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Applied Thermal Engineering 31 (2011) 2702e2708

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Experimental and numerical investigation of convection heat transfer in channelswith different types of ribs

Wei Peng a,b, Pei-Xue Jiang a,*, Yang-Ping Wang a, Bing-Yuan Wei a

aKey Laboratory for Thermal Science and Power Engineering of Ministry of Educations, Department of Thermal Engineering, Tsinghua University, Beijing 100084, Chinab Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

Article history:Received 5 January 2011Accepted 27 April 2011Available online 7 May 2011

Keywords:ExperimentNumerical simulationRibsHeat transferPressure drop

* Corresponding author. Tel.: þ86 10 62772661; faxE-mail address: jiangpx@tsinghua.edu.cn (P.-X. Jia

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.04.040

a b s t r a c t

Convection heat transfer in a channel with 90� ribs and V-shaped ribs were studied experimentally andnumerically. The results showed that both the 90� ribs and V-shaped ribs enhance the convection heattransfer compared with a flat wall without ribs, but the pressure drop also increases. The overallthermal/hydraulic performance of the V-shaped ribs is better than that of the 90� ribs. Numericalsimulations using the SST k-u turbulence model were used to investigate the thermal/hydraulicperformance for six rib bed, the results indicated that the 45� V-shaped continuous ribs had the bestthermal/hydraulic performance. Comparison of continuous ribs and interrupted ribs shows that the heattransfer with the V-shaped interrupted ribs is less than with the V-shaped continuous ribs, but this isreversed for the 90� ribs.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The use of ribs to enhance heat transfer is very important inmodern advanced gas turbines. One reason is that the ribs increasethe fluid flow turbulence near the wall and disrupt the laminarboundary layer to enhance the heat transfer. The other reason isthat the ribs also increase the heat transfer area.

The thermal/hydraulic performance of the ribs is affected bymany factors, including the shape, angle, size, and spacing. Han andDutta [1] reviewed the study of internal cooling in the gas turbine,they analyzed the effects of rib angle, channel aspect ratio, rib angleand 180� sharp turns, rotation, and so on. Han [2,3] experimentallyinvestigated the effects of the rib pitch-to-height and rib height-to-equivalent diameter ratios on the thermal/hydraulic performance insquare ductswith two opposite rib-roughenedwalls using similaritylaws. Han [2,3] then gave a general prediction method for thethermal/hydraulic performance in rectangular ducts with twosmooth and two opposite ribbed walls. This work has been widelyused in research and design studies. The investigation of the localaerodynamic and heat transfer performance in rib-roughenedsquare duct by Rau et al. [4] showed that Han’s correction deviatedfrom the results when e/Dh ¼ 0.1, which creates strong secondaryflows. Wang and Sunden [5] experimentally investigated the heat

: þ86 10 62770209.ng).

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transfer performance of square ribs, equilateral-triangular ribs,trapezoidal ribs with decreasing height in the flow direction andtrapezoidal ribs with increasing height in the flow direction to showthat the trapezoidal-shaped ribs with decreasing height in the flowdirection give the best heat transfer enhancement performance.

The rib angle is an important factor affecting the rib performancefor enhancingheat transfer. Han et al. [6] found that secondaryflowsproduced by oblique ribs enhance the heat transfer performance.The thermal/hydraulic performance of the oblique ribs with 90�,75�, 60� and 45� angles were investigated experimentally by Kimet al. [7]. They studied the capability of the oblique ribs to inducesecondary flow, which is the reason for enhancing heat transfer byoblique ribs. Koroky and Taslim [8] compared the performance of45� and 90� ribswith experimental results showing that the averageheat transfer coefficient for the 45� oblique rib is higher than that ofthe 90� rib and that the shape of the channel cross section and ribspacing were important factors affecting flow resistance and heattransfer. Lu and Jiang [9] investigated the heat transfer of air ina rectangular channel with various ribs to show the channel with20� ribs had the best overall thermal/hydraulic performance.

Though angled ribs can enhance the heat transfer in a channel,better heat transfer was found with V-shaped ribs. Han and Zhang[10] experimentally studied the performance of 45� and 60�

parallel ribs and V-shaped ribs in a square channel to show that theinterrupted ribs will enhance the heat transfer more with lessincrease in the flow resistance. The experiments by Taslim et al. [11]also showed that the secondary flows generated by oblique ribs is

Nomenclature

de hydraulic diameter (mm)x coordinates (mm)T temperature (K)Re Reynolds number based on the plate channel

hydraulic diameterPr Prandtl numberNu Nusselt numberq heat flux (W/m2)DP pressure drop (Pa)u velocity (m/s)f friction factor

Greek symbolsr density (kg/m3)l thermal conductivity (W/(m.K))m molecular viscosity (kg/(m.s))k turbulence kinetic energy (m2/s2)u dissipation of turbulent kinetic energy (1/s)

Subscriptsw wall0 flat platef fluid

Fig. 1. Experimental system, 1 -air compressor; 2- air container; 3-water filter;4- pressure regulator; 5- filter; 6- by pass; 7- high flow rate flow meter; 8-low flowrate flow mete; 9- electrically heated test section; 10-data acquisition system;11-computer; 12-infrared camera.

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e2708 2703

the reason for the enhancement in the heat transfer coefficient, andthat the high heat transfer coefficient region is increased by theV-shaped ribs. Giovanni [12] gave a detailed experimental inves-tigation of the heat transfer coefficient in rib-roughened channelswith continuous ribs, interrupted ribs and V-shaped interruptedribs, with the results showing that the rib shape and geometrystrongly affect the heat transfer with the transverse interruptedribs having the best heat transfer. The experimental investigation ofV-shaped and angled ribs in rotating rectangular channels by Leeet al. [13] also showed that the V-shaped rib gave better heattransfer enhancement than the angled rib configurations. Similar

Test section sketc

90° rib-b

V-shaped rib

h

infrared wa

b

c

Fig. 2. Test section

results were found by Fu et al. [14] who experimentally studied theheat transfer performance for V-shaped ribs and 45� angled ribs forboth rotating and stationary cases, with the results showing thatthe V-shaped ribs and the discrete V-shaped ribs gave better heattransfer enhancement.

However, further investigations of heat transfer enhancementwith ribs are required, especially for detail thermal/hydraulicperformance of different ribs.

The present paper presents an experimental and numericalinvestigation of the heat transfer and pressure drop in a rib bedchannel with 90� ribs and V-shaped ribs. Three-dimensionalnumerical simulations were used to analyze the thermal/hydraulicperformance of six rib designs with continuous ribs or interruptedribs. These results are useful to improve the designs of the internalcooling passages in gas turbine blades.

2. Experimental system and data reduction

The experimental system shown in Fig. 1 consisted ofa compressor, two flow meters, a test section, pressure and temper-ature measurement instruments and a data acquisition system. The

h (unit: mm)

ed plate

-bed plate

eat flux q

indow

s (unit: mm).

0 2 4 6 8 10 12 1410

20

30

40

50

60

70

80

90Nux

X/de

SST κ-ω correction experimental (infrared camera) experimental (thermocoupl)

Re=14767Re=12658Re=10548Re=8438Re=6330

Fig. 3. Local Nu for the flat plate.

0 2 4 6 8 10 12 14

30

40

50

60

70

80

Nu x

X/de

SST κ−ω experimental (infrared camera) experimental (thermocoupl)

Re=6330

Re=8438

Re=10548

Re=12658

Re=14767

Fig. 4. Local Nu for the 90� rib bed plate.

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e27082704

airwasprovidedbyacompressor,whichpressureda tankwith theairthen led into the test section through a pipe.

The study used three test sections, an empty flat plate, 90� rib bedplate and V-shaped rib bed plate, as shown in Fig. 2. The test channelwas 150 mm � 20 mm � 11 mm for 90� rib and 45� V-shaped ribplates, the ribs were 1 mm high and the spacing was 10 mm.

A constant heat flux was applied to the bottom surface by theelectrical heating and the side surfaces were adiabatic. The topsurface, which was made of infrared germanium glass, wasa window for the infrared camera used to measure the local surfacetemperature.

Fourteen thermocoupleswere inserted along the centerline of thebottom surface to measure the surface temperature. Three thermo-couples were placed in the inlet duct to measure the inlet airtemperature, with three thermocouples at the plate channel outletafter a mixer to measure the bulk exit temperature. The thermo-couples accuracies were within �0.1 �C. Comparison of the temper-atures measured by the infrared camera and the thermocouplesshows that the differences between them are less than �0.5 �C.

The pressure drop between the inlet and outlet was measuredusing a differential pressure transducer with an accuracy of 1 Pa ofthe full scale range of 1000 Pa. The air volume flow rate wasmeasured by two volumetric flow meters, one with a full scalerange of 0.7e7 m3/h and the other with a range of 4.5e45 m3/h, sothe maximum error of the flow rate is less than �2.5%.

The local heat transfer coefficient and Nusselt number weredefined as:

hx ¼ q

A�Tw;x � Tf ;x

� ð1Þ

first rib

a

Fig. 5. Flow fields on the center cross

Nux ¼ hxdel

(2)

The heat flux was calculated from the electrical power (Q ¼ VI)generated from the heater after deducting the heat losses to theambient:

q ¼ Q � Qloss

A(3)

The experimental uncertainty for the heat balance was�5%. Theexperimental uncertainties of the convection heat transfer coeffi-cient were estimated to be �11.5%.

Since the Reynolds numbers in this study were between 6000and 15,000, which are in the transition and turbulent regions, thelocal Nusselt numbers for the empty flat plate channel werecalculated using the correlations proposed by Petukhov et al. [15]and Gnielinski [16], which include the effect of the thermalentrance region.

Nuðx=deÞ ¼ Nu0elðx=deÞ (4)

Where:

Nu0 ¼ ðz=8ÞðRe� 1000ÞPr1þ 12:7

ffiffiffiffiffiffiffiffiz=8

p �Pr2=3 � 1

�;�2300 � Re � 104;0:5 � Pr � 5� 105

�ð5Þ

Nu0 ¼z=8RePr

1þ900=Reþ12:7ffiffiffiffiffiffiffiffiz=8

p �Pr2=3�1

�;�104�Re�5�106; 0:5�Pr�5�105

�ð6Þ

last rib

b

section for the 90� rib bed plate.

Fig. 6. Temperature distribution along the center cross section; (a) 90� rib-bed plate; (b) V-shaped rib-bed plate.

200

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e2708 2705

z ¼ ð1:82 logRe� 1:64Þ�2 (7)

elðx=deÞ ¼1þ 0:416Pr�0:4f ðx=deÞ�0:25

� 1þ 3600

Refffiffiffiffiffiffiffiffiffiffix=de

p!expð � 0:17x=deÞ

�4000 � Re � 106; 0:7 � Pr � 100; x=de>0:5

�ð8Þ

3. Numerical simulation method

The numerical simulations were performed using the CFDsoftware package FLUENT 6.3.26. Turbulence closure was achievedusing the shear-stress transport (SST) k-u model.

Thegeneral formsof the governingequations for thisproblemare:Continuity equation:

vrujvxj

¼ 0 (9)

Momentum equation:

v

vxj

�rujui

� ¼ �vpvxj

þ v

vxj

�sij � ru0iu

0j

�(10)

Energy equation:

v

vxi½uiðrE þ pÞ� ¼ v

vxj

"�lþ cpmt

Prt

�vTvxj

þ ui�sij�eff

#(11)

Where:

4000 8000 12000 160000.00

0.01

0.02

0.03

0.04

0.05

0.06 Exp. (90° rib-bed plate) Simulation (90° rib-bed plate) Exp. (V-shaped rib-bed plate) Simulation (V-shaped rib-bed plate) f=0.046Re

f

Fig. 7. Friction factor.

�ru0iu0j ¼ 2mtEij �

23rkdij (12)

Transport Equations for the SST k-u Model:

mt ¼ rku

1

max1a*

;UF2a1u

(13)

v

vxiðrkuiÞ ¼ v

vxj

Gk

vkvxj

!þ Gk � Yk (14)

v

vxiðruuiÞ ¼ v

vxj

Gu

vu

vxj

!þ Gu � Yu þ Du (15)

Where Gk represents the generation of turbulent kinetic energy dueto the mean velocity gradients, Gu represents the generation of u,Yk and Yu represent the dissipation of k and u due to turbulence,and Du represents the cross-diffusion term,

The incompressible ideal gas NaviereStokes equations weresolved by the finite volume method with structured meshes andthe coupling between the velocity and pressure given by theSIMPLE algorithm.

The advection terms in the momentum, energy, mass transport,turbulent kinetic energy and specific dissipation equations werediscretized using the second order upwind algorithm.

Grid independence studies resulted in meshes having about800,000 elements for each case. The convergence criteriawere 10�4

for velocity, 10�6 for k and u and 10�8 for energy. The inlet

0 2 4 6 8 10 12 1440

60

80

100

120

140

160

180

Nu x

X/de

SST κ−ω experimental (infrared camera) experimental (thermocoupl)

Re=6330Re=8438Re=10548Re=12658Re=14767

Fig. 8. Local Nu for the V-shaped rib-bed plate.

Fig. 9. Cross flow velocity vectors in a channel cross section for the V-shaped rib-bed plate.

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e27082706

boundary conditions were set as velocity inlet with the outlet set asoutflow. The heat flux boundary condition was used for the bottomsurface with the other surfaces being adiabatic and no-slip.

4. Results & discussion

4.1. Empty flat plate

The distributions of the local Nu in the flat plate channel areshown in Fig. 3. The local Nusselt numbers decreased along the testsection. The experimental results for the local Nusselt numberobtained using the infrared camera are very close to the data usingthe thermocouples, with differences less than �5%. The numericalsimulation results using the SST k-u turbulence model agreed wellwith the experimental data with the differences between thenumerically calculated Nusselt number and the experimental dataof less than �10%. The correlation predictions are also comparedwith the numerical and experimental results in Fig. 3, which indi-cates that the numerical results agree better with the experimentaldata than the correlations in Eqs. (4) to (8).

4000 8000 12000 160000.5

1.0

1.5

2.0

2.5

Re

V-shape ribs (exp.) V-shape ribs (simulation) 90 ribs (exp.) 90 ribs (simulation) flat

(Nu/

Nu 0) /

(f/f 0

)

Fig. 10. Thermal/hydraulic performance for the 90� rib-bed and V-shaped rib-bedplates.

4.2. 90� rib-bed plate

The local Nu for the 90� rib flat plate shown in Fig. 4 illustratesthat the local Nu first decreases before the first rib due to theentrance effect with the boundary layer thickness increasing alongthe plate, then increases after the first rib especially for high Re,because the boundary layer is disrupted by the rib. This phenom-enon is illustrated in Fig. 5, by the distinct vortex after the first rib,which enhances the turbulence mixing of the flow field, to increasethe heat transfer. Although the thermal boundary layer was dis-rupted, the velocity in the region near the surface between the tworibs is lower, so the overall trend for the Nu decreases along theplate. The local Nu increases at the test channel outlet, becausethe fluid flow is not constrained after the last rib. The velocity nearthe surface then increases, resulting in enhancement of the heattransfer. This phenomenon can also be found in Fig. 5, where thevortex after the last rib is smaller than that between two ribs.

The simulated fluid temperature in the center cross section isshown in Fig. 6. The temperature near the wall decreases as Reincreases, while the fluid temperature far from the wall remains atthe inlet temperature, which indicates that the turbulent mixing isnot enhanced much by the 90� rib.

The experimental results in Fig. 7 indicate that the frictionfactor with the 90� ribs is about twice that of the flat plate. Thenumerical results for friction factor are much larger than theexperimental data.

4.3. V-shaped rib-bed plate

The local Nu for the V-shaped rib bed plate is shown in Fig. 8.For a given inlet Re, the local Nu first decreases before the first riband then increases after the first rib for the same reason as for the90� rib bed plate. However, unlike for the 90� ribs, the local Nuincreases rapidly along the plate after the first rib, which isbecause for the V-shaped rib, the rib not only disrupts theboundary layer, but also forms a significant secondary longitudinalvortex structures as shown in Fig. 9. This vortex carries cooler fluidfrom the center of the channel towards the side walls whichenhances the heat transfer. With these effects, the V-shaped ribscreate greater heat transfer enhancement than the 90� ribs. At thechannel outlet, the local Nu decreases because the longitudinalvortex structures are weakened near the outlet.

The simulated fluid temperature in the center cross section inFig. 6 shows that the temperature near the wall decreases as Reincreases. However, unlike for the 90� ribs, the temperature of thecenter cross sectionwith the V-shaped ribs is changed not only nearthe wall, but also far from the wall due to the strong turbulentmixing in the fluid. Thus, the heat transfer with the V-shaped ribs isbetter than with the 90� ribs.

Fig. 11. Rib layouts and wall temperature distributions (Re ¼ 10000); (a) 90� continuous rib; (b) 90� interrupted rib; (c) 45� V-shaped continuous rib; (d) 45� V-shaped interruptedrib; (e) 60� V-shaped continuous rib; (f) 60� V-shaped interrupted rib.

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e2708 2707

Unlike for the 90� rib, the friction factor with the V-shaped ribsdecreases as the inlet Re increases. The experimental results inFig. 7 indicated that the friction factor with the V-shaped ribs isabout four times that of the flat plate.

4.4. Comparison of the three channels

ðNu=Nu0Þ=ðf =f0Þ1=3 for these three channels are shown in Fig.10.For the 90� ribs, both the experimental and numerical results showthat ðNu=Nu0Þ=ðf =f0Þ1=3 is about 1 at lower Re and less than 1 forlarge Re, which indicates that the overall thermal/hydraulicperformance of the 90� ribs is not good. For the V-shaped ribs,ðNu=Nu0Þ=ðf =f0Þ1=3 decreases as the inlet Re increases with valueslarger than 1. Therefore, the V-shaped rib has better heat transferenhancement performance.

1x10 2x10 3x10 4x100.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

(Nu/

Nu 0) /

(f/f 0

)

Re

90 Rib, Continuous 90 Rib, Interrupted 45 . V-Shaped Rib, Interrupted 45 . V-Shaped Rib, Continuous 60 . V-Shaped Rib, Interrupted 60 . V-Shaped Rib, Continuous

Fig. 12. Thermal/hydraulic performance of different rib designs.

4.5. Numerical simulations for various 90� and V-shaped ribs

Six different rib arrangements were analyzed to optimize the ribarrangements. The designs include continuous and interrupted rib90�and V-shaped ribs, with angles shown in Fig. 11. The channelswere 450 mm � 100 mm � 20 mm. Each rib is 3 mm wide and3 mm high with a spacing of 37.5 mm. Grid independence studiesresulted in meshes having about 800,000 elements for each case.

The wall temperatures for these six rib designs are shown inFig. 11. The wall temperatures for the 90� continuous ribs aresignificantly higher than for the other rib designs with the 90�

interrupted ribs which disrupt the boundary layer more, resultingin better heat transfer. Comparison of the V-shaped continuous ribsand the V-shaped interrupted ribs shows that the heat transferwith the V-shaped interrupted ribs was less than that of theV-shaped continuous ribs.

ðNu=Nu0Þ=ðf =f0Þ1=3 for these six designs shown in Fig. 12 showthat the 45� V-shaped continuous ribs are the best, while the 90�

continuous rib have the worst performance. Figure 12 also showsthe overall thermal/hydraulic performance of the V-shaped ribs isbetter than that of the 90� ribs.

5. Conclusions

The effect of rib-bed walls on the heat transfer was studiedexperimentally and numerically for various rib geometries.

(1) The experimental and numerical results show that the V-sha-ped rib bed plates have better thermal/hydraulic performancethan the 90� rib bed plates due to V-shaped ribs not only dis-rupting the boundary layer, but also forming significant

W. Peng et al. / Applied Thermal Engineering 31 (2011) 2702e27082708

secondary longitudinal vortices, which enhance the heattransfer.

(2) The results indicate that the 45� V-shaped continuous ribs havethe best thermal/hydraulic performance.

(3) Comparison of continuous and interrupted ribs shows that theheat transfer with the V-shaped interrupted ribs was lowerthanwith the V-shaped continuous ribs, while the 90� ribs hadthe opposite result.

Acknowledgments

This project was supported by the Key Project Fund of theNational Natural Science Foundation of China (No. 50736003) andthe National Basic Research Program (973 Program) (No.2007CB210107).

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