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Laser doppler measurements of flow in a rod bundle
Nuclear Engineering and Design 74 (1982) 105-116 North-Holland Publishing Company
LASER DOPPLER MEASUREMENTS
105
O F F L O W IN A R O D B U N D L E *
S. N E T I Assistant Professor of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA R. E I C H H O R N Dean of Engineering, University of Houston, Houston, TX 77004, USA O.J. H A H N Associate Professor of Mechanical Engineering, University of Kentucky, Lexington, K Y 40506, USA Received 26 October 1982
A two component laser doppler velocimeter with polarized beams and frequency shift was used to measure the turbulent flow field for axial flow between the rods of a nine rod, square pitch rod bundle. Parameters measured include mean axial and lateral velocities, turbulence intensities and the friction factor. The axial velocities for 10000 to 40000 Reynolds number are slightly higher than those reported by Rowe. The maximum lateral velocities measured are about 1% of the bulk velocity; somewhat larger than suggested by earlier authors. Axial and lateral turbulence intensities are larger than those in pipe flows.
1. Introduction Large reactors designed for commercial and other base load purposes consist of a reactor core contained in a pressure vessel. The fuel is almost universally arranged as pellets inside fuel rods. Coolant flows along the outside of the fuel rods and carries thermal energy from the fuel to heat exchangers and turbines. A study of the turbulent flow and heat transfer in the fuel assemblies is an essential part of nuclear reactor design. Safety considerations also require a detailed analysis of the fluid flow and heat transfer inside the fuel bundles. Present day reactor designs are based on flow calculations made with the so called "lumped-parameter" approach [1]. ** In these analyses, the flow area in the rod bundle is divided into subchannels and the flow is presumed to be one dimensional along the rods and average fluid properties are identified in each subchannel. Adjacent subchannels are coupled by cross flow mixing correlations. Unfortunately, the mixing correlations used in this approach are not universal since most do not reflect the effects of geometry. Hence, funda* This work was carried out at the University of Kentucky. ** Numbers in brackets designate items in the list of references at the end of this paper. 0029-5493/82/0000-0000/$02.75
mental studies of rod bundle turbulence are important for a better understanding of these flows. The following sections describe experiments conducted in a nine-rod, square pitch rod bundle. A two component laser doppler velocimeter with polarized beams and frequency shift was used to study various flow parameters.
2. Review of literature The earliest works on rod bundle flow were extensions of work done on flow through pipes and annuli. In one of the first attempts at analysis, Deissler and Taylor [2] calculated the velocity profiles by assuming that circular pipe universal velocity profiles and eddy diffusivity relations held in rod bundles. The first measurements of rod bundle turbulence parameters seem to have been made by Kjellstrom [3,4]. These hot wire anemometer experiments complemented his analytical work and were performed in air flow at the exit of a triangular array of six rods with a pitch to diameter ratio of 1.217. Of great interest is his observation of secondary flows less than one percent of the axial velocity in magnitude. The secondary flows were directed toward the gap along the centerline and away
© 1982 N o r t h - H o l l a n d
106
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
from it along the rods. Trupp and Azad [12] also have made hot wire turbulence measurements of fully developed flow in a triangular array of rod bundles. They concluded that the results for a pitch to diameter ratio of 1.35 bear a closer resemblance to pipe flow turbulence data than do those for smaller pitch to diameter ratios. Their results suggest that the magnitude of the secondary flow velocity increases with decreasing Reynolds number. The first use of laser doppler velocimetry (LDV) for rod bundle measurements was by Rowe [5]. Rowe used a two component reference beam LDV in test sections with pitch to diameter ratios of 1.25 and 1.125 at Reynolds numbers of 50000 to 100000. Rowe's results show that the rod gap has a significant influence on the turbulent flow structure in rod bundles in a way that cannot be deduced from round pipes results. The velocity profiles are in reasonable agreement with pipe flow universal profiles, but the turbulence intensity and mac-
roscale are larger than is found in pipe flow. The secondary flows seem to play a significant role in establishing the flow structure. Carajilescov and Todreas [10] also used a one component forward scatter LDV for flow measurement in a two subchannel triangular pitch rod bundle. Their axial velocity results are in reasonable agreement with calculations made using Ibragimov's [11] method. The secondary flows were too small to measure (~< 0.67%) and the wall shear stress was more uniform at high Reynolds numbers than at low Reynolds numbers. Only a few of the studies in the literature closely related to the present work are reviewed above. Extensive reviews of the rod bundle literature are available [13,14]. Results obtained in the present work are compared to the above works in the following sections, with some new insight into the secondary velocities and Reynolds stress distribution.
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S. Neti et aL / Laser doppler measurements of flow in a rod bundle
3. Experimental setup and equipment The measurements were conducted in a nine-rod square pitch rod bundle with axial water flow. Measurements were made with a two component laser doppler velocimeter (fig. 1) briefly described below. A detailed description of the instrument and its development can be found in [14]. The dual beam velocimeter uses two pairs of light beams of one wavelength from a 15 mW H e - N e laser. The four beams have nearly equal intensity, but the two pairs of beams have orthogonal polarization controlled at various stages along the light path by the polarization rotators (1), (3) and (6). The beam splitters provided a 50-50 split in in polarization. The four beams thus form orthogonal fringes at the point of measurement. One of the pairs of beams is intended to measure the small cross flow velocity component. One beam of this pair is frequency shifted with a Bragg cell, to provide directional sensitivity and permit tracking of the horizontal velocity component. The receiving optics comprises lenses to collect the scattered light, a polarization splitter (14), and a pair of avalanche photodiodes. The polarization splitter provides an ideal extinction ratio of 1000/1, but the light scattered from individual particles is slightly depolarized, so the effective extinction ratio for the separate velocity components is about 40/1 [14]. The photodiode signals were detected and processed with two TSI Inc. Model 1090 frequency trackers. The tracker outputs were digitized and the velocity data acquired with the help of a PDP 8 / e minicomputer. The test section is attached to a recirculating water flow loop that includes a surge tank, an 11.2 kW (15 HP), 0.43 m3/min (115 gpm) motor and pump, a high pressure tank and two heat exchangers. The flow meter is a stainless steel square edge orifice with 1D and 0.7D pressure taps between the high pressure tank and the test section. The orifice section was separately calibrated with a weighing tank over a pipe Reynolds number range of 30 000 to 300 000. The heat exchangers in the loop are cooled by air from outside the laboratory and were designed to remove the dissipative heat. A small filtering loop with a 5/~ filter was operated 24 hours per day to remove suspended particles from the water. Maximum flows corresponding to a test section Reynolds number of 40 000 can be attained. The flow loop and its calibration are described in [14]. The test section consists of the inlet plenum chamber, test channel and outlet plenum chamber shown in fig. 2. The top and bottom plenum chambers are made from 460 mm lengths of 460 mm (18 in) diameter steel
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Fig. 2. Test section.
pipe. The test channel consists of nine rods housed in an 80 mm × 80 mm square channel. The "rods" are stainless steel tubing of 19.05 mm (3/4 in) diameter. The pitch to diameter ratio is 1.4 and the rods closest to the walls are at a distance of 0.5 pitch from the wall. The square channel housing the rods is made of two aluminum sides and two Plexiglas sides, all nominally 13 mm (1/2 in) thick. All LDV measurements were made through optical glass windows inserted in the Plexiglas sidewalls of the channel. The rod bundle is 1.5 m long (85 hydraulic diameters) and the total test section height is about 2.4 m. Water enters at the bottom through the side of the inlet plenum chamber and flow into the rod bundle through holes in the lower cover plate shown in fig. 3. The lower cover plate also supports the rods. Holes in
108
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the cover plate form submerged jets because the pressure drop across the holes is large c o m p a r e d to the pressure drop in the test section itself. The diameters of the jets are proportional to the subchannel areas they supply to o b t a i n as fiat a velocity profile as possible, a few diameters d o w n s t r e a m of the jets. The large pressure drop across the b o t t o m plate also ensures that no large eddies are transported into the rod bundle. The water exits the test section from the side of the top p l e n u m chamber. The rods extend to the top of the test section a n d are positioned a n d supported at the top with holes in the plate covering the outlet p l e n u m chamber. The rods are sealed with O-rings against the top plate. To minimize rod vibrations, the rods are screwed into the b o t t o m plate a n d stretched a n d held snug on top with a screw a n d bolt a r r a n g e m e n t above the O-rings.
4. Experimental procedure Laser doppler measurements were m a d e at 61 hydraulic diameters from the entrance of the test channel. T h e L D V was m o u n t e d on a two dimensional traversing m e c h a n i s m so the m e a s u r e m e n t volume could be translated along the optical axis ( y axis) a n d n o r m a l to it ( x axis). The horizontal velocities measured are normal to the rods, along the x axis with the primary flow in the vertical ( z ) direction. All measurements were
m a d e in the rod gaps. The region of measurement was 0.4 pitch (rod gap) by 3 pitch (width of duct). Half of this region, 7.62 m m × 40 m m was divided into 110 grid points with 5 grid points in the x direction and 22 grid points in the y direction. The position of m e a s u r e m e n t was determined using 0.001 in dial gages. The measured parameters were: the two mean voltages and R M S values of the LDV processor (frequency tracker) outputs, the temperature and pressure of the water in the test section, the mass flow rate a n d the location of measurement. The first two values were n o t e d by the P D P 8 / e system in r a n d o m bursts for a total of 2000 data points for each of the two components, in a b o u t 60 s time [14]. The fluid temperature was measured by a C h r o m e l - A l u m e l thermocouple in the test section a n d the pressure with a Heise pressure gage. A n orifice meter was used to measure the mass flow rate. Those data noted manually were input to the m i n i c o m p u t e r with a Teletype, for inclusion in the calculation of velocity distributions. The water loop was operated for a b o u t two hours prior to a run to remove dissolved air and to achieve steady state conditions. Measurements were m a d e at three nominal Reynolds numbers: 10000, 20000 a n d 40000. The turbulence characteristics and the effects of the entrance jets upon it were checked by inserting a cylinder of small diameter (3 m m ) across the flow near the entrance. N o noticeable differences in mean velocity or the turbulence intensity were found at the m e a s u r e m e n t section with the cylinder in place. Imperfections in the rods gave rise to slightly asymmetrical subchannels. The bow in the rods was less than 0.25 m m (0.010") over the 2 m length, but even this a m o u n t is enough to introduce asymmetries in the flow. Some of the results presented bear out this fact in the form of asymmetrical profiles.
5. Results Fig. 4 shows the distribution of m e a n velocity normalized with the bulk (average) velocity for a Reynolds n u m b e r of 21000. The y coordinate is normal to the glass wall a n d along the optical axis; the x coordinate is measured in the rod gap, n o r m a l to y. The values of x range from zero to unity across the rod gap. The measurement volume of the L D V had a diameter of 0.4 mm, so the data closest to the rods were at least half of this distance away. The location of the five traverses in the y direction are also shown in fig. 4. The velocity profiles for x = 0.0 a n d 1.0 show m i n i m a adjacent to the rods, at y = 0.5 a n d 1.5. The presence of
109
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the rods is discernible for the other traverses ( x = 0.25, 0.5 and 0.75) as well, but the minima are not as pronounced. The local mean axial velocity is a complex function of the space variables. The maximum normalized vertical velocities are about 1.45, 1.39 and 1.35 for Reynolds numbers of 10000, 20000 and 40000 respectively and are larger than the 1.28 reported by Rowe [5] at Re = 100 000. A discussion of this topic is postponed for a later section. Fig. 5 is a plot of vertical velocity across the rod gap at several values o f y for Re = 41 000. The local maxima in the gap center between rods at y = 0.5 and y = 1.5 can be clearly seen, with rather flat profiles for other locations. Fig. 6 shows a composite of the above vertical velocity results in contour maps for Re = 10000, 20000 and 40000. The movement of the maxima locations and their decrease with Reynolds number are clearly brought out in this figure. The effect of the near wall can be observed at all Reynolds numbers, but the character of the effect changes with Reynolds number. To study the overall flow patterns, measurements were also made for the total width of the test section in the center of the rod gap (x = 0.5). Figs. 7 and 8 are
plots of these data. The y value ranges from 0 to 3, the vertical velocity has maxima of 1.32 and 1.3 and there is a local minimum at y = 1.5. The axial turbulence intensity across the channel is shown in fig. 8 for a Reynolds number of 40 000. The lowest values of the turbulence intensity are slightly over five percent and highest values near the walls are about ten percent. Turbulence intensity profiles at Re = 20000 are shown in fig. 9 for five x values. The turbulence intensity is in general higher than that seen in pipe flows. Near the channel walls and rods, the highest values are noticeable. Near wall values reach about 13 to 15%. The minimum values are about 6%. These turbulence intensity results are shown in contour form in fig. 10. At these Reynolds numbers the turbulence intensity appears to be only minimally dependent on Reynolds number. Fig. 11 shows the horizontal turbulence intensity along the center line of a rod-gap ( x = 0.5). The measured values range from 4.0 to 5.5% with minima between rods and maxima at the subchannel center. The maxima and minima are clearly seen in the figure. To visualize what may be expected for the mean
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horizontal velocity results, let us consider the plausible lateral flow loops indicated in fig. 12. The y traverses for various x values, along with some ideal flow cells, are depicted there. In general, the secondary flow is always toward a gap in the middle of the subchannel, toward the rods on the symmetry lines across the rod gap and back to the center of the subchannel along a diagonal
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bisector. For the traverses at x = 1.0 and 0.25, inferred velocity peaks in such ideal lateral flow cells are also sketched in fig. 12. Fig. 13 shows an LDV traverse in the subchannel adjacent to the plane wall, next to one of the rods (x = 1.0), for R e = 2 0 0 0 0 . The negative and positive peaks are clearly shown, but a positive value was obtained for the first point. Data were obtained only part way into the second subchannel ( y = 0.7) because of the divergent character of the horizontal beam and interference with the first rod. The maximum values are about 1% of the bulk velocity. Similar results are shown in figs. 14 and 15 at x = 0.25 for Re = 40000 and 20000 respectively. In fig. 14, we can identify the first two positive peaks and the first two negative peaks similar to those in fig. 12 for x = 0.25. The second negative peak seems to be disproportionately large and the third negative peak is missing. Parameters of small magnitude, such as the horizontal velocity, may take on unexpected values even with the smallest of disturbances. As mentioned earlier, we had difficulty positioning the rods symmetrically since they tended to bow. This eccentricity could easily explain the above behavior. Also since these measure-
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ments were made using a frequency shift in the doppler signal, and the velocities plotted were calculated by subtracting the Bragg cell frequency shift, the zero could be in error by as much as 0.1% of bulk velocity. To minimize this error, the Bragg cell frequency shift was measured directly, before every data set, using the light scattered from a wall. The overall uncertainty in the electronics was about + 5 1 0 Hz. Corresponding to a typical 0.01 MHz doppler shift for the lateral velocities the uncertainty in the normalized mean horizontal velocities is expected to be about _+ 10%. The Reynolds stress (u'w') was computed directly from the cross correlation of the vertical and horizontal velocities and also from measurements of _+45 ° component turbulence intensities. Fig. 16 shows a traverse between the rods at x = 0.25 for u'w' nondimensionalized with the friction velocity based on the overall pressure drop in the bundle. A t y = 0.5, 1.5 and 2.5 u'w' normalized with the square of the local friction velocity (W*2) should vary from - 1 to + 1 across the rod gap. If the variation of u'w' (with x) along the rod gap were linear, the normalized value should be _+0.5. At x = 0.25, the actual value as indicated in fig. 16 is close to 0.2. Measurements repeated by the +45 ° technique also
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postpone discussion of this anomaly to a later section. The results presented above were all obtained with the use of a LAB 8 / e minicomputer. This system was fast in acquiring data, but slow in analyzing it• Analog electronic processing does not have this limitation. Hence it was decided to acquire some data manually, with analog electronic processing, for verification purposes. A voltage to frequency converter (VFC) and an events per unit time (EPUT) meter were used to average mean velocity data over ten second intervals. The turbulence intensities were measured with a D I S A type 55D35 R M S unit, with a ten second time constant. The results obtained by this method were virtually identical to those presented earlier. The LDV processor output voltages plotted directly on an x - y plotter are shown in figs. 17 and 18. To produce these figures, the x-axis of the plotter was driven by the output of a linear displacement transducer (Hewlett-Packard 24DCDT-1000). The vertical velocity profile close to the rods, at a Reynolds number of about 10000, shows the relationship between the mean velocity and turbulence intensity. The horizontal velocity profile in the rod gap, fig. 18, shows positive and negative directional changes of the horizontal velocity• The magnitude of the horizontal turbulence is comparable to or even larger than the horizontal mean velocity.
114
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
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6. Discussion of results
The maximum values of mean velocity measured in units of the bulk (average) velocity were 1.35, 1.39 and 1.45 at 40000, 20000 and 10000 Reynolds numbers, respectively. This Reynolds number trend agrees with that observed by Laufer [7] for pipe flow and by Trupp and Azad [12] for a triangular pitch rod bundle with a pitch to diameter ratio of 1.35. Rowe's [5] work in square pitch rod bundles shows only a minor dependence of the maximum vertical velocity on Reynolds number, but his results were for much higher Reynolds numbers where we expect the dependence on Reynolds number to disappear. The maximum of mean vertical velocities reported by Rowe were smaller than those seen here. The measurement locations were about 60 hydraulic diameters from inlet in Rowe's as well as the present work. It is conceivable that the maxima in the vertical velocities decrease to the lower values (1.28) at higher Reynolds numbers (100000). The inlet conditions used in this work are different from those of Rowe [5]. Rowe used a side entrance with a ninety degree turn, followed by staggered grids and parallel tube banks to straighten the flow. We used a jet type of entrance geometry. Some of
the differences in these two data sets may also be due to the different entrances used. Our measured vertical turbulence intensities are larger than those found in pipe flows. The minimum values of turbulence intensity measured in the subchannel centers are about 6%. Large turbulence intensities (10 to 15%) were found near channel walls and close to the rods. Reynolds number is not a dominant factor for turbulence intensity at least not at the present measurement conditions. Vertical turbulence intensities measured here are about one percent larger than those reported by Rowe [5]. The scatter in the turbulence data is large, possibly due to three reasons: (1) fluctuations in the overall flow giving rise to scatter in the data, (2) apparent scatter caused by the convection of turbulence kinetic energy by the secondary flows and , (3) the jet type of entrance used in the present work which may have contributed to the larger turbulence intensities measured. The mean horizontal velocity distributions presented here are believed to be the first measurements made in rod bundles. The maximum horizontal velocities are about one percent of bulk velocity. Some of the horizontal velocity data support the existence of the ideal secondary flow loops depicted in fig. 12, that could not be inferred from the vertical velocity data. Rowe [5] inferred the existence of similar secondary flow loops based on his vertical turbulence intensity contours. He also proposed the possibility of additional flow cells. Such extra cells might also have occurred in the present work, but they could not be identified from the measurements. Horizontal velocities measured here are larger than those proposed by Trupp and Azad [12] and Carajilescov and Todreas [10]. Both these works are related to triangular pitch rod bundles. These authors suggested 0.67% and 0.5% maximum lateral velocities respectively from their turbulence intensity data. In the results presented here, the scatter in the horizontal velocity is large because the parameter being measured is very small in magnitude. Another possible explanation for the seeming scatter is the existence of more secondary flow cells as suggested by Rowe. The scatter is larger at lower Reynolds numbers probably because the velocities measured are even smaller. The horizontal velocity data do indicate an overall trend similar to that in fig. 12. Horizontal turbulence intensity measurements indicate values from 4 to 5.5%. These data are normalized with the bulk velocity. Larger values are noticeable near the walls (parallel to horizontal velocity) and in the subchannel centers where maximum mean horizontal velocities are possible. In the center of the rod gap
S. Neti et al. / Laser doppler measurements of flow in a rod bundle spacing, smaller values are seen to occur. The measured Reynolds stress u'w' has been noted to be much smaller than expected. In the rod gap, u'w' normalized with the square of the friction velocity was expected to vary from + 1 to - 1 across the rod gap. The absolute values of the measured maxima were less than 0.5. The data were measured by two completely different techniques: (1) by the cross correlation of the vertical and horizontal velocities and (2) as the difference of +45 ° component turbulence intensities. Using the latter method u'w' is half of the difference of the +45 ° component turbulence intensities. Both these methods gave consistent and repeatably low values of u'w'. While in search of an explanation for this anomaly, we found that Trupp and Azad [12] had similar difficulties for two of their three data sets. They made hot wire anemometer X-probe measurements in a triangular pitch rod bundle. For a pitch to diameter ratio of 1.5 and 36000 Reynolds number, their maximum value of ( u ' w ' / W .2) near the wall reached only 0.46. Their values of u'w' measured for smaller Reynolds numbers were farther from unity than those at large Reynolds numbers. They report lower values of near wall u'w', when larger secondary velocities were indicated. From the above observations and in consideration of the fairly large horizontal velocities measured in this work, the ( u ' w ' / W .2) measurements are in agreement with Trupp's work. Three more possible comments can be made in this regard: (1) The u'w' should, in the strictest sense, be nondimensionalized with the square of the local friction velocity. Use of the local wall shear stress values [15,16] which are about 0.95 of mean shear stress do not quite explain the present discrepancy. (2) The variation of u'w' in the rod gap may not be linear in the presence of secondary flows of the type reported here, (3) u'w' may not behave linearly in the rod gap due to asymmetries in the flow. The small u'w' values remain to be explained. Measurements made in the -I-45° component mode yielded reasonable data for the mean vertical velocity but not for the horizontal velocity. Horizontal velocities of very small magnitude cannot be measured as the difference of the two large +45 ° component mean velocities. As mentioned earlier, u'w' values measured with this technique were similar to those measured in the vertical and horizontal velocity mode.
115
7. Conclusions (1) Measurements have been made in fully developed turbulent flow in a simulated nuclear fuel rod bundle of square pitch lattice. Three different measurement techniques were used. Most of the data presented were acquired with the use of a minicomputer. (2) Measured vertical velocities are somewhat larger than those reported by Rowe [5] but the discrepancy may be explained by the large difference in Reynolds numbers in the two experiments. (3) Vertical turbulence intensities are larger than those reported for pipe flows. The minimum values range from 5.5 to 6.5%. The horizontal turbulence intensities range from 4 to 5.5%, and are larger in regions of larger lateral velocities. (4) Measurements of mean horizontal velocities are reported and the maximum horizontal velocities are about one percent of bulk velocity, somewhat larger than suggested by some earlier authors. The measured velocities indicate lateral flow loops in a subchannel. (5) Reynolds stresses measured by two different techniques (cross-correlation and +45 ° measurement) were much lower than those in pipe flow and are similar to some of those observed by Trupp and Azad [12].
Nomenclature D P Re U u' W w' W* u'w' x
y z
rod diameter (19.05 mm, 3/4") pitch ( = 1.4D) Reynolds number based on bulk velocity and bundle hydraulic diameter mean lateral velocity (along x-direction) horizontal turbulence intensity mean axial velocity (along z-direction) vertical turbulence intensity friction velocity based on overall pressure drop Reynolds stress non-dimensional rod gap (0.0 to 1.0, rod to rod) horizontal coordinate normal to the rods and the laser velocimeter axis horizontal coordinate normal to the rods and along the laser velocimeter axis vertical coordinate along the rods and primary flow
116
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
References [1] J. Weisman and R.W. Bowring, Methods for detailed thermal and hydraulic analysis for water cooled reactors, Nucl. Sc. Engrg. 57 (1975) 4. [2] R.G. Diessler and M.F. Taylor, Analysis of axial turbulent flow and heat transfer through banks of rods or tubes, Reactor Heat Transfer Conference, 1956, TID-7529, Part I, Bk, 2, pp. 416-461. [3] B. Kjellstrom, Studies of turbulent flow parallel to a rod bundle of triangular array, A.B. Atomenergi, Studsvik, 611 01, Nykoping, Sweden, STU 68-263/U210 (1971). [4] B. Kjellstrom, Transport processes in turbulent channel flow, A.B. Atomenergi, Studsvik, 611 01 Nykoping, Sweden, STU 70-409/U340 (final report) AE-RL-1344. [5] D.S. Rowe, Measurement of turbulent velocity, intensity and scale in rod bundle flow channels, Ph.D. Thesis, Oregon State University, Corvallis, Oregon (1973). [6] J. Laufer, Investigation of turbulent flow in a two-dimensional channel, NACA Report No. 1053 (1951). [7] J. Laufer, The structure of turbulence in fully developed pipe flow, NACA-TN-2954 or NACA Report No. 1174 (1954). [8] R. Nijsing, I. Gargantini and W. Eifler, Analysis of fluid flow and heat transfer in a triangular array of parallel heat generating rods, Nucl. Engrg. Des. 4 (1966) 375-398. [9] L. lngesson and S. Hedberg, Heat transfer between sub-
[10]
[11]
[12]
[13]
[14]
[15]
[16]
channels in a rod bundle, Heat Transfer 3 (1970) p. FC7. 12p. P. Carajilescov and N.E. Todreas, Experimental and analytical study of axial turbulent flows in an interior subchannel of a bare rod bundle, Trans. ASME, Ser. C., J. Heat Transfer 98 (1978) 262-271. M.Kh. Ibraglmov, I.A. Isupov, L.L. Kobzar and V.I. Subbotin, Calculation of the tangential stresses at the wall in a channel and the velocity distribution in a turbulent flow of liquid, Soviet Atomic Energy 21 (1966) 731-739. A.C. Trupp and R.S. Azad, The structure of turbulent flow in triangular array rod bundles, Nucl. Engrg. Des. 32 (1975) 47-84. D.S. Rowe, Progress in thermal hydraulics for rod and tube bundle geometries, in: Fluid Flow and Heat Transfer Over Rod and Tube Bundles, Eds. S.C. Yao and P.A. Pfund, ASME (1979) pp. 1-12. S. Neti, Measurement and analysis of flow in ducts and rod bundles, Ph.D. Thesis, University of Kentucky, Lexington, Kentucky (1977). R. Eichhorn, H.C. Kao and S. Neti, Measurements of shear stress in a square array rod bundle, Nucl. Engrg. Des. 56 (1980) 385-391. M. Abdel-Ghany and R. Eichhorn, Measurements of wall shear stress in axial flow in a square lattice rectangular rod bundle, A I A A / A S M E Fluids, Plasma, Thermophysics and Heat Transfer Conference, St. Louis, MO, June 1982.
LASER DOPPLER MEASUREMENTS
105
O F F L O W IN A R O D B U N D L E *
S. N E T I Assistant Professor of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA R. E I C H H O R N Dean of Engineering, University of Houston, Houston, TX 77004, USA O.J. H A H N Associate Professor of Mechanical Engineering, University of Kentucky, Lexington, K Y 40506, USA Received 26 October 1982
A two component laser doppler velocimeter with polarized beams and frequency shift was used to measure the turbulent flow field for axial flow between the rods of a nine rod, square pitch rod bundle. Parameters measured include mean axial and lateral velocities, turbulence intensities and the friction factor. The axial velocities for 10000 to 40000 Reynolds number are slightly higher than those reported by Rowe. The maximum lateral velocities measured are about 1% of the bulk velocity; somewhat larger than suggested by earlier authors. Axial and lateral turbulence intensities are larger than those in pipe flows.
1. Introduction Large reactors designed for commercial and other base load purposes consist of a reactor core contained in a pressure vessel. The fuel is almost universally arranged as pellets inside fuel rods. Coolant flows along the outside of the fuel rods and carries thermal energy from the fuel to heat exchangers and turbines. A study of the turbulent flow and heat transfer in the fuel assemblies is an essential part of nuclear reactor design. Safety considerations also require a detailed analysis of the fluid flow and heat transfer inside the fuel bundles. Present day reactor designs are based on flow calculations made with the so called "lumped-parameter" approach [1]. ** In these analyses, the flow area in the rod bundle is divided into subchannels and the flow is presumed to be one dimensional along the rods and average fluid properties are identified in each subchannel. Adjacent subchannels are coupled by cross flow mixing correlations. Unfortunately, the mixing correlations used in this approach are not universal since most do not reflect the effects of geometry. Hence, funda* This work was carried out at the University of Kentucky. ** Numbers in brackets designate items in the list of references at the end of this paper. 0029-5493/82/0000-0000/$02.75
mental studies of rod bundle turbulence are important for a better understanding of these flows. The following sections describe experiments conducted in a nine-rod, square pitch rod bundle. A two component laser doppler velocimeter with polarized beams and frequency shift was used to study various flow parameters.
2. Review of literature The earliest works on rod bundle flow were extensions of work done on flow through pipes and annuli. In one of the first attempts at analysis, Deissler and Taylor [2] calculated the velocity profiles by assuming that circular pipe universal velocity profiles and eddy diffusivity relations held in rod bundles. The first measurements of rod bundle turbulence parameters seem to have been made by Kjellstrom [3,4]. These hot wire anemometer experiments complemented his analytical work and were performed in air flow at the exit of a triangular array of six rods with a pitch to diameter ratio of 1.217. Of great interest is his observation of secondary flows less than one percent of the axial velocity in magnitude. The secondary flows were directed toward the gap along the centerline and away
© 1982 N o r t h - H o l l a n d
106
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
from it along the rods. Trupp and Azad [12] also have made hot wire turbulence measurements of fully developed flow in a triangular array of rod bundles. They concluded that the results for a pitch to diameter ratio of 1.35 bear a closer resemblance to pipe flow turbulence data than do those for smaller pitch to diameter ratios. Their results suggest that the magnitude of the secondary flow velocity increases with decreasing Reynolds number. The first use of laser doppler velocimetry (LDV) for rod bundle measurements was by Rowe [5]. Rowe used a two component reference beam LDV in test sections with pitch to diameter ratios of 1.25 and 1.125 at Reynolds numbers of 50000 to 100000. Rowe's results show that the rod gap has a significant influence on the turbulent flow structure in rod bundles in a way that cannot be deduced from round pipes results. The velocity profiles are in reasonable agreement with pipe flow universal profiles, but the turbulence intensity and mac-
roscale are larger than is found in pipe flow. The secondary flows seem to play a significant role in establishing the flow structure. Carajilescov and Todreas [10] also used a one component forward scatter LDV for flow measurement in a two subchannel triangular pitch rod bundle. Their axial velocity results are in reasonable agreement with calculations made using Ibragimov's [11] method. The secondary flows were too small to measure (~< 0.67%) and the wall shear stress was more uniform at high Reynolds numbers than at low Reynolds numbers. Only a few of the studies in the literature closely related to the present work are reviewed above. Extensive reviews of the rod bundle literature are available [13,14]. Results obtained in the present work are compared to the above works in the following sections, with some new insight into the secondary velocities and Reynolds stress distribution.
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107
S. Neti et aL / Laser doppler measurements of flow in a rod bundle
3. Experimental setup and equipment The measurements were conducted in a nine-rod square pitch rod bundle with axial water flow. Measurements were made with a two component laser doppler velocimeter (fig. 1) briefly described below. A detailed description of the instrument and its development can be found in [14]. The dual beam velocimeter uses two pairs of light beams of one wavelength from a 15 mW H e - N e laser. The four beams have nearly equal intensity, but the two pairs of beams have orthogonal polarization controlled at various stages along the light path by the polarization rotators (1), (3) and (6). The beam splitters provided a 50-50 split in in polarization. The four beams thus form orthogonal fringes at the point of measurement. One of the pairs of beams is intended to measure the small cross flow velocity component. One beam of this pair is frequency shifted with a Bragg cell, to provide directional sensitivity and permit tracking of the horizontal velocity component. The receiving optics comprises lenses to collect the scattered light, a polarization splitter (14), and a pair of avalanche photodiodes. The polarization splitter provides an ideal extinction ratio of 1000/1, but the light scattered from individual particles is slightly depolarized, so the effective extinction ratio for the separate velocity components is about 40/1 [14]. The photodiode signals were detected and processed with two TSI Inc. Model 1090 frequency trackers. The tracker outputs were digitized and the velocity data acquired with the help of a PDP 8 / e minicomputer. The test section is attached to a recirculating water flow loop that includes a surge tank, an 11.2 kW (15 HP), 0.43 m3/min (115 gpm) motor and pump, a high pressure tank and two heat exchangers. The flow meter is a stainless steel square edge orifice with 1D and 0.7D pressure taps between the high pressure tank and the test section. The orifice section was separately calibrated with a weighing tank over a pipe Reynolds number range of 30 000 to 300 000. The heat exchangers in the loop are cooled by air from outside the laboratory and were designed to remove the dissipative heat. A small filtering loop with a 5/~ filter was operated 24 hours per day to remove suspended particles from the water. Maximum flows corresponding to a test section Reynolds number of 40 000 can be attained. The flow loop and its calibration are described in [14]. The test section consists of the inlet plenum chamber, test channel and outlet plenum chamber shown in fig. 2. The top and bottom plenum chambers are made from 460 mm lengths of 460 mm (18 in) diameter steel
)ptical Glass Vindow
1.475m 61
Fig. 2. Test section.
pipe. The test channel consists of nine rods housed in an 80 mm × 80 mm square channel. The "rods" are stainless steel tubing of 19.05 mm (3/4 in) diameter. The pitch to diameter ratio is 1.4 and the rods closest to the walls are at a distance of 0.5 pitch from the wall. The square channel housing the rods is made of two aluminum sides and two Plexiglas sides, all nominally 13 mm (1/2 in) thick. All LDV measurements were made through optical glass windows inserted in the Plexiglas sidewalls of the channel. The rod bundle is 1.5 m long (85 hydraulic diameters) and the total test section height is about 2.4 m. Water enters at the bottom through the side of the inlet plenum chamber and flow into the rod bundle through holes in the lower cover plate shown in fig. 3. The lower cover plate also supports the rods. Holes in
108
S. Neti et al. / Laser doppler measurements of flow in a rod bundle I
) I
i I
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the cover plate form submerged jets because the pressure drop across the holes is large c o m p a r e d to the pressure drop in the test section itself. The diameters of the jets are proportional to the subchannel areas they supply to o b t a i n as fiat a velocity profile as possible, a few diameters d o w n s t r e a m of the jets. The large pressure drop across the b o t t o m plate also ensures that no large eddies are transported into the rod bundle. The water exits the test section from the side of the top p l e n u m chamber. The rods extend to the top of the test section a n d are positioned a n d supported at the top with holes in the plate covering the outlet p l e n u m chamber. The rods are sealed with O-rings against the top plate. To minimize rod vibrations, the rods are screwed into the b o t t o m plate a n d stretched a n d held snug on top with a screw a n d bolt a r r a n g e m e n t above the O-rings.
4. Experimental procedure Laser doppler measurements were m a d e at 61 hydraulic diameters from the entrance of the test channel. T h e L D V was m o u n t e d on a two dimensional traversing m e c h a n i s m so the m e a s u r e m e n t volume could be translated along the optical axis ( y axis) a n d n o r m a l to it ( x axis). The horizontal velocities measured are normal to the rods, along the x axis with the primary flow in the vertical ( z ) direction. All measurements were
m a d e in the rod gaps. The region of measurement was 0.4 pitch (rod gap) by 3 pitch (width of duct). Half of this region, 7.62 m m × 40 m m was divided into 110 grid points with 5 grid points in the x direction and 22 grid points in the y direction. The position of m e a s u r e m e n t was determined using 0.001 in dial gages. The measured parameters were: the two mean voltages and R M S values of the LDV processor (frequency tracker) outputs, the temperature and pressure of the water in the test section, the mass flow rate a n d the location of measurement. The first two values were n o t e d by the P D P 8 / e system in r a n d o m bursts for a total of 2000 data points for each of the two components, in a b o u t 60 s time [14]. The fluid temperature was measured by a C h r o m e l - A l u m e l thermocouple in the test section a n d the pressure with a Heise pressure gage. A n orifice meter was used to measure the mass flow rate. Those data noted manually were input to the m i n i c o m p u t e r with a Teletype, for inclusion in the calculation of velocity distributions. The water loop was operated for a b o u t two hours prior to a run to remove dissolved air and to achieve steady state conditions. Measurements were m a d e at three nominal Reynolds numbers: 10000, 20000 a n d 40000. The turbulence characteristics and the effects of the entrance jets upon it were checked by inserting a cylinder of small diameter (3 m m ) across the flow near the entrance. N o noticeable differences in mean velocity or the turbulence intensity were found at the m e a s u r e m e n t section with the cylinder in place. Imperfections in the rods gave rise to slightly asymmetrical subchannels. The bow in the rods was less than 0.25 m m (0.010") over the 2 m length, but even this a m o u n t is enough to introduce asymmetries in the flow. Some of the results presented bear out this fact in the form of asymmetrical profiles.
5. Results Fig. 4 shows the distribution of m e a n velocity normalized with the bulk (average) velocity for a Reynolds n u m b e r of 21000. The y coordinate is normal to the glass wall a n d along the optical axis; the x coordinate is measured in the rod gap, n o r m a l to y. The values of x range from zero to unity across the rod gap. The measurement volume of the L D V had a diameter of 0.4 mm, so the data closest to the rods were at least half of this distance away. The location of the five traverses in the y direction are also shown in fig. 4. The velocity profiles for x = 0.0 a n d 1.0 show m i n i m a adjacent to the rods, at y = 0.5 a n d 1.5. The presence of
109
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the rods is discernible for the other traverses ( x = 0.25, 0.5 and 0.75) as well, but the minima are not as pronounced. The local mean axial velocity is a complex function of the space variables. The maximum normalized vertical velocities are about 1.45, 1.39 and 1.35 for Reynolds numbers of 10000, 20000 and 40000 respectively and are larger than the 1.28 reported by Rowe [5] at Re = 100 000. A discussion of this topic is postponed for a later section. Fig. 5 is a plot of vertical velocity across the rod gap at several values o f y for Re = 41 000. The local maxima in the gap center between rods at y = 0.5 and y = 1.5 can be clearly seen, with rather flat profiles for other locations. Fig. 6 shows a composite of the above vertical velocity results in contour maps for Re = 10000, 20000 and 40000. The movement of the maxima locations and their decrease with Reynolds number are clearly brought out in this figure. The effect of the near wall can be observed at all Reynolds numbers, but the character of the effect changes with Reynolds number. To study the overall flow patterns, measurements were also made for the total width of the test section in the center of the rod gap (x = 0.5). Figs. 7 and 8 are
plots of these data. The y value ranges from 0 to 3, the vertical velocity has maxima of 1.32 and 1.3 and there is a local minimum at y = 1.5. The axial turbulence intensity across the channel is shown in fig. 8 for a Reynolds number of 40 000. The lowest values of the turbulence intensity are slightly over five percent and highest values near the walls are about ten percent. Turbulence intensity profiles at Re = 20000 are shown in fig. 9 for five x values. The turbulence intensity is in general higher than that seen in pipe flows. Near the channel walls and rods, the highest values are noticeable. Near wall values reach about 13 to 15%. The minimum values are about 6%. These turbulence intensity results are shown in contour form in fig. 10. At these Reynolds numbers the turbulence intensity appears to be only minimally dependent on Reynolds number. Fig. 11 shows the horizontal turbulence intensity along the center line of a rod-gap ( x = 0.5). The measured values range from 4.0 to 5.5% with minima between rods and maxima at the subchannel center. The maxima and minima are clearly seen in the figure. To visualize what may be expected for the mean
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112
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
bisector. For the traverses at x = 1.0 and 0.25, inferred velocity peaks in such ideal lateral flow cells are also sketched in fig. 12. Fig. 13 shows an LDV traverse in the subchannel adjacent to the plane wall, next to one of the rods (x = 1.0), for R e = 2 0 0 0 0 . The negative and positive peaks are clearly shown, but a positive value was obtained for the first point. Data were obtained only part way into the second subchannel ( y = 0.7) because of the divergent character of the horizontal beam and interference with the first rod. The maximum values are about 1% of the bulk velocity. Similar results are shown in figs. 14 and 15 at x = 0.25 for Re = 40000 and 20000 respectively. In fig. 14, we can identify the first two positive peaks and the first two negative peaks similar to those in fig. 12 for x = 0.25. The second negative peak seems to be disproportionately large and the third negative peak is missing. Parameters of small magnitude, such as the horizontal velocity, may take on unexpected values even with the smallest of disturbances. As mentioned earlier, we had difficulty positioning the rods symmetrically since they tended to bow. This eccentricity could easily explain the above behavior. Also since these measure-
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ments were made using a frequency shift in the doppler signal, and the velocities plotted were calculated by subtracting the Bragg cell frequency shift, the zero could be in error by as much as 0.1% of bulk velocity. To minimize this error, the Bragg cell frequency shift was measured directly, before every data set, using the light scattered from a wall. The overall uncertainty in the electronics was about + 5 1 0 Hz. Corresponding to a typical 0.01 MHz doppler shift for the lateral velocities the uncertainty in the normalized mean horizontal velocities is expected to be about _+ 10%. The Reynolds stress (u'w') was computed directly from the cross correlation of the vertical and horizontal velocities and also from measurements of _+45 ° component turbulence intensities. Fig. 16 shows a traverse between the rods at x = 0.25 for u'w' nondimensionalized with the friction velocity based on the overall pressure drop in the bundle. A t y = 0.5, 1.5 and 2.5 u'w' normalized with the square of the local friction velocity (W*2) should vary from - 1 to + 1 across the rod gap. If the variation of u'w' (with x) along the rod gap were linear, the normalized value should be _+0.5. At x = 0.25, the actual value as indicated in fig. 16 is close to 0.2. Measurements repeated by the +45 ° technique also
113
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postpone discussion of this anomaly to a later section. The results presented above were all obtained with the use of a LAB 8 / e minicomputer. This system was fast in acquiring data, but slow in analyzing it• Analog electronic processing does not have this limitation. Hence it was decided to acquire some data manually, with analog electronic processing, for verification purposes. A voltage to frequency converter (VFC) and an events per unit time (EPUT) meter were used to average mean velocity data over ten second intervals. The turbulence intensities were measured with a D I S A type 55D35 R M S unit, with a ten second time constant. The results obtained by this method were virtually identical to those presented earlier. The LDV processor output voltages plotted directly on an x - y plotter are shown in figs. 17 and 18. To produce these figures, the x-axis of the plotter was driven by the output of a linear displacement transducer (Hewlett-Packard 24DCDT-1000). The vertical velocity profile close to the rods, at a Reynolds number of about 10000, shows the relationship between the mean velocity and turbulence intensity. The horizontal velocity profile in the rod gap, fig. 18, shows positive and negative directional changes of the horizontal velocity• The magnitude of the horizontal turbulence is comparable to or even larger than the horizontal mean velocity.
114
S. Neti et al. / Laser doppler measurements of flow in a rod bundle
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6. Discussion of results
The maximum values of mean velocity measured in units of the bulk (average) velocity were 1.35, 1.39 and 1.45 at 40000, 20000 and 10000 Reynolds numbers, respectively. This Reynolds number trend agrees with that observed by Laufer [7] for pipe flow and by Trupp and Azad [12] for a triangular pitch rod bundle with a pitch to diameter ratio of 1.35. Rowe's [5] work in square pitch rod bundles shows only a minor dependence of the maximum vertical velocity on Reynolds number, but his results were for much higher Reynolds numbers where we expect the dependence on Reynolds number to disappear. The maximum of mean vertical velocities reported by Rowe were smaller than those seen here. The measurement locations were about 60 hydraulic diameters from inlet in Rowe's as well as the present work. It is conceivable that the maxima in the vertical velocities decrease to the lower values (1.28) at higher Reynolds numbers (100000). The inlet conditions used in this work are different from those of Rowe [5]. Rowe used a side entrance with a ninety degree turn, followed by staggered grids and parallel tube banks to straighten the flow. We used a jet type of entrance geometry. Some of
the differences in these two data sets may also be due to the different entrances used. Our measured vertical turbulence intensities are larger than those found in pipe flows. The minimum values of turbulence intensity measured in the subchannel centers are about 6%. Large turbulence intensities (10 to 15%) were found near channel walls and close to the rods. Reynolds number is not a dominant factor for turbulence intensity at least not at the present measurement conditions. Vertical turbulence intensities measured here are about one percent larger than those reported by Rowe [5]. The scatter in the turbulence data is large, possibly due to three reasons: (1) fluctuations in the overall flow giving rise to scatter in the data, (2) apparent scatter caused by the convection of turbulence kinetic energy by the secondary flows and , (3) the jet type of entrance used in the present work which may have contributed to the larger turbulence intensities measured. The mean horizontal velocity distributions presented here are believed to be the first measurements made in rod bundles. The maximum horizontal velocities are about one percent of bulk velocity. Some of the horizontal velocity data support the existence of the ideal secondary flow loops depicted in fig. 12, that could not be inferred from the vertical velocity data. Rowe [5] inferred the existence of similar secondary flow loops based on his vertical turbulence intensity contours. He also proposed the possibility of additional flow cells. Such extra cells might also have occurred in the present work, but they could not be identified from the measurements. Horizontal velocities measured here are larger than those proposed by Trupp and Azad [12] and Carajilescov and Todreas [10]. Both these works are related to triangular pitch rod bundles. These authors suggested 0.67% and 0.5% maximum lateral velocities respectively from their turbulence intensity data. In the results presented here, the scatter in the horizontal velocity is large because the parameter being measured is very small in magnitude. Another possible explanation for the seeming scatter is the existence of more secondary flow cells as suggested by Rowe. The scatter is larger at lower Reynolds numbers probably because the velocities measured are even smaller. The horizontal velocity data do indicate an overall trend similar to that in fig. 12. Horizontal turbulence intensity measurements indicate values from 4 to 5.5%. These data are normalized with the bulk velocity. Larger values are noticeable near the walls (parallel to horizontal velocity) and in the subchannel centers where maximum mean horizontal velocities are possible. In the center of the rod gap
S. Neti et al. / Laser doppler measurements of flow in a rod bundle spacing, smaller values are seen to occur. The measured Reynolds stress u'w' has been noted to be much smaller than expected. In the rod gap, u'w' normalized with the square of the friction velocity was expected to vary from + 1 to - 1 across the rod gap. The absolute values of the measured maxima were less than 0.5. The data were measured by two completely different techniques: (1) by the cross correlation of the vertical and horizontal velocities and (2) as the difference of +45 ° component turbulence intensities. Using the latter method u'w' is half of the difference of the +45 ° component turbulence intensities. Both these methods gave consistent and repeatably low values of u'w'. While in search of an explanation for this anomaly, we found that Trupp and Azad [12] had similar difficulties for two of their three data sets. They made hot wire anemometer X-probe measurements in a triangular pitch rod bundle. For a pitch to diameter ratio of 1.5 and 36000 Reynolds number, their maximum value of ( u ' w ' / W .2) near the wall reached only 0.46. Their values of u'w' measured for smaller Reynolds numbers were farther from unity than those at large Reynolds numbers. They report lower values of near wall u'w', when larger secondary velocities were indicated. From the above observations and in consideration of the fairly large horizontal velocities measured in this work, the ( u ' w ' / W .2) measurements are in agreement with Trupp's work. Three more possible comments can be made in this regard: (1) The u'w' should, in the strictest sense, be nondimensionalized with the square of the local friction velocity. Use of the local wall shear stress values [15,16] which are about 0.95 of mean shear stress do not quite explain the present discrepancy. (2) The variation of u'w' in the rod gap may not be linear in the presence of secondary flows of the type reported here, (3) u'w' may not behave linearly in the rod gap due to asymmetries in the flow. The small u'w' values remain to be explained. Measurements made in the -I-45° component mode yielded reasonable data for the mean vertical velocity but not for the horizontal velocity. Horizontal velocities of very small magnitude cannot be measured as the difference of the two large +45 ° component mean velocities. As mentioned earlier, u'w' values measured with this technique were similar to those measured in the vertical and horizontal velocity mode.
115
7. Conclusions (1) Measurements have been made in fully developed turbulent flow in a simulated nuclear fuel rod bundle of square pitch lattice. Three different measurement techniques were used. Most of the data presented were acquired with the use of a minicomputer. (2) Measured vertical velocities are somewhat larger than those reported by Rowe [5] but the discrepancy may be explained by the large difference in Reynolds numbers in the two experiments. (3) Vertical turbulence intensities are larger than those reported for pipe flows. The minimum values range from 5.5 to 6.5%. The horizontal turbulence intensities range from 4 to 5.5%, and are larger in regions of larger lateral velocities. (4) Measurements of mean horizontal velocities are reported and the maximum horizontal velocities are about one percent of bulk velocity, somewhat larger than suggested by some earlier authors. The measured velocities indicate lateral flow loops in a subchannel. (5) Reynolds stresses measured by two different techniques (cross-correlation and +45 ° measurement) were much lower than those in pipe flow and are similar to some of those observed by Trupp and Azad [12].
Nomenclature D P Re U u' W w' W* u'w' x
y z
rod diameter (19.05 mm, 3/4") pitch ( = 1.4D) Reynolds number based on bulk velocity and bundle hydraulic diameter mean lateral velocity (along x-direction) horizontal turbulence intensity mean axial velocity (along z-direction) vertical turbulence intensity friction velocity based on overall pressure drop Reynolds stress non-dimensional rod gap (0.0 to 1.0, rod to rod) horizontal coordinate normal to the rods and the laser velocimeter axis horizontal coordinate normal to the rods and along the laser velocimeter axis vertical coordinate along the rods and primary flow
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S. Neti et al. / Laser doppler measurements of flow in a rod bundle
References [1] J. Weisman and R.W. Bowring, Methods for detailed thermal and hydraulic analysis for water cooled reactors, Nucl. Sc. Engrg. 57 (1975) 4. [2] R.G. Diessler and M.F. Taylor, Analysis of axial turbulent flow and heat transfer through banks of rods or tubes, Reactor Heat Transfer Conference, 1956, TID-7529, Part I, Bk, 2, pp. 416-461. [3] B. Kjellstrom, Studies of turbulent flow parallel to a rod bundle of triangular array, A.B. Atomenergi, Studsvik, 611 01, Nykoping, Sweden, STU 68-263/U210 (1971). [4] B. Kjellstrom, Transport processes in turbulent channel flow, A.B. Atomenergi, Studsvik, 611 01 Nykoping, Sweden, STU 70-409/U340 (final report) AE-RL-1344. [5] D.S. Rowe, Measurement of turbulent velocity, intensity and scale in rod bundle flow channels, Ph.D. Thesis, Oregon State University, Corvallis, Oregon (1973). [6] J. Laufer, Investigation of turbulent flow in a two-dimensional channel, NACA Report No. 1053 (1951). [7] J. Laufer, The structure of turbulence in fully developed pipe flow, NACA-TN-2954 or NACA Report No. 1174 (1954). [8] R. Nijsing, I. Gargantini and W. Eifler, Analysis of fluid flow and heat transfer in a triangular array of parallel heat generating rods, Nucl. Engrg. Des. 4 (1966) 375-398. [9] L. lngesson and S. Hedberg, Heat transfer between sub-
[10]
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[16]
channels in a rod bundle, Heat Transfer 3 (1970) p. FC7. 12p. P. Carajilescov and N.E. Todreas, Experimental and analytical study of axial turbulent flows in an interior subchannel of a bare rod bundle, Trans. ASME, Ser. C., J. Heat Transfer 98 (1978) 262-271. M.Kh. Ibraglmov, I.A. Isupov, L.L. Kobzar and V.I. Subbotin, Calculation of the tangential stresses at the wall in a channel and the velocity distribution in a turbulent flow of liquid, Soviet Atomic Energy 21 (1966) 731-739. A.C. Trupp and R.S. Azad, The structure of turbulent flow in triangular array rod bundles, Nucl. Engrg. Des. 32 (1975) 47-84. D.S. Rowe, Progress in thermal hydraulics for rod and tube bundle geometries, in: Fluid Flow and Heat Transfer Over Rod and Tube Bundles, Eds. S.C. Yao and P.A. Pfund, ASME (1979) pp. 1-12. S. Neti, Measurement and analysis of flow in ducts and rod bundles, Ph.D. Thesis, University of Kentucky, Lexington, Kentucky (1977). R. Eichhorn, H.C. Kao and S. Neti, Measurements of shear stress in a square array rod bundle, Nucl. Engrg. Des. 56 (1980) 385-391. M. Abdel-Ghany and R. Eichhorn, Measurements of wall shear stress in axial flow in a square lattice rectangular rod bundle, A I A A / A S M E Fluids, Plasma, Thermophysics and Heat Transfer Conference, St. Louis, MO, June 1982.