Effect of number of round jets on impingement heat transfer from a heated cylinder

Applied Thermal Engineering 162 (2019) 114308

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Effect of number of round jets on impingement heat transfer from a heated cylinder Sharad Pachpute, B. Premachandran

T

⁎

Department of Mechanical Engineering, IIT Delhi, Haus Khas, New Delhi 110016, India

H I GH L IG H T S

arranged multi-jet impingement improves heat transfer significantly. • Circumferentially very high curvature ratio, the secondary peak in local Nusselt number is not observed. • AtNumber of round jets required for the uniform cooling increases as the curvature ratio increases. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Impingement Round nozzles Multi-jets Circular cylinder

The details of an experimental study carried out on a single jet and multiple jets emerging from round nozzles of diameter, d and impinging over a uniformly heated cylinder of diameter, D are presented. The number of jets are varied from one to six in the parametric study. In the multi-jet configurations, the jets are arranged circumferentially around the heated cylinder. The range of Reynolds number, Red considered is 5000 – 20,000. The curvature ratio, D/d is varied from 5.1 to 20.4 and the nozzle-to-cylinder spacing, H/d is varied from 2 to 12. The present results show that the Nusselt number at the stagnation point (Nustag) is not affected when the number of jets is increased. However, in multi-jet configurations with four and six jets, the interaction between the wall jets increases heat transfer in the fountain regions. The number of round jets required for the uniform cooling increases with increase in the curvature of the target cylinder, D/d. Based on the experimental study, correlations are given for the stagnation point Nusselt number (Nustag) and average Nusselt number (Nuavg).

1. Introduction Jet impingement cooling of curved objects have various industrial applications in manufacturing and process industries due to its high convective heat removal rate. Reviews of single jet impingement heat transfer from flat surfaces are presented in [1,2]. Because of higher cooling rate, a single circular or slot jet impingement cooling is often used for cooling of curved objects. However, in many applications, single jet impingement cooling is not sufficient for uniform heat transfer. For the cooling of a large sized cylindrical furnace containing the metal slurry or circular welding spot over an offshore pipe, cooling of steel pipes and cooling of the cylindrical cement kiln in cement industries and the casting of large sized pipes, multi-jet impingement is used for the uniform cooling of the cylindrical target surface. In many applications, uniform cooling of circular heated objects is essential in order to retain the structural strength. Chan et al. [3] conducted experiments on cooling of convex surfaces

⁎

with a single slot jet configuration. The heat transfer decreases substantially away from the impingement region of the cylinder. Hence, multiple round or slot jets are used for the effective cooling of curved surfaces. Studies [4–8] were conducted on multi-jet impingement of concave geometries with circular jet holes for wide ranges of geometric and flow parameters. However, only a few studies have been carried on cylindrical convex surfaces. Gori and Bossi [9] reported the results of single slot jet impingement cooling of a circular cylinder. Their single jet configuration provides effective cooling only over the top part of the cylinder. In this configuration, heat transfer is not effective at the rear portion of the cylinder. To enhance heat transfer in this configuration, Pachpute and Premachandran [10] used a semi-cylindrical confinement with an opening. They commented that the heat transfer enhancement with a flow confinement for a single slot jet is dependent on the confinement size and the width of the opening in flow confinements. They also reported the flow and heat transfer features for different geometries of confinements

Corresponding author. E-mail address: [email protected] (B. Premachandran).

https://doi.org/10.1016/j.applthermaleng.2019.114308 Received 1 April 2019; Received in revised form 20 August 2019; Accepted 24 August 2019 Available online 26 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 162 (2019) 114308

S. Pachpute and B. Premachandran

Nomenclature Ajet D d h H kf ṁ jet Nu

q” Red T

cross-sectional area of nozzle exit, πd 2 4 (m2) Cylinder diameter, m Nozzle diameter, m Local heat transfer coefficient, W/m2-K Nozzle-to-target spacing, m Thermal conductivity of air, W/m-K mass flow rate of the jet fluid, kg/s local Nusselt number, hiD/kf

heat flux, W/m2 Reynolds number, ṁ jet d /ν temperature, K

Greek Symbol θ ν

angle measured with respect the impingement point of first jet, degree (°) kinematic viscosity, m2/s

study, they found that the local Nusselt number is improved due to the interaction of jets. A slot jet requires higher mass flow rate because of higher crosssectional area of the jet hole opening. Hence, round jets are widely considered in many applications for the cooling of curved objects. Sparrow et al. [15] and Tawfek [16] studied circular jet impingement cooling of a circular cylinder which is maintained at constant temperature. As single jet impingement cooling is not sufficient to cool a large portion of the cylinder, Singh et al. [17] investigated impingement cooling with two jets with an inline arrangement. The results of flow and heat transfer due to double jet impinging at the top of the cylinder is also reported by Singh et al. [17] in their study and they found more local cooling rate at the top of cylinder rather than the case of a single jet. Wang et al. [18] conducted experiments with two opposite jets impinging over a uniformly heated cylinder at θ = 0° and 180°, respectively for D/d = 2.5 – 10 at a fixed Reynolds number of Red = 20,000 to increase the local Nusselt number from the rear surface of the circular cylinder. They noted an increase in Nuavg due to the

in [11]. They found that the quadrilateral and hexagonal confinements provide higher local Nusselt number at the rear portion of the target cylinder compared to the other confinement geometries for ReD = 6000 – 20,000. Multi-jet impingement cooling of circular objects with different arrangements of jets has been discussed in the literature. Nada [12] experimentally analyzed heat transfer from a circular heated object with one as well as three slot jets. They found that the three-jet configuration significantly improves cooling on the top part of the cylinder because of the strong interactions of slot jets at the lower spacing between two adjacent jets. Zuckerman and Lior [13] investigated the effect of number of slot jets located in the circumferential direction over a heated circular cylinder on impingement heat transfer. Due to more number of impingement and fountain regions formed over the cylinder, the cooling is almost uniform in the configuration of multiple rectangular slot jet configuration. Chauchat and Schall [14] investigated four radial slot jets impinging over a large size heated cylinder with an annular confinement for ReS = 1123, D/S = 15 and H/S = 4.4. In their

Fig. 1. Schematics representation for number of round jet impinging over a heated circular target (a) a single jet, (b) two jets, (c) four jets, (c) six jets. 2

Applied Thermal Engineering 162 (2019) 114308

S. Pachpute and B. Premachandran

second jet at θ = 180° for D/d = 10 for fixed Red and H/d. Csernyei and Stratman [19] studied on cooling of a large size cylindrical cement kiln with a series of round jets for different geometric and jet flow parameters. However, this multi-jet configuration provide higher cooling only on the top surface of cylindrical objects. In the literature, many researchers have investigated jet impingement cooling of curved objects with only one jet. In the case of a cylindrical heated surface, the heat removal rate from the rear side of the cylindrical target is low in comparison with the top surface of the cylinder. This results in high thermal stress of the cylindrical objects. The use of confinements provides only limited enhancement in local heat transfer. Furthermore, a single jet is not sufficient for the effective cooling of a large circular object. Multiple round jets impinging at the top of the cylinder provides effective cooling only at the top surface. The configuration of multiple-rectangular slot impingement cooling requires higher mass flow rate compared to multi-round jet impingement cooling. Multiple jets arranged circumferentially may provide better cooling at a particular section of a heated cylinder. Hence, the effect of number of round jets impinging radially over a heated cylinder should be studied to get an optimum value of the angular spacing between two round jets for a fixed diameter of the cylinder and various diameters of nozzles. An experimental study has been carried for multiple round jets impinging at the middle portion of the circular cylinder for various ranges of parameters.

Table 1 Uncertainties determined in the measured quantities. Parameter

Uncertainty

Mass flow rate of air Temperature of cylinder wall Temperature at the nozzle exit Voltage Current

± 0.16 mg/s ± 0.054 °C ± 0.032 °C ± 0.014 V ± 0.081 A

2. Problem description Fig. 3. Local Nusselt number distribution at the centre (Z/D = 0) of the cylinder for single (n = 1) and double (n = 2) jet impingement at Redvmax = 20,000 and H/d = 2.

In this paper, cooling of a circular object with a single circular jet and multiple circular jets is investigated experimentally. For the double and multi-jet impingement cases, the round nozzles are placed circumferentially. Fig. 1 shows the schematic for a number of round jets arranged over the cylinder of diameter, D = 5.1 mm. In the parametric study, the D/d is varied from 5.1 to 20.4. The length of the round tube used as a nozzle is taken to be around 60d. The Reynolds number, Red = ṁ jet d (Ajet μ) is varied from 5000 to 20,000. The dimensionless distance from the nozzle to the cylinder, H/d is considered in the range

of 2 – 12. For all the cases, the dimensionless cylinder length, L/D is fixed as 12. In order to identify the number of nozzles required for the effective cooling over the cylinder, number of round nozzles, n are varied from one to six.

Fig. 2. Schematic diagram (a) experimental set up, (b) positions of multiple round jets over a heated circular cylinder. 3

Applied Thermal Engineering 162 (2019) 114308

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Table 2 Details of parameters for the present experimental study.

Red =

Parameter

values

n D/d H/d Red

1, 2, 4, 6 5.1, 10.2, 20.4 2, 4, 6, 8, 10, 12 5000, 10,000, 15,000, 20,000

ṁ jet d Ajet μ

(1)

In the parametric study, Red was varied from 5000 to 20,000. The local Nusselt number (Nu) was obtained based on the local temperature over the heated cylinder, Tw acquired using the IR camera and jet temperature at the nozzle exit, Tj as

Nu = 3. Experimental methodology

qconv " _HF (Tw − Tj ) kair

D

(2)

is the convective heat flux and kair is the thermal conhere, ductivity of air at Tj. The Nuavg over the heated cylinder is determined as below.

′ ′ _HF qconv

3.1. Experimental set up To conduct experimental work, the experimental setup used by Singh et al. [17] was modified. Fig. 2(a) presents a schematic of the experimental set up with the nozzles mounted radially over a circular heated cylinder. The compressed air passes through the nozzle and impinges over the cylinder. The angular direction starts from the impingement point of the top jet (θ = 0°) which is fixed in all the cases of present multiple-jet impingement studies. A uniform heat flux condition was maintained over stainless steel foil which was wound around the low thermal conductivity Phenolic cylinder with a DC power unit. An Infrared-camera (IR) was used for acquire surface temperature over the cylinder. The positions of the nozzles used for circumferential multi-jet impingement cooling is shown in Fig. 2(b) for four jets.

Nuavg =

1 πL

L

π

∫ ∫ NuD dθdz 0

0

(3)

The heat generated due to electric heating of the stainless steel (SS) foil is transferred to the surrounding by all modes of heat transfer. Due to the use of a very thin foil (30 µm) which was wound over a very low thermal conductivity material of phenolic tube, the conduction heat loss is low and hence neglected in this study. The convective heat flux over the cylinder is determined considering only the radiation loss as

qconv " _HF = qtotal " _HF − qrad " _HF

(4)

where qtotal " _HF = EI (Afoil ) . Here, Afoil is the area of the SS foil. The following expression is used to calculate the heat flux due to radiation.

3.2. Experimental analysis

4 4 qrad " _HF = εσ (Tw − Tamb)

For each jet, a digital mass flow controller was used to control the mas flow of air (ṁ jet ) at the nozzle exit. The jet Reynolds number is calculated as

In this study, the emissivity ε of the foil coated with black matt paint is 0.96. The overall uncertainty in the local Nusselt number was calculated based on Kline and McClintock [20] as follows:

Red = 20000, H/d = 2, D/ d = 5.1, n = 1

Red = 5000, H/d = 2, D/ d = 5.1, n = 1

Z

θ

Fig. 4. Infra-red camera image of a heated circular cylinder at D/d = 5.1 and H/d = 2 (a) single jet impingement (n = 1), Red = 5000; (b) multijet impingement (n = 4), Red = 5000; (c) single jet impingement (n = 1), Red = 20,000; (d) multi-jet impingement (n = 4), Red = 20,000. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Z θ

(a)

(c)

Red = 5000, H/d = 2, D/ d = 5.1, n = 4

Red = 20000, H/d = 2, D/ d = 5.1, n = 4

θ Z

Z

θ

(b)

(d) 4

(5)

Applied Thermal Engineering 162 (2019) 114308

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800

1800

n=1 n=2 n=4 n=6

Red = 5000, H/d = 2, D/ d = 10.2

Red = 20000, H/d = 2, D/ d = 10.2

n=1 n=2 n=4 n=6

1500

600

1200

NuD

NuD 400

900 600

200 300 0

0 0

20

40

60

80

100

120

140

160

0

180

20

40

60

80

100

120

140

160

180

Angle, θ

Angle, θ

(b)

(a) 1800 n=1 n=2 n=4 n=6

800

Red = 5000, H/d = 8, D/ d = 10.2

n=1 n=2 n=4 n=6

Red = 20000, H/d = 8, D/ d = 10.2

1200

NuD

NuD

600

1500

400

900 600

200 300 0

0 0

20

40

60

80

100

120

140

160

180

0

20

40

60

Angle, θ

80

100

120

140

160

180

Angle, θ

(d)

(c)

Fig. 5. Effect of number of jets on the local Nusselt number at D/d = 10.2: (a) Red = 5000, H/d = 2; (b) Red = 20,000, H/d = 2; (c) Red = 5000, H/d = 8; (d) Red = 20,000, H/d = 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 180 150

2

δNu =

n=1 n=2 n=4 n =6

Nuavg

⎜

2

⎟

(6)

where δE and δI denote the absolute uncertainties calculated for voltage and current, respectively. δTi and δTj are the absolute uncertainties in Tw and Tj, respectively. The uncertainty in the measured quantities are presented in Table 1. The overall uncertainties calculated in the local Nusselt number for Red = 5000 and Red = 20,000 are ± 5.2% and ± 4.6%, respectively.

120 90 60 30 0 5000

2

2

⎛ ∂Nu ⎞ δE2 + ⎛ ∂Nu ⎞ δI2 + ⎛ ∂Nu ⎞ δT2 + ⎜⎛ ∂Nu ⎟⎞ δT2 i j ⎝ ∂E ⎠ ⎝ ∂I ⎠ ⎝ ∂Ti ⎠ ⎝ ∂Tj ⎠

3.3. Comparison of present data with the available experimental data

10000

15000

The local Nusselt number variation obtained over a heated cylindrical target from the experimental data of present study is compared with those of Wang et al. [18] for the jet Reynolds number, calculated considering the maximum velocity the nozzle exit, Redvmax = 20,000 at H/d = 2. In both the studies, single (n = 1) jet impinges at θ = 0° and double jets (n = 2) impinge at θ = 0° and 180° at Z/D = 0. The experimental data of present study is compared with those of Wang et al. [18] in Fig. 3 for H/d = 2. The comparison between stagnation Nusselt number (Nustag) obtained with the present data with those of Wang et al. [18] shows around 3% deviation. The secondary peak is noted in the local Nusselt number in both the experimental studies. For θ > 0°, the difference in local Nu of both experimental studies is very small for

20000

Red Fig. 6. Effect of number of jets (n) on the Nuavg of the cylinder at H/d = 2 and D/d = 10.2 and Red = 5000–20,000. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5

Applied Thermal Engineering 162 (2019) 114308

S. Pachpute and B. Premachandran

1600

1600

Red = 5000, H/d = 2

n = 2, D/d = 5.1 n = 2, D/d = 10.2 n = 2, D/d = 20.4

1200

NuD

1200

NuD

Red = 5000, H/d = 2

n = 1, D/d =5.1 n = 1, D/d =10.2 n = 1, D/d =20.4

800

400

800

400

0

0 0

30

60

90

120

150

180

0

30

60

90

Angle, θ

Angle, θ

(a)

(b)

120

150

180

1600

Red = 5000, H/d = 2

n = 4, D/d = 5.1 n = 4, D/d = 10.2 n = 4, D/d = 20.4

1200

n = 6, D/d = 5.1 n = 6, D/d = 10.2 n = 6, D/d = 20.4

Red = 5000, H/d = 2

1600

NuD

NuD

1200

800

400

800

400

0

0

0

30

60

90

120

150

180

0

30

60

90

120

150

180

Angle, θ

Angle, θ

(c)

(d)

Fig. 7. Effect of curvature ratio (D/d) on the local Nusselt number (NuD) for Red = 5000 and H/d = 2 (a) single jet (n = 1), (b) two jets (n = 2), (c) four jets (n = 4), (d) six jets (n = 6). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

at Z/D = 0 for Red = 5000, D/d = 10.2 and H/d = 2 is show in Fig. 5(a). For the single jet configuration, the local Nusselt number shows its peak value at θ = 0˚. For θ > 0˚, the local Nusselt number continuously reduces. For the double jet (n = 2) configuration, the second jet is placed at an angle of 180°. The rear part of the target is cooled very effectively with this additional stagnation jet. For n = 2, the effect of the second jet on the local Nusselt number is considerable from θ = 120° to θ = 180° from the first jet, but the local Nusselt number at the middle portion of cylinder from θ = 40° to θ = 120° is lower compared to that of the stagnation regions for the double jet (n = 2) configuration. To enhance heat transfer further, two more jets are added and the angle between two adjacent jets is 90°. This configuration enhances the local Nusselt number at the middle region from θ = 60° to θ = 120° which is not cooled considerably in the configuration of double jet. When a six-jet configuration is used, cooling of the cylinder is uniform compared to that of two and four jets. In Fig. 5 (b), the effect of number of jets on the local Nusselt number over the cylinder at Z/D = 0 for Red = 20,000 is shown. The local Nusselt number in the region of jet impingement is increased because of higher nozzle exit velocity. In the single jet impingement, the secondary peak of local Nusselt number is noted at around 25˚ from the impingement point. The secondary peak in the local Nusselt number is observed due to the transition from the laminar flow to turbulent flow for Red > 7000 at the lower spacing between the cylinder and the

both single and double jet impingement cases. 4. Results and discussion The local Nusselt number (Nu) and the average Nusselt number (Nuavg) over the cylindrical heated surface for various number of nozzles were obtained for different geometric and flow parameter which are given in Table 2. 4.1. Effect of number of jets (n) To understand impingement cooling of a cylindrical target by circumferentially arranged jets the number of jets is varied from 1 to 6. The temperature contours acquired from the IR camera are presented in Fig. 4 for Red = 5000 and 20,000, D/d = 5.1 and H/d = 2 for jet impingement with a single jet and four jets. The local temperature over the cylinder due to the jet impingement with a single nozzle is shown in Fig. 4(a) and (c). It is found that the local surface temperature of the target is lower at the top and its value increases as the local distance from the impinging point increases. With increasing of the number of round jets (n) from one to four, multiple stagnation points are observed over the target (Refer Fig. 4(b) and (d)). The portion of the cylinder between two jets is cooled significantly when four jets are used. The effect of number of jets on the variation of local Nusselt number 6

Applied Thermal Engineering 162 (2019) 114308

S. Pachpute and B. Premachandran

3500

3500

Red = 20000, H/d = 2

3000

2000

2000

1500

1500

1000

1000

500

500

0

0

0

30

60

90

150

180

0

30

60

90

Angle, θ

(a)

(b) 3500

n = 4, D/d = 5.1 n = 4, D/d = 10.2 n = 4, D/d = 20.4

Red = 20000, H/d = 2

3000

120

Angle, θ

3500

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

120

150

Red = 20000, H/d = 2

n = 6, D/d = 5.1 n = 6, D/d = 10.2 n = 6, D/d = 20.4

30

120

3000

NuD

NuD

n = 2, D/d = 5.1 n = 2, D/d = 10.2 n = 2, D/d = 20.4

2500

NuD

NuD

2500

Red = 20000, H/d = 2

3000

n = 1, D/d = 5.1 n = 1, D/d = 10.2 n = 1, D/d = 20.4

180

0

0

30

60

90

120

150

180

0

60

90

Angle, θ

Angle, θ

(c)

(d)

150

180

Fig. 8. Effect of curvature ratio (D/d) on the local Nusselt number for Red = 20,000 and H/d = 2 (a) single jet (n = 1), (b) two jets (n = 2), (c) four jets (n = 4), (d) six jets (n = 6). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

of the free round jet. Hence, the jet velocity decreases away from the potential core. Because of low jet fluid velocity at H/d = 8 close to the cylinder in comparison with H/d = 2, the enhancement in local Nusselt number due to wall-jet interaction in the fountain region between two jets is not observed at n = 6. Zukerman and Lior [13] found from their numerical analysis that the wall jet formed over the cylinder collide each other and form a fountain region with a strong recirculation region at the base of the fountain region over the cylinder. It was also observed that the turbulent intensity increases significantly in the strong recirculation region of fountains compared to the wall jet region. Overall, both strong recirculation and higher turbulent intensity increase local heat transfer in the fountain region. The average Nusselt number (Nuavg) has been compared for H/d = 2 for different number of jets in Fig. 6 for the range of Red considered. It is noted that the Nuavg increases as the number of round jets (n) increases for any fixed Red. The percentage increase in Nuavg due to an increase in the number of round jet from n = 1 to 2 is higher compared to percentage increase in Nuavg increase when the number of nozzles increased from 4 to 6. The experimental data obtained for Red = 5000 – 20,000, D/d = 10.2 and H/d = 2 shows that the enhancement in the Nuavg is found in the range of 37–42 % when n increased from 1 to 2, 18 – 23% when n is increased from 2 to 4. The increase in Nuavg is around 10–15% when n is increased from 4 to 6. Hence, for D/d = 10.2, the number of jets more than four does not

nozzle exit [3]. Wang et al. [18] also observed the same in their investigation of jet impingement cooling of the circular target with a single round nozzle. After the secondary peak, the local heat transfer continuously decreases. When the second jet is placed at θ = 180°, the local Nusselt number variation is almost unaffected till θ = 80˚ from the jet impingement point of the first jet. But the local Nusselt number from θ = 120° to 180° is enhanced due the second counter jet. In the double jet configuration, two secondary peaks are found at θ = 25° and 155°. At Z/D = 0, from θ = 60° to 120°, the local heat transfer is very low compared to that in the stagnation regions. In the same region, the local Nusselt number increases considerably when four jets are used. As the numbers of jets further increases to 6, the portion of the cylinder with low heat transfer decreases. Because of the interactions of wall jets with high velocity jet fluid, the local Nusselt number increases in the fountain region formed at θ = 30°, 90° and 120° at Z/D = 0 for n = 6, Red = 20,000 and H/d = 2 (Refer Fig. 5(b)). For H/d = 8 and Red = 5000, the Nustag decreases compared to that noted at and H/ d = 2 (Refer Fig. 5(c)). For the single or multi-jet impingement at H/ d = 8, the secondary peak in the variation of local Nusselt number is not observed at the centre of the cylinder (Z/D = 0). In the multi jet impingement cooling (n ≥ 2) at H/d = 8, the local Nusselt number increases from θ = 60° to 120°. Fig. 5(d) shows that the local Nusselt number also decreases continuously for a single jet configuration at Red = 20,000. At H/d = 8, the cylinder is placed in the transition zone 7

Applied Thermal Engineering 162 (2019) 114308

S. Pachpute and B. Premachandran

3500 n=1 n=2 n=4 n=6

Red = 20000, H/d = 2, D/ d = 5.1

800

2500

NuD

600

NuD

n=1 n=2 n=4 n=6

Red = 20000, H/d = 2, D/ d = 20.4

3000

400

2000 1500 1000

200 500 0

0 0

20

40

60

80

100

120

140

160

180

0

20

40

60

Angle, θ

80

(a) 800

120

140

160

180

(b) 3500

n=1 n=2 n=4 n=6

Red = 20000, H/d = 8, D/ d = 5.1

600

Red = 20000, H/d = 8, D/ d = 20.4

n=1 n=2 n=4 n=6

3000 2500

NuD

NuD

100

Angle, θ

400

2000 1500 1000

200

500

0

0

0

20

40

60

80

100

120

140

160

180

Angle, θ

0

20

40

60

80

100

120

140

160

180

Angle, θ

(c)

(d)

Fig. 9. Effect of number of round jets (n) on the local Nusselt number at Red = 20,000: (a) D/d = 5.1, H/d = 2; (b) D/d = 20.4, H/d = 2; (c) D/d = 5.1, H/d = 8; (d) D/d = 20.4, H/d = 8. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

a fixed jet Reynolds number for D/d = 20.4. Wang et al. [18] also noted the maximum local Nusselt number at the impingement point for the higher value of D/d compared to that of lower value of D/d for a fixed Reynolds number. From θ = 120° to 180°, the effect of curvature ratio (D/d) is relatively very small for single jet impingement cooling (n = 1). For the double jet impingement, from θ = 0° to 80°, the local Nusselt number is the same that of a single jet. From θ = 100° to 180°, the local Nusselt number increases continuously due to the second jet for D/d = 5.1–20.4 (Refer Fig. 7(b)). The effect of D/d on heat transfer at θ = 90° is minimal and the local Nusselt number is low for all the D/d values in the case of double jet impingement. Fig. 7(c) and (d) show that for four and six jets, the local Nusselt number (NuD) is higher for D/ d = 20.4 similar to the single and double jet cases. As Red increases to 20,000, the secondary peak in the variation of local Nusselt number along the circumference is observed only for D/d = 5.1 and 10.2 at H/ d = 2 for n = 1, 2, and 4 as given in Fig. 8(a–c). In the six-jet configuration (n = 6), the local heat transfer in the fountain regions is enhanced considerably for D/d = 5.1 at Red = 20,000 (Refer Fig. 8(d)). This is observed because of strong wall -jet interactions. To clearly explain the local heat transfer characteristics for D/ d = 5.1 and D/d = 20.4 at H/d = 2, the local Nusselt number variation at Z/D = 0 for the number jet varied from n = 1 to 6 is presented in Fig. 9 for Red = 20,000. When six jets are used to cool the cylinder, the wall jet interaction increases the local Nusselt number in the fountain

significantly increase Nuavg. Zuckerman and Lior [13] reported the numerical results of Nuavg of a heated cylinder for single and multiple slot-jet impingement for H/S = 6, D/d = 10 and Reynolds number, defined based on the hydraulic diameter of the nozzle, Re2S = 5000 – 80,000. Similar to the present study, Zuckerman and Lior [13] also noted significant enhancement in Nuavg when the number of slot jets increased from n = 1 to 2 compared to the increase in Nuavg when the number of slot jets increased from n = 2 to 4. 4.2. Effect of curvature ratio (D/d) Apart from Red, the jet impingement cooling rate of a circular object is also a function of the curvature ratio (D/d). Hence experiments were also carried out for three different sizes of round nozzles to know the effect of curvature ratio (D/d) on the cooling of the cylinder. Based on Eq. (1), at a given Red, the flow rate of air is lower for D/d = 20.4 and higher at D/d = 5.1. Heat transfer results for the case of D/d = 10.2 have already been discussed in details in the previous section. Hence, in this section the results are presented only for D/d = 5.1 and 20.4. The influence of D/d on the local Nusselt number variation over the cylinder is presented in Fig. 7 at Z/D = 0 for H/d = 2 and Red = 5000 for the impingement cooling. For the single jet configuration, at D/ d = 20.4, the local Nusselt number is higher than that of D/d = 5.1 and 10.2 at the top side of the target. This is due to higher velocity of jet for 8

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S. Pachpute and B. Premachandran

100

180 Red = 5000, H/d =2

n=1 n=2 n=4 n=6

n=1 n=2 n=4 n =6

60

40

90 60 30 0 5000

20 0

5

10

15

20

25

10000

15000

20000

Red

D/d

(a)

(a) 180

250 Red = 20000, H/d =2

n=1 n=2 n=4 n=6

150

n=1 n=2 n=4 n =6

D/ d = 20.4

120

Nuavg

200

Nuavg

D/ d = 5.1

120

Nuavg

Nuavg

80

150

150

90 60

100

30 0 5000

50 0

5

10

15

20

25

10000

15000

20000

Red

D/d

(b)

(b)

Fig. 11. Effect of number of round jets on the Nuavg at H/d = 2 (a) D/d = 5.1, (b) D/d = 20.4.

Fig. 10. Effect of number of round jets on the Nuavg of the cylinder for H/d = 2 (a) Red = 5000, (b) Red = 20,000. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

impingement cooling with four and six jets. As the number of jets, n increases from 4 to 6, the area-averaged Nusselt number increases due to an increase in number of stagnation regions with higher local Nusselt numbers formed over the cylinder for higher D/d. For Red = 20,000, the variation of Nuavg with curvature ratio (D/d) for n = 1 – 6 is found to be similar to that at Red = 5000 as presented in Fig. 10 (b). Overall, the Nuavg is higher at D/d = 5.1 in the cases of a single round jet due to higher flow rate of air. The configuration of multiple round jets with the higher curvature ratio of D/d = 20.4 provides higher average heat transfer because of multiple stagnation regions of higher local Nusselt number at n = 6. To know the percentage change in the average cooling rate of the cylinder due to an increase in the number of round jets, the Nuavg over the circular cylinder is calculated using the present experimental data for Red = 5000 – 20,000, D/d = 5.1 – 20.4 and H/d = 2 – 12. Fig. 11(a) presents the effect of Reynolds number on the Nuavg at D/d = 5.1 and H/d = 2. The average Nusselt number (Nuavg) increases with increasing of Reynold's number for a given number of jets. At D/d = 5.1, the increase in Nuavg with increasing in the number of round jets is observed in the range of 33–39 % when n is increased from 1 to 2, 16 – 23% when n is increased from 2 to 4 and it is around 9 – 12% from n = 4 to 6 for 5000 ≤ Red ≤ 20,000. As D/d increases to 20.4 for 5000 ≤ Red ≤ 20,000, the enhancement in Nuavg of the cylindrical target is in the range of 48–57 % when the number of nozzles, n is increased from 1 to 2 (Refer Fig. 11(b)). The increase in Nuavg is

regions at D/d = 5.1 and at H/d = 2 as shown in Fig. 9. However, at D/ d = 20.4, the change in heat transfer in the fountain regions is not found. A similar variation is also observed at H/d = 8 (See Fig. 9(c) and (d)). Overall, multiple round jets increase heater transfer rate for higher curvature ratios. The number of jets (n) required for uniform cooling at Z/D = 0 increases as the curvature ratio (D/d) increases. To comprehend the effect of number of round jets (n) on the average heat transfer for various D/d values, the Nuavg obtained at H/d = 2 for n = 1 – 6, Red = 5000 and 20,000 are shown in Fig. 10. Fig. 10(a) presents that the Nuavg reduces with increasing the curvature ratio (D/ d) for the cases of single and double jet impingement. This observation is also found by Wang et al. [18] for the jet impingement cooling of a cylinder with single and double circular jets for D/d = 2.5 – 10. However, in the case of four jet configuration, the average heat transfer is almost same for three sizes of nozzles (D/d = 5.1, 10.2 and 20.4). For the six jet configuration, the average Nusselt number (Nuavg) increases with increasing of D/d from 10.2 to 20.4 (Refer Fig. 10(a)). Because of higher mass flow rate and wide spreading jet fluid over the cylinder at the lower value of D/d, the cylinder is cooled more significantly for single and double jets compared that at higher D/d. Hence, the average Nusselt number (Nuavg) decreases with an increase in D/d for single and double jets. A similar trend was also noted by Wang et al. [18]. However, the variation of Nuavg with D/d is not observed for multi-jet

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100 D/d = 5.1, n=1 D/d =10.2, n =1 D/d =20.4, n =1 D/d = 5.1, n = 6 D/d =10.2, n = 6 D/d =20.4, n = 6

Red = 5000

80

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20

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6

8

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14

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D/d = 5.1, n=1 D/d =10.2, n =1 D/d =20.4, n =1 D/d = 5.1, n = 6 D/d =10.2, n = 6 D/d =20.4, n = 6

Red = 20000

Num,D

200

160

120

80

40 0

2

4

6

8

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(b) Fig. 13. Effect of curvature ratio (D/d) on the Nuavg for single jet and multi-jet impingement at n = 6 (a) Red = 5000, (b) Red = 20,000. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 12. Effect of H/d on the Nuavg (a) Red = 5000, D/d = 10.2; (b) Red = 20,000, D/d = 10.2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

27 – 32% when n is increased from 2 to 4. However, when the number of nozzles changed from 4 to 6, the increase in the average Nusselt number is 14 – 19% which is relatively less. Overall, the number of jets required for effective cooling of the heated cylinder is four for D/ d = 5.1 and six at D/d = 20.4 at H/d = 2 for Red = 5000–20,000. As a part of the analysis, the effects of Red and D/d on local Nusselt number over the cylinder at Z/D = 0 for H/d = 2 and 8 are discussed in the above section. Hence, the change in Nuavg due to increase in H/d is discussed in detail for D/d = 10.2 and H/d = 2–12.

Table 3 Constants for the correlations of Nustag. Ranges of Parameters

a

b

c

D/d = 5.1, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12 D/d = 10.2, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12 D/d = 20.4, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12

0.43 0.53 0.81

−0.006 −0.008 −0.008

0.38 0.4 0.4

because of higher jet velocity. Overall, the maximum Nuavg due to multiple round jets (n > 2) is observed at H/d = 2 for H/d = 2–12 and Red = 5000–20,000. Fig. 13(a) presents the effect of H/d on Nuavg for D/d = 5.1, 10.2 and 20.4 at Red = 5000 for n = 1 and 6. The enhancement in Nuavg is noted to be higher at H/d = 2. For the configuration of single jet impingement, the Nuavg is observed to be maximum for relatively larger nozzles (D/d = 5.5). This is because of higher flow rate in the case of large sized nozzles (D/d = 5.5). For the single jet impingement with D/ d = 20.4, the average heat transfer is observed to be lower. However, for the multiple circular jets of n = 6, the maximum average heat transfer is found for D/d = 20.4. This is due to the multiple impingement regions of higher local Nusselt number found at the middle of the cylinder. No considerable change in Nuavg is found between D/d = 5.1 and 10.2 for H/d = 2–12 for Red = 5000. As Red increases to 20,000,

4.3. Effect of H/d Fig. 12 (a) shows the variation of Nuavg due to the change in H/d at Red = 5000, D/d = 10.2 for n = 1 – 6. For a fixed Red, the Nuavg reduces gradually as H/d increases. At H/d = 12, the increase in the Nuavg is 30.5% when the number of jets increases from n = 1 to 2, 24.8% when n is increased from 2 to 4 and it is around19% when n is increased from 4 to 6. In all the cases at D/d = 10.2, the Nuavg increases as the number of jets (n) increases and the maximum increase in the Nuavg is observed at H/d = 2. Fig. 12(b) presents the effect of H/d on the Nuavg for Red = 20,000, D/d = 10.2 and n = 1–6. Similar to Red = 5000, the Nuavg reduces gradually with an increase in H/d from 2 to 12 for a given number of jets for Red = 20,000. In comparison with Red = 5000, the Nuavg values are higher for Red = 20,000 for different H/d values 10

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Table 3. Fig. 14(a) shows a parity plot for the correlations for the local Nusselt number at the jet impingement point. The maximum difference between the Nustag obtained from the correlation (Eq. (7)) and from the experimental data is within ± 15%. For the given geometric and flow variables, the average Nusselt number, Nuavg is dependent on the number of nozzles (n), Reynolds number (Red), curvature ratio (D/d) and non-dimensional spacing between the nozzle and the cylinder, H/d. The correlation for the Nuavg is provided as

Nuavg = p (n)q (H d )−0.2 (D d )0.01Red0.6

(8)

The constants, p and q in the above Eq. (8) are provided in Table 4. The Nuavg over the target cylinder obtained from the correlation is within ± 15% of the Nuavg obtained from the present experimental data (Refer Fig. 14(b)). 5. Conclusions A detailed experimental study on jet impingement cooling has been performed with a single round jet and multiple round jets arranged circumferentially over a cylinder to understand the effects of number of round jets (n), nozzle-to-target spacing (H/d), curvature ratio (D/d) and jet Reynolds number (Red). The major conclusions arrived at from the analysis of the present experimental data of single and multi-jet impingement cooling are presented below. 1. The local Nusselt number (Nu) reduces drastically from the point of jet impingement in the circumferential direction with increasing of D/d. The second counter jet cools effectively the bottom of the target cylinder for D/d = 10.2 and 20.4. 2. In all the cases, Nustag is unaffected by the number jets considered. However, the local Nusselt number increases over the cylinder due to multiple stagnation and fountain regions formed on a cylinder. 3. For any fixed value of Red and D/d, the maximum enhancement in Nuavg is noted at H/d = 2. 4. With an increase in D/d, the number jets required for effective cooling increases. While maintaining the jet Red and the curvature ratio, D/d, the Nuavg reduces as H/d increases.

Fig. 14. Parity plots for the correlations of Nustag (a) and Nuavg (b). Table 4 Constants for the correlations of Nuavg.

Appendix A. Supplementary material

Ranges of Parameters

p

q

D/d = 5.1, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12 D/d = 10.2, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12 D/d = 20.4, 5000 ≤ Red ≤ 20,000, 2 ≤ H/d ≤ 12

0.23 0.22 0.2

0.4 0.35 0.5

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114308. References [1] S.J. Downs, E.H. James, Jet Impingement Heat Transfer – A Literature Survey, ASME, New York, 1987, p. 87-H-35. [2] K. Mujumdar, V. Ranade, Simulation of rotary cement kiln using a one dimensional model, Chem. Eng. Des 84 (2006) 165–177. [3] T.L. Chan, C.W. Leung, K. Jambunathan, S. Ashforth -Forst, Y. Zhou, M.H. Liu, heat transfer characteristics of a slot jet impinging on a semi-circular convex surface, Int. J. Heat Mass Trans. 45 (2002) 993–1006. [4] C.H. Lee, K.B. Lim, S.H. Lee, Y.J. Yoo, N.W. Sung, A study of the heat transfer characteristics of turbulent round jet impinging on an inclined concave surface using liquid crystal transient method, Exp. Thermal Fluid Science 31 (2007) 559–565. [5] E. Oztekin, O. Aydin, M. Avci, Heat transfer in a turbulent slot jet impinging on concave surface, Int. Commun. Heat Mass Transf. 44 (2013) 77–82. [6] X. Bu, L. Peng, G. Lin, L. Bai, D. Wen, Jet impingement heat transfer on a concave surface in a wing leading edge: Experimental study and correlation development, Exp. Therm. Fluid Sci. 78 (2016) 199–207. [7] A. Hadipour, M.R. Zargarabadi, Heat transfer and flow characteristics of impinging jet on a concave surface at small nozzle to surface distances, App. Therm. Eng. 138 (2018) 534–541. [8] V.S. Patil, R.P. Vedula, Local heat transfer for jet impingement onto a concave surface including injection nozzle length to diameter and curvature ratio effects, Exp. Therm. Science 92 (2018) 375–389. [9] F. Gori, L. Bossi, Optimal slot height in the jet cooling of a circular cylinder, App. Therm. Eng. 23 (2003) 859–870. [10] S. Pachpute, B. Premachandran, Experimental and Numerical investigations of slot

the Nuavg is also found higher at H/d = 2 (Refer Fig. 13(b)). Thereafter, it shows a decreasing trend with respect to H/d for all the three sizes of nozzles. For both the Reynolds numbers, the relatively large size nozzle (D/d = 5.1) provides maximum Nuavg for the single jet with a small sized nozzle (D/d = 20.4) provides maximum average cooling in the configuration of multi-jet impingement with n = 6. 4.4. The correlations for Nustag and Nuavg From the present experimental studies of single and multi-jet impingement cooling of a cylinder, it is noted that the local Nusselt number in the jet impingement region is not significantly affected by the number of jets. However, it strongly depends on Red, D/d and H/d. Hence, a correlation for Nustag is obtained from the present experimental data for 5000 ≤ Red ≤ 20,000, 5.1 ≤ D/d ≤ 20.4 and 2 ≤ H/ d ≤ 12 as given below.

Nustag = a (H d )b (D d )c Red0.7

(7)

where a, b, c and d are constants. These constant values are presented in 11

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[11]

[12] [13] [14] [15]

570–657. [16] A.A. Tawfek, Heat transfer due to round jet impinging normal to a circular cylinder, Heat Mass Transf. 35 (1999) 327–333. [17] D. Singh, B. Premachandran, S. Kohli, Double circular air jet impingement cooling of a heated circular cylinder, Int. J. Heat Mass Transf. 109 (2017) 619–646. [18] X.L. Wang, J.H. Lee, T.J. Lu, S.J. song, T. Kim, A Comparative study of single/twojet cross flow heat transfer on a circular cylinder, Int. J. Heat Mass Transf. 78 (2014) 588–598. [19] C. Csernyei, A.G. Stratman, Forced convective heat transfer on a horizontal circular cylinder due to multiple impinging circular jets, App. Therm. Eng. 105 (2016) 290–303. [20] J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 75 (1953) 3–8.

jet impingement with and without a semicircular confinement, Int. J. Heat Mass Trans. 114 (2017) 866–890. S. Pachpute, B. Premachandran, Effect of the shape of flow confinement on turbulent slot jet impingement cooling of a heated circular cylinder, Int. J. Therm. Sci. 131 (2018) 114–131. S.A. Nada, Slot/slots air jet impinging cooling of a cylinder for different jets–cylinder configurations, Heat Mass Trans. 43 (2006) 135–148. N. Zuckerman, N. Lior, Radial slot jet impingement flow and heat transfer on a cylindrical target, J. Ther. Heat Trans. 21 (2007) 548–561. N. Chauchat, E. Schall, Cooling of a heating cylinder by confined impacting air jets, Int. J. Num. Meth. Heat Fluid Flow 26 (7) (2016) 2013–2032. E.W. Sparrow, C.A.C. Altemani, A. Chaboki, Jet-impingement heat transfer for a circular jet impinging in cross flow on a cylinder, ASME J. Heat Transf. 106 (1984)

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