Simultaneous multiple droplet impact and their interactions on a heated surface

Experimental Thermal and Fluid Science 120 (2021) 110255

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Simultaneous multiple droplet impact and their interactions on a heated surface Ahmet Gultekin a, b, *, Nejdet Erkan b, Erdal Ozdemir b, Uner Colak a, Shunichi Suzuki b a b

Istanbul Technical University, Energy Institute, 34469 Istanbul, Turkey Department of Nuclear Engineering and Management, The University of Tokyo, Tokyo, Japan

A R T I C L E I N F O

A B S T R A C T

Keywords Droplet impact Multiple droplet interactions Spray cooling Weber number

Multiple droplet impact on a heated sapphire glass is experimentally investigated to compare the hydrodynamic behavior of single and multiple droplet cases employing high-speed imaging techniques. Experiments are per­ formed for a wide range of surface temperatures (23 ◦ C – 350 ◦ C) and different Weber numbers. By using an image analysis software, the hydrodynamic behavior of the multiple droplets after the impact, uprising sheets and effective spreading areas are examined. Results indicate that, compared to a single droplet, the simultaneous impact of multiple droplets show rather different dynamics owing to the involved interaction phenomena. Be­ sides, it is found that horizontal spacing and Weber number have strong effects on the effective spreading area and uprising sheet. The higher uprising sheet means the less spreading area and the less heat transfer from the heated surface. Furthermore, it is observed that for a larger horizontal spacing between the droplets, liquid la­ mellas lose more energy because of viscous dissipation and this causes forming weaker and delayed uprising sheet. In addition, increasing surface temperature decreases viscosity of the liquid causing more instabilities at the uprising sheet. Subsequently, uprising sheet smashes into several small pieces earlier since relative molecular motion is easier with increasing temperature. This paper introduces one of the limited experimental studies for the simultaneous multiple droplet impact on the heated surface and provides real-time high quality images and data.

We = 1. Introduction The impingement of droplets on solid surfaces can be encountered in many areas such as ink-jet printing [1], spray coating [2-4], and spray cooling [5-9]. Droplet impact is particularly significant for spray cooling applications, where heat transfer from surfaces to droplets affects collision behavior. Droplet hot surface interactions contain highly complicated transport mechanisms which occur in a very short time and millimeter scales [10]. Therefore, it is critical to understand the phe­ nomenon of droplet impact on a heated wall. Comprehensive reviews about the recent studies on spray cooling and droplet impact on heated surfaces can be found in Ref. [11-13]. Bernardin et al. [14,15] pointed out that surface temperature (Ts) and the Weber number are the main factors governing impact behavior and heat transfer. The Weber number represents the ratio of droplet kinetic energy to surface tension and defined as

ρu20 Do σ

(1)

where ρ is the density of the liquid, u0 is the droplet velocity, D0 is the initial droplet diameter and σ is the surface tension for the fluid. Depending on the We and Ts, the droplet can show different impact regimes such as deposition, partial rebound, total rebound, break up, and break up with secondary atomization [16]. The magnitude of sur­ face temperature severely affects the heat transfer upon droplet impact. When Ts is below the saturation temperature of the liquid (Tsat), heat transfer is mostly controlled by heat conduction. If Ts exceeds Tsat, the droplet starts to boil on the surface, and tiny bubbles are composed in the droplet. These bubbles grow and coalesce. A thin vapor layer forms between the droplet and the surface if Ts exceeds the Leidenfrost point [17]. This vapor layer prevents the contact between the droplets in other words this layer causes poor heat transfer from the surface. In the literature, studies have mostly focused on single droplets, while those concerning multiple-droplet impacts are quite more limited [18-33]. In fact, real physical processes involve multiple droplets rather

* Corresponding author at: Istanbul Technical University, Energy Institute, 34469 Istanbul, Turkey. E-mail address: [email protected] (A. Gultekin). https://doi.org/10.1016/j.expthermflusci.2020.110255 Received 13 April 2020; Received in revised form 8 September 2020; Accepted 13 September 2020 Available online 19 September 2020 0894-1777/© 2020 Elsevier Inc. All rights reserved.

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Nomenclature A A C cp Do dh

spreading area (m2) non-dimensional spreading area Constant specific heat capacity at constant pressure (kJ/(kg K)) initial droplet diameter (mm) horizontal distance (mm)

dv Ds D E H H Hs Hs h hl

non-dimensional vertical distance spreading diameter (mm) non-dimensional spreading diameter total heat transfer (J) droplet height (mm) non-dimensional droplet height uprising sheet height (mm) non-dimensional uprising sheet height heat transfer coefficient thickness of lamella (mm)

dh dv

hl N q’’ T t u

u We Re

non-dimensional velocity Weber number Reynolds number

Greek Letters μ dynamic viscosity (Ns/m2) δ Uncertainty ρ density (kg/m3) σ surface tension (N/m) τ non-dimensional time θ contact angle η constant non-dimensional parameter ω constant non-dimensional parameter

non-dimensional horizontal distance vertical distance (mm)

Subscripts avg eff l ND r s sat SD

non-dimensional thickness of lamella number of droplets heat flux (W/m2) temperature (oC) time (s) velocity (m/s)

Average Effective Lamella number of droplets Rim Surface Saturation single Droplet

Abbreviations MAPE Mean Absolute Percentage Error VOF Volume of Fluid

because of the interaction of droplet pairs. They indicated that their analytical model has good agreement with the experimental results. Liang et al. [25] experimentally investigated droplet pair for simulta­ neous and non-simultaneous cases at room temperature. They have classified non-simultaneous cases into three main subcases according to the interaction types. They also emphasized that rising vertical spacing causes reduction in spreading area and central uprising sheet height because of increased viscous dissipation. Cossali et al. [26] performed experiments to observe the interaction after simultaneous droplet trio impact on the heated surface. They indicated that in the transition boiling regime growth and separation of vapor bubbles cause numerous small secondary droplets. In another study, Cossali et al. [27] investi­ gated the effects of wall material on secondary droplet atomization for multiple droplet impact onto heated surfaces. They indicated that impact morphology looks to be intensely influenced by wall material. Ersoy and Eslamian [28] experimentally investigated evolution of up­ rising sheet with time for simultaneous impact of double droplets with high Weber number onto dry and wet surfaces using liquids with different colors. They observed three different forms for the uprising sheet for double droplet impact onto dry surface. Batzdorf et al. [29] numerically studied heat transfer in both droplet and solid material during simultaneous droplet pair impact. They also developed a theo­ retical model to estimate the heat transfer between liquid and solid surface. Liang et al. [30] numerically investigated the simultaneous impact of multiple droplets on a liquid film without considering heat transfer process, using the couple level set and VOF. They emphasized that there is a need for further studies to understand the droplets impact on the surface with heat transfer mechanisms. Liang et al. numerically investigated single-phase [31] and two-phase [32] heat transfer behavior for multiple droplet impact on a liquid film. They indicated that the heat transfer coefficient in the impact area by multiple droplet impact on a liquid film was pretty higher than the unaffected film area. Wang et al. [33] numerically studied the heat transfer behavior with a simultaneous impact on a flowing liquid film. They demonstrated that the asymmetry becomes more significant and the heat transfer removal

than single isolated ones. The complexity of understanding of the physical process and modeling the spray-cooling phenomenon comes from its randomness and untraceable behavior of the droplets. Because of that, analysis of a simpler system with known number of droplets is required. Multiple droplet impact can simply be classified as successive impact, non-simultaneous impact and simultaneous impact. Fujimoto et al. [18,19] experimentally studied the successive impact of two droplets with normal and oblique surfaces for a wide range of temper­ atures and low Weber numbers using high-resolution cameras. They stated that there is a relationship between the evaporation duration of the droplets and the equivalent Weber number. Guggilla et al. [20] numerically investigated drop on drop collisions on hot surfaces, which is one of the basic processes in spray cooling applications by using Volume of Fluid (VOF) method. The hydrodynamic behavior and evaporation dynamics of drop-on-drop impact is compared to a single droplet impact on the heated surface. The results reveal that the spread factor is higher compared with a single droplet impact. Li et al. [21] numerically investigated the impact of droplet pairs with a horizontal distance and vertical distance on liquid film using a simplified lattice Boltzmann method. They indicated that nonsimultaneous droplets would cause asymmetry by changing the upris­ ing sheet direction and height. Soriano et al. [22] studied the effects of single and multiple periodic droplet train impacts on liquid film heat transfer. They stated that spacing between adjacent impinging droplets is also an important factor in surface cooling when multiple droplets are used. Zhang et al. [23] experimentally investigated the heat transfer and hydrodynamics of multiple droplet train (double, triple and hexagonally arranged) impinging a pre-wetted solid surface. They examined the ef­ fects of Weber number, spacing, and impingement pattern on liquid film hydrodynamics and heat transfer using high-speed camera and IR thermal imaging techniques. They indicated that spacing and impinge­ ment pattern play important roles in cooling performance concerning the minimum temperature in the surface. Roisman et al. [24] experi­ mentally studied on droplet pair impact on isothermal surfaces. They also developed an analytical model to describe the uprising sheet 2

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in the impact region is more notable for a narrow spacing between the droplets. In the case of single droplet, after the impact on the surface droplet spreads and a circular liquid lamella occurs. The total heat transfer at the droplet-heated surface interaction can be calculated by taking the in­ tegral of the heat transfer rate regarding time and the spreading area. q’’ (t) = h(Ts (t) − Tliq (t)) ∫ t ∫∫ q’’ (t)dAdt

ESD = 0

2. Experimental methodology 2.1. Experimental setup Schematic diagram of the experimental setup is given in Fig. 1. The experimental setup consists of three main systems. These are droplet generator and control system, temperature controlled hot plate, visual­ ization and data acquisition system. Droplet generator and control sys­ tem have been developed to achieve simultaneous multiple droplet production. The system consists of a syringe pump, signal generator, speaker, piston and needles. The capillary tubes were attached to the outlets of the syringes separately. Needles were siliconized at the end of these capillary tubes and mounted to the piston with the same distance from each other. It is adjustable to change the number of needles and the distance between them. The flow rate and continuity of the fluid were supplied to the system using a syringe pump (KD Scientific KDS210). Besides, a signal generator system (Quantum Composers 9600) was connected to the speaker using an electronic circuit. Depending on the mode and frequency received from the signal generator, the loudspeaker can apply pressure at different intensities. When the droplets reach a certain size, for simultaneous breaking of the droplets from the tip of the needles, 100 kHz frequency and single mode signal was applied. Temperature controlled test plate system is composed of a copper block, insulation material, cartridge heaters, thermocouple, tempera­ ture controller, and sapphire glass. A copper block with six holes on both sides was manufactured and 12 cartridge heaters (200 V, 1.25 A 250 W) were installed in the holes on the sides. The maximum operating tem­ peratures of cartridge heaters are 871 ◦ C. The temperature of the heated surface is controlled by a temperature controller integrated with a calibrated thermocouple type K, which is fixed on the top of the sapphire glass using high temperature tape. The temperature controller activates the cartridge heaters with data from the thermocouple. In this way, the desired temperature on the surface of sapphire glass was provided. Maximum absolute uncertainty value is 1.5 ◦ C for the thermocouple. In addition, to make sure of the temperature of the sapphire glass is correct; digital pocket thermometer Yokogawa TX10 is used. A circular hole (20 mm-diameter) in the center of the copper block was provided to visu­ alize the interaction of the droplets on the surface under the sapphire glass. Sapphire glass surface was preferred because of its transparent and high thermal conductivity. Synchronized two high-speed cameras (Photron Fastcam SA5 and Fastcam Mini) that was capable of capturing images at a speed 20,000 frames per second have been used to record the dynamic shape change of droplets during the interaction. Using the synchronized cameras, the

(2) (3)

However, after the multiple droplets impact onto a solid surface, the interaction phenomenon can take place if the droplets are sufficiently close to each other depending on their impact parameters. Because of this interaction, the hydrodynamic and heat transfer behaviors of the droplets are quite different from single droplet cases. This interaction phenomenon leads to uprising sheets which leads to smaller spreading area per droplet on the heated surface. The total heat transfer for the multiple droplet interaction with the heated surface can be calculated the same as in Eq. (3). ∫ t ∫∫ END = (4) q’’ (t)dAeff dt 0

As seen from the Eq. (4), effective spreading area directly affects the total heat transfer from the heated surface. Effective spreading area depends on the impact conditions of droplets and number of droplets as well as horizontal distance between the impinging droplets. As mentioned above, multiple droplet interactions during simulta­ neous impacts affect the heat transfer extensively. In order to design an efficient spray cooling system, analysis of a simpler system with known number of droplets is required. For this purpose, a droplet generator and control system has been developed for simultaneous multiple droplet generation. In this study, we investigated the effects of Weber number, surface temperature and horizontal droplet spacing on hydrodynamics behavior and effective spreading area for simultaneous multiple drop­ lets. These hydrodynamic parameters have ultimate importance for the effective heat transfer. To comprehend the interaction between droplets experiments with high spatial and temporal resolutions have been performed.

Fig. 1. Schematic diagram of the experimental setup. 3

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droplets were displayed in the bottom and side direction after the impact. Fastcam cameras use an advanced CMOS image sensor opti­ mized for light sensitivity. CMOS sensors used in Fastcam are supplied without an IR absorbing filter, extending the camera spectral response up to 1000 nm. The backlight source is used in the experiments for the shadowgraph method. The type of light source in the experimental setup was an infrared led lamp with 940 nm wavelength, which is suitable for the experiments. The liquid used in the droplet production was distilled and nondegassed water. Non-degassed water was used to investigate the droplet-heated surface interactions under the realistic conditions. The physical properties of distilled water are given in Table 1. The experi­ ments were performed on a surface for a wide range of heated surface temperatures (23 ◦ C-350 ◦ C) under atmospheric conditions. The droplet generator was placed vertically up from the heated surface with a known distance. By changing this distance, the impact velocity of droplets can be changed. Droplets impact on the heated surface with the velocities of 0.79–1.93 m/s. It should be stated that it is technically too difficult to control accurately the dynamic impact conditions of multiple droplets (droplet diameters, droplet velocities and the distance between multiple drop­ lets) for all experiments. The reported values represent only one case, as far as possible, we tried to select simultaneous case. For any given case, droplets are almost simultaneous and similar in size, however, they are not always identical. The circularity ratio of droplets varies between 0.89 and 0.92 and average droplet diameter in this study is 2.27 ± 0.05 mm.

Effective spreading area is also determined using standard image conversion operations (binary image conversion followed by edge and region identification) as shown in Fig. 3. Secondary droplets are elimi­ nated adjusting minimum object size. 2.3. Uncertainty analysis The measuring errors in this study mainly involve measurement of the surface temperature and impact conditions of droplets. The tem­ perature of sapphire glass is measured with K type thermocouple and maximum absolute uncertainty value is 1.5 ◦ C. Uncertainty in pixel analysis in image processing is 1 pixel, corresponding to a 0.02 mm and 0.05 mm errors for side view and bottom view, respectively. By exam­ ining the last 10 frames before each droplet hits the surface, the impact velocity of the droplets calculated using consecutive two images, with an accuracy ranges from ± 0.03 to ± 0.05 m/s for different cases. Uncer­ tainty of impact Weber number can be calculated as √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ )2 ( )2 ( δWe δ D0 δu (8) + 2 0 = We D0 u0 which ranges from 3.52% to 5.28%. 3. Results and discussion By using an image analysis software, droplet height (H), spreading diameter (Ds), uprising sheet (Hs), center to center horizontal spacing (dh) and vertical spacing (dv) between droplets, effective spreading area (A) after the impact are examined. These parameters nondimensionalized using initial average droplet diameter and number of

2.2. Image Post-processing From the shadowgraph images, droplet diameter, droplet velocity, the variation of effective spreading area and the creation of an uprising sheet can be obtained by pixel analyzing and calibration is performed using a ruler. A Java based open source image program (ImageJ) [34] is used for the post-processing of shadowgraph images, as shown in Fig. 2. Droplets are made more prominent by background subtraction. After that, droplet images were converted to an 8 bit black and white image using Otsu method [35] which is one of the available option in ImageJ to determine threshold. In addition, fill holes filter was used to eliminate the white gaps typically located inside the droplets. Sometimes, tiny objects can occur in the transformed image because of any processing errors, this objects can be eliminated adjusting minimum object size to get only the main droplets detail. Equivalent initial droplet diameter can be calculated as follows √̅̅̅̅̅̅̅̅̅̅ Area D0 = 2 (5)

droplets (N), H =

ASD , D0,avg 2

(6)

The impact velocity of the droplets can easily be found by dividing the change in the position of the droplets in the vertical direction by the time difference between the consecutive images. y3 − y1 Δt

(7)

Table 1 Physical properties of the distilled water used in the study, at 23 ◦ C. Properties

Unit

Value

Saturation temperature, Tsat Density, ρ Dynamic viscosity, μ Surface tension, σ Specific heat capacity, cp

[◦ C] [kg/m3] [Ns/m2] [N/m] [kJ/(kg K)]

100 998 0.001 0.0725 4.18

D =

Ds D0,avg ,

dh s Hs = DH0,avg , dh = D0,avg , dv =

dv D0,avg ,

ASD =

Non-dimensional time is used in the present study, and

droplet diameter and droplet velocity, respectively. Fig. 4 shows the impact of a single and multiple droplets on the sapphire glass at 23 ◦ C when Weber number is around 115 for different dimensionless time intervals and the impact conditions of droplets are given in Table 2. In the case of single droplet, after the impact on the surface a circular liquid lamella occurs and spreads radially while the droplet height declines constantly with non-dimensional time up to τ≈2. The rim of the liquid lamella rolls owing to the surface tension (τ≈3). Subsequently, the liquid lamella starts to recoil from the rim in the di­ rection of the center. Then, an upward increase starts in the center after τ ≈ 10. In the cases of Fig. 4(b) and (c), after the impact of the multiple droplets to the surface, droplets spread on the sapphire glass like a single droplet case until a certain time (τ≈0.5). At some point, the liquid la­ mellas interact each other. The interaction of the flow in the middle areas lead to a unique phenomenon which is called uprising sheet. This formation of uprising sheet is a characteristic feature of multiple droplet interaction and occurs at sufficiently high We numbers and small hori­ zontal spacing. In other words, it is required to have high kinetic energy at the contact point of droplets. With increasing non-dimensional time further, the uprising sheet height constantly increases (τ≈2), and then, it starts to decrease under gravitation and loses its stability at some point (τ≈3). When uprising sheet withdraws to the surface, two cusps can be seen at the two ends of the uprising sheet, as seen in Fig. 4(c) at τ≈5. On the other hand, the other side of the rim continue to spread without being affected by the interaction (τ≈7.5). Similar recoiling behavior take place as in the case of single droplet. The amount of spreading area determines the contact area between the liquid lamella and the heated surface, therefore it is a significant parameter that affects heat transfer during spray cooling. This value is highly related with the initial kinetic energy of the droplet collision and energy losses due to the viscous dissipation. In the case of single droplet, after the impact on the surface droplet spreads and a circular liquid

Horizontal and vertical distance between multiple droplets can be found using the coordinates of each droplet center as follows

u0 =

H Do,avg ,

τ is defined as (τ = t Du0o ) where t, D0 and u0 denote physical time, initial

π

dh = x2 − x1 , dv = y2 − y1

A =

Atotal . ND0,avg 2

4

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Fig. 2. Image post-processing steps a) original image b) binarized image c) area and edge recognition.

Fig. 3. Image post-processing to determine effective spreading area a) original image b) binarized image c) area and edge recognition.

(a) Single Droplet

τ 0

(bn) Droplet Pair

(c) Droplet Trio

1 2 3 5 7.5 10

Fig. 4. Single and multiple droplet impact on the surface at Ts = 23 ◦ C.

lamella occurs. Roisman et al. [24] have proposed the following equa­ tion for the motion of rim for a single droplet. ( )2 dur 12Rr 1 − cosθ 6ur sinθ − ] (9) = [h u − u − l l r 2 We Re(1 − cosθ) dτ 1 − 6Rr hl

Table 2 The impact conditions of droplets at Ts = 23 ◦ C. Parameters

Single Droplet

Droplet Pair

Droplet trio

Droplet diameter [mm] Droplet velocity [m/s] We

2.30

2.32

2.28

2.32

2.27

2.24

dh

1.92 118 –

1.90 116 1.80

1.90 114

1.90 116 1.63

1.89 113 1.58

1.90 112

dv

0.03

0.04

–

0.03

θ

105◦

103◦

106◦

ω

0.277

0.270

0.268

η

0.151

0.152

τ0

–

0.37

where the angle θ is the average value of the advancing contact angle, advancing contact angles were measured using ImageJ for each case. The spreading radius, Rr , in the ordinary differential Eq. (9) can be solved numerically using the below equations hl =

0.151 0.37

η (τ + ω)2

and ul =

R (τ + ω)

(10)

where ω and η constant non-dimensional parameters which are deter­ mined using the initial conditions. The details of the theoretical model are given in their study. Also, several empirical correlations have been proposed to determine the maximum spreading diameter for a single droplet [36-39]. A comparison of our experimental results with the numerical results reproduced from Eq. (9) for the variation of dimen­ sionless spreading diameter with non-dimensional time is given in Fig. 5.

0.37

5

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⎛ ) ( 2*(N − 1) ⎝ − 1 dh ⎣ A(τ) = πR (τ) 1 − cos πN 2R(τ) ⎞ ⎤ √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ dh 2 dh 4 ⎠⎦ − ( ) − ( ) 2R(τ) 2R(τ) ⎡

2

where dh is non-dimensional center to center horizontal spacing. As can be seen from the Eq. (13), effective spreading area depends on the impact conditions of droplets and number of droplets as well as hori­ zontal distance between the impinging droplets. After the interaction, multiple droplet cases cover less area compared with a single droplet case and these values decreases with increasing the uprising sheet height, this situation can be seen clearly in Fig. 7. Eventually, the nondimensional spreading area equilibrates to a similar value with decreasing the uprising sheet height. Roisman et al. [21] have proposed the following equation to estimate the variation of uprising sheet height with non-dimensional time for simultaneous droplet pair interaction. ( )] [ dh τ+ω (τ − τ0 )(τ + τ0 + 2ω) Hs (τ) = exp − (14) − 1+ √̅̅̅̅̅̅̅̅̅̅ τ0 + τ 2 dh η.We

Fig. 5. Variation of non-dimensional spreading diameter for a single droplet. Symbols represent the experimental data while the solid curve represents Eq. (9).

It is clear that experimental and numerical results are in good agree­ ment. Spreading diameter reaches the maximum value at τ≈2.5, and is approximately 3.6 times as high as the initial droplet diameter. If we assume an ideal condition for spray cooling where there is no interaction, each droplet spreads like a single droplet so total spreading area goes to the multiplication of spreading area for a single droplet with number of droplets, N. However, after the multiple droplet impact onto a solid surface, the interaction phenomenon can take place if the droplets are sufficiently close to each other depending on their impact parame­ ters. Therefore, it is possible to propose the following expression to predict the effective spreading area for simultaneous multiple droplet impact onto solid surface AND = NASD − (N − 1)Ai

(13)

where τ is the non-dimensional time and τ0 is the first interaction time which is determined from the shadowgraph images. Fig. 8 shows the comparison of experimental data with the theory for the variation of uprising sheet height with non-dimensional time. As can be seen from the figure, the experimental observations do not exactly match with the theoretical results. While the theoretical uprising sheet begins to decline right after the maximum height, the uprising sheet begins to decline under gravitation in some experimental cases, then, it stagnates and becomes stable in a short period. After that the uprising sheet loses its stability at some point and shows a three-dimensional characteristic which produces cusp and finger formation at the rim of the uprising sheet, similar observations have been seen in Refs. [25,28]. As a result, cusp formations and instabilities increase the period it takes for the uprising sheet to disappear completely.

(11)

where N is number of droplets, ASD is the spreading area for single droplet and Ai is the area loss because of the interaction. If we assume the physical properties of droplets are same and spreading liquid la­ mellas are circle shape as shown in Fig. 6, then the interaction area Ai can be calculated simply from the geometry as √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ( ) dh dh dh Ai = 2[r2 cos− 1 (12) − r2 − ( )2 ] 2r 2 2

3.1. Effects of horizontal spacing One of the most important factors which affect the size of droplet interaction is the droplet spacing. Droplet pair impact on the surface for different horizontal spacing is given in Fig. 9 and the impact conditions of droplets are given in Table 3. The interaction in the middle area earlier leads to an uprising sheet height for shorter distance case. For the wider distance between the droplets, a delay in the creation of uprising

The non-dimensional spreading area per droplet number can be written with the help of Eq. (9), Eq. (10), Eq. (11) and Eq. (12) in the form

Fig. 7. Variation of non-dimensional spreading area for single and multiple droplets with time at Ts = 23 ◦ C. Symbols represent the experimental data while the solid curves represent Eq. (13).

Fig. 6. Sketch of liquid lamellas for simultaneous droplet pair. 6

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height increases due to the larger initial kinetic energy of the droplets in other cases. For highest Weber number case, there is a slight slope in the uprising sheet because of the vertical distance is significant. This is due to the second lamella has more energy because of less energy dissipa­ tion. To examine quantitatively, the effect of Weber number on the size of interaction, variations of dimensionless uprising sheet heights were measured and the results are given in the Fig. 12. It is clearly seen that the uprising sheet is the largest for the case of We = 118. The dimen­ sionless uprising sheet reaches the highest point at when τ≈2.8, and it is approximately 1.4 times as high as the initial droplet diameter. After this point, owing to continuous expansion with constant liquid mass, the Table 3 The impact conditions of droplets for different horizontal spacing at Ts = 145 ◦ C. Fig. 8. Variation of non-dimensional uprising sheet height with time for droplet pair at Ts = 23 ◦ C. Symbols represent the experimental data while the solid curve represents Eq. (14).

Parameters

dh = 1.45

sheet is observed while the spreading area increases. In other words, liquid lamellas will lose more energy because of viscous dissipation and that will cause a weaker uprising sheet. To examine quantitatively, the effect of the horizontal spacing on the size of interaction, variations of dimensionless uprising sheet heights were measured for different hori­ zontal spacing. The results are given in the Fig. 10. It is seen that the creation and magnitude of the uprising sheet dependency becomes more significant in case of shorter droplet spacing. In other words, the higher the uprising sheet, the less spreading area and the less heat transfer from the heated surface The dimensionless uprising sheets reach the highest point at when τ≈1.4, τ≈2.0, τ≈1.5 and they are approximately 0.88, 0.74, 0.35 times as high as the initial droplet diameter in case of dh =

Droplet diameter [mm] Droplet velocity [m/s] We

dh

2.30 1.28 52 1.45

dv

dh = 1.80 2.22 1.30 52

2.27 1.30 53 1.80

dh = 2.15 2.32 1.28 53

2.22 1.30 52 2.15

0.07

0.01

θ

74o

71o

73o

ω

0.147

0.150

0.247

η

0.145

0.144

0.147

τ0

0.29

0.44

0.62

2.32 1.28 53

0.08

1.45, dh = 1.80, dh = 2.15 horizontal spacing respectively.

3.2. Effects of Weber number When the surface temperature is at 145 ◦ C, the behaviors of droplets for different Weber numbers are given in Fig. 11 and the impact con­ ditions of droplets are given in Table 4. In the case of lowest Weber number, after the impact on the heated surface liquid lamella occurs and spreads. After τ ≈ 0.5 the interaction in the middle area leads to the smallest uprising sheet height due to the least initial kinetic energy provide by the droplets. With increasing non-dimensional time further, the uprising sheet height constantly increases up to τ≈1.6, then it starts to decrease up to τ≈2.5. As the Weber number increases, the impact behavior also shows a similar way but the magnitude of uprising sheet

τ 0

(a)

1.45

Fig. 10. Variation of non-dimension al uprising sheet height for droplet pair for different horizontal spacing at Ts = 145 ◦ C. Symbols represent the experimental data while the solid curves represent Eq. (14).

(b)

1.80

(c)

0.5 1 2 3

Fig. 9. Droplet pair impact on the surface for different horizontal spacing at Ts = 145 ◦ C. 7

2.15

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Experimental Thermal and Fluid Science 120 (2021) 110255

(a) We=28

τ

(b) We=53

(c) We=118

0 0.5 1 2 3 Fig. 11. Droplet pair impact on the surface at 145 ◦ C for different Weber numbers.

3.3. Effects of high surface temperature

Table 4 The impact conditions of droplets for different We at Ts = 145 ◦ C. Parameters

We = 28

Droplet diameter [mm] Droplet velocity [m/s] We

2.27 0.94 28 1.81

dh

We = 53 2.32 0.93 28

2.27 1.30 53 1.80

2.32 1.28 53

2.32 1.91 117 1.77

0.02

0.01

θ

62o

71o

107o

ω

0.259

0.150

0.273

η

0.141

0.144

0.152

τ0

0.45

0.44

0.42

dv

3.3.1. Single and multiple droplet impact on the surface at 185 ◦ C When the surface temperature is increased at 185 ◦ C, the behaviors of droplets (side view and bottom view) are given in Fig. 13 and the impact conditions of droplets are given in Table 5. In the case of a single droplet, droplet impacts on the surface and then change form into a circular liquid lamella (τ≈2). The growth and explosion of vapor bub­ bles in the boiling process produce several small secondary droplets occur and scatter around randomly up to τ≈5. The dynamics of vapor bubble growth throughout spreading, are affected by the flow in the liquid lamella, and by the pressure change during the droplet collision. Afterward, the liquid lamella starts to recede from the rim in the di­ rection of the center. Secondary droplets accompany during the receding process of lamella up to τ≈10. Finally, the droplet rebound from the surface after τ≈10. In the case of multiple droplet, the impact behavior also shows a similar way up to τ≈0.5. While the droplets are spreading on the surface the interaction starts to produce uprising sheets up to τ≈2, then the uprising sheet loses its stability at some point and produce some cusp and finger formations at the rim of the uprising sheet. The growth and explosion of vapor bubbles in the boiling process produce numerous tiny secondary droplets in addition to the uprising sheets up to τ≈3. The uprising sheets break-up into relatively large droplets at τ≈5 under the influence of surface tension force and explosion of vapor bubbles. In a similar way, the liquid lamella starts to recede from the rim in the direction of the center τ≈10. However, the rebound process could not be observed for multiple droplet cases up to τ≈20. No significant difference in hydrodynamic behavior was observed between droplet pair and droplet trio interactions.

We = 118 2.30 1.92 118

0.08

3.3.2. Single and droplet pair impact with low We number in film boiling regime When a droplet with low Weber number impacts on a heated surface above the Leidenfrost temperature, droplet spreads onto vapor layer and then rebound. Fig. 14 shows single, simultaneous and non-simultaneous droplet pair interactions with the surface temperature at 300 ◦ C and the impact conditions of droplets are given in Table 6. In the film boiling, the maximum spreading factor and droplet resi­ dence time for single droplet are investigated by many researcher. In several research [40-43], the maximum spreading factor for a single droplet in film boiling regime is calculated roughly by the following expression

Fig. 12. Variation of non-dimensional uprising sheet for droplet pair for different We at Ts = 145 ◦ C. Symbols represent the experimental data while the solid curves represent Eq. (14).

uprising sheet loses its stability and breaking away takes place. For the lowest Weber number, the dimensionless uprising sheet reaches the highest point when τ≈1.5, and it is approximately 0.3 times as high as the initial droplet diameter, then it starts to decrease. The magnitude of the uprising sheet strongly connected with We number and horizontal spacing between the droplets. Additionally, it is obvious that the maximum spreading area increases with the increasing impact kinetic energy, which allows the liquid lamella to spread more.

Dmax = CWea

(15)

Liang et al. [43] used following empirical correlation to determine 8

A. Gultekin et al.

τ

Experimental Thermal and Fluid Science 120 (2021) 110255

(a) Single Droplet

(b) Droplet Pair

(c) Droplet Trio

τ

0

(a) Single Droplet

(b) Simultaneous Droplet Pair

(b) Non-simultaneous Droplet Pair

0.5

1

1

2

3

2

4

5

Fig. 14. Single and droplet pair with low We impact on the surface at 300 ◦ C.

3

Table 6 The impact conditions of droplets at Ts = 300 ◦ C. 5

10

Parameters

Single Droplet

Simultaneous Droplet Pair

Nonsimultaneous Droplet Pair

Droplet diameter [mm] Droplet velocity [m/s] We dh

2.32 0.79 20 –

2.28 0.79 20 1.68

2.30 0.80 20 1.76

dv

–

0.02

tr = C 20

Table 5 The impact conditions of droplets at Ts = 185 ◦ C. Single Droplet

Droplet Pair

Droplet Trio

Droplet diameter [mm] Droplet velocity [m/s] We

dh

2.30 1.88 113 –

2.27 1.93 117 1.70

2.27 1.92 116 1.70

2.32 1.89 116 1.71

dv

–

0.07

0.01

0.02

2.28 1.90 114

σ

2.22 0.79 19

0.37

(17)

where C is a constant. Fig. 15 shows the comparison of the nondimensional droplet residence time in the film boiling regime between the experimental data and the estimated results from existing correla­ tions. The result of correlation by Biance et al. [41] are pretty close to our experimental data. The mean absolute percentage error (MAPE) values of the empirical correlations are given in Table 7. In our experimental results, single droplet rebound from the heated surface around τ ≈ 4.12 and the result of correlation by Biance et al. [41] is τ = 4.19. Although the results are pretty close to each other, the correlation a little overestimates the residence time. Interestingly, it is

Fig. 13. Single and multiple droplet impact on the surface at 185 ◦ C.

Parameters

√̅̅̅̅̅̅̅̅ ρD3o

2.22 0.80 20

2.30 1.92 118

the maximum spreading factor Dmax = 0.788We0.306

(16)

For our results, the maximum spreading factor is 2.04 and the pre­ diction from Eq. (16) is 1.97. It is clear that experimental and empirical results are in good agreement. As expected, due to the interaction in droplet pairs, the maximum spreading area per droplet is lower than the single droplet maximum spreading factor. A short period of time between the droplet’s first contact of the heated surface and the moment it leaves the heated surface is called the residence time. Generally, the residence time is calculated roughly by the following expression in the literature [41,43-45]

Fig.15. Comparison of single droplet residence time between the experimental data and the predictions from existing correlations. 9

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Experimental Thermal and Fluid Science 120 (2021) 110255

Table 7 MAPE values of some correlations in the literature for droplet residence time. Reference

Liquids

MAPE, %

Parameters

Single Droplet

Droplet Pair

Droplet Trio

Tran et al. [18]

τr = 0.785We

0.5

Water

14.02

Hatta et al. [19]

τr = 1.25We0.37

Water

13.87

Liang et al. [20]

τr = 1.032We0.494

Water, butanol and ethanol

11.14

Droplet diameter [mm] Droplet velocity [m/s] We dh

2.28 1.89 113 –

2.25 1.90 113 1.78

2.25 1.92 115 1.78

2.25 1.92 115 1.67

dv

–

0

0.03

0.01

Biance et al. [21]

Correlation

Table 8 The impact conditions of droplets at Ts = 350 ◦ C.

τr = 0.937We

0.5

Water

4.36

observed that in the case of a droplet pair, the rebound phenomena takes place earlier (τ ≈ 3.83) comparing with single droplet case. This is most likely due to less spreading area per droplet because of the droplet interaction. For non-simultaneous case, rebound takes place τ ≈ 3.99 and this value is between single droplet and simultaneous droplet pair cases. This situation may be due to the non-simultaneous droplet pair spreads more on the surface than the simultaneous droplet pair.

2.30 1.92 118

2.25 1.92 115

droplet deformation mechanism is described as follows: Before the droplet impact to the heated surface, the droplet is heated by radiation when it comes near to the surface. Nevertheless, the amount of radiation is insignificant and the amount of evaporation is not adequate to create vapor film between the droplet and the heated surface. In contact, the temperature difference between the droplet and the surface cause a great amount of convective heat transfer. The contact area temperature reduces immediately when heating the liquid close to the surface. The generation of vapor bubbles occurs at the contact area due to boiling. The vapor bubbles are separated from the surface, rising in the liquid by the buoyancy force and eventually released into the environment. This bubble movement results in the generation and scattering of a many secondary droplets. Eventually, all the liquid parts are separated from the surface. In the case of multiple droplets, the impact behavior also shows a similar way up to τ ≈ 0.5. After this point the interaction of the flow in the middle area leads to an uprising sheet. With increasing nondimensional time further, the uprising sheet height constantly increases with secondary droplets up to τ≈2. Increasing surface temperature de­ creases viscosity of the liquid, that causes more instabilities at the up­ rising sheet and produces cusp and finger formations in shorter time. Also, it allows the liquid to move away from the heated surface as the relative molecular movement is easier. The liquid lamella and the up­ rising sheets smash into several small pieces under the influence of surface tension force and explosion of vapor bubbles at τ≈3. After τ≈3 uprising sheets cannot be clearly seen. At τ≈5, most of the liquid parts do not remain in contact with the surface. To quantitatively examine the effect of droplet number on the nondimensional spreading area per droplet, variation of dimensionless spreading area for single and multiple droplets with time were measured and the results are compared in the Fig. 17. Due to the interactions, multiple droplet cases cover less area per droplet comparing with a single droplet case up to τ≈3. The effective spreading areas per droplet are 15% and 33% smaller than single droplet configuration in case of droplet pair and trio configurations respectively at τ≈1.5. These values are 11% and 29% respectively at τ≈2. As previously mentioned in the introduction, effective spreading area directly affects the total heat transfer. Therefore, it can be said, the interaction phenomenon strongly

3.3.3. Single and multiple droplet impact with high We number on the surface at 350 ◦ C Fig. 16 shows single and multiple droplets interaction with the sur­ face temperature at 350 ◦ C and the impact conditions of droplets are given in Table 8. In the case of a single droplet, droplet impacts on the surface and then change form into a circular liquid lamella (τ≈1). Several tiny secondary droplets occur and scatter around randomly (τ≈2). The liquid lamella smashes into several small parts and then disperses to minor droplets changing side radially outward (τ≈3). At τ≈5, liquid parts do not remain in contact with the heated surface. The

Fig. 17. Variation of non-dimensional spreading area for single and multiple droplets with time at Ts = 350 ◦ C.

Fig. 16. Single and multiple droplet impact on the surface at 350 ◦ C. 10

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Experimental Thermal and Fluid Science 120 (2021) 110255

affects the cooling efficiency especially in the first stages after the droplet collision. After τ≈2.5, liquid lamellas smash into several small parts and then disperses rapidly. Fig. 18 shows the variation of non-dimensional uprising sheet for droplet pairs with non-dimensional time for different surface tempera­ tures. As the viscosity of the liquid decreases with increasing surface temperature, it allows the liquid to move away from the heated surface then the uprising sheet height increases. The uprising sheets smash into several small pieces and uprising sheet cannot be clearly seen after some point for heated surfaces. This breakage point occurs earlier when the surface temperature increases, since relative molecular motion is easier which leads to more instabilities. Because of the extra uprising sheet, droplet trio cases cover less spreading area per droplet compared with droplet pair case. The vari­ ation of non-dimensional spreading area for droplet trio with nondimensional time for different surface temperatures are given in Fig. 19. After the disappearance of uprising sheets, the non-dimensional spreading area equilibrates to similar values for 23 ◦ C and 185 ◦ C cases. For 350 ◦ C cases, the liquid lamella and the uprising sheets smash into several small pieces earlier under the influence of surface tension force and explosion of vapor bubbles. Then, contact area dramatically de­ creases with non-dimensional time and most of the liquid parts do not remain in contact with the surface after τ ≈ 3. Also, it is clearly seen that there is an important decrease in non-dimensional spreading area with temperature increase.

Fig. 19. Variation of non-dimensional spreading area for droplet trio with time at different surface temperatures.

-

-

4. Conclusions The present study provides experimental results on the hydrody­ namics of a single and multiple droplet impacts and their interactions on heated surfaces. The interaction phenomena of multiple droplets investigated for a wide range of surface temperatures (23 ◦ C − 350 ◦ C) and different Weber numbers. The spacing between multiple droplets in horizontal direction is also investigated. The reported data represents only one experimental case. By using an image analysis software, the hydrodynamic behavior, uprising sheets and spreading area of the multiple droplets after the impact are examined and compared. The results obtained in this study are summarized as follows:

-

-

-

- The simultaneous impact of multiple droplets shows rather different dynamics compared to the case of single droplet impact on a heated surface owing to the complexity of involved interaction phenomena. - The horizontal spacing and Weber number have strong effects on the characteristics of spreading area and uprising sheet. The height of the uprising sheet is larger with shorter spacing between multiple droplets and higher Weber numbers. For a larger horizontal spacing between the droplets, liquid lamellas lose more energy because of

viscous dissipation and this causes a weaker uprising sheet forming late. The variation of uprising sheet height with non-dimensional time is compared with an available analytical model. The analytical model agrees with the experimental data for initial stages. However, the experimental data do not exactly match with the theoretical results in later stages because of the uprising sheet loses its stability. Droplet residence times in the film boiling regime for a single droplet are compared with the existing correlations. The result of correlation by Biance et al. [41] are in good agreement with our experimental data. It is observed that in the case of a droplet pair, the rebound phe­ nomenon takes place earlier than that for single droplet cases. This is most likely due to less spreading area per droplet because of the droplet interaction. For non-simultaneous case, rebound takes place later comparing with simultaneous case. This situation may be due to the nonsimultaneous droplet pair spreads more on the surface than the simultaneous droplet pair. Increasing surface temperature decreases viscosity of the liquid, which causes more instabilities at the uprising sheet and results in cusp and finger formations in shorter time.

Also, it allows the liquid to move away from the heated surface then the uprising sheet height increases. - The variation of the uprising sheet is clearly observed at low surface temperatures. However, for high surface temperatures, the uprising sheets split into several small pieces and uprising sheet cannot be clearly seen after some point. This breakage point occurs earlier when the surface temperature increases, since relative molecular motion is easier which leads to more instabilities. - Non-dimensional spreading area significantly decreases with increasing surface temperature, number of droplets, and shorter droplet spacing. The results obtained in this experimental study are presented with real time high quality images and data. Such valuable information may facilitate the understanding the dynamics of simultaneous multiple droplet interactions. However, the spray cooling is much more complex issue, therefore, more comprehensive studies are needed for better un­ derstanding the interaction of multiple droplets. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence

Fig. 18. Variation of non-dimensional uprising sheet height for droplet pairs with time at different surface temperatures. 11

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Experimental Thermal and Fluid Science 120 (2021) 110255

the work reported in this paper.

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