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Heat transfer and hydrodynamics of free water jet impingement at low nozzle-to-plate spacings
International Journal of Heat and Mass Transfer 108 (2017) 2211–2216
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and hydrodynamics of free water jet impingement at low nozzle-to-plate spacings Abdullah M. Kuraan, Stefan I. Moldovan, Kyosung Choo ⇑ Mechanical and Industrial Engineering Department, Youngstown State University, Youngstown, OH 44555, United States
a r t i c l e
i n f o
Article history: Received 3 November 2016 Received in revised form 19 January 2017 Accepted 21 January 2017
Keywords: Impinging jet Circular Flat plate
a b s t r a c t In this study, heat transfer and hydrodynamics of a free water jet impinging a flat plate surface are experimentally investigated. The effects of the nozzle-to-plate spacing, which is equal to or less than one nozzle diameter (H/d = 0.08–1), on the Nusselt number, hydraulic jump diameter, and pressure at the stagnation point are considered. The results show that the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are divided into two regions: Region (I) jet deflection region (H/ d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-plate spacing, since the stagnation pressure increases due to the jet deflection effect. In region II, the effect of the nozzle-to-plate spacing is negligible on the normalized stagnation Nusselt number and hydraulic jump diameter since the average velocity of the jet is constant, which means the jet deflection effect disappears. Based on the experimental results, new correlations for the normalized hydraulic jump diameter, stagnation Nusselt number, and pressure are developed as a function of the nozzle-to-plate spacing alone. Ó 2017 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– 7,18,19]. For free liquid impinging jets at high nozzle-to-plate spacings (H/d > 1), Elicson and Webb [1] studied local heat transfer of laminar, transitional, and turbulent regions at Reynolds numbers from 300 to 7000 and nozzle-to-plate spacing from 1.5 to 50. They showed that the stagnation Nusselt number is not influenced by the spacing between the nozzle exit and the heated plate. Stevens and Webb [2] investigated local heat transfer coefficients at Reynolds numbers from 9600 to 10,500 and nozzle-to-plate spacing from 1.7 to 34. They suggested an empirical correlation for the stagnation Nusselt number as a function of nozzle-to-plate spacing, Nu0 (H/d)0.032. The effect of the nozzle-to-plate spacing on
⇑ Corresponding author. E-mail address: [email protected] (K. Choo). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.084 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
the Nusselt number was slight. In addition, they found an empirical correlation for the hydraulic jump diameter as a function of the Reynolds number only. The correlation did not include the nozzle-to-plate spacing effect. Brechet and Neda [8] studied both experimentally and theoretically the circular hydraulic jump. They suggested a theoretical correlation for the hydraulic jump radius as a function of the nozzle-to-plate spacing, Rhj (H/d)1/6. For submerged impinging jets at low nozzle-to-plate spacings of less than one nozzle diameter (H/d = 0.1–1.0), Lytle and Webb [9] studied the local heat transfer characteristics using an infrared thermal imaging technique. They observed that the local Nusselt number increases as the nozzle-to-plate spacing decreases when the flow rate (or Reynolds number) is fixed. A power-law relationship between the stagnation Nusselt number and the nozzle-toplate spacing was presented in the form of Nu0 (H/d)0.191. Choo et al. [10–12] investigated heat transfer characteristics of impinging jets under a fixed pumping power condition at low nozzle-toplate spacing (H/d = 0.125–1.0). They show that the Nusselt number is independent of the nozzle-to-plate spacing under a fixed pumping power condition. Choo et al. [13] studied the relationship between the Nusselt number and stagnation pressure of the submerged impinging jets at a large range of nozzle-to-plate spacing (H/d = 0.125–40). They found that the Nusselt number is strongly dependent on the stagnation pressure variation.
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Nomenclature d Dhj Dhj/d g H Nu0 Nu⁄0 P0 P⁄0 Q
nozzle diameter [m] hydraulic jump diameter [m] dimensionless hydraulic jump diameter [–] gravitational acceleration nozzle-to-plate spacing stagnation Nusselt number normalized Nusselt number (Nu0/Nu0,H/d=1) pressure of jet at stagnation point normalized stagnation pressure (P0/P0,H/d=1) water flow rate [m3/s]
Several empirical correlations were suggested for free liquid jets at high nozzle-to-plate spacings and submerged impinging jets at low nozzle-to-plate spacings, respectively. However, the understanding of a relationship for heat transfer and fluid flow characteristics of free liquid jets at low nozzle-to-plate spacings is still limited. The purpose of this study is to determine the heat transfer and fluid flow characteristics of free liquid impinging jets for low nozzle-to-plate spacing (H/d = 0.08–1). Stagnation pressure of the free liquid impinging jets were measured to understand how it affects the Nusselt number and the hydraulic jump diameter. Based on the experimental results, correlations for the normalized stagnation Nusselt number, hydraulic jump diameter, and pressure were also developed as a function of the nozzle-to-plate spacing alone. 2. Experimental procedures Fig. 1 shows a schematic diagram of the experimental apparatus. The liquid flow was supplied by a water reservoir to furnish a steady flow. A gear pump (Micropump) is used to supply water to the test section. The pumped water passed through a flexible tube before entering the test section. A positive-displacementtype flowmeter is used during the experiment. A heat exchanger is connected to a constant temperature bath to control the jet temperature. Three K-type thermocouples were located directly
Pump Water Reservoir
Mass Flow Meters
Heat Exchanger
Power Supply
Test Section
DAQ
Thermocouples Fig. 1. Schematic diagram of the experimental set-up.
Re r Rhj
jet Reynolds number [ud/m] lateral distance from stagnation point [m] hydraulic jump radius [m]
Greek symbol m dynamic fluid viscosity [m2/s] q fluid density [kg/m3]
upstream and downstream of the flowmeters and downstream of the heat exchanger to monitor temperatures. A circular nozzle was used in the experiment. It has a 6.65 mm inner diameter and is 420 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. A flat acrylic plate with a diameter of 100 mm and thickness of 10 mm was used for pressure measurement. A pressure tap with a diameter of 0.1 mm was drilled and placed at the center of the flat acrylic plate. The pressure tap was connected to a micronanometer (Meriam M200-DI001). The manometers have a range of 0–6.89 kPa with accuracies of ±0.05%. The stagnation pressure of the impinging jet was measured at the center of impinging plate. A schematic of the test section is presented in Fig. 2(a). The test section was constructed out of a clear acrylic sheet. The impingement surface was designed to be at a greater elevation than the pool bottom so the impinged liquid would fall off the impinging plate and into the pool. The edge of the impingement plate was chamfered to ensure smooth drainage of liquid. This relieves the impinging fluid from downstream influences. The circular impinging plate was constructed from 0.5 in thick PTFE Teflon disk with a 216 mm diameter and a 1 mm diameter orifice in the center. The orifice was connected to the manometer using flexible tubing. The hydraulic jump created on the impinging plate was measured using a digital camera (Nikon, D50) and a pulse generator (Fovitec Speedlight flash, KD560) [14,15]. For accuracy and repeatability 5 min were given between each flow rate change to allow the system to reach a steady state for the different volumetric qualities. Both hydraulic jump and stagnation pressure were measured with minimum, actual, and maximum values at the steady state time. Fig. 2(b) shows a schematic of the test section for local temperature measurement. The DC power supply was connected to the bus bar soldered to the heater at the center of the impingement surface. The heater is made of stainless steel that is 0.0508 mm thick, 12.5 mm wide and 67.8 mm long. The heater was connected to a high voltage DC power supply (Agilent 6651A #J03) in series with a shunt, rated 0–6 V and 0–60 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. First, impinging fluid was introduced to the unheated heater, and then heat was applied to the heater. Values were recorded once the variation of the temperature difference between the heater and the nozzle exit was within 0.2 °C for 10 min. The voltage and the resistance across the heater were then measured in order to obtain the electrical energy input accurately with a multimeter. A 0.5 in thick PTFE Teflon disk was used to mount the heater, thermocouples, and copper bus. The Teflon disk also provides insulation to minimize heat loss through the dry side of the heater. Five
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Flow in
200
Pressure orifice Impingement plate
+10%
H/d = 1, present data Correlation by Stevens and Webb [2]
180
Nu
160
140
-10%
120
100
Pool Manometer
80 2000
Flow out
3000
4000
5000
6000
7000
8000
9000 10000
Re
(a)
(a)
Pstag [Pa] from Present study
1000
Re = 8053 Re = 7043 Re = 6039 Re = 5032 Re = 4023
800
600
400
200
0 0
(b)
200
400
600
800
1000
Pstag [Pa] from Bernoulli's Equation
(b)
Fig. 2. Test sections: (a) pressure measurement and (b) temperature measurement.
5.0
3. Results and discussion The experimental data of the Nusselt number in the present study for a free water impinging jet was compared with the empirical correlation of Steven and Webb [2] as a validation process. For Reynolds numbers in the range 4023 6 Re 6 8053, the stagnation Nusselt numbers were examined at a nozzle-to-plate spacing of H/d = 1, as shown in Fig. 3(a). The adopted empirical correlation
4.5 4.0
+15% 3.5
Rhj [cm]
K-type thermocouples of diameter 0.08 mm were fixed through 1 mm mounting holes on the centerline of the Teflon disk by a high temperature thermal epoxy. The thermocouples were spaced 21.5 mm apart starting at the center point. A thin double sided adhesive strip was laid directly over the row of thermocouples. The heater was then laid on top of the adhesive strip to keep constant contact with the thermocouples. These thermocouples were connected to the OMEGA OM-CP-QuadTemp2000 digital data acquisition system. A heat resistant latex caulking (Nelson Latex Firestop Sealant) was used to seal any gaps created by machining the Teflon disk. The uncertainty in the local Nusselt numbers is estimated with a 95% confidence level using the methods suggested by Kline and McKlintock [16]. The calculated maximum error of the main variables revealed an uncertainty of 2.7% for the surface temperature with 1.9%; 1.2% for the inlet temperature at the nozzle exit; 1.1% for the heat loss; 1.1% for the input voltage; 0.6% for the input current.
3.0
-15%
2.5 2.0 1.5 1.0 15
20
25
30
35
40
45
50
q [cm3/s]
(c) Fig. 3. Validation for single phase water impinging jet: (a) stagnation Nusselt number, (b) stagnation pressure, and (c) hydraulic jump diameter.
of Steven and Webb is Nu = 3.62Re 0.362Pr0.4. As shown in the figure, good agreements between the present data and the previous empirical correlation were observed within ±10%. Validation for the stagnation pressure comes from the comparison of the single
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8 7 6
P0/(1/2)ρV2
d
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
5
u1 u2
4
Impinging plate
3 2
Hydraulic Jump Diameter
+20% -20%
1
Fig. 6. Notation for the velocity at low nozzle-to-plate spacing.
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 4. Normalized stagnation pressure for the nozzle-to-plate spacing.
phase liquid impingement data from Bernoulli’s equation as shown in Fig. 3(b). The Bernoulli’s equation at stagnation point is given below.
P0 ¼
1 2 qu þ qgH 2
ð1Þ
where P0 is stagnation pressure and H is nozzle-to-plate spacing. The present data agrees with the experimental results of the previous experiments and the Bernoulli’s equation within ±10%. In addition, the measured hydraulic jump radius is validated with an empirical correlation of Brechet and Neda [8]. The adopted empirical correlation is Rhj ¼ 0:8Q m . As shown in Fig. 3(c), good agreements between the present data and the previous empirical correlation were observed within ±15%. Fig. 4 shows that the influence of the nozzle-to-plate spacing on the normalized stagnation pressure, P 0 ¼ P 0 = 12 qu2 for various Reynolds numbers. The results show that the normalized stagnation pressure is divided into two regions: Region (I) jet deflection region (H/d 6 0.4) in Fig. 5(a) and Region (II) inertia dominant region (0.4 < H/d 6 1) in Fig. 5(b). In region I, the normalized stagnation pressure drastically increases with decreasing the nozzle-to-plate spacing since flow resistance increases due to the flow deflection
of the impinging plate. In region II, the effect of the nozzle-toplate spacing is negligible on the normalized stagnation pressure. In order to explain the flow resistance of the flow deflection, an extended Bernoulli’s equation is applied below. The pressure at stagnation point includes two effects, one from dynamic pressure at point 1 and another from the jet deflection effect at point 2 as shown in Fig. 6.
P0 ¼
1 2 K 2 qu þ qu 2 1 2 2
ð2Þ
where K is jet deflection coefficient, which is empirically obtained from Fig. 4. From the mass conservation equation, Eq. (3), at points 1 and 2, we can transform Eq. (2) as a function of nozzle-to-plate spacing only as shown in Eq. (4) where the jet deflection loss coefficient K is 0.5.
u1 ðpd =4Þ ¼ u2 ðpdHÞ 2
0:703 0:295
P0 ¼
2 P0 K H ¼ 1 þ 16 d 1=2qu21
ð3Þ ð4Þ
The extended Bernoulli’s equation of Eq. (4) is compared with the measured data in Fig. 4 and matched with the experimental results within ±20%. In Fig. 7, the results show that the normalized stagnation Nusselt number, Nu⁄0 (Nu0/Nu0,H/d=1) has a similar trend with the normalized stagnation pressure and is divided into two regions: Region (I) jet deflection region (H/d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized
Fig. 5. Water jet impingement at Reynolds number of 6039: (a) H/d = 0.08 and (b) H/d = 1.
A.M. Kuraan et al. / International Journal of Heat and Mass Transfer 108 (2017) 2211–2216
2.0
Nu0* = Nu0 / Nu0, H/d=1
empirical correlation for the normalized hydraulic jump diameter is developed as a function of nozzle-to-plate spacing alone shown below.
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
1.8
1.6
2215
ðDhj =dÞ ¼ P0:2 0 " ¼ 1þ
2 #0:2 1 H 32 d
ð6Þ
1.4
+15%
1.2
1.0
-15% 0.8 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 7. Normalized stagnation Nusselt numbers for the nozzle-to-plate spacing.
stagnation Nusselt number drastically increases with decreasing the nozzle-to-plate spacing since the impingement power (product of stagnation pressure and flow rate [17]) increases as the nozzleto-plate spacing decreases. In region II, the effect of the nozzle-toplate spacing is negligible on the normalized stagnation Nusselt number since the inertia is the dominant factor of this region, which means the average velocity of the jet is constant. An empirical correlation for the normalized stagnation Nusselt number is developed as a function of the nozzle-to-plate spacing alone. The correlation of the normalized stagnation Nusselt number for the impinging jet has the following form:
Nu0 ¼ P0:2 0 "
2 #0:3 1 H ¼ 1þ 32 d
ð5Þ
The correlation of the normalized hydraulic jump diameter was compared with the experimental results, and matched with the experimental results within ±15%. The suggested empirical correlations in Eqs. (4)–(6) are available in the range of Reynolds number of 4023–8053 and the nozzle-to-plate spacing of 0.08–1. As mentioned in the introduction, several correlations were suggested for large nozzle-to-plate spacings of H/d > 1.5. However, the understanding of a relationship for heat transfer and fluid flow characteristics at low nozzle-to-plate spacings H/d < 1 is still limited. The results in this study showed that the stagnation pressure is a governing parameter for heat transfer characteristics of impinging jets at stagnation point at low nozzle-to-plate spacing.
4. Conclusion In this paper, heat transfer and fluid flow characteristics of a free water jet impinging a flat plate surface are experimentally investigated. The effects of low nozzle-to-plate spacing (H/ d = 0.08–1) on the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are considered. It was found that the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are divided into two regions: Region (I) jet deflection region (H/d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-plate spacing since the stagnation pressure increases due to the jet deflection loss effect. The Nusselt number and hydraulic jump diameter were pro0:6
The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±15%. In Fig. 8, the results show that the normalized hydraulic jump diameter, ðDhj =dÞ ¼ ðDhj =dÞ=ðDhj =dÞH=d¼1 has a similar trend with
0:4
portional to ðH=dÞ and ðH=dÞ , respectively. In region II, the effect of the nozzle-to-plate spacing is negligible on the normalized stagnation Nusselt number and hydraulic jump diameter since the average velocity of the jet is constant, which means the jet deflection loss effect disappeared.
the normalized stagnation pressure and Nusselt number. An References 1.8
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
(Dhj/d)* = (Dhj/d) / (Dhj/d)H/d=1
1.7 1.6 1.5 1.4 1.3
+15%
1.2 1.1 1.0 0.9
-15%
0.8 0.7 0.6 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 8. Normalized hydraulic jump diameter for the nozzle-to-plate spacing.
[1] B. Elicson, B.W. Webb, Local heat transfer to impinging liquid jets in the initially laminar, transitional, and turbulent regimes, Int. J. Heat Mass Transfer 37 (8) (1994) 1207–1216. [2] J. Stevens, B.W. Webb, Local heat transfer coefficients under an axisymmetric, single-phase liquid jet, ASME J. Heat Transfer 113 (1991) 71–78. [3] B.W. Webb, C.-F. Ma, Single-phase liquid jet impingement heat transfer, Adv. Heat Transfer 26 (1995) 105–217. [4] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Therm. Fluid Sci. 6 (1) (1993) 111–134. [5] H. Martin, Heat and mass transfer between impinging gas jets and solid surface, Adv. Heat Transfer 13 (1977) 1–60. [6] 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. [7] X. Liu, J.H. Lienhard, The hydraulic jump in circular jet impingement and in other thin liquid films, Exp. Fluids 15 (1993) 108–116. [8] Y. Brechet, Z. Neda, On the circular hydraulic jump, Am. J. Phys. 67 (8) (1999) 723–731. [9] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle-plate spacings, Int. J. Heat Mass Transfer 37 (1994) 1687–1697. [10] K.S. Choo, S.J. Kim, Heat transfer characteristics of impinging air jets under a fixed pumping power condition, Int. J. Heat Mass Transfer 53 (2010) 320–326. [11] 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. [12] K. Choo, T.Y. Kang, S.J. Kim, The effect of inclination on impinging jets at small nozzle-to-plate spacing, Int. J. Heat Mass Transfer 55 (2012) 3327–3334.
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[13] K. Choo, B.K. Friedrich, A.W. Glaspell, K. Schilling, The influence of nozzle-toplate spacing on heat transfer and fluid flow of submerged jet impingement, Int. J. Heat Mass Transfer 97 (2016) 66–69. [14] B.K. Friedrich, T.D. Ford, A.W. Glaspell, K. Choo, Experimental study of the hydrodynamic and heat transfer of air-assistant circular water jet impinging a flat circular disk, Int. J. Heat Mass Transfer 106 (2017) 804–809. [15] B.K. Friedrich, A.W. Glaspell, K. Choo, The effect of volumetric quality on heat transfer and fluid flow characteristics of air-assistant jet impingement, Int. J. Heat Mass Transfer 101 (2016) 261–266.
[16] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 75 (1) (1953) 3–8. [17] K. Choo, S.J. Kim, The influence of nozzle diameter on the circular hydraulic jump of liquid jet impingement, Exp. Therm. Fluid Sci. 72 (2016) 12–17. [18] D.J. Womac, S. Ramadhyani, F.P. Incropera, Correlating equations for impingement cooling of small heat sources with single circular liquid jets, ASME J. Heat Transfer 115 (1) (1993) 106–115. [19] T. Bohr, P. Dimon, V. Putkaradze, Shallow-water approach to the circular hydraulic jump, J. Fluid Mech. 254 (1993) 635–648.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer and hydrodynamics of free water jet impingement at low nozzle-to-plate spacings Abdullah M. Kuraan, Stefan I. Moldovan, Kyosung Choo ⇑ Mechanical and Industrial Engineering Department, Youngstown State University, Youngstown, OH 44555, United States
a r t i c l e
i n f o
Article history: Received 3 November 2016 Received in revised form 19 January 2017 Accepted 21 January 2017
Keywords: Impinging jet Circular Flat plate
a b s t r a c t In this study, heat transfer and hydrodynamics of a free water jet impinging a flat plate surface are experimentally investigated. The effects of the nozzle-to-plate spacing, which is equal to or less than one nozzle diameter (H/d = 0.08–1), on the Nusselt number, hydraulic jump diameter, and pressure at the stagnation point are considered. The results show that the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are divided into two regions: Region (I) jet deflection region (H/ d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-plate spacing, since the stagnation pressure increases due to the jet deflection effect. In region II, the effect of the nozzle-to-plate spacing is negligible on the normalized stagnation Nusselt number and hydraulic jump diameter since the average velocity of the jet is constant, which means the jet deflection effect disappears. Based on the experimental results, new correlations for the normalized hydraulic jump diameter, stagnation Nusselt number, and pressure are developed as a function of the nozzle-to-plate spacing alone. Ó 2017 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– 7,18,19]. For free liquid impinging jets at high nozzle-to-plate spacings (H/d > 1), Elicson and Webb [1] studied local heat transfer of laminar, transitional, and turbulent regions at Reynolds numbers from 300 to 7000 and nozzle-to-plate spacing from 1.5 to 50. They showed that the stagnation Nusselt number is not influenced by the spacing between the nozzle exit and the heated plate. Stevens and Webb [2] investigated local heat transfer coefficients at Reynolds numbers from 9600 to 10,500 and nozzle-to-plate spacing from 1.7 to 34. They suggested an empirical correlation for the stagnation Nusselt number as a function of nozzle-to-plate spacing, Nu0 (H/d)0.032. The effect of the nozzle-to-plate spacing on
⇑ Corresponding author. E-mail address: [email protected] (K. Choo). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.084 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
the Nusselt number was slight. In addition, they found an empirical correlation for the hydraulic jump diameter as a function of the Reynolds number only. The correlation did not include the nozzle-to-plate spacing effect. Brechet and Neda [8] studied both experimentally and theoretically the circular hydraulic jump. They suggested a theoretical correlation for the hydraulic jump radius as a function of the nozzle-to-plate spacing, Rhj (H/d)1/6. For submerged impinging jets at low nozzle-to-plate spacings of less than one nozzle diameter (H/d = 0.1–1.0), Lytle and Webb [9] studied the local heat transfer characteristics using an infrared thermal imaging technique. They observed that the local Nusselt number increases as the nozzle-to-plate spacing decreases when the flow rate (or Reynolds number) is fixed. A power-law relationship between the stagnation Nusselt number and the nozzle-toplate spacing was presented in the form of Nu0 (H/d)0.191. Choo et al. [10–12] investigated heat transfer characteristics of impinging jets under a fixed pumping power condition at low nozzle-toplate spacing (H/d = 0.125–1.0). They show that the Nusselt number is independent of the nozzle-to-plate spacing under a fixed pumping power condition. Choo et al. [13] studied the relationship between the Nusselt number and stagnation pressure of the submerged impinging jets at a large range of nozzle-to-plate spacing (H/d = 0.125–40). They found that the Nusselt number is strongly dependent on the stagnation pressure variation.
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Nomenclature d Dhj Dhj/d g H Nu0 Nu⁄0 P0 P⁄0 Q
nozzle diameter [m] hydraulic jump diameter [m] dimensionless hydraulic jump diameter [–] gravitational acceleration nozzle-to-plate spacing stagnation Nusselt number normalized Nusselt number (Nu0/Nu0,H/d=1) pressure of jet at stagnation point normalized stagnation pressure (P0/P0,H/d=1) water flow rate [m3/s]
Several empirical correlations were suggested for free liquid jets at high nozzle-to-plate spacings and submerged impinging jets at low nozzle-to-plate spacings, respectively. However, the understanding of a relationship for heat transfer and fluid flow characteristics of free liquid jets at low nozzle-to-plate spacings is still limited. The purpose of this study is to determine the heat transfer and fluid flow characteristics of free liquid impinging jets for low nozzle-to-plate spacing (H/d = 0.08–1). Stagnation pressure of the free liquid impinging jets were measured to understand how it affects the Nusselt number and the hydraulic jump diameter. Based on the experimental results, correlations for the normalized stagnation Nusselt number, hydraulic jump diameter, and pressure were also developed as a function of the nozzle-to-plate spacing alone. 2. Experimental procedures Fig. 1 shows a schematic diagram of the experimental apparatus. The liquid flow was supplied by a water reservoir to furnish a steady flow. A gear pump (Micropump) is used to supply water to the test section. The pumped water passed through a flexible tube before entering the test section. A positive-displacementtype flowmeter is used during the experiment. A heat exchanger is connected to a constant temperature bath to control the jet temperature. Three K-type thermocouples were located directly
Pump Water Reservoir
Mass Flow Meters
Heat Exchanger
Power Supply
Test Section
DAQ
Thermocouples Fig. 1. Schematic diagram of the experimental set-up.
Re r Rhj
jet Reynolds number [ud/m] lateral distance from stagnation point [m] hydraulic jump radius [m]
Greek symbol m dynamic fluid viscosity [m2/s] q fluid density [kg/m3]
upstream and downstream of the flowmeters and downstream of the heat exchanger to monitor temperatures. A circular nozzle was used in the experiment. It has a 6.65 mm inner diameter and is 420 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. A flat acrylic plate with a diameter of 100 mm and thickness of 10 mm was used for pressure measurement. A pressure tap with a diameter of 0.1 mm was drilled and placed at the center of the flat acrylic plate. The pressure tap was connected to a micronanometer (Meriam M200-DI001). The manometers have a range of 0–6.89 kPa with accuracies of ±0.05%. The stagnation pressure of the impinging jet was measured at the center of impinging plate. A schematic of the test section is presented in Fig. 2(a). The test section was constructed out of a clear acrylic sheet. The impingement surface was designed to be at a greater elevation than the pool bottom so the impinged liquid would fall off the impinging plate and into the pool. The edge of the impingement plate was chamfered to ensure smooth drainage of liquid. This relieves the impinging fluid from downstream influences. The circular impinging plate was constructed from 0.5 in thick PTFE Teflon disk with a 216 mm diameter and a 1 mm diameter orifice in the center. The orifice was connected to the manometer using flexible tubing. The hydraulic jump created on the impinging plate was measured using a digital camera (Nikon, D50) and a pulse generator (Fovitec Speedlight flash, KD560) [14,15]. For accuracy and repeatability 5 min were given between each flow rate change to allow the system to reach a steady state for the different volumetric qualities. Both hydraulic jump and stagnation pressure were measured with minimum, actual, and maximum values at the steady state time. Fig. 2(b) shows a schematic of the test section for local temperature measurement. The DC power supply was connected to the bus bar soldered to the heater at the center of the impingement surface. The heater is made of stainless steel that is 0.0508 mm thick, 12.5 mm wide and 67.8 mm long. The heater was connected to a high voltage DC power supply (Agilent 6651A #J03) in series with a shunt, rated 0–6 V and 0–60 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. First, impinging fluid was introduced to the unheated heater, and then heat was applied to the heater. Values were recorded once the variation of the temperature difference between the heater and the nozzle exit was within 0.2 °C for 10 min. The voltage and the resistance across the heater were then measured in order to obtain the electrical energy input accurately with a multimeter. A 0.5 in thick PTFE Teflon disk was used to mount the heater, thermocouples, and copper bus. The Teflon disk also provides insulation to minimize heat loss through the dry side of the heater. Five
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Flow in
200
Pressure orifice Impingement plate
+10%
H/d = 1, present data Correlation by Stevens and Webb [2]
180
Nu
160
140
-10%
120
100
Pool Manometer
80 2000
Flow out
3000
4000
5000
6000
7000
8000
9000 10000
Re
(a)
(a)
Pstag [Pa] from Present study
1000
Re = 8053 Re = 7043 Re = 6039 Re = 5032 Re = 4023
800
600
400
200
0 0
(b)
200
400
600
800
1000
Pstag [Pa] from Bernoulli's Equation
(b)
Fig. 2. Test sections: (a) pressure measurement and (b) temperature measurement.
5.0
3. Results and discussion The experimental data of the Nusselt number in the present study for a free water impinging jet was compared with the empirical correlation of Steven and Webb [2] as a validation process. For Reynolds numbers in the range 4023 6 Re 6 8053, the stagnation Nusselt numbers were examined at a nozzle-to-plate spacing of H/d = 1, as shown in Fig. 3(a). The adopted empirical correlation
4.5 4.0
+15% 3.5
Rhj [cm]
K-type thermocouples of diameter 0.08 mm were fixed through 1 mm mounting holes on the centerline of the Teflon disk by a high temperature thermal epoxy. The thermocouples were spaced 21.5 mm apart starting at the center point. A thin double sided adhesive strip was laid directly over the row of thermocouples. The heater was then laid on top of the adhesive strip to keep constant contact with the thermocouples. These thermocouples were connected to the OMEGA OM-CP-QuadTemp2000 digital data acquisition system. A heat resistant latex caulking (Nelson Latex Firestop Sealant) was used to seal any gaps created by machining the Teflon disk. The uncertainty in the local Nusselt numbers is estimated with a 95% confidence level using the methods suggested by Kline and McKlintock [16]. The calculated maximum error of the main variables revealed an uncertainty of 2.7% for the surface temperature with 1.9%; 1.2% for the inlet temperature at the nozzle exit; 1.1% for the heat loss; 1.1% for the input voltage; 0.6% for the input current.
3.0
-15%
2.5 2.0 1.5 1.0 15
20
25
30
35
40
45
50
q [cm3/s]
(c) Fig. 3. Validation for single phase water impinging jet: (a) stagnation Nusselt number, (b) stagnation pressure, and (c) hydraulic jump diameter.
of Steven and Webb is Nu = 3.62Re 0.362Pr0.4. As shown in the figure, good agreements between the present data and the previous empirical correlation were observed within ±10%. Validation for the stagnation pressure comes from the comparison of the single
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8 7 6
P0/(1/2)ρV2
d
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
5
u1 u2
4
Impinging plate
3 2
Hydraulic Jump Diameter
+20% -20%
1
Fig. 6. Notation for the velocity at low nozzle-to-plate spacing.
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 4. Normalized stagnation pressure for the nozzle-to-plate spacing.
phase liquid impingement data from Bernoulli’s equation as shown in Fig. 3(b). The Bernoulli’s equation at stagnation point is given below.
P0 ¼
1 2 qu þ qgH 2
ð1Þ
where P0 is stagnation pressure and H is nozzle-to-plate spacing. The present data agrees with the experimental results of the previous experiments and the Bernoulli’s equation within ±10%. In addition, the measured hydraulic jump radius is validated with an empirical correlation of Brechet and Neda [8]. The adopted empirical correlation is Rhj ¼ 0:8Q m . As shown in Fig. 3(c), good agreements between the present data and the previous empirical correlation were observed within ±15%. Fig. 4 shows that the influence of the nozzle-to-plate spacing on the normalized stagnation pressure, P 0 ¼ P 0 = 12 qu2 for various Reynolds numbers. The results show that the normalized stagnation pressure is divided into two regions: Region (I) jet deflection region (H/d 6 0.4) in Fig. 5(a) and Region (II) inertia dominant region (0.4 < H/d 6 1) in Fig. 5(b). In region I, the normalized stagnation pressure drastically increases with decreasing the nozzle-to-plate spacing since flow resistance increases due to the flow deflection
of the impinging plate. In region II, the effect of the nozzle-toplate spacing is negligible on the normalized stagnation pressure. In order to explain the flow resistance of the flow deflection, an extended Bernoulli’s equation is applied below. The pressure at stagnation point includes two effects, one from dynamic pressure at point 1 and another from the jet deflection effect at point 2 as shown in Fig. 6.
P0 ¼
1 2 K 2 qu þ qu 2 1 2 2
ð2Þ
where K is jet deflection coefficient, which is empirically obtained from Fig. 4. From the mass conservation equation, Eq. (3), at points 1 and 2, we can transform Eq. (2) as a function of nozzle-to-plate spacing only as shown in Eq. (4) where the jet deflection loss coefficient K is 0.5.
u1 ðpd =4Þ ¼ u2 ðpdHÞ 2
0:703 0:295
P0 ¼
2 P0 K H ¼ 1 þ 16 d 1=2qu21
ð3Þ ð4Þ
The extended Bernoulli’s equation of Eq. (4) is compared with the measured data in Fig. 4 and matched with the experimental results within ±20%. In Fig. 7, the results show that the normalized stagnation Nusselt number, Nu⁄0 (Nu0/Nu0,H/d=1) has a similar trend with the normalized stagnation pressure and is divided into two regions: Region (I) jet deflection region (H/d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized
Fig. 5. Water jet impingement at Reynolds number of 6039: (a) H/d = 0.08 and (b) H/d = 1.
A.M. Kuraan et al. / International Journal of Heat and Mass Transfer 108 (2017) 2211–2216
2.0
Nu0* = Nu0 / Nu0, H/d=1
empirical correlation for the normalized hydraulic jump diameter is developed as a function of nozzle-to-plate spacing alone shown below.
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
1.8
1.6
2215
ðDhj =dÞ ¼ P0:2 0 " ¼ 1þ
2 #0:2 1 H 32 d
ð6Þ
1.4
+15%
1.2
1.0
-15% 0.8 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 7. Normalized stagnation Nusselt numbers for the nozzle-to-plate spacing.
stagnation Nusselt number drastically increases with decreasing the nozzle-to-plate spacing since the impingement power (product of stagnation pressure and flow rate [17]) increases as the nozzleto-plate spacing decreases. In region II, the effect of the nozzle-toplate spacing is negligible on the normalized stagnation Nusselt number since the inertia is the dominant factor of this region, which means the average velocity of the jet is constant. An empirical correlation for the normalized stagnation Nusselt number is developed as a function of the nozzle-to-plate spacing alone. The correlation of the normalized stagnation Nusselt number for the impinging jet has the following form:
Nu0 ¼ P0:2 0 "
2 #0:3 1 H ¼ 1þ 32 d
ð5Þ
The correlation of the normalized hydraulic jump diameter was compared with the experimental results, and matched with the experimental results within ±15%. The suggested empirical correlations in Eqs. (4)–(6) are available in the range of Reynolds number of 4023–8053 and the nozzle-to-plate spacing of 0.08–1. As mentioned in the introduction, several correlations were suggested for large nozzle-to-plate spacings of H/d > 1.5. However, the understanding of a relationship for heat transfer and fluid flow characteristics at low nozzle-to-plate spacings H/d < 1 is still limited. The results in this study showed that the stagnation pressure is a governing parameter for heat transfer characteristics of impinging jets at stagnation point at low nozzle-to-plate spacing.
4. Conclusion In this paper, heat transfer and fluid flow characteristics of a free water jet impinging a flat plate surface are experimentally investigated. The effects of low nozzle-to-plate spacing (H/ d = 0.08–1) on the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are considered. It was found that the normalized stagnation Nusselt number, pressure, and hydraulic jump diameter are divided into two regions: Region (I) jet deflection region (H/d 6 0.4) and Region (II) inertia dominant region (0.4 < H/d 6 1). In region I, the normalized stagnation Nusselt number and hydraulic jump diameter drastically increase with decreasing the nozzle-to-plate spacing since the stagnation pressure increases due to the jet deflection loss effect. The Nusselt number and hydraulic jump diameter were pro0:6
The correlation of the normalized stagnation Nusselt number was compared with the experimental results, and matched with the experimental results within ±15%. In Fig. 8, the results show that the normalized hydraulic jump diameter, ðDhj =dÞ ¼ ðDhj =dÞ=ðDhj =dÞH=d¼1 has a similar trend with
0:4
portional to ðH=dÞ and ðH=dÞ , respectively. In region II, the effect of the nozzle-to-plate spacing is negligible on the normalized stagnation Nusselt number and hydraulic jump diameter since the average velocity of the jet is constant, which means the jet deflection loss effect disappeared.
the normalized stagnation pressure and Nusselt number. An References 1.8
Present data, Re = 4,023 Re = 5,032 Re = 6,039 Re = 7,046 Re = 8,053
(Dhj/d)* = (Dhj/d) / (Dhj/d)H/d=1
1.7 1.6 1.5 1.4 1.3
+15%
1.2 1.1 1.0 0.9
-15%
0.8 0.7 0.6 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H/d Fig. 8. Normalized hydraulic jump diameter for the nozzle-to-plate spacing.
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