Impact Behavior of Single Water Drop Impacting onto Burning Ethanol

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Impact behavior of single water drop impacting onto burning ethanol surface Mingjun Xu, JiaQing Zhang, ChaoPeng Wu, Changhai Li, Xiao Chen, and Shouxiang Lu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04008 • Publication Date (Web): 20 Nov 2017 Downloaded from http://pubs.acs.org on November 20, 2017

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Industrial & Engineering Chemistry Research

Impact behavior of single water drop impacting onto burning ethanol surface MingJun Xua, JiaQing Zhangb, ChaoPeng Wua, ChangHai Lia , Xiao Chena , ShouXiang Lua* a

State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230027, China

b

State Grid Anhui Electric Power Research Institute, Hefei 230022, China

Corresponding author: ShouXiang Lu, [email protected];

Abstract A series of experimental and theoretical work are performed to enrich the previous research concerning single water drop impacting on burning ethanol surface. Three typical impact regimes including crater-first-jet, crater-second-jet and surface bubble are discussed detailedly, and an impact regime map is built up. For crater-first-jet and crater-second-jet regimes, the dimensionless maximum crater depth increases with the impact Weber number, but there is a sharp decrease for the regime transitioning from crater-second-jet to surface bubble. In addition, the theoretical maximum crater depth and jet length scales are derived based on energy conservation and conversion. For crater formation, as the drop initial total energy increases, gravity gradually dominates the surface tension effects. For jet formation, however, the surface energy is around nine times larger than gravitational potential energy when the energy stored in crater is the lowest. Keywords: drop impact; burning surface; fire suppression; water spray Nomenclature Subscripts

C

coefficient

D

diameter

Dmax

maximum crater depth

E Fr

energy drop Froude number ( Fr = vt 2 gd )

0

initial drop diameter

crater

energy used to form crater structure

d dissipated-crater

Drop liquid energy dissipated when crater forms

1

ACS Paragon Plus Environment


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g

gravitational acceleration

h

jet height −2/ 5

dissipated-first-jet

energy dissipated when first jet forms

dissipated-bubble

energy dissipated when bubble forms

K

Nondimensional parameter ( K = We ⋅ Oh

K’

Nondimensional parameter ( K ' = We 0.375 ⋅ Re 0.25 )

m

drop mass

Re v

drop Reynolds number ( Re = ρ d vt D0 µ d ) impact velocity

g-crown g-bubble

W

work

g-second-jet

We

drop Weber number ( We = ρ d vt2 D0 / σ d )

j s-crater s-second-jet

density

σ

surface tension

µ

viscosity

χ

energy dissipated when second jet forms crater gravitational potential energy gravitational potential energy used to form the first jet

ρ

ϕ=

dissipated-second-jet g-crater g-first-jet

Greek symbols

ϕ

)

crown gravitational potential energy bubble gravitational potential energy gravitational potential energy used to form the second jet jet crater surface energy surface energy used to form the second jet

s-crown

crown surface energy

s-first-jet

surface energy used to form the first jet

s-bubble

bubble surface energy

t

target liquid

total

total impact energy

πρt gh D / 8 + πσ t h j D j 2 j

2 j

Wcrater

energy conversion rate ( Wcrater = χ Etotal )

1 Introduction Drop impact has many actual applications1-3, such as surface cooling4, thermal spray coating, and fire suppression by water spray/mist5. From a scientific standpoint, after a single drop impacts on a liquid surface, the phenomena involves floating, bouncing, coalescence, jet break, splashing and canopy6-10, which are determined by physicochemical properties of drop liquid and the target liquid11. Drop impingement on liquid surface has been studied more than one century12-14. There are many investigations on drop impinging upon deep liquid pool15-21. For example, Rein15 experimentally investigated the impact outcomes and given the classification of the phenomena characteristic of the transitional regime. Liow16 carried out a systematic experiment on single water drop striking the same liquid surface and established a We-Fr regime map of different types of 2


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impact outcomes. Cole17 conducted a series of experiments on drop impact process and provided a global picture of different impact regimes based on drop Froude number. Morton et al.18 used a validated numerical approach to investigate the impact behavior resulting from the impact of single water drop on a deep water pool. The simulation results successfully predicted the formation of vortex rings, bubble entrapment and the development of vertical Rayleigh jets. Ray et al.19 numerically studied the conditions and outcome of coalescence events by using the coupled level set and volume of fluid method (CLSVOF). The phenomena of partial and complete coalescence were shown and discussed detailedly. Additionally, Ray et al.20 also performed systematic studies on the interaction process of single water drop impacting on a deep water pool. Various regimes were observed on the air-water interface and were plotted on a We-Fr regime map. Deka et al.21 numerically and experimentally studied the impact process during single water drop impacting on a liquid pool. The regime of large bubble entrapment on the v-D0 map and on the We-Fr map was built up. In addition, the formation mechanism of large bubble entrapment was discussed in detail. Overall, all the studies described above were conducted at room temperature, however, only a few investigations focus on single water drop interaction with a burning surface from fire suppression perspective. In order to deepen the knowledge of fire suppression mechanism of water suppressant, Manzello and Yang22 experimentally studied single drop impacting onto a hot liquid surface with increasing temperature and reported that the pool temperature has a significant influence on critical impact Weber number for splashing, which decreases with increasing pool temperature. Furthermore, Manzello et al.23 performed a series of experiments for water or HFE-7100 drops impinging on hot oil surface. It was found that the vapor explosion may occur when the oil temperature is less than 180 oC for HFE-7100 drops. Wang et al.24 pointed out that the influence of pool temperature on impact phenomena is not evident, and the pool temperature just affects the sizes of splashed daughter drops and the bounced jet height. Besides, Wang et al.25 carried out experiments

3



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on a water drop with or without additives impinging on a hot molten-ghee surface and stated that the vapor explosion behavior can be weaken by additives. Generally, the target surface used in the above studies is not a real burning surface. Therefore, Xu et al.26 investigated the drop impact phenomena using a real burning surface as the target surface. Results showed that three typical impact behaviors including splashing-injecting, splashinginjecting-secondary injecting and splashing-bubble are observed and the impact velocity is affected by the fire plume. However, they did not provide the critical condition for the appearance of each typical regime since the range of Weber number was too small in their work. In addition, Xu et al.27 experimentally and theoretically explored the single water drop impacting onto pool liquid with or without burning surface. The influence of fire plume on the theoretical impact velocity was quantified. Moreover, the comparison between the burning surface and the common surface was made. It indicated that the temperature is near the boiling point (78℃) among the area from fuel surface to a depth of about 6–8 mm during the quasi-steady state for burning ethanol surface, while the fuel temperature is uniform room temperature (20℃) for unburned case, as shown in Figure 127. However, there is a shortage that the falling height is kept constant. Thus the effect of Weber number on impact behavior is not taken into consideration.

Figure 1. The trend of temperature distribution in fuel pool: (a) burning pool, (b) unburned pool 4


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On the basis of our previous work above-described, here we present more details for single water drop interacting with burning ethanol pool with a wide range of Weber number. The critical conditions for the occurrence of each typical regime are discussed detailedly and a global picture of different impact regimes is provided. The theoretical value of the maximum crater depth and central jet length scales are derived from the perspective of energy conservation.

2 Experimental setup Figure 2 exhibits the experimental setup, including a drop generator, a liquid container, and an image capture device with LED backlighting, which has been used in previous investigations26-28. The water drop is generated by a syringe pump and detaches off the needle tip due to gravity. The needles with different sizes are used to produce water drop of various diameters. The drop diameter is ranging from 1.98 mm to 2.98 mm, and measuring error is one pixel with size of 0.25 mm. The dropping height is changed to get varied impact velocity. The impact velocity is also measured by tracking the location of the droplet centroid 2 ms prior to impact using image processing software, with a measuring accuracy ±0.05 m/s. The image processing methodology has been described in previous study29. Ethanol is chosen as the target liquid, which is widely used in water mist/spray fire extinguishing experiments24, 30, 31, The target liquid is held by a transparent quartz glass with the size of 75 mm (width) ×75 mm (length) ×80 (height). The liquid properties and experimental conditions are shown in Table 1. A high speed digital camera (Phantom V710) with a Nikon 60-mm micro lens is used to record the impact behaviors and a 1000 W LED light is used as a backlighting. The exposure time and the frame rate are set as 9 microsecond and 2000 fps, respectively. Figure 3 presents the water drop and flame on burning ethanol surface. To diminish the temperature change of target liquid and keep the fuel depth constant, ten K-type microthermocouples with accuracy of 0.5 oC are located at different positions along the centerline of the pool to monitor the temperature variations. According to temperature profile, the pool fire reaches a 5



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stable stage after ignition. At this stage, the temperature of the burning surface is approximately constant and remains equal to its boiling point 78 ℃, which is similar to what is expressed in Figure 1 (a). Each experiment is conducted at the stable stage, thus the temperature distribution is nearly identical for burning pool in each experiment. Additionally, each repeated test is done at the same time after ignition. So we can keep the fuel depth same for each experiment as well. The whole experiment is performed according to the following procedure. (1) The target liquid is ignited and a stopwatch starts to work. (2) The water drop is released from the needle after the pool temperature reaches the stable stage according to the temperature profile with time (this moment is recorded). (3) after the drop reaches the surface, the high speed digital camera begins to work and the impact behavior is recorded. (4) The fire is extinguished. (5) The target liquid that has been used is replaced with new liquid. (6) The repeated test is carried out. To ensure the reliability of the data, each test is repeated 20 times.

Syringe Pump Diffusion 1000W 1000W light

High speed digital camera Pool

Computer

Figure 2. Schematic diagram of the experimental apparatus.

6


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Figure 3. The water drop and flame on burning ethanol surface Table 1. Liquid properties and experimental conditions.

σ

µ

ρ

D0 × 10−3

(N/m)

(mPa·s)

(kg/m3)

(m)

Water(20℃)

0.072

1.005

997

Ethanol(78℃)

0.01756

0.433

728

Liquid

v (m/s)

We

Re

K’

1.98-2.98

2.29-3.79

143-594

4498-11213

52-113

-

-

-

-

-

3 Results and discussion 3.1 Energy conversion and conservation According to many previous studies24, 26, 27, the impact regimes for a single drop impacting onto a hot surface or a burning surface can be divided into three main categories: crater-first-jet, cratersecond-jet and surface bubble. After a water drop reaches the target surface, the impacted liquid around the impact point expands outward and a crater structure can be observed beneath the surface. The crater continues to expand outward until it approaches the maximum value. All round fluids begin to flow inward to fill the crater and then a jet rises from the apex points of the crater. After the first jet reaches the maximum height, it collapses under the effect of its weight and falls back to the target liquid surface without second jet. The whole impact behavior is named as crater-first-jet. For 7



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the crater-second-jet regime, the second jet can be formed after the first jet falls back to the liquid surface. The surface bubble is defined as the crown structure closing above the liquid surface and forming a bubble. The evolution processes for each phenomenon are shown in Figure 4, which has been described detailedly in the previous investigation26. Here we concern about the energy conservation and transformation for each phenomenon. For phase I to phase II, after single water drop reaches the target surface, a crater with crown structure forms, then expands outward and approaches its maximum size. The total initial impact energy Etotal is mainly converted to the energy used to form crater, the energy used to form crown, and the energy Edissipated −crater dissipated due to the viscous force during the impact process. The energy used to form crater contains the work W

g − crater

against the gravitational force and the work

W s −crater against the surface tension force. The energy used to form crown involves work Wg − crown

against the gravitational force and the work W s −crown against the surface tension force. Thus, the equation of energy conversion for Phase I to phase II can be written as:

Etotal = Wg −crater + Ws −crater + Edissipated −crater + Wg −crown + Ws −crown

(1)

For phase II to phase III, the energy stored in crater and crown is converted to the first jet, and

the equation of energy conversion for Phase II to phase III can be expressed as equation (2) both for crater-first-jet regime and crater-second-jet regime:

Wg −crater + Ws −crater + Wg −crown + Ws −crown = Wg − first − jet + Ws − first − jet + Edissipated − first − jet

(2)

But the energy conversion formula can be written as equation (3) for surface bubble regime:

Wg −crater + Ws −crater + Wg −crown + Ws −crown = Wg −bubble + Ws −bubble + E dissipated −bubble

(3)

For phase III to phase IV, the energy contained in the first jet is converted to second jet, energy

formula can be obtained for crater-second-jet regime:

Wg − first − jet + Ws − first − jet = Wg −sec ond − jet + Ws −sec ond − jet + E dissipated −sec ond − jet 8


(4)

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Overall, it should be noted that the Wg − x and Ws − x (x denotes the crater, crown, surface bubble, first-jet or second-jet) are determined by gravity and target liquid surface tension, respectively. According to the energy conversion formulas described above, when the initial impact energy is not enough, a crater with one jet can be observed, but the energy contained in the first jet cannot raise a second jet above the target surface after the first jet collapses. With an increase of impact energy, when Etotal is large enough, more initial impact energy is stored in first jet, thus the second jet can form on the surface after the first jet collapses. With the further increase of impact energy, the energy converted to the crown structure also increases, and the crown height increases. The surface tension of target liquid plays a leading role to make the upper rim of crown contraction, a bubble appears finally.

Figure 4. Evolution process of impact behavior with an increase of impact energy

9



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3.2 Transition of impact regimes Many studies have mapped the outcomes of single drop impacting on the liquid surface based on related non-dimension parameters such as We, Fr, Re, K and K’6. The outcomes are mainly determined by the density ρ d , surface tension σ d , viscosity µd , diameter D0 , and impact velocity v

of the drop, and the density ρt , surface tension σ t , and viscosity µt of the target liquid. In this

work, the parameters of target liquid are constant and so only the drop parameters are focused.

[ ρ d ] = ML−3 , [σ d ] = MT −2 , [ µd ] = L−1MT −1 , [ D0 ] = L , [ v ] = LT −1 .

L, M, and T denote the

dimension of length, mass and time, respectively. Assuming that the ρ d , σ d , µd and D0 have the relationship f ( ρ d , σ d , µ d , D0 , vt ) = 0 , based on simple dimensional analysis, it can be found that the formula

has

myriad

of

solutions.

Here,

we

choose

one

of

the

solutions

( We = ρ d vt2 D0 / σ d , K ' = We0.375 ⋅ Re0.25 =（ρ d vt2 D0 / σ d）0.375 ( ρ d vt D0 µd )0.25 ) to map the impact outcomes as shown in Figure 5. Here, the outcomes of single water drop impinging onto burning ethanol surface are mapped and compared with experimental data of Wang 24 and Xu26, 27, which focus on water drop impinging onto heated ethanol or burning ethanol surface. The We-K’ map can be divided into four regions, including A: crater-first-jet, B: crater-second-jet, C: transition region of crater-second-jet and surface bubble, D: surface bubble. In general, the regions of A, B, C, D appear in succession as the Weber number increases. Surface bubble occurs more easily in the case of high lgWe and K’, the critical Weber number for surface bubble occurrence is about 275 (lg275=2.44), which is far less than the critical value 1000 for normal impact at room temperature32. It suggests that burning condition is conducive to the appearance of surface bubble. However, Zou et al.6 stated that the required impact We for the occurrence of surface bubble decreases sharply with the pool diameter decreasing, the critical impact Weber number is only 192 for the drop impacting on the liquid surface in the tube of inner diameter 8 mm. On the other hand, the lower limit for the occurrence of secondary jet is 194 (lg194=2.29) which is not exactly determined in previous studies. 10


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The correlations of the regions and Weber number are given by the following relations:

 A crater − first − jet   B crater − sec ond − jet Re gions =  B or D C  D surface bubble

for lg We < 2.29 for 2.29 ≤ lg We < 2.44 for 2.44 ≤ lg We < 2.54 for 2.54 ≤ lg We

(5)

Figure 5. Distribution of impact regimes for water drop impinging onto burning or heated surface 3.3 Characteristic parameters 3.3.1 Maximum crater depth For a water drop impinging onto a burning fuel surface, a crater forms, and the maximum crater depth Dmax varies with drop impact Weber number as presented in Figure 6. Only part of total initial impact energy is converted to the work to form the crater structure:

Wcrater = χ Etotal The total initial impact energy can be expressed as: 11


(6)


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3

Etotal

2 1 1 4  D0  2 1 1 2 2 ρ d v D0 = md v = ⋅ ρ d π   v = πσ d D0 = πσ d D02We 2 2 3  2  12 12 σd

(7)

The work W crater can be calculated by：

Wcrater = Wg −crater + Ws −crater W

g − crater

(8)

and W s −crater have been derived by Engel33 and Fedorchenko34, respectively

Wg −crater =

πρt gDmax 4

(9)

4

Ws −crater = πσ t Dmax 2

(10)

Submitting the Eq. (7), (8), (9) and (10) into Eq. (6), it can be re-written as:

πρt gDmax 4 4

+πσ t Dmax 2 =

χ 12

πσ d D02We

(11)

2

Solving the Eq. (11) and choosing the positive sign of the root, Dmax can be obtained:

2 = Dmax

2 max

D

σ t2 +

1 ρt gσ d ( χ D02We) − σ t 12 0.5 ρt g

(12)

3.08 × 10−4 + 43.28( χ D02We) − 0.01756 = 3567.2

(13)

It can be found that Dmax is determined by χ D0 We . Assuming the energy conversion rate χ 2

2

is constant and the value χ = 0.248 can be obtained by fitting the present experimental data using 2

2

equation (13), the correlation between Dmax and D0 We is plotted in Figure 6. It is noticeable that the correlation coefficient R Square is only 91.9. The main reason may be that the crater is only approximated hemisphere, not a real hemisphere. The experimental data

χ = 0.248 confirms that

only part of initial total energy transfers into crater. This is resulted from two main reasons, firstly, 12


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the crown structure emerges with the crater structure which occupies part of the total initial energy, and secondly, capillary waves and a small viscous dissipation consume energy. From Table 2, it is clearly that, comparing with the results obtained by Liow16, Prosperetti et al. 35

and Michon et al.36, only a small part of initial energy is converted to W g −crater and W s −crater for

drop impacting on liquid surface. In addition, it is obvious that the energy conversion rate obtained in Prosperetti’s study is overestimated since they equated the Ecrater and Etotal, which is confirmed by Liow’s, Michon’s and the present experimental data. Table 2. Energy conversion rate Experiments

Drop liquid

Target liquid

Condition

energy conversion rate χ

Present

Water

Ethanol

Burning

Around 0.248

Prosperetti et al.35

Water

Water

At room temperature

1

Liow 16

Water

Water

At room temperature

0.28

Michon et al.36

Water

Water

At room temperature

Around 0.55

7x10-5 6x10-5

Experimental data Calculated value by Eq.(13) with χ=0.248

5x10-5 D2max(m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4x10-5 3x10-5 2x10-5 -5

1x10

2 Dmax =

3.08 × 10−4 + 43.28(0.428 D02We) − 0.01756 ， R 2 = 91.9 3567.2

5.0x10-4 1.0x10-3 1.5x10-3 2.0x10-3 2.5x10-3 3.0x10-3 3.5x10-3

D20We(m2) 13



2

2

Figure 6. Correlation between Dmax and D0 We (the data points are obtained from the cases of crater-first-jet and crater-second-jet and the data points of surface bubble are not contained) Both the gravity and surface tension play an important role in the crater evolution process36, Figure 7 presents the gravitational potential energy and surface energy of crater as a function of drop total initial impact energy, and the insert in the figure displays the ratio of gravitational potential energy to surface energy, which ranges from 1.44 to 5.64. As the total initial impact energy increases, the increase of surface energy is slight, which is similar to Prosperetti’s study35. It can be deduced that gravity gradually dominates the surface tension effects as the drop total initial impact energy increases. -5

3.0x10-5

Potential energy/ Surface energy

6.0x10

Energy (J)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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6

Crater surface energy Crater potential energy

Potential energy/ Surface energy

5 4 3 2 1

1.0x10-5 2.0x 10-5 3.0x10-5 4.0x10-5 5.0x10-5 6.0x10- 5

0.0

Droplet total impact energy (J)

0.0 -5

1x10

-5

2x10

3x10

-5

-5

4x10

Droplet total impact energy (J)

Figure 7. Gravitational potential energy

-5

5x10

-5

6x10

πρ gDmax 4 4 and surface energy πσ t Dmax 2 of crater as

a function of drop total impact energy πσ d D0 We 12 . 2

14


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Moreover, the correlation between dimensionless maximum crater depth (Dmax/D0) and We is also plotted combining the present and Xu’s26 experimental data, as shown in Figure 8. The data points appear in the transition region including the crater-second-jet regime and surface bubble regime. For crater-first-jet and crater-second jet regimes, the dimensionless maximum crater depth increases with impact We, but there is a sharp decrease for surface bubble regime comparing with the crater-second-jet regime. The decrement magnitude is between 21.7% and 30.0%. The equation Dmax D0 = C ( Fr 3ρt /

ρ d )1/4 16,

35

is widely used to predict the non-

dimensional maximum crater depth Dmax/D0 for normal impact at room temperature, while attempts to fit the present experimental data using the equation prove unsatisfied, which suggests that the model derived for normal impact at room temperature is not applicable for single water drop impinging onto the burning surface. Under burning condition, the coefficient C may be affected by many factors such as the fluctuation of physics properties of burning liquid, heat and mass transfer during combustion. Additionally, the surface tension cannot be ignored.

Maximum crater depth (Dmax/D0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.6

Present experimental data Xu et al26

2.4 Region D 2.2 Region C

2.0 1.8

Region B Region A

1.6 1.4 2.1

2.2

2.3

2.4

2.5

lgWe 15


2.6

2.7

2.8


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Figure 8. The dimensionless maximum crater depth (Dmax/D0) as a function of drop impact lgWe 3.3.2 Jet length scale After the crater size approaches its maximum value, all round fluids recoil and the apex points of crater move upward, then a liquid column raise continuously until it reaches the maximum height. In the aspect of energy conversion, the energy stored in crater transfers to the first jet. Here, the jet is assumed to be a circular cylinder and has the height hj and the diameter Dj, thus the gravitational potential energy and surface energy of jet can be expressed as equation (14) and equation (15), respectively 34: 2

Wg − first − jet = ∫

hj

0

D  ρtπ  j  g ( h j − h ) dh = πρt gh 2j D 2j / 8  2  Ws − first − jet = πσ t h j D j

(14)

(15)

Only small part of the total initial energy converts to the first jet 28, thus:

πρt gh D / 8 + πσ t h j D j = ϕWcrater = ϕ ( 2 j

2 j

πρt gDmax 4 4

+πσ t Dmax 2 )

(16)

The solution of Eq. (16) takes the form:

 ρt gDmax 4  +σ t Dmax 2  / 2 − σ t 4  

σ 2 + ρt gϕ  t

hj Dj =

hj Dj =

ρt g / 4

3.08 × 10 −4 + ϕ ( 6.36 × 106 Dmax 4 +62.64Dmax 2 ) − 0.01756 1783.6

It can be seen that the h j D j is determined by

( 6.36 ×10 D 6

max

4

(17)

(18)

+62.64Dmax 2 ) . Assuming

the conversion rate ϕ is constant, and fitting the present experimental data using the equation (18), the correlation can be obtained with ϕ =0.363 , as shown in Figure 9.

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2

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hjDj(m )

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8.0x10

-5

7.0x10

-5

6.0x10

-5

5.0x10

-5

4.0x10

-5

3.0x10

-5

2.0x10

-5

Experimnetal value Calculated value by Eq.(18) with ϕ =0.363

-2

1.0x10

-2

2.0x10

-2

3.0x10

4.0x10

-2

-2

5.0x10

-2

6.0x10

(6.36×106D4max+62.46D2max)(N/m)2 Figure 9. The jet length scale hjDj as a function of Dmax Fedorchenko et al.34 experimentally and theoretically investigated the length scales of the central jet h j D j for water drop impacting onto a water surface at room temperature. However, they equates the energy formed jet to the total energy of the drop, which means that total energy of the impacting drop completely transforms into central jet. It is apparent that the central jet length scale is overpredicted since there must be one part of energy dissipating in the interaction process, which is confirmed by present data. Figure 10 presents the gravitational potential energy and surface energy of jet as a function of sum of crater gravitational potential energy and surface energy. When the sum is the lowest, the surface energy is around nine times as much as gravitational potential energy. As the sum increases, the ratio of surface energy to gravitational potential energy decreases from 9.2 to 2.7, as shown in the insert of Figure 10. It can be deduced that the surface energy is dominant at lower sum of crater potential energy and surface energy.

17


-5

1.0x10

Energy(J)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-6

5.0x10

P otent ial energy /surfac e e ner gy


0.4 5

Pote nti al e ner gy/su rfac e ene rgy

0.4 0

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Jet surface energy Jet potential energy

0.3 5 0.3 0 0.2 5 0.2 0 0.1 5 0.1 0

-6 -5 -5 -5 0.0 5.0 x10 1 .0x1 0 1.5x 10 2 .0 x10 Sum of crat er po tential energy a nd sur face energy ( J)

0.0 0.0

5.0x10

-6

1.0x10

-5

-5

1.5x10

2.0x10

-5

Sum of crater potential energy and surface energy (J) Figure 10. Gravitational potential energy

πρt gh 2j D 2j / 8 and surface energy πσ t h j D j of jet as a

function of sum of crater potential energy and surface energy（πρt gDmax

4

4 + πσ t Dmax 2）.

4 Conclusions A series of experiments are conducted for single water drop impinging onto burning ethanol surface with a wide range of drop impact Weber number. Key conclusions from this work can be summarized as follows. (1) Three outcomes after impact including crater-first-jet, crater-second-jet and surface bubble occurs in succession and the critical appearance condition for each outcome follows the relationship:

18


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A crater − one jet   B crater − sec ond jet Re gions =  B or D C  D surface bubble

for lg We < 2.29 for 2.29 ≤ lg We < 2.44 for 2.44 ≤ lg We < 2.54 for 2.54 ≤ lg We

(2) For crater-first-jet and crater-second-jet regimes, the dimensionless maximum crater depth increases with impact We, but there is a sharply decrease for surface bubble regime. In addition, the maximum crater depth is derived based on energy conservation and conversion. Only small part of drop initial total energy converts to the crater gravitational potential energy and surface energy. Moreover, as the drop initial total energy increases, gravity gradually dominates the surface tension effects. (3) Also, the jet length scale is derived based on energy conservation and conversion for craterfirst-jet and crater-second-jet regimes. However, the surface energy is around nine times as much as gravitational potential energy when the sum of crater gravitational potential energy and surface energy is lowest. As the sum increases, the ratio of surface energy to gravitational potential energy decreases from 9.2 to 2.7. Notes

The authors declare no competing financial interest. Acknowledgements

The authors gratefully acknowledge the Fundamental Research Funds for the Central Universities (No. WK2320000034), Class General Financial Grant from the China Postdoctoral Science Foundation (No. 2016M592068), the Fundamental Research Funds for the Central Universities (No. WK2320000037), and the Opening Fund of State Key Laboratory of Fire Science (No. HZ2017-KF06). Reference

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For table of contents only

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Impact Behavior of Single Water Drop Impacting onto Burning Ethanol

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