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Experimental study on effect of support fiber on fuel droplet vaporization at high temperatures
Fuel 268 (2020) 117407
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Full Length Article
Experimental study on effect of support fiber on fuel droplet vaporization at high temperatures ⁎
T
⁎
Jigang Wang, Xiaoyu Huang, Xinqi Qiao , Dehao Ju , Chunhua Sun Key Laboratory of Power Machinery and Engineering, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Droplet vaporization Support fiber Thermal conductivity Multicomponent fuel
The effect of support fiber on fuel droplet vaporization is experimentally investigated in a stagnant high-temperature environment (673–973 K) using high-speed backlit imaging technique. Droplets with nearly identical initial diameter suspended on the different support fibers, thus the effect of support fiber on droplet vaporization due to different initial droplet diameter is removed. The fiber diameters are 0.08, 0.1 and 0.15 mm, and thermal conductivities are 1.4, 80 and 400 W/m·K, respectively. Meanwhile, the experimental results are verified by theoretical analysis. The results show that the droplet vaporization rate constant is linearly related to the squared diameter and thermal conductivity of fiber, which is consistent with the results in the literature. Moreover, the droplet lifetime changes linearly with fiber diameter and thermal conductivity. An increase in the droplet vaporization rate constant with thermal conductivity of fiber, but, a decrease for droplet lifetime. It is proved for the first time that support fiber can cause fuel droplet micro-explosion at high temperatures, however, the previous studies have not been reported. When the fiber diameter is greater than 0.15 mm or the thermal conductivity is higher than 400 W/m·K, the fiber heat transfer induced micro-explosion occurred. This is caused by support fiber induced local boiling or Leidenfrost effect inside the droplet. The optimum choice is that the fiber diameter is less than 0.1 mm and thermal conductivity is less than 80 W/m·K.
1. Introduction
contact with other objects and its shape is similar to spherical. While its limitation is that it is only suitable for low-temperature environment and multi-field coupling will affect the vaporization of droplets. The second method is to continuously supply fuel to a porous sphere to keep a certain amount of liquid on its surface. And consider the porous sphere as a droplet. The principle of this method is simple, the operation is simple, and the droplet shape is standard spherical. However, the experimental error is large, it only be used to study the steady vaporization process of droplets. The third method is to suspend droplets on fibers. The main advantage of this method is that the droplet is stationary, the whole vaporization process can be recorded conveniently. Thus the vaporization of droplets in a complex environment can be studied. The disadvantage is that the support fiber can affect droplet vaporization. According to the literatures of the past 50 years, the third method is the most commonly used method. Using fiber support method, extensive studies are carried out to investigate the influence of support fiber on droplet vaporization, including experimental and theoretical studies. Yang et al. [19] studied the effect of heat conduction through support fiber on droplet vaporization at weakly convective flow under 490–750 K. They reported that the droplet vaporization is enhanced by support fiber, which is more
Over the last few decades, spray combustion has many practical and relevant aspects in modern society especially in energy generating devices such as internal combustion engines, gas turbines, and furnaces. In spray combustion, liquid fuel is converted into a spray containing a large number of droplets. The heating and vaporization of droplets is an important part of the mixture formation, which directly affects the distribution of fuel vapor and the formation of combustible mixture. The vaporization rate of fuel droplets and the spatial distribution of fuel vapor largely control the final energy release rate and component mass conversion rate, and ultimately determine the combustion, fuel economy and emission performance of the engine [1]. Therefore, the study of single droplet vaporization is the basis for better understanding the mechanism of spray combustion and realizing high-efficiency clean combustion. Three major methods are applied to experiments of single droplet vaporization, namely, gas levitation method [2,3], porous sphere method, and fiber support method [4–14]. The gas levitation method adopts gas suspending, acoustic levitation or magnetic levitation to levitate droplets in the air. Its advantage is that the droplet does not
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Corresponding authors. E-mail addresses: [email protected] (X. Qiao), [email protected] (D. Ju).
https://doi.org/10.1016/j.fuel.2020.117407 Received 16 December 2019; Received in revised form 1 February 2020; Accepted 13 February 2020 0016-2361/ © 2020 Elsevier Ltd. All rights reserved.
Fuel 268 (2020) 117407
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τ λ s
Nomenclature A C d m K t T
Contact area [mm2] Coefficient [–] Droplet diameter [mm] Coefficient [–] Evaporation rate constant [mm2/s] Droplet evaporation time [s] Ambient temperature [K]
Time [s] Thermal conductivity [W/m·K] Heat transfer distance [mm]
Subscripts 0 f λ
effective for lower gas temperatures and thicker fiber. However, when the fiber diameter was 300 μm, the total heat input decreased. Shringi et al. [20] numerically investigated the influence of support fiber on vaporizing fuel droplets at high temperatures and pressure. They found that the temperature distribution inside the support fiber was almost one-dimensional, and a significant gradient along the fiber axis led to heat transfer to the droplet. Due to the heating of support fiber, strong thermocapillary flow occurred on the droplet surface, which substantially influences droplet vaporization rate, especially for larger fiber and low Reynolds numbers. Ghata et al. [21] numerically studied the effect of fiber and thermocapillary stresses on droplet vaporization rate and shapes in reduced gravity. The results indicated that a large fiber diameter led to faster Marangoni convection. This was because the radial temperature and species gradient at the interface increase with time, and then increased the vaporization rate. Han et al. [22] using experimental and theoretical methods investigated the effect of thermocouple and single quartz fiber on dodecane/hexadecane droplet vaporization. They demonstrated that droplet vaporization rate changed non-linearly with the increasing fiber diameter. The vaporization rate of droplet supported by thermocouple is larger than droplet with quartz fiber. Chauveau et al. [23] experimentally investigated the effect of support fiber diameter on n-decane droplet vaporization at normal gravity. They used three different quartz fiber diameters (106, 144, 181 μm) to suspended an initial diameter of 0.8 mm droplet, and found that the droplet vaporization rate is increased as the fiber diameter increases, which is an indication of the enhancement of the droplet heat and mass transfer rates. In another study, they [24] neglected the effect of initial droplet diameter on droplet vaporization and compared the published experimental results using similar test conditions. The results showed that the n-heptane droplet vaporization rate constant is linearly related to the square of fiber diameter and ambient temperature. As reviewed above, previous studies have focused on the effect of diameter of support fiber on fuel droplet vaporization. The effect of thermal conductivity of fiber on droplet vaporization has not been revealed. The vaporization process of fuel droplet is often accompanied by micro-explosion, previous studies have suggested that this is due to the difference in boiling point of fuel components [12,14]. The support fiber is insufficient to cause micro-explosion at low temperatures or the fiber diameter is very small (less than 20 μm) [4,5,23,24]. However, many researchers studied the vaporization and micro-explosion characteristic of various fuel droplets using large support fiber diameters (greater than 0.05 mm) [3,4,6,7,10–18], it is very difficult to distinguish whether micro-explosion is caused by support fiber or fuel properties. As well known, support fiber increases heat transfer inside the droplet, and it will become nucleation sites of micro-bubbles and increases the probability of bubbles formation at high temperatures. Thus may cause droplet micro-explosion. In this way, the fiber induced micro-explosion will change the vaporization law of droplet. Motivated by this regard, the purpose of the present work is to experimentally investigate the effect of diameter and thermal conductivity of support fiber on fuel droplet vaporization. Three large fiber diameters, thermal conductivities, and four ambient temperatures are tested to analysis its influence on vaporization rate constant and droplet
Initial fiber Thermal conductivity
Table 1 Physical properties of JME. Fuel property
JME 3
Density at 15 °C (kg/m ) Kinematic viscosity at 40 °C (cSt) Boiling point (K) Latent heat (kJ/kg) Calorific value (MJ/kg)
882 4.5 632 256.8 39.6
lifetime.
2. Experimental apparatus and methods In order to easily obtain the droplet experimental data at high temperatures, jatropha methyl ester (JME) is chosen as the test fuel. This is because JME has a high boiling point and is easy to observe at high temperatures. Table 1 shows the physical properties of JME [25]. According to previous studies, there are three ways to suspend droplets using quartz fiber, as shown in Fig. 1. For vertical fiber supported method, there is a ball at the end of the fiber for droplet suspension (see Fig. 1a). Its shortcoming is that the diameter of quartz fiber can not be too fine (not less than 0.1 mm), and the terminal ball is large in volume which has a greater impact on droplet vaporization. For horizontal fiber supported method, the contact area between fiber and droplet is the smallest among the three ways (see Fig. 1b). However, droplet suspension is very difficult. Droplets are suspended with an initial diameter of 0.8 mm in three ways. As shown in Fig. 1, the droplet is ellipsoid in shape when suspended on vertical or horizontal fiber, whereas it is nearly spherical when suspended on the cross-fiber (see Fig. 1c). The cross-fiber support method does not cause any obvious interference in the transmission process between droplets and the surrounding gas medium [23,24]. It is the main way for droplet suspension and is widely used in droplet vaporization and combustion researches [4,5,23,24,26,27]. Therefore, the third method is used in this study. The schematic diagram of the experimental apparatus is shown in Fig. 2. The apparatus contained a heating system, a stepper motor ball screw control system and a data acquisition system. The heating system consisted of a heating chamber, a temperature controller and two thermocouples. The chamber was a cylinder with an inner diameter of 100 mm and a height of 250 mm. Two quartz windows were installed in the front and rear sides of the chamber to provide the windows of the camera and backlight source, respectively. The chamber heated by spiral-wound heating wires was capable of attaining a temperature up to 1200 K. The maximum power of heating resource was 2 KW. The accuracy of the temperature control was within ± 5 K. Two thermocouples were used to measure the temperature of the upper and lower part of the inner chamber. The stepper motor-ball screw control system contained a stepper motor controller, a stepper motor, a ball screw, and a droplet temperature protection device. The droplet was suspended on the quartz fiber, and placed in the temperature protection device. Then transported to the target position by the stepper motor-ball screw system. The droplet temperature protection device was designed to reduce droplet vaporization in the falling process. The data acquisition 2
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(a)
(b)
(c)
Ball
Fig. 1. Different droplet supported methods. (a) Vertical fiber; (b) Horizontal fiber; (c) Cross-fiber.
1 1
2
3
4
5
6
7
8
9
19 18 17 4
1. Stepper motor controller 2. Computer 3. High - speed video camera 4. Stepper motor 5. Ball screw moving device 6. Heating chamber 7. Thermocouple#1 8. Thermocouple#2 9. Nitrogen vessel 10. Air vessel 11. LED backlight 12. Insulation layer 13. Scattering film 14. Quartz glass 15. Heating wires 16. Thermal baffle 17. Droplet 18. Support framer 19. Thick quartz tube 20. Temperature controller
20 1200 K +
SET
-
16 15 14 13
6
5
3
11
12 7
8
2
9
10
Fig. 2. Schematic diagram of the experimental apparatus for droplet evaporation.
Initial droplet diameter [mm]
1 0.95 0.84
0.9 0.85 0.8 0.75 0.7 0.65 0.6 0
5
10
15
20
Droplet number [-]
25
30
Fig. 4. The initial diameter of droplets in experiments.
approximately 1200 images were recorded. In addition, at least three experiments were performed for each test condition to verify the repeatability of the results as well as to minimize statistical errors. Details of the experimental apparatus and procedures are reported in our previous papers [4,6,7]. Fig. 3 shows the schematic diagram of the image processing program. An in-house developed MATLAB code is used to determine the
Fig. 3. Schematic diagram of the image processing program.
system included a high-speed video camera (PCO. dimax S1), a LED backlight, a computer, and an acquisition system. Images were recorded at 1000 fps with a resolution of 1008 × 1008. For each experiment, 3
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1.1
diameter have some effects on the vaporization rate. In order to avoid the influence of the initial droplet diameter on droplet vaporization, the good repeatability of the initial droplet diameter is crucial. Since it is too difficult to generate a fuel droplet with exactly the same diameter in all experiments. In this work, the droplet is generated by a microsyringe and suspended at the intersection of two quartz fibers. The initial droplet diameter is evaluated using image processing. As shown in Fig. 4, the diameter of generated droplets is in the range of 0.79 mm and 0.88 mm, and the average diameter is 0.84 mm with a standard deviation of 0.03. It is found that droplets with an initial diameter of 0.8 mm will fall down from the support fiber when the fiber diameter is less than 0.08 mm. Therefore, the minimum diameter of support fiber selected in this paper is 0.08 mm. Furthermore, the repeatability and validity of experimental apparatus are very important. Two experiments under the same test conditions are selected to verify the validity of the experiment. As shown in Fig. 5, the droplet normalized squared diameter shows good consistency in the vaporization process. The maximum error is in the range of 5%.
Experiment 1 Experiment 2
1
(d/d0)2 [-]
0.9 0.8 0.7 0.6 0.5 0.4 0
2
4
6
t/d 20 [s/mm2]
8
10
12
Fig. 5. Comparison of two experiments.
3. Results and discussion
1.2
Fig. 6 shows the definitions of droplet vaporization rate constant and lifetime. For multicomponent fuel, the droplet normalized squared diameter curve is composed of two completely different stages (t1 and t2). In the first stage (t1), the droplet diameter increases and after some times starts to decrease. This is due to the thermal expansion. Afterwards, a balance between thermal expansion and vaporization determines droplet diameter. When the temperature inside the droplet reaches a quasi-steady state, the droplet diameter is determined only by evaporation, which is obey classical d2 law. Vaporization rate constant is determined by d2 law [31,32],
1
t1
t2
0
2
(d/d ) [-]
0.8 0.6
K 0.4 0.2 0
IJ 0
d2 t =1−K 2 d 02 d0
total
5
t/d
2 0
10 2
15
where d is droplet diameter [mm], t is time [s], d0 is droplet initial diameter [mm], and K is vaporization rate constant [mm2/s]. For the purpose of vaporization study, the first expansion stage is not important, because the vaporization rate constant is determined by the second part of droplet behavior [11]. In this study, the vaporization rate constant is defined as the slope of the best-fit straight line in second vaporization stage, obtained by the least square method [8–11]. The time from 0 s/mm2 to the intersection of the fitting straight line and abscissa axis is defined as droplet lifetime.
[s/mm ]
Fig. 6. Definitions of droplet evaporation rate constant and lifetime.
droplet diameter. In order to avoid the influence of background in image processing, the background of all images is removed first. Then the binarization process is applied to images. The classical Otsu's method is used to get the best threshold for each part of the region. The quartz fiber outside the droplet is removed by the morphological method. Without the image of the quartz fiber, the number of the pixels occupied by the droplet is calculated. Droplet diameter is extracted by equating the projected droplet area to that of an equivalent circle with diameter. The uncertainty of R can be calculated by Eq. (1) [28]. 2
(1)
R = X1a , X2b , X3c , ....
(2)
⎜
⎟
⎜
⎟
3.1. Effect of support fiber diameter In order to eliminate the influence of fiber thermal conductivity on droplet vaporization, three different diameters of quartz fibers are used to support droplets. Fig. 7 shows the normalized squared diameter of JME droplet with different support fiber diameter at ambient temperatures ranging from 673 K to 973 K. Each curve is the average value of three experimental data. The curve for the micro-explosion case is the best data in three trials. Because of the limited vaporization data of JME droplets in the literature, comparison with published literature data by other researchers is not given in this work. As shown in Fig. 7 ac, apart from droplet supported by 0.15 mm fiber at 973 K, the vaporization process of droplets under other experimental conditions includes two stages: initial expansion and steady vaporization stage. Moreover, droplets approximately obey d2 law in steady vaporization stage. With the increase of support fiber diameter, the droplet lifetime decreases. This indicates that the heat transfer rate of droplets increases. This is mainly due to the heat conduction of the fiber through the droplets, which results in the droplet temperature rising and the vaporization accelerating. Interestingly, the micro-explosion occurred when the fiber diameter is 0.15 mm at 973 K (Fig. 7d). Comparing with
2
2
ΔR ΔX ΔX ΔX = ⎛a 1 ⎞ + ⎛b 1 ⎞ + ⎛c 1 ⎞ + ⋯0.5 R X X 1 2 ⎝ ⎠ ⎝ ⎠ ⎝ Xn ⎠ ⎜
⎟
where R is a variable, a, b, c are coefficients. Assuming that the droplet is spherical, according to Eq. (1), the uncertainty of droplet squared diameter is
Δd 2 2 Δv = d2 3 v
(4)
(3)
where d is droplet diameter, v is droplet volume. After calculation, the uncertainty of droplet squared diameter is 4.08%. According to our and previous studies [29,30], initial droplet 4
Fuel 268 (2020) 117407
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1.2
0.08 mm quartz fiber 0.1 mm quartz fiber 0.15 mm quartz fiber
a
1
b
0.8
(d/d0) [-]
0
0.6
2
2
(d/d ) [-]
0.8
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0.6 0.4
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0 0
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20 2
30 2
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t/d0 [s/mm ] 1.2
c
0.15 mm quartz fiber 0.08 mm quartz fiber 0.1 mm quartz fiber
1
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0.6 0.4
d
25
0.08 mm quartz fiber 0.1 mm quartz fiber 0.15 mm quartz fiber
2 1.5 1
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t/d02 [s/mm2]
micro-explosion
(d/d0)2 [-]
0
2
(d/d ) [-]
5
2.5
0.8
0 0
0.15 mm quartz fiber 0.1 mm quartz fiber 0.08 mm quartz fiber
1
droplet falling
0.5
5
10
t/d20 [s/mm 2]
0 0
15
1
2
3
4
t/d20 [s/mm2]
5
6
7
Fig. 7. Normalized squared diameter of JME droplet with different support fiber diameter. (a) 673, (b) 773, (c) 873 and (d) 973 K.
Fig. 8. Sequence images of JME droplets. (unit: s).
5
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is droplet vaporization rate constant without fiber.
673 K 773 K 873 K 973 K
0.25
K [mm2/s]
0.2 0.15
0.05
0.01
0.015
d2f [mm2]
0.02
0.025
Fig. 9. The evaporation rate constant of JME droplet as a function of squared diameter of support fiber.
45
673 K 773 K 873 K 973 K
40
IJtotal [s/mm2]
35 30 25 20 15 10 5 0 0.06
0.08
0.1
0.12
0.14
(5)
q ∝df2
(6)
q ∝ (T − Ts )
(7)
K∝q
(8)
Since the fiber diameter is very small, the heat flux through fiber can be regarded as one-dimensional, the heat flux is proportional to the cross-section of fiber or df2 [24]. According to the quasi-steady theory, the heat flux is proportional to the difference between the ambient temperature and the droplet surface temperature (T − Ts), while Ts is approximately constant, thus the vaporization rate constant varies linearly with the heat flux. This is consistent with the influence of fiber on n-heptane droplets in literature. It can also be seen from the figure that when the ambient temperature exceeds 773 K, the droplet vaporization rate constant increases sharply with the increase of fiber diameter, which indicates that the droplet vaporization rate is more obvious with the increase of fiber diameter at 773 K. Therefore, when the ambient temperature is lower than 773 K, the fiber diameter should be less than 0.15 mm, but when the ambient temperature is higher than 773 K, the fiber diameter should be less than 0.1 mm. Meanwhile, the influence of fiber diameter on droplet lifetime at different ambient temperatures is also analyzed. As shown in Fig. 10, the linear slope gradually decreased with the temperature improved. This indicates that the increase of fiber diameter at high temperature has less effect on droplet lifetime, but greater influence at low temperatures. This is because the initial volume expansion rate of droplet is greater than the vaporization rate at low temperatures, while the vaporization rate is greater than the volume expansion rate at high temperatures. Therefore, the droplet has entered the stable vaporization stage ahead of time before it has fully expanded. The droplet lifetime decreases linearly with the increase of fiber diameter. The relationship between support fiber diameter and droplet lifetime is described by as follow:
0.1
0
K (T ) = Cf (T ) × df2 + K 0 (T )
0.16
df [mm]
τtotal (T ) = −mf (T ) × df + t0 (T )
Fig. 10. The evaporation lifetime of JME droplet as a function of diameter of support fiber.
(9)
where mf is a temperature-dependent coefficient, t0 is droplet lifetime without fiber.
the normalized squared diameter curves of supported by other two fibers (0.08 and 0.1 mm), JME droplet does not undergo micro-explosions at 973 K. Therefore, the micro-explosion is caused by the heat transfer of support fiber. This is because the droplet temperature is slightly below the boiling point of the fuel. With the local heat gain from the fiber, and local hot-spots will form inside the droplet. Meanwhile, local boiling [33–35] or Leidenfrost effect [36] at the dropletfiber interface may take place, thus some small bubbles are formed. Small bubbles form large bubbles through coalescence and eventually ruptured. Fig. 8 shows the sequence images of JME droplets with fiber diameter of 0.08 and 0.15 mm at 973 K. It can be seen that the JME droplet vaporization is relatively stable when the fiber diameter is 0.08 mm, and the droplet diameter decreases uniformly. However, when the fiber diameter is 0.15 mm, the droplet expands obviously and micro-explosion occurs. Typical processes such as 2.66 ~ 2.67 s, 3.37 ~ 3.38 s, 4.06 ~ 4.07 s and 4.41 ~ 4.42 s. Fig. 9 represent the vaporization rate constant of JME droplet as a function of squared diameter of support fiber at elevated temperatures. The influence of fiber diameter on droplet vaporization rate constant shows a linear relationship at different temperatures. The relationship between the fiber diameter and the vaporization rate constant of droplet can be described by Eq. (5). The slope of a straight line Cf is a temperature-dependent coefficient, and the intercept of straight line K0
3.2. Effect of thermal conductivity The thermal conductivity of support fiber also affects the vaporization of droplets, which has been neglected in previous studies. In order to study the effect of the thermal conductivity on the droplet vaporization characteristics, three materials with different thermal conductivity are selected in this study: quartz, iron, and copper. Their thermal conductivities are 1.4, 80, 400 W/m·K, respectively. Fig. 11 shows the normalized squared diameter of JME droplet with different thermal conductivities of support fiber. Higher thermal conductivity leads to a faster droplet vaporization rate. At 973 K, the thermal conductivity of fiber has the greatest influence on droplet vaporization, droplet micro-explosion occurs (Fig. 11d). This indicates that the thermal conductivity of fiber with a diameter of 0.08 mm can not be used in droplet vaporization experiments after its thermal conductivity exceeds 400 W/m·K. On the other hand, the larger the thermal conductivity of the fiber, the less obvious the volume expansion rate of the droplet in the initial stage. This is because the large thermal conductivity will accelerate the droplet vaporization rate and make the volume expansion rate in the initial stage smaller than its vaporization rate. The results presented in Fig. 12 suggest that there exists an increasing linear relation between the enhancement in droplet vaporization rate constant associated with the thermal conductivity of 6
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1.2 0.08 mm quartz fiber 0.08 mm iron fiber 0.08 mm copper fiber
a 1
1 0.8
(d/d0)2 [-]
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(d/d ) [-]
0.8 0.6
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20 30 t/d20 [s/mm2]
c
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0.08 mm iron fiber 0.08 mm copper fiber 0.08 mm quartz fiber
1
5
10 15 2 2 t/d0 [s/mm ]
20
25
0.08 mm quartz fiber 0.08 mm iron fiber 0.08 mm copper fiber
d
1.2 1
micro-explosion
(d/d0)2 [-]
0.8
(d/d0)2 [-]
0.6
0.4
1.2
0.08 mm quartz fiber 0.08 mm copper fiber 0.08 mm iron fiber
b
0.6
0.8 0.6
0.4
0.4
0.2
0.2
0 0
5
t/d20
2
10
0 0
15
1
[s/mm ]
2
3
4
t/d20 [s/mm2]
5
6
7
Fig. 11. Normalized squared diameter of JME droplet with different thermal conductivities of support fiber. (a) 673, (b) 773, (c) 873 and (d) 973 K.
45 673 K 773 K 873 K 973 K
0.25
35
IJtotal [s/mm2]
0.2
K [mm2/s]
673 K 773 K 873 K 973 K
40
0.15 0.1
30 25 20 15 10
0.05
5 0 0
100
200
Ȝ [W/m·K]
300
0 0
400
Fig. 12. The vaporization rate constant of JME droplet as a function of thermal conductivity of support fiber.
K (T ) = Cλ (T ) × λ +
where Cλ is a temperature-dependent coefficient, poration rate constant at zero thermal conductivity.
300
400
According to Fourier law, (10)
K 0'
200
Ȝ [W/m·K]
Fig. 13. The vaporization lifetime of JME droplet as a function of thermal conductivity of support fiber.
support fiber. The relationship can be expressed as follows:
K 0' (T )
100
q=
is droplet eva-
λAΔT s
(11)
The heat flux is linear related to the thermal conductivity of fiber. 7
Fuel 268 (2020) 117407
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Declaration of Competing Interest
Therefore, the vaporization rate constant is linear related to the thermal conductivity of fiber. When the ambient temperature is lower than 773 K, the slope of the straight line is smaller, which indicates that the thermal conductivity of fiber has little effect on droplet vaporization. This means that when the ambient temperature is lower than 773 K, the effect of fiber on droplet vaporization can be neglected. Furthermore, when the ambient temperature is higher than 873 K, the linear slope increases obviously, and the effect of fiber thermal conductivity on droplet vaporization increases obviously. Therefore, the thermal conductivity of fiber in the droplet vaporization study should not exceed 80 W/m·K. Fig. 13 shows the evaporation lifetime of JME droplet as a function of thermal conductivity of support fiber. The relationship between the thermal conductivity of fiber and the lifetime of droplet is also linear, and its expression is as follows:
τtotal (T ) = −mλ (T ) × λ + τ0' (T )
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is supported by Key Intergovernmental Specialities in International Scientific and Technological Innovation Cooper (2017YFE0130800), National Natural Science Foundation of China (Grant Nos. 91441124 & 91741122), Science Technology Department of Zhejiang Province (Grant No. GG19E060001). The authors would like to acknowledge the teachers and the students of Shanghai Jiao Tong University for their helpful comments and advice during the preparation of this paper. In addition, the first author is grateful to Ms. Qian Li for all her support and companionship.
(12)
where mλ is a temperature-dependent coefficient, τ0' is the lifetime of droplet at zero thermal conductivity. The droplet lifetime decreases with the increase of thermal conductivity, which has the greatest influence on the droplet lifetime at 673 K. This indicates that the droplet lifetime is more sensitive to the thermal conductivity of fiber at low temperatures. When the thermal conductivity of fiber is below 80 W/m·K, the effect of thermal conductivity on droplet vaporization can be neglected.
References [1] Robison JA, Brehob WM. The influence of improved mixture quality on engine exhaust emissions and performance. J Air Pollut Control Assoc 2012;17:446–53. [2] Tuckermann R, Bauerecker S, Cammenga HK. IR-Thermography of evaporating acoustically levitated drops. Int J Thermophys 2005;26:1583–94. [3] Al Zaitone BA, Tropea C. Vaporization of pure liquid droplets: Comparison of droplet vaporization in an acoustic field versus glass-filament. Chem Eng Sci 2011;66:3914–21. [4] Wang L, Wang J, Qiao X, Ju D, Lin Z. Effect of ambient temperature on the microexplosion characteristics of soybean oil droplet: The phenomenon of vaporization induced vapor cloud. Int J Heat Mass Transfer 2019;139:736–46. [5] Verwey C, Birouk M. Experimental investigation of the effect of natural convection on the vaporization characteristics of small fuel droplets at moderately elevated temperature and pressure. Int J Heat Mass Transfer 2018;118:1046–55. [6] Wang J, Qiao X, Ju D, Wang L, Sun C. Experimental study on the vaporization and micro-explosion characteristics of nanofuel droplet at dilute concentrations. Energy 2019;183:149–59. [7] Wang J, Qiao X, Ju D, Sun C, Wang T. Bubble nucleation, micro-explosion and residue formation in superheated jatropha oil droplet: The phenomena of vapor plume and vapor cloud. Fuel 2020;261:116431. [8] Nomura H, Murakoshi T, Suganuma Y, Ujiie Y, Hashimoto N, Nishida H. Microgravity experiments of fuel droplet vaporization in sub- and supercritical environments. P Combust Inst 2017;36:2425–32. [9] Verwey C, Birouk M. Experimental investigation of the effect of natural convection on the vaporization characteristics of small fuel droplets at moderately elevated temperature and pressure. Int J Heat Mass Transfer 2018;118:1046–55. [10] Manjunath M, Raghavan V, Mehta PS. Vaporization characteristics of suspended droplet of biodiesel fuels of Indian origin and their diesel blends – An experimental study. Int J Heat Mass Transfer 2015;88:28–41. [11] Ghassemi H, Baek SW, Khan QS. Experimental study on binary droplet vaporization at elevated pressures and temperatures. Combust Sci Technol 2006;178:1031–53. [12] Ma X, Zhang F, Han K, Yang B, Song G. Vaporization characteristics of acetone–butanol–ethanol and diesel blends droplets at high ambient temperatures. Fuel 2015;160:43–9. [13] Javed I, Baek SW, Waheed K. Vaporization characteristics of heptane droplets with the addition of aluminum nanoparticles at elevated temperatures. Combust Flame 2013;160:170–83. [14] Qian Y, Zhao P, Tao C, Meng S, Wei J, Cheng X. Experimental study on vaporization characteristics of lubricating oil/gasoline blended droplet. Exp Therm Fluid Sci 2019;103:99–107. [15] Meng K, Wu Y, Lin Q, Shan F, Fu W, Zhou K, et al. Micro-explosion and ignition of biodiesel/ethanol blends droplets in oxygenated hot co-flow. J Energy Inst 2019;92:1527–36. [16] Meng K, Fu W, Lei Y, Zhao D, Lin Q, Wang G. Study on micro-explosion intensity characteristics of biodiesel, RP-3 and ethanol mixed droplets. Fuel 2019;256:115942. [17] Meng K, Fu W, Li F, Lei Y, Lin Q, Wang G. Comparison of ignition, injection and micro-Explosion characteristics of RP-3 ethanol and biodiesel/ethanol mixed drops. J Energy Inst 2020;93:152–64. [18] Wu MS, Yang SI. Combustion characteristics of multi-component Cedar Bio-oil/ kerosene droplet. Energy 2016;113:788–95. [19] Yang JR, Wong SC. An experimental and theoretical study of the effects of heat conduction through the support fiber on the vaporization of a droplet in a weakly convective flow. Int J Heat Mass Transfer 2002;45:4589–98. [20] Shringi D, Dwyer HA, Shaw BD. Influences of support fibers on vaporizing fuel droplets. Comput Fluids 2013;77:66–75. [21] Ghata N, Shaw BD. Computational modeling of the effects of support fibers on vaporization of fiber-supported droplets in reduced gravity. Int J Heat Mass Transfer 2014;77:22–36. [22] Han K, Song G, Ma X, Yang B. An experimental and theoretical study of the effect of suspended thermocouple on the single droplet vaporization. Appl Therm Eng
4. Conclusion The present work experimentally investigated the effect of diameter and thermal conductivity of support fiber on fuel droplet vaporization at elevated temperatures (673–973 K) and atmospheric pressure. The average initial droplet diameter is 0.84 mm with a standard deviation of 0.03, thus the effect of initial droplet diameter on droplet vaporization is neglected. Conclusions are addressed as follows. (1) The droplet vaporization rate constant is positive linear correlated with the squared diameter of support fiber, which is consistent with the conclusion of literatures at low temperatures. However, droplet lifetime is negative linear correlated with the diameter of support fiber. (2) The droplet vaporization rate constant and lifetime are linearly related to the thermal conductivity of support fiber. The thermal conductivity has a great influence on the droplet vaporization rate constant when the temperature high than 773 K. (3) It is proved for the first time that support fiber can cause fuel droplet micro-explosion. When the fiber diameter is greater than 0.15 mm or the thermal conductivity is higher than 400 W/m·K, the micro-explosion occurs, which is due to the local boiling or Leidenfrost effect caused by support fiber inside the droplet. (4) Among the two factors affecting droplet vaporization, fiber diameter is the main factor. When the thermal conductivity of fiber is below 80 W/m·K, the effect of thermal conductivity on droplet vaporization can be neglected. The optimum combination is that the fiber diameter is less than 0.1 mm and the thermal conductivity is less than 80 W/m·K.
CRediT authorship contribution statement Jigang Wang: Conceptualization, Experiments and writing, Formal analysis, Investigation, Methodology, Writing - original draft. Xiaoyu Huang: Experiments, software, image and data processing. Xinqi Qiao: Review and editing. Dehao Ju: Review and editing. Chunhua Sun: Analysis and plotting, Visualization. 8
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Energy 2015;86:257–66. [30] Verwey C, Birouk M. Fuel vaporization: Effect of droplet size and turbulence at elevated temperature and pressure. Combust Flame 2018;189:33–45. [31] Law CK. Recent advances in droplet vaporization and combustion. Prog Energy Combust Sci 1982;8:171–201. [32] Godsave GAE. Studies of the combustion of drops in a fuel spray - the burning of single drops of fuel. Symposium (Int) Combust 1953;4:818–30. [33] Zhang Y, Huang R, Huang Y, Huang S, Ma Y, Xu S, et al. Effect of ambient temperature on the puffing characteristics of single butanol-hexadecane droplet. Energy 2018;145:430–41. [34] Zhang Y, Huang R, Xu S, Huang Y, Huang S, Ma Y, et al. The effect of different nbutanol-fatty acid methyl esters (FAME) blends on puffing characteristics. Fuel 2017;208:30–40. [35] Zhang Y, Huang R, Wang Z, Xu S, Huang S, Ma Y. Experimental study on puffing characteristics of biodiesel-butanol droplet. Fuel 2017;191:454–62. [36] Rasid AFA, Zhang Y. Combustion characteristics and liquid-phase visualisation of single isolated diesel droplet with surface contaminated by soot particles. P Combust Inst 2018;000:1–8.
2016;101:568–75. [23] Chauveau C, Birouk M, Gökalp I. An analysis of the d2-law departure during droplet vaporization in microgravity. Int J Multiphas Flow 2011;37:252–9. [24] Chauveau C, Birouk M, Halter F, Gökalp I. An analysis of the droplet support fiber effect on the vaporization process. Int J Heat Mass Transfer 2019;128:885–91. [25] Kumar MS, Prabhahar M, Sendilvelan S, Singh S, Venkatesh R, Bhaskar K. Combustion, performance and emission analysis of a diesel engine fueled with methyl esters of Jatropha and fish oil with exhaust gas recirculation. Energy Procedia 2019;160:404–11. [26] Xu Y, Keresztes I, Condo Jr. AM, Phillips D, Pepiot P, Avedisian CT. Droplet combustion characteristics of algae-derived renewable diesel, conventional #2 diesel, and their mixtures. Fuel 2016;167:295–305. [27] Liu YC, Xu Y, Avedisian CT, Hicks MC. The effect of support fibers on micro-convection in droplet combustion experiments. P Combust Inst 2015;35:1709–16. [28] Kline SJ, McClintock FA. Describing uncertainties in single sample experiment. Mech Eng 1953;75:3–9. [29] Ju D, Zhang T, Xiao J, Qiao X, Huang Z. Effect of droplet sizes on vaporization of a bi-component droplet at DME (dimethyl ether)/n-heptane-fueled engine conditions.
9
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Fuel journal homepage: www.elsevier.com/locate/fuel
Full Length Article
Experimental study on effect of support fiber on fuel droplet vaporization at high temperatures ⁎
T
⁎
Jigang Wang, Xiaoyu Huang, Xinqi Qiao , Dehao Ju , Chunhua Sun Key Laboratory of Power Machinery and Engineering, Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Droplet vaporization Support fiber Thermal conductivity Multicomponent fuel
The effect of support fiber on fuel droplet vaporization is experimentally investigated in a stagnant high-temperature environment (673–973 K) using high-speed backlit imaging technique. Droplets with nearly identical initial diameter suspended on the different support fibers, thus the effect of support fiber on droplet vaporization due to different initial droplet diameter is removed. The fiber diameters are 0.08, 0.1 and 0.15 mm, and thermal conductivities are 1.4, 80 and 400 W/m·K, respectively. Meanwhile, the experimental results are verified by theoretical analysis. The results show that the droplet vaporization rate constant is linearly related to the squared diameter and thermal conductivity of fiber, which is consistent with the results in the literature. Moreover, the droplet lifetime changes linearly with fiber diameter and thermal conductivity. An increase in the droplet vaporization rate constant with thermal conductivity of fiber, but, a decrease for droplet lifetime. It is proved for the first time that support fiber can cause fuel droplet micro-explosion at high temperatures, however, the previous studies have not been reported. When the fiber diameter is greater than 0.15 mm or the thermal conductivity is higher than 400 W/m·K, the fiber heat transfer induced micro-explosion occurred. This is caused by support fiber induced local boiling or Leidenfrost effect inside the droplet. The optimum choice is that the fiber diameter is less than 0.1 mm and thermal conductivity is less than 80 W/m·K.
1. Introduction
contact with other objects and its shape is similar to spherical. While its limitation is that it is only suitable for low-temperature environment and multi-field coupling will affect the vaporization of droplets. The second method is to continuously supply fuel to a porous sphere to keep a certain amount of liquid on its surface. And consider the porous sphere as a droplet. The principle of this method is simple, the operation is simple, and the droplet shape is standard spherical. However, the experimental error is large, it only be used to study the steady vaporization process of droplets. The third method is to suspend droplets on fibers. The main advantage of this method is that the droplet is stationary, the whole vaporization process can be recorded conveniently. Thus the vaporization of droplets in a complex environment can be studied. The disadvantage is that the support fiber can affect droplet vaporization. According to the literatures of the past 50 years, the third method is the most commonly used method. Using fiber support method, extensive studies are carried out to investigate the influence of support fiber on droplet vaporization, including experimental and theoretical studies. Yang et al. [19] studied the effect of heat conduction through support fiber on droplet vaporization at weakly convective flow under 490–750 K. They reported that the droplet vaporization is enhanced by support fiber, which is more
Over the last few decades, spray combustion has many practical and relevant aspects in modern society especially in energy generating devices such as internal combustion engines, gas turbines, and furnaces. In spray combustion, liquid fuel is converted into a spray containing a large number of droplets. The heating and vaporization of droplets is an important part of the mixture formation, which directly affects the distribution of fuel vapor and the formation of combustible mixture. The vaporization rate of fuel droplets and the spatial distribution of fuel vapor largely control the final energy release rate and component mass conversion rate, and ultimately determine the combustion, fuel economy and emission performance of the engine [1]. Therefore, the study of single droplet vaporization is the basis for better understanding the mechanism of spray combustion and realizing high-efficiency clean combustion. Three major methods are applied to experiments of single droplet vaporization, namely, gas levitation method [2,3], porous sphere method, and fiber support method [4–14]. The gas levitation method adopts gas suspending, acoustic levitation or magnetic levitation to levitate droplets in the air. Its advantage is that the droplet does not
⁎
Corresponding authors. E-mail addresses: [email protected] (X. Qiao), [email protected] (D. Ju).
https://doi.org/10.1016/j.fuel.2020.117407 Received 16 December 2019; Received in revised form 1 February 2020; Accepted 13 February 2020 0016-2361/ © 2020 Elsevier Ltd. All rights reserved.
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τ λ s
Nomenclature A C d m K t T
Contact area [mm2] Coefficient [–] Droplet diameter [mm] Coefficient [–] Evaporation rate constant [mm2/s] Droplet evaporation time [s] Ambient temperature [K]
Time [s] Thermal conductivity [W/m·K] Heat transfer distance [mm]
Subscripts 0 f λ
effective for lower gas temperatures and thicker fiber. However, when the fiber diameter was 300 μm, the total heat input decreased. Shringi et al. [20] numerically investigated the influence of support fiber on vaporizing fuel droplets at high temperatures and pressure. They found that the temperature distribution inside the support fiber was almost one-dimensional, and a significant gradient along the fiber axis led to heat transfer to the droplet. Due to the heating of support fiber, strong thermocapillary flow occurred on the droplet surface, which substantially influences droplet vaporization rate, especially for larger fiber and low Reynolds numbers. Ghata et al. [21] numerically studied the effect of fiber and thermocapillary stresses on droplet vaporization rate and shapes in reduced gravity. The results indicated that a large fiber diameter led to faster Marangoni convection. This was because the radial temperature and species gradient at the interface increase with time, and then increased the vaporization rate. Han et al. [22] using experimental and theoretical methods investigated the effect of thermocouple and single quartz fiber on dodecane/hexadecane droplet vaporization. They demonstrated that droplet vaporization rate changed non-linearly with the increasing fiber diameter. The vaporization rate of droplet supported by thermocouple is larger than droplet with quartz fiber. Chauveau et al. [23] experimentally investigated the effect of support fiber diameter on n-decane droplet vaporization at normal gravity. They used three different quartz fiber diameters (106, 144, 181 μm) to suspended an initial diameter of 0.8 mm droplet, and found that the droplet vaporization rate is increased as the fiber diameter increases, which is an indication of the enhancement of the droplet heat and mass transfer rates. In another study, they [24] neglected the effect of initial droplet diameter on droplet vaporization and compared the published experimental results using similar test conditions. The results showed that the n-heptane droplet vaporization rate constant is linearly related to the square of fiber diameter and ambient temperature. As reviewed above, previous studies have focused on the effect of diameter of support fiber on fuel droplet vaporization. The effect of thermal conductivity of fiber on droplet vaporization has not been revealed. The vaporization process of fuel droplet is often accompanied by micro-explosion, previous studies have suggested that this is due to the difference in boiling point of fuel components [12,14]. The support fiber is insufficient to cause micro-explosion at low temperatures or the fiber diameter is very small (less than 20 μm) [4,5,23,24]. However, many researchers studied the vaporization and micro-explosion characteristic of various fuel droplets using large support fiber diameters (greater than 0.05 mm) [3,4,6,7,10–18], it is very difficult to distinguish whether micro-explosion is caused by support fiber or fuel properties. As well known, support fiber increases heat transfer inside the droplet, and it will become nucleation sites of micro-bubbles and increases the probability of bubbles formation at high temperatures. Thus may cause droplet micro-explosion. In this way, the fiber induced micro-explosion will change the vaporization law of droplet. Motivated by this regard, the purpose of the present work is to experimentally investigate the effect of diameter and thermal conductivity of support fiber on fuel droplet vaporization. Three large fiber diameters, thermal conductivities, and four ambient temperatures are tested to analysis its influence on vaporization rate constant and droplet
Initial fiber Thermal conductivity
Table 1 Physical properties of JME. Fuel property
JME 3
Density at 15 °C (kg/m ) Kinematic viscosity at 40 °C (cSt) Boiling point (K) Latent heat (kJ/kg) Calorific value (MJ/kg)
882 4.5 632 256.8 39.6
lifetime.
2. Experimental apparatus and methods In order to easily obtain the droplet experimental data at high temperatures, jatropha methyl ester (JME) is chosen as the test fuel. This is because JME has a high boiling point and is easy to observe at high temperatures. Table 1 shows the physical properties of JME [25]. According to previous studies, there are three ways to suspend droplets using quartz fiber, as shown in Fig. 1. For vertical fiber supported method, there is a ball at the end of the fiber for droplet suspension (see Fig. 1a). Its shortcoming is that the diameter of quartz fiber can not be too fine (not less than 0.1 mm), and the terminal ball is large in volume which has a greater impact on droplet vaporization. For horizontal fiber supported method, the contact area between fiber and droplet is the smallest among the three ways (see Fig. 1b). However, droplet suspension is very difficult. Droplets are suspended with an initial diameter of 0.8 mm in three ways. As shown in Fig. 1, the droplet is ellipsoid in shape when suspended on vertical or horizontal fiber, whereas it is nearly spherical when suspended on the cross-fiber (see Fig. 1c). The cross-fiber support method does not cause any obvious interference in the transmission process between droplets and the surrounding gas medium [23,24]. It is the main way for droplet suspension and is widely used in droplet vaporization and combustion researches [4,5,23,24,26,27]. Therefore, the third method is used in this study. The schematic diagram of the experimental apparatus is shown in Fig. 2. The apparatus contained a heating system, a stepper motor ball screw control system and a data acquisition system. The heating system consisted of a heating chamber, a temperature controller and two thermocouples. The chamber was a cylinder with an inner diameter of 100 mm and a height of 250 mm. Two quartz windows were installed in the front and rear sides of the chamber to provide the windows of the camera and backlight source, respectively. The chamber heated by spiral-wound heating wires was capable of attaining a temperature up to 1200 K. The maximum power of heating resource was 2 KW. The accuracy of the temperature control was within ± 5 K. Two thermocouples were used to measure the temperature of the upper and lower part of the inner chamber. The stepper motor-ball screw control system contained a stepper motor controller, a stepper motor, a ball screw, and a droplet temperature protection device. The droplet was suspended on the quartz fiber, and placed in the temperature protection device. Then transported to the target position by the stepper motor-ball screw system. The droplet temperature protection device was designed to reduce droplet vaporization in the falling process. The data acquisition 2
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(a)
(b)
(c)
Ball
Fig. 1. Different droplet supported methods. (a) Vertical fiber; (b) Horizontal fiber; (c) Cross-fiber.
1 1
2
3
4
5
6
7
8
9
19 18 17 4
1. Stepper motor controller 2. Computer 3. High - speed video camera 4. Stepper motor 5. Ball screw moving device 6. Heating chamber 7. Thermocouple#1 8. Thermocouple#2 9. Nitrogen vessel 10. Air vessel 11. LED backlight 12. Insulation layer 13. Scattering film 14. Quartz glass 15. Heating wires 16. Thermal baffle 17. Droplet 18. Support framer 19. Thick quartz tube 20. Temperature controller
20 1200 K +
SET
-
16 15 14 13
6
5
3
11
12 7
8
2
9
10
Fig. 2. Schematic diagram of the experimental apparatus for droplet evaporation.
Initial droplet diameter [mm]
1 0.95 0.84
0.9 0.85 0.8 0.75 0.7 0.65 0.6 0
5
10
15
20
Droplet number [-]
25
30
Fig. 4. The initial diameter of droplets in experiments.
approximately 1200 images were recorded. In addition, at least three experiments were performed for each test condition to verify the repeatability of the results as well as to minimize statistical errors. Details of the experimental apparatus and procedures are reported in our previous papers [4,6,7]. Fig. 3 shows the schematic diagram of the image processing program. An in-house developed MATLAB code is used to determine the
Fig. 3. Schematic diagram of the image processing program.
system included a high-speed video camera (PCO. dimax S1), a LED backlight, a computer, and an acquisition system. Images were recorded at 1000 fps with a resolution of 1008 × 1008. For each experiment, 3
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1.1
diameter have some effects on the vaporization rate. In order to avoid the influence of the initial droplet diameter on droplet vaporization, the good repeatability of the initial droplet diameter is crucial. Since it is too difficult to generate a fuel droplet with exactly the same diameter in all experiments. In this work, the droplet is generated by a microsyringe and suspended at the intersection of two quartz fibers. The initial droplet diameter is evaluated using image processing. As shown in Fig. 4, the diameter of generated droplets is in the range of 0.79 mm and 0.88 mm, and the average diameter is 0.84 mm with a standard deviation of 0.03. It is found that droplets with an initial diameter of 0.8 mm will fall down from the support fiber when the fiber diameter is less than 0.08 mm. Therefore, the minimum diameter of support fiber selected in this paper is 0.08 mm. Furthermore, the repeatability and validity of experimental apparatus are very important. Two experiments under the same test conditions are selected to verify the validity of the experiment. As shown in Fig. 5, the droplet normalized squared diameter shows good consistency in the vaporization process. The maximum error is in the range of 5%.
Experiment 1 Experiment 2
1
(d/d0)2 [-]
0.9 0.8 0.7 0.6 0.5 0.4 0
2
4
6
t/d 20 [s/mm2]
8
10
12
Fig. 5. Comparison of two experiments.
3. Results and discussion
1.2
Fig. 6 shows the definitions of droplet vaporization rate constant and lifetime. For multicomponent fuel, the droplet normalized squared diameter curve is composed of two completely different stages (t1 and t2). In the first stage (t1), the droplet diameter increases and after some times starts to decrease. This is due to the thermal expansion. Afterwards, a balance between thermal expansion and vaporization determines droplet diameter. When the temperature inside the droplet reaches a quasi-steady state, the droplet diameter is determined only by evaporation, which is obey classical d2 law. Vaporization rate constant is determined by d2 law [31,32],
1
t1
t2
0
2
(d/d ) [-]
0.8 0.6
K 0.4 0.2 0
IJ 0
d2 t =1−K 2 d 02 d0
total
5
t/d
2 0
10 2
15
where d is droplet diameter [mm], t is time [s], d0 is droplet initial diameter [mm], and K is vaporization rate constant [mm2/s]. For the purpose of vaporization study, the first expansion stage is not important, because the vaporization rate constant is determined by the second part of droplet behavior [11]. In this study, the vaporization rate constant is defined as the slope of the best-fit straight line in second vaporization stage, obtained by the least square method [8–11]. The time from 0 s/mm2 to the intersection of the fitting straight line and abscissa axis is defined as droplet lifetime.
[s/mm ]
Fig. 6. Definitions of droplet evaporation rate constant and lifetime.
droplet diameter. In order to avoid the influence of background in image processing, the background of all images is removed first. Then the binarization process is applied to images. The classical Otsu's method is used to get the best threshold for each part of the region. The quartz fiber outside the droplet is removed by the morphological method. Without the image of the quartz fiber, the number of the pixels occupied by the droplet is calculated. Droplet diameter is extracted by equating the projected droplet area to that of an equivalent circle with diameter. The uncertainty of R can be calculated by Eq. (1) [28]. 2
(1)
R = X1a , X2b , X3c , ....
(2)
⎜
⎟
⎜
⎟
3.1. Effect of support fiber diameter In order to eliminate the influence of fiber thermal conductivity on droplet vaporization, three different diameters of quartz fibers are used to support droplets. Fig. 7 shows the normalized squared diameter of JME droplet with different support fiber diameter at ambient temperatures ranging from 673 K to 973 K. Each curve is the average value of three experimental data. The curve for the micro-explosion case is the best data in three trials. Because of the limited vaporization data of JME droplets in the literature, comparison with published literature data by other researchers is not given in this work. As shown in Fig. 7 ac, apart from droplet supported by 0.15 mm fiber at 973 K, the vaporization process of droplets under other experimental conditions includes two stages: initial expansion and steady vaporization stage. Moreover, droplets approximately obey d2 law in steady vaporization stage. With the increase of support fiber diameter, the droplet lifetime decreases. This indicates that the heat transfer rate of droplets increases. This is mainly due to the heat conduction of the fiber through the droplets, which results in the droplet temperature rising and the vaporization accelerating. Interestingly, the micro-explosion occurred when the fiber diameter is 0.15 mm at 973 K (Fig. 7d). Comparing with
2
2
ΔR ΔX ΔX ΔX = ⎛a 1 ⎞ + ⎛b 1 ⎞ + ⎛c 1 ⎞ + ⋯0.5 R X X 1 2 ⎝ ⎠ ⎝ ⎠ ⎝ Xn ⎠ ⎜
⎟
where R is a variable, a, b, c are coefficients. Assuming that the droplet is spherical, according to Eq. (1), the uncertainty of droplet squared diameter is
Δd 2 2 Δv = d2 3 v
(4)
(3)
where d is droplet diameter, v is droplet volume. After calculation, the uncertainty of droplet squared diameter is 4.08%. According to our and previous studies [29,30], initial droplet 4
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1.2
0.08 mm quartz fiber 0.1 mm quartz fiber 0.15 mm quartz fiber
a
1
b
0.8
(d/d0) [-]
0
0.6
2
2
(d/d ) [-]
0.8
0.4
0.6 0.4
0.2
0.2
0 0
10
20 2
30 2
0 0
40
t/d0 [s/mm ] 1.2
c
0.15 mm quartz fiber 0.08 mm quartz fiber 0.1 mm quartz fiber
1
3
10
15
0.6 0.4
d
25
0.08 mm quartz fiber 0.1 mm quartz fiber 0.15 mm quartz fiber
2 1.5 1
0.2
20
t/d02 [s/mm2]
micro-explosion
(d/d0)2 [-]
0
2
(d/d ) [-]
5
2.5
0.8
0 0
0.15 mm quartz fiber 0.1 mm quartz fiber 0.08 mm quartz fiber
1
droplet falling
0.5
5
10
t/d20 [s/mm 2]
0 0
15
1
2
3
4
t/d20 [s/mm2]
5
6
7
Fig. 7. Normalized squared diameter of JME droplet with different support fiber diameter. (a) 673, (b) 773, (c) 873 and (d) 973 K.
Fig. 8. Sequence images of JME droplets. (unit: s).
5
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is droplet vaporization rate constant without fiber.
673 K 773 K 873 K 973 K
0.25
K [mm2/s]
0.2 0.15
0.05
0.01
0.015
d2f [mm2]
0.02
0.025
Fig. 9. The evaporation rate constant of JME droplet as a function of squared diameter of support fiber.
45
673 K 773 K 873 K 973 K
40
IJtotal [s/mm2]
35 30 25 20 15 10 5 0 0.06
0.08
0.1
0.12
0.14
(5)
q ∝df2
(6)
q ∝ (T − Ts )
(7)
K∝q
(8)
Since the fiber diameter is very small, the heat flux through fiber can be regarded as one-dimensional, the heat flux is proportional to the cross-section of fiber or df2 [24]. According to the quasi-steady theory, the heat flux is proportional to the difference between the ambient temperature and the droplet surface temperature (T − Ts), while Ts is approximately constant, thus the vaporization rate constant varies linearly with the heat flux. This is consistent with the influence of fiber on n-heptane droplets in literature. It can also be seen from the figure that when the ambient temperature exceeds 773 K, the droplet vaporization rate constant increases sharply with the increase of fiber diameter, which indicates that the droplet vaporization rate is more obvious with the increase of fiber diameter at 773 K. Therefore, when the ambient temperature is lower than 773 K, the fiber diameter should be less than 0.15 mm, but when the ambient temperature is higher than 773 K, the fiber diameter should be less than 0.1 mm. Meanwhile, the influence of fiber diameter on droplet lifetime at different ambient temperatures is also analyzed. As shown in Fig. 10, the linear slope gradually decreased with the temperature improved. This indicates that the increase of fiber diameter at high temperature has less effect on droplet lifetime, but greater influence at low temperatures. This is because the initial volume expansion rate of droplet is greater than the vaporization rate at low temperatures, while the vaporization rate is greater than the volume expansion rate at high temperatures. Therefore, the droplet has entered the stable vaporization stage ahead of time before it has fully expanded. The droplet lifetime decreases linearly with the increase of fiber diameter. The relationship between support fiber diameter and droplet lifetime is described by as follow:
0.1
0
K (T ) = Cf (T ) × df2 + K 0 (T )
0.16
df [mm]
τtotal (T ) = −mf (T ) × df + t0 (T )
Fig. 10. The evaporation lifetime of JME droplet as a function of diameter of support fiber.
(9)
where mf is a temperature-dependent coefficient, t0 is droplet lifetime without fiber.
the normalized squared diameter curves of supported by other two fibers (0.08 and 0.1 mm), JME droplet does not undergo micro-explosions at 973 K. Therefore, the micro-explosion is caused by the heat transfer of support fiber. This is because the droplet temperature is slightly below the boiling point of the fuel. With the local heat gain from the fiber, and local hot-spots will form inside the droplet. Meanwhile, local boiling [33–35] or Leidenfrost effect [36] at the dropletfiber interface may take place, thus some small bubbles are formed. Small bubbles form large bubbles through coalescence and eventually ruptured. Fig. 8 shows the sequence images of JME droplets with fiber diameter of 0.08 and 0.15 mm at 973 K. It can be seen that the JME droplet vaporization is relatively stable when the fiber diameter is 0.08 mm, and the droplet diameter decreases uniformly. However, when the fiber diameter is 0.15 mm, the droplet expands obviously and micro-explosion occurs. Typical processes such as 2.66 ~ 2.67 s, 3.37 ~ 3.38 s, 4.06 ~ 4.07 s and 4.41 ~ 4.42 s. Fig. 9 represent the vaporization rate constant of JME droplet as a function of squared diameter of support fiber at elevated temperatures. The influence of fiber diameter on droplet vaporization rate constant shows a linear relationship at different temperatures. The relationship between the fiber diameter and the vaporization rate constant of droplet can be described by Eq. (5). The slope of a straight line Cf is a temperature-dependent coefficient, and the intercept of straight line K0
3.2. Effect of thermal conductivity The thermal conductivity of support fiber also affects the vaporization of droplets, which has been neglected in previous studies. In order to study the effect of the thermal conductivity on the droplet vaporization characteristics, three materials with different thermal conductivity are selected in this study: quartz, iron, and copper. Their thermal conductivities are 1.4, 80, 400 W/m·K, respectively. Fig. 11 shows the normalized squared diameter of JME droplet with different thermal conductivities of support fiber. Higher thermal conductivity leads to a faster droplet vaporization rate. At 973 K, the thermal conductivity of fiber has the greatest influence on droplet vaporization, droplet micro-explosion occurs (Fig. 11d). This indicates that the thermal conductivity of fiber with a diameter of 0.08 mm can not be used in droplet vaporization experiments after its thermal conductivity exceeds 400 W/m·K. On the other hand, the larger the thermal conductivity of the fiber, the less obvious the volume expansion rate of the droplet in the initial stage. This is because the large thermal conductivity will accelerate the droplet vaporization rate and make the volume expansion rate in the initial stage smaller than its vaporization rate. The results presented in Fig. 12 suggest that there exists an increasing linear relation between the enhancement in droplet vaporization rate constant associated with the thermal conductivity of 6
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1.2 0.08 mm quartz fiber 0.08 mm iron fiber 0.08 mm copper fiber
a 1
1 0.8
(d/d0)2 [-]
0
2
(d/d ) [-]
0.8 0.6
0.4
0.2
0.2
0 0
10
20 30 t/d20 [s/mm2]
c
0 0
40
0.08 mm iron fiber 0.08 mm copper fiber 0.08 mm quartz fiber
1
5
10 15 2 2 t/d0 [s/mm ]
20
25
0.08 mm quartz fiber 0.08 mm iron fiber 0.08 mm copper fiber
d
1.2 1
micro-explosion
(d/d0)2 [-]
0.8
(d/d0)2 [-]
0.6
0.4
1.2
0.08 mm quartz fiber 0.08 mm copper fiber 0.08 mm iron fiber
b
0.6
0.8 0.6
0.4
0.4
0.2
0.2
0 0
5
t/d20
2
10
0 0
15
1
[s/mm ]
2
3
4
t/d20 [s/mm2]
5
6
7
Fig. 11. Normalized squared diameter of JME droplet with different thermal conductivities of support fiber. (a) 673, (b) 773, (c) 873 and (d) 973 K.
45 673 K 773 K 873 K 973 K
0.25
35
IJtotal [s/mm2]
0.2
K [mm2/s]
673 K 773 K 873 K 973 K
40
0.15 0.1
30 25 20 15 10
0.05
5 0 0
100
200
Ȝ [W/m·K]
300
0 0
400
Fig. 12. The vaporization rate constant of JME droplet as a function of thermal conductivity of support fiber.
K (T ) = Cλ (T ) × λ +
where Cλ is a temperature-dependent coefficient, poration rate constant at zero thermal conductivity.
300
400
According to Fourier law, (10)
K 0'
200
Ȝ [W/m·K]
Fig. 13. The vaporization lifetime of JME droplet as a function of thermal conductivity of support fiber.
support fiber. The relationship can be expressed as follows:
K 0' (T )
100
q=
is droplet eva-
λAΔT s
(11)
The heat flux is linear related to the thermal conductivity of fiber. 7
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Declaration of Competing Interest
Therefore, the vaporization rate constant is linear related to the thermal conductivity of fiber. When the ambient temperature is lower than 773 K, the slope of the straight line is smaller, which indicates that the thermal conductivity of fiber has little effect on droplet vaporization. This means that when the ambient temperature is lower than 773 K, the effect of fiber on droplet vaporization can be neglected. Furthermore, when the ambient temperature is higher than 873 K, the linear slope increases obviously, and the effect of fiber thermal conductivity on droplet vaporization increases obviously. Therefore, the thermal conductivity of fiber in the droplet vaporization study should not exceed 80 W/m·K. Fig. 13 shows the evaporation lifetime of JME droplet as a function of thermal conductivity of support fiber. The relationship between the thermal conductivity of fiber and the lifetime of droplet is also linear, and its expression is as follows:
τtotal (T ) = −mλ (T ) × λ + τ0' (T )
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement This work is supported by Key Intergovernmental Specialities in International Scientific and Technological Innovation Cooper (2017YFE0130800), National Natural Science Foundation of China (Grant Nos. 91441124 & 91741122), Science Technology Department of Zhejiang Province (Grant No. GG19E060001). The authors would like to acknowledge the teachers and the students of Shanghai Jiao Tong University for their helpful comments and advice during the preparation of this paper. In addition, the first author is grateful to Ms. Qian Li for all her support and companionship.
(12)
where mλ is a temperature-dependent coefficient, τ0' is the lifetime of droplet at zero thermal conductivity. The droplet lifetime decreases with the increase of thermal conductivity, which has the greatest influence on the droplet lifetime at 673 K. This indicates that the droplet lifetime is more sensitive to the thermal conductivity of fiber at low temperatures. When the thermal conductivity of fiber is below 80 W/m·K, the effect of thermal conductivity on droplet vaporization can be neglected.
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4. Conclusion The present work experimentally investigated the effect of diameter and thermal conductivity of support fiber on fuel droplet vaporization at elevated temperatures (673–973 K) and atmospheric pressure. The average initial droplet diameter is 0.84 mm with a standard deviation of 0.03, thus the effect of initial droplet diameter on droplet vaporization is neglected. Conclusions are addressed as follows. (1) The droplet vaporization rate constant is positive linear correlated with the squared diameter of support fiber, which is consistent with the conclusion of literatures at low temperatures. However, droplet lifetime is negative linear correlated with the diameter of support fiber. (2) The droplet vaporization rate constant and lifetime are linearly related to the thermal conductivity of support fiber. The thermal conductivity has a great influence on the droplet vaporization rate constant when the temperature high than 773 K. (3) It is proved for the first time that support fiber can cause fuel droplet micro-explosion. When the fiber diameter is greater than 0.15 mm or the thermal conductivity is higher than 400 W/m·K, the micro-explosion occurs, which is due to the local boiling or Leidenfrost effect caused by support fiber inside the droplet. (4) Among the two factors affecting droplet vaporization, fiber diameter is the main factor. When the thermal conductivity of fiber is below 80 W/m·K, the effect of thermal conductivity on droplet vaporization can be neglected. The optimum combination is that the fiber diameter is less than 0.1 mm and the thermal conductivity is less than 80 W/m·K.
CRediT authorship contribution statement Jigang Wang: Conceptualization, Experiments and writing, Formal analysis, Investigation, Methodology, Writing - original draft. Xiaoyu Huang: Experiments, software, image and data processing. Xinqi Qiao: Review and editing. Dehao Ju: Review and editing. Chunhua Sun: Analysis and plotting, Visualization. 8
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