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Experimental investigation of turbulent natural convectionflow in a converging channel

T.F. Ayinde

Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, P.O. Box 129, Dhahran 31261, Saudi Arabia

Received 12 September 2007; received in revised form 2 February 2008; accepted 6 February 2008

Abstract

This paper reports the results of fluid flow measurements for natural convection in a converging plates channel using the particleimage velocimetry (PIV) system. The channel walls were symmetrically subjected to uniform temperature conditions. Velocity character-istics were obtained for two inclination angles, h= 15 and 45, and two heating conditions corresponding to RaL= 2.7 10

8 and4.4 108, whereRaLis the Raleigh number based on the length of the channel wall. Results are presented as vector plots as well as pro-files of mean velocities and turbulence quantities. They show that the main flow is aligned with the orientation of the channel walls, dueto the effect of buoyancy force, which is no longer exclusively in the vertical direction. They also reveal the presence of reverse flow, whichleads to the formation of two symmetric vortices in the core. 2008 Elsevier Inc. All rights reserved.

Keywords: Natural convection; Converging channel; Buoyancy; PIV; Experimental investigation

1. Introduction

Buoyancy-driven flow in open-ended channels hasreceived considerable attention from researchers becauseit is representative of many practical heat transfer applica-tions. Common applications include the cooling of elec-tronic equipment and nuclear reactors, room ventilation,grain drying, and solar collectors. Elenbaas [1] carriedout a detailed study of the thermal characteristics of cool-ing by natural convection in smooth parallel-walled verticalchannels. This pioneering experimental work laid the foun-

dation for the study of natural convection in vertical chan-nels of isothermal parallel plates. More investigations havesince followed, both experimentally (e.g.[29]) and numer-ically (e.g.[1015]).

While great efforts have been made to understand thenatural convection flow problem in parallel-plates channel,the flow in converging plates channel has received limited

attention. Converging plates channel with top opening, ifemployed as roof of an enclosure, can be useful both forenhanced air circulation and a means of reducing heattransfer to the enclosure. Both are accomplished as a resultof natural convection flow around the plates.

Sparrow et al.[16] investigated the Nusselt number cor-relation for buoyancy-driven flow in converging channelfor inclination angles of 015. Using water as the workingfluid, they concluded that employing the modified Rayleighnumber based on maximum inter-plate spacing results inthe same Nusselt number correlation for all inclination

angles. This conclusion was also reached by Said [17] forair flow in a converging channel. Kaiser et al.[18]extendedthe study to the upper Rayleigh number range and showedthat correlation was best achieved when the Rayleigh num-ber was modified with the minimum inter-plate spacing.

The numerical analysis of Bianco and Nardini [19] forair in a vertical channel revealed the formation of two sym-metric vortices associated with the choking and reverseflow in the channel. Bianco et al. [20] proposed designcharts for estimation of Nusselt number as a function ofthe Rayleigh number and geometric parameters.

0894-1777/$ - see front matter 2008 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2008.02.001

Tel.: +966 3 8604947; fax: +966 3 8602949.E-mail address:[email protected]

www.elsevier.com/locate/etfs

Available online at www.sciencedirect.com

Experimental Thermal and Fluid Science 32 (2008) 12041212
mailto:[email protected]:[email protected]

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The natural convection flow in converging channel wasinvestigated for different opening-to-length ratio by Kihmet al. [21]. They concluded that for each inclination andGrashof number based on plate length, there is a minimumopening below which the heat transfer is reduced. Habibet al.[22] investigated the velocity characteristics of turbu-lent natural convection in converging channel using thelaser Doppler velocimetry (LDV) system. Their result isthe only reported experimental velocity characteristics dataavailable in the literature. However, they did not report theangle of inclination of the channel walls. Thus, the result isof little or no value.

In view of the very limited available data on natural con-vection in converging channel, the objective of the presentstudy is to contribute to the literature in this regard by car-rying out measurements on turbulent natural convectionflow in a converging channel. The channel walls wereheated above ambient temperature and maintained underuniform temperature conditions. A continuous stream ofambient air flowed through the channel, by natural convec-tion, via the bottom and top openings. A particle imagevelocimetry (PIV) system was used for the measurements.

2. Experiments

2.1. Experimental setup

The experiments were carried out in a symmetricallyheated channel. A schematic diagram of the channel andthe coordinate system used in the study is shown inFig. 1. Each of the two walls is made with 16-mm-thickbrass plate with dimensions of 500 mm by 500 mm. Onthe lower side, the plate is machined to a 45 knife edgeto ensure smooth flow at the leading edge. The plate isgrooved at the back surface to provide passage for the cir-culating water used for heating the plate. The grooved sur-face is covered with aluminum plate of the same size. A

schematic diagram of the experimental setup consisting of

the channel assembly, the enclosing chamber, and the mea-surement system is shown inFig. 2. Each plate is fixed to asupport system on either side. The circular slot in the sup-port system allows the plate to be inclined at any desired

angle. The angles considered in this experiment were 15

Nomenclature

B inter-plate spacing (m), B= b+ 2H[1 y/H]tanh

b opening at the top of the channel (m)

G gravitational acceleration (m/s

2

)H channel height (m),H= L sinhL length of each wall of channel (m)RaL Rayleigh number (dimensionless), RaL=gb

(Ts Tf)L3/(at)

Tf ambient temperature (C)Tfilm film temperature (C), Tfilm= (Ts+ Tf)/2Ts plate surface temperature (C)U mean horizontal velocity component (cm/s)u0 horizontal velocity fluctuation (cm/s)u0v0 Reynolds shear stress (cm2/s2)

V mean vertical velocity component (cm/s)v0 vertical velocity fluctuation (cm/s)W channel depth (m)

X transverse coordinate (m)Y streamwise coordinate (m)Z spanwise coordinate (m)

Greek symbols

a thermal diffusivity (m2/s)b coefficient of volumetric expansion (K1)h Angle of inclination of plates (degrees)t kinematic viscosity (m2/s)

L

b

x

y

z

W

Water in

Water out

Fig. 1. Flow channel and coordinate system.

L : Laser

LS : Light Sheet

M : Mirror

OB : Opening at the bottom

OT : Opening at the top

P : Plate

PS : Plate Support

SP : Seeding pipe

T : Table

Fig. 2. Schematic view of the experimental setup.

T.F. Ayinde / Experimental Thermal and Fluid Science 32 (2008) 12041212 1205

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and 45. In each case the top opening (b) was maintained at10 mm. The channel/support assembly sits on a table. Theplates were kept at uniform surface temperature by meansof circulating hot water supplied by model HAAKE water-heater and pumped through the grooves in the brass plates.

The water inlet and exit ports to the grooves are shown inFig. 1. They are omitted from the schematic in Fig. 2forthe sake of clarity. During the experiments, the inlet andexit ports at the back of the plates are connected to the exitand inlet ports, respectively, of the water heater by meansof rubber hoses. The plates were insulated at the rear sur-

face to reduce heat losses. Twenty calibrated Copper-Con-stantan (K-type) thermocouples were attached to eachplate. The thermocouples were installed in holes drilledinto the rear of the plate, with junctions positioned atabout 0.5 mm from the inner surface of the plates. The dif-ference between the plate mean temperature and individual

Fig. 3. Vector plots of mean velocity magnitude of the top 25% of thechannel forh = 15 and RaL= 2.7 10

8.

Fig. 5. Mean velocity profiles on three x-yplanes in the channel at y/H= 0.80 for h = 45 and Ra = 2.7 108

.

Fig. 4. Vector plots of mean velocity magnitude of the top 40% of thechannel (covering half the channel width) for h= 45 and RaL= 2.7 108.

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thermocouple reading was not more than 1% of the tem-perature difference between the plate and the surroundingair. In order to prevent any air entrainment from the sidesof the channel, both sides were closed with thin transpar-ency film thus creating an adiabatic, no-slip boundary con-dition on the sides of the channel. In order to prevent the

influence of air draft inside the room on the channel flow,the test section was located inside a chamber made of plexi-glass. The chamber has a height of 1.83 m and cross-sectionof 1.24 m 1.24 m. The dimensions of the chamber aremade much larger than those of the experimental channelin order to prevent air stratification and chimney effectsaround the channel. The opening at the bottom of thechamber was used for injecting the seeding particles. Theopenings on the table and the roof of the chamber facili-tated the natural convection flow of the seeded air throughthe heated channel.

2.2. Instrumentation

Measurements were performed with a TSI ParticleImage Velocimetry (PIV) system, which allows two-dimen-sional planar measurements. The system consists of a laserunit, a camera, a frame grabber, a synchronizer, a com-puter and a data reduction software (INSIGHT). The laserunit is composed of a water-cooled double-pulsed laser, thecontrol unit and the light sheet optics assembled fromcylindrical and spherical lenses. The camera is of size1280 1024 pixels and operates at 8 frames per second.The synchronizer is the imaging systems timing and con-trol module. It connects to, and synchronizes, the opera-

tions of the computer, frame grabber, camera and laser.The image acquisition and processing tasks were per-formed via the INSIGHT software. A TSI model 9306six-jet atomizer was used for seeding the air. Silicon oilwas used as the seeding element. The particle diameterwas of the order of 1 lm. The jet was injected from outsideof the enclosing chamber close to, but not directly under,the bottom opening. This helped to avoid any influenceon the natural convection flow, and also to ensure that onlyneutral density particles were passing to the flow. Measure-ments performed prior to the heating of the channel wallsshowed no presence of any seeded flow inside the chamber.This confirmed that the seeding arrangement did not createany forced convection.

2.3. Measurements

Measurements were performed for the vertical center-plane of the channel for two inclination angles (h= 15and 45) and two Rayleigh numbers (RaL= 2.7 10

8

and 4.4 108), where RaL= gb(Ts Tf)L3/am. During

measurements, the double-pulsed laser produced lightpulses which were transformed into a sheet by the lightsheet optics. The sheet was focused on a plane mirror posi-tioned on the floor of the channel. The mirror, inclined at

45to the incident rays, produced a vertical reflected sheet

which illuminated the seeded flow in the channel. The cam-era recorded images by pairs and transmitted them to thecomputer. To obtain a highly magnified image it was notpossible to cover the whole channel with one camera expo-sure. The domain was therefore divided into sections and

Fig. 6. Variation of the horizontal and vertical components of the meanvelocity in the channel at different vertical locations for h= 15 and

Ra= 2.7 108. (a) y/H= 0.95; (b) y/H= 0.75; (c) y/H= 0.50. The

legends in (a) also apply to (b) and (c).


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measurements performed on each section separately. Atotal of 350 image pairs were recorded for each exposure.This was deemed sufficient to give a statistically-steadyflow.

2.4. Data processing and uncertainty analysis

Data processing was carried out using the INSIGHTsoftware to obtain the velocity vectors in the longitudinal


Ra= 4.4 108. (a) y/H= 0.95; (b) y/H= 0.75; (c) y/H= 0.50. The



Ra= 2.7 108. (a) y/H= 0.95; (b) y/H= 0.80; (c) y/H= 0.50. The



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and transverse directions. Further data processing wasdone using TECPLOT software where the mean velocities(Uand V) and the Reynolds stresses (u02; v02; u0v0) were cal-culated. In addition, the TECPLOT software was used togenerate vector plots, which are a collection of arrows.Each arrow is such that its length is proportional to the

velocity magnitude and its orientation is in the same direc-tion as the velocity at that location.The total error in a measured quantity is a sum of the

bias component and a precision component. The biaserrors encountered in PIV measurements result from mea-surements of the widths of the camera view and of the dig-ital image, computation of the particle displacement fromthe correlation algorithm, and the bias in the camera tim-ing. Our computations of the bias and precision errors inthe measured velocity follow those of Adeyinka and Nater-er [23]. The estimated bias errors in the measurements ofthe width of camera view, the width of the digital image,the computation of particle displacement, and the camera

timing are 0.5 mm, 0.5 pixels, 4 pixels and 0.1 lm, respec-tively. Using the root-sum-square (RSS) method of com-puting the total uncertainty [24], the relative error in themeasured peak velocity for inclination angles of 15 and45 are 5.1% and 8.3%, respectively. The uncertainty inthe measured wall temperature is estimated to be 0.5 C.

3. Results and discussion

Velocity measurements were carried out for natural con-vection flow of air in a symmetrically heated vertical con-verging channel using the PIV system. Measurements

were performed at two values of inclination angle of theplates (h= 15and 45) and two heating levels correspond-ing toRaL= 2.7 10

8 and 4.4 108, whereL is the lengthof the plates (500 mm). All fluid properties were evaluatedat the film temperature, Tfilm, which is the average of themeasured ambient temperature (Tf) and the wall surfacetemperature (Ts). The measurements were carried out atthe center plane (i.e. z = 0), from the center (y/H= 0.5)to the exit (y/H = 1). No measurements were performedin the inlet section of the channel because it was largelyobscured from the camera by the plates supportmechanism.

In order to have visual impression of the whole flowfield, the vector plots of the velocity magnitude on the ver-tical center plane (i.e. z= 0) and at RaL= 2.7 10

8 weremade as shown inFigs 3 and 4. Similar plots are obtainedforRaL= 4.4 10

8, but are not shown here. The length ofthe arrow is proportional to the magnitude of the velocityat that location. From the plots, three distinct flow regionscould be identified in the channel. These are the reverseflow region (where the vector arrows point down) andthe regions before and after the reverse flow. In the regionbefore the reverse flow, the flow is essentially within thethin boundary layers around the walls. The flow acceleratesalong the wall (as evidenced by the longer arrows), sucking

the fluid in the core region in the process. The sucking

results in a low pressure region in the core, which leadsto reverse flow. This sequence of events is responsible forthe formation of two symmetric vortices in the core, as


Ra= 4.4 108. (a) y/H= 0.95; (b) y/H= 0.80; (c) y/H= 0.50. The



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can be seen clearly in Fig. 3. The numerical analysis ofBianco and Nardini [19] for air in a vertical channel alsorevealed this trend. The two boundary layers later mergedownstream of the reverse flow region, largely, due to thenarrowing of the channel width. The flow fills the entirecross-section and moves up until it exits the channel.

The two-dimensionality of flow was examined by con-ducting measurements at three different sections in thespanwise (i.e. z) direction. The profiles of the mean hori-zontal and vertical velocity components at these sectionsare shown inFig. 5for inclination angle of 45. Here, thetransverse distance from the center has been normalizedby the inter-plate spacing, B. The formula for the variationofBin the channel is presented in the nomenclature. Thisnormalization is used in all the results presented. The veloc-ity profiles are very similar at the three sections. This justi-fies the assumption of two-dimensionality of flow. The restof the measurements were then confined to the vertical cen-

ter plane i.e. on the xy plane passing through the origin(seeFig. 1).

The profiles of the mean vertical and horizontal compo-nents of velocity for representative locations in the threeregions revealed by the vector plots are presented inFig. 6 for inclination angle of 15 and RaL= 2.7 10

8.

Fig. 6b represents the region where the flow is choked. Itshows reverse flow in the core. The peak of the velocitycomponent in the choked region is higher than beforeand after the choked region. Downstream of the chokedregion (Fig. 6a), there is no reverse flow, the velocity peaksare disappearing and the velocity in the core approachesthat of the wall region. The velocity profiles at the higherheating condition (RaL= 4.4 10

8) are shown in Fig. 7.They are very similar in form and magnitude to the profilesat RaL= 2.7 10

8. This indicates that, at choked state,further increase of wall temperature will not lead toincrease of flow rate. In all cases, the horizontal componentof the mean velocity is anti-symmetric. Its value around the

Fig. 11. Variation of the shear stress and RMS velocity fluctuations at

y/H= 0.95 for h = 45 and Ra = 4.4 108

.

Fig. 10. Variation of the shear stress and RMS velocity fluctuations at

y/H= 0.95 for h = 15 and Ra = 4.4 108

.


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wall region is such that |U/V| 0.27 (tan15) indicatingthat the flow is parallel to the walls.

The profiles of the mean vertical and horizontal compo-nents of velocity for inclination angle of 45 are presentedinFigs. 8 and 9. It is noted that the magnitudes of the ver-tical component of velocity are much less than those of

Figs. 6 and 7. As discussed by Inropera et al. [25], for nat-ural convection in inclined plates, the buoyancy force is nolonger exclusively in the streamwise direction since a com-ponent also exists perpendicular to the heated surface. Thiscomponent acts to maintain the ascending boundary layerflow in contact with the plate, thus reducing the velocityalong the plate. This same trend has been reported by Kai-ser et al.[18]and Marcondes et al.[26]for Nusselt numbervariation.Figs. 8 and 9also show that the velocity profilesat the two heating levels (RaL= 2.7 10

8 and 4.4 108)are similar in form and magnitude, indicating, like in the15inclination case, that the flow is choked. The horizontalcomponent of velocity is of about the same magnitude as

the vertical component, an indication that the flow is par-allel to the walls (since tanh= 1).

Fig. 10 shows the profiles of the Reynolds shear stressand the RMS velocity fluctuations for h = 15. The profilesof the shear stress and the RMS of the vertical velocity fluc-tuations have maximum values very close to the wall, cor-responding to the maximum value of the mean velocitygradient as shown inFig. 7a. These maxima are attributedto the creation of eddies in the shear layer close to the wallregion. Fig. 11 shows the corresponding profiles forh= 45. In this case, the profiles of the horizontal and ver-tical velocity fluctuations are similar. This is consistent with

the observation in respect ofFig. 9, that the magnitudes ofUand Vare about the same due to the equal influence ofthe buoyancy force in the horizontal and verticaldirections.

4. Conclusion

Velocity measurements were conducted for natural con-vection flow in a converging channel using the PIV system.The measurements were carried out at two angles of incli-nation of the channel walls (h= 15 and 45) and coveredtwo heating levels corresponding to RaL= 2.7 10

8 and4.4 108. Mean velocity vector plots and velocity profilesat some representative locations in the channel are pre-sented. The results indicate that

(1) The mean flow is aligned with the orientation of thechannel walls due to the effect of the buoyancy force,which is no longer exclusively in the verticaldirection.

(2) The reverse flow present in the core leads to the for-mation of two symmetric vortices in the core of thechannel.

(3) When the flow becomes chocked in the channels exitregion, further increase of wall temperature will not

lead to increase of flow rate.

Acknowledgements

The author is pleased to acknowledge the support pro-vided for this study by King Fahd University of Petroleumand Minerals. The useful discussion with Prof. B.S. Yilbasduring the manuscript preparation is highly appreciated.

References

[1] W. Elenbaas, Heat dissipation of parallel plates by free convection,Physica 9 (1) (1942) 128.

[2] W. Aung, Fully developed laminar free convection between verticalplates heated asymmetrically, International Journal of Heat and MassTransfer 15 (1972) 15771580.

[3] W. Aung, L.S. Fiectecher, V. Sernas, Development of laminar freeconvection between vertical flat plates with asymmetric heating,International Journalof Heat and MassTransfer 15 (1972) 22932308.

[4] A. La Pica, G. Rodono, R. Volpes, An experimental investigation offree convection heat transfer in vertical channels with backward-facing step, ASME, Journal of Fluids Engineering 238 (1993) 263

270.[5] S.C. Lin, K.P. Chang, Y.H. Hung, Natural convection within a

vertical finite-length channel in free space, Journal of Thermophysicsand Heat Transfer 8 (2) (1994) 366368.

[6] M.A. Habib, S.A.M. Said, A.A. Ahmed, I. Ouwais, Turbulentnatural convection in vertical short channels, in: Turbulent HeatTransfer III Conference, Alaska, March 1821, 2001.

[7] M.A. Habib, S.A.M. Said, S.A. Ahmed, A. Asghar, Velocitycharacteristics of turbulent natural convection in symmetrically andasymmetrically heated vertical channels, Experimental Thermal andFluid Sciences 26 (2002) 7787.

[8] S.A.M. Said, M.A. Habib, A. Asghar, Natural convection inconverging and parallel vertical channels, in: Proceedings of the1998 ASME Fluids Engineering Division Summer Meeting, Wash-ington, DC, June 2125, 1998.

[9] T.F. Ayinde, S.A.M. Said, M.A. Habib, Experimental investigationof turbulent natural convection flow in a channel, Heat and MassTransfer 42 (3) (2006) 169177.

[10] J.R. Bodia, J.F. Osterle, The development of free convection betweenheated vertical plates, Journal of Heat Transfer 84 (1962) 4044.

[11] E.M. Sparrow, S. Shah, C. Prakash, Natural convection in a verticalchannel: I. Interacting convection and radiation. II. The vertical platewith and without shrouding, Numerical Heat Transfer 3 (3) (1980)297314.

[12] E.M. Sparrow, G.M. Chrysler, L.F. Azevedo, Observed flow reversalsand measured-predicted Nusselt numbers for natural convection in aone-sided heated vertical channel, Journal of Heat Transfer 106 (2)(1984) 325332.

[13] E.M. Sparrow, L.F.A. Azevedo, Vertical channel natural convectionspanning between fully-developed limit and the single-plate bound-

ary-layer limit, International Journal of Heat and Mass Transfer 28(10) (1985) 18471857.

[14] T. Inagaki, K. Komori, Numerical modeling on turbulent transportwith combined forced and natural convection between two verticalparallel plates, Numerical Heat Transfer Part A Applications 27 (4)(1995) 417431.

[15] D. Naylor, J.M. Floryan, J.D. Tarasuk, A numerical study ofdeveloping free convection between isothermal vertical plates, Journalof Heat Transfer 113 (1991) 621626.

[16] E.M. Sparrow, R. Ruiz, L.F.A. Azevedo, Experimental and numer-ical investigation of natural convection in convergent verticalchannels, International Journal of Heat and Mass Transfer 31 (5)(1988) 907915.

[17] S.A.M. Said, Investigation of natural convection in convergentvertical channels, International Journal of Energy Research 20 (7)

(1996) 559567.


8/10/2019 Eddies

9/9

[18] A.S. Kaiser, B. Zamora, A. Viedma, Correlation for Nusselt numberin natural convection in vertical convergent channels at uniform walltemperature by a numerical investigation, International Journal ofHeat and Fluid Flow 25 (4) (2004) 671682.

[19] N. Bianco, S. Nardini, Numerical analysis of natural convection in airin a vertical convergent channel with uniformly heated conductivewalls, International Communications in Heat and Mass Transfer 32(6) (2005) 758769.

[20] N. Bianco, L. Langellotto, O. Manca, S. Nardini, Thermal design andoptimization of vertical convergent channels in natural convection,Applied Thermal Engineering 26 (2006) 170177.

[21] K.D. Kihm, J.H. Kim, L.S. Fletcher, Investigation of naturalconvection heat transfer in converging channel flows using a speckle-gram technique, Journal of Heat Transfer 115 (1) (1993) 140148.

[22] M.A. Habib, S.A.M. Said, S.A. Ahmed, Velocity characteristics ofturbulent natural convection in convergent-plates vertical channels,

International Journal of Fluid Mechanics Research 29 (2) (2002) 158178.

[23] O.B. Adeyinka, G.F. Naterer, Experimental uncertainty of measuredentropy production with pulsed laser PIV and planar laser inducedfluorescence, International Journal of Heat and Mass Transfer 48(2005) 14501461.

[24] H.W. Coleman, W.G. Steele, Experimentation and UncertaintyAnalysis for Engineers, John Wiley & Sons, NY, 1989.

[25] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Funda-mentals of Heat and Mass Transfer, sixth ed., John Wiley & Sons,NY, 2007.

[26] F. Marcondes, V. De Souza Melo, J.M. Gurgel, Numerical analysisof natural convection in parallel, convergent, and divergent open-ended channels, International Journal of Numerical Methods forHeat and Fluid Flow 16 (3) (2006) 304323.


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