- Email: [email protected]
Velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe
International Journal of Heat and Mass Transfer 103 (2016) 305–318
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe Qiang Xu, Liejin Guo ⇑, Liang Chang, Yechun Wang State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 5 April 2016 Received in revised form 6 July 2016 Accepted 14 July 2016
Keywords: Velocity field Turbulent jet Direct contact condensation Crossflow Particle Image Velocimetry
a b s t r a c t Direct contact condensation of jets in fluid has been widely applied in many industrial applications owing to the low requirement of driving potential and high efficiency of heat and mass transfer. Here, experiments are carried out to investigate the velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe. Visual equipment is specially invented to investigate the velocity field characteristics by using Particle Image Velocimetry (PIV) measurement technique. The high intensity laser light reflected by the pure steam region just outside the nozzle-exit brings out severe damage to the CCD camera. To solve this technical problem, a black plate is adopted to shield the pure steam region. According to the contours of the velocity fields and streamlines, the influences of jet momentum ratio, jet Reynolds number and water temperature on the jet flow field are explored. The jet centerline trajectory equations in exponential form are established based on the local maximum mean velocity. By introducing the jet Reynolds number and jet momentum ratio, the correlation for prediction of jet centerline trajectory equations is proposed, and the predicted results are within 30% of the experimental data. The reciprocal of the local maximum mean velocity and the halfwidth of the jet are proportional to the downstream coordinate along the jet velocity centerline trajectory. The scaled velocity field complies with the self-similarity principle. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Direct Contact Condensation (DCC) of a vapor jet in liquid has attracted much interest in recent years due to its high efficiency of heat and mass transfer and low requirement of driving potential. It is frequently encountered in lots of industrial applications, such as vapor jet condensing in nuclear industry, vapor jet pumping in process industry, vapor jet heating in power industry, and vapor jet driving in aerospace industry [1–4]. Previous work on DCC of a vapor jet in liquid reported in literature primarily focused on jet penetration length, condensation regime diagram, heat transfer coefficient, pressure oscillation and turbulent jet flow field. Kerney et al. [5] established the first correlation of jet penetration length as a function of condensation driving potential and steam mass flux. After that, a lot of improved correlations were reported by other researchers based on their respective background and experiments [6–14]. The interface behavior of the vapor jet was commonly illustrated in a condensation regime diagram, which were generally divided into three main regimes, such as chugging, bubbling and jetting [13,14,8,15]. Heat ⇑ Corresponding author. Fax: +86 29 82669033. E-mail address: [email protected] (L. Guo). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.07.047 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
transfer mechanisms were generally explored by theory analysis and numerical simulation, and many correlations of heat transfer coefficient were proposed [16–20]. Studies on pressure oscillation induced by vapor jet in liquid usually focused on amplitude and frequency [21,22]. To obtain the detailed velocity and temperature fields of turbulent jet induced by vapor jet in liquid, techniques such as Particle Image Velocimetry (PIV), Planar Laser Induced Fluorescence (PLIF) and mobile thermocouples were used [23–26]. For experimental study on jet interaction with crossflow, fruitful achievements about velocity field, centerline trajectory and jet shape were reported [27–34]. The flow and geometry characteristics of DCC of a vapor jet in crossflow have been studied thoroughly in our previous work [35–37]. However, due to the lack of the basic information on the velocity field of the turbulent jet, the interfacial transport mechanism of the condensing jet in crossflow in pipes is not well understand. The research work on single-phase jet in crossflow has already confirmed that the velocity fields of the turbulent jet contribute a lot to reveal the mass and momentum transport mechanism underlying of this complexity flow phenomenon [27–30]. But the condensation of the jet leads to significant change of the flow field structure and also difficult measurement of the velocity field. Clerx et al. [38–40] conducted a pioneer work on exploring the velocity field characteristics of
306
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Nomenclature A B d D ey Gs J l m n N ps pw Res Rew T u u Umean v
ve
constant in exponential equation, 1 constant in exponential equation, 1 inner diameter of the nozzle, m inner diameter of the vertical round pipe, m unit vector in ordinate direction, m/s steam mass flux at the nozzle exit, kg/m2 s jet momentum ratio equals to qsVs2/qwVw2, 1 ordinate in the Cartesian coordinate system (n, l), m mass flow rate, kg/s abscissa in the Cartesian coordinate system (n, l), m sequence sample size, 1 steam inlet pressure, MPa water pressure at the steam injection point, MPa jet Reynolds number equals to 4ms/pdls, 1 Reynolds number of water flow equals to 4mw/pDlw, 1 inlet temperature, °C velocity in the abscissa direction, m/s velocity vector, m/s mean horizontal velocity, m/s velocity in the ordinate direction, m/s velocity in the ordinate direction in the Cartesian coordinate system (n, l), m/s
DCC of steam jet in crossflow in a square channel at relatively low steam mass flux (Gs < 120 kg/m2 s). However, in actual industrial systems, the approaching fluid flows in round pipes rather than square channels. Besides, when the steam mass flux increases up to a certain value, the condensation regimes change from chugging to bubbling and then to jetting regime [15,35–37]. Therefore, it is desirable to perform investigation on velocity field characteristics of the turbulent jet induced by jet condensation in crossflow in pipes with a large range of steam mass flux. This paper focuses on the velocity field characteristics of the turbulent jet induced by DCC of steam jet in crossflow of water in a vertical pipe, with a range of high steam mass flux up to 740 kg/m2 s. The velocity field, jet centerline trajectory and lateral distribution of velocity are investigated. Visual equipment is specially invented to study the velocity field characteristics of the turbulent jet by means of PIV measurement technique. The high intensity laser light reflected by the pure steam region brings about severe damage to the CCD camera. A black plate is adopted to shield the pure steam region to solve this problem. The influences of jet momentum ratio, jet Reynolds number and water temperature on the velocity field are discussed. Furthermore, empirical correlation for prediction of jet centerline trajectory equations is proposed as a function of jet Reynolds number and jet momentum ratio. Finally, the lateral distribution of the velocity field is discussed and analyzed. This study provides new insights into velocity field characteristics of turbulent jet induced by DCC of steam jet in crossflow of water in pipes. The results would be useful for further theoretical and experimental research on the interfacial transport mechanism underlying DCC of steam jet in crossflow of water in pipes.
2. Experiments 2.1. Experimental setup In order to investigate the velocity field characteristics of the turbulent jet induced by DCC of steam jet in crossflow of water in pipes, a steam water two-phase flow system has been specially
ve, c v1
Va Vmean x y
jet centerline velocity in the ordinate direction in the Cartesian coordinate system (n, l), m/s crossflow velocity vector, m/s magnitude of velocity, m/s mean vertical velocity, m/s abscissa in the Cartesian coordinate system (x, y), m ordinate in the Cartesian coordinate system (x, y), m
Greek letters a angle between the abscissa x and the velocity centerline trajectory-normal direction, ° b angle between the nozzle center line and the pipe wall, ° h angle between the fixed x or y lines and the velocity centerline trajectory-normal direction, ° l dynamic viscosity, m2/s q density, kg/m3 Subscripts s the steam phase w the water phase
designed and built up. A sketch of the experimental system is shown in Fig. 1. It can be divided into four main components, such as a water supply line, a steam supply line, a test section and a data acquisition unit. The main part of the steam supply line is an electric heating boiler (72 kW), which generates saturated steam with a maximum mass flow rate of 0.03 kg/s. To keep the supplied steam saturating, the steam supply line is first covered with tap heaters, and then the tap heaters is wrapped with fiberglass coverings. The steam mass flow rate is measured by a vortex flowmeter with relative maximum deviation of 0.5%. The water volume flow rate is measured by a magnetic flowmeter with relative maximum deviation of 0.5%. In order to eliminate the effects of vibrations on the test section, two flexible metal hoses are connected between the water loop and the vertical pipe, and also a flexible hose is connected between the steam loop and the test section. The vertical pipe has a total length of 4100 mm with an inner diameter of 80 mm. Before entering the visual test section, the water flows in a smooth steel pipe of length 2400 mm (30 times of the hydraulic diameter of the vertical pipe), which is long enough to insure a fully developed turbulent flow entering the visual test section. The visual test section is well designed to investigate the velocity field characteristics of the turbulent jet, as displayed in Fig. 2. The vertical pipe in the visual test section is made of transparent silica glass with 5 mm wall thickness. The steam is discharged into the vertical pipe through a flushmounted nozzle with 3.2 mm inner diameter. The nozzle centerline is perpendicular to the pipe centerline. The temperature and pressure of discharged steam are measured at an upstream position of the nozzle exit. The visual test section is enclosed in a transparent silica glass box, which is filled with deionized water in order to eliminate distortions caused by the curvature of the round pipe. In this study we focus on the center plane A–A, defined by the vertical pipe centerline and the nozzle centerline. The experimental system is configured with high precision instrumentation. The fluid pressure is measured with pressure transducer, which is in the range of 0–1.0 MPa with relative maximum deviation of 0.1%. The fluid temperature is measured with K-type thermocouple, which is in the range of 0–200 °C with
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
307
Fig. 1. Schematic diagram of the experimental setup: (1) water tank; (2) centrifugal water pump; (3) control valve; (4) pressure transducer; (5) thermocouple; (6) magnetic flowmeter; (7) test section; (8) deionized water tank; (9) boiler feed pump; (10) electric steam generator; (11) vortex flowmeter; (12) control valve.
Fig. 2. Local schematic diagram of the test section: (1) water; (2) transparent glass plate; (3) transparent glass pipe; (4) nozzle; (5) pressure transducer; (6) steam inlet; (7) thermocouple; (8) water inlet; (9) CCD camera; (10) laser light.
maximum deviation of 0.5 °C. All signals are collected using data acquisition unit, including a PCI-6259 module for collecting flow and pressure signals, and a SCXI-1102E module for collecting temperature signals. The sampling frequency is 5 kHz for all sensors. The sampling time for each test run is 30 s. The experimental conditions in present work are displayed in Table 1.
Table 1 Range of operating conditions. Parameters
Range
Steam inlet pressure ps, MPa Steam inlet temperature Ts, °C Steam mass flux Gs, kg/m2 s Water flow rate mw, kg/s Water temperature Tw, °C Water pressure at the steam injection point pw, MPa Inner diameter of the nozzle d, m Angle between the nozzle center line and the pipe wall b, ° Inner diameter of the vertical pipe D, m
0.2–0.8 100–172 0–740 0.14–6.65 30–60 0.15 0.0032 90 0.08
2.2. PIV measurement technique PIV is a well-developed method for acquiring quantitative flow-visualization data with high-resolution. The principles of this measurement technique have been well elaborated in the literature [41], and the focus here is merely to describe the specific experimental facility and data processing approach adopted in this work. The flow illumination in a 2-D plane is accomplished by a double-pulsed Nd:YAG laser (532 nm), which is equipped with an optical arrangement for generating light sheets with divergence of 18°. The laser beam is transformed into a thin vertical light sheet of about 1 mm thickness by a series of cylindrical and spherical lenses. The reflected light in the measurement field-of-view (80 115 mm) is recorded by a CCD camera with a 2048 2048 pixels sensor and 12-bit resolution, resulting in a pixel resolution of 7.4 lm/pixel. The camera is fitted with a Nikkor AF 50 mm f/1.8D lens. The high intensity laser light reflected by the pure steam region brings about severe damage to the CCD camera. To solve this technique problem,
308
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 3. Influence of sampling time on time–mean flow characteristics at steam mass flux Gs = 242 kg/m2 s, water temperature Tw = 30 °C and Reynolds number of water flow Rew = 58, 421.
a mobile black plate with width 5 mm is adopted to shield the pure steam region. Initially the laser light is adjusted to relatively low intensity that the bright pure steam region has no damage on the CCD camera. Then a preliminary test at each test conditions is performed, and the position of the bright pure steam region at each test conditions could be recorded successively. Before each formal test, the black plate is adjusted to the proper position, which has been recorded by preliminary test at the same conditions, to shield the bright pure steam region. Based on this method, the high quality velocity field of
the condensing jet apart from the pure steam region could be obtained with no damage on the CCD camera. During each measurement a set of 80 or 160 image pairs is taken at a frequency of 7.25 Hz. The time interval Dt between the two successive images in each image-pair is adjusted to insure a maximum particle displacement of approximately 8–12 pixels. Image calibration is made by taking images of a reference object specially designed for present purpose. The water in the tank is seeded with hollow glass spheres with an average diameter of 3 lm and density of 1050 kg/m3.
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
309
Fig. 4. (a) and (b) two consecutive instantaneous velocity fields at a time interval of 1/7.25 s, and along with mean velocity field (c) and (d) averaged over 80 instantaneous measurements of experimental run with Gs = 242 kg/m2 s, Tw = 30 °C and Rew = 58, 421. The white dashed line enclosed the region where spurious velocity data is detected.
The raw images of the eighty planes are processed by software, Insight 4G [42], into vector maps. Firstly, the displacement vectors of the particles are calculated by Fourier-based cross-correlation and window shifting technique. The calculation starts off with a large interrogation window of 64 64 pixels with 50% overlap of each interrogation region, and then ends with 32 32 pixels. Subsequently, spurious vectors in the raw vector images are validated successively using a Signal/Noise ratio filter, a global filter, a peakheight filter and a local filter. Finally, a nearest-neighbor interpolation algorithm is applied to smooth the vectors in the global flow field. 2.3. Measurement uncertainty Generally, the total uncertainty of a variable can be valued by the bias uncertainty and random uncertainty. For the instantaneous velocity determined by the PIV system, the bias uncertainty is induced by camera calibration (LO/LI, LO represents the length of a real object, and LI represents the pixels in image of the object), time
interval (Dt) and particle displacement detection (Ddisp). In this work, the bias uncertainties of LO, LI, and Dt are 0.1 mm, 0.50 pixel, and 0.1 ls, respectively. The pixel locking error can be reduced to 0.1–0.3 pixels, and consequently the bias uncertainty of Ddisp is lower than about 0.3 pixels. The random uncertainty on the velocity measurement is mainly caused by cross-correlation error and the typical value is lower than about 0.1 pixels. The time–mean velocities are obtained by a sequence of N instantaneous vector images at each point. The selection of N is commonly based on the analysis of data convergence with sampling time. Fig. 3 displays the effects of the sampling time on the time–mean flow characteristics. The velocity data in the region bounded by the dashed white line is not reliable. It contains all positions where spurious vectors are detected for more than 10% of the all instantaneous velocity fields. As displayed in Fig. 3(a–f), the structures of the jet and the distributions of velocities are similar, when N is higher than 20. Based on time–mean over N consecutive samples at three points (points A, B and C) listed in Fig. 3(g), when N equals to 80, the absolute values of relative errors of the
310
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 5. Contours of average velocity on the symmetry-plane along with in plane streamlines (in black) for different jet momentum ratios J at conditions of Tw = 30 °C and Rew = 58, 421.
mean horizontal velocity Umean and mean vertical velocity Vmean from a sequence of 160 samples are lower than 4.02% and 5.07%, respectively. Therefore, 80 consecutively samples are selected to value the time–mean velocities in this work.
3. Results and discussion 3.1. Mean velocity field When steam is injected into crossflow, most of the steam is rapidly condensed in a very small region near the steam injection point. A dynamic balance at the two-phase interface is therefore approached between the continuously discharged steam and rapidly condensed steam. The geometrical shape and dynamic behavior of the interface are determined by both the thermophysical properties of steam/water and flow conditions. After the condensation region the jet becomes a single-phase turbulent jet, which is deflected by both the approaching water flow and the pipe wall. Fig. 4(a) and (b) display two consecutive instantaneous velocity fields with time interval of 1/7.25 s at conditions of jet momentum ratio J = 125, water temperature Tw = 30 °C and Reynolds number of water flow Rew = 58, 421. The jet momentum ratio J is defined as qsVs2/qwVw2. qs and qw are the density of steam jet at the nozzle exit and water flow, respectively. Vs and Vw are the velocity of steam jet at the nozzle exit and water flow, respectively. The instantaneous velocity fields of Fig. 4(a) and (b) show a general ‘waviness’ throughout most of the measurement window especially around the condensing steam jet boundary and far-field regions of the turbulent jet. Additional complexity is evident at
the jet outer boundary, where the velocity vectors diverge rapidly, probably due to entrainment of ambient water flow and also significant three-dimensionality in the flow. The relatively simple wavy flow patterns displayed in Fig. 4(a) and (b) can result in efficient mixing and extremely convoluted turbulent jet flow fields. Also the significantly different appearance of the two instantaneous velocity data (Fig. 4(a) and (b)) indicate that the turbulent jet flow is of a highly fluctuating nature. This demonstrates that the correlation time of the velocity fluctuations in the turbulent jet is lower than 1/7.25 s and all the velocities data in time are independent. Fig. 4(c) displays velocity fields averaged over 80 instantaneous measurements for the same condition with Fig. 4(a) and (b). It is noted that the in-plane velocity components are small near the jet outer boundary due to the entrainment of ambient water flow and the significant three-dimensionality in the flow in this region, this phenomena was also discovered by Su and Mungal [32]. However, the entrainment of ambient water flow into the jet in the averaged velocity field is not obvious in this work because of the average effect. The turbulent jet is well exhibited by the mean velocity field and the flow laws are also easier to found. Fig. 4(d) displays contours of the velocity fields for the same condition with Fig. 4(c), where the contour colors represent the velocity magnitude. The contours of the mean velocity demonstrate that the jet bends in the direction of the crossflow and increases in width as it moves downstream. We note that the jet is wider toward the leeward side than toward the windward side of the center streamline. It is, perhaps, more intuitive to visualize velocity field in terms of stream trace patterns. To compare the mean velocity fields of different jet momentum ratios, Fig. 5 shows the mean velocity fields, in terms of their patterns of stream traces. Each stream trace
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
311
Fig. 6. Contours of average velocity along with streamlines (in black) for different jet Reynolds numbers Res and water temperatures Tw.
shown in Fig. 5 is computed using fourth-order Runge–Kutta path integration through the mean velocity field. Although only two velocity field components are available from the PIV, the computed traces in Fig. 5 represent actual flow streamlines, because the mean out-of-plane velocity component is almost zero in the centerplane, by symmetry. In the jet near field (x ? 0), every patterns show a stagnation point with positive two-dimensional divergence to the lee side (positive y). In contrast, to the windward side (negative y), there is no stagnation point, with all streamlines being entrained into the jet. This behavior has been noted also by Hasselbrink and Mungal [31] in single-phase jet in crossflow.
On the windward of the jet, the outer boundary of the jet is given by the dense cluster of streamlines that follow the center streamline trajectory (the streamline originating from the center of the nozzle exit, (x, y) = (0, 0)). On the lee-side of the jet, the inner boundary might be defined as the line separating those streamlines that have an inflection point in turning toward the center streamline, and those do not turn toward the jet. This behavior has been reported also by Su and Mungal [32] in single-phase jet in crossflow. The difference between the single-phase jet and the condensing jet is that, the stagnation point in the lee side of the condensing jet is lower than that of the single-phase jet.
312
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 7. The Cartesian coordinate systems, (x, y) and (n, l). The two systems are related by rotation in the plane through the angle a, which is defined as the angle between the abscissa x and the velocity centerline trajectory-normal direction.
With further increase of the jet momentum ratio, the jet impinges on the opposite wall. The velocity field thus exhibits a bifurcated structure, with one branch appearing to evolve from the initial jet trajectory and flow along the wall, while the other branch turns backward and results in a clockwise vortex. Besides, the position of the clockwise vortex moves towards to the incoming flow and the intensity of the vortex increase with the jet momentum ratio. The influence of jet Reynolds number Res on the interaction of condensing jet and crossflow can be obtained by comparing the contours of the mean velocity along with the streamlines, as displayed in Fig. 6. For low jet Reynolds number in Fig. 6(a–d), the jet penetration length is very short. The velocity field and the center streamline trajectory are almost unchangeable with increase of the jet Reynolds number. For high jet Reynolds number in Fig. 6(e– h), the jet penetrates longer distance and even hits the opposite
wall and results in a clockwise vortex. The method of control volume analysis can be used to elucidate this phenomenon. For relative low jet Reynolds number, the jet penetration length is relatively shorter. The jet-affected region is relatively small compared to the whole pipe cross-section, so the turbulent jet flow field is dominated by the momentum ratio. For relative high jet Reynolds number, the jet penetration length is relatively longer, and also the pipe wall limits the free development of the jet. The jet-affected region is relatively large compared to the observation window, so the turbulent jet flow field is influenced significantly by the jet Reynolds number. This phenomenon has also been noted by Clerx et al. [38–40] in crossflow jet with Res = 5000. The influence of water temperature Tw on the interaction of condensing jet and crossflow can be illustrated by comparing the contours of mean velocity along with the streamlines, as shown in Fig. 6(i–l). The velocity fields of the four temperatures are similar with each other. An easier way to understand this phenomenon is to build a control volume, which enclose the near field of the jet. The momentum from both the jet and the crossflow entered into the control volume is constant. Although the higher water temperature increases the jet penetration length, the condensation is occurred only within the control volume because of the relatively low jet Reynolds number. The momentum left the control volume at the up and right sides are unchangeable. Therefore, the velocity field is slightly influenced by the water temperature.
3.2. Jet centerline trajectories Jet centerline trajectory in crossflow has been defined in several ways, such as the maximum velocity, the maximum scalar concentration and the streamline originating in the center of the nozzle exit. The jet centerline trajectory used herein is the locus of the points of maximum mean velocity, which is the most common method of jet centerline trajectory measured in experiments. A sketch coordinate system based on the jet centerline trajectory is displayed in Fig. 7. Because the locus of the jet centerline trajectory differs for test runs, it is convenient to keep reference the center point of the nozzle exit when defining the jet centerline trajectory.
Fig. 8. Jet centerline trajectories based on the local maximum mean velocity. (a) The jet centerline trajectories for jet momentum ratios J = 50, 75, 100 and 150, and (b) the jet centerline trajectories for water temperatures Tw = 30 °C, 40 °C, 50 °C and 60 °C.
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
313
Fig. 9. Jet centerline trajectories based on the local maximum mean velocity. (a) The trajectories for J = 50, (b) the trajectories for J = 75, (c) the trajectories for J = 100 and (d) the trajectories for J = 125.
Fig. 10. (a) Comparison of the measured and correlated jet centerline trajectories for all the cases in this work. (b) Comparison of the measured and correlated jet centerline trajectories for two cases, and the predicted jet centerline trajectories according to y/d = 1.38 J1.31(x/d)2.78 reported by Kamotain and Greber [28], and the predicted jet centerline trajectories according to y/d = 0.43 J0.64(x/d)2.38 reported by Clerx et al. [38–40].
The solid red line in the form of y = AxB is therefore fitted to the experimental data with least squares method. Jet centerline trajectories based on the local maximum mean velocity are presented in Fig. 8. Fig. 8(a) gives the locus of different jet momentum ratios J = 50, 75, 100 and 150 from experimental
data. It is easily seen that the positions of the jet centerline trajectories are dominated by the jet momentum ratio J, because inertial force plays a dominated role in the interaction of jet and crossflow. The experimental data are then fitted to the aforementioned exponential equation y = AxB, and constants A and B for different J are
314
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Table 2 Comparisons of experimental parameters between previous studies and present work. Experimental parameters
Kamotani and Greber [28]
Clerx et al. [38–40]
Present work
Working medium Cross-section Nozzle Gas mass flux Jet momentum ratio Jet Reynolds number
Air jet/cross air flow Square, 711 711 mm2 d = 6.35 mm Gs = 10–15 kg/m2 s J = 15–60 Res = 2800–4200
Steam jet/cross water flow Square, 30 30 mm2 d = 2 mm Gs = 0–120 kg/m2 s J = 13–126.3 Res = 6225–20,332
Steam jet/cross water flow Round, D = 80 mm d = 3.2 mm Gs = 0–740 kg/m2 s J = 25–150 Res = 20,192–543,763
Fig. 11. Averaged velocity magnitude profiles. (a) The profiles of the averaged raw velocity magnitude |u|mean, for x = 4d, 8d, 12d, 16d, and (b) the profiles of the averaged crossflow-subtracted velocity magnitude |u–v1ey|mean, for y = d, 2d, 4d, 8d. Also indicated on the plots are the difference of h between the fixed x or y lines and the velocity centerline trajectory-normal direction by using the best fit curve y/d = 0.0028 (x/d)3.00. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Downstream drop of the centerline velocity. (a) 1/|u|max versus l, (b) 1/|u–v1ey|max versus l.
obtained. The discrepancy of the jet centerline trajectories obtained from the correlations and the experiments is also presented in the top left corner of Fig. 8(a). It shows that most of the experimental data lie in the range of ±15% of the correlations. Fig. 8(b) gives the locus of different water temperatures Tw = 30 °C, 40 °C, 50 °C and 60 °C from experimental data. It noticeably shows that the jet centerline trajectories for the four water temperatures appear to coincide. Here we choose a control volume
enclosing the whole region of the condensing jet, in which the steam jet is condensed into water completely. As we knew, the higher water temperature makes the jet penetrate longer distance, but the region influenced by the water temperature is restricted within the control volume. For the entire region of the control volume, the input and output momentum for the four water temperatures are identical. Therefore the jet centerline trajectories outside of the control volume are unaffected by the water
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
315
Fig. 13. Half-width n1/2 of the jet versus downstream coordinate l.
temperature. The experimental data are also fitted to the aforementioned exponential equation. The discrepancy of the jet centerline trajectories between the correlation and the experiment is also shown in the top left corner of Fig. 8(b). It shows that most of the experimental data lie in the range of ±15% of the correlation. The influence of jet Reynolds number Res on the interaction of jet and crossflow could also be revealed by comparing the jet centerline trajectories, as shown in Fig. 9(a–d). For relatively low Res, corresponding to low jet momentum ratios J = 50 and 75 in subfigures (a and b), the jet centerline trajectories of the four Res coincide with each other. For relatively high Res, corresponding to high jet momentum ratios J = 100 and 125 in sub-figures (c and d), the jet centerline trajectories are gradually separate from each other with increase of Res. The apparent difference echo those noted in comparing the mean velocity fields for different Res. A revised correlation for prediction of the jet centerline trajectories is obtained with the Levenberg–Marquardt non-linear fit as,
x2:43 y J 1:19 ¼ 43:55 Re0:24 s d d
ð1Þ
The discrepancy of the jet centerline trajectories obtained from the correlation Eq. (1) and the experiments is presented in Fig. 10 (a). It shows that most of the experimental data lies in the range of ±30% of the correlation. The correlation Eq. (1) is adopted to predict the jet centerline trajectories of two cases J = 50 and J = 100, the correlations obtained from Kamotani and Greber [28] and Clerx et al. [38–40] are also included, as displayed in Fig. 10(b). The comparisons of experimental parameters between previous studies and present work are also displayed in Table 2. For relatively low Res, the
predictions of present correlation and Clerx et al.’s [38–40] correlation show good agreement with the present experiments. But for high Res, Clerx et al.’s correlation deviates considerably from the present experiments. Since the Res in Clerx’s work is in the range of 6, 225–20, 332, so their correlation agrees well with present experiments at relatively low Res and deviates largely at high Res. Kamotani and Greber [28] conducted experiments of singlephase jet in crossflow. Because the mass and momentum transfer of the single-phase jet in crossflow differs prominently from that of the condensing jet in crossflow, their correlation deviates considerably from this work.
3.3. Lateral distribution of velocities From the results of the mean velocity field, we can also draw profiles along lines of fixed x and fixed y. Profiles of mean velocity in Cartesian coordinates might benefit comparisons with other experimental or computational results. Fig. 11 displays profiles of mean velocity, along lines of fixed x = 4d, 8d, 12d and 16d, and fixed y = d, 2d, 4d and 8d. We can quantify the difference of h between the fixed x or y lines and the velocity centerline trajectory-normal direction by using the best fit curve y/d = 0.0028 (x/d)3.00. The angel h is depicted in Fig. 11 by red lines, and the center points of these red lines coincide with the points where the fixed x or y lines and jet centerline trajectory intersect. Near the nozzle exit, h = 9° at x = 4d, increasing to h = 53° at x = 12d, as the jet flow increasingly bends in the crossflow direction. While h = 59° at y = d, dropping to h = 24° at y = 8d, as the jet flow gradually aligns with the crossflow.
316
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 14. Self-similarity characteristics of the condensing jet in crossflow.
The profile at x = 4d is symmetric nearby the position of peak velocity, except for a slight elevation in the tails on the positive-y side, representing jet fluid that has been advected into the wake region on the lee side of the jet. The x = 8d show similar properties, though the increased velocity in the wake region is more pronounced. By x = 16d, the profile gives no hint of symmetry. The fixed-y profiles in Fig. 11(b) are also noticeably asymmetric, with the peak values lying to the windward side of the profiles and a slight elevation in the tails on the lee side of the jet, for y = d, 2d, 4d, and 8d. The similar results on x–y-profiles were also reported by Su and Mungal [32]. In analyzing the self-similarity of the downstream evolution of the jet in crossflow, it is preferable to introduce a new coordinate system that reveals the downstream evolution of the jet flow. We define l as the downstream coordinate along the jet centerline trajectory, and n as the coordinate normal to the jet centerline trajectory (in Fig. 7). The vector transformation among the two coordinate systems reads,
un
vl
¼
cos a sin a sin a
cos a
u
v
ð2Þ
In Pope [27] it is described that self-similarity of a turbulent jet requires that the velocity drop along the jet centerline trajectory follows a decay 1/l. In attempting to detect this characteristic, the choice of appropriate variables is important. In Fig. 12, |u|max and |u–v1ey|max are plotted against the downstream coordinate l. |u|max and |u–v1ey|max are the local maxima in the velocity magnitude field and the local maxima in the crossflow-subtracted velocity magnitude field, respectively. Also plotted in these figures are the least squares lines fitted from experimental data. It appears
that for all four cases, 1/|u|max shows good linearity with l, while 1/|u–v1ey|max shows poor linearity with l. Moreover, the slopes of linear lines of 1/|u|max versus l in Fig. 12(a) are in the range of 0.018–0.021 at different jet momentum ratios, and they are very close with each other. While the slopes of linear lines of 1/|u–v1ey|max versus l in Fig. 12(b) are in the range of 0.029–0.195 at different jet momentum ratios, and they deviate largely from each other. This emphasizes that the local maximum velocity magnitude |u|max is the appropriate variable for revealing the possible jet-like scaling of velocity magnitude decay in the condensing jet in crossflow. The virtual origin of the jet can be estimated as the intercept of the linear fit line with the abscissa, l. In a free turbulent jet, the intercept is positive, which means that the virtual origin exists outside the nozzle-exit, and the turbulent jet can be treated as originated at a point source outside the nozzle-exit. But, for the condensing jet in this work (Fig. 12(a)), the intercepts are negative in cases of J = 50 and 75, and they are positive in cases of J = 100 and 150. For low jet momentum ratios (J = 50 and 75), the jets penetrate shorter distance, leading to a relatively short region of pure steam, so the virtual points exist inside the nozzle-exit. Conversely, for high jet momentum ratios (J = 100 and 150), the jets penetrate longer distance, leading to a relatively long region of pure steam, so the virtual points exist outside the nozzle-exit. The second important feature of self-similarity of a turbulent jet is that the half-width, defined as the distance where velocity becomes half of the centerline velocity, increases linearly with the downstream coordinate l. In Fig. 13(a–d), the half-widths for both sides of the jet axis (i.e., n < 0 represents left side of the jet axis, and n > 0 represents right side of the jet axis) are plotted against the downstream coordinate l. Also plotted in these figures are the least squares lines fitted from experimental data. It appears
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
that for all four different jet momentum ratios (J = 50, 75, 100 and 150), the half-widths for both sides of the jet show good linearity with l. For each jet momentum ratio, the slopes of the linear lines of the right side of the jet axis are significantly higher than that of the left side of the jet axis. Since the pipe flow is blocked by the condensing jet, the flow velocity at the left side of the jet is relatively lower than that at the right side of the jet. As is shown in Fig. 13(a–d), the slopes of the linear lines at the left and right sides of the jet axis for case of J = 50 (sub-figure (a)) are 1.12 and 0.47, and they are significantly higher than the other three cases in sub-figures (b–d) with relatively larger jet momentum ratios. Because, in case of low jet momentum ratio (J = 50), the centerline velocities of the jet are relatively lower and have no prominent differences with the pipe flow velocities. According to discussions on the centerline velocity and halfwidth of the jet versus the downstream coordinate l, it is obvious that the condensing jet in crossflow in this work also has the self-similarity characteristics. Therefore, the experimental data in this work are scaled using the centerline velocity (ve, c) and the half-width (n1/2 > 0), as displayed in Fig. 14(a–d, corresponding to jet momentum ratios of J = 50, 75, 100 and 150, respectively). The scaled velocities fall into one single curve near the jet centerline, except that the velocities at the radial positions far away from the jet centerline deviate slightly. At radial positions far away from the jet centerline, the flow velocities are close to the mainstream pipe flow velocities and are almost constant. Besides, the centerline velocities drop along the jet’s axis. Therefore, at the larger radial positions, the velocities at larger downstream coordinate l are relatively higher than that at smaller l. 4. Conclusions Experimental study on the velocity field characteristics of turbulent jet induced by DCC of steam jet in crossflow of water in a vertical pipe is carried out. Visual equipment is specially invented to investigate the velocity field characteristics by using PIV measurement technique. The pure steam region just outside the nozzle-exit reflects high-intensity laser light, which brings out severe damage to the CCD camera. In order to solve this technical problem, a black plate is used to cover this pure steam region. Based on the contours of the velocity fields and streamlines, the effects of jet momentum ratio, jet Reynolds number and water temperature on the jet flow field are studied. The jet centerline trajectory equations in exponential form are established based on the local maximum mean velocity. By using the jet Reynolds number and jet momentum ratio, the correlation for prediction of the jet centerline trajectory equations is proposed, and the predicted results are within 30% of the experimental data. The reciprocal of the local maximum mean velocity and the half-width of the jet are proportional to the downstream coordinate l. The scaled velocity field complies with the self-similarity principle. Acknowledgement The financial supports of National Nature Science Foundation of China (No. 51236007, No. 51527808) are gratefully acknowledged. References [1] A. Shah, I.R. Chughtai, M.H. Inayat, Experimental study of the characteristics of steam jet pump and effect of mixing section length on direct-contact condensation, Int. J. Heat Mass Transfer 58 (1–2) (2013) 62–69. [2] A. Shah, A.H. Khan, I.R. Chughtai, M.H. Inayat, Numerical and experimental study of steam–water two-phase flow through steam jet pump, Asia-Pac. J. Chem. Eng. 8 (6) (2013) 895–905.
317
[3] A. Shah, I.R. Chughtai, M.H. Inayat, Experimental and numerical analysis of steam jet pump, Int. J. Multiphase Flow 37 (10) (2011) 1305–1314. [4] Y. Li, C. Li, E. Chen, Y. Ying, Pressure wave propagation characteristics in a twophase flow pipeline for liquid-propellant rocket, Aerosp. Sci. Technol. 15 (6) (2011) 453–464. [5] P.J. Kerney, G.M. Faeth, D.R. Olson, Penetration characteristics of a submerged steam jet, AIChE J. 18 (3) (1972) 548–553. [6] H.Y. Kim, Y.Y. Bae, C.H. Song, J.K. Park, S.M. Choi, Experimental study on stable steam condensation in a quenching tank, Int. J. Energy Res. 25 (3) (2001) 239– 252. [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. Multiphase Flow 33 (12) (2007) 1296–1307. [8] 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. [9] A. de With, Steam plume length diagram for direct contact condensation of steam injected into water, Int. J. Heat Fluid Flow 30 (5) (2009) 971–982. [10] X. Zong, J.P. Liu, X.P. Yang, J.J. Yan, Experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber, Int. J. Heat Mass Transfer 80 (2014) 448–457. [11] D.T. Chong, Q.B. Zhao, F. Yuan, W. Wang, W.X. Chen, J.J. Yan, Research on the steam jet length with different nozzle structures, Exp. Thermal Fluid Sci. 64 (2015) 134–141. [12] J.C. Weimer, G.M. Faeth, D.R. Olscn, Penetration of vapor jets submerged in subcooled liquids, AIChE J. 19 (1973) 552–558. [13] S.S. Gulawani, S.S. Deshpande, J.B. Joshi, M.S. Shah, C.S.R. Prasad, D.S. Shukla, Submerged gas jet into a liquid bath: a review, Ind. Eng. Chem. Res. 46 (10) (2007) 3188–3218. [14] C.H. Song, Y.S. Kim, Direct contact condensation of steam jet in a pool, in: I.C. Young, A.G. George (Eds.), Advances in Heat Transfer, Elsevier, 2011, pp. 227– 288. [15] A. 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. [16] 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. [17] S.S. Gulawani, J.B. Joshi, M.S. Shah, C.S. RamaPrasad, D.S. Shukla, CFD analysis of flow pattern and heat transfer in direct contact steam condensation, Chem. Eng. Sci. 61 (16) (2006) 5204–5220. [18] S.K. Dahikar, M.J. Sathe, J.B. Joshi, Investigation of flow and temperature patterns in direct contact condensation using PIV, PLIF and CFD, Chem. Eng. Sci. 65 (16) (2010) 4606–4620. [19] S.K. Dahikar, J.B. Joshi, M.S. Shah, A.S. Kalsi, C.S. RamaPrasad, D.S. Shukla, Experimental and computational fluid dynamic study of reacting gas jet in liquid: flow pattern and heat transfer, Chem. Eng. Sci. 65 (2) (2010) 827–849. [20] H.S. Kang, C.H. Song, CFD analysis of turbulent jet behavior induced by a steam jet discharge through a vertical upward single hole in a subcooled water pool, Nucl. Eng. Technol. 42 (4) (2010) 382–393. [21] S.J. Hong, G.C. Park, S. Cho, C.H. Song, Condensation dynamics of submerged steam jet in subcooled water, Int. J. Multiphase Flow 39 (2012) 66–77. [22] B.B. Qiu, S. Tang, J.J. Yan, J.P. Liu, D.T. Chong, X.Z. Wu, Experimental investigation on pressure oscillations caused by direct contact condensation of sonic steam jet, Exp. Thermal Fluid Sci. 52 (2014) 270–277. [23] Y.S. Kim, Y.J. Youn, Experimental study of turbulent jet induced by steam jet condensation through a hole in a water tank, Int. Commun. Heat Mass Transfer 35 (1) (2008) 21–29. [24] C.H. Song, S. Cho, H.S. Kang, Steam jet condensation in a pool: from fundamental understanding to engineering scale analysis, J. Heat Transfer 134 (3) (2012) 401–415. [25] Y.J. Choo, C.H. Song, PIV measurements of turbulent jet and pool mixing produced by a steam jet discharge in a subcooled water pool, Nucl. Eng. Des. 240 (9) (2010) 2215–2224. [26] A. Khan, N.U. Haq, I.R. Chughtai, A. Shah, K. Sanaullah, Experimental investigations of the interface between steam and water two phase flows, Int. J. Heat Mass Transfer 73 (2014) 521–532. [27] S.B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, 2000, pp. 227–288. [28] Y. Kamotani, I. Greber, Experiments on a turbulent jet in a cross flow, AIAA J. 10 (11) (1972) 1425–1429. [29] K. Mahesh, The interaction of jets with crossflow, Annu. Rev. Fluid Mech. 45 (1) (2013) 379–407. [30] A.R. Karagozian, The jet in crossflow, Phys. Fluids 26 (10) (2014) 101303. [31] E.F. Hasselbrink, M.G. Mungal, Transverse jets and jet flames. Part 1. Scaling laws for strong transverse jets, J. Fluid Mech. 443 (2001) 1–25. [32] L.K. Su, M.G. Mungal, Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets, J. Fluid Mech. 513 (2004) 1–45. [33] R. Sullivan, B. Wilde, D.R. Noble, J.M. Seitzman, T.C. Lieuwen, Time-averaged characteristics of a reacting fuel jet in vitiated cross-flow, Combust. Flame 161 (7) (2014) 1792–1803. [34] J. Oh, J.G. Lee, W. Lee, Vaporization of a liquid hexanes jet in cross flow, Int. J. Multiphase Flow 57 (2013) 151–158.
318
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
[35] Q. Xu, L.J. Guo, S.F. Zou, J.W. Chen, X.M. Zhang, Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe, Int. J. Heat Mass Transfer 66 (2013) 808–817. [36] L. J. Guo, Q. Xu, Direct contact condensation of steam jet in water pipe flow, in: 8th World Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, Lisbon, Portugal, 2013. [37] Q. Xu, L.J. Guo, Direct contact condensation of steam jet in crossflow of water in a vertical pipe. Experimental investigation on condensation regime diagram and jet penetration length, Int. J. Heat Mass Transfer 94 (2016) 528–538. [38] N. Clerx, Experimental study of direct contact condensation of steam in turbulent duct flow (Ph. D. thesis), Eindhoven University of Technology, Eindhoven, The Netherlands, 2010.
[39] N. Clerx, L.G.M. Deurzen, A. Pecenko, R. Liew, C.W.M. Geld, J.G.M. Kuerten, Temperature fields induced by direct contact condensation of steam in a crossflow in a channel, Heat Mass Transfer 47 (8) (2011) 981–990. [40] N. Clerx, C.W.M. van der Geld, J.G.M. Kuerten, Turbulent stresses in a direct contact condensation jet in cross-flow in a duct with implications for particle break-up, Int. J. Heat Mass Transfer 66 (2013) 684–694. [41] C.E. Willert, M. Gharib, Digital particle image velocimetry, Exp. Fluids 10 (4) (1991) 181–193. [42] Insight 4G, User’s Guide, 2011.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe Qiang Xu, Liejin Guo ⇑, Liang Chang, Yechun Wang State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 5 April 2016 Received in revised form 6 July 2016 Accepted 14 July 2016
Keywords: Velocity field Turbulent jet Direct contact condensation Crossflow Particle Image Velocimetry
a b s t r a c t Direct contact condensation of jets in fluid has been widely applied in many industrial applications owing to the low requirement of driving potential and high efficiency of heat and mass transfer. Here, experiments are carried out to investigate the velocity field characteristics of the turbulent jet induced by direct contact condensation of steam jet in crossflow of water in a vertical pipe. Visual equipment is specially invented to investigate the velocity field characteristics by using Particle Image Velocimetry (PIV) measurement technique. The high intensity laser light reflected by the pure steam region just outside the nozzle-exit brings out severe damage to the CCD camera. To solve this technical problem, a black plate is adopted to shield the pure steam region. According to the contours of the velocity fields and streamlines, the influences of jet momentum ratio, jet Reynolds number and water temperature on the jet flow field are explored. The jet centerline trajectory equations in exponential form are established based on the local maximum mean velocity. By introducing the jet Reynolds number and jet momentum ratio, the correlation for prediction of jet centerline trajectory equations is proposed, and the predicted results are within 30% of the experimental data. The reciprocal of the local maximum mean velocity and the halfwidth of the jet are proportional to the downstream coordinate along the jet velocity centerline trajectory. The scaled velocity field complies with the self-similarity principle. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Direct Contact Condensation (DCC) of a vapor jet in liquid has attracted much interest in recent years due to its high efficiency of heat and mass transfer and low requirement of driving potential. It is frequently encountered in lots of industrial applications, such as vapor jet condensing in nuclear industry, vapor jet pumping in process industry, vapor jet heating in power industry, and vapor jet driving in aerospace industry [1–4]. Previous work on DCC of a vapor jet in liquid reported in literature primarily focused on jet penetration length, condensation regime diagram, heat transfer coefficient, pressure oscillation and turbulent jet flow field. Kerney et al. [5] established the first correlation of jet penetration length as a function of condensation driving potential and steam mass flux. After that, a lot of improved correlations were reported by other researchers based on their respective background and experiments [6–14]. The interface behavior of the vapor jet was commonly illustrated in a condensation regime diagram, which were generally divided into three main regimes, such as chugging, bubbling and jetting [13,14,8,15]. Heat ⇑ Corresponding author. Fax: +86 29 82669033. E-mail address: [email protected] (L. Guo). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.07.047 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
transfer mechanisms were generally explored by theory analysis and numerical simulation, and many correlations of heat transfer coefficient were proposed [16–20]. Studies on pressure oscillation induced by vapor jet in liquid usually focused on amplitude and frequency [21,22]. To obtain the detailed velocity and temperature fields of turbulent jet induced by vapor jet in liquid, techniques such as Particle Image Velocimetry (PIV), Planar Laser Induced Fluorescence (PLIF) and mobile thermocouples were used [23–26]. For experimental study on jet interaction with crossflow, fruitful achievements about velocity field, centerline trajectory and jet shape were reported [27–34]. The flow and geometry characteristics of DCC of a vapor jet in crossflow have been studied thoroughly in our previous work [35–37]. However, due to the lack of the basic information on the velocity field of the turbulent jet, the interfacial transport mechanism of the condensing jet in crossflow in pipes is not well understand. The research work on single-phase jet in crossflow has already confirmed that the velocity fields of the turbulent jet contribute a lot to reveal the mass and momentum transport mechanism underlying of this complexity flow phenomenon [27–30]. But the condensation of the jet leads to significant change of the flow field structure and also difficult measurement of the velocity field. Clerx et al. [38–40] conducted a pioneer work on exploring the velocity field characteristics of
306
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Nomenclature A B d D ey Gs J l m n N ps pw Res Rew T u u Umean v
ve
constant in exponential equation, 1 constant in exponential equation, 1 inner diameter of the nozzle, m inner diameter of the vertical round pipe, m unit vector in ordinate direction, m/s steam mass flux at the nozzle exit, kg/m2 s jet momentum ratio equals to qsVs2/qwVw2, 1 ordinate in the Cartesian coordinate system (n, l), m mass flow rate, kg/s abscissa in the Cartesian coordinate system (n, l), m sequence sample size, 1 steam inlet pressure, MPa water pressure at the steam injection point, MPa jet Reynolds number equals to 4ms/pdls, 1 Reynolds number of water flow equals to 4mw/pDlw, 1 inlet temperature, °C velocity in the abscissa direction, m/s velocity vector, m/s mean horizontal velocity, m/s velocity in the ordinate direction, m/s velocity in the ordinate direction in the Cartesian coordinate system (n, l), m/s
DCC of steam jet in crossflow in a square channel at relatively low steam mass flux (Gs < 120 kg/m2 s). However, in actual industrial systems, the approaching fluid flows in round pipes rather than square channels. Besides, when the steam mass flux increases up to a certain value, the condensation regimes change from chugging to bubbling and then to jetting regime [15,35–37]. Therefore, it is desirable to perform investigation on velocity field characteristics of the turbulent jet induced by jet condensation in crossflow in pipes with a large range of steam mass flux. This paper focuses on the velocity field characteristics of the turbulent jet induced by DCC of steam jet in crossflow of water in a vertical pipe, with a range of high steam mass flux up to 740 kg/m2 s. The velocity field, jet centerline trajectory and lateral distribution of velocity are investigated. Visual equipment is specially invented to study the velocity field characteristics of the turbulent jet by means of PIV measurement technique. The high intensity laser light reflected by the pure steam region brings about severe damage to the CCD camera. A black plate is adopted to shield the pure steam region to solve this problem. The influences of jet momentum ratio, jet Reynolds number and water temperature on the velocity field are discussed. Furthermore, empirical correlation for prediction of jet centerline trajectory equations is proposed as a function of jet Reynolds number and jet momentum ratio. Finally, the lateral distribution of the velocity field is discussed and analyzed. This study provides new insights into velocity field characteristics of turbulent jet induced by DCC of steam jet in crossflow of water in pipes. The results would be useful for further theoretical and experimental research on the interfacial transport mechanism underlying DCC of steam jet in crossflow of water in pipes.
2. Experiments 2.1. Experimental setup In order to investigate the velocity field characteristics of the turbulent jet induced by DCC of steam jet in crossflow of water in pipes, a steam water two-phase flow system has been specially
ve, c v1
Va Vmean x y
jet centerline velocity in the ordinate direction in the Cartesian coordinate system (n, l), m/s crossflow velocity vector, m/s magnitude of velocity, m/s mean vertical velocity, m/s abscissa in the Cartesian coordinate system (x, y), m ordinate in the Cartesian coordinate system (x, y), m
Greek letters a angle between the abscissa x and the velocity centerline trajectory-normal direction, ° b angle between the nozzle center line and the pipe wall, ° h angle between the fixed x or y lines and the velocity centerline trajectory-normal direction, ° l dynamic viscosity, m2/s q density, kg/m3 Subscripts s the steam phase w the water phase
designed and built up. A sketch of the experimental system is shown in Fig. 1. It can be divided into four main components, such as a water supply line, a steam supply line, a test section and a data acquisition unit. The main part of the steam supply line is an electric heating boiler (72 kW), which generates saturated steam with a maximum mass flow rate of 0.03 kg/s. To keep the supplied steam saturating, the steam supply line is first covered with tap heaters, and then the tap heaters is wrapped with fiberglass coverings. The steam mass flow rate is measured by a vortex flowmeter with relative maximum deviation of 0.5%. The water volume flow rate is measured by a magnetic flowmeter with relative maximum deviation of 0.5%. In order to eliminate the effects of vibrations on the test section, two flexible metal hoses are connected between the water loop and the vertical pipe, and also a flexible hose is connected between the steam loop and the test section. The vertical pipe has a total length of 4100 mm with an inner diameter of 80 mm. Before entering the visual test section, the water flows in a smooth steel pipe of length 2400 mm (30 times of the hydraulic diameter of the vertical pipe), which is long enough to insure a fully developed turbulent flow entering the visual test section. The visual test section is well designed to investigate the velocity field characteristics of the turbulent jet, as displayed in Fig. 2. The vertical pipe in the visual test section is made of transparent silica glass with 5 mm wall thickness. The steam is discharged into the vertical pipe through a flushmounted nozzle with 3.2 mm inner diameter. The nozzle centerline is perpendicular to the pipe centerline. The temperature and pressure of discharged steam are measured at an upstream position of the nozzle exit. The visual test section is enclosed in a transparent silica glass box, which is filled with deionized water in order to eliminate distortions caused by the curvature of the round pipe. In this study we focus on the center plane A–A, defined by the vertical pipe centerline and the nozzle centerline. The experimental system is configured with high precision instrumentation. The fluid pressure is measured with pressure transducer, which is in the range of 0–1.0 MPa with relative maximum deviation of 0.1%. The fluid temperature is measured with K-type thermocouple, which is in the range of 0–200 °C with
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
307
Fig. 1. Schematic diagram of the experimental setup: (1) water tank; (2) centrifugal water pump; (3) control valve; (4) pressure transducer; (5) thermocouple; (6) magnetic flowmeter; (7) test section; (8) deionized water tank; (9) boiler feed pump; (10) electric steam generator; (11) vortex flowmeter; (12) control valve.
Fig. 2. Local schematic diagram of the test section: (1) water; (2) transparent glass plate; (3) transparent glass pipe; (4) nozzle; (5) pressure transducer; (6) steam inlet; (7) thermocouple; (8) water inlet; (9) CCD camera; (10) laser light.
maximum deviation of 0.5 °C. All signals are collected using data acquisition unit, including a PCI-6259 module for collecting flow and pressure signals, and a SCXI-1102E module for collecting temperature signals. The sampling frequency is 5 kHz for all sensors. The sampling time for each test run is 30 s. The experimental conditions in present work are displayed in Table 1.
Table 1 Range of operating conditions. Parameters
Range
Steam inlet pressure ps, MPa Steam inlet temperature Ts, °C Steam mass flux Gs, kg/m2 s Water flow rate mw, kg/s Water temperature Tw, °C Water pressure at the steam injection point pw, MPa Inner diameter of the nozzle d, m Angle between the nozzle center line and the pipe wall b, ° Inner diameter of the vertical pipe D, m
0.2–0.8 100–172 0–740 0.14–6.65 30–60 0.15 0.0032 90 0.08
2.2. PIV measurement technique PIV is a well-developed method for acquiring quantitative flow-visualization data with high-resolution. The principles of this measurement technique have been well elaborated in the literature [41], and the focus here is merely to describe the specific experimental facility and data processing approach adopted in this work. The flow illumination in a 2-D plane is accomplished by a double-pulsed Nd:YAG laser (532 nm), which is equipped with an optical arrangement for generating light sheets with divergence of 18°. The laser beam is transformed into a thin vertical light sheet of about 1 mm thickness by a series of cylindrical and spherical lenses. The reflected light in the measurement field-of-view (80 115 mm) is recorded by a CCD camera with a 2048 2048 pixels sensor and 12-bit resolution, resulting in a pixel resolution of 7.4 lm/pixel. The camera is fitted with a Nikkor AF 50 mm f/1.8D lens. The high intensity laser light reflected by the pure steam region brings about severe damage to the CCD camera. To solve this technique problem,
308
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 3. Influence of sampling time on time–mean flow characteristics at steam mass flux Gs = 242 kg/m2 s, water temperature Tw = 30 °C and Reynolds number of water flow Rew = 58, 421.
a mobile black plate with width 5 mm is adopted to shield the pure steam region. Initially the laser light is adjusted to relatively low intensity that the bright pure steam region has no damage on the CCD camera. Then a preliminary test at each test conditions is performed, and the position of the bright pure steam region at each test conditions could be recorded successively. Before each formal test, the black plate is adjusted to the proper position, which has been recorded by preliminary test at the same conditions, to shield the bright pure steam region. Based on this method, the high quality velocity field of
the condensing jet apart from the pure steam region could be obtained with no damage on the CCD camera. During each measurement a set of 80 or 160 image pairs is taken at a frequency of 7.25 Hz. The time interval Dt between the two successive images in each image-pair is adjusted to insure a maximum particle displacement of approximately 8–12 pixels. Image calibration is made by taking images of a reference object specially designed for present purpose. The water in the tank is seeded with hollow glass spheres with an average diameter of 3 lm and density of 1050 kg/m3.
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
309
Fig. 4. (a) and (b) two consecutive instantaneous velocity fields at a time interval of 1/7.25 s, and along with mean velocity field (c) and (d) averaged over 80 instantaneous measurements of experimental run with Gs = 242 kg/m2 s, Tw = 30 °C and Rew = 58, 421. The white dashed line enclosed the region where spurious velocity data is detected.
The raw images of the eighty planes are processed by software, Insight 4G [42], into vector maps. Firstly, the displacement vectors of the particles are calculated by Fourier-based cross-correlation and window shifting technique. The calculation starts off with a large interrogation window of 64 64 pixels with 50% overlap of each interrogation region, and then ends with 32 32 pixels. Subsequently, spurious vectors in the raw vector images are validated successively using a Signal/Noise ratio filter, a global filter, a peakheight filter and a local filter. Finally, a nearest-neighbor interpolation algorithm is applied to smooth the vectors in the global flow field. 2.3. Measurement uncertainty Generally, the total uncertainty of a variable can be valued by the bias uncertainty and random uncertainty. For the instantaneous velocity determined by the PIV system, the bias uncertainty is induced by camera calibration (LO/LI, LO represents the length of a real object, and LI represents the pixels in image of the object), time
interval (Dt) and particle displacement detection (Ddisp). In this work, the bias uncertainties of LO, LI, and Dt are 0.1 mm, 0.50 pixel, and 0.1 ls, respectively. The pixel locking error can be reduced to 0.1–0.3 pixels, and consequently the bias uncertainty of Ddisp is lower than about 0.3 pixels. The random uncertainty on the velocity measurement is mainly caused by cross-correlation error and the typical value is lower than about 0.1 pixels. The time–mean velocities are obtained by a sequence of N instantaneous vector images at each point. The selection of N is commonly based on the analysis of data convergence with sampling time. Fig. 3 displays the effects of the sampling time on the time–mean flow characteristics. The velocity data in the region bounded by the dashed white line is not reliable. It contains all positions where spurious vectors are detected for more than 10% of the all instantaneous velocity fields. As displayed in Fig. 3(a–f), the structures of the jet and the distributions of velocities are similar, when N is higher than 20. Based on time–mean over N consecutive samples at three points (points A, B and C) listed in Fig. 3(g), when N equals to 80, the absolute values of relative errors of the
310
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 5. Contours of average velocity on the symmetry-plane along with in plane streamlines (in black) for different jet momentum ratios J at conditions of Tw = 30 °C and Rew = 58, 421.
mean horizontal velocity Umean and mean vertical velocity Vmean from a sequence of 160 samples are lower than 4.02% and 5.07%, respectively. Therefore, 80 consecutively samples are selected to value the time–mean velocities in this work.
3. Results and discussion 3.1. Mean velocity field When steam is injected into crossflow, most of the steam is rapidly condensed in a very small region near the steam injection point. A dynamic balance at the two-phase interface is therefore approached between the continuously discharged steam and rapidly condensed steam. The geometrical shape and dynamic behavior of the interface are determined by both the thermophysical properties of steam/water and flow conditions. After the condensation region the jet becomes a single-phase turbulent jet, which is deflected by both the approaching water flow and the pipe wall. Fig. 4(a) and (b) display two consecutive instantaneous velocity fields with time interval of 1/7.25 s at conditions of jet momentum ratio J = 125, water temperature Tw = 30 °C and Reynolds number of water flow Rew = 58, 421. The jet momentum ratio J is defined as qsVs2/qwVw2. qs and qw are the density of steam jet at the nozzle exit and water flow, respectively. Vs and Vw are the velocity of steam jet at the nozzle exit and water flow, respectively. The instantaneous velocity fields of Fig. 4(a) and (b) show a general ‘waviness’ throughout most of the measurement window especially around the condensing steam jet boundary and far-field regions of the turbulent jet. Additional complexity is evident at
the jet outer boundary, where the velocity vectors diverge rapidly, probably due to entrainment of ambient water flow and also significant three-dimensionality in the flow. The relatively simple wavy flow patterns displayed in Fig. 4(a) and (b) can result in efficient mixing and extremely convoluted turbulent jet flow fields. Also the significantly different appearance of the two instantaneous velocity data (Fig. 4(a) and (b)) indicate that the turbulent jet flow is of a highly fluctuating nature. This demonstrates that the correlation time of the velocity fluctuations in the turbulent jet is lower than 1/7.25 s and all the velocities data in time are independent. Fig. 4(c) displays velocity fields averaged over 80 instantaneous measurements for the same condition with Fig. 4(a) and (b). It is noted that the in-plane velocity components are small near the jet outer boundary due to the entrainment of ambient water flow and the significant three-dimensionality in the flow in this region, this phenomena was also discovered by Su and Mungal [32]. However, the entrainment of ambient water flow into the jet in the averaged velocity field is not obvious in this work because of the average effect. The turbulent jet is well exhibited by the mean velocity field and the flow laws are also easier to found. Fig. 4(d) displays contours of the velocity fields for the same condition with Fig. 4(c), where the contour colors represent the velocity magnitude. The contours of the mean velocity demonstrate that the jet bends in the direction of the crossflow and increases in width as it moves downstream. We note that the jet is wider toward the leeward side than toward the windward side of the center streamline. It is, perhaps, more intuitive to visualize velocity field in terms of stream trace patterns. To compare the mean velocity fields of different jet momentum ratios, Fig. 5 shows the mean velocity fields, in terms of their patterns of stream traces. Each stream trace
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
311
Fig. 6. Contours of average velocity along with streamlines (in black) for different jet Reynolds numbers Res and water temperatures Tw.
shown in Fig. 5 is computed using fourth-order Runge–Kutta path integration through the mean velocity field. Although only two velocity field components are available from the PIV, the computed traces in Fig. 5 represent actual flow streamlines, because the mean out-of-plane velocity component is almost zero in the centerplane, by symmetry. In the jet near field (x ? 0), every patterns show a stagnation point with positive two-dimensional divergence to the lee side (positive y). In contrast, to the windward side (negative y), there is no stagnation point, with all streamlines being entrained into the jet. This behavior has been noted also by Hasselbrink and Mungal [31] in single-phase jet in crossflow.
On the windward of the jet, the outer boundary of the jet is given by the dense cluster of streamlines that follow the center streamline trajectory (the streamline originating from the center of the nozzle exit, (x, y) = (0, 0)). On the lee-side of the jet, the inner boundary might be defined as the line separating those streamlines that have an inflection point in turning toward the center streamline, and those do not turn toward the jet. This behavior has been reported also by Su and Mungal [32] in single-phase jet in crossflow. The difference between the single-phase jet and the condensing jet is that, the stagnation point in the lee side of the condensing jet is lower than that of the single-phase jet.
312
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 7. The Cartesian coordinate systems, (x, y) and (n, l). The two systems are related by rotation in the plane through the angle a, which is defined as the angle between the abscissa x and the velocity centerline trajectory-normal direction.
With further increase of the jet momentum ratio, the jet impinges on the opposite wall. The velocity field thus exhibits a bifurcated structure, with one branch appearing to evolve from the initial jet trajectory and flow along the wall, while the other branch turns backward and results in a clockwise vortex. Besides, the position of the clockwise vortex moves towards to the incoming flow and the intensity of the vortex increase with the jet momentum ratio. The influence of jet Reynolds number Res on the interaction of condensing jet and crossflow can be obtained by comparing the contours of the mean velocity along with the streamlines, as displayed in Fig. 6. For low jet Reynolds number in Fig. 6(a–d), the jet penetration length is very short. The velocity field and the center streamline trajectory are almost unchangeable with increase of the jet Reynolds number. For high jet Reynolds number in Fig. 6(e– h), the jet penetrates longer distance and even hits the opposite
wall and results in a clockwise vortex. The method of control volume analysis can be used to elucidate this phenomenon. For relative low jet Reynolds number, the jet penetration length is relatively shorter. The jet-affected region is relatively small compared to the whole pipe cross-section, so the turbulent jet flow field is dominated by the momentum ratio. For relative high jet Reynolds number, the jet penetration length is relatively longer, and also the pipe wall limits the free development of the jet. The jet-affected region is relatively large compared to the observation window, so the turbulent jet flow field is influenced significantly by the jet Reynolds number. This phenomenon has also been noted by Clerx et al. [38–40] in crossflow jet with Res = 5000. The influence of water temperature Tw on the interaction of condensing jet and crossflow can be illustrated by comparing the contours of mean velocity along with the streamlines, as shown in Fig. 6(i–l). The velocity fields of the four temperatures are similar with each other. An easier way to understand this phenomenon is to build a control volume, which enclose the near field of the jet. The momentum from both the jet and the crossflow entered into the control volume is constant. Although the higher water temperature increases the jet penetration length, the condensation is occurred only within the control volume because of the relatively low jet Reynolds number. The momentum left the control volume at the up and right sides are unchangeable. Therefore, the velocity field is slightly influenced by the water temperature.
3.2. Jet centerline trajectories Jet centerline trajectory in crossflow has been defined in several ways, such as the maximum velocity, the maximum scalar concentration and the streamline originating in the center of the nozzle exit. The jet centerline trajectory used herein is the locus of the points of maximum mean velocity, which is the most common method of jet centerline trajectory measured in experiments. A sketch coordinate system based on the jet centerline trajectory is displayed in Fig. 7. Because the locus of the jet centerline trajectory differs for test runs, it is convenient to keep reference the center point of the nozzle exit when defining the jet centerline trajectory.
Fig. 8. Jet centerline trajectories based on the local maximum mean velocity. (a) The jet centerline trajectories for jet momentum ratios J = 50, 75, 100 and 150, and (b) the jet centerline trajectories for water temperatures Tw = 30 °C, 40 °C, 50 °C and 60 °C.
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
313
Fig. 9. Jet centerline trajectories based on the local maximum mean velocity. (a) The trajectories for J = 50, (b) the trajectories for J = 75, (c) the trajectories for J = 100 and (d) the trajectories for J = 125.
Fig. 10. (a) Comparison of the measured and correlated jet centerline trajectories for all the cases in this work. (b) Comparison of the measured and correlated jet centerline trajectories for two cases, and the predicted jet centerline trajectories according to y/d = 1.38 J1.31(x/d)2.78 reported by Kamotain and Greber [28], and the predicted jet centerline trajectories according to y/d = 0.43 J0.64(x/d)2.38 reported by Clerx et al. [38–40].
The solid red line in the form of y = AxB is therefore fitted to the experimental data with least squares method. Jet centerline trajectories based on the local maximum mean velocity are presented in Fig. 8. Fig. 8(a) gives the locus of different jet momentum ratios J = 50, 75, 100 and 150 from experimental
data. It is easily seen that the positions of the jet centerline trajectories are dominated by the jet momentum ratio J, because inertial force plays a dominated role in the interaction of jet and crossflow. The experimental data are then fitted to the aforementioned exponential equation y = AxB, and constants A and B for different J are
314
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Table 2 Comparisons of experimental parameters between previous studies and present work. Experimental parameters
Kamotani and Greber [28]
Clerx et al. [38–40]
Present work
Working medium Cross-section Nozzle Gas mass flux Jet momentum ratio Jet Reynolds number
Air jet/cross air flow Square, 711 711 mm2 d = 6.35 mm Gs = 10–15 kg/m2 s J = 15–60 Res = 2800–4200
Steam jet/cross water flow Square, 30 30 mm2 d = 2 mm Gs = 0–120 kg/m2 s J = 13–126.3 Res = 6225–20,332
Steam jet/cross water flow Round, D = 80 mm d = 3.2 mm Gs = 0–740 kg/m2 s J = 25–150 Res = 20,192–543,763
Fig. 11. Averaged velocity magnitude profiles. (a) The profiles of the averaged raw velocity magnitude |u|mean, for x = 4d, 8d, 12d, 16d, and (b) the profiles of the averaged crossflow-subtracted velocity magnitude |u–v1ey|mean, for y = d, 2d, 4d, 8d. Also indicated on the plots are the difference of h between the fixed x or y lines and the velocity centerline trajectory-normal direction by using the best fit curve y/d = 0.0028 (x/d)3.00. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Downstream drop of the centerline velocity. (a) 1/|u|max versus l, (b) 1/|u–v1ey|max versus l.
obtained. The discrepancy of the jet centerline trajectories obtained from the correlations and the experiments is also presented in the top left corner of Fig. 8(a). It shows that most of the experimental data lie in the range of ±15% of the correlations. Fig. 8(b) gives the locus of different water temperatures Tw = 30 °C, 40 °C, 50 °C and 60 °C from experimental data. It noticeably shows that the jet centerline trajectories for the four water temperatures appear to coincide. Here we choose a control volume
enclosing the whole region of the condensing jet, in which the steam jet is condensed into water completely. As we knew, the higher water temperature makes the jet penetrate longer distance, but the region influenced by the water temperature is restricted within the control volume. For the entire region of the control volume, the input and output momentum for the four water temperatures are identical. Therefore the jet centerline trajectories outside of the control volume are unaffected by the water
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
315
Fig. 13. Half-width n1/2 of the jet versus downstream coordinate l.
temperature. The experimental data are also fitted to the aforementioned exponential equation. The discrepancy of the jet centerline trajectories between the correlation and the experiment is also shown in the top left corner of Fig. 8(b). It shows that most of the experimental data lie in the range of ±15% of the correlation. The influence of jet Reynolds number Res on the interaction of jet and crossflow could also be revealed by comparing the jet centerline trajectories, as shown in Fig. 9(a–d). For relatively low Res, corresponding to low jet momentum ratios J = 50 and 75 in subfigures (a and b), the jet centerline trajectories of the four Res coincide with each other. For relatively high Res, corresponding to high jet momentum ratios J = 100 and 125 in sub-figures (c and d), the jet centerline trajectories are gradually separate from each other with increase of Res. The apparent difference echo those noted in comparing the mean velocity fields for different Res. A revised correlation for prediction of the jet centerline trajectories is obtained with the Levenberg–Marquardt non-linear fit as,
x2:43 y J 1:19 ¼ 43:55 Re0:24 s d d
ð1Þ
The discrepancy of the jet centerline trajectories obtained from the correlation Eq. (1) and the experiments is presented in Fig. 10 (a). It shows that most of the experimental data lies in the range of ±30% of the correlation. The correlation Eq. (1) is adopted to predict the jet centerline trajectories of two cases J = 50 and J = 100, the correlations obtained from Kamotani and Greber [28] and Clerx et al. [38–40] are also included, as displayed in Fig. 10(b). The comparisons of experimental parameters between previous studies and present work are also displayed in Table 2. For relatively low Res, the
predictions of present correlation and Clerx et al.’s [38–40] correlation show good agreement with the present experiments. But for high Res, Clerx et al.’s correlation deviates considerably from the present experiments. Since the Res in Clerx’s work is in the range of 6, 225–20, 332, so their correlation agrees well with present experiments at relatively low Res and deviates largely at high Res. Kamotani and Greber [28] conducted experiments of singlephase jet in crossflow. Because the mass and momentum transfer of the single-phase jet in crossflow differs prominently from that of the condensing jet in crossflow, their correlation deviates considerably from this work.
3.3. Lateral distribution of velocities From the results of the mean velocity field, we can also draw profiles along lines of fixed x and fixed y. Profiles of mean velocity in Cartesian coordinates might benefit comparisons with other experimental or computational results. Fig. 11 displays profiles of mean velocity, along lines of fixed x = 4d, 8d, 12d and 16d, and fixed y = d, 2d, 4d and 8d. We can quantify the difference of h between the fixed x or y lines and the velocity centerline trajectory-normal direction by using the best fit curve y/d = 0.0028 (x/d)3.00. The angel h is depicted in Fig. 11 by red lines, and the center points of these red lines coincide with the points where the fixed x or y lines and jet centerline trajectory intersect. Near the nozzle exit, h = 9° at x = 4d, increasing to h = 53° at x = 12d, as the jet flow increasingly bends in the crossflow direction. While h = 59° at y = d, dropping to h = 24° at y = 8d, as the jet flow gradually aligns with the crossflow.
316
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
Fig. 14. Self-similarity characteristics of the condensing jet in crossflow.
The profile at x = 4d is symmetric nearby the position of peak velocity, except for a slight elevation in the tails on the positive-y side, representing jet fluid that has been advected into the wake region on the lee side of the jet. The x = 8d show similar properties, though the increased velocity in the wake region is more pronounced. By x = 16d, the profile gives no hint of symmetry. The fixed-y profiles in Fig. 11(b) are also noticeably asymmetric, with the peak values lying to the windward side of the profiles and a slight elevation in the tails on the lee side of the jet, for y = d, 2d, 4d, and 8d. The similar results on x–y-profiles were also reported by Su and Mungal [32]. In analyzing the self-similarity of the downstream evolution of the jet in crossflow, it is preferable to introduce a new coordinate system that reveals the downstream evolution of the jet flow. We define l as the downstream coordinate along the jet centerline trajectory, and n as the coordinate normal to the jet centerline trajectory (in Fig. 7). The vector transformation among the two coordinate systems reads,
un
vl
¼
cos a sin a sin a
cos a
u
v
ð2Þ
In Pope [27] it is described that self-similarity of a turbulent jet requires that the velocity drop along the jet centerline trajectory follows a decay 1/l. In attempting to detect this characteristic, the choice of appropriate variables is important. In Fig. 12, |u|max and |u–v1ey|max are plotted against the downstream coordinate l. |u|max and |u–v1ey|max are the local maxima in the velocity magnitude field and the local maxima in the crossflow-subtracted velocity magnitude field, respectively. Also plotted in these figures are the least squares lines fitted from experimental data. It appears
that for all four cases, 1/|u|max shows good linearity with l, while 1/|u–v1ey|max shows poor linearity with l. Moreover, the slopes of linear lines of 1/|u|max versus l in Fig. 12(a) are in the range of 0.018–0.021 at different jet momentum ratios, and they are very close with each other. While the slopes of linear lines of 1/|u–v1ey|max versus l in Fig. 12(b) are in the range of 0.029–0.195 at different jet momentum ratios, and they deviate largely from each other. This emphasizes that the local maximum velocity magnitude |u|max is the appropriate variable for revealing the possible jet-like scaling of velocity magnitude decay in the condensing jet in crossflow. The virtual origin of the jet can be estimated as the intercept of the linear fit line with the abscissa, l. In a free turbulent jet, the intercept is positive, which means that the virtual origin exists outside the nozzle-exit, and the turbulent jet can be treated as originated at a point source outside the nozzle-exit. But, for the condensing jet in this work (Fig. 12(a)), the intercepts are negative in cases of J = 50 and 75, and they are positive in cases of J = 100 and 150. For low jet momentum ratios (J = 50 and 75), the jets penetrate shorter distance, leading to a relatively short region of pure steam, so the virtual points exist inside the nozzle-exit. Conversely, for high jet momentum ratios (J = 100 and 150), the jets penetrate longer distance, leading to a relatively long region of pure steam, so the virtual points exist outside the nozzle-exit. The second important feature of self-similarity of a turbulent jet is that the half-width, defined as the distance where velocity becomes half of the centerline velocity, increases linearly with the downstream coordinate l. In Fig. 13(a–d), the half-widths for both sides of the jet axis (i.e., n < 0 represents left side of the jet axis, and n > 0 represents right side of the jet axis) are plotted against the downstream coordinate l. Also plotted in these figures are the least squares lines fitted from experimental data. It appears
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
that for all four different jet momentum ratios (J = 50, 75, 100 and 150), the half-widths for both sides of the jet show good linearity with l. For each jet momentum ratio, the slopes of the linear lines of the right side of the jet axis are significantly higher than that of the left side of the jet axis. Since the pipe flow is blocked by the condensing jet, the flow velocity at the left side of the jet is relatively lower than that at the right side of the jet. As is shown in Fig. 13(a–d), the slopes of the linear lines at the left and right sides of the jet axis for case of J = 50 (sub-figure (a)) are 1.12 and 0.47, and they are significantly higher than the other three cases in sub-figures (b–d) with relatively larger jet momentum ratios. Because, in case of low jet momentum ratio (J = 50), the centerline velocities of the jet are relatively lower and have no prominent differences with the pipe flow velocities. According to discussions on the centerline velocity and halfwidth of the jet versus the downstream coordinate l, it is obvious that the condensing jet in crossflow in this work also has the self-similarity characteristics. Therefore, the experimental data in this work are scaled using the centerline velocity (ve, c) and the half-width (n1/2 > 0), as displayed in Fig. 14(a–d, corresponding to jet momentum ratios of J = 50, 75, 100 and 150, respectively). The scaled velocities fall into one single curve near the jet centerline, except that the velocities at the radial positions far away from the jet centerline deviate slightly. At radial positions far away from the jet centerline, the flow velocities are close to the mainstream pipe flow velocities and are almost constant. Besides, the centerline velocities drop along the jet’s axis. Therefore, at the larger radial positions, the velocities at larger downstream coordinate l are relatively higher than that at smaller l. 4. Conclusions Experimental study on the velocity field characteristics of turbulent jet induced by DCC of steam jet in crossflow of water in a vertical pipe is carried out. Visual equipment is specially invented to investigate the velocity field characteristics by using PIV measurement technique. The pure steam region just outside the nozzle-exit reflects high-intensity laser light, which brings out severe damage to the CCD camera. In order to solve this technical problem, a black plate is used to cover this pure steam region. Based on the contours of the velocity fields and streamlines, the effects of jet momentum ratio, jet Reynolds number and water temperature on the jet flow field are studied. The jet centerline trajectory equations in exponential form are established based on the local maximum mean velocity. By using the jet Reynolds number and jet momentum ratio, the correlation for prediction of the jet centerline trajectory equations is proposed, and the predicted results are within 30% of the experimental data. The reciprocal of the local maximum mean velocity and the half-width of the jet are proportional to the downstream coordinate l. The scaled velocity field complies with the self-similarity principle. Acknowledgement The financial supports of National Nature Science Foundation of China (No. 51236007, No. 51527808) are gratefully acknowledged. References [1] A. Shah, I.R. Chughtai, M.H. Inayat, Experimental study of the characteristics of steam jet pump and effect of mixing section length on direct-contact condensation, Int. J. Heat Mass Transfer 58 (1–2) (2013) 62–69. [2] A. Shah, A.H. Khan, I.R. Chughtai, M.H. Inayat, Numerical and experimental study of steam–water two-phase flow through steam jet pump, Asia-Pac. J. Chem. Eng. 8 (6) (2013) 895–905.
317
[3] A. Shah, I.R. Chughtai, M.H. Inayat, Experimental and numerical analysis of steam jet pump, Int. J. Multiphase Flow 37 (10) (2011) 1305–1314. [4] Y. Li, C. Li, E. Chen, Y. Ying, Pressure wave propagation characteristics in a twophase flow pipeline for liquid-propellant rocket, Aerosp. Sci. Technol. 15 (6) (2011) 453–464. [5] P.J. Kerney, G.M. Faeth, D.R. Olson, Penetration characteristics of a submerged steam jet, AIChE J. 18 (3) (1972) 548–553. [6] H.Y. Kim, Y.Y. Bae, C.H. Song, J.K. Park, S.M. Choi, Experimental study on stable steam condensation in a quenching tank, Int. J. Energy Res. 25 (3) (2001) 239– 252. [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. Multiphase Flow 33 (12) (2007) 1296–1307. [8] 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. [9] A. de With, Steam plume length diagram for direct contact condensation of steam injected into water, Int. J. Heat Fluid Flow 30 (5) (2009) 971–982. [10] X. Zong, J.P. Liu, X.P. Yang, J.J. Yan, Experimental study on the direct contact condensation of steam jet in subcooled water flow in a rectangular mix chamber, Int. J. Heat Mass Transfer 80 (2014) 448–457. [11] D.T. Chong, Q.B. Zhao, F. Yuan, W. Wang, W.X. Chen, J.J. Yan, Research on the steam jet length with different nozzle structures, Exp. Thermal Fluid Sci. 64 (2015) 134–141. [12] J.C. Weimer, G.M. Faeth, D.R. Olscn, Penetration of vapor jets submerged in subcooled liquids, AIChE J. 19 (1973) 552–558. [13] S.S. Gulawani, S.S. Deshpande, J.B. Joshi, M.S. Shah, C.S.R. Prasad, D.S. Shukla, Submerged gas jet into a liquid bath: a review, Ind. Eng. Chem. Res. 46 (10) (2007) 3188–3218. [14] C.H. Song, Y.S. Kim, Direct contact condensation of steam jet in a pool, in: I.C. Young, A.G. George (Eds.), Advances in Heat Transfer, Elsevier, 2011, pp. 227– 288. [15] A. 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. [16] 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. [17] S.S. Gulawani, J.B. Joshi, M.S. Shah, C.S. RamaPrasad, D.S. Shukla, CFD analysis of flow pattern and heat transfer in direct contact steam condensation, Chem. Eng. Sci. 61 (16) (2006) 5204–5220. [18] S.K. Dahikar, M.J. Sathe, J.B. Joshi, Investigation of flow and temperature patterns in direct contact condensation using PIV, PLIF and CFD, Chem. Eng. Sci. 65 (16) (2010) 4606–4620. [19] S.K. Dahikar, J.B. Joshi, M.S. Shah, A.S. Kalsi, C.S. RamaPrasad, D.S. Shukla, Experimental and computational fluid dynamic study of reacting gas jet in liquid: flow pattern and heat transfer, Chem. Eng. Sci. 65 (2) (2010) 827–849. [20] H.S. Kang, C.H. Song, CFD analysis of turbulent jet behavior induced by a steam jet discharge through a vertical upward single hole in a subcooled water pool, Nucl. Eng. Technol. 42 (4) (2010) 382–393. [21] S.J. Hong, G.C. Park, S. Cho, C.H. Song, Condensation dynamics of submerged steam jet in subcooled water, Int. J. Multiphase Flow 39 (2012) 66–77. [22] B.B. Qiu, S. Tang, J.J. Yan, J.P. Liu, D.T. Chong, X.Z. Wu, Experimental investigation on pressure oscillations caused by direct contact condensation of sonic steam jet, Exp. Thermal Fluid Sci. 52 (2014) 270–277. [23] Y.S. Kim, Y.J. Youn, Experimental study of turbulent jet induced by steam jet condensation through a hole in a water tank, Int. Commun. Heat Mass Transfer 35 (1) (2008) 21–29. [24] C.H. Song, S. Cho, H.S. Kang, Steam jet condensation in a pool: from fundamental understanding to engineering scale analysis, J. Heat Transfer 134 (3) (2012) 401–415. [25] Y.J. Choo, C.H. Song, PIV measurements of turbulent jet and pool mixing produced by a steam jet discharge in a subcooled water pool, Nucl. Eng. Des. 240 (9) (2010) 2215–2224. [26] A. Khan, N.U. Haq, I.R. Chughtai, A. Shah, K. Sanaullah, Experimental investigations of the interface between steam and water two phase flows, Int. J. Heat Mass Transfer 73 (2014) 521–532. [27] S.B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, 2000, pp. 227–288. [28] Y. Kamotani, I. Greber, Experiments on a turbulent jet in a cross flow, AIAA J. 10 (11) (1972) 1425–1429. [29] K. Mahesh, The interaction of jets with crossflow, Annu. Rev. Fluid Mech. 45 (1) (2013) 379–407. [30] A.R. Karagozian, The jet in crossflow, Phys. Fluids 26 (10) (2014) 101303. [31] E.F. Hasselbrink, M.G. Mungal, Transverse jets and jet flames. Part 1. Scaling laws for strong transverse jets, J. Fluid Mech. 443 (2001) 1–25. [32] L.K. Su, M.G. Mungal, Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets, J. Fluid Mech. 513 (2004) 1–45. [33] R. Sullivan, B. Wilde, D.R. Noble, J.M. Seitzman, T.C. Lieuwen, Time-averaged characteristics of a reacting fuel jet in vitiated cross-flow, Combust. Flame 161 (7) (2014) 1792–1803. [34] J. Oh, J.G. Lee, W. Lee, Vaporization of a liquid hexanes jet in cross flow, Int. J. Multiphase Flow 57 (2013) 151–158.
318
Q. Xu et al. / International Journal of Heat and Mass Transfer 103 (2016) 305–318
[35] Q. Xu, L.J. Guo, S.F. Zou, J.W. Chen, X.M. Zhang, Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe, Int. J. Heat Mass Transfer 66 (2013) 808–817. [36] L. J. Guo, Q. Xu, Direct contact condensation of steam jet in water pipe flow, in: 8th World Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, Lisbon, Portugal, 2013. [37] Q. Xu, L.J. Guo, Direct contact condensation of steam jet in crossflow of water in a vertical pipe. Experimental investigation on condensation regime diagram and jet penetration length, Int. J. Heat Mass Transfer 94 (2016) 528–538. [38] N. Clerx, Experimental study of direct contact condensation of steam in turbulent duct flow (Ph. D. thesis), Eindhoven University of Technology, Eindhoven, The Netherlands, 2010.
[39] N. Clerx, L.G.M. Deurzen, A. Pecenko, R. Liew, C.W.M. Geld, J.G.M. Kuerten, Temperature fields induced by direct contact condensation of steam in a crossflow in a channel, Heat Mass Transfer 47 (8) (2011) 981–990. [40] N. Clerx, C.W.M. van der Geld, J.G.M. Kuerten, Turbulent stresses in a direct contact condensation jet in cross-flow in a duct with implications for particle break-up, Int. J. Heat Mass Transfer 66 (2013) 684–694. [41] C.E. Willert, M. Gharib, Digital particle image velocimetry, Exp. Fluids 10 (4) (1991) 181–193. [42] Insight 4G, User’s Guide, 2011.