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Mass transfer measurements and flow separation behavior in a 90° short elbow
International Journal of Heat and Mass Transfer 136 (2019) 1106–1114
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Mass transfer measurements and flow separation behavior in a 90° short elbow Yuya Ikarashi a, Nobuyuki Fujisawa b,⇑ a b
Graduate School of Science and Technology, Niigata University, Niigata, Japan Department of Mechanical Engineering, Niigata University, Niigata, Japan
a r t i c l e
i n f o
Article history: Received 18 December 2018 Received in revised form 8 March 2019 Accepted 13 March 2019
Keywords: 90° short elbow Mass transfer measurement PIV Flow separation Flow accelerated corrosion
a b s t r a c t The mass transfer distribution and flow separation behavior in a 90° short elbow (radius to diameter ratio 1.0) were investigated experimentally in the Reynolds number range Re = (3–15) 104. The mass transfer distribution in the 90° short elbow showed two high peaks on both sides of the elbow centerline of the inner elbow wall at lower Reynolds numbers (Re = (3–5) 104). In order to characterize this phenomenon, velocity measurements were carried out using particle image velocimetry (PIV) to explain the flow separation in the short elbow, followed by the flow reattachment in the downstream. A comparative study of the mass transfer distribution and the flow fields on and near the inner wall indicated that the high mass transfer is highly responsible for the flow separation, where the turbulence intensity increased and contributed to the high mass transfer on the inner elbow wall. By increasing the Reynolds number, the flow separation region decreased in size and it came closer to the elbow centerline, which resulted in a lower mass transfer coefficient on the inner elbow wall at higher Reynolds numbers. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Flow-accelerated corrosion (FAC) in pipeline elements, such as elbow and orifice, is an important topic of interest in the safety management of pipelines in nuclear/fossil power plants. FAC is a mass transfer phenomenon of diffusing iron ions from the carbon steel pipe wall into the turbulent bulk flow through the oxide layer on the wall, which is highly promoted by the influence of flow turbulence. In the prototype pipe wall thinning, water chemistry also plays an important role because of its pH dependency on wall thinning. Therefore, FAC in nuclear/fossil power plants has been studied from the viewpoint of mass transfer and water chemistry [1–6]. Mass transfer measurements of the pipeline elements are important topics of research in understanding the FAC mechanism in nuclear/fossil power plant pipelines. Many experimental and numerical studies have investigated the mass and momentum transfer characteristics of the flow behind an orifice [7–16]. Experimental results indicated that the high mass transfer occurred downstream of the orifice where high turbulence intensity was generated in the separating flow region behind it. In addition, numerical studies were carried out to understand the physical
⇑ Corresponding author. E-mail address: [email protected] (N. Fujisawa). https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.076 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
mechanism of the mass transfer enhancement downstream of the orifice [10,15]. Furthermore, the combined effect of swirling flow and elbow on the mass transfer enhancement downstream of an orifice was investigated experimentally [17] to understand the pipe break mechanism of Mihama power plant [18], which is known to be caused by FAC. It was found that the peak mass transfer coefficient reaches more than three times higher the magnitude of the smooth pipe, suggesting an importance of the combined effect of swirling flow and elbow on the pipe-wall thinning [18– 21]. In comparison with the orifice case, less studies were performed on the mass transfer measurements in the elbow, which might be due to its complex geometry. In the literature, mass transfer measurements in a 90°elbow were performed on the long elbow (radius to pipe diameter ratio: 1.5) in the range of Reynolds number, Re (=Ud/m) = (4–39) 104 [22–25]. The coefficients were measured by the plaster dissolution method because of the working fluid water through the pipe [23– 25], while the naphthalene sublimation method was used for the air flow through the elbow [22], where the Schmidt number is much smaller than that of the water flow in the power plant application. It should be mentioned that the mass transfer coefficients on the elbow reported in the literature are highly affected by the Reynolds number, Schmidt number, and surface roughness [26]. Therefore, it is still difficult to fully explain the mass transfer phenomenon in the 90° long elbow from these limited number of
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Nomenclature D d K K0 Re r Sc U
molecular diffusion coefficient [m2/s] pipe diameter [m] mass transfer coefficient [m/s] mass transfer coefficient in straight pipe [m/s] Reynolds number (=Ud/m) [–] radius of elbow curvature [m] Schmidt number (=m/D) [–] bulk velocity [m/s]
experiments. However, it is understood that the mass transfer coefficient on the inner wall of the long elbow is decreased on the first half of the inner wall while it is increased on the second half, which is correlated with the surface-flow-pattern variations on the inner wall using the oil-flow method. The mass transfer coefficients on the inner wall of the long elbow tend to increase at higher Reynolds numbers except for the elbow centerline. However, the mass transfer characteristics of the 90° short elbow has not been reported in the literature, in spite of its importance in application to power plant. The flow through a 90° elbow is featured by the secondary flow in and downstream of the elbow, which is caused by the centrifugal forces arising from the elbow curvature. The secondary flow directs from the inner wall to the outer wall through the elbow centerline, and returns to the inner wall along the side walls of the elbow. Furthermore, the flow over the inner wall experiences adverse pressure gradient in the second half of the elbow arising from its curvature, which when increased, leads to flow separation on the inner wall [27,28]. Therefore, the flow separation on the inner elbow wall that is not observed in the long elbow, is one of the features of the short elbow. The mean flow and turbulence measurements in a 90° elbow were reported by several researchers in a wider range of Reynolds number (Re = (4–40) 104) using velocity measurements by hotwire anemometry, laser Doppler velocimetry, and particle image velocimetry [29–38]. Furthermore, numerical studies on elbow flows were carried out to understand the complex flow phenomenon and to show the formation of secondary flow caused by the centrifugal forces in and downstream of the elbow [39,40]. These past studies were conducted on elbows for different elbow-radius-to-diameter ratios r/d ranging from 1.0 to 2.8 and in the Reynolds number range (Re = (4–32) 104). Among these past studies, the velocity measurements by particle image velocimetry (PIV) were conducted in the short elbow (r/d = 1.0) [31–35]. Experimental results showed that the mean velocity in the short elbow underwent the flow separation in the inner wall, recovered gradually, and ended by the flow reattachment in the elbow downstream. The separation and reattachment points are slightly modified by the Reynolds number even if it is greater than Re = 2 105, which suggests that the highly complex nature of the separating flow is observed on the second half of the inner wall of the 90° elbow at higher Reynolds number. However, the influence of Reynolds number on the separating flow region of the elbow for lower Reynolds number Re < 2 105 is not so well understood owing to insufficient experimental data. The mass transfer coefficient and the separating flow behavior of a 90° short elbow of r/d = 1.0 were studied by plaster dissolution method and planar PIV measurement, respectively, in the Reynolds number range Re = (3–15) 104. Furthermore, we focused on the separating flow behavior in the inner elbow wall to elucidate the relationship between mass transfer distribution and flow separation behavior in and downstream of the elbow.
Us u’ v’ x, y
a dh/dt
m h
friction velocity [m/s] axial turbulent intensity [m/s] wall normal turbulent intensity [m/s] streamwise and wall normal coordinates [m] angle of elbow curvature [°] wall thinning rate [m/s] kinematic viscosity of fluid [m2/s] circumferential angle [°]
2. Experimental apparatus and procedures 2.1. Experimental set-up The experiments on mass transfer coefficients and the separating flow behavior in the 90° short elbow were conducted in a closed-circuit water tunnel, which was described in a previous experiment [24]. The apparatus consisted of a water tank with temperature controller, pump, settling chamber, straight pipe, and a test elbow, with pipe diameter d = 56 mm and straight pipe length of 1340 mm (=24d). The short elbow has r/d of 1.0, as illustrated in Fig. 1. The temperature of working fluid water was kept at 303 K, and the Schmidt number was Sc (=m/D) = 680 owing to the plaster layer on the elbow surface in the mass transfer measurements (D: molecular diffusion coefficient). The bulk flow velocity in the major experiments was set to U = 0.43 m/s, 0.72 m/s, and 1.44 m/s, which corresponds to the Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. 2.2. Mass transfer measurement The mass transfer measurements were carried out at five cross sections perpendicular to the elbow axis at angles a = 0, 22.5, 45, 67.5, and 90°, where a is defined by the angle from the elbow inlet, as shown in Fig. 1. To evaluate the cross sectional distribution of mass transfer coefficient on the elbow, two types of test elbows were designed: one was for the measurement on the inner and outer walls of the elbow and the other for the side walls. The measurements were carried out in the circumferential angle range of 45 to 45° (=90°) in the plane perpendicular to the elbow axis. Therefore, the whole circular distribution (=360°) of mass transfer coefficient normal to the elbow axis was evaluated by combining the results of four measurements on each half pipe section of elbow.
Fig. 1. Illustration of 90° short elbow.
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The mass transfer coefficients were evaluated from the measurements of the depth distribution of the plaster layer in water flow before and after the experiment [11,24,25]. The plaster layer casted on the wall was maintained at 3 mm. The surface of the plaster layer on the elbow was polished by #2000 sand paper to ensure smoothness after molding the plaster layer into the elbow. Gas bubbles generated in the liquid plaster layer were removed using the vacuum pump during the preparation of the liquid plaster. Fig. 2 shows the experimental test section for the measurement of mass transfer coefficients on the elbow wall, which are evaluated from the dissolved thickness of the plaster layer into the water flow. The dissolution of the plaster layer is expected to be caused by the mass transfer, which is highly influenced by the turbulence in the water flow. It consisted of a traversing device driven by a stepping motor and the test section of half elbow on it, and a laser displacement sensor [24]. Note that the wall thinning rate distribution normal to the elbow wall was evaluated from the depth distribution measurement before and after the experiments, where correction was made on the circumferential wall angle of the elbow arising from the wall and traversing direction. The mass transfer coefficient K was obtained from the equation
K¼
qb dh =dt
ð1Þ
cw cb
where dh/dt is the wall-thinning rate of the plaster layer in a unit time, dh is evaluated from the depth variation of the plaster layer before and after the experiment, qb and cw are the density and con-
Fig. 2. Experimental apparatus for mass transfer measurement.
centration of the plaster layer, respectively, and cb is the density of dissolved plaster in the water flow. Here, cw is assumed as the saturated concentration of the dissolved plaster and cb is evaluated from the volume of dissolved plaster in the water flow. The dissolved concentration of the plaster in the bulk flow was measured by a concentration meter and was less than 10% of cw. The uncertainty of the mass transfer coefficient measurement was estimated 5.6% in 95% confidence level, which consists of the setting error 10 lm of the test elbow in estimating the depth distribution and 2% error in the concentration measurement, 1% time derivative error, and 0.25% minor bias error in depth measurement by laser displacement sensor [24]. The mass transfer coefficient K was normalized by that of the straight pipe K0. The wall surface of this experiment was considered hydraulically smooth, because the roughness height y (=4 lm) was small enough and it satisfied the condition yUs/m < 1 (Us: friction velocity, m: kinematic viscosity). It should be mentioned that the shear strength of the plaster is approximately 0.8 MPa [41], which is much larger than the wallshear stress caused by the flow through the pipe.
2.3. PIV measurement of velocity field on inner elbow wall The instantaneous velocity field around the separating flow region on the inner elbow wall was measured by PIV, which consists of the pulsed Nd:YAG laser (70 mJ/pulse), CCD camera (1018 1008 pixels with 8 bits in gray level), and the pulse controller. Flow visualization was performed by adding a certain amount of nylon tracer particles 40 lm in diameter and specific gravity of 1.02 to the working fluid water. The flow was observed by a CCD camera located over the elbow model, while a 1 mm thick light sheet illumination was provided from the side wall of the test section, as illustrated in Fig. 3. Camera observations were made perpendicular to the target wall to minimize image distortion owing to refractive index difference. Nevertheless, the near-wall velocity field was deformed by the refractive index difference at the interface of acrylic resin material and water so that the theoretical correction was introduced into the analysis near the wall, which has been described in Ref. [38]. The statistical properties of the mean flow and fluctuating velocities were evaluated from 500 instantaneous velocity fields captured at 15 frames/s by a CCD camera in the Reynolds number range Re = (3–15) 104. The observations were made in the area 60 mm 60 mm. The PIV analysis was conducted using the interrogation window size 31 31 pixels with 50% overlap, where the sub-pixel interpolation was incorporated into the analysis [42]. The maximum pixel displacement of the particle images was about 4 pixels in the velocity measurements by tuning the time interval
Fig. 3. Experimental test section for velocity measurements.
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between the two sequential images. As a result, the number of invalid velocity vectors was found less than 1% of the total. The uncertainty in velocity measurement was estimated 4.9% at 95% confidence level with respect to the maximum velocity, while it increased near the wall owing to the increased image deformation near the acrylic resin–water interface [38]. The details of this uncertainty analysis has been described in Ref. [38]. 2.4. Evaluation of separation and reattachment points by near-wall PIV measurement The separation and reattachment points of the separating flow on the inner wall was determined from the mean velocity profiles of the near-wall PIV measurement. This experimental technique relies on the transformation of image in boundary-fitted coordinates into rectangular image and the PIV analysis, followed by the transformation back into the velocity field in the original coordinates [43]. The PIV analysis with the sub-pixel interpolation technique was carried out using the interrogation window size 21 41 pixels with 50% overlap because of the high-resolution requirement in vertical coordinate y from the wall. The observation area of the near-wall PIV measurement was 30 mm 30 mm, and the nearest velocity vectors to the wall were obtained at y = 0.2 mm. The separation and reattachment points were obtained at the beginning and end of the reverse flow at the nearest point to the wall. 3. Results and discussion 3.1. Distribution of mass transfer coefficients in short elbow Fig. 4(a), (b), and (c) show the cross-sectional distributions of mass transfer coefficients in the 90° short elbow at three Reynolds numbers Re = 3 104, 5 104, and 10 104 measured by the plaster dissolution method. The experimental results were averaged over ±5° in circumferential angle of the elbow obtained from three repeated experiments. In the figures, scattering of the data is shown by the error bars. Note that each circular graph shows the normalized mass transfer coefficient K/K0 plotted against the circumferential angle h from the outer wall of the elbow. When K/ K0 equals to 1, the local mass transfer coefficient in the elbow is the same magnitude as that of the straight pipe. Note that the circumferential angle h = 0° corresponds to the outer wall, h = 180° is the inner wall, and h = 90° and 270° are the side walls, as illustrated in Fig. 1(b). Fig. 4(a) and (b) show the normalized mass transfer coefficients at lower Reynolds numbers (Re = 3 104 and 5 104), respectively, for some elbow angles a = 0°, 22.5°, 45°, 67.5°, and 90°. Both results show a similar mass transfer variation with elbow angle a. The mass transfer coefficient is almost equal to 1 at the inlet of the elbow at a = 0°, while it shows a large variation in magnitude with increasing a on the inner wall, which is apparent on the inner wall of the elbow. A detailed examination on the mass transfer distribution shows that K/K0 on the inner wall decreases at a = 22.5° (Fig. 4 (a) and (b)) with respect to that on the elbow inlet (a = 0°), while it increases on the side walls and retains the same magnitude on the outer wall. A similar trend is observed for the elbow angle a = 45° although there is a local minimum ±20° on both sides of the elbow centerline. This variation of mass transfer coefficient with the elbow angle may be related to the start of high mean velocity of converging flow outside the separating flow region on the inner wall of the elbow, which is shown in Fig. 11. With further increases in the elbow angle to a = 67.5° and 90°, the mass transfer coefficient on the side wall keeps roughly the same magnitude as that of a = 45°; nevertheless, the significant increase is observed on
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both sides of the inner wall at h = ±20–25° (double peaks), where the mass transfer coefficient reaches almost twice the magnitude of the smooth pipe. This was not observed in the long elbow; therefore, it can be considered as a special feature of the short elbow. When the Reynolds number of the flow through the elbow increases to Re = 1 105 (Fig. 4(c)), the mass transfer coefficient distribution changes drastically owing to its influence. Otherwise, the mass transfer coefficient decreases on the inner wall of the elbow (a = 22.5° and 45°), while it increases on the inner side walls (a = 67.5° and 90°) that results to the disappearance of the double peaks on the mass transfer distribution and to a more uniform mass transfer coefficient distribution on the inner wall of the elbow. Therefore, the mass transfer distribution on the whole elbow at higher Reynolds numbers (Re = 1 105) behaves differently from that at the lower Reynolds number (Re = (3–5) 104). It is seen that the double peaks are suppressed on both sides of the elbow centerline, while the mass transfer coefficient on the inner wall near the centerline retains the high magnitude. This can be caused by variation of the flow field on the inner wall at higher Reynolds number, which is the formation of separating flow region on the second half of the inner wall of the short elbow shown in Fig. 5. On the other hand, the mass transfer coefficient on the outer elbow wall slightly decreases at high Reynolds number (Re = 1 105), which results in a mass transfer coefficient smaller than the straight pipe. This may be due to the flow acceleration effect on the outer elbow wall by increasing the Reynolds number. Fig. 4(d) shows a comparative study of mass transfer coefficient distribution at a = 90° of the short (r/d = 1.0) and long (r/d = 1.5) elbows at two Reynolds numbers Re = 5 104 and 1 105, which are the typical values used in this study. The double peaks on both sides of the centerline and the single peak on the long elbow around it, indicates that the major difference of mass transfer distribution appears on the inner short elbow wall at a low Reynolds number. When the Reynolds number is increased to Re = 1 105, both the observed double peaks and single peak are decreased on the inner elbow wall, while they are increased on the neighboring side wall, which results in a uniform mass transfer distribution on the inner elbow wall in the circumferential direction. A decrease in the mass transfer coefficient is observed on the outer elbow wall on short and long elbows. 3.2. PIV measurement of velocity field over the separating flow region To characterize the separating flow behavior on the inner wall of the elbow, the velocity field on the second half of the elbow’s inner wall was measured by a planar PIV at some Reynolds numbers Re = (3–15) 104. Fig. 5(a)–(c) show the axial cross-section of mean velocity distributions of the flow at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. It is observed that the high velocity region prevails near the inlet of the inner wall of the elbow, where the mass transfer coefficient stays in a low level, as seen in the mass transfer coefficient in Fig. 4. This result indicates that the mass transfer coefficient near the elbow inlet does not increase in proportional to the velocity magnitude of the flow. This suggests that the influence of turbulence on the mass transfer is more pronounced than that of the velocity magnitude. The mean velocity contour in Fig. 5(a) shows a clear indication of flow separation and prevails over the downstream region of the elbow. The separating flow region ends by the flow attachment at x/d = 0.5 on the downstream of the elbow. When the Reynolds number is increased to Re = 5 104, the separation point is approximately the same as the lower Reynolds number case (Re = 3 104), but the reattachment point moves upstream, resulting in a decrease in the axial length of the separating flow region.
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(a) Re = 3
104
(c) Re = 1
105
(b) Re = 5
104
(d) Comparison with long elbow ( = 90°) Fig. 4. Cross-sectional mass transfer distributions in short elbow.
(a) Re = 3×104
(b) Re = 5×104
(c) Re = 1×105
Fig. 5. Mean velocity contours in and downstream of short elbow (S: separation, R: reattachment).
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With a further increase in the Reynolds number to Re = 1 105, the separating flow region becomes much smaller than that of the low Reynolds number; however, the lower velocity region still remains in the elbow downstream. A detailed examination of the mean velocity over the inner elbow wall and downstream can be performed in the mean velocity profiles in Fig. 6, which shows the near-wall velocity distribution more clearly. The results indicate the delay of flow separation on the inner wall by increasing the Reynolds number, and the subsequent recovery of the mean velocity in the elbow downstream. Fig. 7(a), (b), and (c) show the axial turbulence intensity contour in the second half of the elbow and downstream at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. The turbulence intensity increases near the separation points and develops along the shear layer, which results in the formation of high turbulence in the elbow downstream. By increasing the Reynolds number, the magnitude of axial turbulence intensity increases along the shear layer but the highly turbulent region is suppressed because of the decrease in the separating flow region on the inner wall of the elbow (Fig. 5). Note that the increase of turbulence intensity in the shear layer at higher Reynolds number is related to the separating flow behavior near the separation point. A detailed examination of the axial turbulence intensity profiles in and downstream of the short elbow is shown in Fig. 8. The results indicate that the maximum axial turbulence intensity is located near the wall at higher Reynolds numbers, which is caused by the downstream movement of the separation point. This results in the higher axial turbulence intensity near the wall and lower
intensity in the far region of the inner wall at higher Reynolds numbers. The turbulence intensity profile recovers downstream of the elbow, in which the behavior of the reattachment-point variation seems to be independent with the Reynolds number. 3.3. Characteristics of separation and reattachment points To clarify the Reynolds number effect on the separating flow region, the near-wall mean velocity profiles are measured by the near-wall PIV, owing to the high spatial resolution requirement of the near-wall velocity to obtain the separation and reattachment points. Sample mean velocity profiles near the separation point are illustrated in Fig. 9 at Re = 3 104, 5 104, and 1 105. The results show that the flow separation occurs at a = 36° (Re = 3 104), a = 39° (Re = 5 104), a = 48° (Re = 1 105), which are the start of reverse flow in the near-wall velocity profiles. The separation and reattachment points obtained from the near-wall PIV measurements with respect to the Reynolds number Re are summarized in Fig. 10. The results indicate that the separation point behaves weakly dependent on the Reynolds number and moves slightly downstream with an increase in the Reynolds number. On the other hand, the reattachment point moves upstream with increasing Reynolds number, which is apparent on the low Reynolds number. Therefore, the axial length of the separating flow region, which corresponds to the axial distance between the separation and reattachment points, decreases with increasing Reynolds number. The variation of the axial length seems to be saturated at higher Reynolds numbers (Re = (10–15) 104). The
Fig. 6. Mean velocity distributions in and downstream of short elbow.
(a) Re = 3×104
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(b) Re = 5×104
(c) Re = 1×105
Fig. 7. Axial turbulence intensity contours in and downstream of short elbow (S: separation, R: reattachment).
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Fig. 8. Axial turbulence intensity distributions in and downstream of short elbow.
Fig. 9. Example of mean velocity profiles near separation point (S: separation).
Fig. 10. Downstream variation of separating flow region in and downstream of short elbow.
uncertainties in separation and reattachment points are shown by error bars in Fig. 10, which are obtained from the repeated experiments. Fig. 11 shows the mean velocity distribution over the inner wall of the elbow and downstream in the cross-sectional plane parallel to the inner wall at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. The light-sheet plane from the inner wall was set to y = 4 mm. The results indicate that the separating flow region is formed in the mid plane down to x/d = 0.5 at a lower Reynolds number (Re = 3 104). With an increase in the Reynolds number (Re = 5 104), the separation region decreases mainly due to the reattachment point movement, and it is almost diminished at a higher Reynolds number (Re = 1 105) because of the
small distance from the inner wall. These results agree with the observation of reattachment points in Fig. 10. This figure also shows the circumferential distribution of separating flow region, which extends to z/d = ±0.07 that corresponds to ± 8° on the inner wall of the elbow. The mean velocity distribution around the separating flow region indicates the formation of conversing flow in its downstream, which shows a local maximum velocity on both sides of the elbow centerline z/d = ±0.19 (22°). It should be mentioned that the velocity gradient in z direction gradually decreases with an increase in the Reynolds number because of the decrease in the separating flow region. Fig. 12 shows the corresponding axial turbulence intensity contours in the cross-sectional plane parallel to the inner wall at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively, with a distance y = 4 mm from the inner wall. The turbulence intensity contour at Re = 3 104 shows the high turbulence intensity on both sides of the elbow centerline, which corresponds to the outer shear layer surrounding the separating flow region z/ d = ±0.16 (19°). It should be mentioned that the highly turbulent intensity region is located in the middle of the shear layer with high velocity gradient and is slightly closer to the elbow centerline than the position of maximum velocity. By increasing the Reynolds number to Re = 5 104, the high turbulence intensity region comes closer to the elbow centerline and they almost merge at a higher Reynolds number (Re = 1 105). It should be mentioned that the location of the maximum turbulence intensity z/d = ±0.16 (±19°) agrees with that of the double peak positions (±20°) in the mass transfer distribution (Fig. 4). This suggests that the double peaks
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(a) Re = 3×104
(b) Re = 5×104
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(c) Re = 1×105
Fig. 11. Near-wall mean velocity contours in horizontal cross section.
(a) Re = 3 × 104
(b) Re = 5 × 104
(c) Re = 1 × 105
Fig. 12. Near-wall axial turbulence intensity contours in horizontal cross section.
in mass transfer distribution may be caused by the local high turbulence. Furthermore, the Reynolds number effect on the maximum turbulence intensity position is similarly observed in the behavior of double peak positions in the mass transfer coefficient, which comes closer to the elbow centerline with an increase in Reynolds number. Therefore, the high mass transfer coefficient on the inner wall of the elbow is considered to be from the high turbulence intensity on the inner wall caused by the high velocity gradient of the converging shear layer on both sides of the elbow centerline. It should be mentioned that the mass transfer in the flow through the elbow is associated with the turbulence as well as the dynamic behavior of vortex shedding from the flow separation in the elbow, both of them contribute to the growth of mass transfer in and downstream of elbow. 4. Conclusion The mass transfer coefficient distribution and flow separation behavior in a 90° short elbow with a radius to pipe diameter ratio of 1.0 were experimentally studied using the plaster dissolution method and PIV measurements in a Reynolds number range Re = (3–15) 104. The influence of Reynolds number on the mass transfer coefficient distribution was observed to be weak in the first half of the inner elbow wall, while it showed a large change in the second half, where the double peaks in mass transfer distribution occur on both sides of the elbow centerline on the inner wall. To understand this phenomenon, PIV measurements were carried out on the inner elbow wall and the flow separation and reattachment in the second half of the elbow were observed. The high mass transfer characteristics on the inner wall of the second half of the elbow was found to be highly correlated with the separating flow behavior in and downstream of the short elbow. With an increase in the Reynolds number, the separation point moves downstream while the reattachment point moves upstream, which results in the suppression of the separation region. Furthermore, the circum-
ferential extent of the separation region decreases with increasing Reynolds number, which arises from the shift of converging flow on both sides of the separating flow region. Thus, the high turbulence intensity region comes closer to the elbow centerline with increasing Reynolds number, and its variation with the Reynolds number on both sides of the centerline, is consistent with that of the high mass transfer region. Therefore, the high mass transfer behavior in the 90° short elbow arises from the generation of separating flow region and the behavior of converging flow over the inner wall of the elbow. Conflict of interests The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported. Acknowledgements This work was supported by JSPS KAKENHI Grant Number JP18K04632. The authors acknowledge the helpful suggestions of Dr. T. Yamagata of Niigata University, Dr. F. Inada, and Dr. K. Fujiwara from Central Res. Inst. of Electric Power Industry, during the study. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.076. References [1] F.P. Berger, K.F.F.L. Hau, Mass transfer in turbulent pipe flow measured by the electrochemical method, Int. J. Heat Mass Transf. 20 (1977) 1185–1194. [2] T. Sydberger, U. Lotz, Relation between mass transfer and corrosion in a turbulent pipe flow, J. Electrochem. Soc. 129 (1982) 276–283.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Mass transfer measurements and flow separation behavior in a 90° short elbow Yuya Ikarashi a, Nobuyuki Fujisawa b,⇑ a b
Graduate School of Science and Technology, Niigata University, Niigata, Japan Department of Mechanical Engineering, Niigata University, Niigata, Japan
a r t i c l e
i n f o
Article history: Received 18 December 2018 Received in revised form 8 March 2019 Accepted 13 March 2019
Keywords: 90° short elbow Mass transfer measurement PIV Flow separation Flow accelerated corrosion
a b s t r a c t The mass transfer distribution and flow separation behavior in a 90° short elbow (radius to diameter ratio 1.0) were investigated experimentally in the Reynolds number range Re = (3–15) 104. The mass transfer distribution in the 90° short elbow showed two high peaks on both sides of the elbow centerline of the inner elbow wall at lower Reynolds numbers (Re = (3–5) 104). In order to characterize this phenomenon, velocity measurements were carried out using particle image velocimetry (PIV) to explain the flow separation in the short elbow, followed by the flow reattachment in the downstream. A comparative study of the mass transfer distribution and the flow fields on and near the inner wall indicated that the high mass transfer is highly responsible for the flow separation, where the turbulence intensity increased and contributed to the high mass transfer on the inner elbow wall. By increasing the Reynolds number, the flow separation region decreased in size and it came closer to the elbow centerline, which resulted in a lower mass transfer coefficient on the inner elbow wall at higher Reynolds numbers. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Flow-accelerated corrosion (FAC) in pipeline elements, such as elbow and orifice, is an important topic of interest in the safety management of pipelines in nuclear/fossil power plants. FAC is a mass transfer phenomenon of diffusing iron ions from the carbon steel pipe wall into the turbulent bulk flow through the oxide layer on the wall, which is highly promoted by the influence of flow turbulence. In the prototype pipe wall thinning, water chemistry also plays an important role because of its pH dependency on wall thinning. Therefore, FAC in nuclear/fossil power plants has been studied from the viewpoint of mass transfer and water chemistry [1–6]. Mass transfer measurements of the pipeline elements are important topics of research in understanding the FAC mechanism in nuclear/fossil power plant pipelines. Many experimental and numerical studies have investigated the mass and momentum transfer characteristics of the flow behind an orifice [7–16]. Experimental results indicated that the high mass transfer occurred downstream of the orifice where high turbulence intensity was generated in the separating flow region behind it. In addition, numerical studies were carried out to understand the physical
⇑ Corresponding author. E-mail address: [email protected] (N. Fujisawa). https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.076 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
mechanism of the mass transfer enhancement downstream of the orifice [10,15]. Furthermore, the combined effect of swirling flow and elbow on the mass transfer enhancement downstream of an orifice was investigated experimentally [17] to understand the pipe break mechanism of Mihama power plant [18], which is known to be caused by FAC. It was found that the peak mass transfer coefficient reaches more than three times higher the magnitude of the smooth pipe, suggesting an importance of the combined effect of swirling flow and elbow on the pipe-wall thinning [18– 21]. In comparison with the orifice case, less studies were performed on the mass transfer measurements in the elbow, which might be due to its complex geometry. In the literature, mass transfer measurements in a 90°elbow were performed on the long elbow (radius to pipe diameter ratio: 1.5) in the range of Reynolds number, Re (=Ud/m) = (4–39) 104 [22–25]. The coefficients were measured by the plaster dissolution method because of the working fluid water through the pipe [23– 25], while the naphthalene sublimation method was used for the air flow through the elbow [22], where the Schmidt number is much smaller than that of the water flow in the power plant application. It should be mentioned that the mass transfer coefficients on the elbow reported in the literature are highly affected by the Reynolds number, Schmidt number, and surface roughness [26]. Therefore, it is still difficult to fully explain the mass transfer phenomenon in the 90° long elbow from these limited number of
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Nomenclature D d K K0 Re r Sc U
molecular diffusion coefficient [m2/s] pipe diameter [m] mass transfer coefficient [m/s] mass transfer coefficient in straight pipe [m/s] Reynolds number (=Ud/m) [–] radius of elbow curvature [m] Schmidt number (=m/D) [–] bulk velocity [m/s]
experiments. However, it is understood that the mass transfer coefficient on the inner wall of the long elbow is decreased on the first half of the inner wall while it is increased on the second half, which is correlated with the surface-flow-pattern variations on the inner wall using the oil-flow method. The mass transfer coefficients on the inner wall of the long elbow tend to increase at higher Reynolds numbers except for the elbow centerline. However, the mass transfer characteristics of the 90° short elbow has not been reported in the literature, in spite of its importance in application to power plant. The flow through a 90° elbow is featured by the secondary flow in and downstream of the elbow, which is caused by the centrifugal forces arising from the elbow curvature. The secondary flow directs from the inner wall to the outer wall through the elbow centerline, and returns to the inner wall along the side walls of the elbow. Furthermore, the flow over the inner wall experiences adverse pressure gradient in the second half of the elbow arising from its curvature, which when increased, leads to flow separation on the inner wall [27,28]. Therefore, the flow separation on the inner elbow wall that is not observed in the long elbow, is one of the features of the short elbow. The mean flow and turbulence measurements in a 90° elbow were reported by several researchers in a wider range of Reynolds number (Re = (4–40) 104) using velocity measurements by hotwire anemometry, laser Doppler velocimetry, and particle image velocimetry [29–38]. Furthermore, numerical studies on elbow flows were carried out to understand the complex flow phenomenon and to show the formation of secondary flow caused by the centrifugal forces in and downstream of the elbow [39,40]. These past studies were conducted on elbows for different elbow-radius-to-diameter ratios r/d ranging from 1.0 to 2.8 and in the Reynolds number range (Re = (4–32) 104). Among these past studies, the velocity measurements by particle image velocimetry (PIV) were conducted in the short elbow (r/d = 1.0) [31–35]. Experimental results showed that the mean velocity in the short elbow underwent the flow separation in the inner wall, recovered gradually, and ended by the flow reattachment in the elbow downstream. The separation and reattachment points are slightly modified by the Reynolds number even if it is greater than Re = 2 105, which suggests that the highly complex nature of the separating flow is observed on the second half of the inner wall of the 90° elbow at higher Reynolds number. However, the influence of Reynolds number on the separating flow region of the elbow for lower Reynolds number Re < 2 105 is not so well understood owing to insufficient experimental data. The mass transfer coefficient and the separating flow behavior of a 90° short elbow of r/d = 1.0 were studied by plaster dissolution method and planar PIV measurement, respectively, in the Reynolds number range Re = (3–15) 104. Furthermore, we focused on the separating flow behavior in the inner elbow wall to elucidate the relationship between mass transfer distribution and flow separation behavior in and downstream of the elbow.
Us u’ v’ x, y
a dh/dt
m h
friction velocity [m/s] axial turbulent intensity [m/s] wall normal turbulent intensity [m/s] streamwise and wall normal coordinates [m] angle of elbow curvature [°] wall thinning rate [m/s] kinematic viscosity of fluid [m2/s] circumferential angle [°]
2. Experimental apparatus and procedures 2.1. Experimental set-up The experiments on mass transfer coefficients and the separating flow behavior in the 90° short elbow were conducted in a closed-circuit water tunnel, which was described in a previous experiment [24]. The apparatus consisted of a water tank with temperature controller, pump, settling chamber, straight pipe, and a test elbow, with pipe diameter d = 56 mm and straight pipe length of 1340 mm (=24d). The short elbow has r/d of 1.0, as illustrated in Fig. 1. The temperature of working fluid water was kept at 303 K, and the Schmidt number was Sc (=m/D) = 680 owing to the plaster layer on the elbow surface in the mass transfer measurements (D: molecular diffusion coefficient). The bulk flow velocity in the major experiments was set to U = 0.43 m/s, 0.72 m/s, and 1.44 m/s, which corresponds to the Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. 2.2. Mass transfer measurement The mass transfer measurements were carried out at five cross sections perpendicular to the elbow axis at angles a = 0, 22.5, 45, 67.5, and 90°, where a is defined by the angle from the elbow inlet, as shown in Fig. 1. To evaluate the cross sectional distribution of mass transfer coefficient on the elbow, two types of test elbows were designed: one was for the measurement on the inner and outer walls of the elbow and the other for the side walls. The measurements were carried out in the circumferential angle range of 45 to 45° (=90°) in the plane perpendicular to the elbow axis. Therefore, the whole circular distribution (=360°) of mass transfer coefficient normal to the elbow axis was evaluated by combining the results of four measurements on each half pipe section of elbow.
Fig. 1. Illustration of 90° short elbow.
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The mass transfer coefficients were evaluated from the measurements of the depth distribution of the plaster layer in water flow before and after the experiment [11,24,25]. The plaster layer casted on the wall was maintained at 3 mm. The surface of the plaster layer on the elbow was polished by #2000 sand paper to ensure smoothness after molding the plaster layer into the elbow. Gas bubbles generated in the liquid plaster layer were removed using the vacuum pump during the preparation of the liquid plaster. Fig. 2 shows the experimental test section for the measurement of mass transfer coefficients on the elbow wall, which are evaluated from the dissolved thickness of the plaster layer into the water flow. The dissolution of the plaster layer is expected to be caused by the mass transfer, which is highly influenced by the turbulence in the water flow. It consisted of a traversing device driven by a stepping motor and the test section of half elbow on it, and a laser displacement sensor [24]. Note that the wall thinning rate distribution normal to the elbow wall was evaluated from the depth distribution measurement before and after the experiments, where correction was made on the circumferential wall angle of the elbow arising from the wall and traversing direction. The mass transfer coefficient K was obtained from the equation
K¼
qb dh =dt
ð1Þ
cw cb
where dh/dt is the wall-thinning rate of the plaster layer in a unit time, dh is evaluated from the depth variation of the plaster layer before and after the experiment, qb and cw are the density and con-
Fig. 2. Experimental apparatus for mass transfer measurement.
centration of the plaster layer, respectively, and cb is the density of dissolved plaster in the water flow. Here, cw is assumed as the saturated concentration of the dissolved plaster and cb is evaluated from the volume of dissolved plaster in the water flow. The dissolved concentration of the plaster in the bulk flow was measured by a concentration meter and was less than 10% of cw. The uncertainty of the mass transfer coefficient measurement was estimated 5.6% in 95% confidence level, which consists of the setting error 10 lm of the test elbow in estimating the depth distribution and 2% error in the concentration measurement, 1% time derivative error, and 0.25% minor bias error in depth measurement by laser displacement sensor [24]. The mass transfer coefficient K was normalized by that of the straight pipe K0. The wall surface of this experiment was considered hydraulically smooth, because the roughness height y (=4 lm) was small enough and it satisfied the condition yUs/m < 1 (Us: friction velocity, m: kinematic viscosity). It should be mentioned that the shear strength of the plaster is approximately 0.8 MPa [41], which is much larger than the wallshear stress caused by the flow through the pipe.
2.3. PIV measurement of velocity field on inner elbow wall The instantaneous velocity field around the separating flow region on the inner elbow wall was measured by PIV, which consists of the pulsed Nd:YAG laser (70 mJ/pulse), CCD camera (1018 1008 pixels with 8 bits in gray level), and the pulse controller. Flow visualization was performed by adding a certain amount of nylon tracer particles 40 lm in diameter and specific gravity of 1.02 to the working fluid water. The flow was observed by a CCD camera located over the elbow model, while a 1 mm thick light sheet illumination was provided from the side wall of the test section, as illustrated in Fig. 3. Camera observations were made perpendicular to the target wall to minimize image distortion owing to refractive index difference. Nevertheless, the near-wall velocity field was deformed by the refractive index difference at the interface of acrylic resin material and water so that the theoretical correction was introduced into the analysis near the wall, which has been described in Ref. [38]. The statistical properties of the mean flow and fluctuating velocities were evaluated from 500 instantaneous velocity fields captured at 15 frames/s by a CCD camera in the Reynolds number range Re = (3–15) 104. The observations were made in the area 60 mm 60 mm. The PIV analysis was conducted using the interrogation window size 31 31 pixels with 50% overlap, where the sub-pixel interpolation was incorporated into the analysis [42]. The maximum pixel displacement of the particle images was about 4 pixels in the velocity measurements by tuning the time interval
Fig. 3. Experimental test section for velocity measurements.
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between the two sequential images. As a result, the number of invalid velocity vectors was found less than 1% of the total. The uncertainty in velocity measurement was estimated 4.9% at 95% confidence level with respect to the maximum velocity, while it increased near the wall owing to the increased image deformation near the acrylic resin–water interface [38]. The details of this uncertainty analysis has been described in Ref. [38]. 2.4. Evaluation of separation and reattachment points by near-wall PIV measurement The separation and reattachment points of the separating flow on the inner wall was determined from the mean velocity profiles of the near-wall PIV measurement. This experimental technique relies on the transformation of image in boundary-fitted coordinates into rectangular image and the PIV analysis, followed by the transformation back into the velocity field in the original coordinates [43]. The PIV analysis with the sub-pixel interpolation technique was carried out using the interrogation window size 21 41 pixels with 50% overlap because of the high-resolution requirement in vertical coordinate y from the wall. The observation area of the near-wall PIV measurement was 30 mm 30 mm, and the nearest velocity vectors to the wall were obtained at y = 0.2 mm. The separation and reattachment points were obtained at the beginning and end of the reverse flow at the nearest point to the wall. 3. Results and discussion 3.1. Distribution of mass transfer coefficients in short elbow Fig. 4(a), (b), and (c) show the cross-sectional distributions of mass transfer coefficients in the 90° short elbow at three Reynolds numbers Re = 3 104, 5 104, and 10 104 measured by the plaster dissolution method. The experimental results were averaged over ±5° in circumferential angle of the elbow obtained from three repeated experiments. In the figures, scattering of the data is shown by the error bars. Note that each circular graph shows the normalized mass transfer coefficient K/K0 plotted against the circumferential angle h from the outer wall of the elbow. When K/ K0 equals to 1, the local mass transfer coefficient in the elbow is the same magnitude as that of the straight pipe. Note that the circumferential angle h = 0° corresponds to the outer wall, h = 180° is the inner wall, and h = 90° and 270° are the side walls, as illustrated in Fig. 1(b). Fig. 4(a) and (b) show the normalized mass transfer coefficients at lower Reynolds numbers (Re = 3 104 and 5 104), respectively, for some elbow angles a = 0°, 22.5°, 45°, 67.5°, and 90°. Both results show a similar mass transfer variation with elbow angle a. The mass transfer coefficient is almost equal to 1 at the inlet of the elbow at a = 0°, while it shows a large variation in magnitude with increasing a on the inner wall, which is apparent on the inner wall of the elbow. A detailed examination on the mass transfer distribution shows that K/K0 on the inner wall decreases at a = 22.5° (Fig. 4 (a) and (b)) with respect to that on the elbow inlet (a = 0°), while it increases on the side walls and retains the same magnitude on the outer wall. A similar trend is observed for the elbow angle a = 45° although there is a local minimum ±20° on both sides of the elbow centerline. This variation of mass transfer coefficient with the elbow angle may be related to the start of high mean velocity of converging flow outside the separating flow region on the inner wall of the elbow, which is shown in Fig. 11. With further increases in the elbow angle to a = 67.5° and 90°, the mass transfer coefficient on the side wall keeps roughly the same magnitude as that of a = 45°; nevertheless, the significant increase is observed on
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both sides of the inner wall at h = ±20–25° (double peaks), where the mass transfer coefficient reaches almost twice the magnitude of the smooth pipe. This was not observed in the long elbow; therefore, it can be considered as a special feature of the short elbow. When the Reynolds number of the flow through the elbow increases to Re = 1 105 (Fig. 4(c)), the mass transfer coefficient distribution changes drastically owing to its influence. Otherwise, the mass transfer coefficient decreases on the inner wall of the elbow (a = 22.5° and 45°), while it increases on the inner side walls (a = 67.5° and 90°) that results to the disappearance of the double peaks on the mass transfer distribution and to a more uniform mass transfer coefficient distribution on the inner wall of the elbow. Therefore, the mass transfer distribution on the whole elbow at higher Reynolds numbers (Re = 1 105) behaves differently from that at the lower Reynolds number (Re = (3–5) 104). It is seen that the double peaks are suppressed on both sides of the elbow centerline, while the mass transfer coefficient on the inner wall near the centerline retains the high magnitude. This can be caused by variation of the flow field on the inner wall at higher Reynolds number, which is the formation of separating flow region on the second half of the inner wall of the short elbow shown in Fig. 5. On the other hand, the mass transfer coefficient on the outer elbow wall slightly decreases at high Reynolds number (Re = 1 105), which results in a mass transfer coefficient smaller than the straight pipe. This may be due to the flow acceleration effect on the outer elbow wall by increasing the Reynolds number. Fig. 4(d) shows a comparative study of mass transfer coefficient distribution at a = 90° of the short (r/d = 1.0) and long (r/d = 1.5) elbows at two Reynolds numbers Re = 5 104 and 1 105, which are the typical values used in this study. The double peaks on both sides of the centerline and the single peak on the long elbow around it, indicates that the major difference of mass transfer distribution appears on the inner short elbow wall at a low Reynolds number. When the Reynolds number is increased to Re = 1 105, both the observed double peaks and single peak are decreased on the inner elbow wall, while they are increased on the neighboring side wall, which results in a uniform mass transfer distribution on the inner elbow wall in the circumferential direction. A decrease in the mass transfer coefficient is observed on the outer elbow wall on short and long elbows. 3.2. PIV measurement of velocity field over the separating flow region To characterize the separating flow behavior on the inner wall of the elbow, the velocity field on the second half of the elbow’s inner wall was measured by a planar PIV at some Reynolds numbers Re = (3–15) 104. Fig. 5(a)–(c) show the axial cross-section of mean velocity distributions of the flow at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. It is observed that the high velocity region prevails near the inlet of the inner wall of the elbow, where the mass transfer coefficient stays in a low level, as seen in the mass transfer coefficient in Fig. 4. This result indicates that the mass transfer coefficient near the elbow inlet does not increase in proportional to the velocity magnitude of the flow. This suggests that the influence of turbulence on the mass transfer is more pronounced than that of the velocity magnitude. The mean velocity contour in Fig. 5(a) shows a clear indication of flow separation and prevails over the downstream region of the elbow. The separating flow region ends by the flow attachment at x/d = 0.5 on the downstream of the elbow. When the Reynolds number is increased to Re = 5 104, the separation point is approximately the same as the lower Reynolds number case (Re = 3 104), but the reattachment point moves upstream, resulting in a decrease in the axial length of the separating flow region.
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(a) Re = 3
104
(c) Re = 1
105
(b) Re = 5
104
(d) Comparison with long elbow ( = 90°) Fig. 4. Cross-sectional mass transfer distributions in short elbow.
(a) Re = 3×104
(b) Re = 5×104
(c) Re = 1×105
Fig. 5. Mean velocity contours in and downstream of short elbow (S: separation, R: reattachment).
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With a further increase in the Reynolds number to Re = 1 105, the separating flow region becomes much smaller than that of the low Reynolds number; however, the lower velocity region still remains in the elbow downstream. A detailed examination of the mean velocity over the inner elbow wall and downstream can be performed in the mean velocity profiles in Fig. 6, which shows the near-wall velocity distribution more clearly. The results indicate the delay of flow separation on the inner wall by increasing the Reynolds number, and the subsequent recovery of the mean velocity in the elbow downstream. Fig. 7(a), (b), and (c) show the axial turbulence intensity contour in the second half of the elbow and downstream at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. The turbulence intensity increases near the separation points and develops along the shear layer, which results in the formation of high turbulence in the elbow downstream. By increasing the Reynolds number, the magnitude of axial turbulence intensity increases along the shear layer but the highly turbulent region is suppressed because of the decrease in the separating flow region on the inner wall of the elbow (Fig. 5). Note that the increase of turbulence intensity in the shear layer at higher Reynolds number is related to the separating flow behavior near the separation point. A detailed examination of the axial turbulence intensity profiles in and downstream of the short elbow is shown in Fig. 8. The results indicate that the maximum axial turbulence intensity is located near the wall at higher Reynolds numbers, which is caused by the downstream movement of the separation point. This results in the higher axial turbulence intensity near the wall and lower
intensity in the far region of the inner wall at higher Reynolds numbers. The turbulence intensity profile recovers downstream of the elbow, in which the behavior of the reattachment-point variation seems to be independent with the Reynolds number. 3.3. Characteristics of separation and reattachment points To clarify the Reynolds number effect on the separating flow region, the near-wall mean velocity profiles are measured by the near-wall PIV, owing to the high spatial resolution requirement of the near-wall velocity to obtain the separation and reattachment points. Sample mean velocity profiles near the separation point are illustrated in Fig. 9 at Re = 3 104, 5 104, and 1 105. The results show that the flow separation occurs at a = 36° (Re = 3 104), a = 39° (Re = 5 104), a = 48° (Re = 1 105), which are the start of reverse flow in the near-wall velocity profiles. The separation and reattachment points obtained from the near-wall PIV measurements with respect to the Reynolds number Re are summarized in Fig. 10. The results indicate that the separation point behaves weakly dependent on the Reynolds number and moves slightly downstream with an increase in the Reynolds number. On the other hand, the reattachment point moves upstream with increasing Reynolds number, which is apparent on the low Reynolds number. Therefore, the axial length of the separating flow region, which corresponds to the axial distance between the separation and reattachment points, decreases with increasing Reynolds number. The variation of the axial length seems to be saturated at higher Reynolds numbers (Re = (10–15) 104). The
Fig. 6. Mean velocity distributions in and downstream of short elbow.
(a) Re = 3×104
1111
(b) Re = 5×104
(c) Re = 1×105
Fig. 7. Axial turbulence intensity contours in and downstream of short elbow (S: separation, R: reattachment).
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Fig. 8. Axial turbulence intensity distributions in and downstream of short elbow.
Fig. 9. Example of mean velocity profiles near separation point (S: separation).
Fig. 10. Downstream variation of separating flow region in and downstream of short elbow.
uncertainties in separation and reattachment points are shown by error bars in Fig. 10, which are obtained from the repeated experiments. Fig. 11 shows the mean velocity distribution over the inner wall of the elbow and downstream in the cross-sectional plane parallel to the inner wall at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively. The light-sheet plane from the inner wall was set to y = 4 mm. The results indicate that the separating flow region is formed in the mid plane down to x/d = 0.5 at a lower Reynolds number (Re = 3 104). With an increase in the Reynolds number (Re = 5 104), the separation region decreases mainly due to the reattachment point movement, and it is almost diminished at a higher Reynolds number (Re = 1 105) because of the
small distance from the inner wall. These results agree with the observation of reattachment points in Fig. 10. This figure also shows the circumferential distribution of separating flow region, which extends to z/d = ±0.07 that corresponds to ± 8° on the inner wall of the elbow. The mean velocity distribution around the separating flow region indicates the formation of conversing flow in its downstream, which shows a local maximum velocity on both sides of the elbow centerline z/d = ±0.19 (22°). It should be mentioned that the velocity gradient in z direction gradually decreases with an increase in the Reynolds number because of the decrease in the separating flow region. Fig. 12 shows the corresponding axial turbulence intensity contours in the cross-sectional plane parallel to the inner wall at three Reynolds numbers Re = 3 104, 5 104, and 1 105, respectively, with a distance y = 4 mm from the inner wall. The turbulence intensity contour at Re = 3 104 shows the high turbulence intensity on both sides of the elbow centerline, which corresponds to the outer shear layer surrounding the separating flow region z/ d = ±0.16 (19°). It should be mentioned that the highly turbulent intensity region is located in the middle of the shear layer with high velocity gradient and is slightly closer to the elbow centerline than the position of maximum velocity. By increasing the Reynolds number to Re = 5 104, the high turbulence intensity region comes closer to the elbow centerline and they almost merge at a higher Reynolds number (Re = 1 105). It should be mentioned that the location of the maximum turbulence intensity z/d = ±0.16 (±19°) agrees with that of the double peak positions (±20°) in the mass transfer distribution (Fig. 4). This suggests that the double peaks
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(a) Re = 3×104
(b) Re = 5×104
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(c) Re = 1×105
Fig. 11. Near-wall mean velocity contours in horizontal cross section.
(a) Re = 3 × 104
(b) Re = 5 × 104
(c) Re = 1 × 105
Fig. 12. Near-wall axial turbulence intensity contours in horizontal cross section.
in mass transfer distribution may be caused by the local high turbulence. Furthermore, the Reynolds number effect on the maximum turbulence intensity position is similarly observed in the behavior of double peak positions in the mass transfer coefficient, which comes closer to the elbow centerline with an increase in Reynolds number. Therefore, the high mass transfer coefficient on the inner wall of the elbow is considered to be from the high turbulence intensity on the inner wall caused by the high velocity gradient of the converging shear layer on both sides of the elbow centerline. It should be mentioned that the mass transfer in the flow through the elbow is associated with the turbulence as well as the dynamic behavior of vortex shedding from the flow separation in the elbow, both of them contribute to the growth of mass transfer in and downstream of elbow. 4. Conclusion The mass transfer coefficient distribution and flow separation behavior in a 90° short elbow with a radius to pipe diameter ratio of 1.0 were experimentally studied using the plaster dissolution method and PIV measurements in a Reynolds number range Re = (3–15) 104. The influence of Reynolds number on the mass transfer coefficient distribution was observed to be weak in the first half of the inner elbow wall, while it showed a large change in the second half, where the double peaks in mass transfer distribution occur on both sides of the elbow centerline on the inner wall. To understand this phenomenon, PIV measurements were carried out on the inner elbow wall and the flow separation and reattachment in the second half of the elbow were observed. The high mass transfer characteristics on the inner wall of the second half of the elbow was found to be highly correlated with the separating flow behavior in and downstream of the short elbow. With an increase in the Reynolds number, the separation point moves downstream while the reattachment point moves upstream, which results in the suppression of the separation region. Furthermore, the circum-
ferential extent of the separation region decreases with increasing Reynolds number, which arises from the shift of converging flow on both sides of the separating flow region. Thus, the high turbulence intensity region comes closer to the elbow centerline with increasing Reynolds number, and its variation with the Reynolds number on both sides of the centerline, is consistent with that of the high mass transfer region. Therefore, the high mass transfer behavior in the 90° short elbow arises from the generation of separating flow region and the behavior of converging flow over the inner wall of the elbow. Conflict of interests The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported. Acknowledgements This work was supported by JSPS KAKENHI Grant Number JP18K04632. The authors acknowledge the helpful suggestions of Dr. T. Yamagata of Niigata University, Dr. F. Inada, and Dr. K. Fujiwara from Central Res. Inst. of Electric Power Industry, during the study. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.076. References [1] F.P. Berger, K.F.F.L. Hau, Mass transfer in turbulent pipe flow measured by the electrochemical method, Int. J. Heat Mass Transf. 20 (1977) 1185–1194. [2] T. Sydberger, U. Lotz, Relation between mass transfer and corrosion in a turbulent pipe flow, J. Electrochem. Soc. 129 (1982) 276–283.
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