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Jet impingement heat transfer of a lobed nozzle: Measurements using temperature-sensitive paint and particle image velocimetry
International Journal of Heat and Fluid Flow 71 (2018) 111–126
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Jet impingement heat transfer of a lobed nozzle: Measurements using temperature-sensitive paint and particle image velocimetry He Chuangxina,b, Liu Yingzhenga,b,
T
⁎
a
Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China b Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Impinging jet Lobed nozzle Heat transfer TSP PIV
The impingement jet issuing from the lobed nozzles constructed using three small circular orifices is intensively investigated; the heat transfer characteristics and flow fields are respectively determined using temperaturesensitive paint (TSP) and particle image velocimetry (PIV). A piece of fluorine-doped tin oxide (FTO)-coated glass with uniform wall heat flux is used for optical access in TSP measurements. In particular, the effects of the geometrical variations are compared by varying the ratio of the orifice centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all configurations to ensure a constant cross-section area of the nozzles. The TSP measurements of the impingement heat transfer at Reynolds numbers Re = 10,000 and 40,000 are performed using different nozzle-to-wall distances, i.e., H / De = 2, 4 and 6, to determine the mean Nusselt number distribution on the heated wall. The results show that the heat transfer is enhanced using lobed jets at H/De ≤ 4. At H / De = 2, the optimal Nusselt number is obtained using a lobed nozzle a/ b = 0.8 in the region 1 < r/De < 4, with a heat transfer enhancement of up to 10% compared with that in the case of a circular jet. At H / De = 4, the azimuthal-averaged Nusselt number increases (up to 16%) consistently in the region r/De < 0.5 with an increase in a/b, while the Nusselt number shows a slight decay in the region 2 < r/De < 4. However, at H / De = 6, the Nusselt number in the entire measured region decays with an increase in a/b. Finally, the PIV measurements of the flow fields at Re = 10,000 are performed at H / De = 2 and 4 and a/ b = 0, 0.8 and 1.15. The results show that the heat transfer enhancement can be attributed to the increased turbulence level in the wall-jet zone at H / De = 2 and in the stagnation region at H / De = 4.
1. Introduction Impingement jets, which substantially improve heat transfer rates in the stagnation region, have been widely used for applications such as gas-turbine and aircraft de-icing (Han et al., 2012). To this end, a perforated thin frame constructed with a large number of small nozzles is usually placed inside a considerably limited space to generate an arrayed jet impinging onto a hot surface. These nozzles are mostly featured by circular orifices in terms of the compromise between the heat transfer characteristics and manufacturing cost. However, studies (Koseoglu and Baskaya, 2010; Violato et al., 2012) have established that varying the nozzle geometry alters the flow patterns and then modifies the heat transfer characteristics. Therefore, an exploration of an economical geometrical variation strategy with effective heat transfer intensification is highly desirable. A literature survey shows that various experimental efforts have
been sought to improve the jet impingement heat transfer by changing the nozzle geometry. Lee and Lee (2000a) proposed an elliptic nozzle to increase the stagnation heat transfer rate in the case of a nozzle-to-wall distance smaller than the potential core length of a jet. This heat transfer augmentation in the stagnation region results from the enhanced turbulent kinetic energy along the jet centreline due to the different spreading rates along the major and minor axis planes. Subsequently, Lee and Lee (2000b) measured the impingement heat transfer of a sharp-edged orifice jet at H / D = 2–6; the results showed a significantly high heat transfer rate in the stagnation region when compared with that observed in the cases of standard- and square-edged orifice jets. By chamfering the nozzle inlet, Brignoni and Garimella (2000) demonstrated a substantial reduction in the pressure drop, while the average heat transfer coefficient was not strongly affected when compared with that in the case of a square-edged nozzle. As for the chevron nozzle, an infrared thermography measurement by Violato
⁎ Corresponding author at: Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China. E-mail address: [email protected] (Y. Liu).
https://doi.org/10.1016/j.ijheatfluidflow.2018.03.017 Received 26 September 2017; Received in revised form 17 March 2018; Accepted 26 March 2018 Available online 04 April 2018 0142-727X/ © 2018 Elsevier Inc. All rights reserved.
International Journal of Heat and Fluid Flow 71 (2018) 111–126
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Nomenclature A A0 a b De dp fT H I IR k qw qr qc r T0 Tw
area of the heated surface area of the nozzle cross-section orifice centre offset orifice radius nozzle's equivalent diameter ( = 4A0 ) π black paint thickness TSP calibration function nozzle-to-wall distance light intensity of the images light intensity ratio two-dimensional turbulent kinetic energy joule heating on the FTO glass heating loss due to the radiation heating loss due to the tangential conduction radial coordinate reference (room) temperature wall temperature
U0 x y z Bi
mean (bulk) axial velocity at the nozzle exit coordinate coordinate coordinate dp h Biot number ( = λ )
Nu
Nusselt number (=
Nu Re
mean Nusselt number U D Reynolds number ( = 0υ e )
p
(qw − qr − qc ) De λA (Tw − T0)
)
Greek symbols λ λp
air conductivity black paint conductivity
Abbreviations PIV TSP
particle image velocimetry temperature-sensitive paint
2. Experimental apparatus and method
et al. (2012) showed that this nozzle exhibited better performance in impingement heat transfer than a circular one; a particle image velocimetry measurement of the flow field attributed this improved performance to the development of stream-wise vortices associated with a deep penetration of turbulence-induced mixing. Subsequent measurements by Vinze et al. (2016) revealed that the mean Nusselt number increased with an increase in the number of chevrons for a given chevron angle, as well as an increase in the tip angle for a given number of chevrons. However, for the perforated thin frame, these geometrical variations of small holes (usually less than 1 mm in practice) pose a challenging issue in the manufacturing process. As for free jets using lobed nozzles, early studies revealed a pair of large-scale stream-wise vortices at each lobe crest (Fig. 1(a)), dominating the jets’ spreading and mixing processes (Hu et al., 2000); the lobe troughs (Fig. 1(a)) served as mixing tabs in the shear layers of the jets, which generated counter-rotating stream-wise vortex pairs shed from each tab and then dramatically increased the thickness of the mixing layer (Samimy et al., 1993). Such flow behaviour, when it occurs in the impingement jet, activates a considerably favourable heat removal mechanism (Sodjavi et al., 2016), as demonstrated by infrared thermography measurements by Martin and Buchlin (2011). However, the impingement flow and heat transfer of a lobed nozzle have not been studied sufficiently as yet. The present study is focused on the jet impingement heat transfer and flow quantities of a lobed nozzle, and uses complementary techniques of temperature-sensitive paint (TSP) and planar particle image velocimetry (PIV). Here, the lobed nozzle is constructed by three circular orifices (Martin and Buchlin, 2011), and the effects of the geometrical variations are compared by varying the ratio of the orifice centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15 (as shown in Fig. 1(a)), at a constant equivalent diameter De for all of the configurations to ensure a constant cross-section area of the nozzles. The configuration with a/b = 0 is in fact a large circular orifice of diameter De and is considered as the benchmark configuration. In the experiments, TSP measurements are performed at Reynolds numbers Re = 10,000 and 40,000 and nozzle-to-wall distances of H / De= 2, 4 and 6 for different configuration a/b values, quantifying the spatial distribution of the mean Nusselt number. Finally, the PIV measurements of the flow fields are performed at two different distances H / De= 2 and 4 for three configurations, i.e., a/ b = 0 (circular nozzle), 0.8 and 1.15. The distinctly different distributions of the flow quantities are clarified to reveal the underlying mechanism of the intensified impingement heat transfer.
2.1. Impingement plate and flow configurations In the TSP measurement, the impingement wall is constructed using a piece of fluorine-doped tin oxide (FTO)-coated glass of size 200 × 300 mm. The FTO glass is a type of heat-resistant glass with a thickness of 0.4 mm, which is coated with a 200-nm-thick FTO layer on one side (the front side as shown in Fig. 1(b)) forming a square resistance of 10 Ω. As shown in Fig. 1(b), two copper-foil strip electrodes are attached to both ends of the FTO glass on the front side to establish good electrical contact. The copper electrodes are then connected to a 100-W direct-current (DC) power supply. With the DC electric current flowing through the FTO layer, an essentially uniform wall heat flux boundary condition is established on the front side of the FTO glass. The wall temperature of the heated surface is measured by TSP, which is airsprayed on the front side of the FTO glass above the FTO layer. To prevent the background light, which is mainly generated by the reflection from the nozzle, from passing through the transparent FTP glass, a very thin layer of black paint is sprayed onto the TSP layer. To minimize the heat transfer from the rear side of the heated wall, a 20mm-thick Plexiglas plate is attached to the rear of the FTO glass. A 500mm-long pipe with an inner diameter of 28 mm and the jet nozzle are installed on the right-hand side as shown in the figure, forming the jet impingement on the front side of the FTO glass. The wall-normal position of the nozzle is accurately controlled with a precision of 0.01 mm by using a traverse mechanism. The jet fluid is air and is supplied by a fan, while the flow rate is calibrated using a Pitot tube. The nozzle geometries tested in the heat transfer experiment are shown in Fig. 1(a). The nozzle orifice has an equivalent diameter of De = 14 mm and a rather small orifice length (0.14De). The pipe diameter (2De) and length (500 mm) are selected so as to have no effect on the velocity distribution in the orifice. Precursor Reynolds-averaged Navier–Stokes simulations using a considerably long pipe to provide the fully developed velocity distribution, or a relatively large diameter to provide uniform velocity upstream the nozzle, showed no effect on the velocity distribution at the orifice exit. The lobed nozzles are formed using three smaller circular orifices with the nozzle parameter, i.e., the ratio of the orifice centre offset to the orifice radius, a/ b = 0 (circular nozzle), 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all nozzle configurations to ensure a constant cross-section area of the nozzles. The Reynolds number of the impinging jet based on the bulk velocity at the nozzle exit U0 and the nozzle's equivalent diameter De is Re = 10,000 and 40,000. Measurements are performed at the 112
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Fig. 1. Nozzle geometries (a) and schematic representation of the TSP measurement setup (b).
and the constant pressure difference is maintained by a 20 L constanthead tank placed 1.5 m above the glass tank. To minimize disturbance of the water surface induced by the inflow and eliminate the small bubbles in the jet fluid, two plates are installed near the supply tube, staggered to form a labyrinthine passage in the constant-head tank. In this experiment, the nozzle size is kept identical to that shown in Fig. 1(a), while only a/ b = 0 (circular nozzle), 0.8 and 1.15 and H / De= 2 and 4 are selected according to the TSP measurements (which will be shown in Figs. 9 and 10). The Reynolds number based on the bulk velocity (U0) in the nozzle orifice and the nozzle's equivalent diameter (De) is Re = 10,000.
dimensionless nozzle-to-wall distance of H / De= 2, 4 and 6 to determine the mean Nusselt number distribution. The PIV measurements are performed in a glass tank with size 3000 mm (length) × 550 mm (width) × 700 mm (depth), which was previously used in He and Liu (2017a, 2017b) as shown in Fig. 2(a). The back, bottom, left, and right sides of the tank are covered with black light-absorbing material to eliminate the reflection of the laser on the glass walls. The glass tank is filled with tap water filtered by a 5 μm filter. An empty, open plexiglass tank is placed in contact with the free surface to avoid the optical distortion associated with surface waves. A submerged round pipe with a length of L = 1200 mm and a diameter of D = 28 mm is installed horizontally in the glass tank at a height of 350 mm to achieve a fully developed flow. It is noted that the turbulence level in the long pipe is around two orders lower than that in the jet region. The effects of the inflow turbulence on the impingement heat transfer are insignificant compared with variation of the nozzle configuration. The jet fluid is supplied by a pump installed in the glass tank
2.2. Measurement systems and methods In the heat transfer experiment, the wall temperature of the heated surface is measured by TSP. The TSP layer uses an oxygen-impermeable automobile clear-coat (Dupont ChromClear HC7776S) as the binder and 113
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Fig. 2. Schematic representation of the PIV measurement setup (a) and the PIV measurement planes (b).
The TSP calibration is performed before the measurement in a static environment. Four thermocouple sensors are fixed on the front side of the FTO glass to provide the reference temperature values. The ratio of TSP emission intensity at a temperature T to the emission intensity at a specified reference temperature T0 is as follows:
Ru (dpp) (GFS Chemical, Inc.) as the temperature sensor. The TSP sensor is dissolved in methanol, mixed with the clear-coat binder and then air-sprayed onto the front side of the FTO glass above the FTO layer. During the measurements, the TSP layer is excited by a lightemitting diode (LED) light (ISSI LM2X-DM) with a wavelength of 400 nm installed on the rear side of the FTO glass, and the TSP images are captured by a 12-bit charged coupled device (CCD) camera (IPX 16 M, Imperx, USA) from the side with an installed long-pass filter. Because of the transparency of the Plexiglas and FTO glass, the fluorescence of the TSP layer can be easily captured by the CCD camera, while the effect of the nozzle on the front side is eliminated by the black paint.
IR =
I (T ) = fT (T ; T0) I (T0)
(1)
The function fT depends only on the local temperature T in the experiment and the reference temperature T0. Therefore, it can be determined using curve-fitting calibration data with a polynomial that can later be used in the TSP measurements. To obtain I(T0), images at the 114
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on the impingement heat transfer is accurately determined. Finally, the Nusselt number on the heated surface is determined, which is defined as
ambient temperature for each case are recorded by the CCD camera. After turning on the DC power and fan, 100 thermal images for each nozzle and nozzle-to-wall distance are taken to obtain I(T) when the static steady state is reached. The time-averaged temperature fields are calculated using the calibration curve. A pixel-wise adaptive Wiener filter (Lim, 1990) measuring 20 × 20 is used in the post-processing to eliminate noise. Note that considerable care is taken to perform all of the measurements without turning off the heating power, the LED light, the fan, and the camera, so that the effect of the geometrical variations
Nu =
(qw − qr − qc ) De λA (Tw − T0)
(2)
Here, qw represents the Joule heating on the FTO glass, qr and qc are respectively the heat losses due to the radiation and tangential conduction on the impingement wall (Astarita and Carlomagno, 2012). λ denotes the heat conductivity of the air. A indicates the area of the
Fig. 3. Mean Nusselt number distribution on the heated wall at H / De = 2 and Re = 10,000. (The dashed circles indicate the locaion of the second peak.) (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 115
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acquisition is performed at the frame rate of 2 Hz, and 2,000 images of the seeded flow in the fields of view, as shown in Fig. 2(a), are successively acquired; three planes, i.e., I, II and III, as shown in Fig. 2(b), are separately measured. The standard cross-correlational PIV algorithm (in combination with the window offset, sub-pixel recognition by Gaussian fitting and sub-region distortion) with an interrogation window size of 32 × 32 pixels and 50% overlap is applied to the image pairs to determine the velocity fields. Thus, a spatial resolution of 0.1 × 0.1 mm is obtained.
heated surface. T0 refers to the room temperature, and Tw stands for the temperature of the heated wall measured using TSP. In PIV measurements, global seeding of the entire water tank is performed using hollow polymer beads with a mean diameter of approximately 20 µm. The vertical-centre plane of the jet is illuminated by a laser sheet generated from a 5-W continuous-wave semiconductor laser (532 nm). The semiconductor laser is triggered by a transistor–transistor logic signal and synchronised with a high-resolution (4872 × 3248 pixels) CCD camera (IPX 16 M, Imperx, USA). Image
Fig. 4. Mean Nusselt number distribution on the heated wall at H / De = 4 and Re = 10,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 116
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paint on the heat conduction can be neglected as the Biot number Bi = dp h/ λp (dp and λp respectively denote thickness and thermal conductivity of the black paint, and h represents heat transfer coefficient on the heated wall) is in the order of 10−2. In addition, non-uniformity of the heat flux on the heated surface is estimated to be 3.8%. In the present study, however, the main concern is focused on the heat transfer enhancement by varying configuration of the lobed nozzles. When carefully control the flow and heating system to ensure a stable heat flux, along with the correction of the radiation and the tangential
2.3. Uncertainty analysis The TSP measurements are subject to experimental uncertainties due to the radiation and the tangential conduction of the heat through the impingement plate, Reynolds number, camera imaging and nonuniform heat flux on the heated surface. The radiation heat flux is estimated to be less than 2.6% of the total imposed heat flux. Estimation of the tangential heat conduction through the impingement plate shows it is around 2.4% of the total imposed heat flux. The effect of the black
Fig. 5. Mean Nusselt number distribution on the heated wall at H / De = 6 and Re = 10,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 117
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3. Results and discussion
heat conduction in Nusselt number calculation, the relative uncertainty of the measurement system without the effects of non-uniform heat flux, radiation and the tangential heat conduction is reduced to approximately 1.5% according to the procedure by Kline and Mcclintock (1953). In the PIV measurement, the error in measuring the particle displacement between two images is less than 0.1 pixel, and the uncertainty in the measurement of the velocity field is less than 2%.
3.1. Heat transfer analysis The mean Nusselt number distributions on the heated wall measured using TSP at Re = 10,000 are presented in Figs. 3–5 for the nozzle-to-wall distances of H / De = 2, 4 and 6, respectively. At H / De = 2 (Fig. 3), all of the cases with different nozzle configurations exhibit the largest mean Nusselt number Nu ≈ 100 in the jet
Fig. 6. Mean Nusselt number distribution on the heated wall at H / De = 2 and Re = 40,000. (The dashed circles indicate the location of the second peak.) (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 118
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positions where the lobe troughs and crests are located. Moreover, the medium Nu regions (green-coloured areas), which exhibit a hexagonal pattern in the case of a/ b = 1.0, are more significant than those in the case of small a/b, having a 30° azimuthal shift with respect to the high Nu pattern (red-coloured area in the jet stagnation region). Note that these patterns are not observable in Martin and Buchlin (2011) for a three-lobe jet, while the present measurement provides an insightful view of the Nu pattern. The snowflake-shaped pattern is more significant for the cases of a/ b = 1.1 (Fig. 3(e)) and 1.15 (Fig. 3(f)).
stagnation region (the region close to the jet centre), while the second peak located around r / De = 1.7 is significant and indicated by the black dashed circle. As a/b increases from 0 (circular nozzle) to 0.8, as shown in Fig. 3(a)–(c), the breakdown of the axisymmetry of the mean Nusselt number pattern as well as the increase in Nu at the second peak location can be observed because of the non-axisymmetry of the nozzle. The snowflake-shaped Nu pattern is established in the case of a/ b = 1.0 (Fig. 3(d)), which is characterised by the radial stretch of the high Nu regions from the jet stagnation region at the azimuthal
Fig. 7. Mean Nusselt number distribution on the heated wall at H / De = 4 and Re = 40,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 119
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increase in a/b, which is expected to be induced by the enhanced mixing at the jet centreline. A further increase in the nozzle-to-wall distance to H / De = 6 (Fig. 5) reveals no statistically significant difference as that in the case of H / De = 4, except the blunt inverted-triangle high Nu patterns for all of the lobed jets. In fact, the turbulence dispersion will damp the nonaxisymmetry of the jet flow in the downstream region, particularly beyond the jet potential core. From Fig. 12, we infer that x / De = 6 is definitely beyond the jet potential core. Further, Nu increases in the
However, a slight decrease in Nu at r/De > 1.7 can be detected from the area reduction of the medium Nu regions (green-coloured areas). At the nozzle-to-wall distance of H / De = 4, as shown in Fig. 4, significantly different Nu patterns are observed compared with the cases at H / De = 2. The inverted-triangle-shaped high Nu patterns (redcoloured regions) in the stagnation region are established with an increase in a/b. This finding indicates that the mixing effect of the lobe troughs is considerably stronger than that of the lobe crest at this nozzle-to-wall distance. Nu increases in the stagnation region with an
Fig. 8. Mean Nusselt number distribution on the heated wall at H / De = 6 and Re = 40,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 120
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(1977). Regarding the current TSP results, the increase in the Reynolds number shows no significant difference in the mean Nusselt number distribution for all of the nozzle configurations. This results in an increase in the global Nusselt number with an increase in the approaching speed of the fluid toward the wall. The Nusselt number differences between different nozzle configurations become slightly more significant than those at Re = 10,000. However, the optimal nozzle for H / De = 2 can be determined at a/ b = 0.8, and the heat transfer rate in the stagnation region increases with an increase in a/b for H / De = 4. Note that this heat transfer enhancement is only observed at H/De ≤ 4 for both Reynolds numbers. The mean Nusselt number variation at the stagnation point with respect to the nozzle-to-wall distance is presented in Fig. 11. For both Reynolds numbers, the heat transfer at H / De = 2 remains nearly identical for all of the nozzle configurations. This indicates that the lobed nozzles have little effect on the jet potential core as explained earlier. At H / De = 4, the stagnation heat transfer is marked by an
stagnation region as the increase in a/b is not significant at this configuration. The mean Nusselt number distributions on the heated wall at Re = 40,000 are presented in Figs. 6–8. In general, no considerable difference is observed when compared with the results at Re = 10,000. The snowflake-shaped Nu pattern is also gradually established with an increase in a/b at H / De = 2, while the mean Nusselt number exhibits the inverted-triangle pattern at H / De = 4 and 6 for relatively large a/b. Only slight differences can be observed. At H / De = 2, as shown in Fig. 6, the second peak of the mean Nusselt number for small a/b is more significant, and the effects of the lobe trough are considerably stronger than those of the lobe crest when compared with the results obtained at Re = 10,000. Moreover, the Nusselt number increases at H / De = 4 (Fig. 7) and decrease at = 6 (Fig. 8) in the stagnation region with the increase of a/b is more observable. A quantitative comparison of the heat transfer performance for each lobed jet and nozzle-to-wall distance is presented in Figs. 9 and 10 at Re = 10,000 and 40,000, respectively. The mean Nusselt numbers are averaged in the azimuthal direction. At Re = 10,000, as shown in Fig. 9, the measurement data of the circular impinging jets from Martin and Buchlin (2011), Lee and Lee (2000c)and Dairay et al. (2015) are presented for comparison. Slight differences are observed between the measurement data from the literature and the current TSP measurements; these differences may be attributed to the different nozzle configurations. At H / De = 2 (Fig. 9(a)), almost the same Nusselt number for all of the nozzle configurations is observed in the stagnation region (r/De < 1), while the difference exists only in the wall-jet zone (three zones, i.e., the free-jet, impingement and wall-jet zones, of the impinging jet are shown in Fig. 12) where r/De > 1. The Nusselt number Nu in the wall-jet zone increases with an increase in a/b from 0 (circular) to 0.8 and then gradually decreases with a further increase in a/b. Optimal heat transfer is obtained using the lobed nozzle a/ b = 0.8 with Nu = 85 at the second peak, which is considerably higher than that in the case of the circular jet; the overall heat transfer enhancement beyond the second peak is up to 10%. When the lobed nozzle a/ b = 1.15 is used, the Nusselt number in the wall-jet zone becomes lower than that in the circular-jet zone. As the nozzle-to-wall distance increases to H / De = 4 (Fig. 9(b)), differences between different nozzle configurations are observed near the jet centreline in r/De < 0.5 and the far wall-jet zone in r/De > 1.5. The mean Nusselt number in the region r/De < 0.5 increases (from Nu = 112 to 127 at the stagnation point) with an increase in a/b from 0 to 1.15, while Nu decreases consistently in the far wall-jet zone. In contrast, the Nusselt number in the region 0.5 < r/De < 1.5 remains almost identical for all of the jet configurations. When the nozzle-to-wall distance further increases to H / De = 6 (Fig. 9(c)), the Nu difference in the entire measured radial region r/De < 4 can be detected for different nozzle configurations. This difference is indicated by the Nu decay with an increase in a/b. This finding suggests that the heat transfer enhancement only occurs at a small nozzle-to-wall distance, i.e., H/De ≤ 4, in the present study. This inference can be preliminarily explained by the mixing enhancement in the entire jet column in the far downstream region when a nozzle with a larger a/b is used, which causes the breakdown of largescale structures and reduces the speed of the fluid approaching the wall, leading to the mean Nusselt number decay in the entire region. Furthermore, from Fig. 9, we infer that the Nusselt number at the stagnation point increases with an increase in H/De from 2 to 4. This is attributed to the jet potential core, at the end of which the turbulent kinetic energy increases at the jet centreline and enhances the heat transfer on the wall. At Re = 40,000, as shown in Fig. 10, the reference experimental data are presented, showing good validation for the current TSP measurements. The reference data are mapped from Baughn and Shimizu (1989) and Baughn et al. (1991) in the case of circular impinging jets and from Martin and Buchlin (2011) for four-lobe jets to the current Reynolds number following a normalisation proposed by Martin
Fig. 9. Azimuthal-averaged mean Nusselt number profiles at Re = 10,000. 121
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Fig. 11. Mean Nusselt number on the stagnation point at different nozzle-towall distances.
except the global elevation in the heat transfer magnitude, the PIV measurements are performed only at Re = 10,000 for a/ b = 0 (circular), 0.8 and 1.15. These nozzles are selected according to the best heat transfer performance at H / De = 2 and 4. Moreover, the nozzle with a/ b = 1.15 is the worst case for the wall heat transfer at H / De = 2. There is no doubt that different heat transfer patterns at H / De = 2, 4 and 6 are closely associated with the flow characteristics. This can be inferred from Fig. 12, where the axial velocities on the jet centreline in both free and impinging jets are presented. The results are normalised using the maximum velocity on the jet centreline. Note that the impinging jet is commonly divided into three zones (Deshpande and Vaishnav, 1982): the free-jet zone, which is defined as the region where the flow is not influenced by the impingement wall; the impingement zone, where the flow is deflected from its axial direction to a radial one; and the wall-jet zone, where the velocity is mainly radial with the formation of a boundary layer that develops along the radial direction. From the data of the free circular jet, we can infer three significantly different locations of the impingement wall: at H / De = 2, the wall is located in the potential core region where the centreline velocity does not decay. At this nozzle-to-wall distance, the flow modification by the lobed nozzles is limited to the shear layer. The heat transfer characteristics in the stagnation region show little difference for all of the nozzle configurations, as they are mainly associated with the flow properties near the jet centreline; the difference in the heat transfer rates in the wall-jet zone is attributed to the modified flow structures in the shear layer in the case of the lobed nozzles. At H / De = 4, the wall is located approximately at the end of the potential core where the shear layers meet at the jet centreline. The lobed nozzles are expected to increase the turbulent kinetic energy in the shear layer and thus enhance the heat transfer in the stagnation region. At H / De = 6, the wall is located far downstream of the potential core. The enhanced mixing of the jet flow leads to the breakdown of the large-scale structures and the decay of the turbulent kinetic energy. This phenomenon is considered a critical reason for the consistent decay of the heat transfer rate with an increase in a/b. The mean velocity magnitude distributions on the various measurement planes at H / De = 2 are presented in Fig. 13. Here, the flow
Fig. 10. Azimuthal-averaged mean Nusselt number profiles at Re = 40,000.
increase in the Nusselt number with an increase in a/b. Fig. 11 shows that this heat transfer enhancement is more pronounced at Re = 40,000 with the Nusselt number increasing up to 16%. In contrast, the stagnation heat transfer deterioration at H / De = 6 is more serious at Re = 40,000 with a Nusselt number decay of up to 9.7%. Consequently, the trend of the increase in the Nusselt number from H / De = 4 to 6 changes when a/b increases; in fact, the stagnation Nusselt number decreases for a/b ≥ 1.0 when the nozzle-to-wall distance increases. This can be explained by the enhanced mixing of the jet at the end of the potential core, which enhances the heat transfer (at H / De = 4), and the breakdown of the large-scale structures beyond the potential, which deteriorates the wall heat transfer (at H / De = 6). 3.2. Flow field analysis As the TSP measurements do not show a considerable difference in the wall heat transfer characteristics at Re = 10,000 and 40,000, 122
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Fig. 12. Axial velocities on the jet centreline at Re = 10,000.
fields on planes I–III in the lobed jet are separately measured using planar PIV. We observe from the circular jet (Fig. 13(a)) that the velocity remains almost constant in a large region inside the jet and gradually decreases until the fluid approaches the wall. The shear layer of the jet is mostly in a narrow region at approximately r / De = 0.5, having little effect on the flow characteristics in the jet impingement zone. This situation prevails in the cases of all of the lobed jets, as shown in Fig. 13(b) and (c), which shows the insignificant difference in heat transfer in the stagnant region, as illustrated in Fig. 9(a). In the lobed jets (Fig. 13(b) and (c)), the inclined flow patterns in the free-jet zone can be observed on planes I and II because of the jet spread decay
on plane I and the mixing enhancement on plane II. On plane I, the jet initially has a larger width than the jets on other planes because of the lobed crests, and this jet width gradually decreases along the jet axis. This finding can be used to explain the hexagonal pattern in the stagnant region at H / De = 2 (Fig. 3(c)–(f)) where the jet widths on planes I and II are comparable. However, excessive mixing of the shear layer leads to the decay of the fluid speed when the flow approaches the wall as shown in the region near r / De = 1.0 in Fig. 13(c). This could be a reason for the heat transfer deterioration in the lobed jet with a/ b = 1.15. 1 The two-dimensional turbulent kinetic energy (k = 2 (ur2 + uz2) ) of
Fig. 13. Mean velocity magnitudes on different measurement planes at H / De = 2 and Re = 10,000. 123
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Fig. 14. Two-dimensional turbulent kinetic energies on different measurement planes at H / De = 2 and Re = 10,000.
the flow at H / De = 2 on planes I–III is shown in Fig. 14. Furthermore, the turbulent kinetic energy differs little in the free-jet and impingement zones for all of the nozzle configurations. This finding provides more evidence for the insignificant heat transfer difference for all of the nozzle configurations in the stagnation region. In the wall-jet zone, the lobed jet with a/ b = 0.8 exhibits a weak decay of the turbulent kinetic energy on planes I and II, but a slight increase on plane III. For the lobed jet with a/ b = 1.15, however, the decay of the turbulent kinetic energy on all of the planes is significant, indicating the deterioration of the heat transfer on the wall. Whereas, the heat transfer rate in the case of the lobed jet with a/ b = 0.8 does not decay owing to the high fluid speed near the wall and the high level of turbulent kinetic energy. Fig. 15 presents the mean velocity magnitude distributions on the jet centre planes at H / De = 4. At this nozzle-to-wall distance, the jet width on plane II is considerably larger than that on plane I, leading to the inverted-triangle pattern of the Nussle number in the stagnant region (Fig. 4(b)–(f) and Fig. 5(b)–(f)). In the free-jet zone, the width of the shear layer increases considerably compared with that at H / De = 2 because of the fluid approaching the end of the jet potential core. Moreover, the fluid speed in the wall-jet zone decreases significantly compared with that at H / De = 2; it decreases further with an increase in a/b. The finding proves the consistent decay of the wall heat transfer rate in relatively large radial locations. As for the two-dimensional turbulent kinetic energy shown in Fig. 16, the significant difference compared with that at H / De = 2 is attributed to the decrease in the turbulent kinetic energy in the wall-jet zone. In the shear layer in the free-jet zone, the turbulent kinetic energy decreases with an increase in a/b. However, the turbulent kinetic energy in the stagnation region increases with an increase in a/b, because of the thickening and the interaction of the jet's shear layer. This finding indicates that the effect of the lobes expands to the jet's stagnation region at H / De = 4 and enhances the local heat transfer. The planar-PIV measurements provide valuable clues to understand
the mechanism for the heat transfer enhancement using a lobed nozzle. It is well accepted that the vortical structures initialled in the shear layer has a significant influence on the impingement heat transfer intensity (O'Donovan and Murria, 2006). The rollup of the Kelvin–Helmholtz (K–H) vortices in circular jets attenuates the streamwise structures that are responsible for the mixing and the momentum flux transport (Martin and Buchlin, 2011). In the lobed jets, either due to the axis-switching phenomenon with the non-circular nozzle (Gutmark and Grinstein, 1999) or subject to the tab effects (Samimy et al., 1993) exerted by the lobe troughs, numerous streamwise structures are induced along with the breakdown of the K–H vortices. This enhances the mixing in the flow and thus has strong effects on the impingement heat transfer. Martin and Buchlin (2011) attributed the heat transfer enhancement using lobed nozzle to the continuous momentum flux transport by the broken K–H vortex segments and the streamwise vortical structures. However, this cannot explain why the lobed nozzle with large a/b yields even lower heat transfer intensity at H / De = 2. Recall that in the Nusselt number distribution at H / De = 2 the distinct differences between various lobed nozzles lie in the region near and beyond the second-peak circle. The secondary vortices (Dairay et al., 2015), which are mainly induced near the impingement wall, are strongly associated with the heat removal near the second-peak circle. This would be a hint for the in-depth investigation of the heat removal mechanism using near-wall turbulence resolving methods. 4. Conclusions In the present study, the impingement jet issuing from the lobed nozzles constructed using three small circular orifices was intensively investigated using complementary techniques of the TSP and PIV methods, which respectively involved the spatial distributions of the wall heat transfer and the flow quantities. In particular, the effects of geometrical variations were compared by varying the ratio of the orifice 124
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Fig. 15. Mean velocity magnitudes on different measurement planes at H / De = 4 and Re = 10,000.
Fig. 16. Two-dimensional turbulent kinetic energies on different measurement planes at H / De = 4 and Re = 10,000.
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centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all of the lobed nozzles to ensure a constant cross-section area of the nozzles. The TSP measurements were performed at Reynolds numbers Re = 10,000 and 40,000 and the nozzle-to-wall distances of H / De= 2, 4 and 6 to determine the mean Nusselt number distribution on the heated wall. The PIV was performed at Re = 10,000 and H / De= 2 and 4 with the lobed nozzles a/ b = 0, 0.8 and 1.15 to understand the flow mechanism for the heat transfer enhancement. The TSP measurements at both Reynolds numbers showed that the snowflake-shaped pattern of the mean Nusselt number distribution was gradually established when a/b increased at H / De= 2, while the inverted-triangle pattern of the Nusselt number distribution was observed at H / De= 4 and 6. The azimuthal-averaged Nusselt number at H / De = 2 showed that the optimal heat transfer was obtained using the lobed nozzle with a/ b = 0.8 in the region 1 < r/De < 4, with a heat transfer enhancement of up to 10% compared with that in the case of the circular jet. At H / De= 4, the azimuthal-averaged Nusselt number increased (up to 16%) consistently in the region r/De < 0.5 with an increase in a/b, while the Nusselt number showed a slight decay in the region 2 < r/De < 4. At H / De = 6, the Nusselt number in the entire measured region decayed with an increase in a/b. The PIV measurements showed that the wall was located in the jet potential core at H / De = 2, meaning that the effects of the lobed nozzles were limited in the jet's shear layer. Due to the fact that the turbulence characteristics close to the jet centreline was nearly unchanged, changing the nozzle configuration did not result in apparent variation of the local Nusselt number distribution in this region. The turbulent kinetic energy in the wall-jet zone in the case of the lobed jet with a/ b = 0.8 increased slightly compared with that in the other cases, resulting in a heat transfer enhancement in 1 < r/De < 4. At H / De = 4, the wall was located at the end of the potential core; the turbulent kinetic energy increased with an increase in a/b. This was the main mechanism for the heat transfer enhancement in the stagnation region at H / De = 4. The consistent decay of the heat transfer rate at a relatively large nozzle-to-wall distance could be attributed to the breakdown of the large-scale structures and the turbulence dispersion beyond the jet potential core. The planar PIV setup used in this study determined the mean flow quantities in different azimuthal planes, which shed light on the causeand-effect relationship between the flow dynamics and wall heat transfer. However, the fluid flow issuing from the lobed nozzle was highly three dimensional and exhibited spatio-temporally varying behaviours, which played an important role in the impingement heat transfer. This will be elucidated using large-eddy simulations in a continuation study, in which the present measurements will serve as the validation database.
Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatfluidflow.2018.03.017. References Astarita, T., Carlomagno, G.M., 2012. Infrared Thermography For Thermofluid-Dynamics. Springer Science & Business Media. Baughn, J.W., Shimizu, S., 1989. Heat transfer measurements from a surface with uniform heat flux and an impinging jet. J. Heat Transf. 111 (4), 1096–1098. Baughn, J.W., Hechanova, A.E., Yan, X., 1991. An experimental study of entrainment effects on the heat transfer from a flat surface to a heated circular impinging jet. J. Heat Transf. 113 (4), 1023–1025. Brignoni, L.A., Garimella, S.V., 2000. Effects of nozzle-inlet chamfering on pressure drop and heat transfer in confined air jet impingement. Int. J. Heat Mass Transf. 43 (7), 1133–1139. Dairay, T., Fortuné, V., Lamballais, E., Brizzi, L.-E., 2015. Direct numerical simulation of a turbulent jet impinging on a heated wall. J. Fluid Mech. 764, 362–394. Deshpande, M.D., Vaishnav, R.N., 1982. Submerged laminar jet impingement on a plane. J. Fluid Mech. 114, 213–236. Gutmark, E.J., Grinstein, F.F., 1999. Flow control with noncircular jets. Ann. Rev. Fluid Mech. 31 (1), 239–272. Han, J.C., Dutta, S., Ekkad, S., 2012. Gas Turbine Heat Transfer and Cooling Technology. CRC Press. He, C., Liu, Y., 2017a. Proper orthogonal decomposition-based spatial refinement of TRPIV realizations using high-resolution non-TR-PIV measurements. Exp. Fluids 58 (7), 86. He, C., Liu, Y., 2017b. Proper orthogonal decomposition of time-resolved LIF visualization: scalar mixing in a round jet. J. Vis. 1–27. Hu, H., Kobayashi, T., Saga, T., Segawa, S., Taniguchi, N., 2000. Particle image velocimetry and planar laser-induced fluorescence measurements on lobed jet mixing flows. Exp. Fluids 29 (1), S141–S157. Kline, S., Mcclintock, F., 1953. Describing uncertainties in single-sample experiments. Mech. Eng. 75 (1), 3–8. Koseoglu, M., Baskaya, S., 2010. The role of jet inlet geometry in impinging jet heat transfer, modeling and experiments. Int. J. Therm. Sci. 49 (8), 1417–1426. Lee, J., Lee, S.-J., 2000a. The effect of nozzle aspect ratio on stagnation region heat transfer characteristics of elliptic impinging jet. Int. J. Heat Mass Transf. 43 (4), 555–575. Lee, J., Lee, S.-J., 2000b. The effect of nozzle configuration on stagnation region heat transfer enhancement of axisymmetric jet impingement. Int. J. Heat Mass Transf. 43 (18), 3497–3509. Lee, J., Lee, S.J., 2000c. The effect of nozzle aspect ratio on stagnation region heat transfer characteristics of elliptic impinging jet. Int. J. Heat Mass Transf. 43 (4), 555–575. Lim, J.S., 1990. Two-dimensional Signal and Image Processing Prentice Hall, Englewood Cliffs: NJ 4(1), pp. 6–8. Martin, R.H., Buchlin, J., 2011. Jet impingement heat transfer from lobed nozzles. Int. J. Therm. Sci. 50 (7), 1199–1206. Martin, H., 1977. Heat and mass transfer between impinging gas jets and solid surfaces. Adv. Heat Transf. 13, 1–60. O'Donovan, T.S., Murria, D.B., 2006. Effect of vortices on jet impingement heat transfer. In: Proceedings of the Thirteenth International Heat Transfer Conference, pp. 12–32. Samimy, M., Zaman, K.B.M.Q., Reeder, M.F., 1993. Effect of tabs on the flow and noise field of an axisymmetric jet. AIAA J. 31 (4), 609–619. Sodjavi, K., Montagné, B., Meslem, A., Byrne, P., Serres, L., Sobolik, V., 2016. Passive control of wall shear stress and mass transfer generated by submerged lobed impinging jet. Heat Mass Transf. 52 (5), 925–936. Vinze, R., Chandel, S., Limaye, M., Prabhu, S., 2016. Local heat transfer distribution between smooth flat surface and impinging incompressible air jet from a chevron nozzle. Exp. Therm. Fluid Sci. 78, 124–136. Violato, D., Ianiro, A., Cardone, G., Scarano, F., 2012. Three-dimensional vortex dynamics and convective heat transfer in circular and chevron impinging jets. Int. J. Heat Fluid Flow 37, 22–36.
Acknowledgements The authors gratefully acknowledge financial support for this study from the National Natural Science Foundation of China (11725209).
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Jet impingement heat transfer of a lobed nozzle: Measurements using temperature-sensitive paint and particle image velocimetry He Chuangxina,b, Liu Yingzhenga,b,
T
⁎
a
Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China b Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Impinging jet Lobed nozzle Heat transfer TSP PIV
The impingement jet issuing from the lobed nozzles constructed using three small circular orifices is intensively investigated; the heat transfer characteristics and flow fields are respectively determined using temperaturesensitive paint (TSP) and particle image velocimetry (PIV). A piece of fluorine-doped tin oxide (FTO)-coated glass with uniform wall heat flux is used for optical access in TSP measurements. In particular, the effects of the geometrical variations are compared by varying the ratio of the orifice centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all configurations to ensure a constant cross-section area of the nozzles. The TSP measurements of the impingement heat transfer at Reynolds numbers Re = 10,000 and 40,000 are performed using different nozzle-to-wall distances, i.e., H / De = 2, 4 and 6, to determine the mean Nusselt number distribution on the heated wall. The results show that the heat transfer is enhanced using lobed jets at H/De ≤ 4. At H / De = 2, the optimal Nusselt number is obtained using a lobed nozzle a/ b = 0.8 in the region 1 < r/De < 4, with a heat transfer enhancement of up to 10% compared with that in the case of a circular jet. At H / De = 4, the azimuthal-averaged Nusselt number increases (up to 16%) consistently in the region r/De < 0.5 with an increase in a/b, while the Nusselt number shows a slight decay in the region 2 < r/De < 4. However, at H / De = 6, the Nusselt number in the entire measured region decays with an increase in a/b. Finally, the PIV measurements of the flow fields at Re = 10,000 are performed at H / De = 2 and 4 and a/ b = 0, 0.8 and 1.15. The results show that the heat transfer enhancement can be attributed to the increased turbulence level in the wall-jet zone at H / De = 2 and in the stagnation region at H / De = 4.
1. Introduction Impingement jets, which substantially improve heat transfer rates in the stagnation region, have been widely used for applications such as gas-turbine and aircraft de-icing (Han et al., 2012). To this end, a perforated thin frame constructed with a large number of small nozzles is usually placed inside a considerably limited space to generate an arrayed jet impinging onto a hot surface. These nozzles are mostly featured by circular orifices in terms of the compromise between the heat transfer characteristics and manufacturing cost. However, studies (Koseoglu and Baskaya, 2010; Violato et al., 2012) have established that varying the nozzle geometry alters the flow patterns and then modifies the heat transfer characteristics. Therefore, an exploration of an economical geometrical variation strategy with effective heat transfer intensification is highly desirable. A literature survey shows that various experimental efforts have
been sought to improve the jet impingement heat transfer by changing the nozzle geometry. Lee and Lee (2000a) proposed an elliptic nozzle to increase the stagnation heat transfer rate in the case of a nozzle-to-wall distance smaller than the potential core length of a jet. This heat transfer augmentation in the stagnation region results from the enhanced turbulent kinetic energy along the jet centreline due to the different spreading rates along the major and minor axis planes. Subsequently, Lee and Lee (2000b) measured the impingement heat transfer of a sharp-edged orifice jet at H / D = 2–6; the results showed a significantly high heat transfer rate in the stagnation region when compared with that observed in the cases of standard- and square-edged orifice jets. By chamfering the nozzle inlet, Brignoni and Garimella (2000) demonstrated a substantial reduction in the pressure drop, while the average heat transfer coefficient was not strongly affected when compared with that in the case of a square-edged nozzle. As for the chevron nozzle, an infrared thermography measurement by Violato
⁎ Corresponding author at: Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China. E-mail address: [email protected] (Y. Liu).
https://doi.org/10.1016/j.ijheatfluidflow.2018.03.017 Received 26 September 2017; Received in revised form 17 March 2018; Accepted 26 March 2018 Available online 04 April 2018 0142-727X/ © 2018 Elsevier Inc. All rights reserved.
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Nomenclature A A0 a b De dp fT H I IR k qw qr qc r T0 Tw
area of the heated surface area of the nozzle cross-section orifice centre offset orifice radius nozzle's equivalent diameter ( = 4A0 ) π black paint thickness TSP calibration function nozzle-to-wall distance light intensity of the images light intensity ratio two-dimensional turbulent kinetic energy joule heating on the FTO glass heating loss due to the radiation heating loss due to the tangential conduction radial coordinate reference (room) temperature wall temperature
U0 x y z Bi
mean (bulk) axial velocity at the nozzle exit coordinate coordinate coordinate dp h Biot number ( = λ )
Nu
Nusselt number (=
Nu Re
mean Nusselt number U D Reynolds number ( = 0υ e )
p
(qw − qr − qc ) De λA (Tw − T0)
)
Greek symbols λ λp
air conductivity black paint conductivity
Abbreviations PIV TSP
particle image velocimetry temperature-sensitive paint
2. Experimental apparatus and method
et al. (2012) showed that this nozzle exhibited better performance in impingement heat transfer than a circular one; a particle image velocimetry measurement of the flow field attributed this improved performance to the development of stream-wise vortices associated with a deep penetration of turbulence-induced mixing. Subsequent measurements by Vinze et al. (2016) revealed that the mean Nusselt number increased with an increase in the number of chevrons for a given chevron angle, as well as an increase in the tip angle for a given number of chevrons. However, for the perforated thin frame, these geometrical variations of small holes (usually less than 1 mm in practice) pose a challenging issue in the manufacturing process. As for free jets using lobed nozzles, early studies revealed a pair of large-scale stream-wise vortices at each lobe crest (Fig. 1(a)), dominating the jets’ spreading and mixing processes (Hu et al., 2000); the lobe troughs (Fig. 1(a)) served as mixing tabs in the shear layers of the jets, which generated counter-rotating stream-wise vortex pairs shed from each tab and then dramatically increased the thickness of the mixing layer (Samimy et al., 1993). Such flow behaviour, when it occurs in the impingement jet, activates a considerably favourable heat removal mechanism (Sodjavi et al., 2016), as demonstrated by infrared thermography measurements by Martin and Buchlin (2011). However, the impingement flow and heat transfer of a lobed nozzle have not been studied sufficiently as yet. The present study is focused on the jet impingement heat transfer and flow quantities of a lobed nozzle, and uses complementary techniques of temperature-sensitive paint (TSP) and planar particle image velocimetry (PIV). Here, the lobed nozzle is constructed by three circular orifices (Martin and Buchlin, 2011), and the effects of the geometrical variations are compared by varying the ratio of the orifice centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15 (as shown in Fig. 1(a)), at a constant equivalent diameter De for all of the configurations to ensure a constant cross-section area of the nozzles. The configuration with a/b = 0 is in fact a large circular orifice of diameter De and is considered as the benchmark configuration. In the experiments, TSP measurements are performed at Reynolds numbers Re = 10,000 and 40,000 and nozzle-to-wall distances of H / De= 2, 4 and 6 for different configuration a/b values, quantifying the spatial distribution of the mean Nusselt number. Finally, the PIV measurements of the flow fields are performed at two different distances H / De= 2 and 4 for three configurations, i.e., a/ b = 0 (circular nozzle), 0.8 and 1.15. The distinctly different distributions of the flow quantities are clarified to reveal the underlying mechanism of the intensified impingement heat transfer.
2.1. Impingement plate and flow configurations In the TSP measurement, the impingement wall is constructed using a piece of fluorine-doped tin oxide (FTO)-coated glass of size 200 × 300 mm. The FTO glass is a type of heat-resistant glass with a thickness of 0.4 mm, which is coated with a 200-nm-thick FTO layer on one side (the front side as shown in Fig. 1(b)) forming a square resistance of 10 Ω. As shown in Fig. 1(b), two copper-foil strip electrodes are attached to both ends of the FTO glass on the front side to establish good electrical contact. The copper electrodes are then connected to a 100-W direct-current (DC) power supply. With the DC electric current flowing through the FTO layer, an essentially uniform wall heat flux boundary condition is established on the front side of the FTO glass. The wall temperature of the heated surface is measured by TSP, which is airsprayed on the front side of the FTO glass above the FTO layer. To prevent the background light, which is mainly generated by the reflection from the nozzle, from passing through the transparent FTP glass, a very thin layer of black paint is sprayed onto the TSP layer. To minimize the heat transfer from the rear side of the heated wall, a 20mm-thick Plexiglas plate is attached to the rear of the FTO glass. A 500mm-long pipe with an inner diameter of 28 mm and the jet nozzle are installed on the right-hand side as shown in the figure, forming the jet impingement on the front side of the FTO glass. The wall-normal position of the nozzle is accurately controlled with a precision of 0.01 mm by using a traverse mechanism. The jet fluid is air and is supplied by a fan, while the flow rate is calibrated using a Pitot tube. The nozzle geometries tested in the heat transfer experiment are shown in Fig. 1(a). The nozzle orifice has an equivalent diameter of De = 14 mm and a rather small orifice length (0.14De). The pipe diameter (2De) and length (500 mm) are selected so as to have no effect on the velocity distribution in the orifice. Precursor Reynolds-averaged Navier–Stokes simulations using a considerably long pipe to provide the fully developed velocity distribution, or a relatively large diameter to provide uniform velocity upstream the nozzle, showed no effect on the velocity distribution at the orifice exit. The lobed nozzles are formed using three smaller circular orifices with the nozzle parameter, i.e., the ratio of the orifice centre offset to the orifice radius, a/ b = 0 (circular nozzle), 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all nozzle configurations to ensure a constant cross-section area of the nozzles. The Reynolds number of the impinging jet based on the bulk velocity at the nozzle exit U0 and the nozzle's equivalent diameter De is Re = 10,000 and 40,000. Measurements are performed at the 112
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Fig. 1. Nozzle geometries (a) and schematic representation of the TSP measurement setup (b).
and the constant pressure difference is maintained by a 20 L constanthead tank placed 1.5 m above the glass tank. To minimize disturbance of the water surface induced by the inflow and eliminate the small bubbles in the jet fluid, two plates are installed near the supply tube, staggered to form a labyrinthine passage in the constant-head tank. In this experiment, the nozzle size is kept identical to that shown in Fig. 1(a), while only a/ b = 0 (circular nozzle), 0.8 and 1.15 and H / De= 2 and 4 are selected according to the TSP measurements (which will be shown in Figs. 9 and 10). The Reynolds number based on the bulk velocity (U0) in the nozzle orifice and the nozzle's equivalent diameter (De) is Re = 10,000.
dimensionless nozzle-to-wall distance of H / De= 2, 4 and 6 to determine the mean Nusselt number distribution. The PIV measurements are performed in a glass tank with size 3000 mm (length) × 550 mm (width) × 700 mm (depth), which was previously used in He and Liu (2017a, 2017b) as shown in Fig. 2(a). The back, bottom, left, and right sides of the tank are covered with black light-absorbing material to eliminate the reflection of the laser on the glass walls. The glass tank is filled with tap water filtered by a 5 μm filter. An empty, open plexiglass tank is placed in contact with the free surface to avoid the optical distortion associated with surface waves. A submerged round pipe with a length of L = 1200 mm and a diameter of D = 28 mm is installed horizontally in the glass tank at a height of 350 mm to achieve a fully developed flow. It is noted that the turbulence level in the long pipe is around two orders lower than that in the jet region. The effects of the inflow turbulence on the impingement heat transfer are insignificant compared with variation of the nozzle configuration. The jet fluid is supplied by a pump installed in the glass tank
2.2. Measurement systems and methods In the heat transfer experiment, the wall temperature of the heated surface is measured by TSP. The TSP layer uses an oxygen-impermeable automobile clear-coat (Dupont ChromClear HC7776S) as the binder and 113
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Fig. 2. Schematic representation of the PIV measurement setup (a) and the PIV measurement planes (b).
The TSP calibration is performed before the measurement in a static environment. Four thermocouple sensors are fixed on the front side of the FTO glass to provide the reference temperature values. The ratio of TSP emission intensity at a temperature T to the emission intensity at a specified reference temperature T0 is as follows:
Ru (dpp) (GFS Chemical, Inc.) as the temperature sensor. The TSP sensor is dissolved in methanol, mixed with the clear-coat binder and then air-sprayed onto the front side of the FTO glass above the FTO layer. During the measurements, the TSP layer is excited by a lightemitting diode (LED) light (ISSI LM2X-DM) with a wavelength of 400 nm installed on the rear side of the FTO glass, and the TSP images are captured by a 12-bit charged coupled device (CCD) camera (IPX 16 M, Imperx, USA) from the side with an installed long-pass filter. Because of the transparency of the Plexiglas and FTO glass, the fluorescence of the TSP layer can be easily captured by the CCD camera, while the effect of the nozzle on the front side is eliminated by the black paint.
IR =
I (T ) = fT (T ; T0) I (T0)
(1)
The function fT depends only on the local temperature T in the experiment and the reference temperature T0. Therefore, it can be determined using curve-fitting calibration data with a polynomial that can later be used in the TSP measurements. To obtain I(T0), images at the 114
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on the impingement heat transfer is accurately determined. Finally, the Nusselt number on the heated surface is determined, which is defined as
ambient temperature for each case are recorded by the CCD camera. After turning on the DC power and fan, 100 thermal images for each nozzle and nozzle-to-wall distance are taken to obtain I(T) when the static steady state is reached. The time-averaged temperature fields are calculated using the calibration curve. A pixel-wise adaptive Wiener filter (Lim, 1990) measuring 20 × 20 is used in the post-processing to eliminate noise. Note that considerable care is taken to perform all of the measurements without turning off the heating power, the LED light, the fan, and the camera, so that the effect of the geometrical variations
Nu =
(qw − qr − qc ) De λA (Tw − T0)
(2)
Here, qw represents the Joule heating on the FTO glass, qr and qc are respectively the heat losses due to the radiation and tangential conduction on the impingement wall (Astarita and Carlomagno, 2012). λ denotes the heat conductivity of the air. A indicates the area of the
Fig. 3. Mean Nusselt number distribution on the heated wall at H / De = 2 and Re = 10,000. (The dashed circles indicate the locaion of the second peak.) (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 115
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acquisition is performed at the frame rate of 2 Hz, and 2,000 images of the seeded flow in the fields of view, as shown in Fig. 2(a), are successively acquired; three planes, i.e., I, II and III, as shown in Fig. 2(b), are separately measured. The standard cross-correlational PIV algorithm (in combination with the window offset, sub-pixel recognition by Gaussian fitting and sub-region distortion) with an interrogation window size of 32 × 32 pixels and 50% overlap is applied to the image pairs to determine the velocity fields. Thus, a spatial resolution of 0.1 × 0.1 mm is obtained.
heated surface. T0 refers to the room temperature, and Tw stands for the temperature of the heated wall measured using TSP. In PIV measurements, global seeding of the entire water tank is performed using hollow polymer beads with a mean diameter of approximately 20 µm. The vertical-centre plane of the jet is illuminated by a laser sheet generated from a 5-W continuous-wave semiconductor laser (532 nm). The semiconductor laser is triggered by a transistor–transistor logic signal and synchronised with a high-resolution (4872 × 3248 pixels) CCD camera (IPX 16 M, Imperx, USA). Image
Fig. 4. Mean Nusselt number distribution on the heated wall at H / De = 4 and Re = 10,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 116
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paint on the heat conduction can be neglected as the Biot number Bi = dp h/ λp (dp and λp respectively denote thickness and thermal conductivity of the black paint, and h represents heat transfer coefficient on the heated wall) is in the order of 10−2. In addition, non-uniformity of the heat flux on the heated surface is estimated to be 3.8%. In the present study, however, the main concern is focused on the heat transfer enhancement by varying configuration of the lobed nozzles. When carefully control the flow and heating system to ensure a stable heat flux, along with the correction of the radiation and the tangential
2.3. Uncertainty analysis The TSP measurements are subject to experimental uncertainties due to the radiation and the tangential conduction of the heat through the impingement plate, Reynolds number, camera imaging and nonuniform heat flux on the heated surface. The radiation heat flux is estimated to be less than 2.6% of the total imposed heat flux. Estimation of the tangential heat conduction through the impingement plate shows it is around 2.4% of the total imposed heat flux. The effect of the black
Fig. 5. Mean Nusselt number distribution on the heated wall at H / De = 6 and Re = 10,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 117
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3. Results and discussion
heat conduction in Nusselt number calculation, the relative uncertainty of the measurement system without the effects of non-uniform heat flux, radiation and the tangential heat conduction is reduced to approximately 1.5% according to the procedure by Kline and Mcclintock (1953). In the PIV measurement, the error in measuring the particle displacement between two images is less than 0.1 pixel, and the uncertainty in the measurement of the velocity field is less than 2%.
3.1. Heat transfer analysis The mean Nusselt number distributions on the heated wall measured using TSP at Re = 10,000 are presented in Figs. 3–5 for the nozzle-to-wall distances of H / De = 2, 4 and 6, respectively. At H / De = 2 (Fig. 3), all of the cases with different nozzle configurations exhibit the largest mean Nusselt number Nu ≈ 100 in the jet
Fig. 6. Mean Nusselt number distribution on the heated wall at H / De = 2 and Re = 40,000. (The dashed circles indicate the location of the second peak.) (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 118
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positions where the lobe troughs and crests are located. Moreover, the medium Nu regions (green-coloured areas), which exhibit a hexagonal pattern in the case of a/ b = 1.0, are more significant than those in the case of small a/b, having a 30° azimuthal shift with respect to the high Nu pattern (red-coloured area in the jet stagnation region). Note that these patterns are not observable in Martin and Buchlin (2011) for a three-lobe jet, while the present measurement provides an insightful view of the Nu pattern. The snowflake-shaped pattern is more significant for the cases of a/ b = 1.1 (Fig. 3(e)) and 1.15 (Fig. 3(f)).
stagnation region (the region close to the jet centre), while the second peak located around r / De = 1.7 is significant and indicated by the black dashed circle. As a/b increases from 0 (circular nozzle) to 0.8, as shown in Fig. 3(a)–(c), the breakdown of the axisymmetry of the mean Nusselt number pattern as well as the increase in Nu at the second peak location can be observed because of the non-axisymmetry of the nozzle. The snowflake-shaped Nu pattern is established in the case of a/ b = 1.0 (Fig. 3(d)), which is characterised by the radial stretch of the high Nu regions from the jet stagnation region at the azimuthal
Fig. 7. Mean Nusselt number distribution on the heated wall at H / De = 4 and Re = 40,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 119
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increase in a/b, which is expected to be induced by the enhanced mixing at the jet centreline. A further increase in the nozzle-to-wall distance to H / De = 6 (Fig. 5) reveals no statistically significant difference as that in the case of H / De = 4, except the blunt inverted-triangle high Nu patterns for all of the lobed jets. In fact, the turbulence dispersion will damp the nonaxisymmetry of the jet flow in the downstream region, particularly beyond the jet potential core. From Fig. 12, we infer that x / De = 6 is definitely beyond the jet potential core. Further, Nu increases in the
However, a slight decrease in Nu at r/De > 1.7 can be detected from the area reduction of the medium Nu regions (green-coloured areas). At the nozzle-to-wall distance of H / De = 4, as shown in Fig. 4, significantly different Nu patterns are observed compared with the cases at H / De = 2. The inverted-triangle-shaped high Nu patterns (redcoloured regions) in the stagnation region are established with an increase in a/b. This finding indicates that the mixing effect of the lobe troughs is considerably stronger than that of the lobe crest at this nozzle-to-wall distance. Nu increases in the stagnation region with an
Fig. 8. Mean Nusselt number distribution on the heated wall at H / De = 6 and Re = 40,000. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.) 120
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(1977). Regarding the current TSP results, the increase in the Reynolds number shows no significant difference in the mean Nusselt number distribution for all of the nozzle configurations. This results in an increase in the global Nusselt number with an increase in the approaching speed of the fluid toward the wall. The Nusselt number differences between different nozzle configurations become slightly more significant than those at Re = 10,000. However, the optimal nozzle for H / De = 2 can be determined at a/ b = 0.8, and the heat transfer rate in the stagnation region increases with an increase in a/b for H / De = 4. Note that this heat transfer enhancement is only observed at H/De ≤ 4 for both Reynolds numbers. The mean Nusselt number variation at the stagnation point with respect to the nozzle-to-wall distance is presented in Fig. 11. For both Reynolds numbers, the heat transfer at H / De = 2 remains nearly identical for all of the nozzle configurations. This indicates that the lobed nozzles have little effect on the jet potential core as explained earlier. At H / De = 4, the stagnation heat transfer is marked by an
stagnation region as the increase in a/b is not significant at this configuration. The mean Nusselt number distributions on the heated wall at Re = 40,000 are presented in Figs. 6–8. In general, no considerable difference is observed when compared with the results at Re = 10,000. The snowflake-shaped Nu pattern is also gradually established with an increase in a/b at H / De = 2, while the mean Nusselt number exhibits the inverted-triangle pattern at H / De = 4 and 6 for relatively large a/b. Only slight differences can be observed. At H / De = 2, as shown in Fig. 6, the second peak of the mean Nusselt number for small a/b is more significant, and the effects of the lobe trough are considerably stronger than those of the lobe crest when compared with the results obtained at Re = 10,000. Moreover, the Nusselt number increases at H / De = 4 (Fig. 7) and decrease at = 6 (Fig. 8) in the stagnation region with the increase of a/b is more observable. A quantitative comparison of the heat transfer performance for each lobed jet and nozzle-to-wall distance is presented in Figs. 9 and 10 at Re = 10,000 and 40,000, respectively. The mean Nusselt numbers are averaged in the azimuthal direction. At Re = 10,000, as shown in Fig. 9, the measurement data of the circular impinging jets from Martin and Buchlin (2011), Lee and Lee (2000c)and Dairay et al. (2015) are presented for comparison. Slight differences are observed between the measurement data from the literature and the current TSP measurements; these differences may be attributed to the different nozzle configurations. At H / De = 2 (Fig. 9(a)), almost the same Nusselt number for all of the nozzle configurations is observed in the stagnation region (r/De < 1), while the difference exists only in the wall-jet zone (three zones, i.e., the free-jet, impingement and wall-jet zones, of the impinging jet are shown in Fig. 12) where r/De > 1. The Nusselt number Nu in the wall-jet zone increases with an increase in a/b from 0 (circular) to 0.8 and then gradually decreases with a further increase in a/b. Optimal heat transfer is obtained using the lobed nozzle a/ b = 0.8 with Nu = 85 at the second peak, which is considerably higher than that in the case of the circular jet; the overall heat transfer enhancement beyond the second peak is up to 10%. When the lobed nozzle a/ b = 1.15 is used, the Nusselt number in the wall-jet zone becomes lower than that in the circular-jet zone. As the nozzle-to-wall distance increases to H / De = 4 (Fig. 9(b)), differences between different nozzle configurations are observed near the jet centreline in r/De < 0.5 and the far wall-jet zone in r/De > 1.5. The mean Nusselt number in the region r/De < 0.5 increases (from Nu = 112 to 127 at the stagnation point) with an increase in a/b from 0 to 1.15, while Nu decreases consistently in the far wall-jet zone. In contrast, the Nusselt number in the region 0.5 < r/De < 1.5 remains almost identical for all of the jet configurations. When the nozzle-to-wall distance further increases to H / De = 6 (Fig. 9(c)), the Nu difference in the entire measured radial region r/De < 4 can be detected for different nozzle configurations. This difference is indicated by the Nu decay with an increase in a/b. This finding suggests that the heat transfer enhancement only occurs at a small nozzle-to-wall distance, i.e., H/De ≤ 4, in the present study. This inference can be preliminarily explained by the mixing enhancement in the entire jet column in the far downstream region when a nozzle with a larger a/b is used, which causes the breakdown of largescale structures and reduces the speed of the fluid approaching the wall, leading to the mean Nusselt number decay in the entire region. Furthermore, from Fig. 9, we infer that the Nusselt number at the stagnation point increases with an increase in H/De from 2 to 4. This is attributed to the jet potential core, at the end of which the turbulent kinetic energy increases at the jet centreline and enhances the heat transfer on the wall. At Re = 40,000, as shown in Fig. 10, the reference experimental data are presented, showing good validation for the current TSP measurements. The reference data are mapped from Baughn and Shimizu (1989) and Baughn et al. (1991) in the case of circular impinging jets and from Martin and Buchlin (2011) for four-lobe jets to the current Reynolds number following a normalisation proposed by Martin
Fig. 9. Azimuthal-averaged mean Nusselt number profiles at Re = 10,000. 121
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Fig. 11. Mean Nusselt number on the stagnation point at different nozzle-towall distances.
except the global elevation in the heat transfer magnitude, the PIV measurements are performed only at Re = 10,000 for a/ b = 0 (circular), 0.8 and 1.15. These nozzles are selected according to the best heat transfer performance at H / De = 2 and 4. Moreover, the nozzle with a/ b = 1.15 is the worst case for the wall heat transfer at H / De = 2. There is no doubt that different heat transfer patterns at H / De = 2, 4 and 6 are closely associated with the flow characteristics. This can be inferred from Fig. 12, where the axial velocities on the jet centreline in both free and impinging jets are presented. The results are normalised using the maximum velocity on the jet centreline. Note that the impinging jet is commonly divided into three zones (Deshpande and Vaishnav, 1982): the free-jet zone, which is defined as the region where the flow is not influenced by the impingement wall; the impingement zone, where the flow is deflected from its axial direction to a radial one; and the wall-jet zone, where the velocity is mainly radial with the formation of a boundary layer that develops along the radial direction. From the data of the free circular jet, we can infer three significantly different locations of the impingement wall: at H / De = 2, the wall is located in the potential core region where the centreline velocity does not decay. At this nozzle-to-wall distance, the flow modification by the lobed nozzles is limited to the shear layer. The heat transfer characteristics in the stagnation region show little difference for all of the nozzle configurations, as they are mainly associated with the flow properties near the jet centreline; the difference in the heat transfer rates in the wall-jet zone is attributed to the modified flow structures in the shear layer in the case of the lobed nozzles. At H / De = 4, the wall is located approximately at the end of the potential core where the shear layers meet at the jet centreline. The lobed nozzles are expected to increase the turbulent kinetic energy in the shear layer and thus enhance the heat transfer in the stagnation region. At H / De = 6, the wall is located far downstream of the potential core. The enhanced mixing of the jet flow leads to the breakdown of the large-scale structures and the decay of the turbulent kinetic energy. This phenomenon is considered a critical reason for the consistent decay of the heat transfer rate with an increase in a/b. The mean velocity magnitude distributions on the various measurement planes at H / De = 2 are presented in Fig. 13. Here, the flow
Fig. 10. Azimuthal-averaged mean Nusselt number profiles at Re = 40,000.
increase in the Nusselt number with an increase in a/b. Fig. 11 shows that this heat transfer enhancement is more pronounced at Re = 40,000 with the Nusselt number increasing up to 16%. In contrast, the stagnation heat transfer deterioration at H / De = 6 is more serious at Re = 40,000 with a Nusselt number decay of up to 9.7%. Consequently, the trend of the increase in the Nusselt number from H / De = 4 to 6 changes when a/b increases; in fact, the stagnation Nusselt number decreases for a/b ≥ 1.0 when the nozzle-to-wall distance increases. This can be explained by the enhanced mixing of the jet at the end of the potential core, which enhances the heat transfer (at H / De = 4), and the breakdown of the large-scale structures beyond the potential, which deteriorates the wall heat transfer (at H / De = 6). 3.2. Flow field analysis As the TSP measurements do not show a considerable difference in the wall heat transfer characteristics at Re = 10,000 and 40,000, 122
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Fig. 12. Axial velocities on the jet centreline at Re = 10,000.
fields on planes I–III in the lobed jet are separately measured using planar PIV. We observe from the circular jet (Fig. 13(a)) that the velocity remains almost constant in a large region inside the jet and gradually decreases until the fluid approaches the wall. The shear layer of the jet is mostly in a narrow region at approximately r / De = 0.5, having little effect on the flow characteristics in the jet impingement zone. This situation prevails in the cases of all of the lobed jets, as shown in Fig. 13(b) and (c), which shows the insignificant difference in heat transfer in the stagnant region, as illustrated in Fig. 9(a). In the lobed jets (Fig. 13(b) and (c)), the inclined flow patterns in the free-jet zone can be observed on planes I and II because of the jet spread decay
on plane I and the mixing enhancement on plane II. On plane I, the jet initially has a larger width than the jets on other planes because of the lobed crests, and this jet width gradually decreases along the jet axis. This finding can be used to explain the hexagonal pattern in the stagnant region at H / De = 2 (Fig. 3(c)–(f)) where the jet widths on planes I and II are comparable. However, excessive mixing of the shear layer leads to the decay of the fluid speed when the flow approaches the wall as shown in the region near r / De = 1.0 in Fig. 13(c). This could be a reason for the heat transfer deterioration in the lobed jet with a/ b = 1.15. 1 The two-dimensional turbulent kinetic energy (k = 2 (ur2 + uz2) ) of
Fig. 13. Mean velocity magnitudes on different measurement planes at H / De = 2 and Re = 10,000. 123
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Fig. 14. Two-dimensional turbulent kinetic energies on different measurement planes at H / De = 2 and Re = 10,000.
the flow at H / De = 2 on planes I–III is shown in Fig. 14. Furthermore, the turbulent kinetic energy differs little in the free-jet and impingement zones for all of the nozzle configurations. This finding provides more evidence for the insignificant heat transfer difference for all of the nozzle configurations in the stagnation region. In the wall-jet zone, the lobed jet with a/ b = 0.8 exhibits a weak decay of the turbulent kinetic energy on planes I and II, but a slight increase on plane III. For the lobed jet with a/ b = 1.15, however, the decay of the turbulent kinetic energy on all of the planes is significant, indicating the deterioration of the heat transfer on the wall. Whereas, the heat transfer rate in the case of the lobed jet with a/ b = 0.8 does not decay owing to the high fluid speed near the wall and the high level of turbulent kinetic energy. Fig. 15 presents the mean velocity magnitude distributions on the jet centre planes at H / De = 4. At this nozzle-to-wall distance, the jet width on plane II is considerably larger than that on plane I, leading to the inverted-triangle pattern of the Nussle number in the stagnant region (Fig. 4(b)–(f) and Fig. 5(b)–(f)). In the free-jet zone, the width of the shear layer increases considerably compared with that at H / De = 2 because of the fluid approaching the end of the jet potential core. Moreover, the fluid speed in the wall-jet zone decreases significantly compared with that at H / De = 2; it decreases further with an increase in a/b. The finding proves the consistent decay of the wall heat transfer rate in relatively large radial locations. As for the two-dimensional turbulent kinetic energy shown in Fig. 16, the significant difference compared with that at H / De = 2 is attributed to the decrease in the turbulent kinetic energy in the wall-jet zone. In the shear layer in the free-jet zone, the turbulent kinetic energy decreases with an increase in a/b. However, the turbulent kinetic energy in the stagnation region increases with an increase in a/b, because of the thickening and the interaction of the jet's shear layer. This finding indicates that the effect of the lobes expands to the jet's stagnation region at H / De = 4 and enhances the local heat transfer. The planar-PIV measurements provide valuable clues to understand
the mechanism for the heat transfer enhancement using a lobed nozzle. It is well accepted that the vortical structures initialled in the shear layer has a significant influence on the impingement heat transfer intensity (O'Donovan and Murria, 2006). The rollup of the Kelvin–Helmholtz (K–H) vortices in circular jets attenuates the streamwise structures that are responsible for the mixing and the momentum flux transport (Martin and Buchlin, 2011). In the lobed jets, either due to the axis-switching phenomenon with the non-circular nozzle (Gutmark and Grinstein, 1999) or subject to the tab effects (Samimy et al., 1993) exerted by the lobe troughs, numerous streamwise structures are induced along with the breakdown of the K–H vortices. This enhances the mixing in the flow and thus has strong effects on the impingement heat transfer. Martin and Buchlin (2011) attributed the heat transfer enhancement using lobed nozzle to the continuous momentum flux transport by the broken K–H vortex segments and the streamwise vortical structures. However, this cannot explain why the lobed nozzle with large a/b yields even lower heat transfer intensity at H / De = 2. Recall that in the Nusselt number distribution at H / De = 2 the distinct differences between various lobed nozzles lie in the region near and beyond the second-peak circle. The secondary vortices (Dairay et al., 2015), which are mainly induced near the impingement wall, are strongly associated with the heat removal near the second-peak circle. This would be a hint for the in-depth investigation of the heat removal mechanism using near-wall turbulence resolving methods. 4. Conclusions In the present study, the impingement jet issuing from the lobed nozzles constructed using three small circular orifices was intensively investigated using complementary techniques of the TSP and PIV methods, which respectively involved the spatial distributions of the wall heat transfer and the flow quantities. In particular, the effects of geometrical variations were compared by varying the ratio of the orifice 124
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Fig. 15. Mean velocity magnitudes on different measurement planes at H / De = 4 and Re = 10,000.
Fig. 16. Two-dimensional turbulent kinetic energies on different measurement planes at H / De = 4 and Re = 10,000.
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centre offset to the orifice radius, i.e., a/b = 0, 0.5, 0.8, 1.0, 1.1 and 1.15, at a constant equivalent diameter De for all of the lobed nozzles to ensure a constant cross-section area of the nozzles. The TSP measurements were performed at Reynolds numbers Re = 10,000 and 40,000 and the nozzle-to-wall distances of H / De= 2, 4 and 6 to determine the mean Nusselt number distribution on the heated wall. The PIV was performed at Re = 10,000 and H / De= 2 and 4 with the lobed nozzles a/ b = 0, 0.8 and 1.15 to understand the flow mechanism for the heat transfer enhancement. The TSP measurements at both Reynolds numbers showed that the snowflake-shaped pattern of the mean Nusselt number distribution was gradually established when a/b increased at H / De= 2, while the inverted-triangle pattern of the Nusselt number distribution was observed at H / De= 4 and 6. The azimuthal-averaged Nusselt number at H / De = 2 showed that the optimal heat transfer was obtained using the lobed nozzle with a/ b = 0.8 in the region 1 < r/De < 4, with a heat transfer enhancement of up to 10% compared with that in the case of the circular jet. At H / De= 4, the azimuthal-averaged Nusselt number increased (up to 16%) consistently in the region r/De < 0.5 with an increase in a/b, while the Nusselt number showed a slight decay in the region 2 < r/De < 4. At H / De = 6, the Nusselt number in the entire measured region decayed with an increase in a/b. The PIV measurements showed that the wall was located in the jet potential core at H / De = 2, meaning that the effects of the lobed nozzles were limited in the jet's shear layer. Due to the fact that the turbulence characteristics close to the jet centreline was nearly unchanged, changing the nozzle configuration did not result in apparent variation of the local Nusselt number distribution in this region. The turbulent kinetic energy in the wall-jet zone in the case of the lobed jet with a/ b = 0.8 increased slightly compared with that in the other cases, resulting in a heat transfer enhancement in 1 < r/De < 4. At H / De = 4, the wall was located at the end of the potential core; the turbulent kinetic energy increased with an increase in a/b. This was the main mechanism for the heat transfer enhancement in the stagnation region at H / De = 4. The consistent decay of the heat transfer rate at a relatively large nozzle-to-wall distance could be attributed to the breakdown of the large-scale structures and the turbulence dispersion beyond the jet potential core. The planar PIV setup used in this study determined the mean flow quantities in different azimuthal planes, which shed light on the causeand-effect relationship between the flow dynamics and wall heat transfer. However, the fluid flow issuing from the lobed nozzle was highly three dimensional and exhibited spatio-temporally varying behaviours, which played an important role in the impingement heat transfer. This will be elucidated using large-eddy simulations in a continuation study, in which the present measurements will serve as the validation database.
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Acknowledgements The authors gratefully acknowledge financial support for this study from the National Natural Science Foundation of China (11725209).
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