Recent developments of jet impingement nucleate boiling

International Journal of Heat and Mass Transfer 89 (2015) 42–58

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

Review

Recent developments of jet impingement nucleate boiling Lu Qiu a,b, Swapnil Dubey a, Fook Hoong Choo a, Fei Duan b,⇑ a b

Energy Research Institute @ NTU, Nanyang Technological University, 1 Cleantech Loop, 06-04 Cleantech One, 637141, Singapore School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore

a r t i c l e

i n f o

Article history: Received 18 December 2014 Received in revised form 28 January 2015 Accepted 5 May 2015

Keywords: Jet impingement Boiling Phase change Heat transfer

a b s t r a c t Jet impingement boiling is one of important branches of flow boiling. Due to its high heat transfer rate, the application potential of this heat transfer approach is significant. Hence, it attracts many researchers attentions. This review examines the development of jet impingement boiling heat transfer that published in the past two decades. The topics covered are fully developed nucleate boiling regime and its two boundaries: onset of nucleate boiling and critical heat flux point. Free surface, submerged, confined circular/planer jet impingement boiling configurations are involved. Effects of jet parameters (impact velocity, impact distance, jet diameter, subcooling, jet array, etc.) and target surface parameters (surface condition, surface aging, etc.) on boiling heat transfer characteristics are emphasized and discussed. The review mainly focuses on experimental studies, but theoretical and numerical developments are also discussed. Ó 2015 Elsevier Ltd. All rights reserved.

Contents 1. 2. 3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fundamentals of jet impingement boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Effects of system parameters on boiling heat transfer for free-surface, circular jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Effect of jet velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Effect of jet subcooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Effect of nanoparticles in liquid jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Effect of nozzle dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5. Effect of impact distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.6. Effect of multiple jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.7. Effect of surface condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.8. Coexistence of single-phase convection and boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Effects of system parameters on boiling heat transfer for submerged and confined jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Effect of jet velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Effect of jet subcooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. Effect of non-condensable gas in liquid jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4. Effect of impact distance (confinement) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5. Effect of multiple jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6. Effect of surface condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7. Coexistence of single-phase convection and boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Effects of system parameters on boiling heat transfer for planar jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Effect of jet velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Effect of jet subcooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Effect of jet width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⇑ Corresponding author. Tel.: +65 6790 5510; fax: +65 6792 4062. E-mail address: [email protected] (F. Duan). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.025 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

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L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

43

Nomenclature Ar AR A Bo C Cp d Dbd Dc D g f G hfg H HTC k L Nu Nw p q00 r T Re

area ratio ðAr ¼ Ajets =Aheater Þ aspect ratio ðAR ¼ length=widthÞ area boiling number ðBo ¼ q00 =qUhfg Þ correlation constants constant pressure heat capacity jet diameter bubble departure diameter diameter of confined cylinder heater diameter gravity bubble departure frequency mass flow rate latent heat impact distance heat transfer coefficient thermal conductivity length Nusselt number ðNu ¼ q00 D=DT sat kl Þ Nucleate site density pitch of jet array heat flux radius from the center of jet temperature Reynolds number ðRe ¼ qUd=ll Þ

U W

q r h, CA

jet velocity width of slot jet density surface tension contact angle

Subscripts 0 correlation for saturated liquid b boiling CHF critical heat flux e evaporation f boiling front FNB fully developed nucleate boiling l liquid ONB onset of nucleate boiling ref reference sat saturation sub subcooling sp single-phase v vapor w wall Superscript m, n correlation constants

3.3.4. Effect of impact distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5. Effect of multiple jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Hybrid configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. Effect of jet velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. Effect of jet subcooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3. Effect of jet pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4. Effect of surface condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Other phenomena and jet impingement configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1. Boiling hysteresis phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2. Unsteady jet impingement boiling (quenching) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3. Cylindrical target surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4. Rotating target surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5. Cryogenic jet impingement boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Numerical models and simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Eulerian based mixture models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Eulerian based PRI boiling models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Single-phase based jet impingement boiling models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Other developments related to jet impingement boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conflict of interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Boiling bears a phenomenal heat transfer performance due to the bubble induced significant flow mixing as well as the phase change required latent heat, therefore, is usually employed in high heat flux thermal management applications, such as power electronics components cooling, large scale integrated circuits cooling, inverters cooling, and metal processing, etc. [1] Boiling investigations can be divided into three major categories: pool boiling, internal flow boiling and external flow boiling. As the simplest configuration in boiling family, pool boiling studies focused on very fundamental aspects of the boiling phenomenon, for instance, pre-existing nuclei, nucleate site density and bubble dynamics, etc. [2] However, purely theoretical approach for the boiling

53 53 53 53 54 54 54 54 54 54 55 55 55 55 55 55 56 56 56 57 57 57

phenomenon has not been well developed yet. Empirical correlations are still applied for modeling boiling flow and heat transfer. Internal flow boiling configuration as tubes presents different heat transfer characteristics from the pool boiling due to the contribution of forced convection. Micro-channel flow boiling presents high heat transfer rate in a compact configuration without a large surface temperature gradient [3,4]. One typical external flow boiling configuration is jet impingement boiling. Single-phase jet impingement is good at heat transfer. It is interesting to know what happens if one combines jet impingement with boiling together. This topic has been studied for decades, many of which before 1993 had been summarized comprehensively by Wolf et al. [5], therefore, this review is a follow-up which shows the recent developments of jet impingement boiling in the last two decades. Jet

44

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

impingement boiling in fully developed nucleate boiling regime and its two boundaries are emphasized: onset nucleate boiling (ONB) and critical heat flux (CHF) where nucleate boiling starts and ends respectively.

Nozzle

The reports of fundamental investigations on jet impingement boiling phenomenon started from 1970s. Copeland experimentally investigated the water jet impingement boiling onto a nickelplated copper surface [6]. In 1973, when Katto and Kunihiro [7] studied the burn-out phenomena in a water pool boiling system, they introduced a water jet to the boiling surface in order to reduce vapor mass. Accidently, they observed that the burn-out phenomena in this jet impingement case was very different from the traditional pool boiling. In the next twenty years, a great amount of studies regarding jet impingement boiling were published. There are basically five different jet impingement configurations: free surface, submerged, confined, plunging and wall jet [5]. And the first three configurations attracts researchers attention most. In a single-phase free surface jet impingement, it is well known that there are four different flow structures exist, namely, a stagnation zone, a boundary layer region, a similarity of fully viscous region, and a turbulent region. Single phase jet impingement produces a considerable heat transfer rate in the stagnation zone, heat transfer can be promoted even higher once boiling is involved. In a typical boiling configuration, the boiling process develops from single phase forced convection, to nucleate boiling, then to transition boiling, and finally to film boiling, along with the increase of wall superheat. The nucleate boiling regime is the most intriguing one because a high heat transfer rate can be generated under a relatively low wall-to-flow temperature difference. In many pool boiling studies, experimental data support the conclusion that the wall heat flux and the superheat obey the following correlation in a variety of working conditions. The statement can be used in jet impingement boiling,

ð1Þ

where the wall superheat DT sat can be calculated as follows,

DT sat ¼ T w  T sat

Vapor

Liquid jet

2. Fundamentals of jet impingement boiling

q00 ¼ C ðDT sat Þm

CHF Occurs

Nucleate Boiling

ð2Þ

Aside from the nucleate boiling regime itself, its two boundaries are also important. In the transition from single phase forced convection regime to the nucleate boiling regime, there is an onset of nucleate boiling. CHF could be reached by the end of nucleate boiling, after which the wall heat flux would sharply reduce with wall superheat. An abrupt decrease of heat transfer may result in a device burn-out. To prevent this, the characteristics of CHF are crucial. When the superheat reaches to a critical value, target wall is segregated from the liquid jets by the enormous bubble that generated and begins to dry-out (see Fig. 1). In this scenario, the wall temperature is elevated significantly, and the nucleate boiling steps into transition boiling. Therefore, following three aspects in nucleate boiling regime are focused on: (1) ONB, (2) Fully developed nucleate boiling heat transfer, and (3) CHF characteristics. 3. Experimental studies In this section, experimental studies are separated into four categories: free surface circular jets, confined/submerged circular jets, different kinds of slot jets, and finally hybrid configurations. Major conclusions that reported in the literatures in a variety of experimental setups are summarized. In each category, the effects of hydrodynamic parameters of jets are introduced firstly, then the geometrical parameters of jets, and finally the effects of target

Vapor Bubbles

Vapor Column

Free Suface

Liquid Sublayer

Stagnation Zone Hot Wall Fig. 1. Schematic of flow pattern for a typical free jet impingement with nucleate boiling (left) and when CHF occurs (right) (reprinted from Haramura and Katto [8], Copyright 1983 from Elsevier).

surface. The operating parameters and the corresponding experimental apparatus of each experiment are summarized in Tables 1 and 2, respectively. 3.1. Effects of system parameters on boiling heat transfer for free-surface, circular jets 3.1.1. Effect of jet velocity Many investigations before 1993 had observed that boiling curve in fully developed nucleate regime was independent of jet velocity with a variety of conventional fluids and wall conditions. The reason could be inferred that the significant bubble generation and collapse induced flow mixing played the most important role in fully developed boiling regime so that the effects of hydrodynamics in the bulk flow were not so apparent [5]. Recently, it was reported that this statement was also true for superhydrophilic surface [28] and nanoparticle solution [21]. For a superhydrophilic surface, the following boiling curve correlation was proposed by Qiu and Liu [28] in the fully developed nucleate boiling regime when the jet velocity was in the range of 0.5–6 m/s,

q00FNB ¼ 2:8  109 ðDT sat Þ9

ð3Þ

Similarly, Liu and Qiu [21] proposed that the correlation constants were 1:4  108 and 8 for water–CuO nanoparticle solution (0.01% concentration by weight) when velocity was in the range of 0.5–6.5 m/s. Though it has been proved that jet velocity makes no difference to the free-surface circular jet boiling curve in fully developed nucleate boiling regime, it influences CHF significantly. Therefore, the research focuses were shifted to discuss the effects of jet velocity on CHF. Liu and Zhu [20] proposed a semi-theoretical model to predict the CHF in the stagnation jet impingement boiling configuration (Ar = 1), which has a form as follows,

      q00CHF q 1=3 rql 1=3 qv 1:4=3 ¼ C1 1 þ v 2 Ghfg ql ql G d

ð4Þ

where C 1 was a correlation constant that needs to be determined by experiments. It revealed that the higher jet velocity resulted in a higher CHF, which was proportional to the U 1=3 . For saturated water, it could be simplified as follows in the jet velocity range of 0.5– 6 m/s,

q00CHF ¼ 3:6  105 ðU=dÞ

1=3

ð5Þ

45

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58 Table 1 Jet impingement boiling – operating parameters (1993–2014). Authors

Year

Jet typeg

Jet(s)

p=d

Working fluid

Subcooling (K)

Jet velocity (m/s)

d or W (mm)

H=d

Max q00 (w/cm2)

Degas

Browne et al. [9] Browne et al. [10]

2010 2012

Circ-conf Circ-conf

10–30 10–30

4–10 4–10

0.112 0.112

1.8 1.8

590 590

– –

2012

Circ-sub

3.21b 3.21, 2.05b –

R134a R134a

Cardenas and Narayanan [11]

9a 9, 22a 1

FC72

0

0–3.4

2

23

Yes

Chang et al. [12] Dukle and Hollingsworth [13] Dukle and Hollingsworth [14] Guo et al. [15] Hong et al. [16]

1995 1996 1996 2011 2014

Circ-conf Circ-sub Circ-sub Circ-hybrid Circ-conf

1 1 1 1 32

– – – – 5

7–16 5 3–5 25–35 36–56

1–4e 0.7–1.4 0.8–1.4 0–2d 0.2–0.5

1.5, 2, 3, 4 8.2 2.3 – 1, 1.5, 3

14 9.3 9.3 167 130

Yes Yes Yes – –

Hong et al. [16]

2014

Circ-conf

50

4

36–56

0.2–0.5

1

1, 1.5, 3

130

–

Li et al. [17] Li et al. [18] Li et al. [19] Liu an Zhu [20] Liu and Qiu [21]

2013 2014 2014 2002 2007

Circ-free Circ-free Slot-free Circ-free Circ-free

1 1 1 1 1

– – – – –

0–50 0–30 0–99 0 0–74

5–40 10–40 4–40 0.5–6 0.5–6.5

3 3 1 (AR = 12) 10, 6, 2 4

1.67 1.67 5 1, 1.67, 5 1.25

3000 3000 8000 500 1000

– – Yes – –

Liu et al. [22]

2004

Circ-free

1

–

R113 R11 R11 FC72 Ethylene glycolc Ethylene glycolc Water Water Water Water Water (CuO) Water

1.16, 2.29, 3.96 4 7.5 7.5 – 1

15–80

0.5–6

12, 8, 6, 3

1000

–

Mahmoudi et al. [23]

2012

Circ-free

1

–

HFE7100

2

1.37, 0.41

100

–

Meyer et al. [24]

2006

Circ-conf

3

FC72

10.6–20.6

139

Yes

2003 2012 2005 2008 2013 2013 2013 2009

Circ-free Circ-conf Circ-free Circ-free Circ-free Circ-free Circ-free Slot-conf

1 1 1 1 1 9 25 1

Water R134a R113 Water HFE7100 HFE7100 HFE7100 PF5056

80–170 5–18 0–33 0–74 10 10 10 25

0.127, 0.254, 0.508 2 2 8, 4 4 3.75 1.25 0.75 2 (AR = 5)

44, 22, 11

Mitsutake and Monde [25] Ndao et al. [26] Qiu and Liu [27] Qiu and Liu [28] Rau and Garimella [29] Rau and Garimella [29] Rau and Garimella [29] Shin et al. [30]

78.7, 39.4, 19.7 – – – – – 4 4 –

0.23– 2.52e 1–8

0.42, 0.63, 0.83, 1.67 3.6–36.5

2.5 0.86 0.63–1.25 1.25 4 4 4 0.5, 1, 4

21200 280 300 3000 24 24 24 40

– – – – Yes Yes Yes Yes

Sung and Mudawar [31]

2006

Slot-hybrid

1

–

PF5052

13.1–36.9

2.13

223

Yes

Sung and Mudawar [32] Sung and Mudawar [33] Sung and Mudawar [34]

2008 2009 2009

Circ-hybrid Circ-hybrid Circ-hybrid

14 14 13

3.67 3.67 3.42f

HFE7100 HFE7100 HFE7100

48.2–108.2 52–111.2 48.0–107.9

7.7 7.7 6.7

311 1127 505

Yes Yes Yes

Sung and Mudawar [34]

2009

Circ-hybrid

12

3.42f

HFE7100

48.0–107.3

6.7

505

Yes

Sung and Mudawar [34]

2009

Circ-hybrid

14

3.44f

HFE7100

48.0–107.9

0.48 (AR = 26.5) 0.39 0.39 0.6, 0.45,0.3 0.3, 0.45,0.6 0.42

7.1

505

Yes

Vader et al. [35] Wolf et al. [36]

1995 1996

Circ-sub Slot-free

1 1

3.40 –

LN2 Water

10 50

5 10

80 634

– No

Wu et al. [37] Wu et al. [37] Zhang et al. [38] Zhao et al. [39]

2007 2007 2011 2013

Circ-conf Circ-conf Circ-sub Circ-conf

1 3 1 1

– 2.5 – –

Water Water LN2 Water

50 50 0 10–50

0.52 10.2 (AR = 10) 2 2 2 2

5.3, 1 5.3, 1 0.75, 1.75 1.5

260 260 65 800

Yes Yes No –

Zhou and Ma [40] Zhou et al. [41]

2004 2004

Circ-sub Circ-sub

1 1

– –

R113 R113 and L12378

18.5–45.9 4–31

0.96, 1.01 0.96, 1.01

5 5

90 50

Yes Yes

5–60 1.1–4.05 0.5–8 0.5–6.5 0.68–2.72 0.68–2.72 0.68–2.72 0.20 0.52 2.15 0.85–4.70 1.05–6.50 3.08– 16.8e 3.08– 16.8e 3.08– 16.8e 4.7–13.3 2–5 3.3–16.2 3.3–16.2 0.34–1.11 0.82– 4.14e 0–11.36 0–11.36

Note: The mean jet velocity and pitch-to-diameter ratio are calculated based on the averaged jet diameter and pitch. a There were 17 jets in total (7 of them in the heater zone, 4 of them partially in the heater zone; 9 effective jets). b Staggered jet configuration (center-to-center distance: 360, 230 lm). c 43% mass concentration aqueous ethylene glycol. d Velocity of crossflow is 0.5–1.5 m/s. e Jet velocity is calculated based on G or Re. f Based on averaged jet diameter and the averaged pitch. g Jet type: circ – circular jet, sub – submerged jet impingement, conf – confined jet impingement, free – free surface jet impingement.

Liu et al. [22] studied the effect jet velocity on CHF. It was proved that this correlation was valid for subcooled water jet impingement. With the same model, Qiu and Liu [27] proposed the following correlation for R113 when the jet velocity was in the range of 0.5–8 m/s,

q00CHF ¼ 5:05  104 ðU=dÞ

1=3

ð6Þ

As mentioned, in the above three works, the area of heater was exactly same with the nozzle cross-section (Ar = 1). However, in most circumstances, the area of heater is usually far larger than

46

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

Table 2 Jet impingement boiling – experimental apparatuses (1993–2014). Authors

Area coverage (Ar %)

Temperature location

Surface orientation

Heating scheme

Materials

Heater size (mm)

Surface furnishing/condition

Browne et al. [9,10]

8.9, 21.4

F

Up

Direct-dc

Silicon oxide

1  1 (Titanium heater)

Cardenas and Narayanan [11] Chang et al. [12] Dukle and Hollingsworth [13,14] Guo et al. [15]

0.17, 0.69, 2.05 0.36 0.21

A

Up

Indirect

Oxygen-free copper

D B, E

Down Up

Indirect-ac Direct-dc

Nickel plate Ni–Cr–W–Mo alloy

D = 27.64 (cartridge heaters) D = 66.6 144  144

30 nm surface roughness 33 nm surface roughness – 200–600 nm surface roughness

–

G

Up

Indirect-dc

Silicon chip

Hong et al. [16]

3.14, 4.91

B

Up

Direct-dc

Li et al. [17,18] Li et al. [19] Liu and Zhu [20]

100 100 78.54, 78.54, 39.27 4 100 2.93, 0.26

A A A

Up Up Up

Indirect Direct-dc Direct-dc

Ni–Cr alloy (Cr15Ni60) Copper Nickel foil Nickel foil

A A B

Up Up Up

Indirect Indirect Indirect

1.27, 2.54, 5.08 15.70

B, C

Up

Indirect

Copper Copper Copper (nickel coating) Oxygen-free copper

–

Up

Direct-dc

Nickel foil

78.54

F

Up

Indirect-dc

Qiu and Liu [27] Qiu and Liu [28]

100 4

A A

Up Up

Indirect Indirect

Rau and Garimella [29] Shin et al. [30]

2.76 4

E D

Up Up

Direct-dc Direct-dc

Oxide layer for heat transfer Copper Copper (TiO2 coating) 304 stainless steel INCONEL alloy 600

Sung and Mudawar [31]

14.45

B

Up

Indirect-ac

Oxygen-free copper

Sung and Mudawar [32,33] Sung and Mudawar [34]

4.57

B

Up

Indirect-ac

Oxygen-free copper

5.65, 5.21, 5.30 0.5 3.92 0.28 16 9.92

B

Up

Indirect-ac

Oxygen-free copper

C D D A A

Vertical Up Up Up Up

Indirect Direct-dc Direct-dc Indirect-dc Indirect

Silicon Ni–Cr–W–Mo alloy INCONEL alloy 600 Oxygen-free copper Oxygen-free copper

2.9,3.2

D

Vertical

Direct-ac

Constantan foil

Liu and Qiu [21] Liu et al. [22] Mahmoudi et al. [23] Meyer et al. [24] Mitsutake and Monde [25] Ndao et al. [26]

Vader et al. [35] Wolf et al. [36] Wu et al. [37] Zhang et al. [38] Zhao et al. [39] Zhou and Ma [40], Zhou et al. [41]

10  10 (copper-wire heater) 20  40

Micro-pin–fins

D=3 1  10 10  10, 6  6, 2  4

3 different CAs CA = 90° Cleaned by acetone

D = 20 D = 12, 8, 6, 3 D = 8 (cartridge heaters) 30  30 (cartridge heaters) 5  4, 10  4

Sand paper #2000

– 200 nm surface roughness – Soldering

2  2 (titanium heater)

Micro-pin–fins

D = 8, 4 D = 20

– 3 different CAs

20  20 8  50, 8  10 (CHF experiments) 2.11  20 (cartridge heaters) 1.83  20 (cartridge heaters) 1.83  20 (cartridge heaters) 6.5  6.5 35.7  260 14  80 D=5 D = 6.35 (cartridge heaters) 55

– Sand paper #2000 – – – – vapor blasted – – Porous surface –

Note: Location of temperature measurements: A – locally at the stagnation point, B – locally at the stagnation point and other locations, C – averaged over the surface, D – locally in the streamwise direction, E – temperature map, F – indirect averaged T measurement (by measuring the current and voltage of the heater, then calculate the average temperature with the resistance of the heater), and G – center of the heater.

the jet. In order to address the effects of different heater and nozzle dimensions, Katto and Yokoya [42] reported a semi-theoretical CHF model based on the hydrodynamic model proposed by Haramura and Katto [8]. The following CHF correlation was suggested.

q00CHF ¼ Ghfg

#m  1:12 !" qv rql 1 0:0166 þ 7:00 ql G2 ðD  dÞ 1 þ D=d

ð7Þ

where m was a function of density ratio. Similarly, the following correlation was proposed by Qiu and Liu [28] in the jet velocity range of 0.5–6.5 m/s for a superhydrophilic surface,

!0:44  0:275   q00CHF q rql 1=3 1 ¼ 0:0985 v 2 Ghfg ql G2 D 1 þ 0:00113ðD=dÞ

ð8Þ

Those experiments were all conducted with the jet velocity less than 10 m/s. However, it was found by Li et al. [17,18] that U = 10 m/s was a threshold, before which, the CHF was found to be proportional to U 1=3 since the physical properties could be

considered as the constant values. After the critical velocity, the stagnation static pressure rise should be concerned, and physical parameters under stagnation pressures should be used in the CHF correlation. Li et al. [18] also reported that the superheat of ONB point was increasing with jet velocity (10–40 m/s), but no correlation was given. Mitsutake and Monde [25] experimentally investigated the effects of jet velocity on CHF with high jet velocity, pressure and subcooling (up to 60 m/s, 1 MPa and 170 K). They compared the experimental data with Monde et al.’s correlation [43–45] in which the CHF was proportional to U 0:314 ,

!0:343  0:645 q00CHF ql 2r 0:364 ¼ 0:221 ð1 þ D=dÞ qv Uhfg qv ql U 2 ðD  dÞ

ð9Þ

The measured CHF was shown to match the predicted one very well at low jet velocity, but predicted values at high velocity were higher than the experimental data apparently. They concluded that this deviation originated from the data uncertainty. However,

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

47

Fig. 2. Comparison of flow patterns under high and low flow rates (reprinted from Mahmoudi et al. [23], Copyright 2012 from Elsevier).

according to the recent study of Li et al. [17,18], it could be speculated that this discrepancy actually came from the stagnation zone pressure increase. Different from the high velocity conditions, Mahmoudi et al. [23] studied the effects of low jet velocity on jet impingement boiling heat transfer. Once the initial jet Reynolds number (Re) was low, the effects of surface tension and gravity became significant during the falling: the jet velocity increases whereas the jet diameter decreases (see Fig. 2). A large disagreement with the higher speed scenarios was observed. The impact distance was an influential parameter to boiling heat transfer in this case. They proposed a new CHF correlation for the saturated fluid in which the effect of jet diameter reduction was included. However, upstream liquid film instability and hydraulic jump effects were not concerned, hence this correlation gave poor prediction compared to the experimental data when the impact distance was higher than 25 mm. They suggested that a further amendment was needed, which showed the significance of those effects. Anyway, the increase of jet velocity decreased the effects of impact distance. 3.1.2. Effect of jet subcooling Same with the effects of jet velocity, previous studies proved that boiling curve in fully developed nucleate boiling regime was also independent of subcooling. For example, Liu et al. [22] found that the data obtained from different degrees of subcooling (15– 80 K) converged into the extending line of pool boiling curve. For the superhydrophilic surface [28] and 2.0 wt.% nanoparticles (water–CuO) solution [21], boiling curves were also independent of subcooling in the fully developed regime (0–74 K and 0–84 K). Moreover, Li et al. [18] found that heat transfer coefficient (HTC) in the fully developed nucleate boiling regime was not influenced by subcooling. But the superheat of ONB point increased with an increase of subcooling. Again, the research focuses shifted to the effect of subcooling on CHF. Monde et al. [44] proposed that the effect of subcooling could be addressed by multiplying a coefficient to the saturate fluid CHF correlation,

q00CHF 1þ ¼ q00CHF;0

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4C 2 Ja 2

ð10Þ

where

 2  0:364 0:95 d 1 þ Dd C 2 ¼  0:43D 0:343 qv ql

 Ja ¼

qv ql

ð11Þ

2r ql U ðDdÞ 2

  C p;l DT sub hfg

ð12Þ

The subcooling of jet is defined as follows,

DT sub ¼ T sat  T jet

ð13Þ

Qiu and Liu [28] proved that this correlation was validate for superhydrophilic surfaces, the predicted CHF ratio matched the experimental data very well in the subcooling range of 0–74 K. Mitsutake and Monde [25] investigated the effect of subcooling on CHF with high jet velocity, pressure and subcooling (up to 170 K). Higher subcooling produced higher CHF. But the measured CHF had 40% deviation with the prediction of Monde et al. [44]. An extremely high heat flux 21,200 W/cm2 was obtained at a pressure of 0.7 MPa, jet velocity of 35 m/s, and subcooling of 151 K. Another method to address the effects of subcooling that proposed by Liu et al. [22] is shown as follows,

 n   C p;l DT sub m q00CHF qv ¼ 1 þ C 3 q00CHF;0 ql hfg

ð14Þ

For water jet, Liu et al. [22] proposed the following correlation in which CHF ratio had a linear relationship with subcooling at 15 to 80 K,

  C p;l DT sub q00CHF ¼ 1 þ 11:82 q00CHF;0 hfg

ð15Þ

For R113, Qiu and Liu [27] reported that the correlation constant was 22.46 when the subcooling was in the range of 0–33 K. Based on the theoretical development of Li and Liu [46] regarding the effect of subcooling, Li et al. [18] proposed a new model to include the subcooling effect with an additional term,

 1:4=3      C p;l DT sub q00CHF q rql 1=3 kl ¼ C4 v þ C5 2 Ghfg ql C p;l Gd hfg G d

ð16Þ

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L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

where C 4 and C 5 were constants. The physical meaning of C 5 is the ratio of two-phase turbulent heat transfer rate compared to single-phase laminar flow heat transfer. Moreover, they deducted that the evaporative heat flux had a form as follows,

      q00e q 1=3 rql 1=3 qv 1:4=3 ¼ C4 1 þ v Ghfg ql ql G2 d

ð17Þ

Hence, the following equation existed,

 1:4=3  1=2 2 !1=3   C p;l DT sub q00CHF C 5 qv kl G d ¼ 1 þ q00e C 4 ql C p;l Gd rql hfg

ð18Þ

where C 5 =C 4 was fitted with experimental data with a value of 15.15 for the subcooled water (20–80 K) and ethanol (8–58 K). It is important since the analytical results provided the theoretical foundation for the previous purely empirical correlation. The simplified version had a similar form with the previous reported correlations,

q00CHF ¼ 1 þ C 6 DT sub q00e

ð19Þ

This analysis also suggested that the so-called ‘‘constant’’, C 6 , was actually a function of jet velocity. And the effect of jet velocity could be neglected if it was small. 3.1.3. Effect of nanoparticles in liquid jet Liu and Qiu [21] mixed nanoparticles of CuO into the water as the working fluid in jet impingement boiling. It was shown that the nanofluid jet impingement boiling heat transfer was significantly worse than that of base fluid (water). Higher superheat was required to achieve the same wall heat flux. The boiling incipience for the nanofluid was greatly delayed. CHF increased 25% compared to pure water (0% concentration). But the concentration of nanofluid will not influenced CHF when it was higher than 1.0 wt.%. Besides, the data for pure water matched the correlation of Wolf et al. [36] well. An updated boiling curve correlation was proposed for the solution. 3.1.4. Effect of nozzle dimensions Liu et al. [22] studied the effect of jet diameter (four different diameters from 3 to 12 mm) on CHF. It was found that CHF was 1=3

proportional to the ðU=dÞ for both saturated and subcooled water. This means that a higher jet diameter results in a lower CHF for the same jet velocity when the area ratio equals to 1. Same conclusion was obtained by Liu and Zhu [20] and Qiu and Liu [27]. 3.1.5. Effect of impact distance Mahmoudi et al. [23] investigated the effect of impact distance on boiling curve and CHF under a low jet velocity impingement boiling. Under the lowest exit jet velocity, higher impact distance resulted in a lower heat transfer rate and lower CHF. The impact distance had limited influence on boiling curve and CHF under high jet velocities. Increasing jet velocity decreased the effect of impact distance. 3.1.6. Effect of multiple jets Multiple jets impingement boiling was firstly studied by Monde et al. [47], in which two to four saturated water jets impinged onto a circular heating surface. The jet spacing was also varied, and a character length Lc (maximum distance from the jet center to the edge of the jet controlled area) was defined to distinguish different configurations. Finally, they found that the jet number had little effects on critical heat flux, and a CHF correlation as follows was

Fig. 3. Effect of surface condition on critical heat flux (reprinted from Qiu and Liu [28], Copyright 2008 from Elsevier).

proposed for all the jet configurations. The correlation constants 0.150 and 0.615 were developed for CHF occurring at the heater boundary, and should be replaced by 0.0941 and 0.646 for CHF occurring at heater center. Monde and Inoue [48] later re-examined the data and suggested that the data for multiple jets could be correlated with the single jet CHF correlation that developed for single jet with acceptable accuracy.

!1=3  0:615 q00CHF q r 1 ¼ 0:150 l 2 qv Uhfg qv ql U 2 Lc 1 þ 0:00113ð2Lc =dÞ

ð20Þ

Rau and Garimella [29] investigated jet impingement boiling heat transfer phenomenon in single jet and jet array (3  3 and 5  5 jets) configurations. The nozzle diameter and impact distance varied from single jet to multiple jets but the p=d and H=d were both maintained at a value of 4.0. Multiple jets produced better area-averaged heat transfer but more significant surface temperature gradient than the single jet. However, it should be noticed that this conclusion was drawn under the scenario that single-phase and boiling coexisted together. Moreover, they also reported the pressure drop characteristics. The pressure drop was mainly generated by the single-phase flow through the ejection holes, and the boiling two-phase flow had little contribution to the overall pressure drop. 3.1.7. Effect of surface condition Qiu and Liu [28] investigated the effect of surface condition on jet impingement boiling heat transfer. The copper target surface was coated with titanium dioxide (TiO2) which had significantly reduced the contact angle to nearly zero and made the surface superhydrophilic. It was founded that the wall heat transfer in fully developed nucleate boiling regime was weakened and the boiling incipient was delayed. However, compared to the correlation developed by Monde et al. [44,45], the CHF in the superhydrophilic surface case remarkably increased by around 30% (see Fig. 3). Qiu and Liu [49] deducted a semi-theoretical solution to predict the effects of contact angle to the stagnation zone CHF in jet impingement boiling. The results showed that the effect of contact angle (CA) was independent of other effects. For saturated water, the following correlation was proposed, 1=3

q00CHF ¼ 3:6  105 ð1:49  0:009hÞðU=dÞ

ð21Þ

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

49

Fig. 4. Temperature maps in single jet (left) and multiple jets (right) configurations at the same wall heat flux magnitude (reprinted from Rau and Garimella [29], Copyright 2013 from Elsevier).

Li et al. [17] found that the CA did not influence the single-phase convection heat transfer, but significantly influence the fully developed nucleate boiling curve, CHF and ONB. In the nucleate boiling regime, a lower CA resulted in a later boiling incipient (higher the superheat of ONB) and higher CHF. For boiling curve, the coefficients were 3:9  106 ; 2:8  106 and 1:75  106 for 5°, 60° and 105° of CA, respectively. For CHF correlation, likewise, the effect of CA was independent of the other parameters, such as jet velocity and subcooling. The following correlation was proposed for saturated fluid when the CA was in the range of 5–105°,

q00CHF ¼ f ðhÞhfg ðrq2l Þ

1=3



qv ql

1:4=3  1=3 U d

ð22Þ

where

f ðhÞ ¼ ð0:191  0:055hÞ

ð23Þ

Moreover, Li et al. [18] proposed the correlation for ONB and CHF wall superheat and heat flux, in which the effect of CA, jet velocity and subcooling were included. It showed that the superheat of ONB decreased with CA.

kl  ½15 lnð2 þ UÞð1 d þ 0:00606DT sub Þð1  0:00281hÞ þ DT sub 

q00ONB ¼ 0:278Re0:633 Pr 0:333

" q00CHF ¼ f ðhÞ hfg ðrq2l Þ

1=3



qv ql

ð24Þ

# 1:4=3  1=3  12 1 U U þ 15:15ðkl ql C p;l Þ2 DT sub d d ð25Þ

In the nucleate boiling regime, the correlation for HTC were also proposed as follows,

HTC FNB ¼ 3:045  1011 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:333 

r

gðql  qv Þ

ð1  cos hÞ0:5 ð1  3:333

kl

cos 55 Þ0:5

DT 2:333 sat

Pr1:167



P qv hfg rU l

2:333

ð26Þ

3.1.8. Coexistence of single-phase convection and boiling In the experiments of Rau and Garimella [29], the target surface was a thin-foil heater on which the temperature distribution was measured by infrared camera. It was found that both single-phase convection region and boiling region coexisted in the tested domain under a moderate wall heat flux (see Fig. 4). The thin foil heater supplies an isoflux boundary condition. The single-phase flow dominated in the stagnation zone since the jet impingement increased the heat transfer and decreased the wall temperature, however, boiling was already initiated in the area far from stagnation zone with the same wall heat flux. It is well know that the HTC is independent of wall heat flux in a moderate wall-to-fluid temperature difference in single-phase convection, whereas it is a function of wall heat flux in boiling regime. Therefore, it was observed that HTC was independent of wall heat flux in the stagnation zone (single-phase convection dominated), but increased with wall heat flux in the far field (see Fig. 5). The boiling dominated region was spreading into the stagnation zone when the wall heat flux kept increasing. Finally, boiling was dominated on the entire surface, and the temperature distribution (or HTC distribution) became relatively uniform. The phenomenon was observed if a thin-foil heater was employed as the target surface in the experiments and the span-wise conduction could be neglected [29,25]. However, if the target wall had a considerable thickness and thermal conductivity, the results would be different since the above mentioned jet impingement generated wall temperature difference will be weakened by the span-wise conduction inside of the solid wall. This means that a conjugation heat transfer problem should be concerned. 3.2. Effects of system parameters on boiling heat transfer for submerged and confined jets 3.2.1. Effect of jet velocity Unlike the free-surface jet impingement boiling, conflicting observations were reported regarding the effect of jet velocity in the studies of submerged and confined jet impingement boiling.

L. Qiu et al. / International Journal of Heat and Mass Transfer 89 (2015) 42–58

Fully developed nucleate boiling

Co-exist of boiling and single-phase convection

Region dominated by boiling

HTC

Region dominated by single-phase convection

Stagnation zone

increase q’’

50

Single-phase convection

0

Radius from jet centreline

Fig. 5. Spatial HTC distribution on heater under the constant wall heat flux wall boundary condition: boiling reduces the wall temperature difference between stagnation and non-stagnation zones (reprinted from Rau and Garimella [29], Copyright 2013 from Elsevier).

Zhou and Ma [40] examined the effect of jet velocity on submerged jet impingement boiling heat transfer. It was found that the jet velocity had little effect on the boiling curve in the fully developed regime in the velocity range from 0 to 11.34 m/s. This means that those boiling curves can be obtained by extrapolating the pool boiling curve. Besides, the boiling curves at downstream locations are basically same with that at stagnation point. When U > 10 m/s, the effect of stagnation pressure induced saturation temperature rise should be considered. It was proved that the experimental CHF data matched the below correlation of Monde and Katto [50] well.  0:725   "  1=2  2 # C p;l DT sub q00CHF r 1=3 ql 2 ql ¼ 7:45  10 1 þ 2:7 qv Uhfg qv ql UD qv hfg ð27Þ

Cardenas and Narayanan [11] found that higher jet velocity increased the CHF but not boiling curve in the nucleate boiling regime. CHF enhancement ratios increased with increasing Re of jet. By comparing the experimental data with seven CHF correlations in open literatures reported in 1978–1991, it was found that the free surface jet correlation of Monde and Katto [50] matched the data in the best way under the high jet velocity region (0.9– 3.4 m/s) while the discrepancy at the low velocity band (0– 0.9 m/s) came from the liquid pool. Similar observations were made by Zhao et al. [39] and Hong et al. [16]. For both the porous and smooth surfaces, Zhao et al. found that the wall heat flux was independent of jet velocity at 0.82–4.24 m/s in the fully developed boiling regime. Hong et al. employed 43% mass concentration aqueous ethylene glycol as the working fluid, and found that the effect of jet velocity was apparent in the single-phase and incipient boiling regimes, but not in the fully developed boiling regime when the jet velocity was in the range of 0.2–0.5 m/s. Jet velocity promoted the ONB and CHF in the case of impact distance equaled to jet diameter. Different from the observations that mentioned above, however, it was found that the jet velocity influenced the boiling curve even in the fully developed boiling regime in other studies. Vader et al. [35] investigated the effect of jet velocity at 4.7– 13.3 m/s on boiling heat transfer in a submerged liquid nitrogen (LN2) jet impingement configuration. The results showed that the jet velocity increased the heat transfer at both single-phase and

nucleate boiling regimes. Besides, Ndao et al. [26] studied the effect of jet velocity on impingement boiling heat transfer with smooth and micro-pin–fin roughened surfaces. With smooth surface, the jet velocity at 1.1–4.05 m/s greatly influenced the ONB and boiling curves. The reason was inferred that the wall jet region overshadowed the effects of jet velocity. With the pin–fin arrayed surface, increasing jet velocity resulted in a low superheat of ONB and a higher CHF. This is good for cooling since it reduces thermal stress and delays CHF. Browne et al. [9,10] investigated the effect of jet velocity at 0 to 10 m/s in two jet impingement boiling configurations with micro-jet. They found that increasing jet velocity resulted in higher ONB and better overall heat transfer. It was explained that the higher jet velocity resulted in a high single-phase heat transfer rate, hence, it requires a higher heat flux to initiate the boiling. In the boiling regime, the effect of jet velocity decreased with wall superheat. Zhang et al. [38] investigated the effect of jet velocity in a sidewall confined LN2 jet impingement boiling configuration with different impact distances (H). The diameter of confinement cylinder (Dc ) was only 2.5 times of the jet diameter (d). It was found that the two phase flow patterns were very distinct from the free jet cases. They suggested that the heat transfer in this confined impingement case was mainly governed by convective evaporation rather than nucleate boiling. Due to the heat transfer correlation that proposed for flat surface case, it was shown that jet Re made a significant difference to the heat transfer rate compared to the effects of boiling number and impact ratio.

Nu ¼ 227:7Re0:195 Bo0:007 ðDc =HÞ0:061 ðflat surfaceÞ

ð28Þ

Three different surface configurations (flat surface, hemispherical surface and flat surface with a needle) were tested. Similarly, Re of jet played an important role to impingement boiling heat transfer of hemispherical and needle roughened surface.

Nu ¼ 420:2Re0:145 Bo0:007 ðDc =HÞ0:070 ðhemi surfaceÞ

ð29Þ

Nu ¼ 332:0Re0:166 Bo0:048 ðDc =HÞ0:027 ðneedle surfaceÞ

ð30Þ

They also developed a correlation for CHF prediction under hemispherical surface case in the jet velocity range from 0.34 to 1.11 m/s.

!0:267   0:399 0:44 q00CHF qv 2r H ¼ 0:16 1þ 2 D Ghfg ql ql U d

ð31Þ

This correlation showed that the CHF increased with an increase of jet velocity, but decreased with an increase of impact distance. 3.2.2. Effect of jet subcooling Zhao et al. [39] studied the effect of subcooling on jet impingement boiling heat transfer of a structured-porous target surface as well as smooth one. It was reported that the wall heat flux was independent of subcooling in the fully developed regime for both smooth and porous surfaces. This result was in accordance with the free-surface configuration. However, different observations were made by the other researchers. Vader et al. [35] investigated the effect of subcooling on boiling heat transfer for LN2 jet impingement. By pressuring helium gas into the LN2 container, they were able to obtain a 10 K subcooling. The results showed that the subcooling apparently influenced the boiling curve in the fully developed regime. There were also some conflicting reports regarding the effect of subcooling on ONB. Vader et al. [35] found that a higher subcooling resulted in a higher superheat of ONB and higher CHF. Browne et al. [9] also found that increasing subcooling resulted in higher ONB in

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the confined micro-jet configuration. However, Hong et al. [16] found that the subcooling promoted the ONB with a low wall superheat and heat flux. Zhou et al. [41] found the incipient boiling superheat decreases only with fluid subcooling regardless of jet parameters. 3.2.3. Effect of non-condensable gas in liquid jet Liquids as highly wetting fluids are capable to absorb non-condensable gases, hence, the effect of non-condensable gas is worth being investigated. Zhou et al. [41] found that non-condensable gases increased wall heat transfer. More recently, in studying the confined micro-jet array jet impingement boiling heat transfer, Browne et al. [9] found that the nucleate boiling region was broadened and the maximum wall heat flux was elevated to 600 W/cm2 by accidently mixing non-condensable gas nitrogen into the impingement jet. Then in the following study, Browne et al. [10] examined the effects of dissolved nitrogen to the jet impingement boiling heat transfer. At three different nitrogen partial pressures (0, 103 and 241 kPa), it showed that the nitrogen partial pressure did not significantly influence the boiling curve but apparently depress the CHF (a higher partial pressure related to a lower CHF). 3.2.4. Effect of impact distance (confinement) Hong et al. [16] investigated the effects of impact distance in two jet array configuration. It was found that boiling curve in fully developed boiling regime was independent of impact distance, but the CHF was apparently influenced by impact distance. The middle impact distance (H=d = 1.5) presented the highest CHF among the three tested configurations (H=d = 1, 1.5, 3). This was induced by the upper-wall confinement which enforced mixing of the jet and bubbles. Hence, it was proposed that there should be an optimum impact distance to achieve the best CHF. The results were different from the previous studies of Shih et al. in a planar jet configuration. It can be inferred that this discrepancy comes from the different jet velocity. The jet Reynolds number was 200 to 600 in the experiments of Hong et al. whereas 2000 to 5000 in the experiments of Shih et al. [30]. Hence, the magnitude of jet momentum influenced the interaction of bubble and subcooled jet. In the side-wall confined LN2 jet impingement boiling configuration, Zhang et al. [38] found that the impact distance did not apparently influence the heat transfer rate since the exponent of impact distance was relatively small. Moreover, Wu et al. [37] investigated the effect of impact distance in the single jet and jet array (1  3 jets) configurations. For both jet configurations, the confined configurations (H=d = 1) presented higher heat transfer compared to the ‘‘un-confined’’ ones (H=d = 5.3) in single-phase regime, because the channel-type confinement increased the actual near-wall Re. However, most of the presented data were obtained in the single-phase regime, boiling only happened on the edge of the heater (far from the jet) in very small amount of working conditions. The boiling related heat transfer was barely discussed. 3.2.5. Effect of multiple jets Hong et al. [16] compared the boiling heat transfer in 50 jets and 32 jets configurations. It was found that the 50 jets (p=d = 5) configuration showed higher overall heat transfer rates than 32 jets one (p=d = 4) with the same total mass flow rate. Browne et al. [9,10] also compared the boiling heat transfer in two different jet configurations: with 9 (p=d = 3.2, Ar = 8.9%) and 22 (p=d = 2.05, Ar = 21.4%) effective jets. Jets were staggered arrayed in both micro-chambers (jets center-to-center distances are 360 lm and 230 lm, respectively). Effective-jets stands for the number of jet that impinges onto the heated surface. The HTC

was almost constant in the single phase regime but had a linear relation with wall heat flux in the boiling regime. An apparent ONB point could be distinguished. Hence, the averaged HTC was correlated in the following forms,

HTC ¼ HTC sp þ HTC b ¼ HTC sp þ C 7 ðq00  q00ONB Þ in which, the coefficient C 7 and ONB heat flux follows,

C7 ¼

2152Ar0:267 0:268 DT 0:533 sub U

0:448 q00ONB ¼ 20:3ðcos ArÞ3:26 DT 0:417 sub U

ð32Þ q00ONB

were given as

ð33Þ

ð34Þ

The significance of multiple jets was shown by the area ratio Ar. The correlation showed that the area ratio did not apparently influence the ONB heat flux. A higher area ratio resulted in a better heat transfer rate at the same wall superheat, jet velocity and subcooling. Although CHF correlations were not provided, the experimental data showed that higher area ratio decreased the CHF apparently. 3.2.6. Effect of surface condition Zhao et al. [39] investigated the effect of structured-porous surface on jet impingement boiling. The porous surfaces were fabricated by bounding single or multiple layers of copper mesh. It showed that boiling started earlier on the porous surface. The fully developed boiling regime was achieved under a lower wall superheat (around 10 K) compared to the plane surface (around 22 K). The four layer mesh surface transferred highest heat energy under the same superheat in the fully developed boiling regime. A thicker layer introduced higher flow resistance for flow penetration whereas thinner layer produced less bubble nucleation. Besides, they also found that surface aging influenced the boiling curve apparently. Ndao et al. [26] investigated the effect of micro-pin–fins on the jet impingement boiling heat transfer. Micro-pin–fin structures were manufactured as circular, square and hydrofoil shapes. The smooth surface had the lowest heat transfer whereas the micro

Fig. 6. Effect of surface condition (micro-pin–fins roughened) on boiling curve (reprinted from Nado et al. [26], Copyright 2012 from Elsevier).

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circular pin–fin arrayed surface had the highest one. As shown in Fig. 6, the circular pin–fin with a larger diameter (125 lm) presented a higher heat transfer rate and CHF than lower diameter one (75 lm). Interestingly, it was found that the boiling curves for different diameter pin–fins were different if the wall heat flux was calculated with base area. However, the boiling curves in those two configurations were basically same if total surface area was used to calculate the wall heat flux. This suggested that the heat transfer enhancement in the pin fins configuration was mainly caused by the increase of nucleate site. Moreover, it also showed that the surface aging greatly influenced the impingement boiling heat transfer. Moreover, Zhang et al. [38] reproduced the experiments that conducted by Aihara et al. [51]. They compared the heat transfer under three different shapes of target surface: flat surface, hemisphere surface, and a needle roughened flat surface. The hemisphere surface showed the highest CHF whereas the flat surface showed the lowest one. Surface contamination shifted the boiling curve to the lower heat flux direction. This means that the surface contamination decreases the heat transfer rate and CHF. 3.2.7. Coexistence of single-phase convection and boiling Dukle and Hollingsworth [13,14] investigated the boiling front phenomenon in incipient jet impingement boiling regime under different jet velocities (0.7–1.4 m/s) and impact distances (H=d = 2.3 and 8.2) via thermal liquid crystal technique. In this case, the single-phase convection and nucleate boiling existed simultaneously. A stable and reproducible boundary between them (boiling front) was observed in the experiments. The radius of boiling front rf was proposed to obey the following correlation,

  1=2 q00f rf ¼ C 8 ln  C 10 d=2 C 9 DT ref ;incip

ð35Þ

ð36Þ

It was suggested that a good prediction of boiling front could be obtained based on the single-phase impingement HTC distribution. The reference temperature (T ref ) used in calculating the heat transfer coefficient was the local bulk temperature obtained by averaging the jet temperature in the nozzle and far-field temperature of the pool. Although the effects of jet velocity and impact distance were not included in the model, it showed that a higher jet velocity and smaller impact distance secured a larger surface area of single-phase convective regime, then resulted in a larger radius boiling front. 3.3. Effects of system parameters on boiling heat transfer for planar jets 3.3.1. Effect of jet velocity Wolf et al. [36] investigated the effect of jet velocity on free-surface planar jet impingement boiling heat transfer. As same as the circular free jets, the boiling curve was not notably influenced by the jet velocity (2 and 5 m/s) in fully developed nucleate boiling regime, but was significantly influenced in single-phase and partial boiling regime. The following correlation was proposed for both the jet velocities in the superheat range from 23 to 51 K,

q00 ¼ 63:7ðDT sat Þ2:95

rendered a higher CHF. The surface temperature difference was very limited for both single and two-phase conditions. Based on the CHF correlation of Mudawar and Wadsworth [52], they proposed a CHF correlation as follows, q00CHF =ðqv hfg Þ

where the C 8 ; C 9 ; C 10 were correlation constants that fitted from experimental data at different working conditions. And DT ref ;ONB was calculated as follows,

DT ref ;ONB ¼ ðT w  T ref ÞONB ¼ q00f =HTC f

Fig. 7. Effects of high jet velocity and high liquid subcooling on CHF (theoretical prediction and experimental data) (reprinted from Li et al. [19], Copyright 2014 from Elsevier).

ð37Þ

Meyer et al. [24] investigated the effect of jet velocity in a slot jet array configuration. They also found that boiling curve in fully developed boiling regime was independent of jet velocity. However, higher jet velocity delayed the ONB and consequently

U ~00CHF ¼  2=3  q   C p;l DT sub 1=3 ql 1 þ 1 þ 0:034 qql qv hfg v " #0:157

¼ 0:0919

 C p;l DT sub 2=3  W 0:031 hfg LW

r ql U 2 ðL  WÞ

ð38Þ ~00CHF was the dimensionless critical heat flux. where q Li et al. [19] investigated the effect of jet velocity at 4 to 40 m/s on the jet impingement boiling under high jet velocities (see Fig. 7). A new CHF correlation was proposed as follows,

 1:4=3   q00CHF q rql 1=3 ¼ 0:160 v 2 Ghfg ql G W

ð39Þ

Similar to the free surface circular jets, jet velocity at 10 m/s was the threshold for slot jets. When U < 10 m/s, the experimental data supported that the CHF was proportional to U 1=3 . If the jet velocity was higher than 10 m/s, the fluid properties used in the above correlation should be calculated with the stagnation pressure. In the range that experimental data were collected, they agreed well with the prediction. Interestingly, the theoretical model predicted that CHF would reduce after a critical value which would happen at around jet velocity with 130 m/s. Hence, an ultimate CHF would exist at highest subcooling. The maximum subcooling of the water in their experiments reached up to 99 K which meant that water almost approached the frozen point under the atmosphere pressure. Shin et al. [30] investigated the effects of jet velocity on slot-jet (with a width of W) impingement boiling heat transfer under different upper-wall confinement. With the narrowest slot (H=W ¼ 4), the influence of upper wall was relatively small. Hence, in accordance with the free-surface jet configurations, the

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boiling curve was independent of jet velocity. However, with the widest slot (H=W ¼ 0:5), increasing the jet velocity resulted in a higher heat transfer rate at the stagnation point. A strong interaction between the bubble generation and jet impingement in the stagnation zone produced a higher heat transfer than downstream locations. Moreover, increasing jet velocity resulted in a higher CHF. The following CHF correlation was proposed which included the effects of jet velocity, impact distance and jet width,

q00CHF ¼ 7:47 log ðGÞ2 þ 8:5831 log ð10H=WÞ2 þ 11:7931  logðGÞ logð10H=WÞ  83:7 logðGÞ  50:251  logð10H=WÞ þ 138:1

ð40Þ

3.3.2. Effect of jet subcooling Li et al. [19] studied the effect of subcooling on CHF ratio in a free-surface planer jet impingement boiling configuration, and the following correlation was recommended in the subcooling range of 0–99 K,

 0:55  0:64 C p;l DT sub q00CHF q ¼ 1 þ 0:26 v 00 qCHF;0 ql hfg

ð41Þ

Meyer et al. [24] investigated the effect of subcooling on impingement boiling heat transfer in a confined slot jet array configuration. Subcooling did not influence the heat transfer rate in single-phase regime, but delayed the ONB apparently. Besides, CHF was also elevated by subcooling. Pressure drop was not apparently influenced by the subcooling, but significantly influenced by jet velocity. 3.3.3. Effect of jet width Meyer et al. [24] investigated the effect of jet width on boiling ~00CHF ) corheat transfer. Based on the proposed dimensionless CHF (q relation, the following relation existed,

~00CHF / U 0:686 W 0:331 ¼ U 0:355 ðUWÞ0:331 ¼ ðUWÞ0:686 W 0:355 q

ð42Þ

It suggested that the narrower jet width (higher jet velocity) produced higher CHF at the same flow rate. The CHF could be enhanced by simply employing smaller jets under the same mass flow rate. A wider jet rendered a higher CHF at the same jet velocity. 3.3.4. Effect of impact distance Shin et al. [30] investigated the effects of impact distance on jet impingement boiling heat transfer. It was reported that the high H=W resulted in a weak spatial temperature gradient whereas the low H=W rendered a significant one. It means that the confinement increases the wall temperature gradient. For example, the average temperature differences between two typical locations (r=W = 0 and 1.5) were 2.1 K, 5.6 K and 9.6 K for H=W = 4, 1 and 0.5, respectively. The bubbles near the stagnation zone were notably less in the lower H=W experiment, because bubbles could easily departure from the surface in the high H=W configuration. For a given jet velocity, CHF decreased at first and then increased with H=W. Hence, the worst CHF was expected in the middle of the H=W tested range (see Fig. 8). The critical H=W for lowest CHF was a function of the mass flow rate of jet (G) as follows,

H=WjlowestCFH ¼ 1:4016 log ðGÞ2  9:54548 logðGÞ þ 16:493

ð43Þ

3.3.5. Effect of multiple jets Meyer et al. [24] employed three slot-jets in their jet impingement boiling studies. However, the fluid outlets located in the middle of two inlets, which makes those arrayed jets bear a periodical

Fig. 8. Effect of upper-wall confinement on CHF at different jet velocities (reprinted from Shin et al. [30], Copyright 2009 from Elsevier).

characteristics. In this scenario, the ‘‘jet array’’ was only a stacking of single jet units. 3.4. Hybrid configuration In some experiments, the jet impingement boiling configuration was accompanied with cross flow or channel flow, which made the flow and heat transfer characteristics of hybrid configuration special. A series of studies regarding a hybrid jet impingement boiling configuration were reported by Sung and Mudawar [31–34], which combined the in-line jet impingement array with micro channel. Liquid ejected from 12 to 14 jets into a micro channel and then boiled. They found that the nucleation, growth, departure and coalescence of bubbles in the micro-channel with jets were very special. The generated bubbles in the micro-channels collapsed when they encountered a lower temperature flow in the downstream. The hybrid cooling scheme produced a less temperature gradient on the wall while it generated a relatively strong heat transfer. Besides, Guo et al. [15] introduced a cross flow passing through the jet impinged surface in the investigation. It was found that the mechanism of bubble behavior was complicated due to the cross flow. 3.4.1. Effect of jet velocity Sung and Mudawar [31] investigated the effect of slot-jet velocity on heat transfer in the hybrid configuration. They observed that increasing jet velocity delays the ONB to a higher heat flux and a higher wall superheat. In the fully developed nucleate boiling regime, the high jet velocity resulted in a higher heat flux especially at high subcooling, and finally increased the CHF apparently. Similar conclusion was also drawn in the study of the jet array based hybrid configuration. A higher jet velocity resulted in a higher CHF but generated a higher pressure drop. For example, a heat flux of 1080 W/cm2 was measured at U = 5.7 m/s with a pressure drop of 1.2 bar, whereas a heat flux of 1127 W/cm2 was achieved at U = 6.5 m/s, with a pressure drop of 1.7 bar. For the slot jet and circular jet configuration, a new simple CHF correlation scheme was proposed: the CHF of the hybrid

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configuration was the area weighted CHF of the jet impingement boiling and channel flow boiling,

q00CHF;hybrid Atotal ¼ q00CHF;jet Ajet þ q00CHF;channel ðAtotal  Achannel Þ q00CHF;jet

ð44Þ

q00CHF;channel

where the and were the correlations for jet impingement boiling and channel flow boiling in open literatures. Guo et al. [15] studied the effect of jet velocity on boiling heat transfer in micro-pin–fin arrayed configuration. Increasing the jet velocity resulted in a higher ONB and CHF. It was found that the effect of jet velocity was phenomenal at low crossflow velocity, but not so apparent at the high crossflow velocity. Due to the data obtained at different combination of jet and crossflow velocities, the case that the low cross velocity combined with a high jet velocity was considered to be a more effective and economical method for heat transfer enhancement. 3.4.2. Effect of jet subcooling Sung and Mudawar [32,34] found that the subcooling showed a relatively weak relation with single-phase convective heat transfer due to the mild variation of liquid properties with temperature. However, when boiling occurred, it was found that both heat flux and surface temperature of ONB enhanced with an increase of subcooling. The CHF also increased considerably with an increase of subcooling. Moreover, it was found that the heat transfer coefficient varied with wall heat flux and subcooling in the following form for three different jet patterns,

q00FNB HTC FNB ¼  00 1=3:252 q FNB

64:81

ð45Þ þ DT sub

3.4.3. Effect of jet pattern Sung and Mudawar [34] compared the heat transfer characteristics under three different patterns of the jets: jet diameter decreasing, unvarying and increasing from the channel center to the two outlets. It was found that the jet pattern did not apparently influence the heat transfer in the boiling regime but significantly influence the pressure drop. The decreasing-jet-size pattern had the highest CHF since it produced the largest outlet subcooling of the main flow. The equal-jet-size pattern produced the highest pressure drop. Moreover, it was shown that pressure drop in such kind of hybrid boiling channel decreased with wall heat flux in both single-phase and boiling regime due to the reduced viscosity and special nucleate boiling pattern, respectively. Finally, the lowest pressure drops happened just before the CHF. This feature of hybrid configuration in boiling regime was very different from conventional convective boiling in long straight channels. 3.4.4. Effect of surface condition By manufacturing micro-pin–fins (thickness = 30 and 60 lm, height = 60 and 120 lm) on the target surface, Guo et al. [15] obtained four different surface roughness in their studies. Pin–fins greatly enhanced the heat transfers compared to the smooth case. They proposed that the staying and growth of bubbles had reinforced the heat transfer especially in the gaps of pin–fins, and consequently increased the CHF. However, the CHF of pin–fin arrayed configuration was prone to be influenced by the jet velocity compared to the smooth surface. 3.5. Other phenomena and jet impingement configurations 3.5.1. Boiling hysteresis phenomenon Boiling hysteresis phenomenon was observed in many experiments in the transition from incipient boiling to fully developed nucleate boiling. Recently, Cardenas and Narayanan [11]

Fig. 9. Boiling curve hysteresis (reprinted from Cardenas and Narayanan [11], Copyright 2012 from Elsevier).

investigated this phenomenon with FC-72 (see Fig. 9). The boiling was not activated immediately when the wall temperature slightly larger than the saturation temperature. Strong bubble generation and mixing accompanied with the heat transfer reinforcement were observed once the superheat was large enough to initiate the boiling. Thus, the boiling paced into the nucleate boiling regime and the corresponding wall temperature reduced abruptly due to the sudden increase of heat transfer rate. This phenomenon was apparent if one employed a highly wetting fluid in the experiments. For example, Shin et al. [30] with the dielectric fluid PF5060, Zhou et al. [41] with R113 and Nado et al. with R134a [26]. However, there are some conflicting observations regarding the superheat excursion (the sudden superheat drop on ONB). Zhou et al. [41] found that superheat excursion increased with an increase of nozzle diameter or radial distance from the stagnation point, but decreased with an increase of jet velocity and fluid subcooling. Zhou and Ma [40] confirmed this observation. Nado et al. [26] found that the increase of jet velocity decreased the superheat excursion. However, Cardenas and Narayanan [11] reported that the superheat excursion was found to vary randomly, and it was independent of jet velocity and nozzle diameter. Interestingly, the probability of boiling incipience was found to be a function of wall superheat. It means that the superheat excursion should be described with probability approach rather than a definite expression.

3.5.2. Unsteady jet impingement boiling (quenching) Quenching process is an important branch in jet impingement boiling heat transfer which is a physical model of steel processing in industry. Unlike the conventional steady-state impingement boiling, quenching means the target surface is heated initially, and then cooled down by the liquid jet accompanied with the boiling phenomenon without the additional energy supplying into the impingement target, hence its temperature keeps reducing during the impingement. Woodfield et al. [53] investigated the flow, heat transfer and sound characteristics in a water impingement quenching process. The flow pattern, quenching sound, and temperature of target surface were measured via high-speed video camera, microphone and thermocouples, respectively. As an unsteady process, it was observed that the initial temperature influenced the flow pattern in quenching process apparently. Four main flow patterns were

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observed in a quenching process, and the so-called ‘‘liquid sheet flow’’ pattern had a higher heat transfer rate than other patterns. Moreover, Hasan et al. [54] developed a model to describe the nucleate boiling process in impingement quenching by applying one dimensional semi-infinite heat conduction and nucleate boiling conception in the study. Karwa et al. [55] observed three distinct regions on the impingement surface via a high-speed camera, namely, an expanding circular wetted region in the center, annular transition zone outside the wetting front, and an unwetted region outside this zone. The detailed flow and heat transfer characteristics in those regions were proposed and analysis. Mitra et al. [56] added nanoparticles in the impingement working fluid in quenching study. It resulted in significant cooling rate enhancement, but a slight CHF variation. Wang et al. [57] employed multiple circular jets in the study. They found that the jet velocity did not influence the heat transfer and CHF in the stagnation zone, but slightly in the outer region of the target surface. 3.5.3. Cylindrical target surface In the investigation of Bartoil et al. [58], the water slot-jet impinged down to a submerged hot wire (long cylinder) in place of flat surface. They found that the vapor bubbles were constrained by the downward impingement. A vapor cavity was formed beneath the cylinder due to the balance of bubble buoyancy and jet impingement momentum. Then, the cavity split and turned upwards as the small bubbles at a distance around 7 times its diameter from the heater. The jet parameter greatly influenced the boiling flow pattern in this process. The heat transfer enhancements in downstream seemed to be caused by fluid mixing. Similarly, a nickel wire was used as the impingement target by Baffigi and Bartoli [59]. The impingement distance was varied from 3 to 8 times of the nozzle diameter. Having found that the boiling curves at different jet velocities were almost same, they suggested that the lowest jet velocity condition, which required the least pumping power, was the most efficient configuration once the energy consuming was concerned. 3.5.4. Rotating target surface Quinn and Cetegen [60] experimentally and analytically investigated a water impingement boiling on a hot rotating disk. The heat fluxes in all the working conditions were constant (7.346 W/cm2). The rotation induced centrifugal force and Coriolis force affected the type of bubble growth near the rotating surface. Three different types of bubbles were observed in the process: detached large scale bubbles, small bubbles attached on the rotating surface in the super-critical flow, and hemispherical bubbles that located on the top of a micro layer of water film under the low rotational speed. It was proposed that a micro layer existed under the radically sliding hemispherical bubbles and enhanced the surface heat transfer. 3.5.5. Cryogenic jet impingement boiling Ashworth and Reagor [61] proposed a novel concept that employing internal phase change impingement of liquid nitrogen to cool three-phase superconducting power cable. Compared to the previous approach that using sub-cooled liquid nitrogen to cool the cable, this innovative design utilized the latent heat of LN2 evaporation and avoided the intermediate cooling station in long distance superconducting power cable power transportation. It is estimated that the new design allows a single section of AC and DC cable have a length of around 100 km and 200 km respectively. Takara et al. [62] had tested two different LN2 evaporators which were designed to use the jet impingement boiling to cool the high power electrical components. Two evaporators that made by copper and aluminum were tested, and the target wall heat fluxes achieved around 70 and 60 W/cm2, respectively. They also

55

reported that adding a nozzle (producing a spray) has very limited contribution to the wall heat flux promotion compared to the direct jet impingement (through a hole). For application concerns, the temperature stability of the evaporators were also tested. 4. Numerical models and simulations Phenomenon as boiling is complex that giving a satisfactory general-purpose boiling model is quite challenging. The fundamentals of boiling must be clearly understood so that a reasonable mechanistic model can be established, based on which numerical simulation is able to be carried out. Computational approach usually consumes less time and money to provide a prediction for a specific problem than experiments. It shows a huge advantage in extreme working conditions that the experiments are difficult to carry out. However, as mentioned, the major obstacle in front of the numerical simulation is to find a physical model which is able to not only describe a complex physical phenomenon precisely, but also be numerically solved within the state-of-art computational capacity. Once the jet impingement involves, it is not clear whether new problems arise. Unfortunately, only a small amount of theoretical and numerical works have been reported for jet impingement boiling flow and heat transfer. 4.1. Eulerian based mixture models A classical approach to model the boiling phenomenon is using Eulerian based multi-phase framework. It is assumed that both liquid and vapor phase are treated as continues fluid so that two sets of Navier–Stokes (NS) equations are solved separately. Wang et al. [63] employed Eulerian mixture model to simulate a jet impingement boiling configuration which had been experimentally investigated by Chrysler et al. [64]. The significance of boiling was shown by inter-phase models: (1) an interphase mass transfer rate was given by an empirical correlation that based on bubble departure diameter, (2) the drag force was assumed to be dominating inter-phase momentum transfer mechanism, which also depended on departure bubble diameter, and (3) the inter-phase heat transfer coefficient was assumed infinite high so that the temperature difference between the two phases could be negligible. The predicted boiling curve had the same trend with the measured one, so they concluded that this two-phase model was able to predict the jet impingement boiling heat transfer. 4.2. Eulerian based PRI boiling models Given that the bubble generation, growth and departure start from the boiling wall, we must be careful when modeling the wall heat transfer. To address this problem, the wall heat flux partitioning models are employed. In PRI model (proposed by researchers in Rensselaer Polytechnic Institute), wall heat flux is separated into three portions: single-phase convective heat flux, quenching heat flux and evaporation heat flux.

q00wall ¼ q00Conv ectiv e þ q00Quenching þ q00Ev aporativ e

ð46Þ

The convective heat flux is calculated as follows,

q00Conv ectiv e

¼ HTC Conv ectiv e ð1  Ab ÞðT w  T l Þ

ð47Þ

where the convective HTC and the vapor bubble covered area ratio Ab are given by sub-models, Ab is usually correlated with nucleate site density (N w ) and bubble departure diameter (Dbd ) which also needs to be modeled. The quenching heat flux is calculated as follows,

q00Quenching ¼ HTC Quenching Ab ðT w  T l Þ

ð48Þ

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where the quenching HTC is correlated with bubble departure frequency f that based on the Dbd . Finally, the evaporative heat flux is calculated as follows,

q00Ev aporativ e ¼

p 6

D3bd fNw qv hfg

ð49Þ

Besides, in RPI boiling model, more inter-phase transfers sub-models are included: (1) inter-phase mass transfer is calculated based on the interfacial evaporation–condensation model, (2) inter-phase momentum transfer is modeled by imposing interfacial forces, such as drag force, lift force, turbulent dispersion force and wall lubrication force on the primary phase (liquid), and (3) inter-phase heat transfer depends on the interfacial heat transfer area (which is given by bubble diameter) and heat transfer rate [65]. An case study was given by Narumanchi et al. [66]. They adopted RPI boiling model in the study of a confined jet impingement boiling configuration which was a geometry that practically used in insulated-gate bipolar transistors (IGBTs) via ANSYS-Fluent solver. In order to validate this simulation tool, two jet impingement boiling cases that reported in the literatures were simulated. The predicted results reached a very good agreement with the experimental data (see Fig. 10). Moreover, Abishek et al. [67] employed RPI boiling model in the study of a confined subcooled jet impingement cooling configuration via commercial computational fluid dynamics (CFD) software ANSYS-Fluent. Validations were carried out by running both free surface and confined jet impingement cases that reported in previous studies. The effect of heater size on boiling heat transfer was investigated. It showed that smaller heater always presented a higher heat transfer coefficient in all the conditions they tested. Finally, the variation of each component of wall heat flux against wall superheat was presented. 4.3. Single-phase based jet impingement boiling models Timm et al. [68] developed an analytical model for high superheat jet impingement boiling (wall superheat higher than 800 K). In the model, the fluid was treated as incompressible and single-phase by neglecting the net vapor generation. The laminar

sub-layer adjacent to the wall was replaced by a highly diffusive turbulent zone that generated by bubble growth and collapse. Hence, additional diffusive terms were added in the single-phase NS equations. The bubble induced additional diffusivities in momentum and energy equation were assumed same (diffusion Prandtl number = 1). Similarly, by adding additional diffusivity into the momentum and energy equations, Omar et al. [69] proposed a physical model for free planar jet impingement boiling heat transfer. At the same time, experiments were conducted to determine the correlation between the artificial diffusivity and the dimensionless bubble parameters (Reynolds number, Weber number, superheat Jacob number and subcooling Jacob number). The characteristic length and velocity in those definitions were bubble diameter and jet velocity. It showed that the simulation results matched the experimental data very well. 4.4. Other developments related to jet impingement boiling Since the boiling heat transfer greatly depends on bubble behaviors, the mechanism of bubble heat transfer is important. Kim [70] summarized the bubble heat transfer models in the literatures: transient conduction model, micro-layer heat transfer model and contact line heat transfer model. However, it is reported that any of them is able to give a reasonable prediction compared to the experimental data that obtained by Yaddanapuddi and Kim [71]. It means that further investigation regarding bubble heat transfer model is required. The bubble diameter is one of the most crucial parameters in mechanistic boiling models. Therefore, many researchers improved the traditional approach ‘‘mono-dispersed assumption’’ by adopting the MUSIG (Multi-Size-Group) in the boiling model. In order to achieve this goal, population balance method is developed to calculate the distribution of bubble size that caused by breakage and coalescence effects. Tu and Yeoh [72] embedded population balance method into the traditional RPI model. More recently, Wang et al. [73] introduced the population balance method based boiling model for subcooled boiling flow in a vertical pipe with liquid nitrogen as the working fluid. Likewise, Krepper et al. [74] also adopted population balance method to enhance the bubble diameter treatment. Besides, based on the chaotic nature of boiling phenomenon, nonlinear approaches were adopted in many researches as another broad avenue to solving the boiling problems. Shoji [75] comprehensively review the experimental, theoretical and computational works that accomplished in nonlinear interactive and conjugated processes of boiling. Moreover, Cong et al. [76] employed the artificial neural network (ANN) and genetic algorithm to predict the CHF in jet impingement boiling. Having selected 1079 experimental data from open literatures, they trained, validated, and tested the ANN. The predicted CHF and experimental data have a maximum 20% discrepancy. 5. Conclusion

Fig. 10. Validation of the RPI boiling model in solving jet impingement boiling problem (experimental data were reported by Zhou and Ma [40]) (reprinted from Narumanchi et al. [66], Copyright 2008 from Elsevier).

Investigations regarding the jet impingement boiling heat transfer that reported in the last two decades were summarized here. Those studies involve experiments, analytical works, and numerical simulations. However, due to the complex nature of boiling accompanied jet impingement, experimental approach is the most popular one to investigate the boiling heat transfer characteristics. Effects of jet parameters (impact velocity, impact distance, jet diameter, subcooling, jet array, etc.) as well as target surface parameters (surface condition, surface aging, etc.) on jet impingement boiling heat transfer (fully developed nucleate

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boiling regime) were discussed. Major conclusions in those works have been summarized. (1) In fully developed nucleate boiling regime, a variety of experimental data supported the conclusion that the boiling curves for free circular/planer configurations were independent of jet parameters as jet velocity, diameter and subcooling etc. Hence, it could be inferred that the boiling curve in jet impingement configuration could be extrapolated from the pool boiling correlations. However, ONB and CHF were greatly influenced by those parameters. Attentions have been paid to theoretical analysis and experimental correlations for CHF. The effects of jet velocity, subcooling, jet diameter, impact distance as well as heater size and target surface contact angle etc. on CHF as well as ONB were investigated. (2) Conflicting observations were reported regarding submerged and confined jet impingement boiling heat transfer in the fully developed boiling regime. Some researchers reported that the jet velocity and subcooling made no difference to the boiling curve, whereas the others reported that those parameter influenced the boiling heat transfer obviously. In the submerged configuration, the variation of far-field temperature in the pool greatly influenced the boiling heat transfer. In the confined configuration, the confinement enforced the mixing of bubbles and jet. (3) Aside from the effects of jet parameters, target surface condition was found to be crucial to the jet impingement boiling heat transfer. Both conventional scale and micro/nano scale surface roughness were investigated. It influenced the boiling heat transfer with the different mechanisms in different surface roughness scales: the micro-scale surface roughness (micro-pin–fins) usually increases the heat transfer area and influences the bubble generation pattern and finally increases the boiling heat transfer, whereas manipulating the nano-scale surface roughness allows to vary the contact angle and wettability of the surface. It was found that the wall heat transfer was independent of contact angle in single phase convection regime, but was influenced in boiling regime. (4) Once the surface area of heater is far larger than the jet dimension, and the thermal boundary condition approaches to isoflux (e.g. produced by thin film heater), the coexistence of single-phase convection (at the stagnation zone) and boiling (at the far field) on the heater could be observed. With the same wall heat flux, the wall temperature of stagnation zone could be lower than the saturation point, whereas boiling has been initiated at the far field. Hence, the conjugation heat transfer should be concerned in the scenario because the span-wise conduction inside the solid influences the wall temperature gradient and then varies the boiling pattern on the surface. (5) Compared to the experimental studies, only a small amount of theoretical and numerical works have been reported regarding the jet impingement boiling. Eulerian based models were adopted in the simulation. Due to the validation results, it showed that the RPI boiling model is very promising to predict subcooled jet impingement boiling heat transfer. Conflict of interest None declared. Acknowledgments The authors would like to thank National Research Foundation, Energy Innovation Programme Office, and Energy Market Authority (EMA) of Singapore for their full support to work carried out in this paper under a research Grant No. NRF2013EWT-EIRP001-017.

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