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Experimental investigation on subcooled boiling heat transfer of emulsified kerosene
International Journal of Heat and Mass Transfer 145 (2019) 118744
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation on subcooled boiling heat transfer of emulsified kerosene Hui Pan, Qincheng Bi ⇑, Fan Feng, Zhaohui Liu, Song Feng State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
a r t i c l e
i n f o
Article history: Received 9 June 2019 Received in revised form 13 September 2019 Accepted 14 September 2019 Available online 1 October 2019 Keywords: Emulsified kerosene Subcooled boiling Heat transfer Correlation
a b s t r a c t To investigate heat transfer characteristics of emulsified kerosene in a mini tube, experiments were conducted at the pressure of 3.0–5.0 MPa, mass flow rate of 0.8–2.4 gs1, and water mass fraction of 10%–50%. Water in oil type emulsion was prepared using the surfactant of span-80. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range were revealed. More attention was focused on subcooled boiling of emulsified kerosene. Depending mainly on low-boiling temperature dispersed phase of water, the heat transfer of emulsified kerosene could be divided into 6 regions: single liquid-phase convection, subcooled boiling, saturated nucleate boiling, film boiling, steam-kerosene convection, and single gas-phase convection. Heat transfer deterioration characterized by a significant soar in wall temperature could be observed in the film boiling region. In the fully developed subcooled boiling region, higher heat transfer coefficient could be achieved at lower pressure. With an increase in mass flow rate, subcooled boiling was postponed to higher heat flux. At the same heat flux, the fluid temperature was negatively correlated with the water mass fraction. However, the effect of water mass fraction on inner wall temperature could be ignored. The subcooled boiling heat transfer was enhanced at lower water mass fraction. Most of the existing enhancement-factor type correlations underestimated the subcooled boiling heat transfer of emulsified kerosene. According to the experimental data, a new enhancement-factor type correlation was proposed for subcooled boiling heat transfer of emulsified kerosene. The mean absolute deviation of the new correlation was 9.9%. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The active regenerative cooling technology [1] has been widely applied to the thermal protection of the scramjet. In this technology, endothermic hydrocarbon fuel flows through the minor channels in the wall of the engine, absorbing the aerodynamic heat, and cracks into small molecules, which significantly promote the combustion process. As the speed of the vehicle increases to hypersonic, the physical and chemical heat sink of the fuel is incompetent to meet the cooling requirement. At the speed of 8 Ma, the heat sink requirement is 3.5–4.5 MJkg1 [2], which exceeds the heat sink of most endothermic hydrocarbon fuel. What is worse, coke deposition in the channel attributed to the thermal cracking of hydrocarbon fuel will hinder heat transfer and block fuel channels of the aircraft. It was found that the steam reforming reaction between hydrocarbon fuel and water could increase heat absorption and restrain coke formation [3]. The water/kerosene emulsion has been viewed as the most promising surrogate fuel ⇑ Corresponding author. E-mail address: [email protected] (Q. Bi). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118744 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
for the hypersonic vehicle in recent years, and many investigations were performed on coking [4,5], heat sink [6], and reaction kinetics [7,8] of emulsified kerosene. In particular, a few publications can be available on heat transfer of emulsified kerosene [9,10]. Hou et al. [9] numerically investigated heat transfer characteristics of emulsified kerosene and compared with those of pure kerosene. They reported that emulsified kerosene could bring down the wall temperature and restrain coke deposition compared with pure kerosene. An increase in water content would result in a better heat transfer performance, but the reduction of coke deposition was not sensitive to the water content. Considering the influences of thermophysical properties, thermal cracking, and steam reforming reaction, the same group simulated heat transfer and heat sink of emulsified RP-3 in a rectangular channel [10]. Heat transfer deterioration because of film boiling of water was discovered in the result. Both thermal cracking and steam reforming reactions could enhance the heat sink of emulsified fuel. The investigations mentioned above were conducted on the numerical method. Nevertheless, experimental investigations on heat transfer of emulsified kerosene have not been reported in the literature.
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Nomenclature Bo CP d F G H h I Ja L m Nu P Pr q Re r T U V X x
boiling number/– specific heat capacity/kJkg1°C1 diameter/mm fluid-surface parameter/– mass flux/kgm2s1 heat sink or specific enthalpy/kJkg1 heat transfer coefficient/kWm2°C1 heating current/A Jacob number/– length/mm mass flow rate/gs1 Nusselt number/– pressure/MPa Prandtl number/– heat flux/kWm2 Reynolds number/– radius/mm temperature/°C heating voltage/V velocity/ms1 quality/– distance/cm
Greek symbols l dynamic viscosity/Pas k thermal conductivity/Wm1°C1 q density/kgm3 / heat source/Wm3
Emulsified kerosene is an immiscible mixture, which contains kerosene and water. The working pressure (3–5 MPa) is higher than the critical pressure of kerosene but much lower than the critical pressure of water. Evaporation and phase transition of water will occur with an increase in emulsion fluid temperature. Peculiar phenomena such as forced convection of kerosene superposed with subcooled boiling of water can be detected. Although convective heat transfer of aviation kerosene in vertical miniature tubes with various diameters [11], vertical helical tubes [12], and Uturn tubes [13] has been investigated systematically, the heat transfer characteristics of emulsified kerosene are distinctly different from those of pure water [14] or pure kerosene. The heat transfer characteristics of emulsified silicone oil [15– 19] and dilute emulsion [20–22] have drawn much more attention in recent years due to their wide range of applications in distinct industrial sectors. Considering the effect of dispersed particle diameter on heat transfer, Nomura and Kumano [15] reported flow and heat transfer characteristics of silicone oil in water emulsion in a micro channel. The result indicated that the heat transfer was enhanced at larger particle size, and when the relative diameter was less than 0.01, the emulsion could be regarded as singlephase flow. Later, Morimoto et al. [16] experimentally investigated natural convection of silicone oil in water emulsions in a rectangular vessel. Multiple convection layers were observed in the emulsion, and an increase in oil volume fraction could enhance the natural convection heat transfer of the emulsion. Heat transfer deterioration of two kinds of emulsified silicon oils was discussed by Gasanov [17]. They pointed out that the critical heat fluxes of emulsified silicon oils were lower than that of pure silicon oil. While the volume fraction of the dispersed phase is less than 5%, the emulsion can be regarded as a dilute emulsion. Roesle et al. [20] investigated pool boiling of dilute emulsions of FC-72 and pentane in water. The results revealed that dilute emulsions required a lower onset boiling temperature than pure water due
w
u
x
enhancement-factor/– volume fraction/– water mass fraction/–
Subscripts b bulk cal calculation D-B Dittus-Boelter e emulsion eff effective exp experiment G Gnielinski g gas phase i inner K kerosene l liquid phase lg liquid phase to gas phase loss heat loss o outer out outlet sat saturation sp single-phase sub subcooling tp two-phase W water w wall
to the low boiling of the dispersed phase. On the other hand, Janssen and Kulacki [22] experimentally investigated flow boiling of dilute emulsion. The dispersed phase of the emulsion was FC-72 or pentane with the volume fraction of 0.1–2.0%. It was found that the flow boiling heat transfer was enhanced with an increase in the volume fraction of FC-72. However, heat transfer enhancement was not observed for pentane emulsion. Although heat transfer characteristics, including forced convection [15,18], natural convection [16], subcooled flow boiling [19,22], pool boiling [20,23], and heat transfer deterioration [17] of the emulsion have been widely discussed, they were not applied to regenerative active cooling, and the emulsion temperature in these investigations was relatively low. Especially, little information is available in the literature regarding the experimental investigation on heat transfer of emulsified kerosene. It is urgent to conduct the experimental investigation on heat transfer of emulsified kerosene for their potential applications in the scramjet. In this paper, a synthetic kerosene with the critical point of 2.16 MPa and 395.8 °C was used as the base fuel. Experiments were conducted at different pressure, mass flow rate, and water mass fraction to study heat transfer of water/kerosene emulsion. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range were illustrated and much more attention was focused on subcooled boiling.
2. Experimental system and methods 2.1. Experimental system The experimental investigation was conducted on the test loop as shown in Fig. 1. In practical application, the mass fraction of kerosene is much higher than that of water. The structure of the emulsion is dependent on the Hydrophilic-Lipophilic Balance (HLB)
H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
3
T
T 5 6
3 4
dP
1
7
8
2
P 9
13 15 12 11
10
14
1 circulating pump, 2 Fuel tank, 3 constant flow pump, 4 mass flow meter, 5 armored thermocouple, 6 test section, 7 differential pressure transducer, 8 pressure transducer, 9 filter, 10 condenser, 11 back pressure valve, 12 gas-liquid separator, 13 gas flowmeter, 14 waste tank, 15 gas product Fig. 1. Schematic diagram of the experimental system.
number of surfactant. It is reasonable to prepare water in oil (W/O) type emulsion with the help of a low HLB surfactant. The surfactant used in this paper was span-80 (HLB = 4.3) with a mass fraction of 0.2%. The water/kerosene emulsion was prepared in a fuel tank. Due to the density difference between kerosene and water, the emulsion was inclined to stratify, so a circulating pump was applied to mix the kerosene and water during the test. The photographs of emulsified kerosene at different water mass fraction after 1 h standing are exhibited in Fig. 2. At the water mass fraction of 10%, the content of water was much less than kerosene and only a small amount of kerosene formed water in oil type micelles with the aid of surfactant. Most of the kerosene was in a free state. The density of water in oil micelle was large than that of kerosene, so the water in oil micelles with milk-white color deposited on the bottom of the sampling bottle. With an increase in the water mass fraction, the content of kerosene in a free state reduced. When the water mass fraction increased to 30%, the water in oil micelles occupied more than half of the sampling bottle. At the water mass fraction of 50%, almost all the kerosene formed water in oil micelles. As a result, stratification did not occur for emulsified fuel at the water mass fraction of 50%. The emulsion in the fuel tank was driven by a constant flow pump that could accurately control the volume flow rate with a precision of 1 mLmin1. Then the emulsion flowed through a mass flow meter and the test section that was horizontally arranged in the test loop. The pressure drop of the test section was monitored by a differential pressure transducer. The outlet emulsion temperature and the pressure of the
test loop were measured by an armored thermocouple and a pressure transducer respectively. The high temperature emulsion from the outlet of the test section flowed through a filter, and then it was cooled down to the ambient temperature by a condenser. The pressure of the test loop was regulated by a back pressure valve. The reaction product was separated in a gas-liquid separator. A nickel base alloy GH3128 tube with a length of 126 cm was used as the test section owing to its endurance to ultra high temperature. The outer and inner diameters of the tube were 3.0 and 2.0 mm, and the heating length was 120 cm. The test tube was directly heated by large alternating current, and twenty-four thermocouples were spot welded on the side of the tube with a spacing of 5 cm to measure the outer wall temperature, as shown in Fig. 3. Experiments were conducted at the pressure of 3.0–5.0 MPa, water mass fractions of 10–50%, and mass flow rate of 0.8– 2.4 gs1. Before each test, the mass flow rate and pressure were adjusted to the specified values, and then the outlet emulsion temperature slowly increased from 50 °C to 700 °C by an interval of 25 °C. When the heat transfer between the emulsified kerosene and the heating tube reached the balance, at least 90 series of datasets were recorded by a data acquisition system with a sampling frequency of 1.5 Hz. The average value of each measured parameter was used to evaluate the heat transfer characteristics of emulsified kerosene. 2.2. Data reductions The effective heat flux is dependent on the heating power and the inner surface area of the test tube.
qeff ¼
UI
RL
pdo qloss dx pdi L
0
ð1Þ
where U and I are heating voltage and current of the test section, and qloss is the heat loss. The inner wall temperature of the test tube is acquired by solving the one-dimensional heat conduction equation of the cylinder. 2
d T 1 dT / þ ¼0 þ dr 2 r dr k
10%
30%
50%
Fig. 2. Photographs of emulsified kerosene after 1 h standing.
ð2Þ
where / is the heat source of the test tube, and k is the thermal conductivity of GH3128 alloy. The outer wall temperature and heat loss can be used as the boundary condition.
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
10 cm 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
120 cm 126 cm Fig. 3. Arrangement of thermocouples on the test tube.
(
T ¼ T w;o ; ðr ¼ ro Þ ¼ qloss ; ðr ¼ ro Þ k dT dr
ð3Þ
T w;i
UI
RL 0
pdo qloss dx m
ð5Þ
Two dimensionless parameters, Bo number and Ja number are usually used in boiling heat transfer correlations. Bo number is the ratio of external heat and latent heat, and Ja number is the ratio of sensible heat and latent heat.
T b ðxÞ ¼ f
!
Rx
pdi qeff dx 0 m
;H
ð6Þ
Then, the heat transfer coefficient has the form
h¼
qeff T w;i T b
ð7Þ
The superheat temperature of the inner wall and the subcooling of the emulsion are defined as
DT sat ¼ T w;i T sat
ð8Þ
DT sub ¼ T sat T b
ð9Þ
where Tsat is the saturation temperature of water. The thermophysical properties of emulsified kerosene are crucial for analyzing heat transfer characteristics and fitting heat transfer correlation. However, only the specific heat capacity of emulsified kerosene was measured in our previous work [24], as depicted in Fig. 4(a). Other thermophysical properties, such as density, viscosity, and thermal conductivity are calculated by empirical equations. The density of emulsified kerosene is calculated by the weighted average density of kerosene and water.
qe ¼
qW qK
xqK þ ð1 xÞqW
ð10Þ
where x is the mass fraction of water in the emulsion. Maxwell correlation was recommended by many researchers [25] to calculate the thermal conductivity of emulsion.
ke ¼ kK
2kK þ kW þ 2uðkW kK Þ 2kK þ 2kW uðkW kK Þ
ð11Þ
where u is the volume fraction of water. The relationship between u and x is given by
u¼
xqK xqK þ ð1 xÞqW
ð13Þ
Hlg ¼ xðHg;sat Hl;sat Þ
The local emulsion bulk temperature is acquired by linear interpolation between the effective heat absorption and the heat sink of emulsified kerosene. 1
ð4Þ
The heat sink of emulsified kerosene is given by
H¼
lK 1:5ulW 1þ 1u lK þ lW
The latent heat of emulsion is calculated by the latent heat of water and mass fraction.
Then the inner wall temperature is calculated as
/ 2 /r2o qloss ri ro r2i þ ¼ T w;o þ ro ln 4k 2k k ro
le ¼
ð12Þ
The viscosity of emulsified kerosene is obtained from Chen et al. [26] equation. It has been validated that the equation can accurately predict the viscosity of water in oil type emulsion with the water mass fraction less than 60%.
ð14Þ
Bo ¼
qeff GHlg
ð15Þ
Ja ¼
C P DT sub Hlg
ð16Þ
Thermophysical properties of emulsified kerosene at different water mass fraction are shown in Fig. 4. When the temperature exceeds the saturation temperature, water in the emulsion evaporates, and the density of the emulsion decreased abruptly. The structure of emulsified kerosene may not be water in oil type after water evaporates. It may be inaccurate to calculate the viscosity or thermal conductivity by equations, so the viscosity and thermal conductivity of emulsified kerosene are only shown at the temperature lower than the saturation temperature. Before the test, the experimental system was validated by deionized water at the pressure of 3.0 MPa and mass flow rate of 2.0 gs1. The Nu numbers acquired by the validation test and predicted by Gnielinski equation are compared in Fig. 5. A majority of points fell into the error band of ±5%, and the mean absolute deviation was 3.4%. The experimental system is qualified to perform the heat transfer investigation. 3. Results and discussion 3.1. Basic heat transfer characteristics of emulsified kerosene The emulsified kerosene contains water and kerosene, and the working pressure is much lower than the critical pressure of water. Flow boiling heat transfer will take place in the tube when the inner wall temperature is high enough to nucleate bubbles. Flow boiling is a complicated process. In order to understand the basic heat transfer characteristics of emulsified kerosene, it would be better to illustrate the flow boiling heat transfer of water. The heat transfer regions and flow patterns of water flow boiling in the heating tube [27] are shown in Fig. 6. When the wall temperature and fluid temperature are lower than the saturation temperature, no bubbles form in the fluid. The heat transfer region is convective heat transfer to liquid, and the heat transfer coefficient is relatively low. In the subcooled boiling region, the inner wall temperature is higher than the saturation temperature, but the fluid temperature is still lower than the saturation temperature. Steam bubbles growing on the heating wall depart to form bubbly flow. Heat transfer coefficient increases remarkably in this region. When the thermodynamics quality reaches zero, the heat transfer mecha-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Pseudo-critical temperature
-1
Cp/kJ·kg ·°C
10 8 6
400 Tsat = 233.9 °C
200
2
Tsat = 233.9 °C
0
50
100
150
200 250 T/°C
300
350
0
400
0
50
100
(a) Specific heat capacity
200 250 T/°C
300
2500
ω 0% 10% 30% 50% 100%
0.30
1500
P = 3.0 MPa
0.25 0.20 -1
2000
0.15 ω 0% 10% 30% 50%
0.10
1000
0.05
500 0
50
100
400
-1
P = 3.0 MPa
3000
0
350
(b) Density
3500
-6
150
λ/W·m ·°C
4000
μ/10 Pa·s
ω 0% 10% 30% 50%
600
4
0
P = 3.0 MPa
800
-3
12
1000
ρ/kg·m
14
-1
P = 3.0 MPa
0% 20% 30% 50%
16
150 T/°C
200
250
(c) Viscosity
0.00
0
50
100
150 T/°C
200
250
(d) Thermal conductivity Fig. 4. Thermophysical properties of emulsified kerosene.
50
45
Deionized water -1 P = 3.0 MPa m = 2.0 g·s ± 5%
Nu G
40
35
30
25
20 20
25
30
35
Nu exp
40
Fig. 5. Validation of the experimental system.
45
50
nism is viewed as saturated nucleate boiling, the heat transfer coefficient increases to a rather high level. With a growth in the amount of steam bubbles, small bubbles merge to form slug flow, and then the flow pattern develops to annular flow. The heat transfer process for annular flow is forced convective heat transfer through liquid film. The inner wall temperature reduces below the nucleation temperature, and a slight increase in heat transfer coefficient can be observed. The steam is generated on the liquid film-vapor interface. With an increase in the velocity of vapor, some liquid droplets are torn from the film. After the film is depleted by evaporation and entrainment, the heating wall is exposed to steam. The inner wall temperature increases abruptly, which signifies heat transfer deterioration. The droplets still exist after the dryout point, and the flow pattern is called mist flow. In this region, the inner wall temperature slightly decreases due to the evaporation of droplets and the high flow velocity of mist flow. After the droplets totally evaporate, the heat transfer mechanism is convective heat transfer to vapor, and the corresponding flow pattern is single-phase vapor. The flow boiling of emulsified kerosene is more sophisticated than that of pure water. Emulsified kerosene is a non-azeotropic mixture with the pseudo-critical temperature of kerosene higher than the saturation temperature of water. Kerosene could act as the liquid phase during the boiling of water. This paper mainly focuses on the subcooled boiling heat transfer characteristics of emulsified kerosene. The reforming reaction between kerosene and water steam at high temperature was not
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Wall and fluid temperature
X=1
Heat transfer coefficient
Heat transfer regions
Flow patterns Single-phase vapor
Convective heat transfer to vapor
Mist flow
Liquid deficient region
Dryout Annular flow with entrainment Forced convective heat transfer through liquid film Annular flow Fluid temperature
Wall temperature
Slug flow Saturated nucleate boiling X=0
Bubbly flow
Saturation temperature
Subcooled boiling Convective heat transfer to liquid
Single-phase liquid Fig. 6. Heat transfer regions of flow boiling.
500
Pout = 3.0 MPa
ω = 30%
m = 2.4 g·s
-1
-2
q/kW·m 422 457 485 520 563
450 400
Tw,i /°C
involved in this paper. The test conducted at the pressure of 3.0 MPa, mass flow rate of 2.4 gs1 and water mass fraction of 30% was chosen as a typical case to analyze the basic heat transfer characteristics of emulsified kerosene. The inner wall temperature of the test tube demonstrated complex variations along the axis direction at the heat fluxes of 422–563 kWm2, as shown in Fig. 7. The saturation temperature of water is 233.9 °C at the pressure of 3.0 MPa. The inner wall temperature was lower than the saturation temperature near the inlet of the tube. Then the inner wall temperature increased to slightly higher than the saturation temperature, and reached a plateau. At somewhere of the tube, the inner wall temperature would depart from the saturation temperature, and was followed by a sharp soar. At the heat fluxes of 520 and 563 kWm2, the inner wall temperature rose by approximately 100 °C in a 5 cm spacing. With an increase in heat flux, the sharp soar moved towards the inlet direction. After the peak, the inner wall temperature declined gradually, and then monotonously increased along the test tube. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range will be discussed in the following text with the help of fluid bulk temperature and heat transfer coefficient. At the heat flux of 563 kWm2, the outlet emulsion temperature was 402.1 °C. The inner wall temperature, fluid bulk temper-
350 300 250
Tsat = 233.9 °C
200 150
0
20
40
60 x/cm
80
100
120
Fig. 7. Profiles of inner wall temperature at different heat fluxes.
ature, and heat transfer coefficients along the flow direction are shown in Fig. 8(a) and (b). According to the inner wall temperature and fluid bulk temperature, the heat transfer of emulsified kero-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Pout = 3.0 MPa m = 2.4 g·s
400
q = 563 kW·m
(2)
(1)
(3)
Pout = 3.0 MPa -1
125 m = 2.4 g·s
-2
(6)
(4) (5)
ω = 30%
h -2
q = 563 kW·m
100 -1
Tpc = 285.6 °C
-2
300
T/°C
-1
150
ω = 30%
h/kW·m ·°C
500
Tsat = 233.9 °C
200 100
Tw,i
75 50 25
Tb
0
0
20
40
60 x/cm
80
100
120
0
0
20
40
(a) T vs. x
60 x/cm
80
100
120
(b) h vs. x
Fig. 8. Profiles of inner wall temperature, emulsion bulk temperature and heat transfer coefficient at the heat flux of 563 kWm2.
sene could be divided into 6 regions: (1) single liquid-phase convection, (2) subcooled boiling, (3) saturated nucleate boiling, (4) film boiling, (5) steam-kerosene convection, and (6) single gasphase convection. In the single-phase convection region, both the inner wall temperature and fluid temperature were lower than the saturation temperature of water. The heat transfer coefficient in this region was relatively low, approximately 4.0 kWm2°C1. This region only displayed near the inlet of the test tube and did not exceed 10 cm. In the subcooled boiling heat transfer region, the inner wall temperature was slightly higher than the saturation temperature, and remained unchanged along the tube. Water in the emulsion evaporated near the heating wall. The fluid temperature was lower than the saturation temperature, and increased linearly. The temperature difference between the inner wall and the emulsion reduced. As a result, the heat transfer coefficient increased markedly. In the saturated nucleate boiling region, the fluid temperature maintained at the saturation temperature. The temperature difference between the inner wall and the fluid dropped to several degrees. Since plenty of heat was absorbed by water evaporation, heat transfer coefficient reached a high level, approximately 110 kWm2°C1. In the film boiling region, a great deal of steam was generated near the heating wall, and liquid kerosene was embraced by the steam film with inferior heat transfer property. The inner wall temperature exhibited a sharp increase in this region, which indicated heat transfer deterioration. A remarkable decline in heat transfer coefficient could be observed at 75 cm from the inlet. In the steam-kerosene convection region, the fluid temperature was higher than the saturation temperature but lower than the pseudo-critical temperature. The water in the emulsion totally evaporated as steam. The heat transfer mechanism was steamkerosene two-phase convection. The inner wall temperature decreased gradually along the flow direction. This peculiar variation could be attributed to the large specific heat capacity of emulsion near the pseudo-critical temperature. The temperature corresponding to the second peak of specific heat capacity is viewed as the pseudo-critical temperature of emulsified kerosene, as shown in Fig. 4(a). Although the pseudo-critical temperature of the kerosene used in this investigation is 441.1 °C at the pressure of 3.0 MPa, the pseudo-critical temperature of emulsified kerosene will decrease with an increase in the water mass fraction. The pseudo-critical temperature of emulsified kerosene reduces to 303.7 °C, 285.6 °C and 278.1 °C at the water mass fraction of 20%, 30% and 50% respectively [24]. With the fluid temperature
approaching pseudo-critical temperature, the heat capacity reached a peak, and the heat transfer coefficient displayed a visible enhancement. When the fluid temperature was higher than the pseudo-critical temperature, both the kerosene and water were in the gas phase. This region is defined as single gas-phase convection. The inner wall temperature increased monotonously and the heat transfer coefficient changed little along the flow direction, owing to the mild variation of density and specific heat capacity of emulsified kerosene. Since subcooled boiling heat transfer mainly occurred near the inlet of the test tube, the inner wall temperature measured by the 5th thermocouple is chosen to analyze subcooled boiling heat transfer characteristics of emulsified kerosene. The influences of experimental parameters on subcooled boiling heat transfer and heat transfer correlations will be discussed as follows. 3.2. Effects of pressure Effects of pressure on subcooled heat transfer characteristics of emulsified kerosene at the mass flow rate of 2.4 gs1 and the water mass fraction of 10% are shown in Fig. 9. The fluid temperatures at different pressure overlapped with each other because the pressure had little influence on the fluid temperature when the fluid temperature did not exceed the saturation temperature of water. When the heat flux was lower than 100 kWm2, singlephase convection was the main heat transfer method and the heat transfer coefficient was relatively low. When the heat flux increased to 100 kWm2, the inner wall temperature was much lower than the saturation temperature, however, it began to depart from the linear increase. It was notably different from subcooled boiling characteristics of pure water. For subcooled boiling of pure water, the inner wall temperature begins to depart from linear increase only if it is high enough to nucleate bubbles [28]. At the pressure of 3.0 MPa, when the heat flux reached 350 kWm2, the inner wall temperature exceeded the saturation temperature of water, but it still increased with heat flux. This was regarded as partially subcooled boiling heat transfer. When the heat flux was higher than 450 kW, the inner wall temperature reached a plateau, and was independent with the heat flux. It indicated the heat transfer method was fully developed subcooled boiling. In the fully developed subcooled boiling region, the inner wall temperature changed little. However, the fluid temperature increased with the heat flux, and the temperature difference between the inner wall and the emulsion reduced. Consequently, a remarkable enhance-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
300 m = 2.4 g·s
-1
ω = 10 %
30 m = 2.4 g·s
TC5
-1
200
-2
T/°C
150 100
Tw,i
3.0 MPa 4.0 MPa 5.0 MPa
0
200
400 600 -2 q/kW·m
20 15 10
Tb
50 0
TC5
h/kW·m ·°C
Tsat(3.0 MPa)
ω = 10 %
3.0 MPa 4.0 MPa 5.0 MPa
25
250
-1
800
5 0
1000
0
200
400 600 -2 q/kW·m
(a) T vs. q
800
1000
(b) h vs. q Fig. 9. Effects of pressure on subcooled heat transfer.
ment could be observed in heat transfer coefficient with an increase in the heat flux. A higher heat transfer coefficient could be achieved at lower pressure, because the density of emulsified kerosene is positively correlated to the pressure, and the velocity of the emulsion is larger at lower pressure.
cient could be observed in the fully developed boiling region. The experiment of minor mass flow rate could be only conducted at relatively low heat flux.
3.3. Effects of mass flow rate
Influences of water mass fraction are illustrated in Fig. 11. The inner wall temperature, fluid bulk temperature and heat transfer coefficient of pure kerosene are also plotted in Fig. 11. In the single liquid-phase convection region, the inner wall temperature decreased with an increase in water mass fraction. This phenomenon could be attributed to two reasons. On one hand, the fluid temperature was lower at larger water mass fraction. On the other hand, the specific heat capacity and thermal conductivity of the emulsion increase with the mass fraction, which is beneficial to heat transfer. There was a turning point in the inner wall temperature of pure kerosene at the heat flux of 228.3 kWm2. The slope of inner wall temperature decreased after this turning point. The kerosene temperature was 91.7 °C and the corresponding Reynolds number was 2329 at the turning point. The heat transfer was enhanced and the inner wall increased slowly because of the transition from laminar flow to turbulent flow. When the heat flux increased to 450 kWm2, the inner wall temperature at the water mass fraction of 10% was slightly higher than the saturation tem-
3.4. Effects of water mass fraction
The inner wall temperatures, emulsion temperatures, and heat transfer coefficients at different mass flow rate are plotted in Fig. 10. The experiments were conducted at the pressure of 3.0 MPa and water mass fraction of 10%. When the heat flux was lower than 100 kWm2, the heat transfer coefficient of each mass flow rate was relatively low due to single-phase convective heat transfer. At the same heat flux, the emulsified kerosene temperature increased with the reduction of mass flow rate. The higher fluid temperature could promote subcooled boiling, so subcooled boiling firstly occurred at the mass flow rate of 0.8 gs1, and then subcooled boiling successively displayed at the mass flow rate of 1.6 and 2.4 gs1 with an increase in heat flux. In other words, subcooled boiling was restrained at a higher mass flow rate. In the fully developed boiling region, the inner wall temperature was a bit higher than the saturation temperature, and was independent with the mass flow rate. Significant soars in heat transfer coeffi-
250
Pout = 3.0 MPa
50
ω = 10 %
TC5
Tsat
40 30
-2
T/°C
150
h/kW·m ·°C
-1
200
100 Tw,i
2.4 1.6 0.8
50 0
Pout = 3.0 MPa ω = 10 %
0
200
TC5
400 -2 q/kW·m
-1
Tb m/g·s
600
800
20 m/g·s 2.4 1.6 0.8
10 0
0
200
(a)
400 -2 q/kW·m
(b) Fig. 10. Effects of mass flow rate on subcooled heat transfer.
600
800
-1
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Tb
ω
Pout = 3.0 MPa
m = 2.4 g·s
-1
0% 10% 30% 50%
300
T/°C
Tsat
200
-1
TC5
ω 0% 10% 30% 50%
25 -1
400
30 Pout = 3.0 MPa m = 2.4 g·s
TC5
-2
Tw,i
20
h/kW·m ·°C
500
15 10
100 0
5 0 0
200
400
600 -2 q/kW·m
800
1000
0
200
400
(a)
600 -2 q/kW·m
800
1000
(b) Fig. 11. Effects of water mass fraction on subcooled heat transfer.
perature, and almost remained unchanged due to the evaporation of water near the heating wall. However, the inner wall temperature of pure kerosene was remarkably higher than the saturation temperature of water, and increased linearly with the heat flux. In the fully developed subcooled boiling region (q > 600 kWm2), heat transfer coefficient displayed substantial improvement. The inner wall temperature difference between each water mass fraction could be ignored. However, the emulsion temperature was lower at higher water mass fraction because of the large specific heat capacity of water. As a result, the larger heat transfer coefficient could be achieved at lower water mass fraction in the fully developed subcooled boiling region.
The subcooled boiling heat transfer coefficient of emulsified kerosene was compared with these correlations. Comparisons of enhancement-factor type correlations with experimental data at different water mass fraction are shown in Fig. 12, and the deviation of each correlation is listed in Table 2. The mean absolute deviation (MAD) and mean relative deviation (MRD) are used to estimate the prediction accuracy of these correlations.
MAD ¼
n 1X hcal hexp n 1 hexp
ð17Þ
3.5. Subcooled boiling heat transfer correlations
MRD ¼
n 1X hcal hexp n 1 hexp
ð18Þ
In the past five decades, dozens of correlations have been proposed for subcooled flow boiling heat transfer. Fang et al. [29] summarized 21 existing correlations for subcooled flow boiling, and classified them into five categories. The surface tension is an indispensable property for many correlations. However, it is quite difficult to acquire the surface tension of emulsified kerosene. The correlation in enhancement-factor type is independent with the surface tension, as shown in Table 1. For this type correlation, the subcooled boiling heat transfer coefficient is viewed as the heat transfer coefficient of single-phase corrected by an enhancement factor. Usually, the single-phase convective heat transfer coefficient is calculated by Dittus-Boelter correlation or Gnielinski correlation, and the enhancement factor is a function of Bo, Ja, and Pr.
Three correlations, Shah, Papell, and Kandlikar underestimated the subcooled heat transfer coefficient of emulsified kerosene. Shah correlation and Kandlikar correlation exhibited a similar deviation that most of the predicted points fell into the error band of 50% to 0%. Papell correlation had the biggest mean absolutely deviation for every water mass fraction. Most of the predicted points fell in the error band of 20% to 60%. Kandlikar correlation could accurately predict the heat transfer coefficient at the water content of 10%. However, the mean absolute deviation of Kandlikar correlation increased to 21.5% at the water content of 50%. The deviation of Baburajan correlation distributed in the range of 40% to 40%. It overestimated the heat transfer coefficient at the water mass fraction 10% and underestimated the heat trans-
Table 1 Enhancement-factor type correlations for subcooled boiling heat transfer. Author
Correlation
Application condition
Shah [30]
q ¼ WhDB DT sat 230Bo0:5 ; Bo > 0:3 104 W¼ 1 þ 46Bo0:5 ; Bo < 0:3 104 hD-B is the heat transfer coefficient calculated by Dittus-Boelter equation
Water, refrigerant, d = 2.4–27.1 mm, P = 0.1–13.8 MPa, DTsub = 0– 153 °C, q = 0.01–22.9 MWm2, G = 55–24200 kgm2s1
Baburajan [31]
htp =hsp ¼ 267Bo0:86 Ja0:6 Pr 0:23 0:262 l k hsp ¼ 0:023Re0:8 Pr 0:4 l b d w 0:7 q 0:756 Nutp 0:84 q g Hlg q V Nusp ¼ 90:0Ja q
Water, horizontal flow, d = 5.5, 7.5, 9.5 mm, L = 550, 750, 1000 mm, G = 450–935 kgm2s1, DTsub,in = 29, 50, 70 °C
Papell [32]
g
l
Nusp ¼ 0:021Re0:8 Pr 0:4 Kandlikar [33]
q=DT sat ¼ 1058:0Bo0:7 hsp F F is the fluid-surface parameter, and equal to 1.00 for water. hsp is the single-phase heat transfer coefficient calculated by Gnielinski correlation or Petukhov correlation
Distilled water, P = 0.1–13.8 MPa, q = 0.04–91.58 MWm2, V = 0.4– 62.2 ms1, DTsub = 3.3–186.7 °C Water, Refrigerants, cryogenic fluids, fully developed subcooled boiling
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100
100
Shah
Baburajan
ω 10% 30% 50%
40%
-1 -2
hcal/kW·m ·°C
-2
hcal/kW·m ·°C
-1
ω 10% 30% 50%
10 - 50%
1
1
10 -2 -1 hexp/kW·m ·°C
10 - 40%
1
100
1
10 -2 -1 hexp/kW·m ·°C
(a) Shah 100
(b) Baburajan 100
Papell
Kandlikar ω 10% 30% 50%
-2
-2
10
hcal/kW·m ·°C
-1
-1
ω 10% 30% 50%
hcal/kW·m ·°C
100
- 20% - 60%
1
1
10 -2 -1 hexp/kW·m ·°C
100
10 - 50%
1
1
(c) Papell
10 -2 -1 hexp/kW·m ·°C
100
(d) Kandlikar
Fig. 12. Comparison of predicted heat transfer coefficients with experimental data.
Table 2 Deviation of enhancement-factor type correlations. Water mass fraction
Correlation
MRD
MAD
Data predicted within ±10%
±20%
±40%
x = 10%
Shah Baburajan Papell Kandlikar
14.0% 33.6% 41.7% 8.3%
14.0% 36.4% 41.7% 8.3%
39.4% 13.7% 0% 74.9%
82.9% 25.7% 0% 95.5%
98.5% 50.7% 34.3% 99.7%
x = 30%
Shah Baburajan Papell Kandlikar
22.7% 0.9% 38.4% 17.8%
22.7% 13.8% 38.4% 17.8%
0% 36.5% 0% 15.4%
54.8% 75.0% 1.0% 73.1%
91.3% 99.0% 61.5% 98.1%
x = 50%
Shah Baburajan Papell Kandlikar
25.3% 1.3% 37.5% 21.5%
25.3% 12.3% 37.5% 21.5%
0% 44.3% 0.3% 0%
39.3% 73.6% 1.1% 65.7%
89.4% 85.9% 73.6% 91.8%
H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
100
Nutp/NuD-B = 375.36Bo
0.554
Ja
-0.676
0.439
Pr
(Nutp/NuD-B)cal
± 20%
10
1
1
10 (Nutp/NuD-B)exp
100
Fig. 13. Deviation of the new correlation.
(2) In the subcooled boiling region, the heat transfer coefficient was larger at lower pressure, because the density of emulsified kerosene is positively correlated with the pressure. With an increase in mass flow rate, subcooled boiling of emulsified kerosene was postponed to higher heat flux. In the single liquid-phase convection region, the inner wall temperature decreased with an increase in the water mass fraction. In the subcooled boiling region, emulsified kerosene achieved a better heat transfer performance than pure kerosene, especially at low water mass fraction. (3) The heat transfer coefficient of emulsified kerosene was compared with enhancement-factor type correlations. Most of the correlations underestimated the heat transfer coefficient except for Baburajan correlation. Kandlikar correlation could accurately predict the heat transfer coefficient of emulsified kerosene at the water mass fraction of 10%. However, the mean absolute deviation of Kandlikar correlation increased to 17.8% and 21.5% at the water mass fraction of 30% and 50% respectively. A new correlation with the mean absolute deviation of 9.9% was proposed according to the experimental data.
Declaration of Competing Interest
fer coefficient at the water mass fraction 50%. The correlations listed in Table 1 were all incompetent to predict subcooled boiling heat transfer of emulsified kerosene at different water mass fraction owing to the narrow application ranges. A new enhancement-factor type correlation was developed for subcooled boiling heat transfer of emulsified kerosene, as exhibited in Eq. (19). The enhancement factor was a function of Bo, Ja, and Pr. The coefficients in this equation were fitted by multiple regression.
Nutp =NuDB ¼ 375:36Bo0:554 Ja0:676 Pr 0:439
11
ð19Þ
where NuD-B is obtained from Dittus-Boelter correlation. The deviation between heat transfer coefficients predicted by the new correlation and experimental data is shown in Fig. 13. The mean absolutely deviation was 9.9%, and 87.1% of the predicted points fell into the error band of ±20%. The new correlation is accurate enough to predict the subcooled boiling heat transfer coefficient of emulsified kerosene at the water mass fraction of 10–50%, pressure of 3.0–5.0 MPa, and mass flux of 254.6–763.9 kgm2s1. 4. Conclusion In this perspective, the heat transfer characteristics of emulsified kerosene were experimentally investigated in a mini tube. The influences of pressure, mass flow rate, and water mass fraction on subcooled boiling were discussed. The heat transfer coefficient in the subcooled boiling region was compared with the enhancement-factor type correlations. The main conclusions are as follows. (1) According to the variations of wall temperature and fluid bulk temperature, heat transfer of emulsified kerosene covering a wide temperature range could be divided into 6 regions: single liquid-phase convection, subcooled boiling, saturated nucleate boiling, film boiling, steam-kerosene convection, and single gas-phase convection. At the water mass fraction of 30%, heat transfer deterioration accompanying a sharp increase in wall temperature occurred in the film boiling region, and the deterioration point moved towards the inlet direction with an increase in heat flux.
None. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51776167) and the National Science and Technology Major Project (2017-III-0005-0029). References [1] H. Huang, L.J. Spadaccini, D.R. Sobel, Fuel-cooled thermal management for advanced aeroengines, J. Eng. Gas Turbines Power 126 (2004) 284–293. [2] T. Edwards, L. Maurice, Hytech fuels/fuel system research, 8th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Norfolk, VA, U.S.A., 1998, AIAA-98-1562. [3] Q.M. Ming, T. Healey, L. Allen, et al., Steam reforming of hydrocarbon fuels, Catal. Today 77 (2002) 51–64. [4] L.Y. Hou, X.X. Zhang, Z.Y. Ren, Coke suppression of kerosene by wall catalytic steam reforming, Fuel Process. Technol. 154 (2016) 117–122. [5] L.Y. Hou, N. Dong, Z.Y. Ren, et al., Cooling and coke deposition of hydrocarbon fuel with catalytic steam reforming, Fuel Process. Technol. 128 (2014) 128– 133. [6] L.Y. Hou, Z. Jia, J.S. Gong, et al., Heat sink and conversion of catalytic steam reforming for hydrocarbon fuel, J. Propul. Power 28 (3) (2012) 453–457. [7] S.Y. Liu, Y. Feng, Y.C. Chu, et al., Numerical study of catalytic steam reforming of aviation kerosene at supercritical pressures, Fuel 212 (2018) 375–386. [8] I.A. Bassina, Y.P. Malkov, O.N. Molchanov, et al., Thermodynamic study of characteristics of the converter with separated supply of hydrocarbon fuel for thermo-oxidative and steam reforming, Thermophys. Aeromech. 21 (2) (2014) 249–254. [9] L.Y. Hou, H. Wang, B.J. Zhong, et al., Numerical study on heat transfer characteristics of emulsified kerosene at supercritical pressure, J. Propul. Technol. 27 (6) (2006) 488–491 (in Chinese). [10] L.Y. Hou, D.R. Zhang, X.X. Zhang, Interaction between thermal cracking and steam reforming reactions of aviation kerosene, Fuel Process. Technol. 167 (2017) 655–662. [11] Y.C. Fu, H.R. Huang, J. Wen, et al., Experimental investigation on convective heat transfer of supercritical RP-3 in vertical miniature tubes with various diameters, Int. J. Heat Mass Transf. 112 (2017) 814–824. [12] J. Wen, H.R. Huang, Y.C. Fu, et al., Heat transfer performance of aviation kerosene RP-3 flowing in a vertical helical tube at supercritical pressure, Appl. Therm. Eng. 121 (2017) 853–862. [13] Y.C. Fu, J. Wen, Z. Tao, et al., Experimental research on convective heat transfer of supercritical hydrocarbon fuel flowing through U-turn tubes, Appl. Therm. Eng. 116 (2017) 43–55. [14] K. Hata, S. Masuzaki, Subcooled boiling heat transfer for turbulent flow of water in a short vertical tube, J. Heat Transf. 132 (1) (2010) 1–11. [15] K. Nomura, H. Kumano, Experimental study on flow and heat transfer characteristics of oil-in-water emulsions in microchannels, Int. J. Heat Mass Transf. 116 (2018) 1026–1035.
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[16] T. Morimoto, T. Ikeda, H. Kumano, Study on natural convection characteristics of oil/water emulsions inside a rectangular vessel with vertical heating/cooling walls, Int. J. Heat Mass Transf. 127 (2018) 616–628. [17] B.M. Gasanov, Deterioration of heat transfer in boiling of emulsions with a low-boiling disperse phase, High Temp. 56 (4) (2018) 565–568. [18] H. Kumano, K. Hiroi, T. Asaoka, Experimental study on flow and heat transfer characteristics of oil/water emulsions: Part II – heat transfer characteristics, Appl. Therm. Eng. 127 (2017) 1555–1563. [19] B.M. Gasanov, N.V. Bulanov, Effect of the droplet size of an emulsion dispersion phase in nucleate boiling and emulsion boiling crisis, Int. J. Heat Mass Transf. 88 (2015) 256–260. [20] M.L. Roesle, D.L. Lunde, F.A. Kulacki, Boiling heat transfer to dilute emulsions from a vertical heated strip, J. Heat Transf. 137 (4) (2015) 41503. [21] M.M. Sarafraz, S.M. Peyghambarzadeh, Experimental study on subcooled flow boiling heat transfer to water–diethylene glycol mixtures as a coolant inside a vertical annulus, Exp. Therm Fluid Sci. 50 (2013) 154–162. [22] D. Janssen, F.A. Kulacki, Flow boiling of dilute emulsions, Int. J. Heat Mass Transf. 115 (2017) 1000–1007. [23] M.L. Roesle, F.A. Kulacki, An experimental study of boiling in dilute emulsions, part A: heat transfer, Int. J. Heat Mass Transf. 55 (7–8) (2012) 2160–2165. [24] S. Feng, Q.C. Bi, H. Pan, et al., Isobaric specific heat capacities of emulsified kerosene at high temperature and pressure, Thermochim. Acta 665 (2018) 127–133.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental investigation on subcooled boiling heat transfer of emulsified kerosene Hui Pan, Qincheng Bi ⇑, Fan Feng, Zhaohui Liu, Song Feng State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China
a r t i c l e
i n f o
Article history: Received 9 June 2019 Received in revised form 13 September 2019 Accepted 14 September 2019 Available online 1 October 2019 Keywords: Emulsified kerosene Subcooled boiling Heat transfer Correlation
a b s t r a c t To investigate heat transfer characteristics of emulsified kerosene in a mini tube, experiments were conducted at the pressure of 3.0–5.0 MPa, mass flow rate of 0.8–2.4 gs1, and water mass fraction of 10%–50%. Water in oil type emulsion was prepared using the surfactant of span-80. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range were revealed. More attention was focused on subcooled boiling of emulsified kerosene. Depending mainly on low-boiling temperature dispersed phase of water, the heat transfer of emulsified kerosene could be divided into 6 regions: single liquid-phase convection, subcooled boiling, saturated nucleate boiling, film boiling, steam-kerosene convection, and single gas-phase convection. Heat transfer deterioration characterized by a significant soar in wall temperature could be observed in the film boiling region. In the fully developed subcooled boiling region, higher heat transfer coefficient could be achieved at lower pressure. With an increase in mass flow rate, subcooled boiling was postponed to higher heat flux. At the same heat flux, the fluid temperature was negatively correlated with the water mass fraction. However, the effect of water mass fraction on inner wall temperature could be ignored. The subcooled boiling heat transfer was enhanced at lower water mass fraction. Most of the existing enhancement-factor type correlations underestimated the subcooled boiling heat transfer of emulsified kerosene. According to the experimental data, a new enhancement-factor type correlation was proposed for subcooled boiling heat transfer of emulsified kerosene. The mean absolute deviation of the new correlation was 9.9%. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The active regenerative cooling technology [1] has been widely applied to the thermal protection of the scramjet. In this technology, endothermic hydrocarbon fuel flows through the minor channels in the wall of the engine, absorbing the aerodynamic heat, and cracks into small molecules, which significantly promote the combustion process. As the speed of the vehicle increases to hypersonic, the physical and chemical heat sink of the fuel is incompetent to meet the cooling requirement. At the speed of 8 Ma, the heat sink requirement is 3.5–4.5 MJkg1 [2], which exceeds the heat sink of most endothermic hydrocarbon fuel. What is worse, coke deposition in the channel attributed to the thermal cracking of hydrocarbon fuel will hinder heat transfer and block fuel channels of the aircraft. It was found that the steam reforming reaction between hydrocarbon fuel and water could increase heat absorption and restrain coke formation [3]. The water/kerosene emulsion has been viewed as the most promising surrogate fuel ⇑ Corresponding author. E-mail address: [email protected] (Q. Bi). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118744 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
for the hypersonic vehicle in recent years, and many investigations were performed on coking [4,5], heat sink [6], and reaction kinetics [7,8] of emulsified kerosene. In particular, a few publications can be available on heat transfer of emulsified kerosene [9,10]. Hou et al. [9] numerically investigated heat transfer characteristics of emulsified kerosene and compared with those of pure kerosene. They reported that emulsified kerosene could bring down the wall temperature and restrain coke deposition compared with pure kerosene. An increase in water content would result in a better heat transfer performance, but the reduction of coke deposition was not sensitive to the water content. Considering the influences of thermophysical properties, thermal cracking, and steam reforming reaction, the same group simulated heat transfer and heat sink of emulsified RP-3 in a rectangular channel [10]. Heat transfer deterioration because of film boiling of water was discovered in the result. Both thermal cracking and steam reforming reactions could enhance the heat sink of emulsified fuel. The investigations mentioned above were conducted on the numerical method. Nevertheless, experimental investigations on heat transfer of emulsified kerosene have not been reported in the literature.
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Nomenclature Bo CP d F G H h I Ja L m Nu P Pr q Re r T U V X x
boiling number/– specific heat capacity/kJkg1°C1 diameter/mm fluid-surface parameter/– mass flux/kgm2s1 heat sink or specific enthalpy/kJkg1 heat transfer coefficient/kWm2°C1 heating current/A Jacob number/– length/mm mass flow rate/gs1 Nusselt number/– pressure/MPa Prandtl number/– heat flux/kWm2 Reynolds number/– radius/mm temperature/°C heating voltage/V velocity/ms1 quality/– distance/cm
Greek symbols l dynamic viscosity/Pas k thermal conductivity/Wm1°C1 q density/kgm3 / heat source/Wm3
Emulsified kerosene is an immiscible mixture, which contains kerosene and water. The working pressure (3–5 MPa) is higher than the critical pressure of kerosene but much lower than the critical pressure of water. Evaporation and phase transition of water will occur with an increase in emulsion fluid temperature. Peculiar phenomena such as forced convection of kerosene superposed with subcooled boiling of water can be detected. Although convective heat transfer of aviation kerosene in vertical miniature tubes with various diameters [11], vertical helical tubes [12], and Uturn tubes [13] has been investigated systematically, the heat transfer characteristics of emulsified kerosene are distinctly different from those of pure water [14] or pure kerosene. The heat transfer characteristics of emulsified silicone oil [15– 19] and dilute emulsion [20–22] have drawn much more attention in recent years due to their wide range of applications in distinct industrial sectors. Considering the effect of dispersed particle diameter on heat transfer, Nomura and Kumano [15] reported flow and heat transfer characteristics of silicone oil in water emulsion in a micro channel. The result indicated that the heat transfer was enhanced at larger particle size, and when the relative diameter was less than 0.01, the emulsion could be regarded as singlephase flow. Later, Morimoto et al. [16] experimentally investigated natural convection of silicone oil in water emulsions in a rectangular vessel. Multiple convection layers were observed in the emulsion, and an increase in oil volume fraction could enhance the natural convection heat transfer of the emulsion. Heat transfer deterioration of two kinds of emulsified silicon oils was discussed by Gasanov [17]. They pointed out that the critical heat fluxes of emulsified silicon oils were lower than that of pure silicon oil. While the volume fraction of the dispersed phase is less than 5%, the emulsion can be regarded as a dilute emulsion. Roesle et al. [20] investigated pool boiling of dilute emulsions of FC-72 and pentane in water. The results revealed that dilute emulsions required a lower onset boiling temperature than pure water due
w
u
x
enhancement-factor/– volume fraction/– water mass fraction/–
Subscripts b bulk cal calculation D-B Dittus-Boelter e emulsion eff effective exp experiment G Gnielinski g gas phase i inner K kerosene l liquid phase lg liquid phase to gas phase loss heat loss o outer out outlet sat saturation sp single-phase sub subcooling tp two-phase W water w wall
to the low boiling of the dispersed phase. On the other hand, Janssen and Kulacki [22] experimentally investigated flow boiling of dilute emulsion. The dispersed phase of the emulsion was FC-72 or pentane with the volume fraction of 0.1–2.0%. It was found that the flow boiling heat transfer was enhanced with an increase in the volume fraction of FC-72. However, heat transfer enhancement was not observed for pentane emulsion. Although heat transfer characteristics, including forced convection [15,18], natural convection [16], subcooled flow boiling [19,22], pool boiling [20,23], and heat transfer deterioration [17] of the emulsion have been widely discussed, they were not applied to regenerative active cooling, and the emulsion temperature in these investigations was relatively low. Especially, little information is available in the literature regarding the experimental investigation on heat transfer of emulsified kerosene. It is urgent to conduct the experimental investigation on heat transfer of emulsified kerosene for their potential applications in the scramjet. In this paper, a synthetic kerosene with the critical point of 2.16 MPa and 395.8 °C was used as the base fuel. Experiments were conducted at different pressure, mass flow rate, and water mass fraction to study heat transfer of water/kerosene emulsion. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range were illustrated and much more attention was focused on subcooled boiling.
2. Experimental system and methods 2.1. Experimental system The experimental investigation was conducted on the test loop as shown in Fig. 1. In practical application, the mass fraction of kerosene is much higher than that of water. The structure of the emulsion is dependent on the Hydrophilic-Lipophilic Balance (HLB)
H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
3
T
T 5 6
3 4
dP
1
7
8
2
P 9
13 15 12 11
10
14
1 circulating pump, 2 Fuel tank, 3 constant flow pump, 4 mass flow meter, 5 armored thermocouple, 6 test section, 7 differential pressure transducer, 8 pressure transducer, 9 filter, 10 condenser, 11 back pressure valve, 12 gas-liquid separator, 13 gas flowmeter, 14 waste tank, 15 gas product Fig. 1. Schematic diagram of the experimental system.
number of surfactant. It is reasonable to prepare water in oil (W/O) type emulsion with the help of a low HLB surfactant. The surfactant used in this paper was span-80 (HLB = 4.3) with a mass fraction of 0.2%. The water/kerosene emulsion was prepared in a fuel tank. Due to the density difference between kerosene and water, the emulsion was inclined to stratify, so a circulating pump was applied to mix the kerosene and water during the test. The photographs of emulsified kerosene at different water mass fraction after 1 h standing are exhibited in Fig. 2. At the water mass fraction of 10%, the content of water was much less than kerosene and only a small amount of kerosene formed water in oil type micelles with the aid of surfactant. Most of the kerosene was in a free state. The density of water in oil micelle was large than that of kerosene, so the water in oil micelles with milk-white color deposited on the bottom of the sampling bottle. With an increase in the water mass fraction, the content of kerosene in a free state reduced. When the water mass fraction increased to 30%, the water in oil micelles occupied more than half of the sampling bottle. At the water mass fraction of 50%, almost all the kerosene formed water in oil micelles. As a result, stratification did not occur for emulsified fuel at the water mass fraction of 50%. The emulsion in the fuel tank was driven by a constant flow pump that could accurately control the volume flow rate with a precision of 1 mLmin1. Then the emulsion flowed through a mass flow meter and the test section that was horizontally arranged in the test loop. The pressure drop of the test section was monitored by a differential pressure transducer. The outlet emulsion temperature and the pressure of the
test loop were measured by an armored thermocouple and a pressure transducer respectively. The high temperature emulsion from the outlet of the test section flowed through a filter, and then it was cooled down to the ambient temperature by a condenser. The pressure of the test loop was regulated by a back pressure valve. The reaction product was separated in a gas-liquid separator. A nickel base alloy GH3128 tube with a length of 126 cm was used as the test section owing to its endurance to ultra high temperature. The outer and inner diameters of the tube were 3.0 and 2.0 mm, and the heating length was 120 cm. The test tube was directly heated by large alternating current, and twenty-four thermocouples were spot welded on the side of the tube with a spacing of 5 cm to measure the outer wall temperature, as shown in Fig. 3. Experiments were conducted at the pressure of 3.0–5.0 MPa, water mass fractions of 10–50%, and mass flow rate of 0.8– 2.4 gs1. Before each test, the mass flow rate and pressure were adjusted to the specified values, and then the outlet emulsion temperature slowly increased from 50 °C to 700 °C by an interval of 25 °C. When the heat transfer between the emulsified kerosene and the heating tube reached the balance, at least 90 series of datasets were recorded by a data acquisition system with a sampling frequency of 1.5 Hz. The average value of each measured parameter was used to evaluate the heat transfer characteristics of emulsified kerosene. 2.2. Data reductions The effective heat flux is dependent on the heating power and the inner surface area of the test tube.
qeff ¼
UI
RL
pdo qloss dx pdi L
0
ð1Þ
where U and I are heating voltage and current of the test section, and qloss is the heat loss. The inner wall temperature of the test tube is acquired by solving the one-dimensional heat conduction equation of the cylinder. 2
d T 1 dT / þ ¼0 þ dr 2 r dr k
10%
30%
50%
Fig. 2. Photographs of emulsified kerosene after 1 h standing.
ð2Þ
where / is the heat source of the test tube, and k is the thermal conductivity of GH3128 alloy. The outer wall temperature and heat loss can be used as the boundary condition.
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
10 cm 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
120 cm 126 cm Fig. 3. Arrangement of thermocouples on the test tube.
(
T ¼ T w;o ; ðr ¼ ro Þ ¼ qloss ; ðr ¼ ro Þ k dT dr
ð3Þ
T w;i
UI
RL 0
pdo qloss dx m
ð5Þ
Two dimensionless parameters, Bo number and Ja number are usually used in boiling heat transfer correlations. Bo number is the ratio of external heat and latent heat, and Ja number is the ratio of sensible heat and latent heat.
T b ðxÞ ¼ f
!
Rx
pdi qeff dx 0 m
;H
ð6Þ
Then, the heat transfer coefficient has the form
h¼
qeff T w;i T b
ð7Þ
The superheat temperature of the inner wall and the subcooling of the emulsion are defined as
DT sat ¼ T w;i T sat
ð8Þ
DT sub ¼ T sat T b
ð9Þ
where Tsat is the saturation temperature of water. The thermophysical properties of emulsified kerosene are crucial for analyzing heat transfer characteristics and fitting heat transfer correlation. However, only the specific heat capacity of emulsified kerosene was measured in our previous work [24], as depicted in Fig. 4(a). Other thermophysical properties, such as density, viscosity, and thermal conductivity are calculated by empirical equations. The density of emulsified kerosene is calculated by the weighted average density of kerosene and water.
qe ¼
qW qK
xqK þ ð1 xÞqW
ð10Þ
where x is the mass fraction of water in the emulsion. Maxwell correlation was recommended by many researchers [25] to calculate the thermal conductivity of emulsion.
ke ¼ kK
2kK þ kW þ 2uðkW kK Þ 2kK þ 2kW uðkW kK Þ
ð11Þ
where u is the volume fraction of water. The relationship between u and x is given by
u¼
xqK xqK þ ð1 xÞqW
ð13Þ
Hlg ¼ xðHg;sat Hl;sat Þ
The local emulsion bulk temperature is acquired by linear interpolation between the effective heat absorption and the heat sink of emulsified kerosene. 1
ð4Þ
The heat sink of emulsified kerosene is given by
H¼
lK 1:5ulW 1þ 1u lK þ lW
The latent heat of emulsion is calculated by the latent heat of water and mass fraction.
Then the inner wall temperature is calculated as
/ 2 /r2o qloss ri ro r2i þ ¼ T w;o þ ro ln 4k 2k k ro
le ¼
ð12Þ
The viscosity of emulsified kerosene is obtained from Chen et al. [26] equation. It has been validated that the equation can accurately predict the viscosity of water in oil type emulsion with the water mass fraction less than 60%.
ð14Þ
Bo ¼
qeff GHlg
ð15Þ
Ja ¼
C P DT sub Hlg
ð16Þ
Thermophysical properties of emulsified kerosene at different water mass fraction are shown in Fig. 4. When the temperature exceeds the saturation temperature, water in the emulsion evaporates, and the density of the emulsion decreased abruptly. The structure of emulsified kerosene may not be water in oil type after water evaporates. It may be inaccurate to calculate the viscosity or thermal conductivity by equations, so the viscosity and thermal conductivity of emulsified kerosene are only shown at the temperature lower than the saturation temperature. Before the test, the experimental system was validated by deionized water at the pressure of 3.0 MPa and mass flow rate of 2.0 gs1. The Nu numbers acquired by the validation test and predicted by Gnielinski equation are compared in Fig. 5. A majority of points fell into the error band of ±5%, and the mean absolute deviation was 3.4%. The experimental system is qualified to perform the heat transfer investigation. 3. Results and discussion 3.1. Basic heat transfer characteristics of emulsified kerosene The emulsified kerosene contains water and kerosene, and the working pressure is much lower than the critical pressure of water. Flow boiling heat transfer will take place in the tube when the inner wall temperature is high enough to nucleate bubbles. Flow boiling is a complicated process. In order to understand the basic heat transfer characteristics of emulsified kerosene, it would be better to illustrate the flow boiling heat transfer of water. The heat transfer regions and flow patterns of water flow boiling in the heating tube [27] are shown in Fig. 6. When the wall temperature and fluid temperature are lower than the saturation temperature, no bubbles form in the fluid. The heat transfer region is convective heat transfer to liquid, and the heat transfer coefficient is relatively low. In the subcooled boiling region, the inner wall temperature is higher than the saturation temperature, but the fluid temperature is still lower than the saturation temperature. Steam bubbles growing on the heating wall depart to form bubbly flow. Heat transfer coefficient increases remarkably in this region. When the thermodynamics quality reaches zero, the heat transfer mecha-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Pseudo-critical temperature
-1
Cp/kJ·kg ·°C
10 8 6
400 Tsat = 233.9 °C
200
2
Tsat = 233.9 °C
0
50
100
150
200 250 T/°C
300
350
0
400
0
50
100
(a) Specific heat capacity
200 250 T/°C
300
2500
ω 0% 10% 30% 50% 100%
0.30
1500
P = 3.0 MPa
0.25 0.20 -1
2000
0.15 ω 0% 10% 30% 50%
0.10
1000
0.05
500 0
50
100
400
-1
P = 3.0 MPa
3000
0
350
(b) Density
3500
-6
150
λ/W·m ·°C
4000
μ/10 Pa·s
ω 0% 10% 30% 50%
600
4
0
P = 3.0 MPa
800
-3
12
1000
ρ/kg·m
14
-1
P = 3.0 MPa
0% 20% 30% 50%
16
150 T/°C
200
250
(c) Viscosity
0.00
0
50
100
150 T/°C
200
250
(d) Thermal conductivity Fig. 4. Thermophysical properties of emulsified kerosene.
50
45
Deionized water -1 P = 3.0 MPa m = 2.0 g·s ± 5%
Nu G
40
35
30
25
20 20
25
30
35
Nu exp
40
Fig. 5. Validation of the experimental system.
45
50
nism is viewed as saturated nucleate boiling, the heat transfer coefficient increases to a rather high level. With a growth in the amount of steam bubbles, small bubbles merge to form slug flow, and then the flow pattern develops to annular flow. The heat transfer process for annular flow is forced convective heat transfer through liquid film. The inner wall temperature reduces below the nucleation temperature, and a slight increase in heat transfer coefficient can be observed. The steam is generated on the liquid film-vapor interface. With an increase in the velocity of vapor, some liquid droplets are torn from the film. After the film is depleted by evaporation and entrainment, the heating wall is exposed to steam. The inner wall temperature increases abruptly, which signifies heat transfer deterioration. The droplets still exist after the dryout point, and the flow pattern is called mist flow. In this region, the inner wall temperature slightly decreases due to the evaporation of droplets and the high flow velocity of mist flow. After the droplets totally evaporate, the heat transfer mechanism is convective heat transfer to vapor, and the corresponding flow pattern is single-phase vapor. The flow boiling of emulsified kerosene is more sophisticated than that of pure water. Emulsified kerosene is a non-azeotropic mixture with the pseudo-critical temperature of kerosene higher than the saturation temperature of water. Kerosene could act as the liquid phase during the boiling of water. This paper mainly focuses on the subcooled boiling heat transfer characteristics of emulsified kerosene. The reforming reaction between kerosene and water steam at high temperature was not
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Wall and fluid temperature
X=1
Heat transfer coefficient
Heat transfer regions
Flow patterns Single-phase vapor
Convective heat transfer to vapor
Mist flow
Liquid deficient region
Dryout Annular flow with entrainment Forced convective heat transfer through liquid film Annular flow Fluid temperature
Wall temperature
Slug flow Saturated nucleate boiling X=0
Bubbly flow
Saturation temperature
Subcooled boiling Convective heat transfer to liquid
Single-phase liquid Fig. 6. Heat transfer regions of flow boiling.
500
Pout = 3.0 MPa
ω = 30%
m = 2.4 g·s
-1
-2
q/kW·m 422 457 485 520 563
450 400
Tw,i /°C
involved in this paper. The test conducted at the pressure of 3.0 MPa, mass flow rate of 2.4 gs1 and water mass fraction of 30% was chosen as a typical case to analyze the basic heat transfer characteristics of emulsified kerosene. The inner wall temperature of the test tube demonstrated complex variations along the axis direction at the heat fluxes of 422–563 kWm2, as shown in Fig. 7. The saturation temperature of water is 233.9 °C at the pressure of 3.0 MPa. The inner wall temperature was lower than the saturation temperature near the inlet of the tube. Then the inner wall temperature increased to slightly higher than the saturation temperature, and reached a plateau. At somewhere of the tube, the inner wall temperature would depart from the saturation temperature, and was followed by a sharp soar. At the heat fluxes of 520 and 563 kWm2, the inner wall temperature rose by approximately 100 °C in a 5 cm spacing. With an increase in heat flux, the sharp soar moved towards the inlet direction. After the peak, the inner wall temperature declined gradually, and then monotonously increased along the test tube. The basic heat transfer characteristics of emulsified kerosene covering a wide temperature range will be discussed in the following text with the help of fluid bulk temperature and heat transfer coefficient. At the heat flux of 563 kWm2, the outlet emulsion temperature was 402.1 °C. The inner wall temperature, fluid bulk temper-
350 300 250
Tsat = 233.9 °C
200 150
0
20
40
60 x/cm
80
100
120
Fig. 7. Profiles of inner wall temperature at different heat fluxes.
ature, and heat transfer coefficients along the flow direction are shown in Fig. 8(a) and (b). According to the inner wall temperature and fluid bulk temperature, the heat transfer of emulsified kero-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Pout = 3.0 MPa m = 2.4 g·s
400
q = 563 kW·m
(2)
(1)
(3)
Pout = 3.0 MPa -1
125 m = 2.4 g·s
-2
(6)
(4) (5)
ω = 30%
h -2
q = 563 kW·m
100 -1
Tpc = 285.6 °C
-2
300
T/°C
-1
150
ω = 30%
h/kW·m ·°C
500
Tsat = 233.9 °C
200 100
Tw,i
75 50 25
Tb
0
0
20
40
60 x/cm
80
100
120
0
0
20
40
(a) T vs. x
60 x/cm
80
100
120
(b) h vs. x
Fig. 8. Profiles of inner wall temperature, emulsion bulk temperature and heat transfer coefficient at the heat flux of 563 kWm2.
sene could be divided into 6 regions: (1) single liquid-phase convection, (2) subcooled boiling, (3) saturated nucleate boiling, (4) film boiling, (5) steam-kerosene convection, and (6) single gasphase convection. In the single-phase convection region, both the inner wall temperature and fluid temperature were lower than the saturation temperature of water. The heat transfer coefficient in this region was relatively low, approximately 4.0 kWm2°C1. This region only displayed near the inlet of the test tube and did not exceed 10 cm. In the subcooled boiling heat transfer region, the inner wall temperature was slightly higher than the saturation temperature, and remained unchanged along the tube. Water in the emulsion evaporated near the heating wall. The fluid temperature was lower than the saturation temperature, and increased linearly. The temperature difference between the inner wall and the emulsion reduced. As a result, the heat transfer coefficient increased markedly. In the saturated nucleate boiling region, the fluid temperature maintained at the saturation temperature. The temperature difference between the inner wall and the fluid dropped to several degrees. Since plenty of heat was absorbed by water evaporation, heat transfer coefficient reached a high level, approximately 110 kWm2°C1. In the film boiling region, a great deal of steam was generated near the heating wall, and liquid kerosene was embraced by the steam film with inferior heat transfer property. The inner wall temperature exhibited a sharp increase in this region, which indicated heat transfer deterioration. A remarkable decline in heat transfer coefficient could be observed at 75 cm from the inlet. In the steam-kerosene convection region, the fluid temperature was higher than the saturation temperature but lower than the pseudo-critical temperature. The water in the emulsion totally evaporated as steam. The heat transfer mechanism was steamkerosene two-phase convection. The inner wall temperature decreased gradually along the flow direction. This peculiar variation could be attributed to the large specific heat capacity of emulsion near the pseudo-critical temperature. The temperature corresponding to the second peak of specific heat capacity is viewed as the pseudo-critical temperature of emulsified kerosene, as shown in Fig. 4(a). Although the pseudo-critical temperature of the kerosene used in this investigation is 441.1 °C at the pressure of 3.0 MPa, the pseudo-critical temperature of emulsified kerosene will decrease with an increase in the water mass fraction. The pseudo-critical temperature of emulsified kerosene reduces to 303.7 °C, 285.6 °C and 278.1 °C at the water mass fraction of 20%, 30% and 50% respectively [24]. With the fluid temperature
approaching pseudo-critical temperature, the heat capacity reached a peak, and the heat transfer coefficient displayed a visible enhancement. When the fluid temperature was higher than the pseudo-critical temperature, both the kerosene and water were in the gas phase. This region is defined as single gas-phase convection. The inner wall temperature increased monotonously and the heat transfer coefficient changed little along the flow direction, owing to the mild variation of density and specific heat capacity of emulsified kerosene. Since subcooled boiling heat transfer mainly occurred near the inlet of the test tube, the inner wall temperature measured by the 5th thermocouple is chosen to analyze subcooled boiling heat transfer characteristics of emulsified kerosene. The influences of experimental parameters on subcooled boiling heat transfer and heat transfer correlations will be discussed as follows. 3.2. Effects of pressure Effects of pressure on subcooled heat transfer characteristics of emulsified kerosene at the mass flow rate of 2.4 gs1 and the water mass fraction of 10% are shown in Fig. 9. The fluid temperatures at different pressure overlapped with each other because the pressure had little influence on the fluid temperature when the fluid temperature did not exceed the saturation temperature of water. When the heat flux was lower than 100 kWm2, singlephase convection was the main heat transfer method and the heat transfer coefficient was relatively low. When the heat flux increased to 100 kWm2, the inner wall temperature was much lower than the saturation temperature, however, it began to depart from the linear increase. It was notably different from subcooled boiling characteristics of pure water. For subcooled boiling of pure water, the inner wall temperature begins to depart from linear increase only if it is high enough to nucleate bubbles [28]. At the pressure of 3.0 MPa, when the heat flux reached 350 kWm2, the inner wall temperature exceeded the saturation temperature of water, but it still increased with heat flux. This was regarded as partially subcooled boiling heat transfer. When the heat flux was higher than 450 kW, the inner wall temperature reached a plateau, and was independent with the heat flux. It indicated the heat transfer method was fully developed subcooled boiling. In the fully developed subcooled boiling region, the inner wall temperature changed little. However, the fluid temperature increased with the heat flux, and the temperature difference between the inner wall and the emulsion reduced. Consequently, a remarkable enhance-
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
300 m = 2.4 g·s
-1
ω = 10 %
30 m = 2.4 g·s
TC5
-1
200
-2
T/°C
150 100
Tw,i
3.0 MPa 4.0 MPa 5.0 MPa
0
200
400 600 -2 q/kW·m
20 15 10
Tb
50 0
TC5
h/kW·m ·°C
Tsat(3.0 MPa)
ω = 10 %
3.0 MPa 4.0 MPa 5.0 MPa
25
250
-1
800
5 0
1000
0
200
400 600 -2 q/kW·m
(a) T vs. q
800
1000
(b) h vs. q Fig. 9. Effects of pressure on subcooled heat transfer.
ment could be observed in heat transfer coefficient with an increase in the heat flux. A higher heat transfer coefficient could be achieved at lower pressure, because the density of emulsified kerosene is positively correlated to the pressure, and the velocity of the emulsion is larger at lower pressure.
cient could be observed in the fully developed boiling region. The experiment of minor mass flow rate could be only conducted at relatively low heat flux.
3.3. Effects of mass flow rate
Influences of water mass fraction are illustrated in Fig. 11. The inner wall temperature, fluid bulk temperature and heat transfer coefficient of pure kerosene are also plotted in Fig. 11. In the single liquid-phase convection region, the inner wall temperature decreased with an increase in water mass fraction. This phenomenon could be attributed to two reasons. On one hand, the fluid temperature was lower at larger water mass fraction. On the other hand, the specific heat capacity and thermal conductivity of the emulsion increase with the mass fraction, which is beneficial to heat transfer. There was a turning point in the inner wall temperature of pure kerosene at the heat flux of 228.3 kWm2. The slope of inner wall temperature decreased after this turning point. The kerosene temperature was 91.7 °C and the corresponding Reynolds number was 2329 at the turning point. The heat transfer was enhanced and the inner wall increased slowly because of the transition from laminar flow to turbulent flow. When the heat flux increased to 450 kWm2, the inner wall temperature at the water mass fraction of 10% was slightly higher than the saturation tem-
3.4. Effects of water mass fraction
The inner wall temperatures, emulsion temperatures, and heat transfer coefficients at different mass flow rate are plotted in Fig. 10. The experiments were conducted at the pressure of 3.0 MPa and water mass fraction of 10%. When the heat flux was lower than 100 kWm2, the heat transfer coefficient of each mass flow rate was relatively low due to single-phase convective heat transfer. At the same heat flux, the emulsified kerosene temperature increased with the reduction of mass flow rate. The higher fluid temperature could promote subcooled boiling, so subcooled boiling firstly occurred at the mass flow rate of 0.8 gs1, and then subcooled boiling successively displayed at the mass flow rate of 1.6 and 2.4 gs1 with an increase in heat flux. In other words, subcooled boiling was restrained at a higher mass flow rate. In the fully developed boiling region, the inner wall temperature was a bit higher than the saturation temperature, and was independent with the mass flow rate. Significant soars in heat transfer coeffi-
250
Pout = 3.0 MPa
50
ω = 10 %
TC5
Tsat
40 30
-2
T/°C
150
h/kW·m ·°C
-1
200
100 Tw,i
2.4 1.6 0.8
50 0
Pout = 3.0 MPa ω = 10 %
0
200
TC5
400 -2 q/kW·m
-1
Tb m/g·s
600
800
20 m/g·s 2.4 1.6 0.8
10 0
0
200
(a)
400 -2 q/kW·m
(b) Fig. 10. Effects of mass flow rate on subcooled heat transfer.
600
800
-1
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
Tb
ω
Pout = 3.0 MPa
m = 2.4 g·s
-1
0% 10% 30% 50%
300
T/°C
Tsat
200
-1
TC5
ω 0% 10% 30% 50%
25 -1
400
30 Pout = 3.0 MPa m = 2.4 g·s
TC5
-2
Tw,i
20
h/kW·m ·°C
500
15 10
100 0
5 0 0
200
400
600 -2 q/kW·m
800
1000
0
200
400
(a)
600 -2 q/kW·m
800
1000
(b) Fig. 11. Effects of water mass fraction on subcooled heat transfer.
perature, and almost remained unchanged due to the evaporation of water near the heating wall. However, the inner wall temperature of pure kerosene was remarkably higher than the saturation temperature of water, and increased linearly with the heat flux. In the fully developed subcooled boiling region (q > 600 kWm2), heat transfer coefficient displayed substantial improvement. The inner wall temperature difference between each water mass fraction could be ignored. However, the emulsion temperature was lower at higher water mass fraction because of the large specific heat capacity of water. As a result, the larger heat transfer coefficient could be achieved at lower water mass fraction in the fully developed subcooled boiling region.
The subcooled boiling heat transfer coefficient of emulsified kerosene was compared with these correlations. Comparisons of enhancement-factor type correlations with experimental data at different water mass fraction are shown in Fig. 12, and the deviation of each correlation is listed in Table 2. The mean absolute deviation (MAD) and mean relative deviation (MRD) are used to estimate the prediction accuracy of these correlations.
MAD ¼
n 1X hcal hexp n 1 hexp
ð17Þ
3.5. Subcooled boiling heat transfer correlations
MRD ¼
n 1X hcal hexp n 1 hexp
ð18Þ
In the past five decades, dozens of correlations have been proposed for subcooled flow boiling heat transfer. Fang et al. [29] summarized 21 existing correlations for subcooled flow boiling, and classified them into five categories. The surface tension is an indispensable property for many correlations. However, it is quite difficult to acquire the surface tension of emulsified kerosene. The correlation in enhancement-factor type is independent with the surface tension, as shown in Table 1. For this type correlation, the subcooled boiling heat transfer coefficient is viewed as the heat transfer coefficient of single-phase corrected by an enhancement factor. Usually, the single-phase convective heat transfer coefficient is calculated by Dittus-Boelter correlation or Gnielinski correlation, and the enhancement factor is a function of Bo, Ja, and Pr.
Three correlations, Shah, Papell, and Kandlikar underestimated the subcooled heat transfer coefficient of emulsified kerosene. Shah correlation and Kandlikar correlation exhibited a similar deviation that most of the predicted points fell into the error band of 50% to 0%. Papell correlation had the biggest mean absolutely deviation for every water mass fraction. Most of the predicted points fell in the error band of 20% to 60%. Kandlikar correlation could accurately predict the heat transfer coefficient at the water content of 10%. However, the mean absolute deviation of Kandlikar correlation increased to 21.5% at the water content of 50%. The deviation of Baburajan correlation distributed in the range of 40% to 40%. It overestimated the heat transfer coefficient at the water mass fraction 10% and underestimated the heat trans-
Table 1 Enhancement-factor type correlations for subcooled boiling heat transfer. Author
Correlation
Application condition
Shah [30]
q ¼ WhDB DT sat 230Bo0:5 ; Bo > 0:3 104 W¼ 1 þ 46Bo0:5 ; Bo < 0:3 104 hD-B is the heat transfer coefficient calculated by Dittus-Boelter equation
Water, refrigerant, d = 2.4–27.1 mm, P = 0.1–13.8 MPa, DTsub = 0– 153 °C, q = 0.01–22.9 MWm2, G = 55–24200 kgm2s1
Baburajan [31]
htp =hsp ¼ 267Bo0:86 Ja0:6 Pr 0:23 0:262 l k hsp ¼ 0:023Re0:8 Pr 0:4 l b d w 0:7 q 0:756 Nutp 0:84 q g Hlg q V Nusp ¼ 90:0Ja q
Water, horizontal flow, d = 5.5, 7.5, 9.5 mm, L = 550, 750, 1000 mm, G = 450–935 kgm2s1, DTsub,in = 29, 50, 70 °C
Papell [32]
g
l
Nusp ¼ 0:021Re0:8 Pr 0:4 Kandlikar [33]
q=DT sat ¼ 1058:0Bo0:7 hsp F F is the fluid-surface parameter, and equal to 1.00 for water. hsp is the single-phase heat transfer coefficient calculated by Gnielinski correlation or Petukhov correlation
Distilled water, P = 0.1–13.8 MPa, q = 0.04–91.58 MWm2, V = 0.4– 62.2 ms1, DTsub = 3.3–186.7 °C Water, Refrigerants, cryogenic fluids, fully developed subcooled boiling
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H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
100
100
Shah
Baburajan
ω 10% 30% 50%
40%
-1 -2
hcal/kW·m ·°C
-2
hcal/kW·m ·°C
-1
ω 10% 30% 50%
10 - 50%
1
1
10 -2 -1 hexp/kW·m ·°C
10 - 40%
1
100
1
10 -2 -1 hexp/kW·m ·°C
(a) Shah 100
(b) Baburajan 100
Papell
Kandlikar ω 10% 30% 50%
-2
-2
10
hcal/kW·m ·°C
-1
-1
ω 10% 30% 50%
hcal/kW·m ·°C
100
- 20% - 60%
1
1
10 -2 -1 hexp/kW·m ·°C
100
10 - 50%
1
1
(c) Papell
10 -2 -1 hexp/kW·m ·°C
100
(d) Kandlikar
Fig. 12. Comparison of predicted heat transfer coefficients with experimental data.
Table 2 Deviation of enhancement-factor type correlations. Water mass fraction
Correlation
MRD
MAD
Data predicted within ±10%
±20%
±40%
x = 10%
Shah Baburajan Papell Kandlikar
14.0% 33.6% 41.7% 8.3%
14.0% 36.4% 41.7% 8.3%
39.4% 13.7% 0% 74.9%
82.9% 25.7% 0% 95.5%
98.5% 50.7% 34.3% 99.7%
x = 30%
Shah Baburajan Papell Kandlikar
22.7% 0.9% 38.4% 17.8%
22.7% 13.8% 38.4% 17.8%
0% 36.5% 0% 15.4%
54.8% 75.0% 1.0% 73.1%
91.3% 99.0% 61.5% 98.1%
x = 50%
Shah Baburajan Papell Kandlikar
25.3% 1.3% 37.5% 21.5%
25.3% 12.3% 37.5% 21.5%
0% 44.3% 0.3% 0%
39.3% 73.6% 1.1% 65.7%
89.4% 85.9% 73.6% 91.8%
H. Pan et al. / International Journal of Heat and Mass Transfer 145 (2019) 118744
100
Nutp/NuD-B = 375.36Bo
0.554
Ja
-0.676
0.439
Pr
(Nutp/NuD-B)cal
± 20%
10
1
1
10 (Nutp/NuD-B)exp
100
Fig. 13. Deviation of the new correlation.
(2) In the subcooled boiling region, the heat transfer coefficient was larger at lower pressure, because the density of emulsified kerosene is positively correlated with the pressure. With an increase in mass flow rate, subcooled boiling of emulsified kerosene was postponed to higher heat flux. In the single liquid-phase convection region, the inner wall temperature decreased with an increase in the water mass fraction. In the subcooled boiling region, emulsified kerosene achieved a better heat transfer performance than pure kerosene, especially at low water mass fraction. (3) The heat transfer coefficient of emulsified kerosene was compared with enhancement-factor type correlations. Most of the correlations underestimated the heat transfer coefficient except for Baburajan correlation. Kandlikar correlation could accurately predict the heat transfer coefficient of emulsified kerosene at the water mass fraction of 10%. However, the mean absolute deviation of Kandlikar correlation increased to 17.8% and 21.5% at the water mass fraction of 30% and 50% respectively. A new correlation with the mean absolute deviation of 9.9% was proposed according to the experimental data.
Declaration of Competing Interest
fer coefficient at the water mass fraction 50%. The correlations listed in Table 1 were all incompetent to predict subcooled boiling heat transfer of emulsified kerosene at different water mass fraction owing to the narrow application ranges. A new enhancement-factor type correlation was developed for subcooled boiling heat transfer of emulsified kerosene, as exhibited in Eq. (19). The enhancement factor was a function of Bo, Ja, and Pr. The coefficients in this equation were fitted by multiple regression.
Nutp =NuDB ¼ 375:36Bo0:554 Ja0:676 Pr 0:439
11
ð19Þ
where NuD-B is obtained from Dittus-Boelter correlation. The deviation between heat transfer coefficients predicted by the new correlation and experimental data is shown in Fig. 13. The mean absolutely deviation was 9.9%, and 87.1% of the predicted points fell into the error band of ±20%. The new correlation is accurate enough to predict the subcooled boiling heat transfer coefficient of emulsified kerosene at the water mass fraction of 10–50%, pressure of 3.0–5.0 MPa, and mass flux of 254.6–763.9 kgm2s1. 4. Conclusion In this perspective, the heat transfer characteristics of emulsified kerosene were experimentally investigated in a mini tube. The influences of pressure, mass flow rate, and water mass fraction on subcooled boiling were discussed. The heat transfer coefficient in the subcooled boiling region was compared with the enhancement-factor type correlations. The main conclusions are as follows. (1) According to the variations of wall temperature and fluid bulk temperature, heat transfer of emulsified kerosene covering a wide temperature range could be divided into 6 regions: single liquid-phase convection, subcooled boiling, saturated nucleate boiling, film boiling, steam-kerosene convection, and single gas-phase convection. At the water mass fraction of 30%, heat transfer deterioration accompanying a sharp increase in wall temperature occurred in the film boiling region, and the deterioration point moved towards the inlet direction with an increase in heat flux.
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