- Email: [email protected]
Mechanistic modeling for ring-type BWR fuel spacer design
Nuclear Engineering and Design 201 (2000) 177 – 188 www.elsevier.com/locate/nucengdes
Mechanistic modeling for ring-type BWR fuel spacer design 1. Drift flow model Takashi Yano a,*, Ei-ichiro Kodama b,1, Masanori Aritomi a, Hiroshige Kikura a, Hiroyuki Obata c,2 a
Research Laboratory for Nuclear Reactors, Aritomi Laboratory, Tokyo Institute of Technology, 2 -12 -1 O-okayama, Meguro-ku, Tokyo, 152 -8550 Japan b Visual Technology Inc., 1 -9 -15 Kaigan, Minato-ku, Tokyo, 105 -0022 Japan c The Japan Atomic Power Company Co. Ltd., 1 -5 -1 Ohtemachi, Chiyoda-ku, Tokyo, 100 -0004 Japan Received 27 October 1999; accepted 1 December 1999
Abstract The fuel spacer is one of the components of a fuel rod bundle and its role is to maintain an appropriate rod-to-rod clearance. Since the fuel spacer influences liquid film flow on fuel rods in BWR core, its specification has a strong effect on thermal hydraulics in the core such as critical power and pressure drop. Spacers have been developed through empirical modifications, so that a large amount of test data are required for optimum design of the spacer. It is, therefore, important to develop a mechanistic model of the spacer for future design of BWR fuel bundles. The authors considered that enhancement of droplet deposition is induced downstream of the spacer where velocity profiles split by a spacer are recovered into one velocity profile; higher velocity in the core and lower velocity in a gap clearance between the rod surface and the spacer. In this paper, the effect of spacer geometry on the droplet deposition rates downstream of it was investigated experimentally in a open rectangular channel using air and water as test fluids. A Phase Doppler Anemometer (PDA) was used for this measurement. In addition, velocity profile equations were obtained from the drift flow model. From these results, a mechanistic model of enhancing droplet deposition rate downstream of the spacer was proposed. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Two-phase flow; BWR fuel spacer; Drift flow; Annular mist flow; Phase Doppler anemometer; Droplet deposition rate; Critical power; Liquid film; Spacer model
1. Introduction * Corresponding author. Tel.: +81-3-57343063; fax: + 813-57342959. E-mail address: [email protected] (T. Yano). 1 Tel.: +81-3-34340345; fax: + 81-3-34340357. 2 Tel.: +81-3-32016631; fax: + 81-3-32110788.
Toward the top of a Boiling Water Reactor (BWR) fuel rod bundle, the flow pattern becomes annular-dispersed because of the large vapor fraction. A thin liquid film flows upward on the fuel rod surface and channel walls and vapor entrain-
0029-5493/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0029-5493(00)00279-X
178
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
ing liquid droplets flow in the core whose velocity is about 12 m s − 1 at the exit of the core under the rate power condition. The distribution of liquid and steam flows in the fuel bundle is the most important factor for the phenomenon of heat transfer deterioration (film dryout). The fuel spacer is one of the components of a fuel rod bundle and its role is to maintain an appropriate rod-to-rod clearance. The fuel spacer affects the liquid film flow distribution in the fuel rod bundle, so that the spacer geometry has a strong effect on thermal hydraulic characteristics such as critical power and pressure drop in the fuel bundle. BWR vendors have been developing fuel spacers using large-scaled test loops simulating an actual bundle geometry, which yields critical power data under actual BWR operating conditions. However, such testing requires long periods of operation and is costly. Since the spacer has been developed through empirical modifications, a large amount of test data are required to attempt to optimize the spacer geometry. Hence, it is necessary to develop a mechanistic model of the spacer for optimum design of the advanced fuel bundles. Previous modeling of the spacer effect on droplet deposition rate downstream of the spacer is based on the eddy diffusivity. Lahey et al. (1972) proposed the effect for the grid-type spacer introducing an empirical coefficient obtained by experimental data under BWR operating conditions. Recently, some numerical approaches have been performed considering the turbulence of the gas phase induced by the spacer. In the case of ring-type spacers, for example, Yamamoto et al. (1996) calculated droplet trajectories by adopting large eddy simulations in a vapor phase and obtained droplet deposition rates assuming that droplets were transferred by turbulence diffusivity. In their calculation, averaged turbulence diffusivity over the cross section was considered as the driving force for enhancement of the droplet deposition rate. As a result, the turbulence intensity becomes maximum when the spacer is far from the wall surface, and the clearance effects of spacer on the enhancement of the droplet deposition rate cannot be expressed in their model.
On the other hand, in their experimental results of liquid film measurement downstream of the spacer under air–water conditions, Yano et al. (1995) discussed that the droplets deposit in as short a length as about 125 mm (L/DH =10). Turbulence enhancement induced by the spacer is not strong enough to make droplets deposit in such a short length. Therefore, the authors thought that the ‘drift’ flow effect, caused by the recovery process of flow splits due to the spacer, is a dominant effect on enhancement of the droplet deposition rate downstream of the spacer. There is, however, little information about the effect of spacer geometry on the flow characteristics downstream of the spacer. So the following research plans are made in our work: 1. Droplet deposition distribution profiles downstream of the spacer are investigated experimentally in an open rectangular channel as a fundamental study in order to clarify the ‘drift’ flow effect on enhancement of the droplet deposition rate. 2. The local spacer pressure drop is investigated experimentally for various ring-type spacers to clarify the ‘narrow channel’ effect on the split flow and is modeled. 3. The ring-type spacer geometry is modeled mechanistically by integrating the following three effects; the ‘drift’ flow effect, the ‘narrow channel’ effect and the ‘run off’ effect that the liquid film on the spacer formed by droplet deposition is dispersed again. The liquid film flow characteristics downstream of the ringtype spacer are investigated experimentally in a circular channel to confirm the appropriateness of the proposed spacer model. The purpose of this paper is to clarify and model the ‘drift’ flow effect of spacer geometry on the lateral gas velocity distribution which enhances the droplet deposition rates and greatly influences critical power performance. Droplet velocities were measured by Phase Doppler Anemometer (PDA) using air and water as test fluids in a open rectangular channel. Next, the drift flow model was derived by considering two velocity profiles split by the spacer. From these results, a mechanistic model of enhancing droplet deposition rate downstream of the spacer was proposed.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
179
2. Experimental
2.1. Experimental apparatus Fig. 1 shows the experimental apparatus. It was composed of air and water supply systems, two
Fig. 3. PDA measurement section.
Fig. 1. Experimental apparatus.
Fig. 2. Schematic view of droplets mixing section 1.
air/water mixing sections and a test section. Air was supplied from a compressor. The air supply pressure was regulated by a pressure regulation valve installed upstream of the laminar flow meter for measurement of the air flow rate and regulated by a flow control valve. Thermocouples and a pressure transducer were attached to the flow meter to measure air temperature and pressure at the entrance of the test section. After the supplied air passes through the flow meter, part flows into an air/water mixing section 1 as shown in Fig. 2 and attached to the air supply loop to suspend micro-scale water droplets into air as a tracer. This mixing section was composed of a two-fluid nozzle (IKEUCHI, BIMV45075). The remainder of the supplied air flows directly into mixing section 2. The water flow rate was measured by an orifice flow meter regulated by a flow control valve. A thermocouple was attached to a tank to monitor the supplied water temperature which was controlled and kept constant through a cooler at-
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
180
tached in the tank. The air and water mixture was discharged homogeneously into the test section and a mist flow was formed therein. Fig. 3 shows the test section. If droplets deposit on the channel wall and liquid film flows thereon, the droplet velocity and diameter flowing inside the channel cannot be measured by PDA. Hence, a rectangular spacer was attached to the exit of the test section, and thus open flow characteristics downstream of the mimic spacer were measured. Three kinds of clearance and thickness, that is, nine types of mimic spacers in total were examined in this work. The specification of the spacers used in this work is shown in Fig. 4 and tabulated in
Table 1. In this work, experiments under 10 conditions including the case without a spacer were carried out.
2.2. DualPDA system The DualPDA system (Model I-70, DANTEC/ invent Measurement Technology) basically incorporates two PDA arrangements; a conventional PDA and a planar PDA. The size of a particle is measured with both subsystems simultaneously, with subsequent comparison and validation. This method of size measurement provides a very wide dynamic rage combined with high accuracy which is improved, compared to conventional PDA systems, in particular for applications in dispersed droplets. From the principle that the phase difference of Doppler signals detected at two or more locations is proportional to the droplet diameter, the velocity and diameter of entrained droplets can be measured simultaneously without disturbing flow.
2.3. Experimental procedure
Fig. 4. Geometrical shapes of test piece installation position. Table 1 Geometric dimensions of test spacers Spacer number
Thickness (t) (mm)
Clearance (c) (mm)
1 2 3 4 5
1 2 3 2 2
2 2 2 1 3
3. Experimental results
Table 2 Experimental conditions System pressure Superficial air velocity, jg (m s−1) Number of measured droplets Air temperature (°C) Water temperature (°C)
The experimental conditions are shown in Table 2. The measured positions were changed in the horizontal direction, from spacer to 10 mm at intervals of 0.5 mm (21 positions), and in the vertical downward direction, from spacer to 10, 20, 30, 40, 70 and 100 mm (seven positions), so that there were 147 positions in total. The axis of coordinates is shown in Fig. 5. The droplet velocity and diameter consist on average of 10 000 counts.
1 atm 30, 45, 60, 75 10 000 11–18 11–20
The range of measurements with the DualPDA system are shown in Table 3. At first, two-dimensional velocity profiles and droplet diameter distribution were measured under various gas superficial velocity conditions with no spacer. Typical measured results are shown in Fig. 6(a– c). It was confirmed from Fig. 6 (a) that water droplet diameter was very small (about 30 mm) and that the mean velocity of droplets is nearly
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
181
defined as flow from the wider channel to the narrower one. Fig. 7(a,b) shows typical measured results of two-dimensional velocity profiles along the flow direction in reference to the mimic spacer clear-
Fig. 5. Explanation of coordinates. Table 3 The range of measurements in the DualPDA system Velocity, Vx (m s−1) Velocity, Vy (m s−1) Diameter, Dp (mm)
−57.02–169.031 −32.45–32.45 0.41321–169.03
equal to gas superficial velocity. Furthermore, the droplet diameter even at the higher gas superficial velocity of jg =75 m s − 1 is the same order as at the velocity of jg =30 m s − 1. It can be regarded for such as a small diameter droplet that the droplet velocity becomes almost the same as the gas velocity. Longitudinal droplet velocity distributions downstream of the exit of the flow channel have a mild center peak profile near the exit and become flat further from the exit as shown in Fig. 6(b). The average droplet velocity integrated over the measurement points near the exit of the flow channel was almost equal to the gas flow rate. Hence, it seems that the droplet velocity can be regarded as the gas velocity. Fig. 6(c) shows typical measured droplet velocity distributions at the same positions as Fig. 6(b). A positive value is
Fig. 6. An example of the experimental results with no spacer ( jg =30 m s − 1).
182
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
in order to eliminate the diverging effect of the channel induced mist flows discharged into the open space. It can be seen from the figure that lateral flow from the wider to narrower channels is induced downstream of the exit of the test section and becomes positive and large near the spacer as shown at 1 mm. Fig. 8 shows the typical differential lateral velocity profiles at the center line of the spacer thickness along with the flow direction. Going further from the exit of the test section, the differential lateral velocity linearly increases by 70 mm from the exit, has a peak value at 70–80 mm from the exit and linearly decreases downstream of that. The peak value becomes larger with an increase in the gas velocity.
Fig. 7. Distribution of gas velocities downstream of the spacer ( jg = 30 m s − 1).
ance. The spacer position is shown as the break line in these figures. It can be seen from Fig. 7(a) that longitudinal velocity profiles, Vx(y), are different between wider and narrower regions near the exit of the test section because the flow channel is split by the spacer and the frictional losses are different from each channel. The difference between velocity profiles becomes uniform further from the exit of the test section. The differential lateral velocity profiles, Vy(y), are obtained by subtracting the lateral velocity profile measured under the condition with a spacer as shown in Fig. 7(b) from that under the condition without a spacer as shown in Fig. 6(c)
Fig. 8. Lateral velocity distributions downstream of spacers.
Fig. 9. Droplet diameter distributions downstream of the spacer.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
183
recovered into one developed velocity profile in a short length about 100 mm (L/D= 10) downstream of the spacer. The drift flow model is illustrated in Fig. 10. Gas velocities, which flow both in the center core and the gap clearance, are evaluated by a consideration of mass and pressure balances in these regions. rgVnAn + rgVwAw = rgV0A0
(1)
where rg is gas density, V is gas velocity and subscripts n, w and 0 are narrow and wide channels split by the spacer, and test channel upstream of the spacer, respectively. The gas velocity upstream of the spacer, V0, becomes equal to the superficial gas velocity, jg. Eq. (1) can be rewritten as: VnAn + VwAw = jgA0
(2)
The friction and choking losses are considered in the momentum balance. Fig. 10. Definition of virtual boundary.
Fig. 9 shows droplet diameter profiles measured 10 mm downstream of the spacer. The droplet diameter becomes larger near the spacer end (y= 0–4 mm) at the high gas velocity. A great deal of droplets deposit on the spacer surface and form liquid film flow thereon. Then, the liquid film is entrained again with the larger droplet size at the end of the spacer, and the droplets flow together with the air flow motion. This phenomenon is called ‘run off’. With increasing air flow rates, the amount of air flow colliding against the spacer surface increases, so that the liquid film flowing on the spacer surface becomes thicker and the droplet size increases. As the spacer thickens, the amount of droplets deposited on the spacer surface increases and the droplet size becomes larger.
4. Modeling of droplet deposition
4.1. Drift flow model This induces drift flows that the spacer splits the mixture flow in the channel into the narrower and wider channel and that the split flows are
(Pz + Pfric)n(DPz + Pfric)w
(3)
DPz = z·(1/2)rg(Vi)2
(4)
z= ((1/Cc)−1)2
(5)
Cc= Ai/Aup,i
(6)
DPfric = fi/(2Di)·rg(Vi)2·L
(7)
where subscript ‘i’ expresses narrower (n) or wider (w). A means the cross section at each channel and Aup is the virtual cross section in the upper stream for each channel split by the virtual boundary line shown in Fig. 10. Di is the hydraulic diameter of each channel. L is the spacer height (35 mm constant). Frictional loss can be expressed as follows: fi = 0.3164/Re%0.25 i
(8)
Re%i = ViDi/ng
(9)
In the ‘drift’ flow model, virtual boundary coefficient is assumed as the ratio of the cross section in the narrower channel to that in both flow channels written as below Cvb = An/(An + Aw)
(10)
The effect of the clearance on drift flow rates was investigated experimentally and analytically.
184
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
A typical comparison between the experimental and analytical results is shown in Fig. 11(a). The symbols, and mean the experimental and analytical results, respectively. The gas flow rates
in the narrower channel calculated by the drift flow model are in good agreement with the experimental results. The clearance greatly influences the gas flow rates in the narrower channel and thus the gas velocity therein increases with an increase in the clearance because the friction and choking losses become smaller. The difference of air flow rates between both channels becomes smaller with increasing clearance. On the other hand, the air velocity in the wider channel does not vary with a change in the clearance because the friction and the choking losses scarcely change. Since the gas velocities were measured 10 mm downstream of the test section, the gas flow is diverged for discharge to the open channel. As a result, the analytical results of the gas flow rates show slightly higher values than the experimental ones in the wider channel. Next, the effect of spacer thickness on drift flow rates was investigated experimentally and analytically. A typical comparison between the experimental and analytical results is shown in Fig. 11(b). The analytical results in both channels increase with spacer thickness and have the same tendency as the experimental data. The analytical air velocities in the wider channel are slightly larger than the experimental values. Since, the whole flow area is reduced as the spacer becomes thicker, the flow rates both in the narrower and wider channels increase for the thicker spacer.
4.2. Formulation of droplet deposition profile Fig. 11. Comparison of drift velocity data and analytical results ( jg =30 m s − 1).
Fig. 12. Definition of lateral velocity profile.
The formulation of the droplet deposition rate profile was attempted using the proposed drift flow model. The peak value for lateral velocity, Vypeak and its point for the axial direction, Xpeak, were defined as shown in Fig. 12 and were formulated by the drift flow model. The lateral velocity profile was divided into two regions, by the peak point Xpeak, where the lateral peak velocity appears as shown in Fig. 12; the proximal and distal regions from the spacer. The distal region was considered up to L/D=15 from the spacer. The lateral velocity profile was approximated as a linear function both in the proximal and distal regions.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
Fig. 13. Wide channel velocity effects on lateral peak velocity (thickness=2 mm).
Fig. 14. Wide channel velocity effects on lateral peak velocity (clearance= 2 mm).
Figs. 13 and 14 show the effect of the velocity differentials between the wider channel and upstream of the spacer, where almost superficial velocity, Vw −jg, on the lateral peak velocity, Vypeak, in reference to clearance for a constant spacer thickness of 2 mm and in reference to spacer thickness for a constant clearance of 2 mm, respectively. It can be seen from both figures that the lateral peak velocity is almost proportional to the velocity in the wider channel. Then, the effect of gas Reynolds number in the wider channel on the dimensionless lateral peak velocity was examined and the results are demonstrated in Fig. 15. The peak value was expressed as follows
185
Fig. 15. Wide channel velocity effects on lateral peak velocity (all conditions).
Fig. 16. Narrow channel velocity effects on axial distance of lateral peak velocity (thickness = 2 mm).
Fig. 17. Relationship of narrow channel Reynolds number and axial distance of lateral peak velocity.
186
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
ng Rew DH
(11)
Rew = (Vw − V0)·DH/ng
(12)
Vypeak = 0.118
Fig. 18. Relationship of velocity gradient behind peak value and Reynolds numbers obtained by drift velocities.
where DH is the typical length of the test section (10 mm). Superficial velocity, jg, was used for the upstream velocity (V0) in this study because of the discharge to the open channel. Fig. 16 shows the relationship between the dimensionless peak point (Xpeak/DH) and the narrower velocity. The dimensionless peak point increases with an increase in the narrower velocity. The lateral velocity profile is formed as a consequence of counteracting the velocities going toward the position of the spacer in both channels. As result, the peak point is shifted downstream with an increase in the narrower channel velocity. Furthermore, it seems that clearance infl-
Fig. 19. Comparison of lateral velocity profile data and present equation ( jg =30 m s − 1).
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
uences the peak point. The clearance, c, was used as the reference length for the Reynolds number in the narrow channel to introduce the effect of clearance. The relationship between the Reynolds number in the narrow channel and the dimensionless peak point can be arranged as shown in Fig.
187
17. The dimensionless peak point can be expressed as follows: Xpeak/DH = 2.65Re0.12 n
(13)
Ren = Vn·c/ng
(14)
From the above-mentioned results, the lateral velocity profile from x= 0 to Xpeak can be expressed as: Vy(x)=
Vypeak n x x= 0.0445 g Ren− 0.12Rew Xpeak DH DH (15)
On the other hand, as the lateral velocity profile in the distal region has the relation to the proximal region of the spacer, the profiles arranged with the same factors as Eq. (15) are shown in Fig. 18. (Vypeak − Vy150) n = − 0.035 g Ren− 0.12Rew (Xpeak − 0.15)/DH DH (16) Therefore, the lateral velocity profile in the distal region of the spacer (x\ Xpeak) can be expressed as follows. Vy(x)= Vypeak − =
(Vypeak − Vy150) (x−Xpeak) (Xpeak − 0.15)/DH DH
ng x Re 0.211− 0.035Ren− 0.12 DH w DH
(17)
Figs. 19 and 20 show the comparisons between the experimental and analytical results of perpendicular velocity profiles downstream of the spacer. These figures in portrait orientation show the spacer thickness effect. The landscape orientation in Fig. 19 shows the clearance effect. Fig. 20 shows the results with reference to gas velocity, jg = 30, 45, 60, 75 m s − 1. The solid lines shown in the figure mean the velocity profile calculated from the proposed correlation. It can be seen from Figs. 19 and 20 that the proposed correlation can describe the experimental results well.
5. Conclusions Fig. 20. Comparison of lateral velocity profile data and present equation (thickness = 2 mm, clearance = 2 mm).
The effect of spacer geometry on the droplet deposition rates downstream of the spacer was
188
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
investigated in an open rectangular channel using air and water as test fluids, and the following have been clarified. 1. The difference of velocities split by the spacer decreases with an increase in clearance. As a result, the deposition rate of droplets decreases as the clearance becomes wider. 2. Since the velocity in the wider channel increases with an increase in the spacer thickness, the deposition rate of droplets increases as the spacer becomes thicker. 3. The run-off effect was confirmed from the measured lateral profiles of droplet diameter distribution. 4. The drift flow model incorporating the frictional and choking losses is proposed. The proposed model can explain the experimental results of the split flow rates downstream of the spacer. 5. The correlation of the droplet deposition rate downstream of the spacer is proposed along the flow direction. In order to confirm the above-mentioned conclusions, the authors are investigating the liquid film characteristics downstream of mimic spacers in a circular channel as integral tests.
Acknowledgements This work has been carried out at the Tokyo Institute of Technology in collaboration with The Japan Atomic Power Company Co. Ltd.
.
Appendix A. Nomenclature P r m V A Subscripts g n w 0 cr crup i fric z
pressure (Pa) density (kg m−3) static viscosity (N s m−2) velocity (m s−1) cross-sectional area (m2) gas phase narrower wider upper stream of the spacer clearance part upstream of clearance part n or w friction choking
References Lahey, R.T., Shiralkar, B.S., Radcliffe, D.W., Polomik, E., 1972. Out-of-Pile Subchannel Measurements in a NineRod Bundle for Water at 1000 psia. Progress in Heat and Mass Transfer, vol. VI. Pergamon, Oxford. Yamamoto, Y., et al., 1996. Boiling transition phenomenon in BWR fuel assemblies (effect of fuel spacer shape on critical power). J. Atom. Energ. Soc. Japan 38 (4), 315– 323 in Japanese. Yano, T. et al., 1995. Annular two-phase flow characteristics in a circular tube. In: Proceedings of the 2nd International Conference on Multiphase Flow’95, Kyoto, Vol. 1, IP2-19.
Mechanistic modeling for ring-type BWR fuel spacer design 1. Drift flow model Takashi Yano a,*, Ei-ichiro Kodama b,1, Masanori Aritomi a, Hiroshige Kikura a, Hiroyuki Obata c,2 a
Research Laboratory for Nuclear Reactors, Aritomi Laboratory, Tokyo Institute of Technology, 2 -12 -1 O-okayama, Meguro-ku, Tokyo, 152 -8550 Japan b Visual Technology Inc., 1 -9 -15 Kaigan, Minato-ku, Tokyo, 105 -0022 Japan c The Japan Atomic Power Company Co. Ltd., 1 -5 -1 Ohtemachi, Chiyoda-ku, Tokyo, 100 -0004 Japan Received 27 October 1999; accepted 1 December 1999
Abstract The fuel spacer is one of the components of a fuel rod bundle and its role is to maintain an appropriate rod-to-rod clearance. Since the fuel spacer influences liquid film flow on fuel rods in BWR core, its specification has a strong effect on thermal hydraulics in the core such as critical power and pressure drop. Spacers have been developed through empirical modifications, so that a large amount of test data are required for optimum design of the spacer. It is, therefore, important to develop a mechanistic model of the spacer for future design of BWR fuel bundles. The authors considered that enhancement of droplet deposition is induced downstream of the spacer where velocity profiles split by a spacer are recovered into one velocity profile; higher velocity in the core and lower velocity in a gap clearance between the rod surface and the spacer. In this paper, the effect of spacer geometry on the droplet deposition rates downstream of it was investigated experimentally in a open rectangular channel using air and water as test fluids. A Phase Doppler Anemometer (PDA) was used for this measurement. In addition, velocity profile equations were obtained from the drift flow model. From these results, a mechanistic model of enhancing droplet deposition rate downstream of the spacer was proposed. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Two-phase flow; BWR fuel spacer; Drift flow; Annular mist flow; Phase Doppler anemometer; Droplet deposition rate; Critical power; Liquid film; Spacer model
1. Introduction * Corresponding author. Tel.: +81-3-57343063; fax: + 813-57342959. E-mail address: [email protected] (T. Yano). 1 Tel.: +81-3-34340345; fax: + 81-3-34340357. 2 Tel.: +81-3-32016631; fax: + 81-3-32110788.
Toward the top of a Boiling Water Reactor (BWR) fuel rod bundle, the flow pattern becomes annular-dispersed because of the large vapor fraction. A thin liquid film flows upward on the fuel rod surface and channel walls and vapor entrain-
0029-5493/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0029-5493(00)00279-X
178
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
ing liquid droplets flow in the core whose velocity is about 12 m s − 1 at the exit of the core under the rate power condition. The distribution of liquid and steam flows in the fuel bundle is the most important factor for the phenomenon of heat transfer deterioration (film dryout). The fuel spacer is one of the components of a fuel rod bundle and its role is to maintain an appropriate rod-to-rod clearance. The fuel spacer affects the liquid film flow distribution in the fuel rod bundle, so that the spacer geometry has a strong effect on thermal hydraulic characteristics such as critical power and pressure drop in the fuel bundle. BWR vendors have been developing fuel spacers using large-scaled test loops simulating an actual bundle geometry, which yields critical power data under actual BWR operating conditions. However, such testing requires long periods of operation and is costly. Since the spacer has been developed through empirical modifications, a large amount of test data are required to attempt to optimize the spacer geometry. Hence, it is necessary to develop a mechanistic model of the spacer for optimum design of the advanced fuel bundles. Previous modeling of the spacer effect on droplet deposition rate downstream of the spacer is based on the eddy diffusivity. Lahey et al. (1972) proposed the effect for the grid-type spacer introducing an empirical coefficient obtained by experimental data under BWR operating conditions. Recently, some numerical approaches have been performed considering the turbulence of the gas phase induced by the spacer. In the case of ring-type spacers, for example, Yamamoto et al. (1996) calculated droplet trajectories by adopting large eddy simulations in a vapor phase and obtained droplet deposition rates assuming that droplets were transferred by turbulence diffusivity. In their calculation, averaged turbulence diffusivity over the cross section was considered as the driving force for enhancement of the droplet deposition rate. As a result, the turbulence intensity becomes maximum when the spacer is far from the wall surface, and the clearance effects of spacer on the enhancement of the droplet deposition rate cannot be expressed in their model.
On the other hand, in their experimental results of liquid film measurement downstream of the spacer under air–water conditions, Yano et al. (1995) discussed that the droplets deposit in as short a length as about 125 mm (L/DH =10). Turbulence enhancement induced by the spacer is not strong enough to make droplets deposit in such a short length. Therefore, the authors thought that the ‘drift’ flow effect, caused by the recovery process of flow splits due to the spacer, is a dominant effect on enhancement of the droplet deposition rate downstream of the spacer. There is, however, little information about the effect of spacer geometry on the flow characteristics downstream of the spacer. So the following research plans are made in our work: 1. Droplet deposition distribution profiles downstream of the spacer are investigated experimentally in an open rectangular channel as a fundamental study in order to clarify the ‘drift’ flow effect on enhancement of the droplet deposition rate. 2. The local spacer pressure drop is investigated experimentally for various ring-type spacers to clarify the ‘narrow channel’ effect on the split flow and is modeled. 3. The ring-type spacer geometry is modeled mechanistically by integrating the following three effects; the ‘drift’ flow effect, the ‘narrow channel’ effect and the ‘run off’ effect that the liquid film on the spacer formed by droplet deposition is dispersed again. The liquid film flow characteristics downstream of the ringtype spacer are investigated experimentally in a circular channel to confirm the appropriateness of the proposed spacer model. The purpose of this paper is to clarify and model the ‘drift’ flow effect of spacer geometry on the lateral gas velocity distribution which enhances the droplet deposition rates and greatly influences critical power performance. Droplet velocities were measured by Phase Doppler Anemometer (PDA) using air and water as test fluids in a open rectangular channel. Next, the drift flow model was derived by considering two velocity profiles split by the spacer. From these results, a mechanistic model of enhancing droplet deposition rate downstream of the spacer was proposed.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
179
2. Experimental
2.1. Experimental apparatus Fig. 1 shows the experimental apparatus. It was composed of air and water supply systems, two
Fig. 3. PDA measurement section.
Fig. 1. Experimental apparatus.
Fig. 2. Schematic view of droplets mixing section 1.
air/water mixing sections and a test section. Air was supplied from a compressor. The air supply pressure was regulated by a pressure regulation valve installed upstream of the laminar flow meter for measurement of the air flow rate and regulated by a flow control valve. Thermocouples and a pressure transducer were attached to the flow meter to measure air temperature and pressure at the entrance of the test section. After the supplied air passes through the flow meter, part flows into an air/water mixing section 1 as shown in Fig. 2 and attached to the air supply loop to suspend micro-scale water droplets into air as a tracer. This mixing section was composed of a two-fluid nozzle (IKEUCHI, BIMV45075). The remainder of the supplied air flows directly into mixing section 2. The water flow rate was measured by an orifice flow meter regulated by a flow control valve. A thermocouple was attached to a tank to monitor the supplied water temperature which was controlled and kept constant through a cooler at-
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
180
tached in the tank. The air and water mixture was discharged homogeneously into the test section and a mist flow was formed therein. Fig. 3 shows the test section. If droplets deposit on the channel wall and liquid film flows thereon, the droplet velocity and diameter flowing inside the channel cannot be measured by PDA. Hence, a rectangular spacer was attached to the exit of the test section, and thus open flow characteristics downstream of the mimic spacer were measured. Three kinds of clearance and thickness, that is, nine types of mimic spacers in total were examined in this work. The specification of the spacers used in this work is shown in Fig. 4 and tabulated in
Table 1. In this work, experiments under 10 conditions including the case without a spacer were carried out.
2.2. DualPDA system The DualPDA system (Model I-70, DANTEC/ invent Measurement Technology) basically incorporates two PDA arrangements; a conventional PDA and a planar PDA. The size of a particle is measured with both subsystems simultaneously, with subsequent comparison and validation. This method of size measurement provides a very wide dynamic rage combined with high accuracy which is improved, compared to conventional PDA systems, in particular for applications in dispersed droplets. From the principle that the phase difference of Doppler signals detected at two or more locations is proportional to the droplet diameter, the velocity and diameter of entrained droplets can be measured simultaneously without disturbing flow.
2.3. Experimental procedure
Fig. 4. Geometrical shapes of test piece installation position. Table 1 Geometric dimensions of test spacers Spacer number
Thickness (t) (mm)
Clearance (c) (mm)
1 2 3 4 5
1 2 3 2 2
2 2 2 1 3
3. Experimental results
Table 2 Experimental conditions System pressure Superficial air velocity, jg (m s−1) Number of measured droplets Air temperature (°C) Water temperature (°C)
The experimental conditions are shown in Table 2. The measured positions were changed in the horizontal direction, from spacer to 10 mm at intervals of 0.5 mm (21 positions), and in the vertical downward direction, from spacer to 10, 20, 30, 40, 70 and 100 mm (seven positions), so that there were 147 positions in total. The axis of coordinates is shown in Fig. 5. The droplet velocity and diameter consist on average of 10 000 counts.
1 atm 30, 45, 60, 75 10 000 11–18 11–20
The range of measurements with the DualPDA system are shown in Table 3. At first, two-dimensional velocity profiles and droplet diameter distribution were measured under various gas superficial velocity conditions with no spacer. Typical measured results are shown in Fig. 6(a– c). It was confirmed from Fig. 6 (a) that water droplet diameter was very small (about 30 mm) and that the mean velocity of droplets is nearly
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
181
defined as flow from the wider channel to the narrower one. Fig. 7(a,b) shows typical measured results of two-dimensional velocity profiles along the flow direction in reference to the mimic spacer clear-
Fig. 5. Explanation of coordinates. Table 3 The range of measurements in the DualPDA system Velocity, Vx (m s−1) Velocity, Vy (m s−1) Diameter, Dp (mm)
−57.02–169.031 −32.45–32.45 0.41321–169.03
equal to gas superficial velocity. Furthermore, the droplet diameter even at the higher gas superficial velocity of jg =75 m s − 1 is the same order as at the velocity of jg =30 m s − 1. It can be regarded for such as a small diameter droplet that the droplet velocity becomes almost the same as the gas velocity. Longitudinal droplet velocity distributions downstream of the exit of the flow channel have a mild center peak profile near the exit and become flat further from the exit as shown in Fig. 6(b). The average droplet velocity integrated over the measurement points near the exit of the flow channel was almost equal to the gas flow rate. Hence, it seems that the droplet velocity can be regarded as the gas velocity. Fig. 6(c) shows typical measured droplet velocity distributions at the same positions as Fig. 6(b). A positive value is
Fig. 6. An example of the experimental results with no spacer ( jg =30 m s − 1).
182
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
in order to eliminate the diverging effect of the channel induced mist flows discharged into the open space. It can be seen from the figure that lateral flow from the wider to narrower channels is induced downstream of the exit of the test section and becomes positive and large near the spacer as shown at 1 mm. Fig. 8 shows the typical differential lateral velocity profiles at the center line of the spacer thickness along with the flow direction. Going further from the exit of the test section, the differential lateral velocity linearly increases by 70 mm from the exit, has a peak value at 70–80 mm from the exit and linearly decreases downstream of that. The peak value becomes larger with an increase in the gas velocity.
Fig. 7. Distribution of gas velocities downstream of the spacer ( jg = 30 m s − 1).
ance. The spacer position is shown as the break line in these figures. It can be seen from Fig. 7(a) that longitudinal velocity profiles, Vx(y), are different between wider and narrower regions near the exit of the test section because the flow channel is split by the spacer and the frictional losses are different from each channel. The difference between velocity profiles becomes uniform further from the exit of the test section. The differential lateral velocity profiles, Vy(y), are obtained by subtracting the lateral velocity profile measured under the condition with a spacer as shown in Fig. 7(b) from that under the condition without a spacer as shown in Fig. 6(c)
Fig. 8. Lateral velocity distributions downstream of spacers.
Fig. 9. Droplet diameter distributions downstream of the spacer.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
183
recovered into one developed velocity profile in a short length about 100 mm (L/D= 10) downstream of the spacer. The drift flow model is illustrated in Fig. 10. Gas velocities, which flow both in the center core and the gap clearance, are evaluated by a consideration of mass and pressure balances in these regions. rgVnAn + rgVwAw = rgV0A0
(1)
where rg is gas density, V is gas velocity and subscripts n, w and 0 are narrow and wide channels split by the spacer, and test channel upstream of the spacer, respectively. The gas velocity upstream of the spacer, V0, becomes equal to the superficial gas velocity, jg. Eq. (1) can be rewritten as: VnAn + VwAw = jgA0
(2)
The friction and choking losses are considered in the momentum balance. Fig. 10. Definition of virtual boundary.
Fig. 9 shows droplet diameter profiles measured 10 mm downstream of the spacer. The droplet diameter becomes larger near the spacer end (y= 0–4 mm) at the high gas velocity. A great deal of droplets deposit on the spacer surface and form liquid film flow thereon. Then, the liquid film is entrained again with the larger droplet size at the end of the spacer, and the droplets flow together with the air flow motion. This phenomenon is called ‘run off’. With increasing air flow rates, the amount of air flow colliding against the spacer surface increases, so that the liquid film flowing on the spacer surface becomes thicker and the droplet size increases. As the spacer thickens, the amount of droplets deposited on the spacer surface increases and the droplet size becomes larger.
4. Modeling of droplet deposition
4.1. Drift flow model This induces drift flows that the spacer splits the mixture flow in the channel into the narrower and wider channel and that the split flows are
(Pz + Pfric)n(DPz + Pfric)w
(3)
DPz = z·(1/2)rg(Vi)2
(4)
z= ((1/Cc)−1)2
(5)
Cc= Ai/Aup,i
(6)
DPfric = fi/(2Di)·rg(Vi)2·L
(7)
where subscript ‘i’ expresses narrower (n) or wider (w). A means the cross section at each channel and Aup is the virtual cross section in the upper stream for each channel split by the virtual boundary line shown in Fig. 10. Di is the hydraulic diameter of each channel. L is the spacer height (35 mm constant). Frictional loss can be expressed as follows: fi = 0.3164/Re%0.25 i
(8)
Re%i = ViDi/ng
(9)
In the ‘drift’ flow model, virtual boundary coefficient is assumed as the ratio of the cross section in the narrower channel to that in both flow channels written as below Cvb = An/(An + Aw)
(10)
The effect of the clearance on drift flow rates was investigated experimentally and analytically.
184
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
A typical comparison between the experimental and analytical results is shown in Fig. 11(a). The symbols, and mean the experimental and analytical results, respectively. The gas flow rates
in the narrower channel calculated by the drift flow model are in good agreement with the experimental results. The clearance greatly influences the gas flow rates in the narrower channel and thus the gas velocity therein increases with an increase in the clearance because the friction and choking losses become smaller. The difference of air flow rates between both channels becomes smaller with increasing clearance. On the other hand, the air velocity in the wider channel does not vary with a change in the clearance because the friction and the choking losses scarcely change. Since the gas velocities were measured 10 mm downstream of the test section, the gas flow is diverged for discharge to the open channel. As a result, the analytical results of the gas flow rates show slightly higher values than the experimental ones in the wider channel. Next, the effect of spacer thickness on drift flow rates was investigated experimentally and analytically. A typical comparison between the experimental and analytical results is shown in Fig. 11(b). The analytical results in both channels increase with spacer thickness and have the same tendency as the experimental data. The analytical air velocities in the wider channel are slightly larger than the experimental values. Since, the whole flow area is reduced as the spacer becomes thicker, the flow rates both in the narrower and wider channels increase for the thicker spacer.
4.2. Formulation of droplet deposition profile Fig. 11. Comparison of drift velocity data and analytical results ( jg =30 m s − 1).
Fig. 12. Definition of lateral velocity profile.
The formulation of the droplet deposition rate profile was attempted using the proposed drift flow model. The peak value for lateral velocity, Vypeak and its point for the axial direction, Xpeak, were defined as shown in Fig. 12 and were formulated by the drift flow model. The lateral velocity profile was divided into two regions, by the peak point Xpeak, where the lateral peak velocity appears as shown in Fig. 12; the proximal and distal regions from the spacer. The distal region was considered up to L/D=15 from the spacer. The lateral velocity profile was approximated as a linear function both in the proximal and distal regions.
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
Fig. 13. Wide channel velocity effects on lateral peak velocity (thickness=2 mm).
Fig. 14. Wide channel velocity effects on lateral peak velocity (clearance= 2 mm).
Figs. 13 and 14 show the effect of the velocity differentials between the wider channel and upstream of the spacer, where almost superficial velocity, Vw −jg, on the lateral peak velocity, Vypeak, in reference to clearance for a constant spacer thickness of 2 mm and in reference to spacer thickness for a constant clearance of 2 mm, respectively. It can be seen from both figures that the lateral peak velocity is almost proportional to the velocity in the wider channel. Then, the effect of gas Reynolds number in the wider channel on the dimensionless lateral peak velocity was examined and the results are demonstrated in Fig. 15. The peak value was expressed as follows
185
Fig. 15. Wide channel velocity effects on lateral peak velocity (all conditions).
Fig. 16. Narrow channel velocity effects on axial distance of lateral peak velocity (thickness = 2 mm).
Fig. 17. Relationship of narrow channel Reynolds number and axial distance of lateral peak velocity.
186
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
ng Rew DH
(11)
Rew = (Vw − V0)·DH/ng
(12)
Vypeak = 0.118
Fig. 18. Relationship of velocity gradient behind peak value and Reynolds numbers obtained by drift velocities.
where DH is the typical length of the test section (10 mm). Superficial velocity, jg, was used for the upstream velocity (V0) in this study because of the discharge to the open channel. Fig. 16 shows the relationship between the dimensionless peak point (Xpeak/DH) and the narrower velocity. The dimensionless peak point increases with an increase in the narrower velocity. The lateral velocity profile is formed as a consequence of counteracting the velocities going toward the position of the spacer in both channels. As result, the peak point is shifted downstream with an increase in the narrower channel velocity. Furthermore, it seems that clearance infl-
Fig. 19. Comparison of lateral velocity profile data and present equation ( jg =30 m s − 1).
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
uences the peak point. The clearance, c, was used as the reference length for the Reynolds number in the narrow channel to introduce the effect of clearance. The relationship between the Reynolds number in the narrow channel and the dimensionless peak point can be arranged as shown in Fig.
187
17. The dimensionless peak point can be expressed as follows: Xpeak/DH = 2.65Re0.12 n
(13)
Ren = Vn·c/ng
(14)
From the above-mentioned results, the lateral velocity profile from x= 0 to Xpeak can be expressed as: Vy(x)=
Vypeak n x x= 0.0445 g Ren− 0.12Rew Xpeak DH DH (15)
On the other hand, as the lateral velocity profile in the distal region has the relation to the proximal region of the spacer, the profiles arranged with the same factors as Eq. (15) are shown in Fig. 18. (Vypeak − Vy150) n = − 0.035 g Ren− 0.12Rew (Xpeak − 0.15)/DH DH (16) Therefore, the lateral velocity profile in the distal region of the spacer (x\ Xpeak) can be expressed as follows. Vy(x)= Vypeak − =
(Vypeak − Vy150) (x−Xpeak) (Xpeak − 0.15)/DH DH
ng x Re 0.211− 0.035Ren− 0.12 DH w DH
(17)
Figs. 19 and 20 show the comparisons between the experimental and analytical results of perpendicular velocity profiles downstream of the spacer. These figures in portrait orientation show the spacer thickness effect. The landscape orientation in Fig. 19 shows the clearance effect. Fig. 20 shows the results with reference to gas velocity, jg = 30, 45, 60, 75 m s − 1. The solid lines shown in the figure mean the velocity profile calculated from the proposed correlation. It can be seen from Figs. 19 and 20 that the proposed correlation can describe the experimental results well.
5. Conclusions Fig. 20. Comparison of lateral velocity profile data and present equation (thickness = 2 mm, clearance = 2 mm).
The effect of spacer geometry on the droplet deposition rates downstream of the spacer was
188
T. Yano et al. / Nuclear Engineering and Design 201 (2000) 177–188
investigated in an open rectangular channel using air and water as test fluids, and the following have been clarified. 1. The difference of velocities split by the spacer decreases with an increase in clearance. As a result, the deposition rate of droplets decreases as the clearance becomes wider. 2. Since the velocity in the wider channel increases with an increase in the spacer thickness, the deposition rate of droplets increases as the spacer becomes thicker. 3. The run-off effect was confirmed from the measured lateral profiles of droplet diameter distribution. 4. The drift flow model incorporating the frictional and choking losses is proposed. The proposed model can explain the experimental results of the split flow rates downstream of the spacer. 5. The correlation of the droplet deposition rate downstream of the spacer is proposed along the flow direction. In order to confirm the above-mentioned conclusions, the authors are investigating the liquid film characteristics downstream of mimic spacers in a circular channel as integral tests.
Acknowledgements This work has been carried out at the Tokyo Institute of Technology in collaboration with The Japan Atomic Power Company Co. Ltd.
.
Appendix A. Nomenclature P r m V A Subscripts g n w 0 cr crup i fric z
pressure (Pa) density (kg m−3) static viscosity (N s m−2) velocity (m s−1) cross-sectional area (m2) gas phase narrower wider upper stream of the spacer clearance part upstream of clearance part n or w friction choking
References Lahey, R.T., Shiralkar, B.S., Radcliffe, D.W., Polomik, E., 1972. Out-of-Pile Subchannel Measurements in a NineRod Bundle for Water at 1000 psia. Progress in Heat and Mass Transfer, vol. VI. Pergamon, Oxford. Yamamoto, Y., et al., 1996. Boiling transition phenomenon in BWR fuel assemblies (effect of fuel spacer shape on critical power). J. Atom. Energ. Soc. Japan 38 (4), 315– 323 in Japanese. Yano, T. et al., 1995. Annular two-phase flow characteristics in a circular tube. In: Proceedings of the 2nd International Conference on Multiphase Flow’95, Kyoto, Vol. 1, IP2-19.