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Experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber
International Journal of Heat and Mass Transfer 80 (2015) 448–457
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Experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber Xiao Zong a,1, Ji-ping Liu a,⇑, Xiao-ping Yang a,1, Jun-jie Yan b,2 a b
MOE Key Laboratory of Thermal Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China 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 21 March 2014 Received in revised form 31 August 2014 Accepted 10 September 2014
Keywords: Direct contact condensation Water flow Flow pattern Dimensionless penetration length Average heat transfer coefficient
a b s t r a c t An experimental study on the direct contact condensation (DCC) of steam jet in subcooled water flow in a rectangular mix chamber was conducted. A high-speed camera was employed to record the flow field of DCC in the visualized experimental rig, in which, the steam nozzle and water nozzle were both rectangular. The flow field was filmed when the steam mass flux, water mass flux and water temperature were in the range of 200–600 kg/m2 s, 6000–18000 kg/m2 s and 293–333 K, respectively. The results indicated that, the flow field of DCC in the rectangular mix chamber consisted of four regions, and they were steam region, interface, mixture layer and ambient water region. The interface between steam region and mixture layer was clearly observed. The flow pattern of DCC was performed as bubble flow, oscillatory jet, stable jet and divergent jet at various test conditions. The steam region dimensionless penetration length and average heat transfer coefficient of the stable jet were found to be in the range of 1.73–4.40 and 2.89– 7.89 MW/m2 K, respectively. Furthermore, an analytical model was established and a correctional correlation was developed to predict the dimensionless penetration length. An empirical correlation was proposed to predict the average heat transfer coefficient. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Direct contact condensation (DCC) of steam jet in subcooled water flow is the core process of two-phase flow steam injector (TFSI). Due to the advantages of compact, high heat transfer intensity, lifting pressure during heat transfer, it has been widely used in several industrial applications [1,2]. For a fundamental understanding of DCC of steam jet in subcooled water pool, many works on flow pattern, regime diagram, pressure and temperature distributions and heat transfer characteristics had been conducted. Chan and Lee [3] investigated steam jet downward through a pipe into a pool of subcooled water, three different flow patterns were reported to be oscillatory jet, steam chugging and oscillatory bubble. A regime diagram based on steam mass flux and pool temperature was also obtained. Chun et al. [4] experimentally studied the DCC of steam jet in stagnant water, two steam plume shapes in the stable condensation regime were found to be conical and ellipsoidal. Liang and Griffith [5] observed ⇑ Corresponding author. Tel.: +86 29 82665742; fax: +86 29 82675741. E-mail addresses: [email protected] (X. Zong), [email protected] (J.-p. Liu), [email protected] (X.-p. Yang), [email protected] (J.-j. Yan). 1 Tel.: +86 29 82665742; fax: +86 29 82675741. 2 Tel.: +86 29 82665741; fax: +86 29 82675741. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.050 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
chugging, bubbling, oscillatory jet and stable jet in research of DCC, transition criteria between regimes were also proposed. Petrovic et al. [6] conducted a three-dimensional regime diagram and validated against experiments. Wu et al. [7–9] experimentally investigated sonic/supersonic steam jet condensation in quiescent subcooled water, six different steam plume shapes were observed, temperature distribution was discussed and the heat transfer coefficient was found to be within 0.63–3.44 MW/m2 K. Xu et al. [10] carried out experimental study on DCC of stable steam jet in water flow in a vertical pipe, the heat transfer coefficient was reported to be in the range of 0.34–11.36 MW/m2 K. Due to the shear force between walls and fluid, the steam– water DCC has different features when occurs in a restricted channel. Existing researches mostly concentrated on flow characteristics [2,11,12], heat transfer characteristics were little concerned. Celata et al. [13] conducted theoretical research on DCC of steam–water on a horizontal surface, and found that temperature gradient mainly lay on water side of the interface with thickness of millimeter-scale. By using laminar convective heat transfer model, in which the interface was treated as a uniform temperature surface, the results were in good agreement with experiments. Considering saturation pressure corresponding to average water temperature as the mixture pressure, Malibashev [14,15]
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Nomenclature Ai B cp dhe Gs Ge Gm Gw hi hfg 0 h have k l L m
interface area, m2 condensation driving potential water specific heat, J/kg K steam nozzle exit equivalent diameter, m steam mass flux at steam nozzle throat, kg/m2 s steam mass flux at steam nozzle exit, kg/m2 s critical steam mass flux, equals to 275kg/m2 s water mass flux at water nozzle exit, kg/m2 s local heat transfer coefficient, MW/m2 K latent heat of condensation, kJ/kg nominal radius, m average heat transfer coefficient, MW/m2 K arc length of fan-shape to circle, equals to a/360° penetration length, m dimensionless penetration length steam mass flow rate, kg/s
experimentally investigated the flow features of DCC in a channel under different conditions. Deberne et al. [16] carried out visualization research on dynamic and heat transfer performance on DCC. The vapor volume fraction was detected by gamma rays during condensation, and found that the cross-sectional average vapor void fraction was increasing. In recent years, with the development of computer, investigation on the mechanism of interface by molecular dynamics simulation and research on phase change heat transfer by molecular performance on the interface had been focus of this study by many researchers [17,18]. Compared with researches on the steam jet in water pool, investigation on DCC of steam jet in a restricted channel is absent, and a lot of basic issues are still unsolved. Interface is the major area of mass, momentum and energy transfer in DCC. Due to the cylindrical axial symmetric structure of steam jet in water pool with circular nozzles or pipes, details of the inner steam jet could not be obtained directly in existing experimental studies. To solve this problem, a visualized experimental rig with rectangular steam nozzle and water nozzle was designed and fabricated. In this work, investigation on the steam jet in subcooled water flow in a rectangular mix chamber is carried out by constructing a quasi-planar structure of flow field, so that the details of the inner steam jet could be filmed with the high-speed camera easily. Besides, the influence of steam mass flux, water mass flux and water temperature on the steam region dimensionless penetration length of the stable jet and average heat transfer coefficient are discussed. The present experimental study are of theory significant for the further understanding of DCC of steam jet in subcooled water flow in a restricted channel, and it is helpful to the better design and safe operation on the TFSI. 2. Experimental system and methods The experimental system for investigating on steam jet in subcooled water flow in a rectangular mix chamber is schematically presented in Fig. 1. The apparatus mainly consists of a test section, an electric steam generator, a feed pump, a return pump, two water tanks, a high-speed camera, a cooling tower and some valves. The major geometry of the test section is presented in Fig. 2. The test section is made of stainless steel and two pieces of tempered glass are installed at front and back of the test section for observation and filming. The convergent–divergent rectangular steam nozzle is inserted into the test section by soldering, as shown in Fig. 2(a). The steam nozzle throat height and width are both
me Ps Pw S Sm Ts Tw Two Nuave Rc Rew kw
a
steam mass flow rate at steam nozzle exit, kg/s inlet steam pressure, MPa inlet water pressure, MPa analogous to familiar Stanton number of heat transfer, equals to hi/cpG mean value of S steam saturation temperature at the steam nozzle exit, K inlet water temperature, K mix chamber outlet temperature, K average Nusselt number condensation rate, kg/m2s water Reynolds number at water nozzle exit water thermal conductivity, W/mK central angle
8 mm, and 10 mm at the nozzle exit, as shown in Fig. 2(b). The rectangular water nozzle is at top of the steam nozzle, the height of water nozzle exit is the same with that of steam nozzle throat, 8 mm, and the width is 10 mm. Besides, there is 10 mm length of straight section at the water nozzle exit, which ensures that the water flow is horizontally injected into the mix chamber. Because that there is no gap between the tempered glasses and the steam nozzle, water nozzle as well as the test section, the front and back walls of the rectangular mix chamber are the tempered glasses actually. In addition, altogether 11 groups of measure point are installed through center on the upper and bottom wall of the mix chamber for pressure and temperature measurement simultaneously, as shown in Fig. 2(b). In present work, steam and water are injected into the mix chamber though the rectangular steam and water nozzles, respectively. Details of the test conditions are given in Table 1, and the major geometry parameters of the test section and nozzles are presented in Table 2. Steam supply is taken from the steam generator continuously with electric heaters of 330 kW and maximum flow rate of 0.11 kg/s. The steam flow rate is controlled by a valve manually and all the steam lines are wrapped by fiberglass insulation. Filtered water is derived from a single-stage horizontal shaft centrifugal pump and the water flow rate is controlled by valves on feed and by-pass lines. The Phantom V611 type high-speed camera is set as 5 kHz in experiments. All singles are processed by the LabVIEW data acquisition system, which consists of an industrial computer, a NI cDAQ-9178 data acquisition board, two NI 9213 modules to obtain temperature and four NI 9203 modules to obtain current signals of pressure transducers. The steam flow rate is measured by a vortex steam flow meter, which is in the range of (0.75–7.39) 102 kg/s with maximum relative deviation of 1.0%. The water flow rate is measured by an electromagnetic flow meter in the range of 0.08–2.78 kg/s with maximum relative deviation of 0.2%. The high-temperature pressure transducers used in present work are in the range of 0–1 MPa with maximum relative deviation of 0.1%. Calibrated by a standard thermocouple, the steam and water temperature are measured by the K-type thermocouples (diameter 1 mm), which are in the range of 273–473 K with maximum relative deviation of 0.5%. In present work, the steam flow rate, water flow rate, pressure and temperature are in the range of (1.28–3.84) 102 kg/s, 0.47–1.44 kg/s, 0.1–0.5 MPa and 293–423 K respectively, so the relative uncertainties in steam mass flux, water mass flux, pressure and temperature are below 3.0%, 0.7%, 0.6% and 2.9%.
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Fig. 1. Schematic diagram of experimental system.
Fig. 2. Major geometry of test section.
Table 1 Test conditions in experiment.
Table 2 Major geometry parameters of test section.
Parameters
Values
Parameters
Values (mm)
Inlet steam pressure Ps, MPa Inlet water pressure Pw, MPa Steam mass flux at nozzle throat Gs, kg/m2s Water mass flux at nozzle exit Gw 103, kg/m2s Inlet water temperature Tw, K
0.1–0.5 0.1–0.5 200–600 6–18 293–333
Exit size of water nozzle Throat size of steam nozzle Exit size of steam nozzle Mix chamber size
10 8 88 10 10 250 10 19
3. Experimental results and discussion 3.1. Regions of flow field When the high-speed steam is injected into water flow by a rectangular convergent–divergent nozzle in the rectangular mix chamber, DCC occurs between the steam jet and subcooled water
flow. In previous studies, steam was injected into a stagnant water pool by circular nozzles or pipes [7–10], and four different regions in the flow field were identified as steam plume, interface, hot water layer and ambient water. Using the circular nozzles in water pool, steam jet was condensed by stagnant water all around, which formed a three-dimensional structural view field, as shown in Fig. 3. In the three-dimensional view field, inner structure of the steam jet could not be observed directly. To solve
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fourth region is the ambient water, which is on the top of mixture layer. The ambient water region includes subcooled water injected into the mix chamber from water nozzle and hot water from steam condensation. The water moves ever faster as a result of steam condensation and vacuum effect at the steam nozzle exit [20]. The structural difference between circular nozzles in water pool and rectangular steam and water nozzles in the rectangular mix chamber contributes to the phenomenological difference of the flow field. In fact, the steam plume identified in the circular structural one in water pool considers including the steam region, interface and the mixture layer identified in the rectangular one in present study. 3.2. Flow pattern Fig. 3. Different regions of steam injected in water pool by circular nozzles or pipes [7–10].
this problem, in present work, the rectangular steam and water nozzles as well as the mix chamber are used to investigating on the DCC phenomena. The water is injected into the mix chamber just on the top of steam jet, and the front, back and bottom of the steam jet are all solid walls (the front and back walls are the tempered glasses), DCC just occurs in the top side. Due to a rectangular mix chamber, the view field is of quasi-planar structure, as shown in Fig. 4, so the details of the inner steam jet could be clearly observed and distinguished. Similarly, four different regions are identified in the flow field of steam jet in water flow in a rectangular mix chamber, as shown in Fig. 4. The first region is steam region, which is only composed of pure steam. In the steam region, steam is of great velocity, momentum and energy, and in the influence of water flow as well as flow characteristics itself, a series of expansion and compression waves would occur, which is similar to the results of steam jet in a water pool by Wu et al. [7,8]. The second region is the outer surface of steam region – interface, which divides the steam region from the mixture layer. Many researchers simulated with basic theory of molecular dynamics, their results indicated that the interface might be an area with thickness of a few or dozens of molecules [17,18]. Transportation of mass, momentum and energy between steam and water are proceeding at the interface. The mixture layer clearly distinguished in this study is a steam–water two-phase layer. In the mixture layer, steam exists in bubble form and both phases are in turbulent motion. Two-phase turbulent motion generates a large amount of eddies, which has great effect on the shape of the interface and controls the interfacial transportation [19]. The
Fig. 4. Different regions of stable steam jet in subcooled water flow in a rectangular mix chamber. (Gs = 350 kg/m2 s, Gw = 8000 kg/m2 s, Tw = 293 K).
The flow pattern of DCC is a significant characteristic when studying on steam jet in subcooled water flow. In present work, based on different regions in the flow field at various test conditions, four types of flow pattern are identified as bubble flow, oscillatory jet, stable jet and divergent jet, as shown in Fig. 5. When the steam mass flux is low, determined by the combination of the steam and water mass flux, backpressure of the convergent–divergent steam nozzle is relatively high, so the steam flow at the steam nozzle exit is subsonic, and the flow pattern of bubble flow is observed. At first, steam flow rushes out to the mix chamber from steam nozzle, the interface area is small and condensation rate is low accordingly, so steam gathers at the nozzle exit and forms a steam bubble. Along with steam bubble growth, the interface extends. As condensation rate is large enough, the steam bubble collapses due to insufficient supply of steam. As the steam bubble occurs, grows and collapses periodically, the bubble flow never has the structure of Fig. 4. With increasing steam mass flux at high water mass flux, the steam bubble would never collapse any more. Though the steam flow also is subsonic, steam supply is enough to maintain flow characteristics itself near the nozzle exit, so the interface in front part of the steam region is stable. But at steam jet tail, ambient water rushes into the steam region periodically, which leads to the steam jet waving up and down intensively, so the steam region together with the interface are not maintained in a fixed shape, and then the oscillatory jet is observed. In the case of medium steam mass flux and relatively lower water mass flux, the steam nozzle backpressure is low enough, and then the steam flow is supersonic. As pointed by Xu et al. [10], the compression and expansion waves would occur in the supersonic flow in water flow. Due to the relatively higher condensation heat, steam flow would travels a longer distance and the ambient water would not rush into the steam region, all the regions discussed in last section is distinct and stable, and the stable jet is observed. With increasing inlet water temperature, water condensation capacity near the steam jet decreases, so the stable jet tends divergent, and the divergent jet is observed. In addition, the influences of steam mass flux and inlet water temperature on flow pattern are presented in Figs. 6 and 7 respectively. When the steam mass flux increases from 250 to 550 kg/m2 s at Gw = 14000 kg/m2 s and Tw = 303 K, the flow pattern turns from bubble flow to oscillatory jet and then to stable jet, as shown in Fig. 6. As the inlet water temperature increases from 293 to 333 K at Gw = 10,000 kg/m2 s and Gs = 400 kg/m2 s, the flow pattern turns form stable jet to divergent jet, as shown in Fig. 7. In previous studies, flow pattern in stagnant water pool has been known to be determined mainly by steam mass flux and pool temperature [3,4,6–9]. The steam mass flux indicates the condensation heat and flow characteristics, whilst the pool temperature indicates the water condensation capacity. In present work, the water temperature near steam jet cannot remain unchanged, which increases along the steam jet due to condensation and
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Fig. 5. Flow pattern of DCC: (A) bubble flow, (B) oscillatory jet, (C) stable jet, (D) divergent jet.
Fig. 6. Influence of steam mass flux on flow pattern.
mixing. In order to characterize the influence of initial water condensation capacity on the flow pattern, the inlet water temperature is adopted. Fig. 8 shows the change of flow pattern with water mass flux for constant steam mass flux and inlet water temperature. As Gs = 400 kg/m2 s and Tw = 293 K, stable jet is observed at Gw = 6000 kg/m2 s. With increasing water mass flux, Reynolds number of the water will increase, which leads to an enhancement of heat transfer at water side, condensation rate would increase in proportion. At the same time, backpressure of the steam nozzle would increase and the steam flow turns from supersonic to subsonic. Due to these two reasons, bubble flow is observed at Gw = 18,000 kg/m2 s. Results and analysis above clearly indicate that the flow pattern of DCC of steam jet in subcooled water flow in a rectangular mix chamber is not only decided by steam mass flux and inlet water temperature like previous investigations in
stagnant water pool [3,4,6–9], but also the water mass flux plays an important role. In fact, the flow pattern is determined by the heat transfer characteristics between steam and water and by hydrodynamic behaviors at the interface. The heat transfer characteristics and the hydrodynamic behaviors at the interface are determined by the combination of three parameters including steam mass flux, water mass flux and inlet water temperature, with affecting each other. Therefore, based on the experimental data, the two-dimensional regime diagram for DCC of steam jet in subcooled water flow in a rectangular mix chamber is developed, which consists of four different flow patterns, as shown in Fig. 9. When the inlet water temperature is low (Tw = 303 K), with increasing steam mass flux, the flow pattern turns from bubble flow to stable jet at lower water mass flux, while the flow pattern changes from bubble flow to oscillatory jet a higher water mass flux. Further increasing the
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Fig. 7. Influence of inlet water temperature on flow pattern.
Fig. 8. Change of flow pattern with water mass flux.
steam mass flux would lead to occurrence of the divergent jet. When the inlet water temperature is high (Tw = 323 K), the flow pattern changing trend is similar to that at low inlet water temperature, but the divergent jet region extends, which indicates that the steam jet tends to divergent more easily at relatively high inlet water temperature. 3.3. Steam region penetration length of the stable jet Steam region penetration length l is defined as the axial distance of pure steam from nozzle exit, shows in Fig. 4. Due to a fixed and distinct steam region, it is easier to obtain the penetration length for the flow pattern of stable jet. The dimensionless
penetration length L is the ratio of penetration length l to the steam nozzle exit equivalent diameter dhe. The penetration length is obtained by manually measuring and averaging ten photos captured by the high-speed camera at different times. Figs. 10–12 shows the dimensionless penetration length L at various test conditions. As steam mass flux and inlet water temperature increase, penetration length increases, whereas as water mass flux increase, penetration length decreases, the values are in the range of 1.73–4.40. According to Kerney et al. [21], the interface is replaced by a smooth time-averaged surface and steam condensation is assumed to be taking place at the interface. The mass conversation equation can be expressed as,
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600
-2 -1 Gs / kg⋅m ⋅s
500
550
Divergent jet
450
et le j b a St
400
Tw=323 / K
500
tory ill a c s O
-2 -1 Gs / kg⋅m ⋅s
550
600
Tw=303 / K
jet
350 300
Divergent jet
450
jet ble a t S
350 300
Bubble flow
250 200 6
8
10
12
14
tory ill a c s O
400
Bubble flow
250
16
18
jet
200 6
8
10
12
14
16
18
-3 -2 -1 Gw×10 / kg⋅m ⋅s
-3
Gw×10 / kg⋅m-2⋅s -1
(a)
(b)
Fig. 9. Two-dimensional regime diagram for DCC of steam jet in subcooled water flow in a rectangular mix chamber; (a) Tw = 303 K, (b) Tw = 323 K.
5
5 -3
-2 -1
Gw×10 / kg⋅m ⋅s 7 8 9 10 11 12
3
2
3
2
1 250
350
450
1 6
550
8
-2 -1
G / kg⋅m ⋅s s
Fig. 10. Change of dimensionless penetration length with steam mass flux.
5
L
-2 -1 Gs=400 kg⋅m ⋅s
02
m ¼ 4kph G
7 8 9 10 11 12
2
1 273
12
14
ð1Þ
where -3 -2 -1 Gw×10 / kg⋅m ⋅s
3
10 G ×10-3 / kg⋅m-2⋅s-1 w
Fig. 12. Change of dimensionless penetration length with water mass flux.
dm 0 ¼ 2kph Rc dx
4
Tw / K 293 313 323 333
4
L
4
L
-2 -1 Gs=400 kg⋅m ⋅s
Tw=313 K
293
313
333
T /K w Fig. 11. Change of dimensionless penetration length with inlet water temperature.
ð2Þ
where k ¼ a=360 , a is the central angle, which is considered to be constant along the steam jet, so k is the ratio of arc length of the fanshape to the circle, and k is also consider to be a constant, as shown in Fig. 13. The geometry of Kerney et al. [21] is circular, but the geometry of present work is close to square. Due to a small value of a, the quasi-square area is close to 4 times of the fan-shape, 0 whose central angle is a. So the nominal radius of the interface h is introduced to express the cross-sectional steam mass flow rate in Eq. (2), where G is the steam mass flux. Rc ¼ hi =ðT s T w Þhfg is the condensation rate, hi is the local heat transfer coefficient, hfg is 0 the latent heat of condensation. Extracting h from Eq. (2) and then substituting it into Eq. (1), it can be inferred from Eq. (1) that,
pffiffiffiffiffi d m 1 pffiffiffiffiffiffiffiffiffi ¼ kpG BS dx 2
ð3Þ
X. Zong et al. / International Journal of Heat and Mass Transfer 80 (2015) 448–457
Interface
Interface α
A
Steam
m
455
h'
h'
Steam plume
dx
A
A-A
l
Fig. 13. Analytical model of the stable jet.
where B = cp(Ts Tw)/hfg is the condensation driving potential, cp is the liquid special heat, S = hi/cpG is analogous to the familiar Stanton number of heat transfer. Integrate Eq. (3) with the boundary conditions,
x ¼ 0;
x ¼ me ;
x ¼ l;
m¼0
ð4Þ
and then the dimensionless penetration length could be given as,
L¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi l 2 ¼ pffiffiffi ðBSm Þ1 Ge =Gm dhe k
ð5Þ
where Sm is appropriate mean value of the S, which is considered to be constant, Gm = 275 kg/m2 s is the critical steam mass flux, given by Kerney et al. [21], Ge is steam mass flux at the nozzle exit. Based on the analysis above, a correlation by fitting the experimental data for dimensionless penetration length of the stable jet could be given as,
L ¼ 0:356B0:88
Ge Gm
0:99 ð6Þ
In addition, comparison of predicted dimensionless penetration length by Eq. (6) with experimental dimensionless penetration length is presented in Fig. 14, the predicted errors are about ±40%. According the observation, it can be inferred that increasing in water mass flux would lead to reduction of penetration length, water mass flux also plays an important role in the penetration length. But in Eq. (6), there is not any item to express this effect. According to Sonin et al. [22], turbulent intensity is an important factor in condensation, and in the results of Xu et al. [10], the water Reynolds number is introduced to account for the water supply and turbulent movement of water flow on the penetration length. Similarly, in present work, water Reynolds number at the water nozzle exit Rew is also introduced to express the influence of water flow,
Fig. 15. Correctional predicted dimensionless penetration length compared with experimental dimensionless penetration length.
and a correctional correlation for the dimensionless penetration length is given in Eq. (7). The results indicated that introducing the water Reynolds number would decrease the errors to ±25%, as shown in Fig. 15.
L ¼ 15:2B1:8
Gs Gm
2:05
Re0:58 w
ð7Þ
3.4. Condensation heat transfer coefficient of the stable jet For steam jet condensation, several researchers [7,10] had given empirical correlations to predict the average heat transfer coefficient. In present work, due to a distinct steam region, the flow pattern of stable jet is chosen to investigate the heat transfer characteristics. Assuming a uniform heat flux at the interface, the average heat transfer coefficient can be calculated as,
hav e ¼
me hfg A i DT
ð8Þ
Where Ai is the interface area, which is obtained manually, DT is the logarithmic mean temperature difference between steam and water, calculated by,
DT ¼
Fig. 14. Predicted dimensionless penetration length compared with experimental dimensionless penetration length.
ðT s T w Þ ðT s T wo Þ T w ln TTssT wo
ð9Þ
Average heat transfer coefficients at various test conditions are shown in Figs. 16–18. With increasing steam mass flux, average heat transfer coefficient tends to decrease, whereas with increasing water mass flux and inlet water temperature, average heat transfer coefficient tends to increase. It can be inferred from Eq. (8) that there are three factors to affect the average heat transfer coefficient, quantity of condensation heat transfer mehfg, temperature
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10 -3 -2 -1 Gw×10 / kg⋅m ⋅s
8
6
h
ave
/ MW⋅m-2⋅K-1
Tw=303 K
7 8 9 10 11 12
4
2 250
350
450
550
G / kg⋅m-2⋅s-1 s Fig. 16. Influence of steam mass flux on average heat transfer coefficient.
10 -3 -2 -1 Gw×10 / kg⋅m ⋅s
8
6
h
ave
/ MW⋅m-2⋅K-1
-2 -1 Gs=400 kg⋅m ⋅s
7 8 9 10 11 12
4
2 283
293
303
313
323
333
T /K w Fig. 17. Influence of inlet water temperature on average heat transfer coefficient.
10 2 -1 Gs / kg⋅m ⋅s
8
6
difference increase, but the interface area decreases, which lead to the increase of average heat transfer coefficient. Average heat transfer coefficient obtained in this study is in the range of 2.89–7.89 MW/m2 K. It is greater than that of previous investigations [7,10], which are in the range of 0.63–3.44 MW/m2 K and 0.98–1.45 MW/m2 K, but in the same order of magnitude. In fact, according to the results of Kim et al. [23], resistance of heat transfer of DCC mainly concentrates on water side. Eddies in the mixture layer generated in turbulent motion enhance the heat and mass transfer between steam and water, which leads to increase of the heat transfer coefficient. Secondly, in present work, steam jet is condensed in water flow, which is injected into the rectangular mix chamber from a water nozzle unlike previous works in quiescent water pool. The hot water from condensed steam and heated water flows downward, so water around the mixture layer keeps fresh and a low temperature, which increases the temperature difference of heat transfer. Finally, interface defined in this work is smaller than before, which increases the average heat transfer coefficient. According to the analysis above, it can be conclude that the result of a greater average heat transfer is reasonable. In addition, Nusselt number is introduced to fitting the experimental data of average heat transfer coefficient in present work. The Nusselt number can be expressed as Eq. (10), Where kw is the thermal conductivity of water. The predicted errors are within ±25%, which is shown in Fig. 19.
Nuav e ¼
ave
/ MW⋅m-2⋅K-1
Tw=303 K
300 350 400 450 500 550 600
Fig. 19. Predicted Nusselt number compared with experimental Nusselt number.
0:71 hav e dhe Gs ¼ 2:18 103 B0:36 Re0:41 w kw Gm
ð10Þ
h
4. Conclusions
4
2 5
7
9
11 13 15 G ×10-3 / kg⋅m-2⋅s-1 w
17
19
Fig. 18. Influence of water mass flux on average heat transfer coefficient.
difference DT and interface area Ai. Temperature difference and interface area would increase with steam mass flux, which lead to reduction in the average heat transfer coefficient. With increasing inlet water temperature, the interface area increases, however, temperature difference and latent heat of condensation decrease, so the average heat transfer coefficient would increase in general. As water mass flux increases, latent heat of condensation and temperature
In this paper, an experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber is conducted. The high-speed camera is employed to record the flow field of DCC in a visualized experimental rig. The main results could be summarized as follows: (1) Based on experiments, the flow field of DCC in water flow in a rectangular mix chamber mainly consists of four different regions. They are steam region, interface, mixture layer and ambient water region. The interface between steam region and mixture layer is clearly observed. Four different flow patterns are found to be bubble flow, oscillatory jet, stable jet and divergent jet. Besides, a regime diagram based on steam mass flux, water mass flux and temperature is obtained.
X. Zong et al. / International Journal of Heat and Mass Transfer 80 (2015) 448–457
(2) Steam region dimensionless penetration length of the stable jet is found to be in the range of 1.73–4.40. An analytical model is established to predict the dimensionless penetration length, and a correlation is also developed. Errors between predicted dimensionless penetration length and experimental dimensionless penetration length are about ±40%. By introducing the Reynolds number of water, the errors reduce to ±25%. (3) Average condensation heat transfer coefficient of the stable jet is found to be within 2.89–7.89 MW/m2 K, which is greater than previous investigations, but in the same order of magnitude. In addition, correlation is also proposed to predict the average Nusselt number, and the discrepancies are within ±25%. Conflict of interest None declared. Acknowledgements This work was supported by the National Natural Science Foundation Project of China (No. 51176147). References [1] T. Narabayashi, W. Mizumachi, M. Michitugu, Study on two-phase flow steam injectors, Nucl. Eng. Des. 175 (1–2) (1997) 147–156. [2] G. Cattadori, L. Galbiati, L. Mazzocchi, P. Vanini, A single-stage high-pressure steam injector for next-generation reactors: test-results and analysis, Int. J. Multiph. Flow 21 (4) (1995) 591–606. [3] C.K. Chan, C.K.B. Lee, A regime map for direct contact condensation, Int. J. Multiph. Flow 8 (1) (1982) 11–20. [4] M.H. Chun, Y.S. Kim, J.W. Park, An investigation of direct condensation of steam jet in subcooled water, Int. Commun. Heat Mass Transfer 23 (7) (1996) 947– 958. [5] K.S. Liang, P. Griffith, Experimental and analytical study of direct contact condensation of steam in water, Nucl. Eng. Des. 147 (3) (1994) 425–435. [6] A. Petrovic de With, R.K. Calay, G. de With, Three-dimensional condensation regime diagram for direct contact condensation of steam injected into water, Int. J. Heat Mass Transfer 50 (9–10) (2007) 1762–1770.
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[7] X.Z. Wu, J.J. Yan, S.F. Shao, Y. Cao, J.P. Liu, Experimental study on the condensation of supersonic steam jet submerged in quiescent subcooled water: steam plume shape and heat transfer, Int. J. Multiph. Flow 33 (12) (2007) 1296–1307. [8] X.Z. Wu, J.J. Yan, W.J. Li, D.D. Pan, D.T. Chong, Experimental study on sonic steam jet condensation in quiescent subcooled water, Chem. Eng. Sci. 64 (23) (2009) 5002–5012. [9] X.Z. Wu, J.J. Yan, W.J. Li, D.D. Pan, G.Y. Liu, Experimental investigation of overexpanded supersonic steam jet submerged in quiescent water, Exp. Thermal Fluid Sci. 34 (1) (2010) 10–19. [10] Q. Xu, L.J. Guo, S. Zou, J. Chen, X. Zhang, Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe, Int. J. Heat Mass Transfer 66 (11) (2013) 808–817. [11] J.J. Yan, S.F. Shao, J.P. Liu, Z. Zhang, Experiment and analysis on performance of steam-driven jet injector for district-heating system, Appl. Therm. Eng. 25 (8– 9) (2005) 1153–1167. [12] P. Dumaz, G. Geffraye, V. Kalitvianski, E. Verloo, M. Valisi, P. Meloni, A. Achilli, R. Schilling, M. Malacka, M. Trela, The DEEPSSI project, design, testing and modeling of steam injectors, Nucl. Eng. Des. 235 (3–4) (2005) 233–251. [13] G.P. Celata, M. Cumo, G.E. Farello, G. Focardi, Direct contact condensation of steam on a horizontal surface of water, Heat Mass Transfer 21 (2–3) (1987) 169–180. [14] S.K. Malibashev, Experimental investigation of transparent model of steam– water injector with a convergent nozzle, Atomic Energy 90 (6) (2001) 469– 474. [15] S.K. Malibashev, Experimental investigation of a steam-water injector with a tapered nozzle, Atomic Energy 91 (2) (2001) 617–626. [16] N. Deberne, J.F. Leone, A. Duque, A. Lallemand, A model for calculation of steam injector performance, Int. J. Multiph. Flow 25 (5) (1999) 841–855. [17] R.S. Taylor, L.X. Dang, B.C. Garrett, Molecular dynamics simulations of the liquid/vapor interface of SPC/E water, J. Phys. Chem. 100 (28) (1996) 11720– 11725. [18] L.X. Dang, T.M. Chang, Molecular dynamics study of water clusters, liquid, and liquid–vapor interface of water with many-body potentials, J. Chem. Phys. 106 (1997) 8149. [19] A. Petrovic, Analytical study of flow regimes for direct contact condensation based on parametrical investigation, J. Pressure Vessel Technol. Trans. ASME 127 (1) (2005) 20. [20] A. Shah, I.R. Chughtai, M.H. Inayat, Experimental study of the characteristics of steam jet pump and effect of mixing section length on the direct-contact condensation, Int. J. Heat Mass Transfer 58 (3) (2013) 62–69. [21] P.J. Kerney, G.M. Faeth, D.R. Olson, Penetration characteristics of a submerged steam jet, AIChE J. 18 (3) (1972) 548–553. [22] A.A. Sonin, M.A. Shimko, J.H. Chun, Vapor condensation onto a turbulent liquid (I)-the steady condensation rate as a function of liquid-side turbulent, Int. J. Heat Mass Transfer 29 (9) (1986) 1319–1332. [23] Y.S. Kim, J.W. Park, C.H. Song, Investigation of the steam–water direct contact condensation heat transfer coefficients using interfacial transport models, Int. Commun. Heat Mass Transfer 31 (3) (2004) 397–408.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber Xiao Zong a,1, Ji-ping Liu a,⇑, Xiao-ping Yang a,1, Jun-jie Yan b,2 a b
MOE Key Laboratory of Thermal Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China 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 21 March 2014 Received in revised form 31 August 2014 Accepted 10 September 2014
Keywords: Direct contact condensation Water flow Flow pattern Dimensionless penetration length Average heat transfer coefficient
a b s t r a c t An experimental study on the direct contact condensation (DCC) of steam jet in subcooled water flow in a rectangular mix chamber was conducted. A high-speed camera was employed to record the flow field of DCC in the visualized experimental rig, in which, the steam nozzle and water nozzle were both rectangular. The flow field was filmed when the steam mass flux, water mass flux and water temperature were in the range of 200–600 kg/m2 s, 6000–18000 kg/m2 s and 293–333 K, respectively. The results indicated that, the flow field of DCC in the rectangular mix chamber consisted of four regions, and they were steam region, interface, mixture layer and ambient water region. The interface between steam region and mixture layer was clearly observed. The flow pattern of DCC was performed as bubble flow, oscillatory jet, stable jet and divergent jet at various test conditions. The steam region dimensionless penetration length and average heat transfer coefficient of the stable jet were found to be in the range of 1.73–4.40 and 2.89– 7.89 MW/m2 K, respectively. Furthermore, an analytical model was established and a correctional correlation was developed to predict the dimensionless penetration length. An empirical correlation was proposed to predict the average heat transfer coefficient. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Direct contact condensation (DCC) of steam jet in subcooled water flow is the core process of two-phase flow steam injector (TFSI). Due to the advantages of compact, high heat transfer intensity, lifting pressure during heat transfer, it has been widely used in several industrial applications [1,2]. For a fundamental understanding of DCC of steam jet in subcooled water pool, many works on flow pattern, regime diagram, pressure and temperature distributions and heat transfer characteristics had been conducted. Chan and Lee [3] investigated steam jet downward through a pipe into a pool of subcooled water, three different flow patterns were reported to be oscillatory jet, steam chugging and oscillatory bubble. A regime diagram based on steam mass flux and pool temperature was also obtained. Chun et al. [4] experimentally studied the DCC of steam jet in stagnant water, two steam plume shapes in the stable condensation regime were found to be conical and ellipsoidal. Liang and Griffith [5] observed ⇑ Corresponding author. Tel.: +86 29 82665742; fax: +86 29 82675741. E-mail addresses: [email protected] (X. Zong), [email protected] (J.-p. Liu), [email protected] (X.-p. Yang), [email protected] (J.-j. Yan). 1 Tel.: +86 29 82665742; fax: +86 29 82675741. 2 Tel.: +86 29 82665741; fax: +86 29 82675741. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.050 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.
chugging, bubbling, oscillatory jet and stable jet in research of DCC, transition criteria between regimes were also proposed. Petrovic et al. [6] conducted a three-dimensional regime diagram and validated against experiments. Wu et al. [7–9] experimentally investigated sonic/supersonic steam jet condensation in quiescent subcooled water, six different steam plume shapes were observed, temperature distribution was discussed and the heat transfer coefficient was found to be within 0.63–3.44 MW/m2 K. Xu et al. [10] carried out experimental study on DCC of stable steam jet in water flow in a vertical pipe, the heat transfer coefficient was reported to be in the range of 0.34–11.36 MW/m2 K. Due to the shear force between walls and fluid, the steam– water DCC has different features when occurs in a restricted channel. Existing researches mostly concentrated on flow characteristics [2,11,12], heat transfer characteristics were little concerned. Celata et al. [13] conducted theoretical research on DCC of steam–water on a horizontal surface, and found that temperature gradient mainly lay on water side of the interface with thickness of millimeter-scale. By using laminar convective heat transfer model, in which the interface was treated as a uniform temperature surface, the results were in good agreement with experiments. Considering saturation pressure corresponding to average water temperature as the mixture pressure, Malibashev [14,15]
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Nomenclature Ai B cp dhe Gs Ge Gm Gw hi hfg 0 h have k l L m
interface area, m2 condensation driving potential water specific heat, J/kg K steam nozzle exit equivalent diameter, m steam mass flux at steam nozzle throat, kg/m2 s steam mass flux at steam nozzle exit, kg/m2 s critical steam mass flux, equals to 275kg/m2 s water mass flux at water nozzle exit, kg/m2 s local heat transfer coefficient, MW/m2 K latent heat of condensation, kJ/kg nominal radius, m average heat transfer coefficient, MW/m2 K arc length of fan-shape to circle, equals to a/360° penetration length, m dimensionless penetration length steam mass flow rate, kg/s
experimentally investigated the flow features of DCC in a channel under different conditions. Deberne et al. [16] carried out visualization research on dynamic and heat transfer performance on DCC. The vapor volume fraction was detected by gamma rays during condensation, and found that the cross-sectional average vapor void fraction was increasing. In recent years, with the development of computer, investigation on the mechanism of interface by molecular dynamics simulation and research on phase change heat transfer by molecular performance on the interface had been focus of this study by many researchers [17,18]. Compared with researches on the steam jet in water pool, investigation on DCC of steam jet in a restricted channel is absent, and a lot of basic issues are still unsolved. Interface is the major area of mass, momentum and energy transfer in DCC. Due to the cylindrical axial symmetric structure of steam jet in water pool with circular nozzles or pipes, details of the inner steam jet could not be obtained directly in existing experimental studies. To solve this problem, a visualized experimental rig with rectangular steam nozzle and water nozzle was designed and fabricated. In this work, investigation on the steam jet in subcooled water flow in a rectangular mix chamber is carried out by constructing a quasi-planar structure of flow field, so that the details of the inner steam jet could be filmed with the high-speed camera easily. Besides, the influence of steam mass flux, water mass flux and water temperature on the steam region dimensionless penetration length of the stable jet and average heat transfer coefficient are discussed. The present experimental study are of theory significant for the further understanding of DCC of steam jet in subcooled water flow in a restricted channel, and it is helpful to the better design and safe operation on the TFSI. 2. Experimental system and methods The experimental system for investigating on steam jet in subcooled water flow in a rectangular mix chamber is schematically presented in Fig. 1. The apparatus mainly consists of a test section, an electric steam generator, a feed pump, a return pump, two water tanks, a high-speed camera, a cooling tower and some valves. The major geometry of the test section is presented in Fig. 2. The test section is made of stainless steel and two pieces of tempered glass are installed at front and back of the test section for observation and filming. The convergent–divergent rectangular steam nozzle is inserted into the test section by soldering, as shown in Fig. 2(a). The steam nozzle throat height and width are both
me Ps Pw S Sm Ts Tw Two Nuave Rc Rew kw
a
steam mass flow rate at steam nozzle exit, kg/s inlet steam pressure, MPa inlet water pressure, MPa analogous to familiar Stanton number of heat transfer, equals to hi/cpG mean value of S steam saturation temperature at the steam nozzle exit, K inlet water temperature, K mix chamber outlet temperature, K average Nusselt number condensation rate, kg/m2s water Reynolds number at water nozzle exit water thermal conductivity, W/mK central angle
8 mm, and 10 mm at the nozzle exit, as shown in Fig. 2(b). The rectangular water nozzle is at top of the steam nozzle, the height of water nozzle exit is the same with that of steam nozzle throat, 8 mm, and the width is 10 mm. Besides, there is 10 mm length of straight section at the water nozzle exit, which ensures that the water flow is horizontally injected into the mix chamber. Because that there is no gap between the tempered glasses and the steam nozzle, water nozzle as well as the test section, the front and back walls of the rectangular mix chamber are the tempered glasses actually. In addition, altogether 11 groups of measure point are installed through center on the upper and bottom wall of the mix chamber for pressure and temperature measurement simultaneously, as shown in Fig. 2(b). In present work, steam and water are injected into the mix chamber though the rectangular steam and water nozzles, respectively. Details of the test conditions are given in Table 1, and the major geometry parameters of the test section and nozzles are presented in Table 2. Steam supply is taken from the steam generator continuously with electric heaters of 330 kW and maximum flow rate of 0.11 kg/s. The steam flow rate is controlled by a valve manually and all the steam lines are wrapped by fiberglass insulation. Filtered water is derived from a single-stage horizontal shaft centrifugal pump and the water flow rate is controlled by valves on feed and by-pass lines. The Phantom V611 type high-speed camera is set as 5 kHz in experiments. All singles are processed by the LabVIEW data acquisition system, which consists of an industrial computer, a NI cDAQ-9178 data acquisition board, two NI 9213 modules to obtain temperature and four NI 9203 modules to obtain current signals of pressure transducers. The steam flow rate is measured by a vortex steam flow meter, which is in the range of (0.75–7.39) 102 kg/s with maximum relative deviation of 1.0%. The water flow rate is measured by an electromagnetic flow meter in the range of 0.08–2.78 kg/s with maximum relative deviation of 0.2%. The high-temperature pressure transducers used in present work are in the range of 0–1 MPa with maximum relative deviation of 0.1%. Calibrated by a standard thermocouple, the steam and water temperature are measured by the K-type thermocouples (diameter 1 mm), which are in the range of 273–473 K with maximum relative deviation of 0.5%. In present work, the steam flow rate, water flow rate, pressure and temperature are in the range of (1.28–3.84) 102 kg/s, 0.47–1.44 kg/s, 0.1–0.5 MPa and 293–423 K respectively, so the relative uncertainties in steam mass flux, water mass flux, pressure and temperature are below 3.0%, 0.7%, 0.6% and 2.9%.
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Fig. 1. Schematic diagram of experimental system.
Fig. 2. Major geometry of test section.
Table 1 Test conditions in experiment.
Table 2 Major geometry parameters of test section.
Parameters
Values
Parameters
Values (mm)
Inlet steam pressure Ps, MPa Inlet water pressure Pw, MPa Steam mass flux at nozzle throat Gs, kg/m2s Water mass flux at nozzle exit Gw 103, kg/m2s Inlet water temperature Tw, K
0.1–0.5 0.1–0.5 200–600 6–18 293–333
Exit size of water nozzle Throat size of steam nozzle Exit size of steam nozzle Mix chamber size
10 8 88 10 10 250 10 19
3. Experimental results and discussion 3.1. Regions of flow field When the high-speed steam is injected into water flow by a rectangular convergent–divergent nozzle in the rectangular mix chamber, DCC occurs between the steam jet and subcooled water
flow. In previous studies, steam was injected into a stagnant water pool by circular nozzles or pipes [7–10], and four different regions in the flow field were identified as steam plume, interface, hot water layer and ambient water. Using the circular nozzles in water pool, steam jet was condensed by stagnant water all around, which formed a three-dimensional structural view field, as shown in Fig. 3. In the three-dimensional view field, inner structure of the steam jet could not be observed directly. To solve
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fourth region is the ambient water, which is on the top of mixture layer. The ambient water region includes subcooled water injected into the mix chamber from water nozzle and hot water from steam condensation. The water moves ever faster as a result of steam condensation and vacuum effect at the steam nozzle exit [20]. The structural difference between circular nozzles in water pool and rectangular steam and water nozzles in the rectangular mix chamber contributes to the phenomenological difference of the flow field. In fact, the steam plume identified in the circular structural one in water pool considers including the steam region, interface and the mixture layer identified in the rectangular one in present study. 3.2. Flow pattern Fig. 3. Different regions of steam injected in water pool by circular nozzles or pipes [7–10].
this problem, in present work, the rectangular steam and water nozzles as well as the mix chamber are used to investigating on the DCC phenomena. The water is injected into the mix chamber just on the top of steam jet, and the front, back and bottom of the steam jet are all solid walls (the front and back walls are the tempered glasses), DCC just occurs in the top side. Due to a rectangular mix chamber, the view field is of quasi-planar structure, as shown in Fig. 4, so the details of the inner steam jet could be clearly observed and distinguished. Similarly, four different regions are identified in the flow field of steam jet in water flow in a rectangular mix chamber, as shown in Fig. 4. The first region is steam region, which is only composed of pure steam. In the steam region, steam is of great velocity, momentum and energy, and in the influence of water flow as well as flow characteristics itself, a series of expansion and compression waves would occur, which is similar to the results of steam jet in a water pool by Wu et al. [7,8]. The second region is the outer surface of steam region – interface, which divides the steam region from the mixture layer. Many researchers simulated with basic theory of molecular dynamics, their results indicated that the interface might be an area with thickness of a few or dozens of molecules [17,18]. Transportation of mass, momentum and energy between steam and water are proceeding at the interface. The mixture layer clearly distinguished in this study is a steam–water two-phase layer. In the mixture layer, steam exists in bubble form and both phases are in turbulent motion. Two-phase turbulent motion generates a large amount of eddies, which has great effect on the shape of the interface and controls the interfacial transportation [19]. The
Fig. 4. Different regions of stable steam jet in subcooled water flow in a rectangular mix chamber. (Gs = 350 kg/m2 s, Gw = 8000 kg/m2 s, Tw = 293 K).
The flow pattern of DCC is a significant characteristic when studying on steam jet in subcooled water flow. In present work, based on different regions in the flow field at various test conditions, four types of flow pattern are identified as bubble flow, oscillatory jet, stable jet and divergent jet, as shown in Fig. 5. When the steam mass flux is low, determined by the combination of the steam and water mass flux, backpressure of the convergent–divergent steam nozzle is relatively high, so the steam flow at the steam nozzle exit is subsonic, and the flow pattern of bubble flow is observed. At first, steam flow rushes out to the mix chamber from steam nozzle, the interface area is small and condensation rate is low accordingly, so steam gathers at the nozzle exit and forms a steam bubble. Along with steam bubble growth, the interface extends. As condensation rate is large enough, the steam bubble collapses due to insufficient supply of steam. As the steam bubble occurs, grows and collapses periodically, the bubble flow never has the structure of Fig. 4. With increasing steam mass flux at high water mass flux, the steam bubble would never collapse any more. Though the steam flow also is subsonic, steam supply is enough to maintain flow characteristics itself near the nozzle exit, so the interface in front part of the steam region is stable. But at steam jet tail, ambient water rushes into the steam region periodically, which leads to the steam jet waving up and down intensively, so the steam region together with the interface are not maintained in a fixed shape, and then the oscillatory jet is observed. In the case of medium steam mass flux and relatively lower water mass flux, the steam nozzle backpressure is low enough, and then the steam flow is supersonic. As pointed by Xu et al. [10], the compression and expansion waves would occur in the supersonic flow in water flow. Due to the relatively higher condensation heat, steam flow would travels a longer distance and the ambient water would not rush into the steam region, all the regions discussed in last section is distinct and stable, and the stable jet is observed. With increasing inlet water temperature, water condensation capacity near the steam jet decreases, so the stable jet tends divergent, and the divergent jet is observed. In addition, the influences of steam mass flux and inlet water temperature on flow pattern are presented in Figs. 6 and 7 respectively. When the steam mass flux increases from 250 to 550 kg/m2 s at Gw = 14000 kg/m2 s and Tw = 303 K, the flow pattern turns from bubble flow to oscillatory jet and then to stable jet, as shown in Fig. 6. As the inlet water temperature increases from 293 to 333 K at Gw = 10,000 kg/m2 s and Gs = 400 kg/m2 s, the flow pattern turns form stable jet to divergent jet, as shown in Fig. 7. In previous studies, flow pattern in stagnant water pool has been known to be determined mainly by steam mass flux and pool temperature [3,4,6–9]. The steam mass flux indicates the condensation heat and flow characteristics, whilst the pool temperature indicates the water condensation capacity. In present work, the water temperature near steam jet cannot remain unchanged, which increases along the steam jet due to condensation and
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Fig. 5. Flow pattern of DCC: (A) bubble flow, (B) oscillatory jet, (C) stable jet, (D) divergent jet.
Fig. 6. Influence of steam mass flux on flow pattern.
mixing. In order to characterize the influence of initial water condensation capacity on the flow pattern, the inlet water temperature is adopted. Fig. 8 shows the change of flow pattern with water mass flux for constant steam mass flux and inlet water temperature. As Gs = 400 kg/m2 s and Tw = 293 K, stable jet is observed at Gw = 6000 kg/m2 s. With increasing water mass flux, Reynolds number of the water will increase, which leads to an enhancement of heat transfer at water side, condensation rate would increase in proportion. At the same time, backpressure of the steam nozzle would increase and the steam flow turns from supersonic to subsonic. Due to these two reasons, bubble flow is observed at Gw = 18,000 kg/m2 s. Results and analysis above clearly indicate that the flow pattern of DCC of steam jet in subcooled water flow in a rectangular mix chamber is not only decided by steam mass flux and inlet water temperature like previous investigations in
stagnant water pool [3,4,6–9], but also the water mass flux plays an important role. In fact, the flow pattern is determined by the heat transfer characteristics between steam and water and by hydrodynamic behaviors at the interface. The heat transfer characteristics and the hydrodynamic behaviors at the interface are determined by the combination of three parameters including steam mass flux, water mass flux and inlet water temperature, with affecting each other. Therefore, based on the experimental data, the two-dimensional regime diagram for DCC of steam jet in subcooled water flow in a rectangular mix chamber is developed, which consists of four different flow patterns, as shown in Fig. 9. When the inlet water temperature is low (Tw = 303 K), with increasing steam mass flux, the flow pattern turns from bubble flow to stable jet at lower water mass flux, while the flow pattern changes from bubble flow to oscillatory jet a higher water mass flux. Further increasing the
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453
Fig. 7. Influence of inlet water temperature on flow pattern.
Fig. 8. Change of flow pattern with water mass flux.
steam mass flux would lead to occurrence of the divergent jet. When the inlet water temperature is high (Tw = 323 K), the flow pattern changing trend is similar to that at low inlet water temperature, but the divergent jet region extends, which indicates that the steam jet tends to divergent more easily at relatively high inlet water temperature. 3.3. Steam region penetration length of the stable jet Steam region penetration length l is defined as the axial distance of pure steam from nozzle exit, shows in Fig. 4. Due to a fixed and distinct steam region, it is easier to obtain the penetration length for the flow pattern of stable jet. The dimensionless
penetration length L is the ratio of penetration length l to the steam nozzle exit equivalent diameter dhe. The penetration length is obtained by manually measuring and averaging ten photos captured by the high-speed camera at different times. Figs. 10–12 shows the dimensionless penetration length L at various test conditions. As steam mass flux and inlet water temperature increase, penetration length increases, whereas as water mass flux increase, penetration length decreases, the values are in the range of 1.73–4.40. According to Kerney et al. [21], the interface is replaced by a smooth time-averaged surface and steam condensation is assumed to be taking place at the interface. The mass conversation equation can be expressed as,
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600
-2 -1 Gs / kg⋅m ⋅s
500
550
Divergent jet
450
et le j b a St
400
Tw=323 / K
500
tory ill a c s O
-2 -1 Gs / kg⋅m ⋅s
550
600
Tw=303 / K
jet
350 300
Divergent jet
450
jet ble a t S
350 300
Bubble flow
250 200 6
8
10
12
14
tory ill a c s O
400
Bubble flow
250
16
18
jet
200 6
8
10
12
14
16
18
-3 -2 -1 Gw×10 / kg⋅m ⋅s
-3
Gw×10 / kg⋅m-2⋅s -1
(a)
(b)
Fig. 9. Two-dimensional regime diagram for DCC of steam jet in subcooled water flow in a rectangular mix chamber; (a) Tw = 303 K, (b) Tw = 323 K.
5
5 -3
-2 -1
Gw×10 / kg⋅m ⋅s 7 8 9 10 11 12
3
2
3
2
1 250
350
450
1 6
550
8
-2 -1
G / kg⋅m ⋅s s
Fig. 10. Change of dimensionless penetration length with steam mass flux.
5
L
-2 -1 Gs=400 kg⋅m ⋅s
02
m ¼ 4kph G
7 8 9 10 11 12
2
1 273
12
14
ð1Þ
where -3 -2 -1 Gw×10 / kg⋅m ⋅s
3
10 G ×10-3 / kg⋅m-2⋅s-1 w
Fig. 12. Change of dimensionless penetration length with water mass flux.
dm 0 ¼ 2kph Rc dx
4
Tw / K 293 313 323 333
4
L
4
L
-2 -1 Gs=400 kg⋅m ⋅s
Tw=313 K
293
313
333
T /K w Fig. 11. Change of dimensionless penetration length with inlet water temperature.
ð2Þ
where k ¼ a=360 , a is the central angle, which is considered to be constant along the steam jet, so k is the ratio of arc length of the fanshape to the circle, and k is also consider to be a constant, as shown in Fig. 13. The geometry of Kerney et al. [21] is circular, but the geometry of present work is close to square. Due to a small value of a, the quasi-square area is close to 4 times of the fan-shape, 0 whose central angle is a. So the nominal radius of the interface h is introduced to express the cross-sectional steam mass flow rate in Eq. (2), where G is the steam mass flux. Rc ¼ hi =ðT s T w Þhfg is the condensation rate, hi is the local heat transfer coefficient, hfg is 0 the latent heat of condensation. Extracting h from Eq. (2) and then substituting it into Eq. (1), it can be inferred from Eq. (1) that,
pffiffiffiffiffi d m 1 pffiffiffiffiffiffiffiffiffi ¼ kpG BS dx 2
ð3Þ
X. Zong et al. / International Journal of Heat and Mass Transfer 80 (2015) 448–457
Interface
Interface α
A
Steam
m
455
h'
h'
Steam plume
dx
A
A-A
l
Fig. 13. Analytical model of the stable jet.
where B = cp(Ts Tw)/hfg is the condensation driving potential, cp is the liquid special heat, S = hi/cpG is analogous to the familiar Stanton number of heat transfer. Integrate Eq. (3) with the boundary conditions,
x ¼ 0;
x ¼ me ;
x ¼ l;
m¼0
ð4Þ
and then the dimensionless penetration length could be given as,
L¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi l 2 ¼ pffiffiffi ðBSm Þ1 Ge =Gm dhe k
ð5Þ
where Sm is appropriate mean value of the S, which is considered to be constant, Gm = 275 kg/m2 s is the critical steam mass flux, given by Kerney et al. [21], Ge is steam mass flux at the nozzle exit. Based on the analysis above, a correlation by fitting the experimental data for dimensionless penetration length of the stable jet could be given as,
L ¼ 0:356B0:88
Ge Gm
0:99 ð6Þ
In addition, comparison of predicted dimensionless penetration length by Eq. (6) with experimental dimensionless penetration length is presented in Fig. 14, the predicted errors are about ±40%. According the observation, it can be inferred that increasing in water mass flux would lead to reduction of penetration length, water mass flux also plays an important role in the penetration length. But in Eq. (6), there is not any item to express this effect. According to Sonin et al. [22], turbulent intensity is an important factor in condensation, and in the results of Xu et al. [10], the water Reynolds number is introduced to account for the water supply and turbulent movement of water flow on the penetration length. Similarly, in present work, water Reynolds number at the water nozzle exit Rew is also introduced to express the influence of water flow,
Fig. 15. Correctional predicted dimensionless penetration length compared with experimental dimensionless penetration length.
and a correctional correlation for the dimensionless penetration length is given in Eq. (7). The results indicated that introducing the water Reynolds number would decrease the errors to ±25%, as shown in Fig. 15.
L ¼ 15:2B1:8
Gs Gm
2:05
Re0:58 w
ð7Þ
3.4. Condensation heat transfer coefficient of the stable jet For steam jet condensation, several researchers [7,10] had given empirical correlations to predict the average heat transfer coefficient. In present work, due to a distinct steam region, the flow pattern of stable jet is chosen to investigate the heat transfer characteristics. Assuming a uniform heat flux at the interface, the average heat transfer coefficient can be calculated as,
hav e ¼
me hfg A i DT
ð8Þ
Where Ai is the interface area, which is obtained manually, DT is the logarithmic mean temperature difference between steam and water, calculated by,
DT ¼
Fig. 14. Predicted dimensionless penetration length compared with experimental dimensionless penetration length.
ðT s T w Þ ðT s T wo Þ T w ln TTssT wo
ð9Þ
Average heat transfer coefficients at various test conditions are shown in Figs. 16–18. With increasing steam mass flux, average heat transfer coefficient tends to decrease, whereas with increasing water mass flux and inlet water temperature, average heat transfer coefficient tends to increase. It can be inferred from Eq. (8) that there are three factors to affect the average heat transfer coefficient, quantity of condensation heat transfer mehfg, temperature
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X. Zong et al. / International Journal of Heat and Mass Transfer 80 (2015) 448–457
10 -3 -2 -1 Gw×10 / kg⋅m ⋅s
8
6
h
ave
/ MW⋅m-2⋅K-1
Tw=303 K
7 8 9 10 11 12
4
2 250
350
450
550
G / kg⋅m-2⋅s-1 s Fig. 16. Influence of steam mass flux on average heat transfer coefficient.
10 -3 -2 -1 Gw×10 / kg⋅m ⋅s
8
6
h
ave
/ MW⋅m-2⋅K-1
-2 -1 Gs=400 kg⋅m ⋅s
7 8 9 10 11 12
4
2 283
293
303
313
323
333
T /K w Fig. 17. Influence of inlet water temperature on average heat transfer coefficient.
10 2 -1 Gs / kg⋅m ⋅s
8
6
difference increase, but the interface area decreases, which lead to the increase of average heat transfer coefficient. Average heat transfer coefficient obtained in this study is in the range of 2.89–7.89 MW/m2 K. It is greater than that of previous investigations [7,10], which are in the range of 0.63–3.44 MW/m2 K and 0.98–1.45 MW/m2 K, but in the same order of magnitude. In fact, according to the results of Kim et al. [23], resistance of heat transfer of DCC mainly concentrates on water side. Eddies in the mixture layer generated in turbulent motion enhance the heat and mass transfer between steam and water, which leads to increase of the heat transfer coefficient. Secondly, in present work, steam jet is condensed in water flow, which is injected into the rectangular mix chamber from a water nozzle unlike previous works in quiescent water pool. The hot water from condensed steam and heated water flows downward, so water around the mixture layer keeps fresh and a low temperature, which increases the temperature difference of heat transfer. Finally, interface defined in this work is smaller than before, which increases the average heat transfer coefficient. According to the analysis above, it can be conclude that the result of a greater average heat transfer is reasonable. In addition, Nusselt number is introduced to fitting the experimental data of average heat transfer coefficient in present work. The Nusselt number can be expressed as Eq. (10), Where kw is the thermal conductivity of water. The predicted errors are within ±25%, which is shown in Fig. 19.
Nuav e ¼
ave
/ MW⋅m-2⋅K-1
Tw=303 K
300 350 400 450 500 550 600
Fig. 19. Predicted Nusselt number compared with experimental Nusselt number.
0:71 hav e dhe Gs ¼ 2:18 103 B0:36 Re0:41 w kw Gm
ð10Þ
h
4. Conclusions
4
2 5
7
9
11 13 15 G ×10-3 / kg⋅m-2⋅s-1 w
17
19
Fig. 18. Influence of water mass flux on average heat transfer coefficient.
difference DT and interface area Ai. Temperature difference and interface area would increase with steam mass flux, which lead to reduction in the average heat transfer coefficient. With increasing inlet water temperature, the interface area increases, however, temperature difference and latent heat of condensation decrease, so the average heat transfer coefficient would increase in general. As water mass flux increases, latent heat of condensation and temperature
In this paper, an experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber is conducted. The high-speed camera is employed to record the flow field of DCC in a visualized experimental rig. The main results could be summarized as follows: (1) Based on experiments, the flow field of DCC in water flow in a rectangular mix chamber mainly consists of four different regions. They are steam region, interface, mixture layer and ambient water region. The interface between steam region and mixture layer is clearly observed. Four different flow patterns are found to be bubble flow, oscillatory jet, stable jet and divergent jet. Besides, a regime diagram based on steam mass flux, water mass flux and temperature is obtained.
X. Zong et al. / International Journal of Heat and Mass Transfer 80 (2015) 448–457
(2) Steam region dimensionless penetration length of the stable jet is found to be in the range of 1.73–4.40. An analytical model is established to predict the dimensionless penetration length, and a correlation is also developed. Errors between predicted dimensionless penetration length and experimental dimensionless penetration length are about ±40%. By introducing the Reynolds number of water, the errors reduce to ±25%. (3) Average condensation heat transfer coefficient of the stable jet is found to be within 2.89–7.89 MW/m2 K, which is greater than previous investigations, but in the same order of magnitude. In addition, correlation is also proposed to predict the average Nusselt number, and the discrepancies are within ±25%. Conflict of interest None declared. Acknowledgements This work was supported by the National Natural Science Foundation Project of China (No. 51176147). References [1] T. Narabayashi, W. Mizumachi, M. Michitugu, Study on two-phase flow steam injectors, Nucl. Eng. Des. 175 (1–2) (1997) 147–156. [2] G. Cattadori, L. Galbiati, L. Mazzocchi, P. Vanini, A single-stage high-pressure steam injector for next-generation reactors: test-results and analysis, Int. J. Multiph. Flow 21 (4) (1995) 591–606. [3] C.K. Chan, C.K.B. Lee, A regime map for direct contact condensation, Int. J. Multiph. Flow 8 (1) (1982) 11–20. [4] M.H. Chun, Y.S. Kim, J.W. Park, An investigation of direct condensation of steam jet in subcooled water, Int. Commun. Heat Mass Transfer 23 (7) (1996) 947– 958. [5] K.S. Liang, P. Griffith, Experimental and analytical study of direct contact condensation of steam in water, Nucl. Eng. Des. 147 (3) (1994) 425–435. [6] A. Petrovic de With, R.K. Calay, G. de With, Three-dimensional condensation regime diagram for direct contact condensation of steam injected into water, Int. J. Heat Mass Transfer 50 (9–10) (2007) 1762–1770.
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