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Effects of nozzle positioning on single-phase spray cooling
International Journal of Heat and Mass Transfer 115 (2017) 1247–1257
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Effects of nozzle positioning on single-phase spray cooling Xuan Gao, Ri Li ⇑ School of Engineering, The University of British Columbia, 1137 Alumni Ave, Kelowna, BC V1V 1V7, Canada
a r t i c l e
i n f o
Article history: Received 28 June 2017 Received in revised form 18 August 2017 Accepted 28 August 2017 Available online 8 September 2017
a b s t r a c t The effects of nozzle positioning on spray cooling is experimentally studied using water sprays generated by a full-cone nozzle to cool a sputter-coated thin-film heater on a silicon wafer. Infrared camera is used to measure surface temperature with high spatial resolution. The nozzle positioning can be adjusted by moving the nozzle toward or away from the cooling surface to change spray height and/or by tilting the nozzle to change inclination angle. The study is composed of three components: (1). Flow in the spray cone is specified by polar and azimuthal angles ðb; uÞ, and it impacts and cools the surface at ðx; yÞ. The relation between the two coordinates, and the flow flux as a function of ðb; uÞ are derived, and both are dependent on the spray height and inclination angle. (2). The effect of spray height is experimentally investigated for normal spray impact. It is discovered that the optimal spray height providing the most effective cooling is smaller than the height required for covering the entire heater area. It is found that the optimal height decreases with increasing the spray flow rate. (3). The effect of inclination is experimentally studied by changing the inclination angle while maintaining the major-axis length of the elliptical spray-covered area constant. Using the derived relation, from the measured local cooling at ðx; yÞ we track the cooling performance of the flow at ðb; uÞ. The flux of the flow is calculated and compared using the derived flux equation for varied inclination angles. The enhancement and diminishment of the cooling performance are found to be in general agreement with the increase and decrease of the flow flux. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Spray cooling is an effective cooling method for high heat flux applications, due to its large capacity of heat removal with low coolant flow rates. In spray cooling, coolant droplets generated by spray nozzle continuously impinge on a hot surface and remove heat by forced convection, thin film evaporation, and even nucleate boiling. In past few decades, a number of studies have focused on the spray nozzle, coolant, spray characteristics, cooling regimes, and surface enhancement. A few studies [1–6] demonstrated the effects of phase change on cooling performance. In most spray cooling applications, droplets actually land on a liquid film rather than directly onto a bare surface. The liquid film has significant effect on cooling performance. Non-intrusive technologies [7,8] were introduced to determine the thickness of liquid film. Recent studies [9–13] have shown that modifying surface morphology could enhance cooling performance. Micro/mini textured surfaces were found to be helpful for enhancing cooling performance. Spray cooling using multiple nozzles has been reported [14,15] for the cooling of large surfaces.
⇑ Corresponding author. E-mail address: [email protected] (R. Li). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.08.095 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
Another research focus of spray cooling is spray characteristics. Mudawar and Valentine [16] concluded that the volumetric spray flux has a dominant effect on cooling compared to other hydrodynamic properties of the spray. Chen et al. [17] reported that the droplet velocity and droplet flux are the first and second dominant parameters on CHF (critical heat flux) cooling. Studies were also conducted to investigate the effects of nozzle positioning on spray cooling. Mudawar et al. [18] concluded that the optimal orifice-surface distance for achieving the most effective cooling of a given surface is when the spray just covers the cooling surface. A few studies [9,19,20] focused on the effects of spray inclination on heat transfer performance. Silk et al. [9] studied the cooling of flat and textured surfaces by inclined sprays with varied inclination angles. It was found that the inclination improves the cooling of the flat surface. Wang et al. [19] found that the inclination of spray nozzle could enhance heat transfer if optimal orifice-surface distance could be found. However, Visaria and Mudawar [20] concluded that the inclination angle had no noticeable effect on the single-phase or two-phase regions of the boiling curve. The conclusions of these studies are contradictory. The present work is focused on the effects of nozzle positioning on spray cooling. This work differs from previous studies on the following aspects. (1). Both orifice-surface distance and inclination angle are studied. (2). By using an infrared camera, high-resolution
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Nomenclature A A0 Ah An Dj h H Hn H0 k L Q Q 00 Q 000 q00 r
r0 t Tl Ts W
spray impact area perpendicular cross section heater area area of normal impact hydraulic jump diameter heat transfer coefficient spray height spray height for normal impact distance from A0 to nozzle orifice thermal conductivity of silicon spray impact length volumetric flow rate spray flux on impact area spray flux on A0 heat flux radius on A
radius on A0 wafer thickness water coolant temperature surface temperature heater width
Greek symbols a half spray angle b polar angle h inclination angle / azimuthal angle on A u azimuthal angle on A0 X solid angle v location along center line
local cooling is related to the nozzle positioning. (3). A large heater area with 5.5 cm2 (less than 1 cm2 for previous studies) is used so that the positioning variables can be changed in large ranges. (4). Detailed geometrical relations are derived to track the flow for its cooling performance and flow flux. 2. Experimental method 2.1. Experimental setup The experimental setup used for conducting the tests of spray cooling is schematically shown in Fig. 1. It is composed of: (1) a pressurized water supply; (2) a full-cone spray nozzle attached to a positioning system; (3) a heater plate; (4) a high-speed camera for visualizing the spray; (5) an infrared camera for measuring the surface temperature. A high-pressure nitrogen cylinder is connected to a pressurized water tank at room temperature. The pressurized water is supplied to a full-cone spray nozzle (TG SS 0.3, Spraying Systems Company), which atomizes the water flow through an orifice with diameter of 0.51 mm. The volumetric flow rate of the spray, denoted by Q , ranges from 2.5 to 6.7 cm3/s. For the tested range of flow rate, the spray angle denoted by 2a ranges from 51° to 60°. The temperature of water denoted by T l , is measured using a calibrated T-type
thermocouple. The nozzle is attached to a positioning system to change the nozzle location and orientation. Parameters associated with the nozzle positioning will be discussed later in this section. The test surface is made of a silicon wafer (4 in. in diameter) with a thickness of t = 380 lm and thermal conductivity of k = 149 W/mK. The upper surface of the wafer is exposed to the spray, and is called impact surface. At the center of the lower surface, a square area with width W ¼ 23:5 mm is coated with gold. The gold-coated layer serves as a film heater, and its area Ah ¼ W W is called heater area. Between the silicon wafer and the gold layer are a dielectric layer and an adhesive layer. All the layers have a total thickness less than 2 lm, which has negligible resistance to heat conduction. The electrical resistance of the film heater is 1 O. A DC power supply (Model 62050P, Chroma) is connected to the heater, and the heater power is determined based on the electrical current and voltage drop. The coated area and the electrical connection are designed for achieving uniform current density throughout the gold layer. The average heat flux in the heater area, denoted by q00 , is calculated by dividing the heater power with the heater area, and ranges from 26.2 to 26.8 W/cm2. Based on the measurement uncertainties of voltage, current and heater area, the overall uncertainty of q00 is ±2%. A high-speed camera (M310, Vision Research) is used to observe the spray. An infrared (IR) camera (SC660, FLIR) is positioned
Fig. 1. Schematic of the experimental setup.
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underneath the silicon wafer to measure the temperature on the lower surface, denoted by T s . To increase the measurement accuracy, the lower surface of the silicon wafer is painted black to achieve a high emissivity of 0.95. The optical resolution of the IR images is 5.6 pixels/mm2, which provides detailed temperature distribution. Heat loss includes free air convection and radiation from the lower surface of the silicon wafer and also heat conduction through the electrical connections and the peripheral area (no gold coating) of the wafer. The heat losses through the electrical connections and the peripheral area are estimated based on the temperature gradients that can be obtained from the infrared images. In the present work, the heat transfer coefficient of spray cooling, denoted by h, is of the order of magnitude of 1 W=cm2 K. For most tests reported in the present work, the spray impingement is within the heater area, and the total heat loss is estimated to be 1% of the total heater power. Hence, the heat transfer coefficient in the heater area can be calculated using
h¼
q00 Ts Tl
ð1Þ
Here T s is not the temperature at the solid-fluid interface as it is measured from the lower surface. The heat conduction through the thickness of the silicon wafer is neglected as the Biot number ht=k < 0:1. Based on the uncertainty of q00 and the measurement uncertainties of T s and T l (DT s 0:5 C, and DT l 0:1 C), the overall uncertainty of h is ±3%. 2.2. Geometric relations of spray positioning The positioning stage for the spray nozzle can change the location of the nozzle vertically and horizontally. It also can adjust the nozzle orientation relative to the impact surface to achieve normal impact (see Fig. 2a) or inclined impact (see Fig. 2b). Similar to the 2D images shown in Fig. 2a and b, Fig. 2c shows a side-view schematic of spray impact. The nozzle positioning can be specified by the spray height H and the inclination angle h. In the present work, the spray is inclined by rotating the spray nozzle clockwise. The tested ranges of the two positioning variables are 5 mm 6 H 6 28 mm and 0 6 h 6 40 . In this 2D schematic, the length L covered by the spray is called impact length. The relation between the spray height, inclination angle, and impact length is expressed by
L¼
H sin a 1 1 þ cos h cosðh aÞ cosðh þ aÞ
ð2Þ
In Fig. 2, the viewed plane is the z x plane, normal to which is the y axis. Hence, the impact surface is on the x y plane. The footprint of the spray on the impact surface is called impact area, denoted by A. The impact area is circular for h ¼ 0 and elliptical for 0 < h < ð90 aÞ. For all the tests, the impact area, heater area, and impact surface are concentric, and the center is located at ðx; yÞ ¼ ð0; 0Þ. Fig. 3 shows three impact areas with equal impact length L = 20 mm but varied values of h within the square heater area with W = 23.5 mm. The circular impact area is formed by normal impact, i.e. h ¼ 0 , and, therefore, is referred to as the area of normal impact denoted by An . The line passing through vertex-1 and vertex-2 is the centerline of the heater area and impact area. For each impact area shown in Fig. 3, the spray height H can be calculated using Eq. (2). The geometric equation for plotting the impact area will be derived in Section 4. The spray is considered as a solid circular cone with apex angle 2a. The impact area is the cross section formed by intersecting the spray cone with the impact surface on the x y plane. The z x plane shown in Fig. 2c is the central plane of the spray cone per-
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pendicular to the impact surface. And the centerline shown in Fig. 3 is where the central plane intersects the impact surface. As shown in Fig. 2, there are two cross sections perpendicular to the axis of the conical body. One cross section, denoted by A0 , is perpendicular to the axis of the inclined conical body and contains vertex-1. Its distance to the nozzle orifice is
H0 ¼
H cos a cosðh aÞ
ð3Þ
Another cross section is perpendicular to the axis of the vertical conical body, and is actually the area of normal impact An (see Fig. 3). Its distance from the orifice, denoted by Hn , is
Hn ¼
L 2 tan a
ð4Þ
For normal spray impact to cover a given impact length L, Eq. (4) is the required spray height. The two cross sections follow ðA0 =An Þ ¼ ðH0 =Hn Þ2 . Substituting Eq. (2) into Eq. (4) gives Hn as a function of H and h, which is
Hn ¼
H cos a 1 1 þ 2 cos h cosðh aÞ cosðh þ aÞ
ð5Þ
For inclined spray impact with specific spray height and inclination angle, Eq. (5) is the normal spray height for covering the same impact length as the inclined impact. 3. Flow regions on spray-impacted surface Spray impacting a solid surface forms a liquid film flowing away from the impact area. If the flowing film is thin and has high velocity, the radially outward flowing film shows an abrupt increase of film thickness as shown in Fig. 4a. This is similar to the film flow formed by the impact of a liquid jet on a surface [21]. The phenomenon is referred to as hydraulic jump. Upstream from the hydraulic jump, the gravitational wave speed is lower than the flow velocity. As a result of the hydraulic jump, the flow velocity significantly drops and becomes lower than the gravitational wave speed. In case of normal spray impact as shown in Fig. 4a, the hydraulic jump is circular. Inclined spray impact results in noncircular hydraulic jump. As discussed above, there are three flow regions on the surface: impact area, thin-film region, and thick-film region. The heat transfer performance in the three regions varies due to different flow dynamics. In case of normal impact, the three regions can be quantified by the impact length L and the hydraulic jump diameter Dj as defined in Fig. 4a. According to Eq. (4), the diameter of the circular impact area can be calculated using L ¼ 2Hn tan a. The hydraulic jump diameter Dj is measured for the normal spray impact with varied flow rates Q and spray heights Hn , and the measurement in comparison with L are shown in Fig. 4b. The impact length slightly increases with increasing the flow rate due to the change of spray angle. The hydraulic diameter shows significant increase with increasing the flow rate. This indicates that the higher the spray flow rate the stronger the film flow. Fig. 4b also shows that Dj can be enlarged by increasing Hn due to the resulted increase of L. 4. Spray flux: inclined impact versus normal impact The impact area is where the spray flow impinges on the surface. Within the impact area, the volume flow rate per unit area is referred to as spray flux, i.e. Q 00 ¼ dQ =dA. As shown in Fig. 3, the overall spray flux must change with the inclination angle h due to the change of the impact area. To characterize the change of spray flux, one way is to compare the spray flux at a fixed ðx; yÞ location on the impact surface for different inclination angles. Here the
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Fig. 2. (a) Normal impact of spray (Q = 2.5 cm3/s); (b) inclined impact of spray cooling (Q = 5.0 cm3/s, h = 20°); (c) geometrically, the spray impact on a surface is a spray cone insected by a surface. The 2D geometry is on the central plane (z-x plane) of the cone perpendicular to the impacted surface (x-y plane). The positioning of the nozzle is determined by inclination angle h and spray height H. Hn is the required spray height by normal impact to cover a given impact length L. The impact area is shown in Fig. 3.
local spray flux is associated with the location on the impact surface. The other way is to track a specific part of the spray flow and compare its fluxes on the impact surface for different inclination angles. Here the local spray flux is associated with the spray flow. For example, suppose we could repeatedly track a train of spray droplets that fly in the same trajectory and one by one land at the same location on the impact surface. As a result of changing the angle h, the train of droplets would land at a different ðx; yÞ location, and the spray flux associated with the train of droplets would also change. In this section we will focus on the change of local spray flux associated with the spray flow as a result of inclination.
In the spray cone, the spray flow can be imagined as rays discharged from the nozzle orifice. In other words, it is assumed that spray droplets are constantly generated and maintain their trajectories until impacting the surface. Each ray can be specified by ðb; uÞ. As shown in Fig. 5, the polar angle b 2 ½0; a and the azimuthal angle u 2 ½0; 2p. The cone forms a solid angle equal to 2pð1 cos aÞ, within which the volume flow rate of the spray, Q , distributes. We introduce a solid angle 0 6 X 6 2pð1 cos aÞ. Hence, the distribution of the flow rate with respect to solid angle is dQ =dX. Based on visual observation of the spray and the measured temperature distribution in the impact area with normal spray impact,
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Fig. 3. Impact area with constant impact length L formed by the spray inclined at different angles h. The square 23.5 mm 23.5 mm represents the heater area. The impact area is concentric with the heater area. The centerline is the intersection line between the impact surface and the central plane of the spray perpendicular to the impact surface. An is the area of normal impact.
Fig. 5. (a) A small element of the spray flow that is specified by db, and du. (b) The perpendicular cross-section A0 that has been shown in Fig. 2c. (b) The impact area A that has been shown in Fig. 2c.
images in Fig. 2 show that close to the nozzle orifice the spray has fully atomized. Hence, dQ =dX is independent of the distance from the orifice. In summary, the flow rate distribution in the spray cone is a function of b only, i.e. dQ =dX ¼ f ðbÞ. Fig. 5 shows part of the spray cone. Consistent with Figs. 2c and 3, the impact surface is on the x - y plane, and the x - z plane is the central plane of the spray cone. The perpendicular cross section shown in Fig. 5b is the cross section A0 shown in Fig. 2c, and the azimuthal angle on the cross section is u. Hence, we can write
dX ¼ sin bdbdu
ð6Þ
The flow rate within the solid angle dX is dQ . On the cross section A0 , as shown by Fig. 5b, the radius r 0 is given by
r0 ¼
H cos a tan b cosðh aÞ
ð7Þ
A differential area on this cross section is
dr 0 db dA0 ¼ r 0 du db
ð8Þ
Combining Eqs. (6)–(8) gives
dA0 cos b ðr 0 = sin bÞ Fig. 4. (a) Spray impact on a large surface forms three regions: impact area, thinfilm region, and thick-film region. From the thin film region to the thick film region is the hydraulic jump. (b) The calculated impact lengths and measured hydraulic jump diameters for varied spray heights and flow rates.
it is reasonable to assume that the full-cone nozzle generates axisymmetric sprays, i.e. @ðdQ =dXÞ=@ u ¼ 0. Additionally, the
2
¼ dX
ð9Þ
The spray flux on this cross section, Q 000 ¼ dQ =dA0 , then can be expressed as
Q 000 ¼
dQ cos b dX ðr 0 = sin bÞ2
ð10Þ
Next we derive the spray flux in the impact area. As shown in Fig. 5c, the radius in the impact area is
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r¼
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H sin b cos h sin½b þ cos1 ðsin h cos /Þ
ð11Þ
where the angle / is the azimuthal angle in the impact area. From Fig. 5, it can be shown that the azimuthal angles on the perpendicular cross section A0 and impact area A satisfy
tan / ¼ cos h tan u
ð12Þ
Corresponding to u ¼ 0 and p, / ¼ 0 and p, which is the centerline of the impact area as defined in Fig. 3. The flow specified by ðb; uÞ in the spray cone lands on the impact surface at a location ðr; /Þ, and the two locations are connected by Eqs. (11) and (12). With b ¼ a, Eq. (11) becomes
R ¼ rðb ¼ aÞ ¼
H sin a cos h sin½a þ cos1 ðsin h cos /Þ
ð13Þ
Q 00 Q 00 Q 00 Q 00 ¼ 00 ¼ 00 000 Q ðh ¼ 0Þ Q n Q 0 Q n
ð21Þ
00
As shown in Fig. 2c, the spray fluxes on the two cross-sections A0 and An should follow
2 Q 000 Hn ¼ H0 Q 00n
ð22Þ
Putting Eqs. (20) and (22) into Eq. (21) yields
1 2 Q 00 r 20 du @r Hn ¼ H0 Q ðh ¼ 0Þ r sin b cos b d/ @b 00
ð23Þ
Substituting Eqs. (3), (5), (7), (11), and (18) into Eq. (23) gives
Eq. (13) is the equation used for plotting the impact areas in Fig. 3, where the center of the impact area is located at ðx; yÞ ¼ ð0; 0Þ. In the impact area, the relation between two coordinates systems ðr; /Þ and ðx; yÞ is
1 x ¼ r cos / þ ½Rð/ ¼ pÞ Rð/ ¼ 0Þ 2 y ¼ r sin /
Q 00 ðh ¼ 0Þ ¼ Q 00n ¼ dQ =dAn . The comparison between the inclined impact and normal impact can be written as
ð14Þ
Q 00 cos2 a cos h sin ½b þ cos1 ðsin h cos /Þ 00 ðh ¼ 0Þ ¼ 2 Q 4 cos4 bðcos2 h cos2 / þ sin /Þ 2
1 1 tan b cot½b þ cos1 ðsin h cos /Þ 2 1 1 þ cosðh aÞ cosðh þ aÞ
ð24Þ
In the present work, the location ðx; yÞ determined from the recorded IR images can be converted to ðr; /Þ using Eq. (14), which can be further converted to ðb; uÞ using Eqs. (11) and (12). The local cooling analysis that will be presented in Sections 5.1 and 6.1 focuses on the cooling along the centerline of the impact area (see Fig. 3). Here we use v to specifically denote the location along the centerline, which is
Combining Eqs. (24) and (12) gives Q 00 =Q 00 ðh ¼ 0Þ as a function of h, b, and u. The ratio of spray flux here shows the effect of inclination h on the spray flux of the flow located at ðb; uÞ in the spray cone.
v ¼ xð/ ¼ 0; pÞ
Most spray cooling applications rely on normal spray impact (h ¼ 0), for which the spray height Hn is the only positioning variable. By increasing or decreasing Hn , the impact area can be increased or reduced. In this section experimental results of normal impact with varied values of Hn will be analyzed to investigate the local cooling and global cooling of the heater area. The objective here is twofold. The first is to investigate how the cooling performance changes with the spray height. The second is to determine the optimal spray height that provides the most effective cooling for a given flow rate.
ð15Þ
Enclosed by the differential solid angle dX same as in Eq. (9), the differential element of the impact area is
dA ¼ rd/dr ¼ r
d/ @r du db du @b
ð16Þ
Combined with Eq. (6), Eq. (16) can be further written as
dA ¼
r d/ @r dX sin b du @b
ð17Þ
The derivative @r=@b can be obtained from Eq. (11). From Eq. (12), it can be readily shown that 2
d/ cos2 h cos2 / þ sin / cos h ¼ ¼ 2 2 du cos h cos h sin u þ cos2 u
ð18Þ
The flux in the impact area, Q 00 ¼ dQ =dA, is
Q 00 ¼
1 dQ r d/ @r dX sin b du @b
ð19Þ
Based on Eqs. (10) and (19), we can write
1 Q 00 r 20 du @r ¼ Q 000 r sin b cos b d/ @b
ð20Þ
Eq. (20) is the ratio of spray flux associated with the flow located at ðb; uÞ in the spray cone, and the flow has different fluxes on the impact surface and the cross section A0 . In real applications of spray-cooling a given surface, the impact length L usually is maintained constant for both normal impact and inclined impact. Hence, it is useful to compare the spray flux of inclined impact, Q 00 , to that of normal impact, Q 00 ðh ¼ 0Þ, when L remains unchanged. As shown in Fig. 3, the area of normal impact Aðh ¼ 0Þ ¼ An , and spray flux for normal impact is
5. Normal spray impact
5.1. Local cooling by normal spray impact A series of tests are conducted with a constant flow rate Q = 5.0 cm3/s and spray height ranging from 5.1 to 27.4 mm. The temperature along the centerline of the heater area is used to calculate the heat transfer coefficient using Eq. (1). The heat transfer coefficient along the centerline, denoted by hv , is plotted versus v 2 ½W=2; W=2 in Fig. 6, and v ¼ 0 is the concentric center of the heater and impact areas. The 2D symmetric profile of heat transfer coefficient indicates axisymmetric distribution, and v is the radial location for the axisymmetric distribution. From the center outward, the heat transfer coefficient first increases and then decreases. The distance between the two peaks is roughly equal to the impact length L that can be calculated using Eq. (4). In other words, the maximum local heat transfer coefficient appears at the edge of the impact area. Hence, within the impact area hv increases radially. Outside the impact area, i.e. in the thin-film region, hv decreases radially, as the flow in the thinfilm region slows down while flowing radially. Fig. 6 also shows that increasing the spray height reduces the cooling in the impact area. This can be explained by Eq. (22), which shows that the spray flux of normal impact is inversely proportional to H2n . As the spray height increases, the distribution of the
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Fig. 6. Local heat transfer coefficient along the center line of the heater area cooled by normal spray impact with Q ¼ 5:0 cm3/s.
heat transfer coefficient flattens. For Hn ¼ 27:4 mm, along the entire centerline of the heater area, the spray has covered the heater area, but provides cooling less effective than all the other cases. In addition to the distribution of local heat transfer coefficient shown in Fig. 6, it is also useful to evaluate the local areaaveraged cooling. Due to the axisymmetric cooling of normal spray impact and the assumption of uniform heat flux, the area-averaged heat transfer coefficient is defined as
hv ¼
2
v
2
1 Z v 1 vdv 0 hv
ð25Þ
Here hv is the average heat transfer coefficient for the circular area with radius v. To calculate hv based on the data shown in Fig. 6, we define and use a discrete form of Eq. (25), which is
hv1 ¼ hv1 " ! #1 i vj1 þ vj 2 X 1 1 1 hvi ¼ 2 þ Dv 2 vi j¼2 2 hvj1 hvj
ði P 2Þ
ð26Þ
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Fig. 7. The local heat transfer coefficient hv and local area-averaged heat transfer coefficient hv of normal spray impact with Hn ¼ 5.1 mm and Q ¼ 5:0 cm3/s. The radial gap distance, d, is between the edges of the circular impact area and the circular area with maximum average cooling.
of global cooling performance to the spray height for varied flow rates. The global cooling performance is evaluated using an average heat transfer coefficient
q00 h¼ Ts Tl
ð27Þ
where T s is the average of IR image of the heater area (3100 data points of T s ). Fig. 8 shows the global heat transfer coefficient versus the spray height for six different flow rates. Apparently, the higher the flow rate, the higher the heat transfer coefficient. However, this trend diminishes for large spray heights close to Hn = 28 mm when the impact area is already larger than the heater area. For each given flow rate, with increasing the spray height, the global cooling first
Here v1 ¼ 0 and vi ¼ ði 1ÞDv are the measurement locations shown in Fig. 6. The interval Dv ¼ 0:4 mm is determined by the resolution of the IR camera. Eq. (26) is used to calculate the area-averaged heat transfer for the test with Hn = 5.1 mm shown in Fig. 6. The local heat transfer coefficient hx and average heat transfer coefficient hv are plotted in Fig. 7. Similar to the trend of hv , hv first increases and then decreases. However, the location for maximum hv is after the location for maximum hv by a gap distance d. Therefore, for normal impact, the optimal area for achieving the most effective cooling is larger than the impact area. This implies that to cool a given surface effectively, the spray should cover less than the actual heater area. This finding is different from the previous study by Mudawar and Estes [18]. 5.2. Global cooling by normal spray impact Discussion above indicates that to cool a given area effectively, the impact area should be smaller than the heater area. Since the impact area for normal impact is solely dependent on the spray height, a series of tests are conducted to investigate the relation
Fig. 8. Heat transfer coefficient averaged over the heater area, h, versus the spray height, Hn , for varied flow rates, Q . For each flow rate, the peak point of the data curve shows the optimal spray height, Hn;max , for achieving the maximum average heat transfer coefficient, hmax . Within the shaded area are the tests with sprays covering beyond the heater area, i.e. L > W.
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face with the given flow rate. In Fig. 8, the optimal points are con-
Fig. 9. The optimal spray height of normal impact versus the flow rate for cooling the heater area. In the inset graph the radial gap distance d (defined in Fig. 7) shows the difference between the heater area and the optimal impact area.
increases and then decreases. Hence, for each given flow rate, there is maximum cooling, denoted by hmax , and the corresponding spray height, Hn;max , is the optimal spray height for cooling the given sur-
nected by a dashed line, which shows two trends: (1) hmax decreases with decreasing Q ; (2) Hmax increases with decreasing Q . In Fig. 8, the tests with their impact areas larger than the heat area, i.e. L > W, are indicated. All the tests show a decreasing trend of cooling performance with further increasing the impact area by increasing the spray height. Spray impingement outside the heater area could increase the heat loss to the periphery of the heater area, which would bring the actual cooling performance further down. Hence, the decreasing trend of cooling performance would be even more obvious if the heat loss could be taken into account. To further investigate the second trend, in addition to the six flow rates tested in Fig. 8, the optimal spray height Hn;max is determined for another four flow rates. All the data are presented in Fig. 9, which shows the optimal heights versus flow rates. The error bar is the difference between the determined Hn;max and its two neighboring tested spray heights. For all the cases, L < W. This indicates that for achieving the optimal cooling, the spray needs to cover less area than the heater area. Although the heater area is square rather than circular, the gap distance between the edges of the impact area and the heater area (see the inset of Fig. 9) can be approximated as the gap distance, d, defined in Fig. 7. Hence, the gap distance can be calculated using d ¼ ðW LÞ=2. In summary, Fig. 9 shows that to achieve the most effective cooling from an increased flow rate, the nozzle needs to be moved closer to the surface (Hn;max decreases) to reduce the impact area (d increases).
Fig. 10. Temperature distribution of the heater area cooled by inclined sprays (Q ¼ 5:0 cm3/s, L ¼ W = 23.5 mm): (a) h ¼ 20 ; (b) h ¼ 30 ; (c) h ¼ 40 . (d) Average heater transfer coefficient.
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Fig. 12. The local heat transfer coefficient shown in Fig. 11a is plotted versus the b location, and hb denotes the local heat transfer coefficient associated with the b location.
the left side. As h further increases, the cooler region on the right side continues to expand, and the temperature around the center decreases. The temperature in the heater area is averaged to obtain T s , and the global heat transfer coefficient h is calculated using Eq. (27) and plotted in Fig. 10d. The effect of inclination on global cooling can be evaluated by comparing with the normal impact (h ¼ 0 ), for which h ¼ 2:35 W/cm2K. The global cooling for h ¼ 20 is h ¼ 2:22 W/cm2K, showing negative effect of inclination. However, an opposite trend appears for further increased inclination angles h ¼ 30 and 40 , which result in h ¼ 2:79 and 3.01 W/cm2K, respectively.
Fig. 11. (a) Local heat transfer coefficient associated with the v location along the center line for h ¼ 0 ; 20 ; 30 ; 40 . The temperature contours have been shown in Fig. 10 except for h ¼ 0 . (b) The change of local cooling due to inclination is quantified by comparing the inclined impact to the normal impact.
6. Inclined spray impact For inclined spray impact, there are two positioning variables: H and h. Changing either variable would cause both the impact area A and impact length L to change. The focus of our study is on the effect of spray inclination on cooling performance. The experimental study is carried out by changing the angle h and maintaining a constant impact length equal to the width of the heater area, i.e. L ¼ W = 23.5 mm. As a result, the spray height H becomes a dependent variable, and it can be calculated using Eq. (2). As shown by Fig. 3, increasing h while maintaining L constant reduces the impact area A. As a result, the overall spray flux, Q =A, increases. 6.1. Global cooling by inclined spray impact Fig. 10 shows temperature distribution of inclined spray impact with inclination angles h ¼ 20 ; 30 and 40 with Q = 5.0 cm3/s. Consistent with Figs. 2 and 5, the inclination of spray is done by rotating the nozzle clockwise. The ellipses in dashed lines show the impact area. For h ¼ 20 , the temperature contour is close to being axisymmetric, but the right side is generally cooler than
6.2. Local cooling by inclined spray impact To better understand the effect of inclination on global cooling, we look into the local cooling. To simplify the analysis, we focus on the local cooling along the centerline of the impact area. The local heat transfer coefficient along the centerline hv is calculated using Eq. (1) and is plotted in Fig. 11a for the normal impact (h ¼ 0 ) and inclined impact (h ¼ 20 ; 30 , 40 ). For the normal impact, the distribution of hv is symmetric with respect to v ¼ 0, the center of the impact area. The inclination causes hv to increase on the right side (v > 0) and decrease on the left side (v < 0). Since the temperature is measured at the same v locations for all the cases, we can compare the local cooling of inclined impact with that of the normal impact. The comparison, hv =hv ðh ¼ 0 Þ, is plotted in Fig. 11b. For h ¼ 20 , slight enhancement appears only on the right side, whereas the left side shows diminished cooling. For h ¼ 30 and 40 , cooling enhancement increases and extends to the left side. Nevertheless, cooling diminishment still exists on the left side, the far end from the spray nozzle. The inclination affects local cooling in two mechanisms. One is related to the velocity direction of spray droplets. The velocity vector can be decomposed into a vertical component perpendicular to the surface and a horizontal component parallel to the surface. The vertical component determines the impact momentum of spray droplets, while the horizontal component affects the velocity of the flow on the surface. Increasing or decreasing either velocity component could enhance or diminish the cooling performance.
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The inclination must cause one velocity component to increase and the other one to decrease. However, it is difficult to determine the net effect on cooling. The other mechanism is related to local spray flux. The increase or decrease of local spray flux is expected to enhance or diminish local cooling. The analysis in this section is to relate the change of local spray flux to the change of local cooling. The change of local cooling associated with v location has been shown in Fig. 11b. However, the change of local spray flux associated with v location is unknown for the following reason. According to Eq. (15), as a result of changing h, the spray flow impacting any v location is replaced by new flow associated with a new value of b. The spray flow distribution dQ =dX ¼ f ðbÞ is unknown. The change of spray flux associated with ðb; uÞ has been derived in Section 4. The flow impacting the centerline of the impact area has b 2 ½0; a and u ¼ 0 and p. We will try to obtain the change of local cooling associated with the flow impacting the centerline. First, we convert the local heat transfer coefficient associated with v, hv , to the local heat transfer coefficient associated with b, hb , by converting the v locations in Fig. 11a to b locations. Here we will derive the equation that relates v to b. Eq. (15) relates v to b for given H and h, and is composed of v ¼ xð/ ¼ 0Þ and v ¼ xð/ ¼ pÞ for 0 6 b 6 a. From now on, if we define a 6 b 6 a, Eq. (15) then becomes v ¼ xð/ ¼ 0Þ, which can be fully written as
v¼
1 H sin a 1 1 H sin b þ 2 cos h cosðh þ aÞ cosðh aÞ cos h cosðh bÞ
ð28Þ
Here the angle a 6 b 6 a is on the central plane of the spray cone, which is orthogonal to the impact surface. Combining Eq. (2) with Eq. (28) gives
1 1 2 sin b þ cosðh þ aÞ cosðh aÞ sin a cosðh bÞ ¼ 1 1 L=2 þ cosðh þ aÞ cosðh aÞ
v
ð29Þ
Eq. (29) is used to convert the v location to b location, and the data of heat transfer coefficient in Fig. 11a, now denoted by hb , are plotted versus b in Fig. 12. The goal here is to analyze the change of hb due to inclination by comparing the cooling of inclined impact to that of normal impact, i.e. hb =hb ðh ¼ 0 Þ. However, the ratio cannot be calculated at this moment as in Fig. 12 the four cases have different b locations. To address this issue, linear interpolation is carried out based on the data shown in Fig. 12 to calculate hb for unified b locations for all the cases. The interpolated data are presented in Fig. 13a, where the data curves show no visible difference from those in Fig. 12. Based on Fig. 13a, the ratio hb =hb ðh ¼ 0 Þ is calculated and plotted in Fig. 13b. Fig. 13b shows the effect of inclination on the cooling performance of the flow, which distributes on the central plane of the spray. The trends for the three cases of inclined impact are similar. Generally, from b ¼ a to b ¼ a, the cooling enhancement first increases and then decreases. The enhancement peaks are within the angular space b > 0 , and the peak shifts slightly toward the left as h increases. The flow close to b ¼ a shows diminished cooling as a result of inclination. The incline impact with h ¼ 40 provides the highest cooling enhancement for most of the central plane flow. In Section 4, we have derived the change of local spray flux associated with the flow at ðb; uÞ as a function of h. The comparison of spray flux Q 00b =Q 00b ðh ¼ 0Þ along the centerline can be evaluated using Eq. (24) with input / ¼ 0; p. Similar to the derivation of Eq. h i (28), Q 00b =Q 00b ðh ¼ 0Þ can be changed to ½Q 00b =Q 00b ðh ¼ 0Þ/¼0 with /¼0;p
a 6 b 6 a, which can be written as
Fig. 13. (a) By applying interpolation to Fig. 12, hb is plotted versus the same b locations for all the cases of normal impact and inclined impact. (b) The ratio of local cooling of inclined impact to normal impact calculated from the interpolated data.
"
Q 00b
Q 00b ðh ¼ 0Þ
h
# ¼ /¼0
cos a cosðhbÞ 2 cos2 b
i2 h
1 cosðhþaÞ
1 þ cosðh aÞ
cos h½1 tan b tanðh bÞ
i2 ð30Þ
Eq. (30) is plotted in Fig. 14 for the three cases of incline spray impact. Now we have the change of local cooling shown in Fig. 13b and change of local spray flux shown in Fig. 14, both associated with the flow at b location on the central plane of the spray cone. Comparing Figs. 14 and 13b shows the following similarities between the local spray flux and the local cooling. (1) The inclination increases the spray flux for most of the central-plane flow, except for the flow close to b ¼ a where the spray flux decreases. The angular zones of b for the increase and decrease of spray flux (Fig. 14) are similar to the enhancement and diminishment zones of cooling (see Fig. 13d). (2) For the three cases, the larger the inclination angle, the more increase of spray flux (Fig. 14), and the more cooling enhancement (Fig. 13d), showing significant dependence on h.
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diminishment for small inclination angle and enhancement for large inclination angles. Based on the local cooling along the centerline of the impact area, the cooling performance of the flow on the central plane of the spray cone is tracked. The spray flux of the flow on the central plane is analyzed. The enhancement and diminishment of the cooling performance are found to be in general agreement with the increase and decrease of the spray flux. Acknowledgment The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for support. The authors also thank Mr. Yadi Cao for his assistance in conducting the experimental tests. Conflict of interest Authors declare that there is no conflict of interest. References Fig. 14. Corresponding to the local cooling analysis shown in Fig. 13, the ratio of local spray flux of inclined impact to normal impact is calculated using Eq. (30).
(3) Generally, spray flux decreases and cooling enhancement lessens as b changes from a to a. However, the flow at b ¼ a shows the maximum enhancement of spray flux, while the maximum cooling enhancement appears at b < a. The difference could be related to the change of velocity components, which is out of the scope of the present work. Depending on the location ðb; uÞ of the flow, the cooling performance of the flow can be enhanced or diminished by the inclination. One major reason is that the flux of the flow increases or decreases as a result of the inclination. Overall, Figs. 13d and 14 indicate the correlation between the change of local spray flux and the change of local cooling. 7. Conclusion Spray nozzle can be put closer to or farther from the impact surface to change the spray height, and it can be tilted to change the spray inclination. The spray height and inclination angle are the positioning variables tested in the present work. Spray impact is observed to form three regions on the impact surface: impact area, thin-film region, and thick-film region. For given spray height and inclination angle, the flow landing at a location ðx; yÞ in the impact area is located at ðb; uÞ in the spray cone. As a result of changing the nozzle positioning, the flow impacts a different ðx; yÞ location, and its spray flux also changes. The relation between ðx; yÞ and ðb; uÞ is derived. Equations are also derived for evaluating the change of spray flux as a function of the nozzle positioning and ðb; uÞ. Experimental tests of normal spray impact are conducted to investigate the effect of spray height. It is discovered that the optimal spray height providing the most effective cooling is smaller than the height required for covering the entire heater area. This is because the maximum local cooling is located at the edge of the impact area, and the film flow outside the impact area still provides effective cooling. It is found that the optimal height decreases with increasing the flow rate. The effect of inclination is studied by changing the inclination angle while maintaining the impact length constant and equal to the width of the heater area. The global cooling shows slight
[1] K.J. Choi, S.C. Yao, Mechanisms of film boiling heat transfer of normally impacting spray, Int. J. Heat Mass Transf. 30 (1987) 311–318. [2] K.A. Estes, I. Mudawar, Correlation of Sauter mean diameter and critical heat flux for spray cooling of small surfaces, Int. J. Heat Mass Transf. 38 (1995) 2985–2996. [3] J. Yang, L.C. Chow, M.R. Pais, Nucleate boiling heat transfer in spray cooling, ASME J. Heat Transf. 118 (1996) 668–671. [4] D.P. Rini, R.H. Chen, L.C. Chow, Bubble behavior and nucleate boiling heat transfer in saturated FC-72 spray cooling, J. Heat Transf. 124 (2002) 63–72. [5] M.S. EL-Genk, H. Bostanci, Saturation boiling of HFE-7100 from a copper surface, simulating a microelectronic chip, Int. J. Heat Mass Transf. 46 (2003) 1841–1854. [6] Y. Hou, X.F. Liu, J.H. Liu, M.J. Li, L. Pu, Experimental study on phase change spray cooling, Exp. Therm. Fluid Sci. 46 (2013) 84–88. [7] J. Yang, L.C. Chow, M.R. Pais, Liquid film thickness and topography determination using Fresnel diffraction and holography, Exp. Heat Transf. 5 (1992) 239–252. [8] A.G. Pautsch, T.A. Shedd, Adiabatic and diabatic measurements of the liquid film thickness during spray cooling with FC-72, Int. J. Heat Mass Transf. 49 (2006) 2610–2618. [9] E.A. Silk, J. Kim, K. Kiger, Spray cooling of enhanced surfaces: impact of structured surface geometry and spray axis inclination, Int. J. Heat Mass Transf. 49 (2006) 4910–4920. [10] C.C. Hsieh, S.C. Yao, Evaporative heat transfer characteristics of a water spray on microstructured silicon surfaces, Int. J. Heat Mass Transf. 49 (2006) 962– 974. [11] C. Sodtke, P. Stephan, Spray cooling on micro structured surfaces, Int. J. Heat Mass Transf. 50 (2007) 4089–4097. [12] H. Bostanci, D.P. Rini, J.P. Kizito, V. Singh, S. Seal, L.C. Chow, High heat flux spray cooling with ammonia: investigation of enhanced surfaces for HTC, Int. J. Heat Mass Transf. 75 (2014) 718–725. [13] Z. Zhang, P.X. Jiang, X.L. Ouyang, J.N. Chen, D.M. Christopher, Experimental investigation of spray cooling on smooth and micro-structured surfaces, Int. J. Heat Mass Transf. 76 (2014) 366–375. [14] L. Lin, R. Ponnappan, Heat transfer characteristics of spray cooling in a closed loop, Int. J. Heat Mass Transf. 46 (2003) 3737–3746. [15] Z.B. Yan, K.C. Toh, F. Duan, T.N. Wong, K.F. Choo, P.K. Chan, Y.S. Chua, Experimental study of impact spray cooling for high power devices, Appl. Therm. Eng. 30 (2010) 1225–1230. [16] I. Mudawar, W.S. Valentine, Determination of the local quench curve for spraycooled metallic surfaces, J. Heat Treat. 7 (1989) 107–121. [17] R.H. Chen, L.C. Chow, J.E. Navedo, Effects of spray characteristics on critical heat flux in subcooled water spray cooling, Int. J. Heat Mass Transf. 45 (2002) 4033–4043. [18] I. Mudawar, K. Estes, Optimizing and predicting CHF in spray cooling of a square surface, ASME J. Heat Transf. 118 (1996) 672–679. [19] Y.Q. Wang, M.H. Liu, D. Liu, K. Xu, Y.L. Chen, Experimental study on the effects of spray inclination on water spray cooling performance in non-boiling regime, Exp. Therm. Fluid Sci. 34 (2010) 933–942. [20] M. Visaria, I. Mudawar, Theoretical and experimental study of the effects of spray inclination on two-phase spray cooling and critical heat flux, Int. J. Heat Mass Transf. 51 (2008) 2398–2410. [21] B. Mohajer, R. Li, Circular hydraulic jump on finite surfaces with capillary limit, Phys. Fluids 27 (2015) 117102.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Effects of nozzle positioning on single-phase spray cooling Xuan Gao, Ri Li ⇑ School of Engineering, The University of British Columbia, 1137 Alumni Ave, Kelowna, BC V1V 1V7, Canada
a r t i c l e
i n f o
Article history: Received 28 June 2017 Received in revised form 18 August 2017 Accepted 28 August 2017 Available online 8 September 2017
a b s t r a c t The effects of nozzle positioning on spray cooling is experimentally studied using water sprays generated by a full-cone nozzle to cool a sputter-coated thin-film heater on a silicon wafer. Infrared camera is used to measure surface temperature with high spatial resolution. The nozzle positioning can be adjusted by moving the nozzle toward or away from the cooling surface to change spray height and/or by tilting the nozzle to change inclination angle. The study is composed of three components: (1). Flow in the spray cone is specified by polar and azimuthal angles ðb; uÞ, and it impacts and cools the surface at ðx; yÞ. The relation between the two coordinates, and the flow flux as a function of ðb; uÞ are derived, and both are dependent on the spray height and inclination angle. (2). The effect of spray height is experimentally investigated for normal spray impact. It is discovered that the optimal spray height providing the most effective cooling is smaller than the height required for covering the entire heater area. It is found that the optimal height decreases with increasing the spray flow rate. (3). The effect of inclination is experimentally studied by changing the inclination angle while maintaining the major-axis length of the elliptical spray-covered area constant. Using the derived relation, from the measured local cooling at ðx; yÞ we track the cooling performance of the flow at ðb; uÞ. The flux of the flow is calculated and compared using the derived flux equation for varied inclination angles. The enhancement and diminishment of the cooling performance are found to be in general agreement with the increase and decrease of the flow flux. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Spray cooling is an effective cooling method for high heat flux applications, due to its large capacity of heat removal with low coolant flow rates. In spray cooling, coolant droplets generated by spray nozzle continuously impinge on a hot surface and remove heat by forced convection, thin film evaporation, and even nucleate boiling. In past few decades, a number of studies have focused on the spray nozzle, coolant, spray characteristics, cooling regimes, and surface enhancement. A few studies [1–6] demonstrated the effects of phase change on cooling performance. In most spray cooling applications, droplets actually land on a liquid film rather than directly onto a bare surface. The liquid film has significant effect on cooling performance. Non-intrusive technologies [7,8] were introduced to determine the thickness of liquid film. Recent studies [9–13] have shown that modifying surface morphology could enhance cooling performance. Micro/mini textured surfaces were found to be helpful for enhancing cooling performance. Spray cooling using multiple nozzles has been reported [14,15] for the cooling of large surfaces.
⇑ Corresponding author. E-mail address: [email protected] (R. Li). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.08.095 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.
Another research focus of spray cooling is spray characteristics. Mudawar and Valentine [16] concluded that the volumetric spray flux has a dominant effect on cooling compared to other hydrodynamic properties of the spray. Chen et al. [17] reported that the droplet velocity and droplet flux are the first and second dominant parameters on CHF (critical heat flux) cooling. Studies were also conducted to investigate the effects of nozzle positioning on spray cooling. Mudawar et al. [18] concluded that the optimal orifice-surface distance for achieving the most effective cooling of a given surface is when the spray just covers the cooling surface. A few studies [9,19,20] focused on the effects of spray inclination on heat transfer performance. Silk et al. [9] studied the cooling of flat and textured surfaces by inclined sprays with varied inclination angles. It was found that the inclination improves the cooling of the flat surface. Wang et al. [19] found that the inclination of spray nozzle could enhance heat transfer if optimal orifice-surface distance could be found. However, Visaria and Mudawar [20] concluded that the inclination angle had no noticeable effect on the single-phase or two-phase regions of the boiling curve. The conclusions of these studies are contradictory. The present work is focused on the effects of nozzle positioning on spray cooling. This work differs from previous studies on the following aspects. (1). Both orifice-surface distance and inclination angle are studied. (2). By using an infrared camera, high-resolution
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Nomenclature A A0 Ah An Dj h H Hn H0 k L Q Q 00 Q 000 q00 r
r0 t Tl Ts W
spray impact area perpendicular cross section heater area area of normal impact hydraulic jump diameter heat transfer coefficient spray height spray height for normal impact distance from A0 to nozzle orifice thermal conductivity of silicon spray impact length volumetric flow rate spray flux on impact area spray flux on A0 heat flux radius on A
radius on A0 wafer thickness water coolant temperature surface temperature heater width
Greek symbols a half spray angle b polar angle h inclination angle / azimuthal angle on A u azimuthal angle on A0 X solid angle v location along center line
local cooling is related to the nozzle positioning. (3). A large heater area with 5.5 cm2 (less than 1 cm2 for previous studies) is used so that the positioning variables can be changed in large ranges. (4). Detailed geometrical relations are derived to track the flow for its cooling performance and flow flux. 2. Experimental method 2.1. Experimental setup The experimental setup used for conducting the tests of spray cooling is schematically shown in Fig. 1. It is composed of: (1) a pressurized water supply; (2) a full-cone spray nozzle attached to a positioning system; (3) a heater plate; (4) a high-speed camera for visualizing the spray; (5) an infrared camera for measuring the surface temperature. A high-pressure nitrogen cylinder is connected to a pressurized water tank at room temperature. The pressurized water is supplied to a full-cone spray nozzle (TG SS 0.3, Spraying Systems Company), which atomizes the water flow through an orifice with diameter of 0.51 mm. The volumetric flow rate of the spray, denoted by Q , ranges from 2.5 to 6.7 cm3/s. For the tested range of flow rate, the spray angle denoted by 2a ranges from 51° to 60°. The temperature of water denoted by T l , is measured using a calibrated T-type
thermocouple. The nozzle is attached to a positioning system to change the nozzle location and orientation. Parameters associated with the nozzle positioning will be discussed later in this section. The test surface is made of a silicon wafer (4 in. in diameter) with a thickness of t = 380 lm and thermal conductivity of k = 149 W/mK. The upper surface of the wafer is exposed to the spray, and is called impact surface. At the center of the lower surface, a square area with width W ¼ 23:5 mm is coated with gold. The gold-coated layer serves as a film heater, and its area Ah ¼ W W is called heater area. Between the silicon wafer and the gold layer are a dielectric layer and an adhesive layer. All the layers have a total thickness less than 2 lm, which has negligible resistance to heat conduction. The electrical resistance of the film heater is 1 O. A DC power supply (Model 62050P, Chroma) is connected to the heater, and the heater power is determined based on the electrical current and voltage drop. The coated area and the electrical connection are designed for achieving uniform current density throughout the gold layer. The average heat flux in the heater area, denoted by q00 , is calculated by dividing the heater power with the heater area, and ranges from 26.2 to 26.8 W/cm2. Based on the measurement uncertainties of voltage, current and heater area, the overall uncertainty of q00 is ±2%. A high-speed camera (M310, Vision Research) is used to observe the spray. An infrared (IR) camera (SC660, FLIR) is positioned
Fig. 1. Schematic of the experimental setup.
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underneath the silicon wafer to measure the temperature on the lower surface, denoted by T s . To increase the measurement accuracy, the lower surface of the silicon wafer is painted black to achieve a high emissivity of 0.95. The optical resolution of the IR images is 5.6 pixels/mm2, which provides detailed temperature distribution. Heat loss includes free air convection and radiation from the lower surface of the silicon wafer and also heat conduction through the electrical connections and the peripheral area (no gold coating) of the wafer. The heat losses through the electrical connections and the peripheral area are estimated based on the temperature gradients that can be obtained from the infrared images. In the present work, the heat transfer coefficient of spray cooling, denoted by h, is of the order of magnitude of 1 W=cm2 K. For most tests reported in the present work, the spray impingement is within the heater area, and the total heat loss is estimated to be 1% of the total heater power. Hence, the heat transfer coefficient in the heater area can be calculated using
h¼
q00 Ts Tl
ð1Þ
Here T s is not the temperature at the solid-fluid interface as it is measured from the lower surface. The heat conduction through the thickness of the silicon wafer is neglected as the Biot number ht=k < 0:1. Based on the uncertainty of q00 and the measurement uncertainties of T s and T l (DT s 0:5 C, and DT l 0:1 C), the overall uncertainty of h is ±3%. 2.2. Geometric relations of spray positioning The positioning stage for the spray nozzle can change the location of the nozzle vertically and horizontally. It also can adjust the nozzle orientation relative to the impact surface to achieve normal impact (see Fig. 2a) or inclined impact (see Fig. 2b). Similar to the 2D images shown in Fig. 2a and b, Fig. 2c shows a side-view schematic of spray impact. The nozzle positioning can be specified by the spray height H and the inclination angle h. In the present work, the spray is inclined by rotating the spray nozzle clockwise. The tested ranges of the two positioning variables are 5 mm 6 H 6 28 mm and 0 6 h 6 40 . In this 2D schematic, the length L covered by the spray is called impact length. The relation between the spray height, inclination angle, and impact length is expressed by
L¼
H sin a 1 1 þ cos h cosðh aÞ cosðh þ aÞ
ð2Þ
In Fig. 2, the viewed plane is the z x plane, normal to which is the y axis. Hence, the impact surface is on the x y plane. The footprint of the spray on the impact surface is called impact area, denoted by A. The impact area is circular for h ¼ 0 and elliptical for 0 < h < ð90 aÞ. For all the tests, the impact area, heater area, and impact surface are concentric, and the center is located at ðx; yÞ ¼ ð0; 0Þ. Fig. 3 shows three impact areas with equal impact length L = 20 mm but varied values of h within the square heater area with W = 23.5 mm. The circular impact area is formed by normal impact, i.e. h ¼ 0 , and, therefore, is referred to as the area of normal impact denoted by An . The line passing through vertex-1 and vertex-2 is the centerline of the heater area and impact area. For each impact area shown in Fig. 3, the spray height H can be calculated using Eq. (2). The geometric equation for plotting the impact area will be derived in Section 4. The spray is considered as a solid circular cone with apex angle 2a. The impact area is the cross section formed by intersecting the spray cone with the impact surface on the x y plane. The z x plane shown in Fig. 2c is the central plane of the spray cone per-
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pendicular to the impact surface. And the centerline shown in Fig. 3 is where the central plane intersects the impact surface. As shown in Fig. 2, there are two cross sections perpendicular to the axis of the conical body. One cross section, denoted by A0 , is perpendicular to the axis of the inclined conical body and contains vertex-1. Its distance to the nozzle orifice is
H0 ¼
H cos a cosðh aÞ
ð3Þ
Another cross section is perpendicular to the axis of the vertical conical body, and is actually the area of normal impact An (see Fig. 3). Its distance from the orifice, denoted by Hn , is
Hn ¼
L 2 tan a
ð4Þ
For normal spray impact to cover a given impact length L, Eq. (4) is the required spray height. The two cross sections follow ðA0 =An Þ ¼ ðH0 =Hn Þ2 . Substituting Eq. (2) into Eq. (4) gives Hn as a function of H and h, which is
Hn ¼
H cos a 1 1 þ 2 cos h cosðh aÞ cosðh þ aÞ
ð5Þ
For inclined spray impact with specific spray height and inclination angle, Eq. (5) is the normal spray height for covering the same impact length as the inclined impact. 3. Flow regions on spray-impacted surface Spray impacting a solid surface forms a liquid film flowing away from the impact area. If the flowing film is thin and has high velocity, the radially outward flowing film shows an abrupt increase of film thickness as shown in Fig. 4a. This is similar to the film flow formed by the impact of a liquid jet on a surface [21]. The phenomenon is referred to as hydraulic jump. Upstream from the hydraulic jump, the gravitational wave speed is lower than the flow velocity. As a result of the hydraulic jump, the flow velocity significantly drops and becomes lower than the gravitational wave speed. In case of normal spray impact as shown in Fig. 4a, the hydraulic jump is circular. Inclined spray impact results in noncircular hydraulic jump. As discussed above, there are three flow regions on the surface: impact area, thin-film region, and thick-film region. The heat transfer performance in the three regions varies due to different flow dynamics. In case of normal impact, the three regions can be quantified by the impact length L and the hydraulic jump diameter Dj as defined in Fig. 4a. According to Eq. (4), the diameter of the circular impact area can be calculated using L ¼ 2Hn tan a. The hydraulic jump diameter Dj is measured for the normal spray impact with varied flow rates Q and spray heights Hn , and the measurement in comparison with L are shown in Fig. 4b. The impact length slightly increases with increasing the flow rate due to the change of spray angle. The hydraulic diameter shows significant increase with increasing the flow rate. This indicates that the higher the spray flow rate the stronger the film flow. Fig. 4b also shows that Dj can be enlarged by increasing Hn due to the resulted increase of L. 4. Spray flux: inclined impact versus normal impact The impact area is where the spray flow impinges on the surface. Within the impact area, the volume flow rate per unit area is referred to as spray flux, i.e. Q 00 ¼ dQ =dA. As shown in Fig. 3, the overall spray flux must change with the inclination angle h due to the change of the impact area. To characterize the change of spray flux, one way is to compare the spray flux at a fixed ðx; yÞ location on the impact surface for different inclination angles. Here the
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Fig. 2. (a) Normal impact of spray (Q = 2.5 cm3/s); (b) inclined impact of spray cooling (Q = 5.0 cm3/s, h = 20°); (c) geometrically, the spray impact on a surface is a spray cone insected by a surface. The 2D geometry is on the central plane (z-x plane) of the cone perpendicular to the impacted surface (x-y plane). The positioning of the nozzle is determined by inclination angle h and spray height H. Hn is the required spray height by normal impact to cover a given impact length L. The impact area is shown in Fig. 3.
local spray flux is associated with the location on the impact surface. The other way is to track a specific part of the spray flow and compare its fluxes on the impact surface for different inclination angles. Here the local spray flux is associated with the spray flow. For example, suppose we could repeatedly track a train of spray droplets that fly in the same trajectory and one by one land at the same location on the impact surface. As a result of changing the angle h, the train of droplets would land at a different ðx; yÞ location, and the spray flux associated with the train of droplets would also change. In this section we will focus on the change of local spray flux associated with the spray flow as a result of inclination.
In the spray cone, the spray flow can be imagined as rays discharged from the nozzle orifice. In other words, it is assumed that spray droplets are constantly generated and maintain their trajectories until impacting the surface. Each ray can be specified by ðb; uÞ. As shown in Fig. 5, the polar angle b 2 ½0; a and the azimuthal angle u 2 ½0; 2p. The cone forms a solid angle equal to 2pð1 cos aÞ, within which the volume flow rate of the spray, Q , distributes. We introduce a solid angle 0 6 X 6 2pð1 cos aÞ. Hence, the distribution of the flow rate with respect to solid angle is dQ =dX. Based on visual observation of the spray and the measured temperature distribution in the impact area with normal spray impact,
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Fig. 3. Impact area with constant impact length L formed by the spray inclined at different angles h. The square 23.5 mm 23.5 mm represents the heater area. The impact area is concentric with the heater area. The centerline is the intersection line between the impact surface and the central plane of the spray perpendicular to the impact surface. An is the area of normal impact.
Fig. 5. (a) A small element of the spray flow that is specified by db, and du. (b) The perpendicular cross-section A0 that has been shown in Fig. 2c. (b) The impact area A that has been shown in Fig. 2c.
images in Fig. 2 show that close to the nozzle orifice the spray has fully atomized. Hence, dQ =dX is independent of the distance from the orifice. In summary, the flow rate distribution in the spray cone is a function of b only, i.e. dQ =dX ¼ f ðbÞ. Fig. 5 shows part of the spray cone. Consistent with Figs. 2c and 3, the impact surface is on the x - y plane, and the x - z plane is the central plane of the spray cone. The perpendicular cross section shown in Fig. 5b is the cross section A0 shown in Fig. 2c, and the azimuthal angle on the cross section is u. Hence, we can write
dX ¼ sin bdbdu
ð6Þ
The flow rate within the solid angle dX is dQ . On the cross section A0 , as shown by Fig. 5b, the radius r 0 is given by
r0 ¼
H cos a tan b cosðh aÞ
ð7Þ
A differential area on this cross section is
dr 0 db dA0 ¼ r 0 du db
ð8Þ
Combining Eqs. (6)–(8) gives
dA0 cos b ðr 0 = sin bÞ Fig. 4. (a) Spray impact on a large surface forms three regions: impact area, thinfilm region, and thick-film region. From the thin film region to the thick film region is the hydraulic jump. (b) The calculated impact lengths and measured hydraulic jump diameters for varied spray heights and flow rates.
it is reasonable to assume that the full-cone nozzle generates axisymmetric sprays, i.e. @ðdQ =dXÞ=@ u ¼ 0. Additionally, the
2
¼ dX
ð9Þ
The spray flux on this cross section, Q 000 ¼ dQ =dA0 , then can be expressed as
Q 000 ¼
dQ cos b dX ðr 0 = sin bÞ2
ð10Þ
Next we derive the spray flux in the impact area. As shown in Fig. 5c, the radius in the impact area is
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r¼
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H sin b cos h sin½b þ cos1 ðsin h cos /Þ
ð11Þ
where the angle / is the azimuthal angle in the impact area. From Fig. 5, it can be shown that the azimuthal angles on the perpendicular cross section A0 and impact area A satisfy
tan / ¼ cos h tan u
ð12Þ
Corresponding to u ¼ 0 and p, / ¼ 0 and p, which is the centerline of the impact area as defined in Fig. 3. The flow specified by ðb; uÞ in the spray cone lands on the impact surface at a location ðr; /Þ, and the two locations are connected by Eqs. (11) and (12). With b ¼ a, Eq. (11) becomes
R ¼ rðb ¼ aÞ ¼
H sin a cos h sin½a þ cos1 ðsin h cos /Þ
ð13Þ
Q 00 Q 00 Q 00 Q 00 ¼ 00 ¼ 00 000 Q ðh ¼ 0Þ Q n Q 0 Q n
ð21Þ
00
As shown in Fig. 2c, the spray fluxes on the two cross-sections A0 and An should follow
2 Q 000 Hn ¼ H0 Q 00n
ð22Þ
Putting Eqs. (20) and (22) into Eq. (21) yields
1 2 Q 00 r 20 du @r Hn ¼ H0 Q ðh ¼ 0Þ r sin b cos b d/ @b 00
ð23Þ
Substituting Eqs. (3), (5), (7), (11), and (18) into Eq. (23) gives
Eq. (13) is the equation used for plotting the impact areas in Fig. 3, where the center of the impact area is located at ðx; yÞ ¼ ð0; 0Þ. In the impact area, the relation between two coordinates systems ðr; /Þ and ðx; yÞ is
1 x ¼ r cos / þ ½Rð/ ¼ pÞ Rð/ ¼ 0Þ 2 y ¼ r sin /
Q 00 ðh ¼ 0Þ ¼ Q 00n ¼ dQ =dAn . The comparison between the inclined impact and normal impact can be written as
ð14Þ
Q 00 cos2 a cos h sin ½b þ cos1 ðsin h cos /Þ 00 ðh ¼ 0Þ ¼ 2 Q 4 cos4 bðcos2 h cos2 / þ sin /Þ 2
1 1 tan b cot½b þ cos1 ðsin h cos /Þ 2 1 1 þ cosðh aÞ cosðh þ aÞ
ð24Þ
In the present work, the location ðx; yÞ determined from the recorded IR images can be converted to ðr; /Þ using Eq. (14), which can be further converted to ðb; uÞ using Eqs. (11) and (12). The local cooling analysis that will be presented in Sections 5.1 and 6.1 focuses on the cooling along the centerline of the impact area (see Fig. 3). Here we use v to specifically denote the location along the centerline, which is
Combining Eqs. (24) and (12) gives Q 00 =Q 00 ðh ¼ 0Þ as a function of h, b, and u. The ratio of spray flux here shows the effect of inclination h on the spray flux of the flow located at ðb; uÞ in the spray cone.
v ¼ xð/ ¼ 0; pÞ
Most spray cooling applications rely on normal spray impact (h ¼ 0), for which the spray height Hn is the only positioning variable. By increasing or decreasing Hn , the impact area can be increased or reduced. In this section experimental results of normal impact with varied values of Hn will be analyzed to investigate the local cooling and global cooling of the heater area. The objective here is twofold. The first is to investigate how the cooling performance changes with the spray height. The second is to determine the optimal spray height that provides the most effective cooling for a given flow rate.
ð15Þ
Enclosed by the differential solid angle dX same as in Eq. (9), the differential element of the impact area is
dA ¼ rd/dr ¼ r
d/ @r du db du @b
ð16Þ
Combined with Eq. (6), Eq. (16) can be further written as
dA ¼
r d/ @r dX sin b du @b
ð17Þ
The derivative @r=@b can be obtained from Eq. (11). From Eq. (12), it can be readily shown that 2
d/ cos2 h cos2 / þ sin / cos h ¼ ¼ 2 2 du cos h cos h sin u þ cos2 u
ð18Þ
The flux in the impact area, Q 00 ¼ dQ =dA, is
Q 00 ¼
1 dQ r d/ @r dX sin b du @b
ð19Þ
Based on Eqs. (10) and (19), we can write
1 Q 00 r 20 du @r ¼ Q 000 r sin b cos b d/ @b
ð20Þ
Eq. (20) is the ratio of spray flux associated with the flow located at ðb; uÞ in the spray cone, and the flow has different fluxes on the impact surface and the cross section A0 . In real applications of spray-cooling a given surface, the impact length L usually is maintained constant for both normal impact and inclined impact. Hence, it is useful to compare the spray flux of inclined impact, Q 00 , to that of normal impact, Q 00 ðh ¼ 0Þ, when L remains unchanged. As shown in Fig. 3, the area of normal impact Aðh ¼ 0Þ ¼ An , and spray flux for normal impact is
5. Normal spray impact
5.1. Local cooling by normal spray impact A series of tests are conducted with a constant flow rate Q = 5.0 cm3/s and spray height ranging from 5.1 to 27.4 mm. The temperature along the centerline of the heater area is used to calculate the heat transfer coefficient using Eq. (1). The heat transfer coefficient along the centerline, denoted by hv , is plotted versus v 2 ½W=2; W=2 in Fig. 6, and v ¼ 0 is the concentric center of the heater and impact areas. The 2D symmetric profile of heat transfer coefficient indicates axisymmetric distribution, and v is the radial location for the axisymmetric distribution. From the center outward, the heat transfer coefficient first increases and then decreases. The distance between the two peaks is roughly equal to the impact length L that can be calculated using Eq. (4). In other words, the maximum local heat transfer coefficient appears at the edge of the impact area. Hence, within the impact area hv increases radially. Outside the impact area, i.e. in the thin-film region, hv decreases radially, as the flow in the thinfilm region slows down while flowing radially. Fig. 6 also shows that increasing the spray height reduces the cooling in the impact area. This can be explained by Eq. (22), which shows that the spray flux of normal impact is inversely proportional to H2n . As the spray height increases, the distribution of the
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Fig. 6. Local heat transfer coefficient along the center line of the heater area cooled by normal spray impact with Q ¼ 5:0 cm3/s.
heat transfer coefficient flattens. For Hn ¼ 27:4 mm, along the entire centerline of the heater area, the spray has covered the heater area, but provides cooling less effective than all the other cases. In addition to the distribution of local heat transfer coefficient shown in Fig. 6, it is also useful to evaluate the local areaaveraged cooling. Due to the axisymmetric cooling of normal spray impact and the assumption of uniform heat flux, the area-averaged heat transfer coefficient is defined as
hv ¼
2
v
2
1 Z v 1 vdv 0 hv
ð25Þ
Here hv is the average heat transfer coefficient for the circular area with radius v. To calculate hv based on the data shown in Fig. 6, we define and use a discrete form of Eq. (25), which is
hv1 ¼ hv1 " ! #1 i vj1 þ vj 2 X 1 1 1 hvi ¼ 2 þ Dv 2 vi j¼2 2 hvj1 hvj
ði P 2Þ
ð26Þ
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Fig. 7. The local heat transfer coefficient hv and local area-averaged heat transfer coefficient hv of normal spray impact with Hn ¼ 5.1 mm and Q ¼ 5:0 cm3/s. The radial gap distance, d, is between the edges of the circular impact area and the circular area with maximum average cooling.
of global cooling performance to the spray height for varied flow rates. The global cooling performance is evaluated using an average heat transfer coefficient
q00 h¼ Ts Tl
ð27Þ
where T s is the average of IR image of the heater area (3100 data points of T s ). Fig. 8 shows the global heat transfer coefficient versus the spray height for six different flow rates. Apparently, the higher the flow rate, the higher the heat transfer coefficient. However, this trend diminishes for large spray heights close to Hn = 28 mm when the impact area is already larger than the heater area. For each given flow rate, with increasing the spray height, the global cooling first
Here v1 ¼ 0 and vi ¼ ði 1ÞDv are the measurement locations shown in Fig. 6. The interval Dv ¼ 0:4 mm is determined by the resolution of the IR camera. Eq. (26) is used to calculate the area-averaged heat transfer for the test with Hn = 5.1 mm shown in Fig. 6. The local heat transfer coefficient hx and average heat transfer coefficient hv are plotted in Fig. 7. Similar to the trend of hv , hv first increases and then decreases. However, the location for maximum hv is after the location for maximum hv by a gap distance d. Therefore, for normal impact, the optimal area for achieving the most effective cooling is larger than the impact area. This implies that to cool a given surface effectively, the spray should cover less than the actual heater area. This finding is different from the previous study by Mudawar and Estes [18]. 5.2. Global cooling by normal spray impact Discussion above indicates that to cool a given area effectively, the impact area should be smaller than the heater area. Since the impact area for normal impact is solely dependent on the spray height, a series of tests are conducted to investigate the relation
Fig. 8. Heat transfer coefficient averaged over the heater area, h, versus the spray height, Hn , for varied flow rates, Q . For each flow rate, the peak point of the data curve shows the optimal spray height, Hn;max , for achieving the maximum average heat transfer coefficient, hmax . Within the shaded area are the tests with sprays covering beyond the heater area, i.e. L > W.
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face with the given flow rate. In Fig. 8, the optimal points are con-
Fig. 9. The optimal spray height of normal impact versus the flow rate for cooling the heater area. In the inset graph the radial gap distance d (defined in Fig. 7) shows the difference between the heater area and the optimal impact area.
increases and then decreases. Hence, for each given flow rate, there is maximum cooling, denoted by hmax , and the corresponding spray height, Hn;max , is the optimal spray height for cooling the given sur-
nected by a dashed line, which shows two trends: (1) hmax decreases with decreasing Q ; (2) Hmax increases with decreasing Q . In Fig. 8, the tests with their impact areas larger than the heat area, i.e. L > W, are indicated. All the tests show a decreasing trend of cooling performance with further increasing the impact area by increasing the spray height. Spray impingement outside the heater area could increase the heat loss to the periphery of the heater area, which would bring the actual cooling performance further down. Hence, the decreasing trend of cooling performance would be even more obvious if the heat loss could be taken into account. To further investigate the second trend, in addition to the six flow rates tested in Fig. 8, the optimal spray height Hn;max is determined for another four flow rates. All the data are presented in Fig. 9, which shows the optimal heights versus flow rates. The error bar is the difference between the determined Hn;max and its two neighboring tested spray heights. For all the cases, L < W. This indicates that for achieving the optimal cooling, the spray needs to cover less area than the heater area. Although the heater area is square rather than circular, the gap distance between the edges of the impact area and the heater area (see the inset of Fig. 9) can be approximated as the gap distance, d, defined in Fig. 7. Hence, the gap distance can be calculated using d ¼ ðW LÞ=2. In summary, Fig. 9 shows that to achieve the most effective cooling from an increased flow rate, the nozzle needs to be moved closer to the surface (Hn;max decreases) to reduce the impact area (d increases).
Fig. 10. Temperature distribution of the heater area cooled by inclined sprays (Q ¼ 5:0 cm3/s, L ¼ W = 23.5 mm): (a) h ¼ 20 ; (b) h ¼ 30 ; (c) h ¼ 40 . (d) Average heater transfer coefficient.
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Fig. 12. The local heat transfer coefficient shown in Fig. 11a is plotted versus the b location, and hb denotes the local heat transfer coefficient associated with the b location.
the left side. As h further increases, the cooler region on the right side continues to expand, and the temperature around the center decreases. The temperature in the heater area is averaged to obtain T s , and the global heat transfer coefficient h is calculated using Eq. (27) and plotted in Fig. 10d. The effect of inclination on global cooling can be evaluated by comparing with the normal impact (h ¼ 0 ), for which h ¼ 2:35 W/cm2K. The global cooling for h ¼ 20 is h ¼ 2:22 W/cm2K, showing negative effect of inclination. However, an opposite trend appears for further increased inclination angles h ¼ 30 and 40 , which result in h ¼ 2:79 and 3.01 W/cm2K, respectively.
Fig. 11. (a) Local heat transfer coefficient associated with the v location along the center line for h ¼ 0 ; 20 ; 30 ; 40 . The temperature contours have been shown in Fig. 10 except for h ¼ 0 . (b) The change of local cooling due to inclination is quantified by comparing the inclined impact to the normal impact.
6. Inclined spray impact For inclined spray impact, there are two positioning variables: H and h. Changing either variable would cause both the impact area A and impact length L to change. The focus of our study is on the effect of spray inclination on cooling performance. The experimental study is carried out by changing the angle h and maintaining a constant impact length equal to the width of the heater area, i.e. L ¼ W = 23.5 mm. As a result, the spray height H becomes a dependent variable, and it can be calculated using Eq. (2). As shown by Fig. 3, increasing h while maintaining L constant reduces the impact area A. As a result, the overall spray flux, Q =A, increases. 6.1. Global cooling by inclined spray impact Fig. 10 shows temperature distribution of inclined spray impact with inclination angles h ¼ 20 ; 30 and 40 with Q = 5.0 cm3/s. Consistent with Figs. 2 and 5, the inclination of spray is done by rotating the nozzle clockwise. The ellipses in dashed lines show the impact area. For h ¼ 20 , the temperature contour is close to being axisymmetric, but the right side is generally cooler than
6.2. Local cooling by inclined spray impact To better understand the effect of inclination on global cooling, we look into the local cooling. To simplify the analysis, we focus on the local cooling along the centerline of the impact area. The local heat transfer coefficient along the centerline hv is calculated using Eq. (1) and is plotted in Fig. 11a for the normal impact (h ¼ 0 ) and inclined impact (h ¼ 20 ; 30 , 40 ). For the normal impact, the distribution of hv is symmetric with respect to v ¼ 0, the center of the impact area. The inclination causes hv to increase on the right side (v > 0) and decrease on the left side (v < 0). Since the temperature is measured at the same v locations for all the cases, we can compare the local cooling of inclined impact with that of the normal impact. The comparison, hv =hv ðh ¼ 0 Þ, is plotted in Fig. 11b. For h ¼ 20 , slight enhancement appears only on the right side, whereas the left side shows diminished cooling. For h ¼ 30 and 40 , cooling enhancement increases and extends to the left side. Nevertheless, cooling diminishment still exists on the left side, the far end from the spray nozzle. The inclination affects local cooling in two mechanisms. One is related to the velocity direction of spray droplets. The velocity vector can be decomposed into a vertical component perpendicular to the surface and a horizontal component parallel to the surface. The vertical component determines the impact momentum of spray droplets, while the horizontal component affects the velocity of the flow on the surface. Increasing or decreasing either velocity component could enhance or diminish the cooling performance.
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The inclination must cause one velocity component to increase and the other one to decrease. However, it is difficult to determine the net effect on cooling. The other mechanism is related to local spray flux. The increase or decrease of local spray flux is expected to enhance or diminish local cooling. The analysis in this section is to relate the change of local spray flux to the change of local cooling. The change of local cooling associated with v location has been shown in Fig. 11b. However, the change of local spray flux associated with v location is unknown for the following reason. According to Eq. (15), as a result of changing h, the spray flow impacting any v location is replaced by new flow associated with a new value of b. The spray flow distribution dQ =dX ¼ f ðbÞ is unknown. The change of spray flux associated with ðb; uÞ has been derived in Section 4. The flow impacting the centerline of the impact area has b 2 ½0; a and u ¼ 0 and p. We will try to obtain the change of local cooling associated with the flow impacting the centerline. First, we convert the local heat transfer coefficient associated with v, hv , to the local heat transfer coefficient associated with b, hb , by converting the v locations in Fig. 11a to b locations. Here we will derive the equation that relates v to b. Eq. (15) relates v to b for given H and h, and is composed of v ¼ xð/ ¼ 0Þ and v ¼ xð/ ¼ pÞ for 0 6 b 6 a. From now on, if we define a 6 b 6 a, Eq. (15) then becomes v ¼ xð/ ¼ 0Þ, which can be fully written as
v¼
1 H sin a 1 1 H sin b þ 2 cos h cosðh þ aÞ cosðh aÞ cos h cosðh bÞ
ð28Þ
Here the angle a 6 b 6 a is on the central plane of the spray cone, which is orthogonal to the impact surface. Combining Eq. (2) with Eq. (28) gives
1 1 2 sin b þ cosðh þ aÞ cosðh aÞ sin a cosðh bÞ ¼ 1 1 L=2 þ cosðh þ aÞ cosðh aÞ
v
ð29Þ
Eq. (29) is used to convert the v location to b location, and the data of heat transfer coefficient in Fig. 11a, now denoted by hb , are plotted versus b in Fig. 12. The goal here is to analyze the change of hb due to inclination by comparing the cooling of inclined impact to that of normal impact, i.e. hb =hb ðh ¼ 0 Þ. However, the ratio cannot be calculated at this moment as in Fig. 12 the four cases have different b locations. To address this issue, linear interpolation is carried out based on the data shown in Fig. 12 to calculate hb for unified b locations for all the cases. The interpolated data are presented in Fig. 13a, where the data curves show no visible difference from those in Fig. 12. Based on Fig. 13a, the ratio hb =hb ðh ¼ 0 Þ is calculated and plotted in Fig. 13b. Fig. 13b shows the effect of inclination on the cooling performance of the flow, which distributes on the central plane of the spray. The trends for the three cases of inclined impact are similar. Generally, from b ¼ a to b ¼ a, the cooling enhancement first increases and then decreases. The enhancement peaks are within the angular space b > 0 , and the peak shifts slightly toward the left as h increases. The flow close to b ¼ a shows diminished cooling as a result of inclination. The incline impact with h ¼ 40 provides the highest cooling enhancement for most of the central plane flow. In Section 4, we have derived the change of local spray flux associated with the flow at ðb; uÞ as a function of h. The comparison of spray flux Q 00b =Q 00b ðh ¼ 0Þ along the centerline can be evaluated using Eq. (24) with input / ¼ 0; p. Similar to the derivation of Eq. h i (28), Q 00b =Q 00b ðh ¼ 0Þ can be changed to ½Q 00b =Q 00b ðh ¼ 0Þ/¼0 with /¼0;p
a 6 b 6 a, which can be written as
Fig. 13. (a) By applying interpolation to Fig. 12, hb is plotted versus the same b locations for all the cases of normal impact and inclined impact. (b) The ratio of local cooling of inclined impact to normal impact calculated from the interpolated data.
"
Q 00b
Q 00b ðh ¼ 0Þ
h
# ¼ /¼0
cos a cosðhbÞ 2 cos2 b
i2 h
1 cosðhþaÞ
1 þ cosðh aÞ
cos h½1 tan b tanðh bÞ
i2 ð30Þ
Eq. (30) is plotted in Fig. 14 for the three cases of incline spray impact. Now we have the change of local cooling shown in Fig. 13b and change of local spray flux shown in Fig. 14, both associated with the flow at b location on the central plane of the spray cone. Comparing Figs. 14 and 13b shows the following similarities between the local spray flux and the local cooling. (1) The inclination increases the spray flux for most of the central-plane flow, except for the flow close to b ¼ a where the spray flux decreases. The angular zones of b for the increase and decrease of spray flux (Fig. 14) are similar to the enhancement and diminishment zones of cooling (see Fig. 13d). (2) For the three cases, the larger the inclination angle, the more increase of spray flux (Fig. 14), and the more cooling enhancement (Fig. 13d), showing significant dependence on h.
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diminishment for small inclination angle and enhancement for large inclination angles. Based on the local cooling along the centerline of the impact area, the cooling performance of the flow on the central plane of the spray cone is tracked. The spray flux of the flow on the central plane is analyzed. The enhancement and diminishment of the cooling performance are found to be in general agreement with the increase and decrease of the spray flux. Acknowledgment The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for support. The authors also thank Mr. Yadi Cao for his assistance in conducting the experimental tests. Conflict of interest Authors declare that there is no conflict of interest. References Fig. 14. Corresponding to the local cooling analysis shown in Fig. 13, the ratio of local spray flux of inclined impact to normal impact is calculated using Eq. (30).
(3) Generally, spray flux decreases and cooling enhancement lessens as b changes from a to a. However, the flow at b ¼ a shows the maximum enhancement of spray flux, while the maximum cooling enhancement appears at b < a. The difference could be related to the change of velocity components, which is out of the scope of the present work. Depending on the location ðb; uÞ of the flow, the cooling performance of the flow can be enhanced or diminished by the inclination. One major reason is that the flux of the flow increases or decreases as a result of the inclination. Overall, Figs. 13d and 14 indicate the correlation between the change of local spray flux and the change of local cooling. 7. Conclusion Spray nozzle can be put closer to or farther from the impact surface to change the spray height, and it can be tilted to change the spray inclination. The spray height and inclination angle are the positioning variables tested in the present work. Spray impact is observed to form three regions on the impact surface: impact area, thin-film region, and thick-film region. For given spray height and inclination angle, the flow landing at a location ðx; yÞ in the impact area is located at ðb; uÞ in the spray cone. As a result of changing the nozzle positioning, the flow impacts a different ðx; yÞ location, and its spray flux also changes. The relation between ðx; yÞ and ðb; uÞ is derived. Equations are also derived for evaluating the change of spray flux as a function of the nozzle positioning and ðb; uÞ. Experimental tests of normal spray impact are conducted to investigate the effect of spray height. It is discovered that the optimal spray height providing the most effective cooling is smaller than the height required for covering the entire heater area. This is because the maximum local cooling is located at the edge of the impact area, and the film flow outside the impact area still provides effective cooling. It is found that the optimal height decreases with increasing the flow rate. The effect of inclination is studied by changing the inclination angle while maintaining the impact length constant and equal to the width of the heater area. The global cooling shows slight
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