Critical heat flux enhancement of pool boiling with adaptive fraction control of patterned wettability

International Journal of Heat and Mass Transfer 96 (2016) 504–512

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Critical heat flux enhancement of pool boiling with adaptive fraction control of patterned wettability Jung Shin Lee, Joon Sang Lee ⇑ School of Mechanical Engineering, Yonsei University, Seoul, Republic of Korea

a r t i c l e

i n f o

Article history: Received 29 May 2015 Received in revised form 25 November 2015 Accepted 16 January 2016

Keywords: Critical heat flux Patterned wettability Boiling heat transfer Pool boiling Adaptive control of area fraction

a b s t r a c t Conventional patterned wettability with a periodic checkerboard pattern shows intermediate critical heat flux (CHF) between uniform hydrophilic and hydrophobic surfaces. To solve this high superheat problem and maintain the high CHF, we propose adaptive fraction control of the pitch of hydrophobic dots. With actual heat source, the temperature distribution is the highest at the center and decreases as the radius from the center increases. Patterned wettability in the high temperature region is created with a low area fraction of hydrophobic dots, while the area fraction gradually increases with distance from the center. Using this adaptive fraction control, CHF can be avoided in the center region and superheat can be dropped for nucleation in the outer region at low temperature. However, if the concentration gradient of hydrophobic dots is too large, nucleation at the center of surface will be suppressed and boiling crisis will occur in the outer region. Therefore we also optimized the concentration of hydrophobic dots with respect to CHF and start of nucleation. In this research, a multiphase single component lattice Boltzmann model was used for the simulation. The simulation model is modified to establish heterogeneous wettability. The effects of size and concentration of hydrophobic dots are analyzed by observing the tendency of CHF, superheat, and local Nusselt number. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Numerous parametric studies have been carried out on enhancing the heat transfer rate of boiling heat transfer (BHT) for applications in thermal energy transfer devices. The most commonly used parameters are roughness [1,2], surface energy [3–5], and capillarity [6–8]. A single terminology which represents these parameters is the wettability, while the main performance indicators are heat transfer coefficient (HTC) and critical heat flux (CHF) [3–9]. Costello and Frea [9] optimized the capillary wicking in pool boiling. High capillarity for water makes a good capillary feeding system, providing a higher CHF. However, the optimization strategy was performed only for the system geometry but not the wettability of the surface. Chowdhury and Winterton [10] investigated the effect of roughness and surface energy individually. HTC of pool boiling increased with surface roughness, while higher wettability due to surface energy modification increased CHF. However, a detailed theoretical description was insufficient in this study. Yang and Kim [11] described how to predict nucleation site density on a specific surface, and showed an example of mathematical ⇑ Corresponding author at: School of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea. E-mail address: [email protected] (J.S. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.01.044 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

modeling for nucleation site density in pool boiling. Their work provided theoretical support on the wettability effect of pool boiling. However, homogeneous wetting surfaces have clear disadvantages. A hydrophilic surface has higher superheat than a hydrophobic surface, and a hydrophobic surface has lower CHF than a hydrophilic surface [12–14]. Therefore, patterned wettability has been studied to develop a surface superior in both CHF and superheat. After the study of Takata et al. [15], patterned wettability has been studied to uncover the correlation between CHF, superheat, and parameters of a pattern. Experimental work of Nam et al. [16] proved that nucleation speed of patterned wettability is faster than homogeneous wettability while reported superheat is reduced. However, the patterned wettability is not remarkably better than homogeneous wettability for CHF. Results of the experimental work by Takata et al. [15], who performed the boiling experiment on the checkerboard pattern of wettability, show that transition from nucleate boiling to filmwise boiling should be faster than on a hydrophilic surface. Jo et al. [17] proved that the CHF of patterned wettability is the same or less than on a hydrophilic surface. From the research above, patterned wettability is composed of hydrophobic dots placed on hydrophilic bases [18]. Heat transfer rate depends on the geometrical parameters of this pattern, such

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as the fraction of hydrophobic area to total area [19], the number of hydrophobic dots, or the size of the hydrophobic dots [17]. If the dots are too big or if the pitch is too short, the surface would act like a hydrophobic surface and the heat transfer rate of the surface will be smaller than that of a bare hydrophilic surface [19]. Even if the dots are small, a long pitch would be not much different than the case of a bare hydrophilic surface [19]. Therefore, patterned wettability is not a perfect solution for CHF. Thanks to the contribution of previous parametric studies, a new design theory is evolving. Small dot size, lots of dots and optimized pitch allow high CHF [15–19]. However, this solution is insufficient. In real applications, the temperature distribution is not homogeneous. In most cases where the temperature distribution is co-axial, a hot spot is located at the center of the surface, and the marginal region of the surface has a lower temperature than the center. This indicates that if parameters of patterned wettability were optimized only for the center of the temperature field, patterned wettability would not be optimized for the marginal region of the surface and therefore shows weak boiling. To overcome this insufficient optimization, we propose adaptive fraction control of hydrophobic dots. The adaptive fraction control is set to be dependent on the radial distance from the center. The fraction of hydrophobic dots at the center is low, which should increase CHF, while the fraction of hydrophobic dots in the marginal region is high to increase the frequency of nucleation. By this optimization method, the overall CHF and superheat should be enhanced.

eq

eq

Df i ðx; tÞ ¼ f i ðqðx; tÞ; u þ DuÞ  f i ðqðx; tÞ; uÞ:

ð7Þ

The velocity change Du ¼ F  dt=q is given by force F:

F ¼ F int ðxÞ þ F s ðxÞ þ F g ðxÞ;

ð8Þ

where Fint is the interparticle interaction force which is given by

X F int ðxÞ ¼ bwðxÞ Gðx; x0 Þwðx0 Þðx0  xÞ 0

 1b 2

Xx Gðx; x0 Þw2 ðx0 Þðx0  xÞ:

ð9Þ

x0

b is selected from the numerical work of Gong et al. [22]. G(x, x0 ) has a non-zero value when x and x0 adjust to each other:

8 0 1; > < g 1 ; jx  x j ¼ p ffiffiffi Gðx; x0 Þ ¼ g 2 ; jx  x0 j ¼ 2; > : 0; otherwise;

ð10Þ

where g1 = g0, g2 = g0/2 for the D3Q19 scheme. The effective mass pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wðxÞ ¼ 2fpðxÞ  qðxÞg=ð6gÞ is based on the Peng–Robinson (P–R) equation of state as follows:

p¼

qRT aq2 /0 ðTÞ  ; 1  bq 1 þ 2bq  b2 q2

ð11Þ

where a = 0.45724R2Tc2/pc, b = 0.0778RTc/pc, and /0(T) are given by

h pffiffiffiffiffiffiffiffiffiffi i2 /0 ðTÞ ¼ 1 þ ð0:37464 þ 1:54226x  0:26992x2 Þð1  T=T c Þ ; ð12Þ

2. Numerical method In this section, we describe the modified pseudo-potential lattice Boltzmann method (LBM) model. This numerical method was proposed by Gong et al. [20]. Fluid is solved by stream and collision of distribution function. In our numerical approach, the Bhat nagar–Gross–Krook (BGK) collision operator was used:

1 eq f i ðx þ ei dt ; t þ dt Þ  f i ðx; tÞ ¼  ½f i ðx; tÞ  f i ðx; tÞ þ Df i ðx; tÞ;

s

g i ðx þ ei dt ; t þ dt Þ  g i ðx; tÞ ¼ 

1

sT

½g i ðx; tÞ  g eq i ðx; tÞ þ dt xi /:

ð1Þ ð2Þ

where fi, gi are density and temperature distribution function. Evolution of distribution functions depend on position x, time t, and relaxation times. s is the density relaxation time, and sT is the thermal relaxation time. Density and temperature equilibrium distribueq tion function feq i , and gi are given by eq fi

h

2

i

¼ xi q 1 þ 3ei  u þ 4:5ðei  uÞ  1:5u ; h

2

ð3Þ i

2 2 g eq i ¼ xi T 1 þ 3ei  ureal þ 4:5ðei  ureal Þ  1:5ureal :

ð4Þ

X F s ðxÞ ¼ wðxÞ g s xi sðx þ ei dt Þ  ei dt :

ð5Þ

½e0 ; e1 ; e2 ; e3 ; e4 ; e5 ; e6 ; e7 ; e8 ; e9 ; e10 ; e11 ; e12 ; e13 ; e14  2 3 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 6 7 ¼ 4 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 5: 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 ð6Þ The body force term is based on the exact difference method [21] as follows:

ð13Þ

i

Contact angles can be controlled by the fluid-solid interaction strength gs. s(x) is an indicator factor as follows



sðxÞ ¼

0;

x in fluid node;

ð14Þ

1; x in solid node:

The gravity force is given by

F g ðxÞ ¼ ½qðxÞ  qav e g;

ð15Þ

where g is the acceleration of gravity, and qave is the average density. The macroscopic equations for u, T, and q can be expressed as

q¼

X f i; i

qu ¼

X ei f i ;

T¼

i

X gi:

ð16Þ

i

The real fluid velocity ureal is obtained via force correction as follows

qureal ¼

The parameters xi, and ei are given as follows:

8 i ¼ 0; > < 1=3; xi ¼ 1=18; i ¼ 1; . . . ; 6; > : 1=36; i ¼ 7; . . . ; 18;

with x = 0.344 being the acentric factor. The wettability effect is implemented in Fs and it is given by

X dt ei f i þ F: 2 i

ð17Þ

The thermal source about the phase change / is given by

"

  # 1 @p /¼T 1 r  ureal : qcv @T q

ð18Þ

3. Results and discussion 3.1. Computation domain and patterned wettability designs In our numerical approach, the characteristic length unit L0 is capillary length, and characteristic time t0 is computed by L0 and acceleration of gravity g:

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sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L0 ¼

c

gðql  qg Þ

;

sffiffiffiffiffi L0 t0 ¼ ; g

ð19Þ

c is the surface tension of the gas-liquid interface, ql and qg are the liquid and gas phase densities of water at 100 °C and 1 atm. Normalized superheat T⁄, and heat flux Q00 are obtained by:

Fig. 2(a) shows the parametric conditions of the wettability pattern. The shape of the hydrophobic dots is square with the width of Ld. The groups of hydrophobic dots in Fig. 2(a) are used for imposing heterogeneity. Pn (n = 1  4) is set as the pitch length, which corresponds to group numbers n. The tuning method of Pn is explained in Eq. (21).

Pn ¼ P0 f1 þ Mpðn  1Þg; T ¼

ðT  T s Þ ; Tc

Q 00 ¼

QL0 ; kT c

ð20Þ

Ts is the saturation temperature, Tc is the critical temperature, and k is the thermal conductivity of liquid water at 100 °C and 1 atm. Fig. 1(a) is the explanation of simulation conditions with fluid and solid configuration. The boundary condition of the sidewall domain is the periodic boundary. The top of the domain is the convective boundary. The z direction length of the domain is Lh = 3.000L0. The condition for the top surface of the solid is illustrated in Fig. 1(b). Patterned wettability is placed in the square region on the center of the solid surface. The width of the patterned wettability region is Ls = 1.163L0. The other area of the solid surface is uniformly hydrophilic. Both x and y direction lengths of the domain are Lw = 3.200L0. The configuration of the condition for the bottom boundary is illustrated in Fig. 1(c). The center of the bottom boundary has a constant heat flux boundary. The shape of the constant heat flux boundary is square with a width of Lf = 1.282L0. The other region of the bottom boundary is adiabatic.

ðn ¼ 1  4Þ

ð21Þ

P0 is a reference pitch equal to 0.160L0. Mp is the pitch modification factor. The values of Mp are 0.00, 0.08, 0.15, and 0.22 as shown in Table 1. The surface in Fig. 2(a) is S10Mp00. The contact angles (CA) of the hydrophobic dots and the hydrophilic surface are the same as in Fig. 2(b) for all cases. These contact angles are same as those used in the experimental work of Jo et al. [19]. The surface material with CA = 123° is Teflon, and the surface material with CA = 54° is oxidized silicon. The surface configurations of other cases are illustrated in Fig. 2(c). 3.2. Validation of numerical model Before performing numerical simulations and analyzing boiling phenomena with different Mp, we validated our simulation according to the experimental work of Jo et al. [19]. S10Mp00 surface is used for the numerical simulation. Pitch and width of the hydrophobic dots are 0.160L0 and 0.040L0 respectably, and Mp is 0.00. The contact angles of hydrophobic dots and hydrophilic surface are 123° and 54°, respectably. As shown in Table 1, the pattern

Fig. 1. Simulation description: (a) Outline of whole domain, (b) x–y plane of z = Lt, (c) x–y plane of z = 0.

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507

Fig. 2. Patterned wettability: (a) Configuration of groups and parameters, (b) droplet spreading results on the different wettabilities, (c) Surfaces with modified Mp and size of hydrophobic dots.

design and the contact angles of S10Mp00 are the same conditions as those of experiment of Jo et al. [19]. Input heat flux range in Fig. 3 is also referred from the experimental work. The comparison of current numerical data for S10Mp00 and experimental work is shown in Fig. 3. The numerical result is in good agreement with the experimental result, where the convection and nucleate boiling regimes can be seen in both sets of data. At low heat flux, nucleate boiling does not occur and the heat transfer phenomenon is dominated by liquid convection. This regime is called the convection regime [23,24].

3.3. CHF determination criterion Fig. 4 shows superheat of S10Mp00 surface with time for different heat fluxes Q00 = 3.171, 7.400. With both heat fluxes, the heat transfer phenomena are classified as the nucleate boiling regime. However, the superheat data and the bubble shape are quite different for those two heat fluxes. For Q00 = 3.171, we can see bubble nucleation and boiling with small bubbles. When t⁄ > 18.15, the bubbles depart from the surface and this chaotic departure induced superheat perturbation. On the other hand, for Q00 = 7.400, the bub-

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3.4. Effect of Mp on bubble merging behavior

Table 1 Wettability pattern information. Index

Dots width

Reference pitch of dots

Mp

Contact angle of hydrophobic area

Contact angle of hydrophilic area

S10Mp00 S10Mp08 S10Mp15 S10Mp22 S06Mp00 Jo et al. [19]

0.040L0 0.040L0 0.040L0 0.040L0 0.024L0 0.040L0

0.160L0 0.160L0 0.160L0 0.160L0 0.160L0 0.160L0

0.00 0.08 0.15 0.22 0.00 0.00

123° 123° 123° 123° 123° 123°

54° 54° 54° 54° 54° 54°

Fig. 3. Comparison of experimental data from Jo et al. [19] and numerical data of S10Mp00 (current study). Convection regime and nucleate boiling regime are indicated by shades, and slops of both regimes are indicated by dashed lines.

bles merge with each other before departing and form a single gas film. The gas film prevents the drastic departure of bubbles. The superheat has no perturbation after t⁄ = 8.76. This is because the gas film acted as the heat insulator. This film generating phenomenon occurs when the heat flux had reached the CHF. Therefore we can determine the CHF by observing the film generation and superheat change with time. This CHF criterion is also applied to the numerical results of other surfaces.

Fig. 5 shows bubble merging behavior dependency with Mp values of Q00 = 7.400. More than four bubbles merge with each other on the surface of three cases, except for S10Mp15. Cases with Mp of more than 0 have had three bubbles merge at or near the corner of the surfaces, because the hydrophobic dots are concentrated more at the marginal region of the surface compared to S10Mp00. When comparing from S10Mp00 to S10Mp08, the big difference in S10Mp08 is that there is no film formed at the center. However, huge bubbles still occur just off-center. This means that the nucleation site is still dense at the center of S10Mp08. On S10Mp08, the areal fraction of hydrophobic dots in the center region is still big enough to merge many bubbles near the center. Comparing S10Mp08 to S10Mp15, the most significant difference is that there is no huge bubble created by merging more than four bubbles. Because the locations of the hydrophobic dots have moved away from the center, the bubbles near the center did not merge until reaching the departing diameter. However, the case of S10Mp22 is different. When the location of the hydrophobic dots moved too far from the center, the bubbles near the center merged. The temperature at the center increased greatly since there was no nucleation, until the center temperature reached the nucleation temperature of the hydrophilic surface. Bubbles nucleated even at the hydrophilic surface, and those bubbles merged with neighboring bubbles nucleated at the hydrophobic dots. From the merging behavior of bubbles, the Mp value near the optimization condition was Mp = 0.15. In Fig. 6, the contact angle hysteresis of an individual bubble was calculated based on the deviation from the average contact angle to the local contact angle:

R    hdl Hysteresis ¼ h  Lcl 

ð22Þ

where h is the local contact angle of the bubbles and Lcl is the contact line perimeter of the triple contact point. Hysteresis represents the resistance force of movement. Therefore, by analyzing the hysteresis, we can achieve physical insight into triple contact line pinning phenomenon. After merging, the contact line of the bubble does not show a circular form but is rather dented. Moreover, this bubble departs from the surface while maintaining a metastable state without recovering into a circular form. This phenomenon proves that the hysteresis of the contact angle exists due to the heterogeneous sur-

Fig. 4. Superheat with time, and snap shots of bubbles corresponds to heat flux: (a) Q00 = 3.171, (b) Q00 = 7.400.

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509

Fig. 5. Bubble merging behavior on the surfaces with Mp control. Heat flux Q00 = 7.400.

3.5. Effect of Mp on the local heat transfer rate The local Nusselt number (Nu) was calculated from the temperature of the surface, temperature gradient in the z-direction near the surface dT⁄/dz, and superheat T⁄:

Nu ¼

 Lh  Lt dT  T  dz z¼Lt

ð23Þ

In Fig. 7, the local Nusselt number distribution on S10Mp15 is higher than S10Mp00. Because generated gas film on S10Mp00 insulates the heat transfer, the local Nusselt number has a low value. On the other hand, on S10Mp15, the regions adjacent to contact lines have a high Nusselt number as evaporation occurs at the contact line. Because of nucleate boiling, contact lines are well distributed on the surface. This means the high Nusselt number region is well distributed with contact lines [26], while the heat transfer rate is even and high enough across the whole surface. Therefore, the heat transfer rate can be enhanced by controlling the Mp values. Fig. 6. Contour is hysteresis distribution on the solid surface. Dashed squares indicate location of hydrophobic dots.

face with hydrophobic dots and a hydrophilic surface. The contact line of the bubble on the hydrophilic surface experiences a strong force that resists advancing motion, while that on the hydrophobic dot experiences strong force that resists receding motion, which causes hysteresis in the result. For the result, as seen in Fig. 6, the metastable contact line of the bubble shows an oval shape dented by the hydrophobic dots pulling the bubble. Also, the metastable contact line shows a high deviation of the contact angle. The bubble in the metastable state has the advantage of higher heat transfer compared with the normal state since it has a longer contact line. For the case of a controlled Mp value (Mp = 0.08, 0.15, 0.22), the geometrical shape formed by connecting hydrophobic dots will be a triangle or distorted square. This causes the contact line of the bubble to be hard to form into a circular shape [25], increasing the local heat transfer rate.

3.6. Effect of Mp on the CHF CHF can be enhanced by controlling the Mp value via results and discussions from above. Fig. 8 shows boiling curves with superheat and a heat flux graph for all surfaces. The cases with different Mp show CHF enhancement compared to the case of S10Mp00. Other conventional CHF enhancement methods reduce the area fraction of hydrophobic dots by reducing the size of the dots. We have also compared the conventional CHF enhancement scheme S06Mp00 in Fig. 8. The advantage of the Mp controlling method is revealed by superheat value. The side effect of the area fraction reduction increases superheat. However, with the Mp controlling method, there is no remarkable superheat increase. To enhance CHF and maintain low superheat, the Mp controlling method is effective. CHF values are re-plotted in Fig. 9. The biggest CHF value appears in the case with Mp = 0.15 (S10Mp15). Because of nucleate boiling with small bubbles in Fig. 5, and the high local heat transfer

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Fig. 7. Local Nusselt number and triple contact lines distribution on the surface of S10Mp00 and S10Mp15. Heat flux Q00 = 7.400.

rate distribution in Fig. 7, the sustainability of nucleate boiling is highest on S10Mp15. Mp = 0.15 is not the biggest or smallest Mp value, which means that Mp can be optimized with the above numerical approach and analysis. In Fig. 10, the nucleation, departure, or film generation of bubbles is shown for the case of the lowest CHF(Mp = 0.00) and for that of the highest CHF(Mp = 0.15). For the case of Mp = 0.00, the nucleated bubble grows and bubbles merge with each other, creating a film as a result. For the case of Mp = 0.15, bubbles show necking, and then depart. 4. Conclusion

Fig. 8. Boiling curves with superheat, and heat flux graph for all surfaces.

Fig. 9. CHF values of S10Mp00, S10Mp08, S10Mp15, and S10Mp22.

We performed a numerical study for adaptive control of patterned wettability. Before performing numerical simulations and analyzing boiling phenomena with different Mp, we validated our simulation with the experimental work of Jo et al. [19]. The numerical result is in good agreement with the experimental result, while convection and nucleate boiling regimes could be seen in both sets of data. By controlling the Mp value, we can control boiling phenomena from film boiling to nucleate boiling. Because the locations of hydrophobic dots are moved away from the center, the bubbles near the center do not merge until reaching the departing diameter. However, if the location of hydrophobic dots is too far from the center, this wettability configuration would show a totally different aspect. The temperature of the center increase greatly as there is no nucleation, until the center temperature has reached the nucleation temperature of the hydrophilic surface. Bubbles nucleate at the hydrophilic surface, and those bubbles merged with neighboring bubbles nucleate at the hydrophobic dots. From the merging behavior of bubbles, the Mp value near the optimization condition is Mp = 0.15. To analyze bubble merging behavior, the contact angle hysteresis of an individual bubble was calculated. Using hysteresis data, we could prove that the geometrical formation of hydrophobic dots causes metastable contact lines. Local Nusselt number distribution is high across the surface of the Mp = 0.15 case. Because of nucleate boiling, contact lines are well distributed on the surface. The high Nusselt number region is well distributed with contact lines and the heat transfer rate is

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511

Fig. 10. Boiling procedure of (a): S10Mp15 and (b): S10Mp00. Contour is local Nusselt number distribution.

high across the surface. Therefore the heat transfer rate is enhanced by controlling the Mp value. We have evaluated the Mp controlling method with regard to CHF and superheat. However, with Mp control, there is no significant superheat increase. For CHF enhancement and low superheat, the Mp controlling method is effective. The most effective Mp value is Mp = 0.15. Mp = 0.15 is not the biggest or smallest Mp value, which means that Mp can be optimized with a numerical approach and analysis.

Acknowledgment This work was partially supported by the Mid-Career Researcher Programs (NRF-2013R1A2A2A01015333, NRF2015R1A2A1A15056182) and by the Advanced Research Center Program (NRF-2015R1A5A1037668) through a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT, and Future Planning (MSIP).

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