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Heat transfer and fluid flow characteristics of two-phase impinging jets
International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and fluid flow characteristics of two-phase impinging jets Kyosung Choo, Sung Jin Kim ⇑ School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
a r t i c l e
i n f o
Article history: Received 8 March 2010 Received in revised form 31 July 2010 Accepted 31 July 2010 Available online 16 September 2010 Keywords: Two-phase Impingement Heat transfer
a b s t r a c t Heat transfer and fluid flow characteristics of two-phase impinging jets were experimentally investigated under a fixed pumping power condition. The effects of dimensionless pumping power (Ppump ¼ 1:4 1011 —2:8 1012 ) and the volumetric fraction (b = 0.0–1.0) on the Nusselt number were considered. Air and water were used as the test fluids. The results showed that the Nusselt number increased with volumetric fraction, attained a maximum value at around 0.2–0.3 of the volumetric fraction, and then decreased. By observing flow patterns, the optimum value of the Nusselt number was found to be in the bubbly flow region. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers of impinging jets were developed as a function of the volumetric fraction alone. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Impinging jets are widely used in many engineering applications for the heating, cooling, and drying of surfaces as they offer high rates of heating, cooling, and drying. Major industrial applications for impinging jets include turbine blade cooling, electronic equipment cooling, metal annealing, and textile drying. Due to this diverse range of uses, many investigations have examined the heat transfer characteristics of impinging jets in the past decades [1–5]. Webb and Ma [1] and Martin [3] presented comprehensive reviews on single-phase impinging jets and provided extensive heat transfer correlations for a single jet and for jet arrays. Recently, several researchers have observed heat transfer enhancement resulting from the addition of a gas (or vapor) phase to an impinging liquid jet under a fixed liquid flow rate condition. Serizawa et al. [6] experimentally studied the heat transfer characteristics of an impinging circular jet of an air–water mixture for Reynolds numbers in the range 25,000 < Rew < 125,000. Air bubbles were premixed with a water flow and the ensuing bubbly flow was discharged through a circular tube nozzle. Heat transfer coefficient was increased by a factor of two at a volumetric fraction value of 0.53. The enhancements were attributed to high turbulence levels accompanying bubble-induced agitations and to acceleration of the liquid phase by the more rapidly moving air. Chang et al. [7] experimentally investigated the heat transfer characteristics of confined impinging jets using Freon R-113. Relative to a singlephase jet, heat transfer of the liquid–vapor jets was enhanced by a factor of 1.2. The enhancements were attributed to the high velocity of liquid phase due to the presence of the faster moving ⇑ Corresponding author. Tel.: +82 42 350 3043; fax: +82 42 350 8207. E-mail address: [email protected] (S.J. Kim). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.08.013
vapor phase in the incident liquid–vapor jet. Zumbrunnen and Balasubramanian [8] measured convection heat transfer enhancement caused by air bubbles injected into a planar water jet. Over the range of liquid-only Reynolds number of 3700 6 Rew 6 21,000 and the volumetric fraction between 0 6 b 6 0.86, heat transfer was increased by as much as a factor of 2.2 at the stagnation point. Hall et al. [9] performed an experimental study of boiling heat transfer for air–water impinging jets. For the volumetric fraction ranging from 0 to 0.4 and the liquid-only Reynolds number of 11,300 6 Rew 6 22,600, heat transfer increased by as much as a factor of 2.1 at the stagnation point. However, high cooling performance was not achieved free of charge. It was obtained at the expense of high pumping power, which is the product of the pressure drop and the flow rate. As the volumetric fraction increases at a fixed liquid flow rate, the pumping power increases as a result of an increased pressure drop. What will happen to cooling performance as the volumetric fraction increases when the pumping power is fixed? As mentioned by Choo and Kim [10], fixed pumping power is an important constraint in practical applications. Many researchers have conducted studies under the constraint of fixed pumping power [11– 15] because pumping power is directly related to the operating cost of a cooling system. As pumping power increases, cooling performance increases, but at the same time the operating cost also increases. For this reason, it is important to study the heat transfer characteristics of two-phase impinging jets under fixed pumping power conditions. The purpose of this study is to determine the heat transfer characteristics of two-phase impinging jets under a fixed pumping power condition. The effects of the pumping power (P pump ¼ 1:4 1011 —2:8 1012 ) and the volumetric fraction (b = 0.1–1.0) on the Nusselt number are considered at a fixed nozzle-to-plate spacing
K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
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Nomenclature d H Nur Nuw Nutp Nutp Nutp Ppump Pr DP DP*
nozzle diameter (m) nozzle-to-plate spacing (m) lateral variation of Nusselt number () Nusselt number of water jet at stagnation point () Nusselt number of two-phase jet at stagnation point () normalized Nusselt number at stagnation point, (Nutp/ Nuw) () normalized average Nusselt number () dimensionless pumping power, (DP* Q*) () Prandtl number () pressure drop (Pa) dimensionless pressure drop, (DP/l2q1d2) ()
water flow rate (m3/s) air flow rate (m3/s) total flow rate (m3/s) dimensionless total flow rate, (Qtot/lq1d) () Reynolds number () Reynolds number for water () lateral distance from stagnation point (m)
Greek symbol b volumetric fraction, (Qa/Qw + Qa) () l fluid viscosity (kg/m s) q fluid density (kg/m3)
of seven nozzle diameters. Flow patterns of two-phase impinging jets were observed to understand how they affect heat transfer characteristics. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers were also developed as a function of the volumetric fraction alone.
Pump Water Reservoir
Mass Flow Meters
2. Experimental apparatus and procedures
Heat Exchanger
Power Supply Two-phase Mixer Test Section
DAQ
Qw Qa Qtot Q tot Re Rew r
Thermocouples Air Mass Flow Controller Fig. 1. Schematic diagram of experimental set-up.
Fig. 1 shows a schematic diagram of the experimental apparatus. Compressed air passes through a flexible tube before entering the two-phase mixture. The airflow was supplied by a high-pressure tank to furnish a very clean and steady flow. The flow was then regulated and controlled by a mass flow controller (Brooks 5850E). It has an accuracy level of ±1% and a repeatability value of ±0.15%. The full-scale range of the mass flow controller was 50 standard liters per minute. The liquid flow was supplied by a water reservoir to furnish a steady flow. A BLDC (Blushless DC) diaphragm metering pump is used to supply water to the test section. The pumped water passed through a flexible tube before entering a two-phase mixture. One of the two positive-displacement-type flowmeters is used during the experiment according to the flowrate range. A heat exchanger is connected to a constant temperature bath to control the jet temperature. Most portions of the piping were insulated to aid in the regulation of flow temperature. Three E-type thermocouples were located directly upstream and downstream of the flowmeters and downstream of the heat exchanger to monitor temperatures.
Heated surface Impingement plate
Insulation material
Flow out
Bus bar
Thermocouples
Fig. 2. Test section configuration.
Pool
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K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
A circular glass pipe nozzle was used in the experiment. It has 4 mm inner diameter with 320 mm long. The circular pipe was fixed on a 3-axis (x–y–z) stage with a 10 lm resolution made by Thorlabs, Inc. Thus, the nozzle could be moved either parallel or perpendicular to the direction of the jet. To measure the wide range of the pressure drop, two micro-manometers (FCO510 and MP112) were used. The full-scale range of the micro-manometer (FCO510) manufactured by Furness Controls is ±20,000 Pa. The accuracy of the micro-manometer is 0.25%. The full-scale range of the micro-manometer (MP112) manufactured by KIMO Inc. is ±200,000 Pa. The accuracy of the micro-manometers is 0.5%. The pressure drop (DP) of the impinging jet was measured between the pressure at the nozzle exit and the atmospheric pressure. The flow patterns in the pipe nozzle were visualized by using a digital camera (Nikon, D50) and a pulse generator (EG&G Electro-optics, LS-1130-1) [16,17]. A schematic of the test section is presented in Fig. 2. The test section was fixed on an optical table to isolate it from vibration. To avoid leakages, as many parts as possible were constructed to be cylindrical. The impingement surface was placed to be independent of the exit of the test section. Thus, as the wall jets fall off the impingement surface into the pool, the jet flows are not influenced by conditions downstream of the test section. The DC power supply was connected to the bus bar soldered to the heater at the cen-
ter of the impingement surface. The heater is made of INCONEL alloy 600 that is 0.04 mm thick, 8.0 mm wide and 120 mm long. The heater is connected to a high voltage DC power supply in series with a shunt, rated 40 V and 100 A, allowing adjustable DC voltage to the electrodes. With DC electric current applied to the heater, a nearly uniform wall heat flux boundary condition was established. The amount of heat generation was obtained under the steady state condition. We started impinging fluid on the unheated heater, and applied heat to the heater. We waited until the variation of the temperature difference between the heater and the nozzle exit is within 0.2 °C for 10 min. Then, we measured the voltage and the resistance across the heater in order to obtain electrical energy input accurately. Fourteen E-type thermocouples of diameter 0.08 mm were welded to the back side (dry side) of the heater along the centerline. The welded thermocouple wires were fixed on the dry side by a high temperature thermal epoxy. These thermocouples were connected to the HP3852A digital data acquisition system. To keep this side dry, silicon rubber was poured and cured as a sealant and thick glass wool insulation was used to minimize the heat loss from the dry side. The details of data analysis were described in Refs. [10,18]. The uncertainty in the local Nusselt numbers is estimated with a 95% confidence level using the methods suggested by Kline and McKlintock [19]. The calculated error of the main variables revealed an uncertainty of 2.9% for the surface temperature with 1.95%;
3
10
H/d = 1, present data H/d = 2, present data H/d = 4, present data Correlation by Webb and Ma [1]
(a)
500
Fixed Rew = 10,500 Fixed Rew = 15,000
+10% 450
400
Nuw
-10%
Nutp
350
300
250
200 2
10
4
5
10
10
150 0.0
Re
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
β
(b)
2.0
Nu*tp
Fig. 3. Correlation and comparison of stagnation Nusselt numbers.
1.5
Fixed Rew = 10,500 Fixed Rew = 15,000
9
2.0x10
Water, present data Air, present data Correlation from Moody diagram 9
1.6x10
9
Δ P*
1.2x10
8
8.0x10
8
4.0x10
1.0
0.0
0.0
0
5000
10000
15000
20000
25000
30000
35000
0.2
0.4
β
Re Fig. 4. Correlation and comparison of the pressure drop.
Fig. 5. Stagnation Nusselt numbers for volumetric fraction b: (a) stagnation Nusselt numbers and (b) normalized stagnation Nusselt numbers.
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Fixed Rew = 10,500 Fixed Rew = 15,000
(b)
10
ΔP*
9
(a)
10
Fixed Rew = 10,500 Fixed Rew = 15,000
5
Q*tot
10
8
4
10
7
10
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
β
0.6
0.8
1.0
β
Fig. 6. Variation of total flow rate and pressure drop for volumetric fraction b under a fixed flow rate condition: (a) total flow rate and (b) pressure drop.
1.39% for the inlet temperature at the nozzle exit; 1.02% for the heat loss; 0.97% for the input voltage; 0.51% for the input current.
3.2. Fixed flow rate condition Fig. 5(a) shows that the influence of volumetric fraction b on the Nusselt number for Reynolds numbers of Rew = 10,500 and 15,000 at
3. Results and discussion
(a)
The experimental data of the present study for a single-phase impinging jet were compared with the empirical correlation of Webb and Ma [1] as a validation process. Water was used as a working fluid. For Reynolds numbers in the range 10,000 6 Rew 6 30,000, the stagnation Nusselt numbers were examined at three nozzle-toplate spacings of 1, 2 and 4, as shown in Fig. 3. The adopted empirical 0:4 correlation of Webb and Ma is Nuw = 0.93 Re0:5 . As shown in the w Pr figure, good agreements between the present data and the previous empirical correlation were observed within ±10%. In order to validate pressure drop measurement, the pressure drop was measured for both air-only and water-only flows in a circular pipe with a 4 mm inner diameter. The pressure drop was examined for Reynolds numbers in the range 3600 6 Re 6 30,000. As shown in Fig. 4, good agreement was observed between the present data and the empirical correlation for the pressure drop using the Moody diagram friction factor. 2.5
11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
4
10
0.0
0.2
0.4
0.6
1.0
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
-5% 8
2.0
10
ΔP*
Nu*tp (Experiment)
0.8
β
(b)
+5%
Fixed Rew = 10,500 Fixed Rew = 15,000
P*pump
Q*tot
3.1. Validation
1.5
7
10 1.0 1.0
1.5
2.0
2.5
Nu*tp (Correlation) Fig. 7. Comparison between the normalized stagnation Nusselt numbers obtained from the correlation of Eq. (1) and that from experimental results.
0.0
0.2
0.4
β
0.6
0.8
1.0
Fig. 8. Variation of total flow rate and pressure drop for volumetric fraction b under a pumping power condition: (a) total flow rate and (b) pressure drop.
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a fixed nozzle-to-plate spacing of H/d = 7. Nozzle-to-plate spacings of H/d = 3, 5, 7, and 9 were considered in the present study. As mentioned by Webb and Ma [1], the effect of nozzle-to-plate spacing of the free surface impinging jets was negligible. Therefore, the present study used only a fixed nozzle-to-plate spacing of H/d = 7. The stagnation Nusselt number increased as the volumetric fraction increased under a fixed water flow rate condition (a fixed water Reynolds number condition). The results of the present study were similar to those of previous researches studies by Refs. [6–9]. The stagnation Nusselt number for b = 0.9 exceeded that for liquid-only flow by a factor of two. The normalized stagnation Nusselt numbers Nutp (Nutp/Nuw) for the volumetric fraction are shown in Fig. 5(b). Cooling performance increased as the volumetric fraction increased because of the high pumping power P pump . As shown in Fig. 6, as the volumetric fraction increased, pumping power which was producted by the pressure drop (DP*) and the total flow rate (Q tot ) increased. From Fig. 5(b), an empirical correlation for the normalized stagnation Nusselt number is developed as a function of volumetric fraction alone. The normalized stagnation Nusselt numbers for Reynolds numbers of Rew = 10,500 and 15,000 are presented in Fig. 7. The correlation of the normalized stagnation Nusselt number for the impinging jet has the following form:
Nutp ¼ 1 þ 2:13b 4:58b2 þ 3:68b3
ð1Þ
The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±5%, as shown in Fig. 7.
(a)
350
11
P*pump = 1.4 x 10 β = 0.0 β = 0.1 β = 0.3 β = 0.7 β = 0.9
300
250
Nur
200
3.3. Fixed pumping power condition As mentioned in Section 3.2, the stagnation Nusselt number increased as the volumetric fraction increased under a fixed flow rate condition. However, as mentioned by Choo and Kim [10], fixed pumping power is an important constraint to practical application because pumping power is directly related to the operating cost of a cooling system. As shown in Fig. 8, as the volumetric fraction increased, the total flow rate increased, but the pressure drop decreased under the fixed pumping power condition. Fig. 9 shows that the lateral variation of Nusselt number with P pump ¼ 1:4 1011 and 1.4 1012 at H/d = 7. The local Nusselt number decreased with increasing lateral distance. The heat transfer characteristics of the two-phase impinging jets under fixed pumping power conditions are shown in Fig. 10. As shown in this figure, the stagnation Nusselt number attained a maximum value at around 0.2–0.3 of the volumetric fraction. In order to find the reason why the stagnation Nusselt number attained a maximum value at this volumetric fraction, flow patterns were observed in Figs. 11–13. Fig. 11 shows the impinging flow patterns for b = 0–0.9 at H/d = 7. Fig. 12 shows the flow patterns in the pipe nozzle. As shown in this figure, the flow patterns changed from bubbly flow to annular flow as the volumetric fraction increased. The flow patterns for b = 0.1–0.3 showed a bubbly flow: distorted-spherical and discrete bubbles moving in a continuous liquid phase. The flow patterns for b = 0.4–0.5 showed the slug– churn flow, which was dominated by bullet-shaped bubbles that had nearly hemispherical caps and were separated from one another by liquid slugs. The liquid slugs contained small bubbles. The flow patterns for b = 0.6–0.9 show churn–annular flow: an air column in the center of the pipe nozzle, and small bubbles contained in the liquid film. As shown in Fig. 10, the heat transfer characteristics of the twophase impinging jets are divided into three regions. First, the cooling performance at b = 0.1 had an almost 30% higher value than that of the liquid-only flow, due to air injection. As shown in
150
500
100
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
450
50
0 0
1
2
3
4
5
6
7
400
8
r/d
350 350
12
P*pump = 1.4 x 10 β = 0.0 β = 0.1 β = 0.3 β = 0.7 β = 0.9
300
250
300
Nutp
(b)
Nur
200
250 200
150
150 100
100 50
50
0 0
1
2
3
4
5
6
7
8
r/d Fig. 9. Lateral variation of the local Nusselt numbers: (a) P pump ¼ 1:4 1011 and (b) P pump ¼ 1:4 1012 .
0.0
0.2
0.4
β
0.6
0.8
1.0
Fig. 10. Variation of stagnation Nusselt numbers for volumetric fraction b under the fixed pumping power condition.
K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
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Fig. 11. Visualization of flow patterns for the impinged flow at b = 0–0.9.
Fig. 12. Visualization of flow patterns in the pipe nozzle at b = 0–0.9.
Figs. 11 and 13, flow mixing in the impinging jet at b = 0.1 was more vigorous than that at b = 0. Second, the stagnation Nusselt number increased with b from 0.1 to 0.3, caused by more bubbles increasing the disturbance of the impinging flow. Although the water flow rate decreased from b = 0.1 to b = 0.3, the increase in the number of bubbles helped to enhance the heat transfer. Third, the cooling performance of the impinging jet decreased with increasing b from 0.4 to 0.9 due to a decrease in the liquid flow rate. As shown in Figs. 11 and 12, there was an air column in the
center of the pipe nozzle in the slug, churn, and annular flow regions. This means that the air flow dominated the thermal performance of the impinging jet in the slug and annular flow regions. The correlation of the normalized stagnation Nusselt number Nutp (Nutp/Nuw) for the volumetric faction under a fixed pumping power condition is developed. It has the following form:
Nutp ¼ 1 þ 3:4b 13:5b2 þ 19:6b3 10b4
ð2Þ
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K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
Fig. 13. Visualization of flow patterns for the impinged flow at the bottom surface: (a) b = 0 and (b) b = 0.1.
(a)
Nutp ¼ 1 þ 13:3b 45:7b2 þ 58:1b3 26:2b4
+15%
2.0
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
Nu*tp (Experiment)
1.5
-15%
1.0
0.0 0.0
0.5
1.0
1.5
2.0
Nu*tp (Correlation) 3.0
P*pump
+10% 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
2.5
Nu*tp (Experiment)
The above correlation can be used for 0 6 r/d 6 8. The correlation of the normalized average Nusselt number was compared with the experimental results, and matched with the experimental results within ±10%, as shown in Fig. 14(b). The present correlations considering the supplied pumping power and the volumetric fraction should be helpful for researchers and engineers in the design of industrial cooling systems. 4. Conclusion
0.5
(b)
ð3Þ
-10%
2.0
1.5
1.0
0.5
In the present study, the heat transfer and fluid flow characteristics of two-phase impinging jets were experimentally investigated under a fixed pumping power condition. The experimental parameters included a jet diameter of d = 4 mm, dimensionless pumping power of (P pump ¼ 1:4 1011 —2:8 1012 ) and volumetric fraction (b = 0.0–1.0) at a fixed nozzle-to-plate spacing of seven nozzle diameters. Air and water were used as the test fluids. It was found that the Nusselt number increased with volumetric fraction, attained a maximum value at around 0.2–0.3 of the volumetric fraction, and then decreased. Flow patterns of the twophase impinging jets were observed to understand how they affect heat transfer characteristics. The optimum value of the Nusselt number was found to be in the bubbly flow region. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers of impinging jets were developed as a function of the volumetric fraction alone. Acknowledgement
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Nu*tp (Correlaiton) Fig. 14. Comparison between the experimental results and the suggested correlations: (a) for the correlation of the normalized stagnation Nusselt number for Eq. (2) and (b) for the correlation of the normalized average Nusselt number for Eq. (3).
The above correlation can be used for 1:4 1011 6 Ppump 6 2:8 1012 and 0 6 b < 1. The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±15%, as shown in Fig. 14(a). The correlation of the normalized average Nusselt number for the impinging jet has the following form:
This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the National Research Lab. Program funded by the Ministry of Science and Technology (No. M1060000022406J000022410). References [1] B.W. Webb, C.-F. Ma, Single-phase liquid jet impingement heat transfer, Adv. Heat Transfer 26 (1995) 105–217. [2] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Therm. Fluid Sci. 6 (1) (1993) 111–134. [3] H. Martin, Heat and mass transfer between impinging gas jets and solid surface, Adv. Heat Transfer 13 (1977) 1–60. [4] S. Polat, B. Huang, A.S. Majumdar, W.J.M. Douglas, Numerical flow and heat transfer under impinging jets: A Review, Ann. Rev. Num. Fluid Mech. Heat Transfer 2 (1989) 157–197.
K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699 [5] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle-plate spacings, Int. J. Heat Mass Transfer 37 (1994) 1687–1697. [6] A. Serizawa, O. Takahashi, Z. Kawara, T. Komeyama, I. Michiyoshi, Heat transfer augmentation by two-phase bubbly flow impinging jet with a confining wall, in: Proceedings of the 9th Int. Heat Transfer Conference, Jerusalem, 1990, pp. 93–98. [7] C.T. Chang, G. Kojasoy, F. Landis, S. Downing, Confined single- and multiple-jet impingement heat transfer – II. Turbulent two-phase flow, Int. J. Heat Mass Transfer 38 (1995) 843–851. [8] D.A. Zumbrunnen, M. Balasubramanian, Convective heat transfer enhancement due to gas injection into an impinging liquid jet, ASME J. Heat Transfer 117 (1995) 1011–1017. [9] D.E. Hall, F.P. Incropera, R. Viskanta, Jet impingement boiling from a circular free surface jet during quenching; Part 2 – two-phase jet, ASME J. Heat Transfer 123 (2001) 911–917. [10] K.S. Choo, S.J. Kim, Comparison of thermal characteristics of confined and unconfined impinging jets, Int. J. Heat Mass Transfer 53 (2010) 3366–3371. [11] P. Wildi-Tremblay, L. Gosselin, Minimizing shell-and-tube heat exchanger cost with genetic algorithms and considering maintenance, Int. J. Energy Res. 31 (2007) 867–885.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and fluid flow characteristics of two-phase impinging jets Kyosung Choo, Sung Jin Kim ⇑ School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
a r t i c l e
i n f o
Article history: Received 8 March 2010 Received in revised form 31 July 2010 Accepted 31 July 2010 Available online 16 September 2010 Keywords: Two-phase Impingement Heat transfer
a b s t r a c t Heat transfer and fluid flow characteristics of two-phase impinging jets were experimentally investigated under a fixed pumping power condition. The effects of dimensionless pumping power (Ppump ¼ 1:4 1011 —2:8 1012 ) and the volumetric fraction (b = 0.0–1.0) on the Nusselt number were considered. Air and water were used as the test fluids. The results showed that the Nusselt number increased with volumetric fraction, attained a maximum value at around 0.2–0.3 of the volumetric fraction, and then decreased. By observing flow patterns, the optimum value of the Nusselt number was found to be in the bubbly flow region. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers of impinging jets were developed as a function of the volumetric fraction alone. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Impinging jets are widely used in many engineering applications for the heating, cooling, and drying of surfaces as they offer high rates of heating, cooling, and drying. Major industrial applications for impinging jets include turbine blade cooling, electronic equipment cooling, metal annealing, and textile drying. Due to this diverse range of uses, many investigations have examined the heat transfer characteristics of impinging jets in the past decades [1–5]. Webb and Ma [1] and Martin [3] presented comprehensive reviews on single-phase impinging jets and provided extensive heat transfer correlations for a single jet and for jet arrays. Recently, several researchers have observed heat transfer enhancement resulting from the addition of a gas (or vapor) phase to an impinging liquid jet under a fixed liquid flow rate condition. Serizawa et al. [6] experimentally studied the heat transfer characteristics of an impinging circular jet of an air–water mixture for Reynolds numbers in the range 25,000 < Rew < 125,000. Air bubbles were premixed with a water flow and the ensuing bubbly flow was discharged through a circular tube nozzle. Heat transfer coefficient was increased by a factor of two at a volumetric fraction value of 0.53. The enhancements were attributed to high turbulence levels accompanying bubble-induced agitations and to acceleration of the liquid phase by the more rapidly moving air. Chang et al. [7] experimentally investigated the heat transfer characteristics of confined impinging jets using Freon R-113. Relative to a singlephase jet, heat transfer of the liquid–vapor jets was enhanced by a factor of 1.2. The enhancements were attributed to the high velocity of liquid phase due to the presence of the faster moving ⇑ Corresponding author. Tel.: +82 42 350 3043; fax: +82 42 350 8207. E-mail address: [email protected] (S.J. Kim). 0017-9310/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2010.08.013
vapor phase in the incident liquid–vapor jet. Zumbrunnen and Balasubramanian [8] measured convection heat transfer enhancement caused by air bubbles injected into a planar water jet. Over the range of liquid-only Reynolds number of 3700 6 Rew 6 21,000 and the volumetric fraction between 0 6 b 6 0.86, heat transfer was increased by as much as a factor of 2.2 at the stagnation point. Hall et al. [9] performed an experimental study of boiling heat transfer for air–water impinging jets. For the volumetric fraction ranging from 0 to 0.4 and the liquid-only Reynolds number of 11,300 6 Rew 6 22,600, heat transfer increased by as much as a factor of 2.1 at the stagnation point. However, high cooling performance was not achieved free of charge. It was obtained at the expense of high pumping power, which is the product of the pressure drop and the flow rate. As the volumetric fraction increases at a fixed liquid flow rate, the pumping power increases as a result of an increased pressure drop. What will happen to cooling performance as the volumetric fraction increases when the pumping power is fixed? As mentioned by Choo and Kim [10], fixed pumping power is an important constraint in practical applications. Many researchers have conducted studies under the constraint of fixed pumping power [11– 15] because pumping power is directly related to the operating cost of a cooling system. As pumping power increases, cooling performance increases, but at the same time the operating cost also increases. For this reason, it is important to study the heat transfer characteristics of two-phase impinging jets under fixed pumping power conditions. The purpose of this study is to determine the heat transfer characteristics of two-phase impinging jets under a fixed pumping power condition. The effects of the pumping power (P pump ¼ 1:4 1011 —2:8 1012 ) and the volumetric fraction (b = 0.1–1.0) on the Nusselt number are considered at a fixed nozzle-to-plate spacing
K. Choo, S.J. Kim / International Journal of Heat and Mass Transfer 53 (2010) 5692–5699
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Nomenclature d H Nur Nuw Nutp Nutp Nutp Ppump Pr DP DP*
nozzle diameter (m) nozzle-to-plate spacing (m) lateral variation of Nusselt number () Nusselt number of water jet at stagnation point () Nusselt number of two-phase jet at stagnation point () normalized Nusselt number at stagnation point, (Nutp/ Nuw) () normalized average Nusselt number () dimensionless pumping power, (DP* Q*) () Prandtl number () pressure drop (Pa) dimensionless pressure drop, (DP/l2q1d2) ()
water flow rate (m3/s) air flow rate (m3/s) total flow rate (m3/s) dimensionless total flow rate, (Qtot/lq1d) () Reynolds number () Reynolds number for water () lateral distance from stagnation point (m)
Greek symbol b volumetric fraction, (Qa/Qw + Qa) () l fluid viscosity (kg/m s) q fluid density (kg/m3)
of seven nozzle diameters. Flow patterns of two-phase impinging jets were observed to understand how they affect heat transfer characteristics. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers were also developed as a function of the volumetric fraction alone.
Pump Water Reservoir
Mass Flow Meters
2. Experimental apparatus and procedures
Heat Exchanger
Power Supply Two-phase Mixer Test Section
DAQ
Qw Qa Qtot Q tot Re Rew r
Thermocouples Air Mass Flow Controller Fig. 1. Schematic diagram of experimental set-up.
Fig. 1 shows a schematic diagram of the experimental apparatus. Compressed air passes through a flexible tube before entering the two-phase mixture. The airflow was supplied by a high-pressure tank to furnish a very clean and steady flow. The flow was then regulated and controlled by a mass flow controller (Brooks 5850E). It has an accuracy level of ±1% and a repeatability value of ±0.15%. The full-scale range of the mass flow controller was 50 standard liters per minute. The liquid flow was supplied by a water reservoir to furnish a steady flow. A BLDC (Blushless DC) diaphragm metering pump is used to supply water to the test section. The pumped water passed through a flexible tube before entering a two-phase mixture. One of the two positive-displacement-type flowmeters is used during the experiment according to the flowrate range. A heat exchanger is connected to a constant temperature bath to control the jet temperature. Most portions of the piping were insulated to aid in the regulation of flow temperature. Three E-type thermocouples were located directly upstream and downstream of the flowmeters and downstream of the heat exchanger to monitor temperatures.
Heated surface Impingement plate
Insulation material
Flow out
Bus bar
Thermocouples
Fig. 2. Test section configuration.
Pool
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A circular glass pipe nozzle was used in the experiment. It has 4 mm inner diameter with 320 mm long. The circular pipe was fixed on a 3-axis (x–y–z) stage with a 10 lm resolution made by Thorlabs, Inc. Thus, the nozzle could be moved either parallel or perpendicular to the direction of the jet. To measure the wide range of the pressure drop, two micro-manometers (FCO510 and MP112) were used. The full-scale range of the micro-manometer (FCO510) manufactured by Furness Controls is ±20,000 Pa. The accuracy of the micro-manometer is 0.25%. The full-scale range of the micro-manometer (MP112) manufactured by KIMO Inc. is ±200,000 Pa. The accuracy of the micro-manometers is 0.5%. The pressure drop (DP) of the impinging jet was measured between the pressure at the nozzle exit and the atmospheric pressure. The flow patterns in the pipe nozzle were visualized by using a digital camera (Nikon, D50) and a pulse generator (EG&G Electro-optics, LS-1130-1) [16,17]. A schematic of the test section is presented in Fig. 2. The test section was fixed on an optical table to isolate it from vibration. To avoid leakages, as many parts as possible were constructed to be cylindrical. The impingement surface was placed to be independent of the exit of the test section. Thus, as the wall jets fall off the impingement surface into the pool, the jet flows are not influenced by conditions downstream of the test section. The DC power supply was connected to the bus bar soldered to the heater at the cen-
ter of the impingement surface. The heater is made of INCONEL alloy 600 that is 0.04 mm thick, 8.0 mm wide and 120 mm long. The heater is connected to a high voltage DC power supply in series with a shunt, rated 40 V and 100 A, allowing adjustable DC voltage to the electrodes. With DC electric current applied to the heater, a nearly uniform wall heat flux boundary condition was established. The amount of heat generation was obtained under the steady state condition. We started impinging fluid on the unheated heater, and applied heat to the heater. We waited until the variation of the temperature difference between the heater and the nozzle exit is within 0.2 °C for 10 min. Then, we measured the voltage and the resistance across the heater in order to obtain electrical energy input accurately. Fourteen E-type thermocouples of diameter 0.08 mm were welded to the back side (dry side) of the heater along the centerline. The welded thermocouple wires were fixed on the dry side by a high temperature thermal epoxy. These thermocouples were connected to the HP3852A digital data acquisition system. To keep this side dry, silicon rubber was poured and cured as a sealant and thick glass wool insulation was used to minimize the heat loss from the dry side. The details of data analysis were described in Refs. [10,18]. The uncertainty in the local Nusselt numbers is estimated with a 95% confidence level using the methods suggested by Kline and McKlintock [19]. The calculated error of the main variables revealed an uncertainty of 2.9% for the surface temperature with 1.95%;
3
10
H/d = 1, present data H/d = 2, present data H/d = 4, present data Correlation by Webb and Ma [1]
(a)
500
Fixed Rew = 10,500 Fixed Rew = 15,000
+10% 450
400
Nuw
-10%
Nutp
350
300
250
200 2
10
4
5
10
10
150 0.0
Re
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
β
(b)
2.0
Nu*tp
Fig. 3. Correlation and comparison of stagnation Nusselt numbers.
1.5
Fixed Rew = 10,500 Fixed Rew = 15,000
9
2.0x10
Water, present data Air, present data Correlation from Moody diagram 9
1.6x10
9
Δ P*
1.2x10
8
8.0x10
8
4.0x10
1.0
0.0
0.0
0
5000
10000
15000
20000
25000
30000
35000
0.2
0.4
β
Re Fig. 4. Correlation and comparison of the pressure drop.
Fig. 5. Stagnation Nusselt numbers for volumetric fraction b: (a) stagnation Nusselt numbers and (b) normalized stagnation Nusselt numbers.
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Fixed Rew = 10,500 Fixed Rew = 15,000
(b)
10
ΔP*
9
(a)
10
Fixed Rew = 10,500 Fixed Rew = 15,000
5
Q*tot
10
8
4
10
7
10
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
β
0.6
0.8
1.0
β
Fig. 6. Variation of total flow rate and pressure drop for volumetric fraction b under a fixed flow rate condition: (a) total flow rate and (b) pressure drop.
1.39% for the inlet temperature at the nozzle exit; 1.02% for the heat loss; 0.97% for the input voltage; 0.51% for the input current.
3.2. Fixed flow rate condition Fig. 5(a) shows that the influence of volumetric fraction b on the Nusselt number for Reynolds numbers of Rew = 10,500 and 15,000 at
3. Results and discussion
(a)
The experimental data of the present study for a single-phase impinging jet were compared with the empirical correlation of Webb and Ma [1] as a validation process. Water was used as a working fluid. For Reynolds numbers in the range 10,000 6 Rew 6 30,000, the stagnation Nusselt numbers were examined at three nozzle-toplate spacings of 1, 2 and 4, as shown in Fig. 3. The adopted empirical 0:4 correlation of Webb and Ma is Nuw = 0.93 Re0:5 . As shown in the w Pr figure, good agreements between the present data and the previous empirical correlation were observed within ±10%. In order to validate pressure drop measurement, the pressure drop was measured for both air-only and water-only flows in a circular pipe with a 4 mm inner diameter. The pressure drop was examined for Reynolds numbers in the range 3600 6 Re 6 30,000. As shown in Fig. 4, good agreement was observed between the present data and the empirical correlation for the pressure drop using the Moody diagram friction factor. 2.5
11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
4
10
0.0
0.2
0.4
0.6
1.0
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
-5% 8
2.0
10
ΔP*
Nu*tp (Experiment)
0.8
β
(b)
+5%
Fixed Rew = 10,500 Fixed Rew = 15,000
P*pump
Q*tot
3.1. Validation
1.5
7
10 1.0 1.0
1.5
2.0
2.5
Nu*tp (Correlation) Fig. 7. Comparison between the normalized stagnation Nusselt numbers obtained from the correlation of Eq. (1) and that from experimental results.
0.0
0.2
0.4
β
0.6
0.8
1.0
Fig. 8. Variation of total flow rate and pressure drop for volumetric fraction b under a pumping power condition: (a) total flow rate and (b) pressure drop.
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a fixed nozzle-to-plate spacing of H/d = 7. Nozzle-to-plate spacings of H/d = 3, 5, 7, and 9 were considered in the present study. As mentioned by Webb and Ma [1], the effect of nozzle-to-plate spacing of the free surface impinging jets was negligible. Therefore, the present study used only a fixed nozzle-to-plate spacing of H/d = 7. The stagnation Nusselt number increased as the volumetric fraction increased under a fixed water flow rate condition (a fixed water Reynolds number condition). The results of the present study were similar to those of previous researches studies by Refs. [6–9]. The stagnation Nusselt number for b = 0.9 exceeded that for liquid-only flow by a factor of two. The normalized stagnation Nusselt numbers Nutp (Nutp/Nuw) for the volumetric fraction are shown in Fig. 5(b). Cooling performance increased as the volumetric fraction increased because of the high pumping power P pump . As shown in Fig. 6, as the volumetric fraction increased, pumping power which was producted by the pressure drop (DP*) and the total flow rate (Q tot ) increased. From Fig. 5(b), an empirical correlation for the normalized stagnation Nusselt number is developed as a function of volumetric fraction alone. The normalized stagnation Nusselt numbers for Reynolds numbers of Rew = 10,500 and 15,000 are presented in Fig. 7. The correlation of the normalized stagnation Nusselt number for the impinging jet has the following form:
Nutp ¼ 1 þ 2:13b 4:58b2 þ 3:68b3
ð1Þ
The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±5%, as shown in Fig. 7.
(a)
350
11
P*pump = 1.4 x 10 β = 0.0 β = 0.1 β = 0.3 β = 0.7 β = 0.9
300
250
Nur
200
3.3. Fixed pumping power condition As mentioned in Section 3.2, the stagnation Nusselt number increased as the volumetric fraction increased under a fixed flow rate condition. However, as mentioned by Choo and Kim [10], fixed pumping power is an important constraint to practical application because pumping power is directly related to the operating cost of a cooling system. As shown in Fig. 8, as the volumetric fraction increased, the total flow rate increased, but the pressure drop decreased under the fixed pumping power condition. Fig. 9 shows that the lateral variation of Nusselt number with P pump ¼ 1:4 1011 and 1.4 1012 at H/d = 7. The local Nusselt number decreased with increasing lateral distance. The heat transfer characteristics of the two-phase impinging jets under fixed pumping power conditions are shown in Fig. 10. As shown in this figure, the stagnation Nusselt number attained a maximum value at around 0.2–0.3 of the volumetric fraction. In order to find the reason why the stagnation Nusselt number attained a maximum value at this volumetric fraction, flow patterns were observed in Figs. 11–13. Fig. 11 shows the impinging flow patterns for b = 0–0.9 at H/d = 7. Fig. 12 shows the flow patterns in the pipe nozzle. As shown in this figure, the flow patterns changed from bubbly flow to annular flow as the volumetric fraction increased. The flow patterns for b = 0.1–0.3 showed a bubbly flow: distorted-spherical and discrete bubbles moving in a continuous liquid phase. The flow patterns for b = 0.4–0.5 showed the slug– churn flow, which was dominated by bullet-shaped bubbles that had nearly hemispherical caps and were separated from one another by liquid slugs. The liquid slugs contained small bubbles. The flow patterns for b = 0.6–0.9 show churn–annular flow: an air column in the center of the pipe nozzle, and small bubbles contained in the liquid film. As shown in Fig. 10, the heat transfer characteristics of the twophase impinging jets are divided into three regions. First, the cooling performance at b = 0.1 had an almost 30% higher value than that of the liquid-only flow, due to air injection. As shown in
150
500
100
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
450
50
0 0
1
2
3
4
5
6
7
400
8
r/d
350 350
12
P*pump = 1.4 x 10 β = 0.0 β = 0.1 β = 0.3 β = 0.7 β = 0.9
300
250
300
Nutp
(b)
Nur
200
250 200
150
150 100
100 50
50
0 0
1
2
3
4
5
6
7
8
r/d Fig. 9. Lateral variation of the local Nusselt numbers: (a) P pump ¼ 1:4 1011 and (b) P pump ¼ 1:4 1012 .
0.0
0.2
0.4
β
0.6
0.8
1.0
Fig. 10. Variation of stagnation Nusselt numbers for volumetric fraction b under the fixed pumping power condition.
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Fig. 11. Visualization of flow patterns for the impinged flow at b = 0–0.9.
Fig. 12. Visualization of flow patterns in the pipe nozzle at b = 0–0.9.
Figs. 11 and 13, flow mixing in the impinging jet at b = 0.1 was more vigorous than that at b = 0. Second, the stagnation Nusselt number increased with b from 0.1 to 0.3, caused by more bubbles increasing the disturbance of the impinging flow. Although the water flow rate decreased from b = 0.1 to b = 0.3, the increase in the number of bubbles helped to enhance the heat transfer. Third, the cooling performance of the impinging jet decreased with increasing b from 0.4 to 0.9 due to a decrease in the liquid flow rate. As shown in Figs. 11 and 12, there was an air column in the
center of the pipe nozzle in the slug, churn, and annular flow regions. This means that the air flow dominated the thermal performance of the impinging jet in the slug and annular flow regions. The correlation of the normalized stagnation Nusselt number Nutp (Nutp/Nuw) for the volumetric faction under a fixed pumping power condition is developed. It has the following form:
Nutp ¼ 1 þ 3:4b 13:5b2 þ 19:6b3 10b4
ð2Þ
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Fig. 13. Visualization of flow patterns for the impinged flow at the bottom surface: (a) b = 0 and (b) b = 0.1.
(a)
Nutp ¼ 1 þ 13:3b 45:7b2 þ 58:1b3 26:2b4
+15%
2.0
P*pump 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
Nu*tp (Experiment)
1.5
-15%
1.0
0.0 0.0
0.5
1.0
1.5
2.0
Nu*tp (Correlation) 3.0
P*pump
+10% 11
1.4x10 11 5.5x10 12 1.4x10 12 2.8x10
2.5
Nu*tp (Experiment)
The above correlation can be used for 0 6 r/d 6 8. The correlation of the normalized average Nusselt number was compared with the experimental results, and matched with the experimental results within ±10%, as shown in Fig. 14(b). The present correlations considering the supplied pumping power and the volumetric fraction should be helpful for researchers and engineers in the design of industrial cooling systems. 4. Conclusion
0.5
(b)
ð3Þ
-10%
2.0
1.5
1.0
0.5
In the present study, the heat transfer and fluid flow characteristics of two-phase impinging jets were experimentally investigated under a fixed pumping power condition. The experimental parameters included a jet diameter of d = 4 mm, dimensionless pumping power of (P pump ¼ 1:4 1011 —2:8 1012 ) and volumetric fraction (b = 0.0–1.0) at a fixed nozzle-to-plate spacing of seven nozzle diameters. Air and water were used as the test fluids. It was found that the Nusselt number increased with volumetric fraction, attained a maximum value at around 0.2–0.3 of the volumetric fraction, and then decreased. Flow patterns of the twophase impinging jets were observed to understand how they affect heat transfer characteristics. The optimum value of the Nusselt number was found to be in the bubbly flow region. Based on the experimental results, correlations for the normalized stagnation and average Nusselt numbers of impinging jets were developed as a function of the volumetric fraction alone. Acknowledgement
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Nu*tp (Correlaiton) Fig. 14. Comparison between the experimental results and the suggested correlations: (a) for the correlation of the normalized stagnation Nusselt number for Eq. (2) and (b) for the correlation of the normalized average Nusselt number for Eq. (3).
The above correlation can be used for 1:4 1011 6 Ppump 6 2:8 1012 and 0 6 b < 1. The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±15%, as shown in Fig. 14(a). The correlation of the normalized average Nusselt number for the impinging jet has the following form:
This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the National Research Lab. Program funded by the Ministry of Science and Technology (No. M1060000022406J000022410). References [1] B.W. Webb, C.-F. Ma, Single-phase liquid jet impingement heat transfer, Adv. Heat Transfer 26 (1995) 105–217. [2] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Therm. Fluid Sci. 6 (1) (1993) 111–134. [3] H. Martin, Heat and mass transfer between impinging gas jets and solid surface, Adv. Heat Transfer 13 (1977) 1–60. [4] S. Polat, B. Huang, A.S. Majumdar, W.J.M. Douglas, Numerical flow and heat transfer under impinging jets: A Review, Ann. Rev. Num. Fluid Mech. Heat Transfer 2 (1989) 157–197.
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