponding to each frame is indicated on the top right corner
of each frame in milliseconds. The bubble grows in both
positive and negative x directions. At 0.29 ms the bubble has
grown big enough to reach the nearest outlet at x* = 0.
Figure 6 shows the bubble shapes for R = 0.25. Thus the
left outlet of the microchannel is restricted whereas the right
outlet is fully open.
In this case the bubble grows
predominantly in the positive x-direction. The location of the
bubble interface near the restricted outlet stays almost same in
all the frames. At 0.34 ms, the right end of the bubble has
almost reached the outlet at x* = 4. At this time, the bubble has
elongated turning into a plug and vapor patches have formed on
the walls in the x-y plane.
0
0.25
0.5
4
3
2
1
0
X
0.16 ms
1
0.75
0.5
Y
0
0.25
0
-0.5
-0.25
Z
0
0.25
0.5
4
3
2
1
0
X
0.22 ms
1
0.75
0.5
Y
0
1
0.75
0.25
0
-0.5
-0.25
Z
0
0.25
0.5
4
3
2
1
0
X
0.29 ms
1
0.75
0.5
Y
Bubble End Locations (mm)
0.8
=
=
=
=
Y
R
R
R
R
0.9
0.25
0
-0.5
-0.25
Z
0
0.25
0.5
4
3
2
1
0
X
Fig 5 – Bubble shapes for R = 1.0
5
Copyright © 2005 by ASME
0.00 ms
1
0.5
Y
0.75
0.25
0
-0.5
-0.25
Z
0
0.25
0.5
4
3
2
1
0
X
0.07 ms
1
Figure 7 compares the velocity vectors around the bubbles
when at least one bubble interface has reached the channel
outlet. The figure shows the velocity vectors at the central x-y
plane through the bubble. Figure 7(a) shows the case with R =
1, when the bubble reaches the nearest outlet at x* = 0. Figure
7(b) shows the case with R = 0.25, when the bubble reaches the
distant outlet at x* = 4. In the first case the length of the
velocity vectors around the bubble is almost uniform in all
directions. In the second case, the velocity vectors on the right
hand side are much longer than those on the left hand side of
the bubble, indicating that most liquid flow is taking place in
the positive x-direction.
Unit Vector
0.75
Y
0.5
0.75
0.25
0.5
0
-0.5
-0.25
Z
0
0.25
0.5
1
4
0.25
3
2
Y
1
0
0
X
0
Z
X
1
2
0.14 ms
Y
0.25
Y
0
4
3
Z
2
1
Z
1
Y
0.5
0.25
0
-0.5
-0.25
4
3
Z
2
1
0
X
0.27 ms
1
0.5
Y
0.75
0.25
0
-0.5
-0.25
4
3
Z
2
1
0
X
0.34 ms
1
0.5
0.25
0
-0.5
-0.25
4
3
Z
2
1
X
Fig 6 – Bubble shapes for R = 0.25
Y
0.75
0
1
2
3
Fig 7 – Comparison of velocity fields for
(a) R = 1 and (b) R = 0.25
0.75
0
0.25
0.5
0
X
X
0.20 ms
0
0.25
0.5
4
0.5
0.25
0
0
0.25
0.5
(b)
0.75
0.75
0
4
Unit Vector
0.5
0
0.25
0.5
(a)
1
1
-0.5
-0.25
3
DISCUSSION
The vapor bubble dynamics inside the microchannel is
influenced by the geometry of the channel as well as by its
rapid growth rate. As seen from Figs. 5 and 6, the vapor bubble
initially grows in nearly spherical shape but gradually
transforms to a plug under the influence of the enclosing
channel walls. It is also seen that the bubble grows more
towards the channel end without restriction. The reason for this
is the large bubble growth rate, which results in greater liquid
inertia around the bubbles. If the liquid gets restricted in its
flow path, the reaction effect causes the bubble to push itself in
a direction of least resistance.
The instability during flow boiling inside microchannels,
as observed by several researchers, is caused primarily by the
rapid growth and reversed vapor flow into the inlet manifolds.
When a vapor bubble turns into a plug, the length of the plug
increases with time. The end interfaces of the vapor plug have
been observed to accelerate along the channel axis with
interface velocities reaching as high as 3.5 m/s
(Balasubramanian and Kandlikar, 2004).
It has been shown by Mukherjee and Kandlikar (2004) that
a vapor plug traps a thin layer of liquid between its interface
and the channel walls that leads to high vapor generation rate.
However, the shape of the vapor plug itself can be a reason that
causes the ends of the vapor plug to accelerate, increasing the
pressure inside the channel. The following calculations will
illustrate the point.
Figure 8(a) shows a spherical vapor bubble of diameter D
growing in a sea of superheated liquid. The addition of mass to
the bubble per unit time is given by -
6
Copyright © 2005 by ASME
dV
d π
dD
π
= ρv ( D3 ) = ρv D 2
(20)
dt
2
dt
dt 6
Therefore, the rate of change in bubble diameter is –
r
dD 2m
(21)
=
dt
ρv
r
πD 2 m = ρv
of flow thereby allowing the vapor plugs to grow with a
constant interface velocity. This is possible if the crosssectional area of the channel increases with the length of the
channel.
In case of a cylindrical bubble (Fig. 8(b)) of fixed diameter D
but variable length L, the rate of mass addition to the bubble
(neglecting the hemispherical ends for simplicity, since L>>D)
is given by –
Inlet
dV
d π
dL
π
= ρ v ( D 2 L) = ρ v D 2
(22)
dt
dt 4
4
dt
Thus the rate of change of plug length is –
r
dL 4 Lm
(23)
=
dt Dρ v
The above calculations assume constant vapor density.
Outlet
r
πDL m = ρ v
Inlet
Outlet
Vapor
Bubble
D
Vapor
Plug
Liquid
Fig 9 - Stepped micro channels
(a)
D
Microchannel
walls
L
(b)
Figure 9 shows top view of a conceptual microchannel
with stepped walls that will progressively provide increasing
area in the direction of flow. It will also help in preventing
back flow of liquid from each individual section of the channel
with constant cross-sectional area, due to the presence of
restriction at its upstream end.
Fig 8 – (a) Spherical bubble in a pool of liquid
(b) Cylindrical bubble inside a microchannel
Thus, for a spherical bubble, the rate of change of bubble
diameter is independent of the bubble diameter, whereas in the
case of a cylindrical bubble enclosed by walls, the rate of
increase in bubble length is proportional to the length of the
bubble. Thus when the bubble shape changes from spherical to
cylindrical inside a microchannel, its end velocities increase
with the bubble length. This causes the plug interfaces along
the channel axis to accelerate thereby increasing the pressure
inside the channel.
It may be noted here that if the elongated vapor plug
eventually touches the surrounding walls forming vapor
patches, the vapor addition to the bubble will decrease thereby
decreasing the plug interface velocity. However, this leads to
deterioration in heat transfer and possible initiation of the CHF
condition.
Proposed Channel Shapes
The reversed flow in the microchannels occurs mainly due
to pressure build up inside the channel because of rapid vapor
bubble growth. In order to have a unidirectional flow inside the
channels, it is necessary to prevent the vapor plug acceleration
and relieve the build up pressure inside the channels in the
direction of the desired flow. It is proposed that microchannels
be designed with increasing area ratio in the desired direction
Inlet
Outlet
Inlet
Outlet
Fig 10 - Diverging micro channels
If manufacturing stepped microchannels pose a challenge,
smooth diverging microchannels (shown in Fig. 10) may be
used instead, which essentially provides the same benefits as
the stepped channels.
7
Copyright © 2005 by ASME
Kandlikar et al. (2005) have experimentally shown that
inlet constrictions in parallel microchannels decreased liquid
backflow to the channel inlet and stabilized pressure drop
fluctuations.
Their findings are in agreement with the
numerical predictions of this paper.
CONCLUSIONS
The growth of vapor bubble inside a microchannel with
different outlet area ratios is studied. The bubble is found to
move towards the distant but unrestricted outlet. The vapor
plug interface velocity is found to increase with length of the
plug. To prevent flow instabilities and pressure rise inside the
microchannel due to accelerating vapor plugs, it is suggested
that microchannels be designed with increasing area ratio in the
direction of desired flow.
ACKNOWLEDGMENTS
The work was conducted in the Thermal Analysis and
Microfluidics Laboratory at RIT.
REFERENCES
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