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Direct numerical simulation of flow boiling in a finned microchannel
International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
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Direct numerical simulation of flow boiling in a finned microchannel☆ Woorim Lee a, Gihun Son a,⁎, Han Young Yoon b a b
Department of Mechanical Engineering, Sogang University, Seoul, South Korea Korea Atomic Energy Research Institute, Daejeon, South Korea
a r t i c l e
i n f o
Available online 31 August 2012 Keywords: Direct numerical simulation Finned surface Flow boiling Level-set method Microchannel
a b s t r a c t Direct numerical simulations of bubble growth and heat transfer associated with flow boiling in a finned microchannel are performed by solving the conservation equations of mass, momentum and energy in the liquid and vapor phases. The phase interfaces are determined by a sharp-interface level-set method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on the immersed solid surface of fins. The effects of fin height, spacing, and length on the flow boiling in a microchannel are investigated to find the better conditions for heat transfer enhancement. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Flow boiling in a microchannel, which is an attractive cooling method for high-power micro devices, has been studied extensively, as reviewed by Kandlikar [1] and Thome [2]. The boiling heat transfer can be further increased by surface modification with micromachined or MEMS fabricated structures [3–5]. In this study, we focus on a finned surface, which is one of the most popular heat transfer enhancement methods. The applications of fins for heat transfer augmentation in pool boiling were investigated by a number of researchers [6–10]. However, only a few studies were conducted for boiling heat transfer enhancement in a microchannel because of the technological difficulties in obtaining detailed measurements of boiling characteristics occurring on microscale structures. Kosar and Peles [11] investigated flow boiling of R-123 in a finned microchannel of 1.8 mm × 0.243 mm in width and height. The microchannel included 20 arrays of hydrofoil pin fins with 0.1 mm width, 0.243 mm height, and 0.5 mm length. Their experimental data showed three flow pattern regions, such as bubbly flow, wavy intermittent flow, and spray-annular flow, depending on the heat flux and mass velocity. Subsequently, Krishnamurthy and Peles [12] studied flow boiling of HFE-7000 in five parallel 0.2 mm × 0.243 mm channels. Each channel contained a single row of circular pin fins of 0.1 mm diameter, 0.243 mm height, and 0.4 mm pitch. They visualized the existence of bubbly flow, multiple flow, and wavy-annular flow. As the bubbles which nucleated on the channel sidewalls and the pin fin
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author at: Department of Mechanical Engineering, Sogang University, Shinsu-dong, Mapo-ku, Seoul 121-742, South Korea. E-mail address: [email protected] (G. Son). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2012.08.005
surface moved downstream and grew into vapor slugs, bubbly flow developed into multiple flow including vapor slugs as well as bubbles. The multiple flow further evolved into wavy-annular flow, in which thin wavy liquid layers formed along the channel sidewalls and the pin fins while the vapor phase occupied most of the cross-section of the microchannel. Some efforts to enhance boiling heat transfer by fins were reported for minichannel flows rather than microchannel flows. Ma et al. [13] investigated flow boiling of FC-72 on 10 mm square and 0.5 mm high chips which were placed in a 30 mm × 5 mm channel. The chips had square pin fins of 0.03 mm width, 0.06 and 0.12 mm heights, and 0.03 mm spacing. Boiling heat transfer was significantly increased by the addition of fins and further enhanced by increasing the fin height. McNeil et al. [14] studied flow boiling of R-113 on a 50 mm square plate. The plate contained square pin fins of 1 mm width, 1 mm height, and 2 mm pitch. The heat transfer coefficients normalized by the fluid–solid contact area were slightly increased on the pin finned surface, and thus the boiling heat transfer was improved by the pin fins due to the increased heat transfer area. As another way to analyze the boiling phenomena in a microchannel, direct numerical simulation of the bubble dynamics and boiling heat transfer was reported in the literature. Mukherjee and Kandlikar [15] simulated bubble growth during flow boiling in a microchannel by using a level-set (LS) method. The effects of incoming liquid superheat and Reynolds number on the bubble growth rate were investigated. Lee and Son [16] applied the LS method to computation of the bubble dynamics and heat transfer in a microchannel. They demonstrated that the heat transfer rate increased significantly when the channel size was smaller than the bubble departure diameter. The heat transfer rate was observed to depend on a contact angle which determined the existence of a liquid layer forming between the bubble and the channel corner. Subsequently, Suh et al. [17] extended the LS method to flow boiling in parallel microchannels. Their numerical results showed that
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
Nomenclature cp F g Gfin h hlv H L _ m n p S Sfin t T u U vlv W x, y, z
specific heat fraction function gravity gap between the fin segments grid spacing latent heat of vaporization height length mass flux across the interface unit normal vector pressure sign function fin spacing time temperature flow velocity vector interface velocity vector ρv−1 − ρl−1 width Cartesian coordinate
Greek symbols α step function βT coefficient of thermal expansion κ interface curvature λ thermal conductivity μ dynamic viscosity θ contact angle ρ density σ surface tension coefficient τ artificial time τw waiting period ϕ distance function from the liquid–vapor interface ψ distance function from the fluid–solid interface
Subscripts c channel f fluid fin fin l, v liquid, vapor s solid sat saturation w wall
the backward bubble expansion to the channel inlet causing reverse flow became more pronounced when the contact angle decreased and the wall superheat increased. The backward bubble growth pattern reduced the boiling heat transfer rate in multiple microchannels compared to that in a single microchannel. The past numerical computations were limited to flow boiling in a simple geometry of microchannel. In this study, direct numerical simulations are performed for bubble growth and heat transfer in a finned microchannel. The phase interfaces are determined by a sharp-interface LS method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on immersed solid surface of fins. The effects of fin height, spacing, and width on the bubble growth and heat transfer in a microchannel are investigated to find the better conditions for heat transfer enhancement.
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2. Numerical analysis The present numerical approach is based on the sharp-interface LS formulation developed by Lee et al. [18,19] for computation of pool boiling on microstructured surfaces. The method is extended to threedimensional computation of flow boiling in a finned microchannel. Fig. 1 shows the configuration used for computation of bubble growth and heat transfer in a finned microchannel. The flows are taken to be laminar and the fluid properties including density, viscosity, specific heat and thermal conductivity are assumed to be constant in each phase. The liquid–vapor interface is determined by the LS function ϕ, which is defined as a signed distance from the interface. The negative sign is chosen for the vapor phase and the positive sign for the liquid phase. To treat the immersed solid surface of fins, we use another LS function ψ, which is defined as a signed distance from the fluid–solid interface. The negative sign is chosen for the solid region and the positive sign for the fluid region. The conservation equations of mass, momentum and energy for the whole region including liquid, vapor and solid phases are written as _ ∇·u ¼ α ψ vlv mn·∇α ϕ ∂u ¼ −α ψ ∇p þ ∇·μ e ∇u þ α ψ f ∂t
ð1Þ if ψ > 0
ð2Þ
u¼0
if ψ≤0
ð3Þ
∂T ρcp ¼ −α ψ ρcp ul ·∇T þ ∇·λe ∇T e ∂t l
if ϕ > 0 or ψ≤0
ð4Þ
T ¼ T sat
if ϕ ≤0 and ψ > 0
ð5Þ
ρe
where α ϕ=ψ ¼ 1 if ϕ=ψ > 0 ¼ 0 if ϕ=ψ≤0 _ ¼ n·λe ∇T=hlv m n ¼ ∇ϕ=j∇ϕj κ ¼ ∇·ð∇ϕ=j∇ϕjÞ
Fig. 1. Configuration used for computation of flow boiling in a finned microchannel.
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_ 2 ∇α ϕ f ¼ −ρe uf ·∇uf þ ρe ½1−βT ðT−T sat Þg− σ κ−vlv m h T i _ _ þ∇·μ e ð∇uÞT −∇·μ e vlv mn∇α ϕ þ vlv mn∇α ϕ
Here h is a grid spacing and the formulation of sign function S implies that a near-zero level set rather than ϕ = 0 is used as the immobile boundary condition during the reinitialization procedure. The boundary conditions used in this study are as follows (refer to Fig. 1). At the inlet (x = 0),
_ 1−α ϕ ul ¼ u þ vlv mn _ uv ¼ u−vlv mnα ϕ
u ¼ uin
ρe ¼ ρv 1−F ϕ þ ρl F ϕ −1
−1
−1 −1 ¼ λl F ϕ F ψ þ λs 1−F ψ
λe
p¼0
l
u¼0
s
Here, uf (ul or uv) is the velocity for each phase which is extrapolated into the entire domain by using the velocity jump condition at _ the interface, ul ¼ uv þ vlv mn. The effective properties, ρe, μe and λe, are evaluated from the fraction functions, Fϕ and Fψ, which are defined as Fϕ ¼ 1 ¼0 ¼
∂ϕ ¼ 0: ∂x
ð13Þ
ð14Þ
T ¼ Tw
∂ϕ ¼ − cosθ: ∂y
ð15Þ
At the top wall surface (y = Hb + Hc), u¼0
∂T ¼0 ∂y
∂ϕ ¼ cosθ: ∂y
ð16Þ
At the plane of symmetry (z = 0),
if α ϕ ðϕA Þ ¼ α ϕ ðϕB Þ ¼ 1 if α ϕ ðϕA Þ ¼ α ϕ ðϕB Þ ¼ 0
maxðϕA ; ϕB Þ maxðϕA ; ϕB Þ−minðϕA ; ϕB Þ
∂u ∂T ∂ϕ ¼ ¼ ¼ 0: ∂x ∂x ∂x
At the bottom wall surface (y = 0),
1−α ψ : ρcp ¼ ρcp α ψ þ ρcp e
T ¼ T sat
At the outlet (x = L),
−1 −1 ¼ μ v 1−F ϕ F ψ þ μ l F ϕ F ψ
μe
v¼w¼0
w¼0
otherwise
where the subscripts A and B denote the grid points adjacent to the location where Fϕ is evaluated. The heat flux from a liquid microlayer, which forms between the bubble and the wall near the bubble surface– wall contact location, can be formulated as proposed in [18]. In the LS formulation, the interface is described as ϕ = 0. The level sets including ϕ = 0 are advanced as
∂u ∂v ∂T ∂ϕ ¼ ¼ ¼ ¼ 0: ∂z ∂z ∂z ∂z
ð17Þ
At the side wall surface (z = Wc/2 + Ws), u¼0
∂T ¼0 ∂z
∂ϕ ¼ cosθ: ∂z
ð18Þ
where the interface velocity U and the unit normal vector ns pointing into the solid region are written as
The numerical method was tested in our previous study [16] through the computations of flow boiling in a plain microchannel. The numerical results showed good agreement with the experimental data available in the literature. Also, a convergence test for grid resolutions was made in our previous study [18] for bubble growth on a horizontal surface with a cavity by using two different grid spacings of h = 0.01 mm and h = 0.005 mm. The bubble growth rates and the bubble shapes at departure obtained with both grids showed no significant differences. Therefore the present computations are conducted with h = 0.01 mm to save computing time without losing accuracy of numerical results.
_ U ¼ uf þ mn=ρ f
ð8Þ
3. Results and discussion
ns ¼ −∇ψ=j∇ψj:
ð9Þ
∂ϕ ¼ −U·∇ϕ ∂t
if ψ > 0
ð6Þ
∂ϕ ¼ cosθ−ns ·∇ϕ ∂τ
if ψ≤0
ð7Þ
The contact angle condition, ns ⋅ ∇ ϕ = cosθ, defined at the liquid– vapor–solid contact location is extended into the entire solid region by employing the iterative equation. The non-zero level sets are reinitialized (or reconstructed) as a distance (| ∇ ϕ| = 1) from the interface by obtaining a steady-state solution of the equation ∂ϕ ¼ SðϕÞð1−j∇ϕjÞ ∂τ
ð10Þ
where SðϕÞ ¼ 0 ϕ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ϕ2 þ h2
if jϕj < h=2
ð11Þ
otherwise:
ð12Þ
Numerical simulations of flow boiling in a finned microchannel are performed using the properties of saturated water at 1 atm and a constant contact angle of 40 ∘. In presenting the results including figures, lengths are scaled by 1 mm and time by 1 ms. We choose a computational domain of 0 ≤ x ≤ 4, 0 ≤ y ≤ 0.32 and 0 ≤ z ≤ 0.24, (L = 4, Hc + Hb = 0.32, 0.5Wc + Ws = 0.24), as depicted in Fig. 1. The domain includes fins and bottom and side walls of y ≤ 0.12 and z ≥ 0.2 (Hb = 0.12, 0.5Wc = 0.2, Ws = 0.04). The conduction heat transfer through the solid region is also solved with the thermal properties of ρcp s ¼ 0:85 ρcp l and λs = 230λl. At the bottom surface of the computational domain, the temperature is specified as Tw = 110 °C. Also, we use a uniform velocity of uin = 0.3 m/s at the channel inlet. The initial velocity and the temperature fields for computation of bubble growth are taken from the steady-state solution for single-phase liquid flow without including bubble nucleation, which is obtained numerically. In this study, we assume that a single bubble nucleation site is located on the channel bottom surface near the inlet, (x,y,z) = (0.5,Hb,0). A small bubble, whose shape is a truncated
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
a
a
z=0
0.32
y
Bubble 0.16
Solid
0.00 2.5
3.0
y
0.16
0.00 -0.24
b
3.5
x x = 3.0
0.32
y
0
z
0.24
z=0
0.32
0.16 109.9
0.00 2.5
3.0
3.5
x x = 3.0
0.32
y
sphere with a radius of 0.03 that satisfies a specified contact angle at the liquid–vapor–solid contact line, is placed on the nucleation site. To simulate the cyclic process of bubble growth, a new bubble is placed on the nucleation site when it is occupied by a superheated liquid (T > Tsat) during the waiting period τw for bubble generation. We use τw = 4. First, computation is performed for flow boiling in a microchannel without fins. The result for bubble growth is plotted in Fig. 2. The initial bubble grows to occupy the entire cross-section of the channel, and then it expands along the channel and develops into an elongated vapor slug, as observed in slug or annular flows. When the bubble nucleation site is covered by a superheated liquid during the waiting period of τw = 4, a new bubble is placed on the nucleation site. As the new bubble grows along the channel, the previously generated vapor slug is quickly pushed outward. The bubble growth pattern including slug formation and expansion repeats all over again with the new bubble. Fig. 3 shows the temperature field associated with the bubble growth in a microchannel without fins. The solid lines in the figure represent the isotherms of 103, 106 and 109 °C while the dashed lines represent the isotherms of 109.5 and 109.9 °C. The isotherms are crowded in the liquid layers forming near the liquid–vapor–solid contact lines, as seen near the location of (x,y,z) = (2.9,0.12,0) at t = 1.5 and the locations of (x,y,z) = (3.0, 0.12, ± 0.16) and (x,y,z) = (3.0, 0.21, ± 0.2) at t = 3. This indicates that the high heat transfer occurs in those regions. It is observed from the temporal variation of the isotherms in the cross-section of x = 3.0 that the isotherms are more closely packed at t = 3, when the vapor slug further expands to occupy the entire cross-section of the channel, than at t = 1.5. The dashed line for T = 109.9 °C is seen to move down to the bottom wall surface (y = 0), which results in the increased wall heat flux. It is also noted that the dry region, where the wall is in direct contact with the vapor, forms on the channel bottom surface while thin liquid layers exist between the bubble and the channel corner, as seen at t = 3. In the computations of flow boiling in a microchannel with fins, we vary parametrically fin height Hfin, fin spacing Sfin, and fin length Lfin (refer to Fig. 1). The transverse fins are placed in the region of 1 ≤ x ≤ 4. The results with fins of Hfin = 0.05 and Sfin = Lfin = 0.1 are presented in Figs. 4 and 5. The bubble growth at t = 1.5 is observed to be faster in the finned microchannel than in the plain microchannel. While the liquid–vapor interface slides on the fin tips
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0.16 109.5 109.9
0.0 -0.24
0
z
0.24
Fig. 3. Temperature field in a microchannel without fins: (a) t = 1.5 and (b) t = 3.0.
with bubble growth and vapor slug expansion, liquid is trapped between the fins, as seen in Fig. 4(b). This indicates that the liquid– vapor interface contacts the finned surface at more locations and
a t = 1.3
t = 1.3
1.5
1.5
3.0
3.0
5.0
5.0
b
b
t = 1.3
t = 1.3
1.5
1.5
3.0
3.0
5.0
0
1
2
3
4
0.00
x Fig. 2. Bubble growth in a microchannel without fins: (a) top view and (b) cross-sectional view at z=0.
0.32 5.0
y
y
0.32 0
1
2
3
4
0.00
x Fig. 4. Bubble growth in a microchannel with fins of Hfin = 0.05 and Sfin = Lfin = 0.1: (a) top view and (b) cross-sectional view at z = 0.
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z = 0.00
y
0.32
0.16
0.00
z = 0.18
y
0.32
0.16 109.5 109.9
0.00 2.5
3.0
x = 3.05
0.32
y
3.5
x
x = 3.15
0.16 109.5 109.9
0.00 -0.24
0
z
0.24 -0.24
0
z
0.24
Fig. 5. Temperature field at t=3 in a microchannel with fins of Hfin =0.05 and Sfin =Lfin =0.1.
hence the high heat transfer area occupied by thin liquid layers increases. In Fig. 5, the liquid layers between the fins are observed to be thin near the channel center (z = 0) and become thicker near the channel sidewalls. The liquid–vapor–solid contact regions increase also on the sidewalls, as seen in the cross-sections of x = 3.05 (fin region) and x = 3.15 (interfin region). This results in the increased wall heat flux in comparison with the plain microchannel. Fig. 6 shows the bubble shape and the associated temperature field when the fin height is reduced to Hfin = 0.03 while keeping the
a
z = 0.00
160 Hfin = 0.00 0.03 0.05
120
q(W/cm2)
0.32
y
other parameters constant. In contrast to the case of Hfin = 0.05, the liquid–vapor interface for the shorter fins is seen to nearly touch the bottom wall in the interfin region. The closely spaced isotherms near the region reflect the higher heat transfer. The effect of fin height on the wall heat flux is plotted in Fig. 7. The heat flux is averaged over the heating surface of 1 ≤ x ≤ 4, except the channel entrance region where the heat transfer is strongly affected by the inlet boundary condition. The area-averaged heat flux initially increases as the bubble expands along the channel, and then it slightly decreases while the vapor slug leaves out of the computational domain. Thereafter, the heat flux variation pattern repeats all over again with a new bubble. The wall heat fluxes for different fin heights are averaged over the computational time of 2 ≤ t ≤ 12, except the early period when the heat transfer is influenced by the specified initial condition, and compared in Fig. 7(b). The area and time averaged wall heat fluxes are normalized by qw,o for a plain microchannel, whose value is 60.3 W/cm 2. The heat transfer enhancement (qw/qw,o − 1) averaged over the bottom surface area Abot is attributed to the increased heat transfer area as well as the fin structure. To solely account for the contribution of fin structure on the boiling enhancement, we also include the heat transfer enhancement averaged over the total finned surface area Atot. The heat transfer enhancement is maximum at Hfin = 0.03, and its value is 51% when based on Abot and 21% when based on Atot. Fig. 8 presents the bubble shapes and temperature fields for Sfin = 0.05 and Sfin = 0.2. The difference between both results is pronounced in the interfin region rather than in the fin region. For Sfin = 0.05, the bubble surface hardly expands into the narrow interfin region. However, when the fin spacing is increased to 0.2, the bubble surface moves into the interfin region and touches the bottom wall. As a result, the heat flux increases near the liquid–vapor–solid (or three-phase) contact regions, in which thin liquid layers form, whereas the heat flux decreases near the dry regions surrounded by the three-phase contact lines. The heat transfer enhancement based on the total finned surface area Atot increases with fin spacing. This indicates that the wider fin spacing is more effective in improving boiling heat transfer.
0.16
80 40
0.00
z = 0.18
0.32
0
0
4
8
12
y
t(ms) 0.16
b
2.0
109.5
3.0
3.5
x
x = 3.05
0.32
y
Abot Atot
109.9
1.6
qw / qplain
0.00 2.5
x = 3.15
1.2
0.16 0.8
109.5 109.9
0.00 -0.24
0
z
0.24
-0.24
0
0.24
z
Fig. 6. Bubble shape and temperature field at t = 3 with shorter fins of Hfin = 0.03 and Sfin = Lfin = 0.1.
0.00
0.02
0.04
0.06
Hfin Fig. 7. Effect of fin height on heat transfer for Sfin = Lfin = 0.1: (a) area-averaged wall heat flux and (b) heat transfer enhancement.
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
a 0.16
0.00 2.5
z = 0.00
0.32
y
y
a
z = 0.00
0.32
3.0
0.16
0.00 2.5
3.5
3.0
x = 3.00
0.16
109.5
0.00 109.9 -0.24
109.9
0
0.24
-0.24
z
0.24
0.16
3.0
x = 3.00
0
0.24
z
0.16
3.0
3.5
y
x = 3.05
x = 2.90
0.32
0.16
0.16 109.5
109.5 109.9
0.00 -0.24
-0.24
x
x = 2.85
0.32
0.24
z = 0.00
0.32
0.00 2.5
3.5
x
0
z
b
z =0.00
0.32
0.00 2.5
y
0
z
y
y
b
x = 3.05
0.16
109.5
0.00 -0.24
x = 2.98
0.32
y
y
x = 3.07
3.5
x
x 0.32
1465
0
z
0.24
-0.24
0
0.24
0.00 -0.24
109.9
z
Fig. 8. Effect of fin spacing on bubble shape and temperature field at t = 3 for Hfin = 0.03 and Lfin = 0.1: (a) Sfin = 0.05 and (b) Sfin = 0.2.
However, the fin configuration reduces the number of fins to be added to the fixed area and hence the heat transfer area. When based on the bottom surface area Abot, the heat transfer enhancement weakly depends on fin spacing and has a maximum value of 51% at Sfin = 0.1. Fig. 9 shows the bubble shapes and temperature fields for Lfin = 0.05 and Lfin = 0.2. When the fin length is decreased to 0.05 and the number of fins is increased, the liquid–vapor interface contacts the finned surface at more locations than the case of Lfin = 0.1 depicted in Fig. 6, and hence the high heat transfer area including thin liquid layers increases. However, for Lfin = 0.2, the dry (or hot spot) region expands on the increased fin tip area, as indicated by the dashed isotherm for 109.5 °C which meets the channel bottom near the location of (x,y,z) = (2.9,0.15,0). As the fin length decreases, the boiling heat transfer increases significantly. The heat transfer enhancement at Lfin = 0.05 is 77% when based on Abot and 33% when based on Atot. In this study, efforts are made to enhance boiling heat transfer by further modifying the fin surface configuration. The fins are segmented so that the fluid–solid contact area increases. Two types of segmented fins are tested: single-segmented fins of Wfin = 0.3 and doublesegmented fins of Wfin = 0.1 and Gfin = 0.1, where Wfin is the width of fin segment and Gfin is the gap between the fin segments. Fig. 10 presents the bubble shapes and temperature fields for segmented fins while keeping Hfin = 0.03 and Sfin = Lfin = 0.1. Compared with the case of no-segmented fins depicted in Fig. 6, the liquid–vapor–solid contact regions increase with segmented fins. The heat transfer enhancement is more pronounced with the single-segmented fins than with the
0
z
0.24 -0.24
0
0.24
z
Fig. 9. Effect of fin length on bubble shape and temperature field at t = 3 for Hfin = 0.03 and Sfin = 0.1: (a) Lfin = 0.05 and (b) Lfin = 0.2.
double-segmented fins. This indicates that the fin segmentation near the sidewalls (z = ± 0.2), which enlarges the liquid layers forming between the bubble and the channel corners, is more effective in the boiling heat transfer enhancement than the segmentation near the channel center (z = 0). The heat transfer enhancement for the single-segmented fins is 68% when based on Abot and 35% when based on Atot. This enhancement is much larger in comparison with the case of no-segmented fins. 4. Conclusions Direct numerical simulations of flow boiling in a microchannel with transverse fins were performed by employing a sharp-interface level-set method. The computational results showed that the flow boiling in a microchannel was significantly enhanced when the liquid– vapor–solid interface contact region increased with the addition of fins. The boiling heat transfer was pronounced when the fin height was 0.03 mm and the fin length was decreased. The fin segmentation near the sidewalls was effective in boiling heat transfer enhancement by enlarging the liquid layers forming between the bubble and the channel corners. The boiling heat transfer in the finned microchannel was enhanced up to 77% based on the bottom surface area and 33% based on the total fin surface area. Direct numerical simulation based on the present numerical method will help to develop the optimal fin configurations for microchannel flow boiling under various conditions without conducting excessive experiments.
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W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
funded by the MEST (Ministry of Education, Science and Technology) of the Korean government (Grant code: M20702040003-08M0204-00310).
z = 0.00
0.32
y
a
References
0.00 2.5
3.0
3.5
x x = 2.85
y
0.32
x = 2.95
0.16 109.5
0.00 109.9 -0.24
0
0.24
-0.24
z
b
0
0.24
z z = 0.10
y
0.32
0.00 2.5
3.5
x
x = 2.85
0.32
y
3.0
x = 2.95
0.16 109.5
0.00 109.9 -0.24
0
z
0.24
-0.24
0
0.24
z
Fig. 10. Bubble shape and temperature field at t = 3 with segmented fins of Hfin = 0.03 and Sfin = Lfin = 0.1: (a) single-segmented fins of Wfin = 0.3 and (b) double-segmented fins of Wfin = 0.1 and Gfin = 0.1.
Acknowledgments This work was supported by the Nuclear Research & Development Program of the NRF (National Research Foundation of Korea) grant
[1] S.G. Kandlikar, Fundamental issues related to flow boiling in minichannels and microchannels, Experimental Thermal and Fluid Science 26 (2002) 389–407. [2] J.R. Thome, Boiling in microchannels: a review of experiment and theory, International Journal of Heat and Fluid Flow 25 (2004) 128–139. [3] S.G. Kandlikar, W.K. Kuan, D.A. Willistein, J. Borrelli, Stabilization of flow boiling in microchannels using pressure drop elements and fabricated nucleation sites, Journal of Heat Transfer 138 (2006) 389–396. [4] C.-J. Kuo, Y. Peles, Local measurement of flow boiling in structured surface microchannels, International Journal of Heat and Mass Transfer 50 (2007) 4513–4526. [5] H.T. Phan, Effects of nano-and micro-surface treatments on boiling heat transfer, Ph.D. thesis, Grenoble University, France, 2010. [6] G.H. Klein, J.W. Westwater, Heat transfer from multiple spines to boiling liquids, AICHE Journal 17 (1971) 1050–1056. [7] K.N. Rainey, S.M. You, Pool boiling heat transfer from plain and microporous, square pin-finned surfaces in saturated FC-72, Journal of Heat Transfer 122 (2000) 509–516. [8] J.J. Wei, H. Honda, Effects of fin geometry on boiling heat transfer from silicon chips with micro-pin-fins immersed in FC-72, International Journal of Heat and Mass Transfer 46 (2003) 4059–4070. [9] C.K. Yu, D.C. Lu, T.C. Cheng, Pool boiling heat transfer on artificial micro-cavity surfaces in dielectric fluid FC-72, Journal of Micromechanics and Microengineering 16 (2006) 2092–2099. [10] D. Cooke, S.G. Kandlikar, Pool boiling heat transfer and bubble dynamics over plain and enhanced microchannels, Journal of Heat Transfer 133 (2011) 052902. [11] A. Kosar, Y. Peles, Boiling heat transfer in a hydrofoil-based micro pin fin heat sink, International Journal of Heat and Mass Transfer 50 (2007) 1018–1034. [12] S. Krishnamurthy, Y. Peles, Flow boiling on micropin fins entrenched inside a microchannel-flow patterns and bubble departure diameter and bubble frequency, Journal of Heat Transfer 132 (2010) 041002. [13] A. Ma, J. Wei, M. Yuan, J. Fang, Enhanced flow boiling heat transfer of FC-72 on micro-pin-finned surfaces, International Journal of Heat and Mass Transfer 52 (2009) 2925–2931. [14] D.A. McNeil, A.H. Raeisi, P.R. Bobbili, A comparison of flow boiling heat-transfer in in-line mini pin fin and plane channel flows, Applied Thermal Engineering 30 (2010) 2412–2425. [15] A. Mukherjee, S.G. Kandlikar, Numerical simulation of growth of a vapor bubble during flow boiling of water in a microchannel, Microfluidics and Nanofluidics 1 (2005) 137–145. [16] W. Lee, G. Son, Bubble dynamics and heat transfer during nucleate boiling in a microchannel, Numerical Heat Transfer Part A 53 (2008) 1074–1090. [17] Y. Suh, W. Lee, G. Son, Bubble dynamics, flow, and heat transfer during flow boiling in parallel microchannels, Numerical Heat Transfer Part A 54 (2008) 390–405. [18] W. Lee, G. Son, J.J. Jeong, Numerical analysis of bubble growth and departure from a microcavity, Numerical Heat Transfer Part B 58 (2010) 323–342. [19] W. Lee, G. Son, H.Y. Yoon, Numerical study of bubble growth and boiling heat transfer on a microfinned surface, International Communications in Heat and Mass Transfer 39 (2012) 52–57.
Contents lists available at SciVerse ScienceDirect
International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Direct numerical simulation of flow boiling in a finned microchannel☆ Woorim Lee a, Gihun Son a,⁎, Han Young Yoon b a b
Department of Mechanical Engineering, Sogang University, Seoul, South Korea Korea Atomic Energy Research Institute, Daejeon, South Korea
a r t i c l e
i n f o
Available online 31 August 2012 Keywords: Direct numerical simulation Finned surface Flow boiling Level-set method Microchannel
a b s t r a c t Direct numerical simulations of bubble growth and heat transfer associated with flow boiling in a finned microchannel are performed by solving the conservation equations of mass, momentum and energy in the liquid and vapor phases. The phase interfaces are determined by a sharp-interface level-set method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on the immersed solid surface of fins. The effects of fin height, spacing, and length on the flow boiling in a microchannel are investigated to find the better conditions for heat transfer enhancement. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Flow boiling in a microchannel, which is an attractive cooling method for high-power micro devices, has been studied extensively, as reviewed by Kandlikar [1] and Thome [2]. The boiling heat transfer can be further increased by surface modification with micromachined or MEMS fabricated structures [3–5]. In this study, we focus on a finned surface, which is one of the most popular heat transfer enhancement methods. The applications of fins for heat transfer augmentation in pool boiling were investigated by a number of researchers [6–10]. However, only a few studies were conducted for boiling heat transfer enhancement in a microchannel because of the technological difficulties in obtaining detailed measurements of boiling characteristics occurring on microscale structures. Kosar and Peles [11] investigated flow boiling of R-123 in a finned microchannel of 1.8 mm × 0.243 mm in width and height. The microchannel included 20 arrays of hydrofoil pin fins with 0.1 mm width, 0.243 mm height, and 0.5 mm length. Their experimental data showed three flow pattern regions, such as bubbly flow, wavy intermittent flow, and spray-annular flow, depending on the heat flux and mass velocity. Subsequently, Krishnamurthy and Peles [12] studied flow boiling of HFE-7000 in five parallel 0.2 mm × 0.243 mm channels. Each channel contained a single row of circular pin fins of 0.1 mm diameter, 0.243 mm height, and 0.4 mm pitch. They visualized the existence of bubbly flow, multiple flow, and wavy-annular flow. As the bubbles which nucleated on the channel sidewalls and the pin fin
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author at: Department of Mechanical Engineering, Sogang University, Shinsu-dong, Mapo-ku, Seoul 121-742, South Korea. E-mail address: [email protected] (G. Son). 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.icheatmasstransfer.2012.08.005
surface moved downstream and grew into vapor slugs, bubbly flow developed into multiple flow including vapor slugs as well as bubbles. The multiple flow further evolved into wavy-annular flow, in which thin wavy liquid layers formed along the channel sidewalls and the pin fins while the vapor phase occupied most of the cross-section of the microchannel. Some efforts to enhance boiling heat transfer by fins were reported for minichannel flows rather than microchannel flows. Ma et al. [13] investigated flow boiling of FC-72 on 10 mm square and 0.5 mm high chips which were placed in a 30 mm × 5 mm channel. The chips had square pin fins of 0.03 mm width, 0.06 and 0.12 mm heights, and 0.03 mm spacing. Boiling heat transfer was significantly increased by the addition of fins and further enhanced by increasing the fin height. McNeil et al. [14] studied flow boiling of R-113 on a 50 mm square plate. The plate contained square pin fins of 1 mm width, 1 mm height, and 2 mm pitch. The heat transfer coefficients normalized by the fluid–solid contact area were slightly increased on the pin finned surface, and thus the boiling heat transfer was improved by the pin fins due to the increased heat transfer area. As another way to analyze the boiling phenomena in a microchannel, direct numerical simulation of the bubble dynamics and boiling heat transfer was reported in the literature. Mukherjee and Kandlikar [15] simulated bubble growth during flow boiling in a microchannel by using a level-set (LS) method. The effects of incoming liquid superheat and Reynolds number on the bubble growth rate were investigated. Lee and Son [16] applied the LS method to computation of the bubble dynamics and heat transfer in a microchannel. They demonstrated that the heat transfer rate increased significantly when the channel size was smaller than the bubble departure diameter. The heat transfer rate was observed to depend on a contact angle which determined the existence of a liquid layer forming between the bubble and the channel corner. Subsequently, Suh et al. [17] extended the LS method to flow boiling in parallel microchannels. Their numerical results showed that
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
Nomenclature cp F g Gfin h hlv H L _ m n p S Sfin t T u U vlv W x, y, z
specific heat fraction function gravity gap between the fin segments grid spacing latent heat of vaporization height length mass flux across the interface unit normal vector pressure sign function fin spacing time temperature flow velocity vector interface velocity vector ρv−1 − ρl−1 width Cartesian coordinate
Greek symbols α step function βT coefficient of thermal expansion κ interface curvature λ thermal conductivity μ dynamic viscosity θ contact angle ρ density σ surface tension coefficient τ artificial time τw waiting period ϕ distance function from the liquid–vapor interface ψ distance function from the fluid–solid interface
Subscripts c channel f fluid fin fin l, v liquid, vapor s solid sat saturation w wall
the backward bubble expansion to the channel inlet causing reverse flow became more pronounced when the contact angle decreased and the wall superheat increased. The backward bubble growth pattern reduced the boiling heat transfer rate in multiple microchannels compared to that in a single microchannel. The past numerical computations were limited to flow boiling in a simple geometry of microchannel. In this study, direct numerical simulations are performed for bubble growth and heat transfer in a finned microchannel. The phase interfaces are determined by a sharp-interface LS method which is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip and contact-angle conditions on immersed solid surface of fins. The effects of fin height, spacing, and width on the bubble growth and heat transfer in a microchannel are investigated to find the better conditions for heat transfer enhancement.
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2. Numerical analysis The present numerical approach is based on the sharp-interface LS formulation developed by Lee et al. [18,19] for computation of pool boiling on microstructured surfaces. The method is extended to threedimensional computation of flow boiling in a finned microchannel. Fig. 1 shows the configuration used for computation of bubble growth and heat transfer in a finned microchannel. The flows are taken to be laminar and the fluid properties including density, viscosity, specific heat and thermal conductivity are assumed to be constant in each phase. The liquid–vapor interface is determined by the LS function ϕ, which is defined as a signed distance from the interface. The negative sign is chosen for the vapor phase and the positive sign for the liquid phase. To treat the immersed solid surface of fins, we use another LS function ψ, which is defined as a signed distance from the fluid–solid interface. The negative sign is chosen for the solid region and the positive sign for the fluid region. The conservation equations of mass, momentum and energy for the whole region including liquid, vapor and solid phases are written as _ ∇·u ¼ α ψ vlv mn·∇α ϕ ∂u ¼ −α ψ ∇p þ ∇·μ e ∇u þ α ψ f ∂t
ð1Þ if ψ > 0
ð2Þ
u¼0
if ψ≤0
ð3Þ
∂T ρcp ¼ −α ψ ρcp ul ·∇T þ ∇·λe ∇T e ∂t l
if ϕ > 0 or ψ≤0
ð4Þ
T ¼ T sat
if ϕ ≤0 and ψ > 0
ð5Þ
ρe
where α ϕ=ψ ¼ 1 if ϕ=ψ > 0 ¼ 0 if ϕ=ψ≤0 _ ¼ n·λe ∇T=hlv m n ¼ ∇ϕ=j∇ϕj κ ¼ ∇·ð∇ϕ=j∇ϕjÞ
Fig. 1. Configuration used for computation of flow boiling in a finned microchannel.
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_ 2 ∇α ϕ f ¼ −ρe uf ·∇uf þ ρe ½1−βT ðT−T sat Þg− σ κ−vlv m h T i _ _ þ∇·μ e ð∇uÞT −∇·μ e vlv mn∇α ϕ þ vlv mn∇α ϕ
Here h is a grid spacing and the formulation of sign function S implies that a near-zero level set rather than ϕ = 0 is used as the immobile boundary condition during the reinitialization procedure. The boundary conditions used in this study are as follows (refer to Fig. 1). At the inlet (x = 0),
_ 1−α ϕ ul ¼ u þ vlv mn _ uv ¼ u−vlv mnα ϕ
u ¼ uin
ρe ¼ ρv 1−F ϕ þ ρl F ϕ −1
−1
−1 −1 ¼ λl F ϕ F ψ þ λs 1−F ψ
λe
p¼0
l
u¼0
s
Here, uf (ul or uv) is the velocity for each phase which is extrapolated into the entire domain by using the velocity jump condition at _ the interface, ul ¼ uv þ vlv mn. The effective properties, ρe, μe and λe, are evaluated from the fraction functions, Fϕ and Fψ, which are defined as Fϕ ¼ 1 ¼0 ¼
∂ϕ ¼ 0: ∂x
ð13Þ
ð14Þ
T ¼ Tw
∂ϕ ¼ − cosθ: ∂y
ð15Þ
At the top wall surface (y = Hb + Hc), u¼0
∂T ¼0 ∂y
∂ϕ ¼ cosθ: ∂y
ð16Þ
At the plane of symmetry (z = 0),
if α ϕ ðϕA Þ ¼ α ϕ ðϕB Þ ¼ 1 if α ϕ ðϕA Þ ¼ α ϕ ðϕB Þ ¼ 0
maxðϕA ; ϕB Þ maxðϕA ; ϕB Þ−minðϕA ; ϕB Þ
∂u ∂T ∂ϕ ¼ ¼ ¼ 0: ∂x ∂x ∂x
At the bottom wall surface (y = 0),
1−α ψ : ρcp ¼ ρcp α ψ þ ρcp e
T ¼ T sat
At the outlet (x = L),
−1 −1 ¼ μ v 1−F ϕ F ψ þ μ l F ϕ F ψ
μe
v¼w¼0
w¼0
otherwise
where the subscripts A and B denote the grid points adjacent to the location where Fϕ is evaluated. The heat flux from a liquid microlayer, which forms between the bubble and the wall near the bubble surface– wall contact location, can be formulated as proposed in [18]. In the LS formulation, the interface is described as ϕ = 0. The level sets including ϕ = 0 are advanced as
∂u ∂v ∂T ∂ϕ ¼ ¼ ¼ ¼ 0: ∂z ∂z ∂z ∂z
ð17Þ
At the side wall surface (z = Wc/2 + Ws), u¼0
∂T ¼0 ∂z
∂ϕ ¼ cosθ: ∂z
ð18Þ
where the interface velocity U and the unit normal vector ns pointing into the solid region are written as
The numerical method was tested in our previous study [16] through the computations of flow boiling in a plain microchannel. The numerical results showed good agreement with the experimental data available in the literature. Also, a convergence test for grid resolutions was made in our previous study [18] for bubble growth on a horizontal surface with a cavity by using two different grid spacings of h = 0.01 mm and h = 0.005 mm. The bubble growth rates and the bubble shapes at departure obtained with both grids showed no significant differences. Therefore the present computations are conducted with h = 0.01 mm to save computing time without losing accuracy of numerical results.
_ U ¼ uf þ mn=ρ f
ð8Þ
3. Results and discussion
ns ¼ −∇ψ=j∇ψj:
ð9Þ
∂ϕ ¼ −U·∇ϕ ∂t
if ψ > 0
ð6Þ
∂ϕ ¼ cosθ−ns ·∇ϕ ∂τ
if ψ≤0
ð7Þ
The contact angle condition, ns ⋅ ∇ ϕ = cosθ, defined at the liquid– vapor–solid contact location is extended into the entire solid region by employing the iterative equation. The non-zero level sets are reinitialized (or reconstructed) as a distance (| ∇ ϕ| = 1) from the interface by obtaining a steady-state solution of the equation ∂ϕ ¼ SðϕÞð1−j∇ϕjÞ ∂τ
ð10Þ
where SðϕÞ ¼ 0 ϕ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ϕ2 þ h2
if jϕj < h=2
ð11Þ
otherwise:
ð12Þ
Numerical simulations of flow boiling in a finned microchannel are performed using the properties of saturated water at 1 atm and a constant contact angle of 40 ∘. In presenting the results including figures, lengths are scaled by 1 mm and time by 1 ms. We choose a computational domain of 0 ≤ x ≤ 4, 0 ≤ y ≤ 0.32 and 0 ≤ z ≤ 0.24, (L = 4, Hc + Hb = 0.32, 0.5Wc + Ws = 0.24), as depicted in Fig. 1. The domain includes fins and bottom and side walls of y ≤ 0.12 and z ≥ 0.2 (Hb = 0.12, 0.5Wc = 0.2, Ws = 0.04). The conduction heat transfer through the solid region is also solved with the thermal properties of ρcp s ¼ 0:85 ρcp l and λs = 230λl. At the bottom surface of the computational domain, the temperature is specified as Tw = 110 °C. Also, we use a uniform velocity of uin = 0.3 m/s at the channel inlet. The initial velocity and the temperature fields for computation of bubble growth are taken from the steady-state solution for single-phase liquid flow without including bubble nucleation, which is obtained numerically. In this study, we assume that a single bubble nucleation site is located on the channel bottom surface near the inlet, (x,y,z) = (0.5,Hb,0). A small bubble, whose shape is a truncated
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
a
a
z=0
0.32
y
Bubble 0.16
Solid
0.00 2.5
3.0
y
0.16
0.00 -0.24
b
3.5
x x = 3.0
0.32
y
0
z
0.24
z=0
0.32
0.16 109.9
0.00 2.5
3.0
3.5
x x = 3.0
0.32
y
sphere with a radius of 0.03 that satisfies a specified contact angle at the liquid–vapor–solid contact line, is placed on the nucleation site. To simulate the cyclic process of bubble growth, a new bubble is placed on the nucleation site when it is occupied by a superheated liquid (T > Tsat) during the waiting period τw for bubble generation. We use τw = 4. First, computation is performed for flow boiling in a microchannel without fins. The result for bubble growth is plotted in Fig. 2. The initial bubble grows to occupy the entire cross-section of the channel, and then it expands along the channel and develops into an elongated vapor slug, as observed in slug or annular flows. When the bubble nucleation site is covered by a superheated liquid during the waiting period of τw = 4, a new bubble is placed on the nucleation site. As the new bubble grows along the channel, the previously generated vapor slug is quickly pushed outward. The bubble growth pattern including slug formation and expansion repeats all over again with the new bubble. Fig. 3 shows the temperature field associated with the bubble growth in a microchannel without fins. The solid lines in the figure represent the isotherms of 103, 106 and 109 °C while the dashed lines represent the isotherms of 109.5 and 109.9 °C. The isotherms are crowded in the liquid layers forming near the liquid–vapor–solid contact lines, as seen near the location of (x,y,z) = (2.9,0.12,0) at t = 1.5 and the locations of (x,y,z) = (3.0, 0.12, ± 0.16) and (x,y,z) = (3.0, 0.21, ± 0.2) at t = 3. This indicates that the high heat transfer occurs in those regions. It is observed from the temporal variation of the isotherms in the cross-section of x = 3.0 that the isotherms are more closely packed at t = 3, when the vapor slug further expands to occupy the entire cross-section of the channel, than at t = 1.5. The dashed line for T = 109.9 °C is seen to move down to the bottom wall surface (y = 0), which results in the increased wall heat flux. It is also noted that the dry region, where the wall is in direct contact with the vapor, forms on the channel bottom surface while thin liquid layers exist between the bubble and the channel corner, as seen at t = 3. In the computations of flow boiling in a microchannel with fins, we vary parametrically fin height Hfin, fin spacing Sfin, and fin length Lfin (refer to Fig. 1). The transverse fins are placed in the region of 1 ≤ x ≤ 4. The results with fins of Hfin = 0.05 and Sfin = Lfin = 0.1 are presented in Figs. 4 and 5. The bubble growth at t = 1.5 is observed to be faster in the finned microchannel than in the plain microchannel. While the liquid–vapor interface slides on the fin tips
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0.16 109.5 109.9
0.0 -0.24
0
z
0.24
Fig. 3. Temperature field in a microchannel without fins: (a) t = 1.5 and (b) t = 3.0.
with bubble growth and vapor slug expansion, liquid is trapped between the fins, as seen in Fig. 4(b). This indicates that the liquid– vapor interface contacts the finned surface at more locations and
a t = 1.3
t = 1.3
1.5
1.5
3.0
3.0
5.0
5.0
b
b
t = 1.3
t = 1.3
1.5
1.5
3.0
3.0
5.0
0
1
2
3
4
0.00
x Fig. 2. Bubble growth in a microchannel without fins: (a) top view and (b) cross-sectional view at z=0.
0.32 5.0
y
y
0.32 0
1
2
3
4
0.00
x Fig. 4. Bubble growth in a microchannel with fins of Hfin = 0.05 and Sfin = Lfin = 0.1: (a) top view and (b) cross-sectional view at z = 0.
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W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
z = 0.00
y
0.32
0.16
0.00
z = 0.18
y
0.32
0.16 109.5 109.9
0.00 2.5
3.0
x = 3.05
0.32
y
3.5
x
x = 3.15
0.16 109.5 109.9
0.00 -0.24
0
z
0.24 -0.24
0
z
0.24
Fig. 5. Temperature field at t=3 in a microchannel with fins of Hfin =0.05 and Sfin =Lfin =0.1.
hence the high heat transfer area occupied by thin liquid layers increases. In Fig. 5, the liquid layers between the fins are observed to be thin near the channel center (z = 0) and become thicker near the channel sidewalls. The liquid–vapor–solid contact regions increase also on the sidewalls, as seen in the cross-sections of x = 3.05 (fin region) and x = 3.15 (interfin region). This results in the increased wall heat flux in comparison with the plain microchannel. Fig. 6 shows the bubble shape and the associated temperature field when the fin height is reduced to Hfin = 0.03 while keeping the
a
z = 0.00
160 Hfin = 0.00 0.03 0.05
120
q(W/cm2)
0.32
y
other parameters constant. In contrast to the case of Hfin = 0.05, the liquid–vapor interface for the shorter fins is seen to nearly touch the bottom wall in the interfin region. The closely spaced isotherms near the region reflect the higher heat transfer. The effect of fin height on the wall heat flux is plotted in Fig. 7. The heat flux is averaged over the heating surface of 1 ≤ x ≤ 4, except the channel entrance region where the heat transfer is strongly affected by the inlet boundary condition. The area-averaged heat flux initially increases as the bubble expands along the channel, and then it slightly decreases while the vapor slug leaves out of the computational domain. Thereafter, the heat flux variation pattern repeats all over again with a new bubble. The wall heat fluxes for different fin heights are averaged over the computational time of 2 ≤ t ≤ 12, except the early period when the heat transfer is influenced by the specified initial condition, and compared in Fig. 7(b). The area and time averaged wall heat fluxes are normalized by qw,o for a plain microchannel, whose value is 60.3 W/cm 2. The heat transfer enhancement (qw/qw,o − 1) averaged over the bottom surface area Abot is attributed to the increased heat transfer area as well as the fin structure. To solely account for the contribution of fin structure on the boiling enhancement, we also include the heat transfer enhancement averaged over the total finned surface area Atot. The heat transfer enhancement is maximum at Hfin = 0.03, and its value is 51% when based on Abot and 21% when based on Atot. Fig. 8 presents the bubble shapes and temperature fields for Sfin = 0.05 and Sfin = 0.2. The difference between both results is pronounced in the interfin region rather than in the fin region. For Sfin = 0.05, the bubble surface hardly expands into the narrow interfin region. However, when the fin spacing is increased to 0.2, the bubble surface moves into the interfin region and touches the bottom wall. As a result, the heat flux increases near the liquid–vapor–solid (or three-phase) contact regions, in which thin liquid layers form, whereas the heat flux decreases near the dry regions surrounded by the three-phase contact lines. The heat transfer enhancement based on the total finned surface area Atot increases with fin spacing. This indicates that the wider fin spacing is more effective in improving boiling heat transfer.
0.16
80 40
0.00
z = 0.18
0.32
0
0
4
8
12
y
t(ms) 0.16
b
2.0
109.5
3.0
3.5
x
x = 3.05
0.32
y
Abot Atot
109.9
1.6
qw / qplain
0.00 2.5
x = 3.15
1.2
0.16 0.8
109.5 109.9
0.00 -0.24
0
z
0.24
-0.24
0
0.24
z
Fig. 6. Bubble shape and temperature field at t = 3 with shorter fins of Hfin = 0.03 and Sfin = Lfin = 0.1.
0.00
0.02
0.04
0.06
Hfin Fig. 7. Effect of fin height on heat transfer for Sfin = Lfin = 0.1: (a) area-averaged wall heat flux and (b) heat transfer enhancement.
W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
a 0.16
0.00 2.5
z = 0.00
0.32
y
y
a
z = 0.00
0.32
3.0
0.16
0.00 2.5
3.5
3.0
x = 3.00
0.16
109.5
0.00 109.9 -0.24
109.9
0
0.24
-0.24
z
0.24
0.16
3.0
x = 3.00
0
0.24
z
0.16
3.0
3.5
y
x = 3.05
x = 2.90
0.32
0.16
0.16 109.5
109.5 109.9
0.00 -0.24
-0.24
x
x = 2.85
0.32
0.24
z = 0.00
0.32
0.00 2.5
3.5
x
0
z
b
z =0.00
0.32
0.00 2.5
y
0
z
y
y
b
x = 3.05
0.16
109.5
0.00 -0.24
x = 2.98
0.32
y
y
x = 3.07
3.5
x
x 0.32
1465
0
z
0.24
-0.24
0
0.24
0.00 -0.24
109.9
z
Fig. 8. Effect of fin spacing on bubble shape and temperature field at t = 3 for Hfin = 0.03 and Lfin = 0.1: (a) Sfin = 0.05 and (b) Sfin = 0.2.
However, the fin configuration reduces the number of fins to be added to the fixed area and hence the heat transfer area. When based on the bottom surface area Abot, the heat transfer enhancement weakly depends on fin spacing and has a maximum value of 51% at Sfin = 0.1. Fig. 9 shows the bubble shapes and temperature fields for Lfin = 0.05 and Lfin = 0.2. When the fin length is decreased to 0.05 and the number of fins is increased, the liquid–vapor interface contacts the finned surface at more locations than the case of Lfin = 0.1 depicted in Fig. 6, and hence the high heat transfer area including thin liquid layers increases. However, for Lfin = 0.2, the dry (or hot spot) region expands on the increased fin tip area, as indicated by the dashed isotherm for 109.5 °C which meets the channel bottom near the location of (x,y,z) = (2.9,0.15,0). As the fin length decreases, the boiling heat transfer increases significantly. The heat transfer enhancement at Lfin = 0.05 is 77% when based on Abot and 33% when based on Atot. In this study, efforts are made to enhance boiling heat transfer by further modifying the fin surface configuration. The fins are segmented so that the fluid–solid contact area increases. Two types of segmented fins are tested: single-segmented fins of Wfin = 0.3 and doublesegmented fins of Wfin = 0.1 and Gfin = 0.1, where Wfin is the width of fin segment and Gfin is the gap between the fin segments. Fig. 10 presents the bubble shapes and temperature fields for segmented fins while keeping Hfin = 0.03 and Sfin = Lfin = 0.1. Compared with the case of no-segmented fins depicted in Fig. 6, the liquid–vapor–solid contact regions increase with segmented fins. The heat transfer enhancement is more pronounced with the single-segmented fins than with the
0
z
0.24 -0.24
0
0.24
z
Fig. 9. Effect of fin length on bubble shape and temperature field at t = 3 for Hfin = 0.03 and Sfin = 0.1: (a) Lfin = 0.05 and (b) Lfin = 0.2.
double-segmented fins. This indicates that the fin segmentation near the sidewalls (z = ± 0.2), which enlarges the liquid layers forming between the bubble and the channel corners, is more effective in the boiling heat transfer enhancement than the segmentation near the channel center (z = 0). The heat transfer enhancement for the single-segmented fins is 68% when based on Abot and 35% when based on Atot. This enhancement is much larger in comparison with the case of no-segmented fins. 4. Conclusions Direct numerical simulations of flow boiling in a microchannel with transverse fins were performed by employing a sharp-interface level-set method. The computational results showed that the flow boiling in a microchannel was significantly enhanced when the liquid– vapor–solid interface contact region increased with the addition of fins. The boiling heat transfer was pronounced when the fin height was 0.03 mm and the fin length was decreased. The fin segmentation near the sidewalls was effective in boiling heat transfer enhancement by enlarging the liquid layers forming between the bubble and the channel corners. The boiling heat transfer in the finned microchannel was enhanced up to 77% based on the bottom surface area and 33% based on the total fin surface area. Direct numerical simulation based on the present numerical method will help to develop the optimal fin configurations for microchannel flow boiling under various conditions without conducting excessive experiments.
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W. Lee et al. / International Communications in Heat and Mass Transfer 39 (2012) 1460–1466
funded by the MEST (Ministry of Education, Science and Technology) of the Korean government (Grant code: M20702040003-08M0204-00310).
z = 0.00
0.32
y
a
References
0.00 2.5
3.0
3.5
x x = 2.85
y
0.32
x = 2.95
0.16 109.5
0.00 109.9 -0.24
0
0.24
-0.24
z
b
0
0.24
z z = 0.10
y
0.32
0.00 2.5
3.5
x
x = 2.85
0.32
y
3.0
x = 2.95
0.16 109.5
0.00 109.9 -0.24
0
z
0.24
-0.24
0
0.24
z
Fig. 10. Bubble shape and temperature field at t = 3 with segmented fins of Hfin = 0.03 and Sfin = Lfin = 0.1: (a) single-segmented fins of Wfin = 0.3 and (b) double-segmented fins of Wfin = 0.1 and Gfin = 0.1.
Acknowledgments This work was supported by the Nuclear Research & Development Program of the NRF (National Research Foundation of Korea) grant
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