aspect ratio effect on convective heat transfer outward...

International Journal ofRotating Machinery1994, Vol. 1, No. 1, pp. 1-18Reprints available directly from the publisherPhotocopying permitted by license only

(C) 1994 OPA (Overseas Publishers Association) Amsterdam B.V.Published under license by Gordon and Breach Science Publishers SA

Printed in the United States of America

Aspect Ratio Effect on Convective Heat Transfer ofRadially Outward Flow in Rotating Rectangular Ducts

C. R. KUO and G. J. HWANGDepartment of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.

Experiments were conducted to investigate the effects of rotation and aspect ratio on the convective heat transfer of radiallyoutward air flows in rotating rectangular ducts with a uniform wall heat flux by using fiberglass duct walls lined withseparated film heaters. The duct hydraulic diameter, heater active length, and mean rotation radius were 4, 120, and 180 mm,respectively. Ranges of parameters were through-flow Reynolds number, 1,000-15,000; rotation number, 0-0.32; rotationalbuoyancy parameter, 0-1.2; and cross-sectional aspect ratio, 0.5, 1.0, and 2.0. The results showed that the higher the rotationnumber, the greater the enhancement ofthe heat transfer rate especially at the pressure side. The rotational buoyancy parameterdecreases the heat transfer for low Re but enhances the heat transfer for high Re. The largest heat transfer enhancement isseen for AR 1.0, and the enhancement for AR 0.5 is greater than that for AR 2.0.

Key Words: Aspect ratio, convective heat transfer, rotating duct, Coriolis force, centrifugal-buoyancy brce, radiallyoutwardflow

HE study of internal convective heat transfer in rotat-ing ducts is becoming of great significance for engi-

neers because of its potential applications in industry: e.g.,cooling ofturbine blades and cooling ofelectrical machin-ery. Increasing the turbine entry temperature is especiallyrequired to improve the thermodynamic efficiency and toreduce the specific fuel consumption for the compact de-sign ofadvanced gas turbine engines. Increasing the poweroutput of electrical machinery is via the increases in theelectrical and magnetic loadings in the stator and rotorof machine. Moreover, high operating temperature mightcause material degradation on rotating components andexcess ohm loss in electrical conductors; thus efficient in-ternal convective cooling technology introduced by flowsin radially rotating duct is increasingly important. In aradially rotating heated rectangular duct the flow struc-ture and the heat transfer mechanism are simultaneouslyinfluenced by the rotation and the duct geometry. Manyinvestigations on the effects of rotation and duct geometryon flow and internal heat transfer have been reported overthese years.By obtaining an approximate series solution from a per-

turbation equation in a rotating pipe flow, Barua [1955]

showed that two counter-rotating vortices induced byCoriolis acceleration appear symmetrically in the duct.Mori et al. [1968] studied the laminar convective heattransfer in radially rotating circular ducts by assuming ve-locity and temperature boundary layer profiles along thepipe wall. Subsequently, by using the same techniques,Mori et al. [1971] analyzed the turbulent convective heattransfer in a circular pipe. Table I lists recent experimentalinvestigations on the internal convective heat transfer inradially rotating ducts. Under uniform wall temperatureconditions, Wagner et al. [1991a, 1991b] investigated thelocal heat transfer .of radially outward and inward flowsin rotating serpentine passages with smooth walls. Buoy-ant flow is found to be favourable for heat transfer forboth pressure and suction sides. However, the increasein heat transfer for the inward-flowing passage was rela-tively less than that for outward flow. Morris and Ghavami-Nasr 1991] observed that centrifugal buoyancy is shownto influence the heat transfer response in a rectangular-sectioned duct. Heat transfer is improved on pressure andsuction sides as the wall-to-coolant temperature differenceis increased for radially rotating outward flows. Han andZhang [1992] reported the local heat transfer coefficient

C. R. KUO AND G. J. HWANG

Author Year

TABLEExperimental investigations on heat transfer in radially rotating ducts

Duct Dh Max. L/Dh R/Dh Re. 10-3

Type (mm) rpmMax. B.C.Ro

Clifford et al. 1984

Harasgama and Morris 1988

Guidez 1989

Hwang and Soong 1989

Soong et al. 1991

Morris and Ghavami-Nasr 1991

Wagner et al. (a, b) 1991

Han and Zhang 1992

Hwang and Kuo 1993

Present study 1994

A 7.67 1,000 20 33 6.8-38.0 0.004 UHFA 7.67 1,850 20 33 7.0-25.0 0.103 UHFI-’1 7.5 1,000 20 33 7.0-21.0 0.042 UHFC) 5.0 2,000 20 70 7.0-25.0 0.049 UHF

I’-’-’! 10.66 5,000 11.5 27 17.0-41.0 0.2 UHF

I’-’l 4.0 3,000 30 30 0.7-20.0 0.428 UWT

I’--’] I’-’1 4.0 3,000 30 30 0.7-20.0 0.428 UWT

I-"-] 7.3 1,800 20 34 10.0-25.0 0.02 UHF

[’-I 12.7 1,100 14 33, 49 12.5-50.0 0.48 UWT

I-’-! 12.7 800 12 30 2.5-25.0 0.352 UWT, UHF

!-"1 4.0 3,000 30 45 1.0-15.5 0.32 UHF

i-"-I I"-I 4.0 3,000 30 45 1.0-15.5 0.32 UHF

in a square channel with smooth walls and radial outwardflow for cases of uneven wall temperature with experi-ments. Hwang and Kuo 1993] conducted experiments onradially outward flows in a rotating square duct with uni-form wall heat flux. Augmentation of heat transfer on thepressure side is clearly observed.

To increase the effects ofrotation on internal heat trans-fer in the rotating ducts, lightweight and high-strengthtest sections were built for the requirement of high rota-tional speed up to 3,000 rpm. The interior wall surfacesof duct section were lined with separated stainless-steelfilm heaters of 0.01-mm thickness for the uniform wallheat flux. The purpose of his study was to investigate theeffects of forced flow, rotation, and aspect ration on theconvective heat transfer ofradially outward flows in heatedrotating rectangular ducts. The aspect ratio used were 0.5,1.0, and 2.0. Regional average Nusselt numbers on thepressure side, the suction side, and the side walls wereobtained.

GOVERNING PARAMETERS

The physical model and coordinates, as shown in Fig. 1,present the rotation-induced inertial effects on forced con-vection of radially outward air flow in a rotating rectan-gular duct. Observing the force diagram, one discerns thatthe dominant forces due to rotation are force vectors of2pU and pf22X because of U >> V and X >> Y andZ. The Coriolis force term (2pflU) induces cross streamswhich create additional mixing to the flow. The centrifugal

force term (pf22X) generates centrifugal-buoyant radialsecondary flow. The direction of this free convection flowis opposite to that of the radially outward flow in a heatedrotating duct. An analysis ofthe flow-governing equationsgives that the heat transfer coefficient at a certain axial lo-cation in the heated region is functionally influenced byother operating parameters. The results are (Soong et al.[1991]):

Nuf f(Re, Refz, Rafz, Pr, L/Dh, R/Dh, a/b) (1)

The definitions of these dimensionless parameters arelisted in the nomenclature.

In the present study, air with Pr 0.72 is used as thecoolant fluid. The ratio of heated length and hydraulic di-ameter L/Dh 30.0 and the ratio of mean rotation radiusand hydraulic diameter R/Dh 45.0 are also fixed. Thus,Eq. 1 reduces to

Nu2/Nu0 f(Re, Ro, Ra*, AR) (2)

where the Reynolds number Re indicates the forced con-vection effect; the rotation number Ro Re Re/Re2,a ratio of the relative strength of Coriolis force to theinertial force, represents the effects of Coriolis forceon forced convection; the rotational buoyancy parame-ter Ra* Rafz/Re2 denotes the effect of centrifugal-buoyancy; and the cross-sectional aspect ratio AR revealsthe effect ofthe cross-sectional configuration ofthe rectan-gular duct. All the physical properties needed in calculat-ing these parameters is evaluated at the bulk temperatureTb. The enhancement of heat transfer is presented by theratio of the Nusselt number on rotating condition to the

ASPECT RATIO EFFECT

COOLING CHANNELS

DIRECTION OFROTATION

SUCTION SIDE

LEADING EDGE

TRAILING EDGE

RESSURE SIDE

TURBINE BLADE

GEOMETRY:

a=Height of ductb=Width of ductDh=4 mmL= 120 mmXo=120 mmR=180 mm

pg/y

2P U

Cross-stream Axial Velocity Suction SideFlow Profile (S.S.)

7- Pressure SideR 7 (P.S.)

FIGURE Physical model and coordinate.

corresponding nonrotating Nusselt number. The greaterthe Nusselt number ratio, the larger the heat transfer en-hancement. On the contrary, if the Nusselt number ratiois less than unity, the heat transfer is depressed. To scalethe effects of rotation and to deduce the heat transfer fromthe experimental data, nondimensional parameter groupswere applied. Table II depicts the ranges of the experi-mental variables and the corresponding nondimensionalparameters used in the present study.

EXPERIMENTAL FACILITIES ANDTEST PROCEDURE

The experimental facilities, as illustrated in Fig. 2, con-sists of four major parts: coolant air supply, test section,motor with speed controller, and data acquisition system.Coolant air was supplied from a compressor through flowmeters and rotary seal assembly to the test section. Theflow meters ofdifferent flow ranges, from 0.2 to 8.0m3/hr,


2.3.4.5.6.

Air inletFlow meterRotary jointSlip ringSafety glassTest section

7. Support frame8. Motor9. Tachometer

10. Slip ring11. DC-power supply

1 2 2 3 4 5 6 7 8 910

ooo ooo

Air compressor 11 11

FIGURE 2 Experimental setup.

Recorder

Computer

Variables

TABLE IIThe expedmental variables

Ranges

Flow Direction Radially Outward Flowrpm 0, 500, 1,000, 1,500, 2,000, 3,000Tb.o Tb.i (C) 15, 30, 45Tto (C) 40-130x/Dh 2.5, 10.0, 17.5, 25.0Pr 0.72Re 1,000, 2,000, 4,000, 8,200, 10,000, 15,500Re 53.4, 106.8, 162.2, 214.0, 320.4Ro 0-0.32Ra* 0-1.2AR 0.5, 1.0, 2.0

were used for indicating the coolant flow rate. A 0.3-mmtype-T thermocouple was located at the duct inlet to mea-sure the inlet coolant bulk temperature. A mixing chamber

with staggered rod bundles was attached to the exit planefor providing a well-mixed condition for outlet bulk tem-

perature measurement by using another thermocouple setbehind the mixing chamber.

Glass-fiber, reinforced plastic with a low thermal con-ductivity (0.048 W/mC) for reducing heat loss was usedfor smooth duct walls. Four pieces of 0.01-mm thicknessstainless-steel film heaters, heated by electrical power sup-plier through slip rings, were attached separately to eachinterior wall surface of the duct. At a certain axial loca-tion, the wall surface temperatures were measured via ther-mocouples which were firmly attached to copper blocks.Morcos and Bergles [1975], Hwang and Chou [1987],and Chen and Hwang 1989] proposed wall heat conduc-tion parameters for analyzing duct wall thermal boundaryconditions: i.e.,

Kp (kwt)/(kairDh)

Material kw(W/mC)

ASPECT RATIO EFFECT

TABLE IIIEstimation for duct wall thermal boundary condition

kp kp(mm) (Based on air pure (Based on air mixed

conduction)* convection)**

Purpose

Fiber Glass 0.048

Stainless 16.3Film Heater

Copper block 111.0

3.0 1.199 0.199

0.01 1.357 0.1357

0.5 462.0 46.2

*Air thermal conductivity kair 0.03003 W/mC**Assumed the Nusselt number for mixed convection is 10.

wall insulation

wall insulation

regional averagewall temperature

is the ratio of wall heat conduction and air pure conductioninside a duct, and

2Kp (kwt)/(hDh)

is the ratio of wall heat conduction and air mixed convec-tion inside a duct.

values for theTable III gives the estimated Kp and Kppresent test facility. Because of Kp << 1.0 for fiberglassand film heater, both of them can be considered as insu-lators. When the heater is supplied with electrical power,a boundary condition of nearly uniform heat flux can be

of theachieved. On the other hand, the high Kp andcooper block make the measurement of temperature in theblock to be the regional average value.The duct hydraulic diameter, heater active length, and

the mean rotation radius were 4, 120, and 180 mm, re-spectively. This gave a ratio of heater active length to hy-draulic diamter of 30, which covered most of laminar flowentrance region and both the turbulence flow entrance andfully developed regions, and a mean rotation radius to hy-draulic diameter ratio of 45, which was reasonably largeas compared with the ratio in a gas turbine or an electricalmachine. Further construction details of the test sectionare shown in Fig. 3.The test assembly was encased in an elliptical aluminum

tube with the internal void space filled with insulating ce-ramic cotton and was subsequently bolted on the rotatingshafts so that the duct axis was perpendicular to the shaftaxis. The whole model was installed in a test cell enclosedby a support frame with safety-glass plates and ventilationopenings, and it was driven by a controlled electric motor.An inverter which adjusted the electric current frequencywas used for controlling the rotational speed detected bya photoelectric tachometer. A slip ring located at the otherend of the shaft was to transmit the detected data from thethermocouples to a recorder, as shown in Fig. 2.

DATA REDUCTION

In an experiment with either a large flow rate or a large ro-tational speed, the compressibility correction for the mea-sured temperature of coolant flow must be performed. Bydenoting Tr as the recovery temperature, the fluid temper-ature may be corrected by

/(T Tr l q-2 ?’ 2Cp

where k is the specific heat ratio and ?’ is the temperaturerecovery factor (Schlichting [1979]):

?, pr1/2 for laminar flow

?, pr1/3 for turbulent flow

Note that in the present study a temperature correction upto 2.5C was found for the case of Re 15, 000 (M ,0.15) and 1.5C for f2 315 rad/s (3,000 rpm).

At a certain axial location the heat transfer coefficienthx was evaluated as the ratio of the net heat flux qnet,x tothe temperature difference between the heated wall tem-

perature Tw,x and the coolant bulk temperature Tb,x: i.e.,hx qnet,x/(Tw,x Tb,x). The net heat flux imposedon the coolant by convection was obtained by subtract-ing the external heat loss from the electric power suppliedto the heater. The external heat losses were attributed toboth conduction to the structure support and convectionto the ambient air, and were estimated under no-flow con-dition by measuring heater power setting over ranges ofwall temperature. The no-flow condition was achieved byfilling insulation material in the channel. Based on a ther-modynamic energy balance, the rise of local coolant bulktemperature was determined step by step from the inletcoolant temperature by adding the net heat flux to thecoolant along the duct.

Invoking the root-sum-square method introduced byKline and McClintock [1953] for uncertainty analysis, it


A

CoolantOutletB

9

2.3.4.

Aluminum CoverThermocouplesFilled CottonDuet Wall

A

Section on AA

56789

10

7

Film HeaterMixing ScreenRotating ShaftCounter WeightRectangular DuctCopper Bloek

6543 21

Section on BB

8CoolantInlet

FIGURE 3 Details of the test section.

showed in the present study that the estimated uncertain-ties in calculating Nusselt number were mainly affectedby the local wall-to-coolant temperature and the net heatflux added to coolant from each wall. The measured vari-ables and their uncertainties in the measurement could beexpressed as: Xi Xi (measured) 4-$Xi, where the bestestimate of Xi is Xi (measured) and there was an uncer-tainty in Xi that might be as large as ,Xi. For the case ofAR 1.0 and Ref 162.2, Fig. 4 showed the typicalvariations of local wall-to-coolant bulk temperature along

the test duct for Re 1000, qnet 1,150W/m2, and Re10,000, qnet 10,500 W/m2, respectively. Uncertainty inthe Nusselt number increased with the decrease in eitherthe wall-to-coolant temperature difference or the net heatflux. It was found that the largest uncertainty of 20 per-cent was observed for Re 1,000 at x!Dh 25.0 on thepressure side because of the corresponding low wall-to-coolant bulk temperature difference and low heat flux. Theuncertainty in the Nusselt numbers was approximately 8percent when Reynolds number was greater than 10,000.

ASPECT RATIO EFFECT

100

90

70

kRe = 1000 Re =10,000Rely= 162.6 Rely= 162.6, :SUCTION SIDEIq :SIDE WALLC) :PRESSURE__

:3130.0 10.0 20.0 30.0 10.0 20.0 30.0

x//Dh X/DhFIGURE 4 Wall and coolant temperature variations along the test section in the case of AR 1.0.

RESULTS AND DISCUSSION

The thermocouples were installed on two adjacent wallsof the channel only. By rotating the radial channel, clock-wise or counter-clockwise or switching the channel 90degrees, one was able to obtain the data on pressure side,suction side, and two side walls or for AR 0.5, and2.0. Experiments were first conducted to determine the re-gional average Nusslet numbers for the nonrotating casealong the four duct sides for a range of Reynolds num-bers (Re 1,000 15,000), positions (x/Dh 2.5, 10.0,17.5, and 25.0), and outlet-to-inlet temperature differences(Tb,o Tb,i 15.0, 30.0, and 45.0C). For the case ofAR 1.0, Fig. 5 gives the results of nonrotating condi-tion which are compared with the Dittus-Boelter [1930]correlation in the turbulent flow regime and the Perkins etal. 1973] correlation in the laminar flow regime, respec-tively. The correlations are

Dittus-Boeiter [1930]

Nu0 NUTFD[1.0 + 2.0/(x/Dh)]

08forxDh >_ 10.0, where NUTFD 0.023Re Pr0’4 is forfully developed flow in a circular duct with a uniform walltemperature, and

Perkins et al. [1973]

Nu0 1/[0.277 0.152exp (-38.68)]

for square duct with a uniform wall heat flux, where8 x/(Dh Re Pr) >_ 0.005. Fig. 5 shows that for thehigher Reynolds number the Nusselt number is approxi-mately within 10 percent of that of Dittus-Boelter 1930].However, the higher Nusselt number at x /Dh 25.0 wasaffected by the discontinuity of the uniform heat flux ther-mal boundary condition at the duct exit region.

Figures 6(a), (b) and (c) indicate the effects of rota-tion on heat transfer along the test section for selectedthrough-flow Reynolds numbers with aspect ratios 0.5,1.0, and 2.0, respectively. It is noted that the Nusselt num-ber ratios at the pressure side were always greater thanthose at the suction side but this trend was attenuated withthe higher Reynolds number. This was in agreement withthe results of Mori et al. [1968, 1971] that rotational heattransfer enhancement for laminar flow, in general, wasmore prominent than that for turbulent flow. The differentbehaviors on heat transfer over the pressure side and thesuction side were due to the Coriolis-induced secondarycross streams in the form of a vortex pair which impingedtoward the pressure side, then caused a return flow whichcarried already heated, relatively quiescent fluid from thepressure side and side walls to near the suction side. Athigher rotation rate the strength of the Coriolis-induced


25.0

20.0

10.0

’I ’IRe-1000Re-2000

" Perkin et al.( 973)

o :P.S., :S.S.A ’Side wallI ill,

5 10-3 2 5 10

-2 2

x/(DhRe Pr)5 10

0.06

0.04

0.02

I

0.000.0 5.0

Present DataDittus and Boelter(1930)_Circular Duct

.I_ I I

10.0 15.0 20.0 25.0x/Dh

30.0

FIGURE 5 Comparison of Nu in laminar and turbulent flow regime for AR 1.0.

cross streams was more intensified and this trend was morenoticeable than that at lower rotation rate. It is also seenthat the Nusselt number ratios at both pressure and suctionsides dropped near duct outlet for most cases under study.This was due to the increase of Nu0 near exit as shown inFig. 5. For the effect of duct aspect ratio, large aspect ratio(long side aligned with the Coriolis force) gave larger shortside direction Coriolis force gradient, but yielded a greatercross-sectional flow resistance. Due to the combination ofthese two effects, the largest heat transfer enhancementwas seen for the case of AR 1.0, and the enhancementfor AR 0.5 is greater than that for AR 2.0. For somecases, the heat transfer was depressed on the suction side

because of the stabilizing effect of the vortex motion onthe main flow disturbances.

Considering the effect of the Coriolis-induced crossstreams on the main flows, Fig. 7 discloses the variationsof the Nusselt number ratios with rotation number for thecase of aspect ratio of 1.0, along with a comparison to theexperimental results by Han and Zhang 1992]. The resultsshow that both the pressure side and suction side Nusseltnumber ratios of the present study at x/Dh 10.0 agreedfairly with those of Han and Zhang 1992] at x/Dh 9.0and 11.0. Note that the results of Han and Zhang 1992]were based on the following conditions: Ro calculated atrotational speed 400 and 800 rpm, Re between 2,500

ASPECT RATIO EFFECT

Re- 900

Re- 3600

P.So

30.0

Re- 9200

0.0 10.0 20.0

x/DhFIGURE 6 (a)

Re- 1800

Re- 7200P.S.S.S. Re0

53

162.42320.

Re-14,000

10.0 20.0

x/Dh30.0

10 C. R. KUO AND G. J. HWANG

2.0

Z 1.5

Re- 4000

Re-lO,O00

0.0 10.0 20.0 30.0

x/Dh

Re- 2000

Re- 8200

P.S.S.S.(C)

A53.4162.2320.4

Re-15,500

I,

10.0 20.0

x/Dh30.0

FIGURE 6 (b)

ASPECT RATIO EFFECT 11

Re- 900

Re= 3600

1800

7200

o 53.4162.2320.4

Re- 9200 Re-14,000

0.0 10.0 20.0 30.0 10.0 20.0 30.0

x/Dh x/’DhFIGURE 6 (c) Variations ofNua/Nuo withx/Dh based on Tb,o Tb,i 30.0C for the cases ofaspect ratios of(a) 0.5, (b) 1.0, and (c) 2.0.


X/Dh=25.0

AOp.s.

RoFIGURE 7 Variations of Nu/Nuo from Ro for AR 1.0 and Tb,o Tb,i 30.0C.


and 25,000, R/Dh 30, and Dh 12.7 mm. The presentdata were based on: Ro calculated at rotational speed500, 1,500, and 3,000 rpm, Re between 1,000 and 15,500,R/Dh 45, and Dh 4 mm. This confirms that Rois indeed an important heat transfer governing parameterin a rotating channel. By either increasing the rotationalspeed or decreasing the Reynolds number, a higher Ro canbe achieved. In the entry region, x/Dh 2.5, it is alsoseen that the observed enhancement in heat transfer forthe present developing flow was less than that of higherx/Dh. This result was consistent with the experiment ofMetzger and Stan 1977] for entry region heat transfer ina rotating radial tube.To investigate the geometry effect of cross-sectional

aspect ratio, Fig. 8 demonstrates the influence of aspectratio 0.5, 1.0, and 2.0 on the Nusselt number ratios. Theresults show that the enhancement of the Nusselt numberratios for the case of AR 1.0 was always highest, andthe enhancement for the case ofAR 0.5 was higher thanthat for AR 2.0. This was due to the combination effectof weak long side Coriolis force gradient for low AR andhigh flow resistance for high AR. These phenomena canalso be observed in heated horizontal rectangular ducts(Cheng and Hwang [1969] and curved channels (Chengand Akiyama 1970]. The depression of heat transfer onthe suction side was also seen for small Ro case.By definition the rotational buoyancy parameter is af-

fected by the rotation number, wall-to-coolant tempera-ture, eccentricity, and local positions. To highlight thesalient feautres of the centrifugal-buoyant radial sec-ondary flows, three outlet-to-inlet bulk temperature dif-ferences, Tb,o Tb,i 15.0, 30.0, and 45.0C, wereselected while other operating parameters were held con-stant during each measurement. Figs. 9(a), (b), and (c)illustrate the results of the variations of Nusselt numberratios with rotational buoyancy parameters at axial lo-cation of x/Dh 17.5 and for aspect ratios 0.5, 1.0,and 2.0, respectively. As the rotation number was fixed, itwas found that increasing the rotational buoyancy param-eter decreased the Nusselt number ratios at both the pres-sure side and suction side for low Reynolds number flowsRe 1,000, but the trend was reversed for Re 4,000.Then, these trends were diminished for higher Reynoldsnumber. These phenomena can be found from analyzingthe mixed convection of the buoyancy-induced opposingflows in a vertical heated tube for both constant wall tem-perature and uniform wall heat flux: the buoyancy forcestend to decrease the laminar heat transfer rate while theyincrease the turbulent heat transfer rate (Abdelmeguid andSpalding [1979]; Buhr et al. [1974]. With increasing therotational buoyance parameters, the depressed effect onheat transfer agree with those proposed by Morris and Ay-

han [1979], Clifford et al. [1984], Harasgama and Morris[1988], and Soong et al. [1991]; on the other hand, theincreased tendencies on heat transfer were found by Wag-ner et al. 1991a, b], Morris and Ghvami-Nasr 1991], andHan and Zhang 1992]. It is seen that the depression ofNusselt number for the centrifugal buoyancy force is big-ger for the cases of AR 0.5 and 2.0 than that for AR

1.0. One may attribute this phenomenon to the largerperipheral area of AR 0.5 and 2.0 for more heated fluidwith decelerated axial velocity.

PRACTICAL IMPORTANCE

1. The study of internal convective cooling in rotatingducts is of engineering importance for its applicationsto the cooling of turbine blades and cooling of electri-cal machinery.

2. Rectangular ducts of aspect ratios other than 1.0 maybe applied to the internal cooling passage near the trail-ing edge of a turbine blade and in the cooling passagein a rotor of electrical machinery.

CONCLUSION

The investigation has presented rotation effects, Coriolis-induced cross streams, and centrifugal-buoyant radial sec-ondary flows, on convective heat transfer of radially out-ward flows in rotating rectangular ducts with AR 0.5,1.0, and 2.0. According to an analysis with a wall heatconduction parameter (Kp), four pieces of stainless-steelfilm heater of 0.01-mm thickness were separately linedwith the interior wall surfaces of the fiberglass duct to ob-tain the nearly uniform wall heat flux boundary conditions.The results obtained and described in this experiment arepresented as follows.

1. Due to rotation, the Coriolis-induced cross streamsimpinge directly toward the pressure side, then cause areturn flow which carriers already heated, relatively qui-escent fluid from the pressure side and side walls to nearthe suction side. Therefore, the Coriolis-induced crossstreams create additional mixing to the main flows andenhance the heat transfer rate, especially at the pressureside. Also, the enhancement of heat transfer rate is grad-ually attenuated with increasing through-flow Reynoldsnumber because of the effect of the turbulence becomingprogressively larger than that induced by rotation.

2. The rotation number, effect of the Coriolis-inducedcross streams on the forced main flows, performs an im-


X/Dh-17.5

2.0

1.5

X/Dh-lO.O

x/Dh-

P.S.

0

A

0 @V

AR

5z o#

;07

0.0 0.1 0.2 0.3 0.4 0.5

FIGURE 8 Variations of Nun/Nu0 from Ro for the cases of different aspect ratio.

portant parameter to the internal convective heat trans-fer for radially rotating duct flows and a higher valuecan be obtained by either increasing the rotational speedor decreasing the through-flow Reynolds number. Thehigher the rotation number, the more intensified thestrength of the Coriolis-induced cross streams and themore noticeable the enhancement of the heat transferrate.

3. For high aspect ratio narrow duct, the short side Cori-olis force gradient is large, but the Coriolis-induced crossstreams are weakened by viscous force over the longerside walls. Therefore, due to the combination of these twoeffects, the heat-transfer enhancement on the pressure sidefor the largest for AR 1.0 and the enhancement for AR

0.5 are larger than that for AR 2.0. For some cases,the heat transfer is depressed on the suction side because


4.0

z.01.5

.o4.03.0

2.01.5

.o4.03.0

2.01.5

.o

4.03.0

2.01.

.o4.03.0

2.0

.o0.7

II]

Re-14,000

P.S. o.oo.o11

Ro=0.004

IIIll

Re- 9200

P.S.S.S. Tb,o--Tb,

’ so-Iv so’odoJ-

Ro=0.006

IIII]

Re- 3600

Ro=0.015

0.033

o.o7 o0,0,

Re- 1800

IIIIIi1111

Re-

IIIII

IIII

0.084

o.o4 0

IIIll

0.085

Ro=0.031o,

900

Ro=0.059>

tttilIiiii

IIII!

0.166

IIIII

0.332

o %

Itltll Illlil tlllll

10-3

10-z

10-1

1 2

RaFIGURE 9 (a)

of the stabilizing effect of the vortex motion on the mainflow disturbances.

4. Varying the difference of the outlet-to-inlet air bulktemperature while other operating parameters were heldconstant during the experiment, the increasing rotationalbuoyancy parameters made the heat transfer rate de-crease for cases of Re 1,000 but increase for cases

of Re 4,000, and these trends are then diminished forhigher Reynolds numbers. These phenomena can be foundfor buoyancy-induced opposing flows in a vertical heatedtube: the buoyancy effect decreases the laminar heat trans-fer rate but increases the turbulent heat transfer rate, andthis trend is more pronounced for AR 0.5 and 2.0 thanthat for AR 1.0.


4.0

3.0-

2.0

1.5

1.0

4.0

3.0-

2.0

1.5

1.0

4.0

3.0

2.0

1.5

1.0

4.0

3.0-

2.0

1.5

1.0

4.0

3.0

2.0

1.5

1.0

0.7-4

10

Re-15 500P.S.S.S. Tb,o- T b,

Ib *1 .o1IV 30.0

P.S. o.oo21<> 45.o

0.0010Ro=O.O04

_-l’"l’" ’’"":ll ’"’"’ 1’"’":’,Re=lO,O00

0.031O.OLO o,

Ro=0.005

Re= 40000.076

0.040

Ro=O.O14 O

IIII

Re- 2000 0 o.ots

0.079

o,

Ittlll tlill[ ttlttllilliJ iliillo 0.312

Re= 1000 o.s7o

FIGURE 9 (b)

Nomenclature

aARbcpOhhx

height of rectangular ductcross-sectional aspect ratio a/bwidth of rectangular ductspecific heat of air, J/(kgC)hydraulic diameter 2ab/(a + b)local heat transfer coefficient qnet,x/(Tw,x Tb,x),W/(m2C)

kairKpkwLMNuNuoNuP.S.

thermal conductivity of air, W/(m C)wall heat conduction parameter kwt/(kairDh)thermal conductivity of wall, W/(mC)actively heated length of duct, mmmach numberNusselt number hx Oh / kairNusselt number for nonrotating conditionNusselt number for rotating conditionpressure side


FIGURE 9

Re- 9200

Ro=0.006

Re= 3600

Re- 1800

,JillIII

3.0

2.01.5

.o

Ro=O.031

oililll

9OO

0Ro=0.059

3.0

z.o1.{5

.o

Re=

illl

10-Ra.7 Illl

10-4

10-a

0.166

0.085

iill, ll,,,IIII

0.3320-

0 V(

v o_

v,i v1, lilil *1 I-10

-11 2

(c) Effects of Ra* on Nu/Nuo for the cases of aspect ratios of (a) 0.5, (b) 1.0, and (c) 2.0.

PrqnetRRa

Ra*

ReRo

Prandtl number Cp/L/kairnet wall heat flux, W/mmean rotation radius Xo + L/2, mmrotational Rayleigh numberRo2Re2(e -t- x/Dh)[(Tw,x Tb,x)/Tb,x] Prrotational buoyancy parameter Raf/Rethrough-flow Reynolds number pUoDhllZrotational Reynolds number pflD/lRotation number Reu/Re 2Dhl Uo

S.S. suction sidewall thickness, mmbulk temperature of air, Cinlet air bulk temperature, Coutlet air bulk temperature, Cair bulk temperature at local position x, Crecovery temperature of air, Cduct wall temperature at x, Cmean air velocity, m/s


U,V,W

Xo

X,Y,Z

velocity component, m/sstreamwise distance from heated channel inlet, mmdistance between rotating axis and the heated channel inlet,mmsystem coordinates, mm

Greek letters

eccentricity Xo/Dhtemperature recovery factorair dynamic viscosity, kg/msair density, Kg/mrotational speed, rad/s

References

Abdelmeguid, A. M., and Spalding, D. B., 1979. TurbulentFlow and HeatTransfer in Pipes with Buoyancy Effects, Journal ofFluid Mechanics,Vol. 94, pp. 383-400.

Barua, S. N., 1955.. Secondary Flow in a Rotating Straight Pipe, Pro-ceedings of the Society ofRoyal London, Vol. 227 A, pp. 133-139.

Buhr, H. O., Horsten, E. A., and Carr, A. D., 1974. The Distortion ofTurbulent Velocity and Temperature Profiles on Heating for Mercuryin a Vertical Pipe, Transactions ofthe ASME Journal ofHeat Transfer,Vol. 96, pp. 152-158.

Chen, R. S., and Hwang, G. J., 1989. Effect of Wall Conduction Com-bined Free and Forced Laminar Convection in Horizontal Tubes,Transactions of the ASME Journal of Heat Transfer, Vol. 111, No.2, pp. 581-585.

Cheng, K. C., and Akiyama, M., 1970. Laminar Forced Convection HeatTransfer in Curved Rectangular Channels, International Journal ofHeat and Mass Transfer, Vol. 13, pp. 471-490.

Cheng, K. C., and Hwang, G. J., 1969. Numerical Solution for CombinedFree and Forced Laminar Convection in Horizontal Rectangular Chan-nels, Transactions of the ASME Journal ofHeat Transfer, Vol. 91, pp.59-66.

Clifford, R. J., Harasgama, S. E, and Morris, W. D., 1984. AnExperimen-tal Study of Local and Mean Heat Transfer in a Triangular-SectionedDuct Rotating in the Orthogonal Mode, Transactions of the ASMEJournal of Engineering.fir Gas Turbines and Power, Vol. 106, pp.661-667.

Dittus, E W., and Boelter, L. M. K., 1930. Heat Transfer in AutomobileRadiators of the Tubular Type, University of California, Publicationsin Engineering, Vol. 2, No. 13, pp. 443-461; reprinted in 1985, Int.Comm. Heat Mass Transfer, Vol. 12, pp. 3-22.

Guidez, J., 1989. Study of the Convective Heat Transfer in a RotatingCoolant Channel, Transactions ofthe ASMEJournal ofTurbomachin-ery, Vol. 111, pp. 43-50.

Han, J. C., and Zhang, Y., 1992. Effect of Uneven Wall Temperature onLocal Heat Transfer in a Rotating Square Channel with Smooth Wallsand Radial Outward flow, Transactions of the ASME Journal ofHeatTransfer, Vol. 114, pp. 850-858.

Harasgama, S. E, and Morris, W. D., 1988. The Influence of Rotation onthe Heat Transfer Characteristics of Circular, Triangular, and Square-Sectioned Coolant Passage ofGas Turbine Rotor Blades, Transactionsof the ASME Journal ofTurbomachinery, Vol. 110, pp. 44-50.

Hwang, G. J., and Chou, E C., 1987. Effect ofWall Conduction on Com-bined Free and Forced Laminar Convection in Horizontal RectangularChannels, Transactions of the ASME Journal ofHeat Transfer, Vol.109, pp. 936-942.

Hwang, G. J., and Kuo, C. R., 1993. Experimental Study of ConvectiveHeat Transfer in a Rotating Square Duct with Radially Outward Flow,1993 National Heat Transfer Conference, Atlanta, GA, August 8-11.

Hwang, G.J., and Soong, C.Y., 1989. Experimental Automation andHeat Transfer Measurement on a Rotating Thermal System, TransportPhenomena in Thermal Control, edited by G. J. Hwang, HemispherePublishing, New York, pp. 375-388.

Kline, S. J., and McClintock, E A., 1953. Describing Uncertainties inSingle Sample Experiments, Mechanical Engineering, Jan., pp. 3-8.

Metzger, D. E. and Stan, R. L., 1977. Entry Region Heat Transfer inRotating Radial Tubes, AIAA PaperNo. 77-189, presented at the 15thAIAA Aerospace Sciences Meeting, Los Angeles, CA.

Morcos, S. M., and Bergles, A. E., 1975. Experimental Investigation ofCombined Forced and Free Laminar Convection in Horizontal Tubes,Transactions of the ASME Journal of Heat Transfer, Vol. 97, pp.212-219.

Mori, Y., Fukada, T., and Nakayama, W., 1968. Convective Heat Trans-fer in a Rotating Circular Pipe (lst Report, Laminar Region). Inter-national Journal ofHeat and Mass Transfer, Vol. 11, pp. 1027-1040.

Mori, Y., Fukada, T., and Nakayama, W., 1971. Convective Heat Transferin a Rotating Circular Pipe (2nd Report), International Journal ofHeatand Mass Transfer, Vol. 14, pp. 1807-1824.

Morris, W. D., and Ayhan T., 1979. Observation on the Influence ofRotation on Heat Transfer in the Coolant Channels of Gas TurbineRotor Blades, Proceedings ofthe Institute ofMechanical Engg., Vol.193, pp. 303-311.

Morris, W. D. and Ghavami-Nasr, G., 1991. Heat Transfer in RectangularChannel with Orthogonal Mode Rotation, Transactions of the ASMEJournal ofTurbomachinery, Vol. 1i3, pp. 339-345.

Perkins, K. R., Shade, K. W., and McEligot, D. M., 1973. "Heat Lam-inarizing Gas Flow in a Square Duct, International Journal ofHeatand Mass Transfer, Vol. 16, pp. 897-976.

Schlichting, H., 1979. Boundary Layer Theory, 7th ed., McGraw-Hill,New York, pp. 335, 714.

Soong, C. Y., Lin, S. T. and Hwang, G. J., 1991. An Experimental Studyof Convective Heat Transfer in Radially Rotating Rectangular Ducts,Transactions of the ASME Journal of Heat Transfer, Vol. 113, pp.604-611.

Wagner, J. H., Johnson, B. V., and Hajek, T. J., 1991a. Heat Transferin Rotating Passages with Smooth Walls and Radial Outward Flow,Transactions of the ASME Journal ofTurbomachinery, Vol. 113, pp.42-51.

Wagner, J. H., Johnson, B. V., and Kopper, F. C., 1991b. Heat Transferin Rotating Serpentine Passages with Smooth Walls, Transactions ofthe ASME Journal ofTurbomachinery, Vol. 113, pp. 321-330.

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