the structure of turbulent ow in a rectangular channel containing a cylindrical rod - part 1 reynolds-averaged measurements

1、Experimental Thermal and Fluid Science 23 (2000) 59?73www.elsevier.nl/locate/etfsThe structure of turbulent ?ow in a rectangular channel containing a cylindrical rod ? Part 1: Reynolds-averaged measurementsM.S. Guellouz 1, S. Tavoularis *Department of Mechanical Engineering, University of Ottawa, Ot

2、tawa, Ont., Canada K1N 6N5 Received 4 April 2000; received in revised form 28 July 2000; accepted 14 August 2000AbstractFlow visualization and hot-wire anemometry were used to investigate the isothermal velocity ?eld in a rectangular channel containing a single cylindrical rod, focussing on the gap

3、region between the rod and a plane wall. Measurements reported in this paper, which is part 1 of a two-part series, include the variations of the Reynolds-averaged mean velocity, wall shear stress and turbulent stresses. The presence of large-scale, quasi-periodic structures in the vicinity of the g

4、ap, for a range of gap widths, has been demonstrated through ?ow visualization, spectral analysis and space-time correlation measurements. The above measurements appear to be compatible with the ?eld of a street of three-dimensional, counter-rotating vortices, whose convection speed and streamwise s

5、pacing have been determined as functions of the gap width. ? 2000 Elsevier Science Inc. All rights reserved.Keywords: Rod bundle; Gap ?ow; Turbulence; Vortices; Coherent structures; Strouhal number; Hot-wires; Space-time correlations1. Introductionsheath temperature and the maximum allowable cir- cu

6、mferential variation of this temperature. The accurate prediction of temperature ?elds and CHF characteris- tics, both under normal operating conditions and under scenarios of accidents such as the loss-of-coolant acci- dent (LOCA), is essential for a safe and e?cient oper- ation of the reactor. A h

7、ighly accurate prediction can only be based on a detailed knowledge of the three-di- mensional velocity ?eld in the rod bundle and a good understanding of the mixing process between intercon- nected subchannels. Unfortunately, the physical mech- anisms that contribute to the intersubchannel mixing p

8、rocess have not yet been completely described, and the prediction of the thermalhydraulic performance of a reactor is commonly based on empirical procedures. In particular, the well-known fact that the local friction factor and the local convective heat transfer coe?cient in narrow gaps maintain rel

9、atively large values for a wide range of gap sizes, and diminish appreciably only when the gap becomes extremely narrow, is still lacking a sound and precise theoretical explanation. Conven- tional turbulence analyses, based on local transport concepts, have been grossly inadequate to predict the in

10、sensitivity of these parameters, while it is clear that the heat transfer and mixing across the gap occur at a scale much larger than the gap size. Among the various rel- evant explanations, the most successful one appears to be that cross-subchannel mixing is greatly enhanced byFully developed ?ows

11、 in non-circular channels are known to exhibit patterns not encountered in circular pipe ?ows. In particular, distinct ?ow phenomena occur in compound channels with cross-sections containing relatively wide ?ow regions adjacent to narrower ?ow regions, such as the fuel rod bundles that comprise the

12、cores of most nuclear reactors. Rod bundles consist of a parallel matrix of solid rods, containing a ?ssile mate- rial, among which ?ows a coolant ?uid, which removes the heat generated by the nuclear ?ssion. Thus, a rod bundle contains a number of parallel subchannels, in- terconnected through narr

13、ow gaps between two rods or a rod and the surrounding pressure tube wall. Mass, momentum and heat transfer between adjacent sub- channels occur mainly by turbulent transport, referred to as intersubchannel mixing. The maximum thermal power produced by the reactor is controlled to ensure integrity of

14、 the sheath, taking into consideration the critical heat ?ux (CHF), the maximum allowable rod* Corresponding author. Tel.: +1-613-562-5800 ext.6271; fax:+1-613-562-5177.E-mail address: taveng.uottawa.ca (S. Tavoularis).1 Present address: Atomic Energy of Canada Ltd., 2251 Speakman Drive, Mississauga

15、, Ont., Canada L5K 1B2.0894-1777/00/$ - see front matter ? 2000 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 0 0 ) 0 0 0 3 8 - 860M.S. Guellouz, S. Tavoularis / Experimental Thermal and Fluid Science 23 (2000) 59?73transport due to large-scale, quasi-periodic pulsations, whi

16、ch form across the gap.Flow pulsations in rod bundle ?ows were ?rst de- tected by Rowe et al. 1, who observed signi?cant pe- riodicity in the axial velocity autocorrelation function, which diminished as the pitch-to-diameter ratio, P=D, increased. Systematic studies of such pulsations by Hooper 2 an

17、d Hooper and Rehme 3 concluded that the pulsation frequency was proportional to the Rey- nolds number and that the periodic component of the momentum exchange became more dominant as the gap width was reduced. Further experiments by Mo ller 4, using spectral analysis of velocity and pressure signals

18、, identi?ed the presence of nearly periodic ?ow patterns, whose characteristic frequency increased with increasingbeen recently presented by Kraussand Meyer 5,6,while similar types of structures have also been observed in other types of channels containing slot-like narrow regions connected to large

19、r subchannels. For example, Meyer and Rehme 7 documented such structures in the slot region of two simple compound channels, one formed by two rectangular subchannels connected by a slot and the other consisting of a single rectangular channel with a slot, and correlated their frequency with the slo

20、t geometry and the bulk velocity; for the former con?guration, these authors proposed a model of two- dimensional, counter-rotating vortices, with centers on either side of the plane of symmetry and convected ax- ially within the gap; they also found the streamwise spacing of the vortices to be inde

21、pendent of the Rey- nolds number and their convective speed to be roughly equal to the average of the minimum velocity at the center of the gap and the velocity at the edge of the slot. Following the same approach, Meyer and Rehme 8 further documented the formation of large-scale coher- ent structur

22、es in the slot regions of three rectangular channels, containing, respectively, a slot, two ?ns and eight ?ns, even for the case with the low Reynolds number (based on the slot width) of 150. They studied the eect of viscosity by using air, water and a water? glycol mixture, and concluded that, with

23、in the range of their experiments, the axial spacing of the structures depended on the geometry of the slot, but not on theReynolds number and with diminishing gap Mo ller 4 also found that the Strouhal numberwidth.fDSs ? u ;?1?where f is the frequency of the spectral peak and u is the friction velo

24、city, was inversely proportional to the gap width and independent of the Reynolds number. Hooper and Rehme 3 attributed these ?ow pulsations to a parallel-channel instability mechanism, while Mo ller 4 modeled them by a street of vortices in the gap region. Evidence for the formation of quasi-period

25、ic structures in a large-scale, heated, 37-rod bundle hasNomenclatureUbbulk velocity (m/s)Acoe?cient in response equation ofUcmean convection velocity of co- the hot-?lm wall shear stressherent structures (m/s)probe (Eq. (2) (V2)u; v; waxial, transverse and spanwise Bcoe?cient in response equation o

26、fvelocity ?uctuations, respectivelythe hot-?lm wall shear stress(m/s)probe (Eq. (2) (V2=Pa1=3)ufriction velocity (m/s)Cfskin friction coe?cient (dimen-uuazimuthal velocitycomponent sionless)(m/s)D rod diameter (mm)Wsum of rod diameter and gap Dhhydraulic diameter (mm)width (see Fig. 1) (mm)E voltage

27、 (V)x; y; zaxial, transverse and spanwise ffrequency (Hz)coordinates, respectively (m)kturbulent kinetic energy per unitGreeksmass ?m=s2 ?Dttime delay for maximum correla-maxPpitch (distance between adjacenttion (s) rod centers in a rod bundle) (mm)RehReynolds number based on thekstreamwise spacing

28、of structures hydraulic diameter (dimension-(mm)3less)qdensity ?kg=m ?Ruu;Ruw;Rwu;Rwwtwo-point correlation coe?cientsswwall shear stress (Pa) (dimensionless)uazimuthal coordinate (?)rradial coordinate (mm)Other notationSsStrouhal number (dimensionless)?. .?time-averaged quantityTperiod of oscillatio

29、n (s)?. .?root mean square ?uctuationttime (s)D?. .?dierence in the values of a U; V ; Waxial, transverse and spanwisequantity at two positions or times velocity components, respectivelyd?. .?uncertainty of a measured quan-(m/s)tityM.S. Guellouz, S. Tavoularis / Experimental Thermal and Fluid Scienc

30、e 23 (2000) 59?7361?ow velocity and viscosity. The only available analytical study aimed at predicting coherent structures in narrow gaps is a large eddy simulation by Biemu ller et al. 9, in channel consisting of two rectangularsections connected by a slot near the wall. This study was in qualitati

31、ve agreement with an experiment and predicted the forma- tion of two counter-rotating vortices with centers on opposite sides of the gap plane of symmetry. In recent years, a few attempts to incorporate the eects of large- scale pulsations in lumped parameter types of analyses of inter-subchannel mi

32、xing have also been made 10?15. The above studies have demonstrated beyond doubt the presence and importance of quasi-periodic ?ow structures in rod bundles, however, they have not yet adequately described the physical features of these structures. In particular, there has been no known at- tempt to

33、 exploit the sophisticated pattern recognition and phase averaging methods that have been applied suc- cessfully to the detection of coherent structures in other types of turbulent ?ows. The objectives of the present study were to fully characterize experimentally the co- herent structures in narrow

34、 axial regions of compound channels and to develop a physical model that explains their apparent eects. Motivation for this project was providedbythethermalhydraulicperformanceofnuclear reactor rod bundles, particularly those of the CANDU reactor. However, it was realized that ?ow in a channel of ex

35、cessive geometrical complexity, such as a rod bundle, is in?uenced by several phenomena, which might obscure the eects of individual rod-wall gaps. For this reason, it was decided to utilize a prototype channel, which con- tains an adjustable, narrow, axial gap region but is oth- erwise simple. The

36、selected geometry consists of a rectangular channel containing a suspended circular rod with a diameter small enough, compared to the channel height and width, for the ?ow away from the gap region to be relatively free of gap eects. The results will be reported in two complementary papers. In the pr

37、esent paper, we report conventional, Reynolds-averaged turbulence measurements in the channel, as well as two-point cor- relations and spectra documenting the formation of quasi-periodic ?ow pulsations across the gap and the dependenceoftheirfrequencyandamplitudeonthegap- to-rod-diameter ratio. In a

38、 companion paper (Part 2), we shall present conditionally averaged measurements, showing the phase-averaged features of the coherent structures and we will attempt to formulate a relevant physical model. It is hoped that the present work will contribute to the understanding of these important ?ow ph

39、enomena and will facilitate the development of meth- odsincorporatingtheireectsinthepredictionanddesignof rod bundles and other complex engineering systems.Fig. 1. Sketch of the ?ow facility.rectangular channel, with an aspect ratio of 2/3, con- taining a suspended aluminum pipe (rod) with an extern

40、al diameter D ? 101 mm. The rod was positioned so that it would form an adjustable narrow gap with the channel base, made of plexiglass. The other three sides of the channel were formed by bent aluminum sheets. All wetted surfaces were hydraulically smooth. The hydraulic diameter and the length of t

41、he test section were, respectively, Dh ? 1:59D and L ? 54:0D, corre- sponding to L=D 34. The channel was supplied with air produced by a blower through a pressure box with a cross-section 9.4 times the test section ?ow area. A metallic woven screen was stretched across the entrance of the channel in

42、 order to enhance the rate of ?ow de- velopment towards its fully developed state. The rod was suspended at both ends as well as at a location 20D downstream of the channel entrance. Each support was equipped with a traversing mechanism, utilizing ?nely threaded bolt-and-nut assemblies and dial gaug

43、es, to provide accurate positioning of the rod with respect to the channel base. Circular ports were machined at sev- eral positions through the base wall and ?tted with in- terchangeable plugs carrying pressure taps or measuring probes. In addition, spanwise traversing of wall-inserted probes was a

44、chieved by mounting them on a plate sliding through a slot on the base, 2.8D upstream of the channel exit.Flow visualization was eected using smoke injec- tion. A mist of mineral oil droplets, produced by a smoke generator (Nutem, System E), was injected isokinetically at the center of the gap throu

45、gh a thin tube inserted into the channel through one of the plugs on the plane wall. The equidistant plane ?y=D ? 1=2?W=D 1?; see Fig. 2) was illuminated with a thin sheet of light produced by passing the beam of a 100 mW Ar-Ion laser through a cylindrical lens. The visualized ?ow was recorded by a

46、video camera, which had a minimum exposure time of0.001 s and a ?xed speed of 30 frames/s.The mean wall shear stress around the rod was measured with a set of Preston tubes 16, having an outer diameter of 0.79 mm and an inner to outer di- ameter ratio of 0.64, glued to the rod surface at ?xed2. Expe

47、rimental set-up and procedures2.1. Flow facility and instrumentationThe ?ow facility (Fig. 1) was setup as an open-discharge wind tunnel, whose test section consisted of a62M.S. Guellouz, S. Tavoularis / Experimental Thermal and Fluid Science 23 (2000) 59?73coordinate system shown in Fig. 2, at x=D1

48、:8. Inthe gap region, where signi?cant velocity gradients were encountered, the spatial resolution of the three-wire probe was relativelypoor, therefore, only measurements on the equidistant plane ?y=D ? 1=2?W =D 1? were conducted with this probe; additional measurements in the gap region were obtai

49、ned using a cross-wire probe, traversed around the rod at x=D 2:5.2.2. Experimental procedures and accuraciesAll uncertainties reported herein correspond to a con?dence level of 95%, according to current interna- tional standards 18,19.The uncertainty of the wall shear stress, sw, measured with Pres

50、ton tubes and accounting for uncertainties in pressure readings and in Patels expression, was 0.5%. The measurement of wall shear stress with a ?ush- mounted hot-?lm probe was based on the analogy between heat and momentum transfer 20 using the semi-empirical expressionFig. 2. Coordinate systems and

51、 grid (5 mm 5 mm in region 1 and 10 mm 10 mm in region 2) for the three-sensor probe measurements. De?nition of the equidistant and symmetry planes.angular intervals of 10 . The eect of possible interfer- ence between adjacent Preston tubes was investigated by comparing their readings with those of

52、an isolated tube and were found to be negligible. The shear stress was computed by applying the analysis of Patel 17. Mea- surements of the mean and ?uctuating wall shear stress on the channel base were conducted with a ?ush- mounted hot-?lm probe (TSI, model 1268), consisting of a platinum ?lm with

53、 a length of 1.5 mm and a width of0.5 mm, deposited on a quartz cylinder. This probe was?tted on a Te?on sleeve, to prevent local melting of the plexiglass plug due to the high operating temperature of the ?lm (523 K).An assortment of hot-wire probes, including single, cross- and triple-sensor probe

54、s, has been used for mea- suring ?ow velocity. A single hot-wire probe (DAN- TEC, model 55P14 with a wire length of 1.25 mm) and a cross-wire probe (TSI, modi?ed model 1249 with sensor lengths of 1 mm and sensor separation of 0.51 mm) were inserted through the channel base, while a single wire probe

55、 (TSI 1260AJ-T15 with a wire length of 1.30 mm), a cross-wire probe (TSI, model 1248 with wire lengths and separation of 1 and 0.51 mm, respectively) and the three-wire probe were inserted into the ?ow from the exit end of the channel. Except for the latter, these probes were mounted on a mechanism

56、which permitted azimuthal, radial and longitudinal traversings with re- spect to the rod, with resolutions of 0:5 , 0.05 and 1 mm, respectively. The three-wire probe (AUSPEX, AVE-3- 102) had sensors with lengths of 1 mm and arranged on the edges of a pyramid forming angles of 45 with the probe axis

57、and con?ned within a sphere of 1.5 mm di- ameter and was traversed, using a dierent positioning system, in the vertical and spanwise direction, with re- spect to the channel base. All hot-wire and hot-?lm sensors were operated by a multichannel constant tem- perature anemometer (AA Lab Systems, mode

58、l AN- 1003). The signals were conditioned, low-pass ?ltered at3.8 kHz and digitized simultaneously at a rate of 10 kHz using a 16-bit analog-to-digital converter (IOtech, model ADC488/16).Most of the velocity measurements were performed using the three-sensor probe, according to the grid andE2 ? A ? Bs1=3;?2?wwhere E is the voltage output and the adjustable coef-?cients A and B were determined by in situ calibration vs. a Preston tube. The uncertainty on the mean and the variance of the wall shear st