turb_135_3_031004

7/30/2019 turb_135_3_031004

1/9

Sebastien Kunstmann

Jens von Wolfersdorf

Institute of Aerospace Thermodynamics,

Universit at Stuttgart ,

Stuttgart, D-70569, Germany

e-mail: [email protected]

Uwe RuedelALSTOM Power Systems Turbomachines Group,

Brown Boveri Strasse 7,

Baden, CH-5401, Switzerland

e-mail: [email protected]

Heat Transfer and Pressure Lossin Rectangular One-Side-RibbedChannels With Different Aspect

RatiosAn investigation was conducted to assess the thermal performance of W-shaped, 2W-shaped and 4W-shaped ribs in a rectangular channel. The aspect ratios (W/H) were 2:1,4:1, and 8:1. The ribs were located on one channel wall. The rib height (e) was kept con-stant with a rib height-to-hydraulic diameter ratio (e/Dh) of 0.02, 0.03, and 0.06. The ribpitch-to-height ratio (P/e) was 10. The Reynolds numbers investigated (Re> 90 000) aretypical for combustor liner cooling configurations of gas turbines. Local heat transfercoefficients using the transient thermochromic liquid crystal technique and overall pres-sure losses were measured. The rib configurations were investigated numerically to visu-alize the flow pattern in the channel and to support the understanding of the experimentaldata. The results show that the highest heat transfer enhancement is obtained by rib con-figurations with a rib section-to-channel height ratio (Wr/H) of 1:1. W-shaped ribsachieve the highest heat transfer enhancement levels in channels with an aspect ratio of2:1, 2W-shaped ribs in channels with an aspect ratio of 4:1 and 4W-shaped ribs in chan-

nels with an aspect ratio of 8:1. Furthermore, the pressure loss increases with increasingcomplexity of the rib geometry and blockage ratio. [DOI: 10.1115/1.4006871]

Introduction

Nowadays, gas turbines must not only be highly efficient, butalso environmental friendly. Higher turbine inlet temperatures,hence higher combustion chamber temperatures, are needed toincrease efficiency. For the environment, it is important to mini-mize the emissions due to unburned hydrocarbons, carbon monox-ide, and NOx [1]. The high gas temperatures in the combustorchamber demand reliable cooling schemes to protect its walls. Inbackside cooled combustors walls, the addition of cooling fea-tures, such as ribs, increase the heat transfer rates on these walls.If they simultaneously achieve a moderate pressure drop in thecooling channel, the efficiency could be further increased. Thiscooling technique, where all the liner cooling air is fed backthrough the burners, allows a lean and premixed combustion.

Many different convective cooling features, like 90 deg, angled,V-shaped, and W-shaped ribs have been studied for turbine bladecooling schemes. In contrast, a combustor liner cooling scheme isoften characterized by a high channel aspect ratio (W/H> 2), highReynolds numbers and only one ribbed wall. Maurer et al. [24]compared V-shaped, W-shaped, and 2W-shaped ribs with a block-age ratio (e/Dh) of 0.02 and pitch-to-height ratio (P/e) of 5 and 10.The ribs where positioned on only one channel wall. The channelaspect ratio was 2:1 and the Reynolds number varied from 80,000to 500,000. They found that the W-shaped rib with a rib pitch-to-rib height ratio P/e 10 has the best thermal performance for thisW/H. Bailey et al. [5], as well as Kim et al. [6], investigated one

side ribbed channels at high Reynolds number, as found in com-bustor liner cooling. They investigated 90 deg ribs together withother concepts (impingement, dimples). Kim et al. [6] showed thatthe highest heat transfer enhancement in a combustor liner isachieved with impingement cooling, which simultaneously pro-duces the largest pressure loss among the investigated coolingtechniques. Park et al. [7] investigated the combined effects of thechannel aspect ratio, rib angle-of-attack, and flow Reynolds num-ber in rectangular channels with two ribbed walls. The channel

aspect ratio (W/H) varied from 1:4 to 4:1. The blockage ratioswere 0.047 and 0.078. This study recommended 30 deg and 45deg angled ribs for cooling design in a channel with a broad aspectratio (W/H 4:1). Wright et al. [8] conducted a study with angled,W-shaped, and V-shaped ribs in a channel with a high aspect ratioof 4:1. Here, the rib pitch-to-height (P/e) was 10. They investi-gated ribs with a blockage ratio of 0.078. The Reynolds numbervaried from 10,000 to 40,000. In this study, the W-shaped ribsperformed better than the V-shaped and the angled ribs. Chandraet al. [9] investigated the heat transfer and friction loss in a squarechannel with 90 deg-ribs on one, two, three, and four walls. The

tests were performed for Reynolds numbers between 10 000 and80 000. The pitch-to-rib height ratio was kept at 8 and the block-age ratio was 0.0625. The results showed that the heat transferperformance decreases with each additional ribbed wall and that achannel with two opposite ribbed walls achieves only a moderateincrease (6%) in heat transfer over the one side ribbed channel.Cakan [10] investigated the heat transfer and pressure losses insquare channels with one and two ribbed walls. He varied theangle of attack of the ribs, the pitch-to-rib height ratio, and theblockage ratio. For the present study, the most interesting aspectof his investigation is the effect of the blockage ratio on heattransfer enhancement on the sidewall, because of the high gastemperatures possibly found in the gap between two combustorsegments. It was shown that in a channel with one ribbed wall theincrease of the blockage ratio improves the heat transfer enhance-

ment on the opposite smooth wall as well as on the sidewalls.Until now, there was no experimental data available for W-shaped, 2W-shaped, and 4W-shaped ribs in one-side-ribbed cool-ing channels and different channel aspect ratios at high Reynoldsnumbers. The scope of this study is set to assess the effects ofthese variations to the heat transfer on all channel walls and to thepressure loss in the cooling channel. The chosen channel aspectratios comply with the ones found in actual combustor liners.

Experimental Setup

Test Facility. The schematic in Fig. 1 shows the open-loopwind tunnel used for the present study. The air flow is set by ablower, which functions in suction mode.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publi-cation in the JOURNAL OF TURBOMACHINERY. Manuscript received May 1, 2011; finalmanuscript received July 23, 2011; published online March 25, 2013. Editor: DavidWisler.

Journal of Turbomachinery MAY 2013, Vol. 135 / 031004-1CopyrightVC 2013 by ASME

wnloaded From: http://asmedigitalcollection.asme.org/ on 05/13/2013 Terms of Use: http://asme.org/terms

7/30/2019 turb_135_3_031004

2/9

The air flow enters the test rig through a nozzle and is thendirected through the electrical heater before it enters the test chan-nel. Figure 2 shows a by-pass valve installed between the heaterand the test channel. Reference [3] contains a more detaileddescription of the test facility.

Experimental Setup and Measurement Approach. The ratioof the ribbed channel length to hydraulic diameter (L/Dh) is 6 inthe configuration forW/H 2:1. Using two modules with differentspacers as investigated in Ref. [3], it is possible to change the as-pect ratio from W/H 2:1 to W/H 4:1 and W/H 8:1. See

Fig. 3.When the modules are installed, the ribbed channel length-to-hydraulic diameter (L/Dh) is increased to 10 and 18 for aspectratios W/H 4:1 and 8:1, respectively. The walls of the test chan-nel and the modules are made of Perspex plates with a thicknessof 20 mm, which allows an adequate thermal insulation due to thelow thermal conductivity of the material and good optical access.The ribs are also made of Perspex to ensure similar properties asthe walls.

To obtain the friction factor of the installed rib configurations,the static pressure loss is measured in eight consecutive rib seg-ments along the test channel sidewall. At least 15 ribs are placedupstream the first pressure tap to ensure fully developed flow con-ditions. The pressure taps are linked to a digital sensor module

and an integrated 16 bit A/D converter, which allows high fre-quency data acquisition.

To measure the heat transfer on the channel walls of the investi-gated test cases, the transient measurement technique was applied,as described by Poser et al. [11] and Maurer et al. [3]. To measurethe heat transfer on the ribs, three Perspex ribs were replaced bysegmented aluminum ribs, so that the lumped capacitance methodcould be used as detailed in Ref. [4]. All measured surfaces werecovered with narrowband thermochromic liquid crystals (TLC) typeBM/R43C1W/C1710 from HallcrestTM. These crystals were pre-viously calibrated in a dedicated test run to obtain the right greenmaximum intensity-to-temperature dependency. The fluid tempera-ture step (Fig. 4) in the test channel is produced by opening thevalve shown in Fig. 2 when the desired air temperature is reached.

Rib Configurations. Three different rib configurations wereinvestigated: W-shaped, 2W-shaped, and 4W-shaped ribs. Theangle of attack a and the pitch-to-height ratio P/e were kept con-stant at 45 deg and 10, respectively. The blockage ratios e/Dh var-ied from 0.02 to 0.03 and to 0.06 for the channel aspect ratiosW/H 2:1, 4:1, and 8:1, respectively.

The combination ofW/Hvariations and the different rib geome-tries result in a total of six test cases, all listed in Table 1. Allcases were tested in one side ribbed channels with the ribs on thebottom channel wall. The investigated rib configurations, the defi-nition of the rib width used to specify Wr/H and the definition ofrib trailing and leading edges are found in Fig. 5. A minimum of22 ribs were placed in front of the heat transfer measurement

region to achieve fully developed conditions. The assumed perio-dicity of the flow stream was validated by measuring two succes-sive rib segments and comparing the results. The heat transferdata differed by less than three percent.

The maximum achievable Re is influenced in every test casethrough the channel cross section, and limited by the maximummass flow and Dp that the blower can produce. For all test cases,the maximum Mach number is below 0.12 in the test section sothat the flow can be treated as incompressible.

Numerical Setup

Beside the experimental investigation, numerical simulations ofthe test cases were made to analyze the main flow structures in the

Fig. 1 Schematic of test rig [3]

Fig. 2 Schematic of air flow with (a) closed valve and (b) openvalve

Fig. 3 Channel with implemented modules

Fig. 4 Temperature step in the test section

Table 1 Test case configurations, a545 deg, P/e510

Test case Rib type e/Dh W/H Wr/H Re range

W-2 W 0.02 2:1 1:1 130 K-500 KW-4 W 0.03 4:1 2:1 100 K-450 KW-8 W 0.06 8:1 4:1 70 K-250 K2W-4 2W 0.03 4:1 1:1 100 K-450 K2W-8 2W 0.06 8:1 2:1 70 K-250 K4W-8 4W 0.06 8:1 1:1 70 K-250 K

031004-2 / Vol. 135, MAY 2013 Transactions of the ASME


7/30/2019 turb_135_3_031004

3/9

test channel. FLUENTTM (V6.326) was used to solve the Reynolds-averaged NavierStokes equation (RANS) with a second-ordervolume discretization scheme. The energy and the momentumequation were coupled through the ideal gas law. All computa-tions were performed using a realizable k- turbulence model withenhanced wall treatment.

To keep the computational time and demand on computingcapacities low, the channel geometry was reduced to a transla-tional periodic segment. Hence, periodic inlet and outlet condi-tions with defined mass flow rates were applied. Furthermore,only one half of this segment was modeled, which was realizedusing symmetry planes. The wall was modeled with a no-slip

boundary condition and constant wall temperature. The number ofnodes varied from 412 000 to 580 000. All grids met the require-ments of a dimensionless wall distance y< 1 and turbulentReynolds number Rey< 200 in the tenth cell from the wall.

Data Reduction

Equation (1) is used to calculate the friction factor. The pres-sure gradient Dp/Dx is obtained as a pressure loss-regression linefrom the static pressure measurements.

f Dp=DxDh

2qu2AVG(1)

All friction factors presented in this study are normalized by thefriction factor for fully developed turbulent flows in a smooth cir-

cular tube (104

< Re< 106

) proposed by Blasius as:

f=f0 f

0:046Re0:2(2)

The heat transfer coefficient is evaluated with a program [11] thatsolves the one-dimensional solution of Fouriers equation with asemi-infinite wall and a convective boundary condition. To evalu-ate the fluid temperature change different from a sudden tempera-ture step (see Fig. 4), the Duhamel principle is used. As seen inEq. (3), the real temperature development is approximated by a fi-nite number of temperature steps.

Tw T0 XNj1

1 eb2

erfc b h i

DTf j;j1

with b h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit sj

qwcp;wkw

s(3)

The heat transfer on the ribs is calculated with the lumped capaci-tance method presented in Ref. [4]. Here, the heat transfer on thesurface of a solid can be determined using Eq. (4).

TRB T0 XNj1

1 ec

DTf j;j1

with c hRBARB t sj

mRBcRB

(4)

The Nusselt number is normalized using the correlation providedby Kays et al. [12] to compare the heat transfer augmentation ofthe different test cases. The Nusselt number ratio is presented inEq. (5).

Nu

Nu0

Nu

0:021Re0:8Pr0:5(5)

The area-averaged Nusselt number of the ribbed wall includingthe ribs is calculated with Eq. (6):

NuRRB NuRWARW NuRBARB

ARW ARB (6)

The method of error propagation is used to evaluate the experi-mental uncertainties (see also Refs. [24]). A measurement uncer-tainty analysis for the heat transfer measurements was carried outfollowing the method outlined by Moffat [13]. The uncertaintiesfor temperature (60.2 K), time (60.2 s), cP,W (614.7 J/(kgK)),qW (611.9 kg/m

3) and kW (60.0095 W/(mK)) are given with aconfidence level of 95%, which corresponds to 62r. For the over-all uncertainty calculation of h, Eq. (3) with Duhamels principleis taken into account. Here, the overall uncertainties are dependenton the value ofh, with increasing values resulting in higher uncer-tainties. The maximum uncertainty in the presented work for the

highest heat transfer rates is calculated to be6

12% with a confi-dence range level of 95%.Taking the relative errors for mass flow (2%), gradient of pres-

sure distribution (6%) and air properties (2%) into account, themaximum uncertainty for the friction factor is610%.

Results and Discussion

Numerical Results: Velocity Field. A comprehensive analysisof the flow field in the investigated test cases is presented in thefollowing to support the understanding of the experimental data.

The mean velocity distribution in the channel cross section ofall test cases can be seen in Fig. 6 as a contour plot. The stream-lines identify the secondary flow structures and are presented witharrows on the plot. The streamlines move towards the ribbed wall

over the leading edges of the rib and away from the ribbed wallover the trailing edges of the rib.As already described in Ref. [3], the W-shaped ribs produce

two counter rotating vortices in each channel half. In test caseswith the 2W-shaped ribs, a total of four counter rotating vorticescan be identified in every channel half. In the test case 4W-8,eight counter rotating vortices are found in every channel half.Their distribution in the channel cross section and their shape isless regular than in the other test cases.

The mean mass flow moves right through the center of the sec-ondary vortices in test cases W-4, W-8, and 2W-8 (Wr/H 2:1and 4:1), and below them in test cases W-2, 2W-4 (Wr/H 1:1).In test case 4W-8 (Wr/H 1:1) the mean mass flow moves abovethe secondary vortices.

Fig. 5 Investigated rib configurations

Journal of Turbomachinery MAY 2013, Vol. 135 / 031004-3


7/30/2019 turb_135_3_031004

4/9

The shape of the secondary flow structures also changes withvarying Wr/H. for the test cases where Wr/H 1:1, a vertically ori-entated oval shape is observed, while in test cases with Wr/H 2:1,the vortices have an almost circular to square shape. In test caseW-8 (Wr/H 4:1) the vortices become very flat.

The streamlines depicted in Fig. 7 visualize the flow phenom-ena close to the ribbed wall and help understand the generation ofthe secondary flow structures.

In Fig. 7(b), it can be observed that the air flow is acceleratedas it passes over the ribs. Immediately after the ribs, the air flowdetaches and a recirculation region is formed. The vortex in thiszone develops from the leading edge and along the rib towards thetrailing edge (see Fig. 7(a)). Here, the streamlines are ejectedback to the main flow and move away from the ribbed wall, asindicated by the vortex streamlines given in Fig. 6.

Following a streamline downstream from the rib, see Fig. 7(a),a reattachment zone is found before the streamline is deflectedtowards the trailing edge of the following rib. In front of this rib, asmall vortex is formed. The distribution of the streamtracesaround the leading edges of the W-shaped and the 2W-shaped ribsis nearly symmetrical. In contrast to them, only the streamtracesaround the leading edge at Z/(W/2) 5/8 and 3/8 of the 4W-shaped rib do so. The asymmetry of the streamtraces on both sidesof the leading edges at Z/(W/2) 7/8 and 1/8 explain the irregu-larity of the vortices observed in Fig. 6.

Fig. 6 Computational mean velocity and secondary flow distri-butions at Re$250 K

Fig. 7 Flow field close to the ribbed wall with W-shaped, 2W-shaped, and 4W-shaped ribs, (a) top view, (b) sectional sideview, Re$250 K



7/30/2019 turb_135_3_031004

5/9

Experimental Results: Friction Factor. As mentionedbefore, one of the main requirements for regenerative coolingschemes is a low pressure drop in the cooling channel. The experi-mental data is presented in form of the measured friction factor ra-tio f/f0 for all test cases in Fig. 8.

The 4W-shaped ribs produce a higher pressure drop, or frictionfactor ratio, than the 2W-shaped and the W-shaped ribs for the

same Reynolds number and channel aspect ratio. The highest fric-tion factor ratios over the investigated Reynolds number range arefound in test case 4W-8. For comparison, at a Reynolds number of130,000, f/f0 is 7.3, 9.2, and 12.6 for test cases W-8, 2W-8, and4W-8, respectively. This reflects a 26% increase for case 2W-8compared to W-8 and a 37% increase for case 4W-8 compared to2W-8.

The results show that f/f0 increases with increasing Reynoldsnumber. It is also seen that the variation of the channel heightand with it the blockage ratio e/Dh and aspect ratio W/Hhas alarge influence on the friction factor ratio.

Park et al. [7] also observed an increase of f/f0 for increasingchannel aspect ratios and angled ribs on two opposite walls.

However, the dominating effect on friction ratio is the rib com-plexity or in test cases with the same channel aspect ratio, the ribsection width-to-channel height ratio Wr/H. As observed in Refs.[24] and in Fig. 8, the friction factor increases with increasingrib complexity.

The slope of the friction factor plotted over Reynolds numberbecomes steeper with increasing channel aspect ratio and increas-ing complexity of the rib geometry. Test case 4W-8 shows asteeper slope than test cases 2W-8 and W-8; Ref. [3] reported sim-ilar slopes for rib configurations with the same pitch-to-height ra-tio in a channel with a channel aspect ratio of 2:1.

Experimental Results: Area-Averaged Heat TransferEnhancement. In Fig. 9, the measured heat transfer enhancementon the ribbed wall and on the ribs themselves versus the investi-gated Reynolds number range is plotted.

Since the rib height remains unchanged in all test cases, a risein the channel aspect ratio represents a higher blockage ratio.When comparing test cases W-2 and W-4, it is visible that an

increase of the blockage ratio yields only a small rise in heattransfer enhancement. For the W-shaped and 2W-shaped ribbedchannels, a further reduction of the channel height produces alower heat transfer enhancement on the ribbed wall. For compari-son at Reynolds number 130 000, the rise of the blockage ratiofrom 0.02 to 0.03 increases the heat transfer enhancement by 8%for the W-shaped rib. A further step-up of the blockage ratio from0.03 to 0.06 reduces the heat transfer enhancement by 20% and14% for W-shaped and 2W-shaped ribs, respectively. In test caseswith a blockage ratio e/Dh below 0.06, all test cases show a simi-lar trend of heat transfer enhancement over the investigated

Reynolds number range, while in channels with a blockage ratioof 0.06 only test case 4W-8 (Wr/H 1:1) does so.

In their study, Park et al. [7] also observed that an increase ofthe blockage ratio does not always produce higher heat transferenhancement on the ribbed wall of the test channel.

More interesting than the effect of the blockage ratio on theheat transfer enhancement on the ribbed wall is the fact that in test

cases with the same channel aspect ratiohence the same block-age ratiothe highest heat transfer enhancement on the ribbedwall is achieved with rib geometries where Wr/H is 1:1 (seeFig. 9). This relation between rib geometry and channel heightseems to represent an optimum regarding heat transfer augmenta-tion on the ribbed wall.

Figure 10 documents the heat transfer enhancement on the side-wall versus the investigated Reynolds number range. All test casesindicate a moderate increase of the heat transfer enhancement onthe sidewall with rising Reynolds number. The heat transferenhancement level is lower here than on the respective ribbedwall for all test cases. In this chart, it becomes apparent that anincrease in the blockage ratio causes an increase of the heat trans-fer enhancement on the sidewall.

For comparison, at a Reynolds number 130 000, the rise of theblockage ratio from 0.03 to 0.06 causes a rise of the heat transferenhancement by 18% for the W-shaped ribbed channel and by20% for the 2W-shaped ribbed channel. The largest difference(29%) in the heat transfer enhancement between test cases withthe same rib configuration is found between test cases W-2 andW-4.

Test cases with the same blockage ratio achieve very similarheat transfer enhancement levels on the sidewall. Cakan [10]reported the same effect of variations of the blockage ratio to theheat transfer enhancement on the channel sidewall of channelswith one ribbed wall as in this study. In Fig. 10 it can also be

Fig. 8 Friction factor ratios f/f0 Fig. 9 Heat transfer enhancement on the ribbed wall includingthe rib surface

Fig. 10 Heat transfer enhancement on the channel sidewall



7/30/2019 turb_135_3_031004

6/9

observed that the rib geometry has less influence on the heat trans-fer enhancement on the channel sidewall than the blockage ratio.

Figure 11 shows the heat transfer enhancement of all test caseson the top wall of the cooling channel versus the investigatedReynolds number range. Here, a similar trend of increasing heattransfer enhancement with increasing Reynolds numbers as on thesidewall can be observed. Compared to the sidewall, the heattransfer enhancement level is lower for test cases W-2, W-4, 2W-

4, W-8, and 4W-8. Test case 2W-8 achieves the highest heat trans-fer enhancement on the top wall of all test cases. On the top wall,as on the sidewall, the heat transfer enhancement is increased withan increasing blockage ratio. For comparison, at a Reynolds num-ber of 130,000, the rise of the blockage ratio from 0.03 to 0.06reveals a rise of the heat transfer enhancement by 9% for the chan-nel with W-shaped ribs and 45% for the channel with 2W-shapedribs. For the same blockage ratio, test cases with Wr/H 2:1 (W-4and 2W-8) show the highest heat transfer enhancement on the topwall. As seen in Fig. 6, the secondary vortices in these test caseshave an almost square shape.

Experimental Results: Thermal Performance. To assess thecooling ability of the test cases investigated in this study, the heattransfer performance at constant pumping power is computed and

given in Fig. 12. Since the heat transfer on the sidewall and on thetop wall are usually not of primary concern when designing acombustor liner, only the heat transfer on the ribbed wall plus ribsurface is taken into the calculation of the thermal performance.

This figure shows optimum configurations for specific applica-tions. In sections of a combustor liner where a high aspect ratio isfound and the rib height cannot be further reduced, more complexribs are needed to achieve best performances. In other sections,where lower blockage ratios are possible, smaller ribs for low fric-tion coefficients perform better on simple configurations.

The best performance is achieved in test case W-2, which com-bines a pressure loss that is over 25% lower than in all other testcases with heat transfer enhancement ratios only around 10%below test cases 4W-8 and 2W-4. In a test channel with a block-age ratio of 0.06, the 4W-shaped rib performs better than the W-shaped and the 2W-shaped rib. The lowest thermal performanceof all investigated cases is achieved in test case W-8.

Experimental Results: Local Heat Transfer Enhancement.Knowing the local heat transfer enhancement distributions on all

channel walls is of advantage when the thermal stresses of thecombustor liner cooling configurations need to be assessed.

Figures 1315 show the local heat transfer enhancement on thebottom wall, on the sidewall and on the top wall, respectively.

From Fig. 13, it becomes clear that with increasing complexityof the rib geometry the heat transfer enhancement distributionbecomes more homogeneous. This fact has already been docu-mented by Wright et al. [8].

Some effects of flow structures close to the ribbed wall can beobserved directly from the resulting heat transfer enhancementdistributions in Fig. 13. In all test cases, the highest heat transferenhancement ratios are found behind the rib close to the leadingedge, where the flow is shown to reattach. In test case 4W-8,behind the leading edge of the V-rib section close to the sidewall,the heat transfer enhancement is lower than behind the other three

leading edges and also shows a lower degree of symmetry around

Fig. 11 Heat transfer enhancement on the channel top wall

Fig. 12 Thermal performance of all test cases Fig. 13 Nu/Nu0 distribution on the ribbed wall



7/30/2019 turb_135_3_031004

7/9

the leading edge. This correlates to the asymmetry around theleading edge at Z/(W/2) 7/8 observed in the flow field in Fig. 6.

In all test cases, following the streamlines towards the trailing

edges, the heat transfer enhancement is slightly reduced, whichcould be due to the decrease of vortex strength and driving tem-perature for the vortex traveling between the ribs towards the trail-ing edges. Right behind the rib a region of low heat transferenhancement is found due to flow separation. In test cases withthe 2W-shaped and with the 4W-shaped rib, the heat transferenhancement in front of the rib is lower on the segment close tothe sidewall.

The value of the heat transfer enhancement peak at a givenReynolds number is nearly equal for test cases W-2, W-4, 2W-4,and 4W-8 and lower for test cases W-8 and 2W-8. For increasingReynolds number, all test cases show a reduction of high heattransfer enhancement areas, but test cases W-8 and 2W-8 showlarge middle heat transfer enhancement ratio zones. This is espe-cially noticeable in test case 2W-8, where a relatively homogene-

ous heat transfer enhancement distribution is found.The channel sidewalls adjacent to gaps between two combustorsegments are possibly exposed to high gas temperatures and canalso exhibit high thermal stresses. The local heat transfer enhance-ment situation on the sidewall is presented in Fig. 14. As in Fig.13, effects of the flow structures in close proximity to the ribbedwall are directly visible. Right above the ribs and close to theribbed wall, where the streamlines between the ribs hit the side-wall before they are redirected to the main air flow, the heat trans-fer enhancement peaks are found. The heat transfer enhancementpeak values increase with increasing Reynolds numbers in all testcases. Directly after the rib, a small region of low heat transferenhancement is found. This region is best seen in test case 2W-4and can be explained by the recirculation zone behind the rib.

With increasing distance from the ribbed wall, the heat transferenhancement is reduced. In test case W-2, this low heat transferenhancement region occupies around 50% of the sidewall. Withincreasing blockage ratio, this region is reduced and almost disap-pears for e/Dh 0.06. This fact explains the rise of the area-averaged heat transfer enhancement on the sidewall for increasingblockage ratio, as shown in Fig. 10.

The effects of the channel aspect ratio variation on the heattransfer enhancement distribution are more noticeable on the topwall. As shown in Fig. 15, in all test cases the heat transfer

enhancement is increased with rising channel aspect ratio andReynolds numbers. The lowest heat transfer enhancement levelsare reached in test case W-2. Here, an almost homogeneous distri-bution is seen. Regions of slightly higher heat transfer enhance-ment are found to both sides of the middle plane between thesymmetry plane and the sidewall. Having the rib geometry andthe velocity field in mind, it is clear that the low heat transferenhancement region lieswith a slight deviation towards thesymmetry planeabove the leading edges of the ribs. This appliesfor all test cases. The zones of high heat transfer enhancement arefound above the trailing edges of the ribs, except on test case W-2near the sidewall.

In test cases W-8 and 2W-8, the heat transfer enhancement dis-tribution close to the sidewall looks very similar to the distributionon the sidewall near to the ribbed wall. In test case W-8, similarstructures are also found around the symmetry plane. This distri-

bution correlates with the flow field shown earlier, where the sec-ondary flow structures showed flat shapes. In test case 4W-8,which has a rib section width-to-channel height ratio Wr/H 1,such distributions cannot be found.

The heat transfer enhancement distribution on the rib surface isplotted over the dimensionless coordinate Z/(W/2) in Fig. 16. Testcase W-4 achieves the highest heat transfer enhancement ratios,with a peak value of 5.3.

In test cases W-2, W-4, and W-8, the heat transfer enhancementpeak is found around the leading edge of the rib at Z/(W/2) 4/8.In test cases 2W-4 and 2W-8, two peaks are found again aroundthe leading edges of the rib, the heat transfer enhancement ratiosaround Z/(W/2) 2/8 being higher than around Z/(W/2) 6/8.Test case 4W-8 shows a decrease of the heat transfer enhancementratios towards the sidewall. The heat transfer enhancement peak

value is increased when the channel aspect ratio changes from 2:1to 4:1 and then reduced when the channel aspect ratio is increasedfrom 4:1 to 8:1.

The local heat transfer for the various test cases is given inFigs. 1719 for the ribbed wall, the sidewall and the top wall,respectively. In these charts, the heat transfer distribution is shownas the ratio between the in flow direction averaged Nusselt num-ber and the area-averaged Nusselt number of the respective walland is plotted over the respective dimensionless wall coordinate atReynolds number 130 000.

Fig. 14 Nu/Nu0 distribution on the sidewall

Fig. 15 Nu/Nu0 distribution on the top wall

Fig. 16 Nu/Nu0 distribution on the ribs at Re$130 K



7/30/2019 turb_135_3_031004

8/9

In Fig. 17, an almost symmetrical heat transfer distribution intest W-2 and W-4 is observed. The relative peak heat transferreached in case W-8 is comparable to the peaks of test cases W-2and W-4. On the other hand, the deviation from the area-averagedNusselt number towards the symmetry plane is smaller than in testcases W-2 and W-4. Towards the sidewall, the heat transfer ratiois initially smaller than those of the other test cases, but stays at ahigher level near the wall.

Test cases 2W-4 and 2W-8 show very similar distributions. Dif-ferences are visible around the leading edge at Z/(W/2) 2/8,where test case 2W-8 reaches higher relative heat transfer ratios

than test case 2W-4, and at Z/(W/2) 6/8 towards the sidewallwhere test case 2W-4 reaches higher values.

Test case 4W-8 shows the most homogeneous heat transfer dis-tribution of all test cases on the ribbed wall; thus confirming theobservations made in Fig. 13.

On the sidewall (Fig. 18), the heat transfer ratios close to theribbed wall and the peak values decrease with increasing channelaspect ratio for all rib configurations. For comparison, the maxi-mum heat transfer ratio is reduced from 2.1 in test case W-2 to 1.6in test case W-4 and to 1.3 in test case W-8.

All test cases reach similar heat transfer ratios between Y/H 2/8 and 4/8. Above Y/H 4/8, only test case W-2 shows asecond peak. In all other test cases the local heat transferdecreases with increasing Y/H.

On the top wall, it is visible that the deviations from the area-averaged Nusselt number increase with increasing channel aspectratio, as shown in Fig. 19. Here, the maximum heat transfer ratiovaries from 1.2 in test case 2W-4 to 1.4 in test case 2W-8. Testcase W-8 shows the highest relative local variation at the symme-try plane.

The more homogeneous relative heat transfer distribution onthe ribbed and on the opposite smooth wall at a constant aspect ra-tio is achieved with complex rib geometries, or lower Wr/H.

From a comparison of the relative heat transfer distributions onthe ribbed wall (Fig. 17) and on the top wall (Fig. 19), it becomesapparent, that for test cases W-4, W-8, 2W-4, and 2W-8 the rela-

tive peak in heat transfer is positioned at a location where, on theopposite wall, the local heat transfer distribution shows a distincttrough. A detailed analysis of the secondary flow structures shownin Fig. 6 delivers an explanation for this phenomenon: the relativepeaks in heat transfer on a channel wall are found where thestreamtraces of the secondary flow move towards the wall, whileregions of relatively low heat transfer are created where the flowmoves away from the wall. This mirror-effect is less pro-nounced in test cases W-2 and 4W-8, where the secondary flowstructures are found close to the ribbed wall and do not fill thechannel cross section as in the other test cases.

Conclusions

The detailed analysis of the qualitative numerical and quantita-tive experimental data increased the physical understanding of thefundamental mechanisms involved and allows the identification ofthe optimum design configuration of a backside cooled combustorliner using different configurations of W-shaped ribs.

The obtained results show that more complex rib configurationsincrease the friction factor ratios.

It was shown for the area-averaged heat transfer enhancementthat rib configurations with a rib section-width-to-channel heightratio Wr/Hof 1:1 deliver highest heat transfer enhancement on theribbed wall, while on the opposite smooth wall highest heat trans-fer enhancement is produced by rib configurations with a Wr/Hof2:1.

However, best thermal performances are still reached with W-shaped ribs in channels with blockage ratios below 0.06 for low

pressure losses while for higher blockage ratios, more complex ribgeometries achieve better thermal performances.Regarding the local heat transfer enhancement distributions,

more complex rib configurations help to produce homogeneousdistributions; hence reducing thermal stresses on the ribbed wall.On the sidewall, the heat transfer enhancement distributions aremainly influenced by the blockage ratio. High blockage ratiosreduce the low heat transfer enhancement areas.

Furthermore, it was possible to show a correlation between thelocal heat transfer enhancement and the numerically visualizedflow structures in the channel. Areas of high heat transferenhancement are found where streamlines move towards the chan-nel wall, while departing streamlines produce low heat transferenhancement areas.

Fig. 17 Heat transfer distribution on the ribbed wall atRe$130 K

Fig. 18 Heat transfer distribution on the sidewall at Re$130 K

Fig. 19 Heat transfer distribution on the top wall at Re$130 K



7/30/2019 turb_135_3_031004

9/9

Acknowledgment

The authors gratefully acknowledge the financial support pro-vided within the research and innovation initiative KW21 by theMinistry of Baden-Wurttemberg, Germany and ALSTOM and thepermission to publish this paper.

NomenclatureA Area, (m2)

cP,W specific heat capacity of Perspex 1470 J/(kgK),(J/kgK)

Dh hydraulic diameter, (m)e rib height, (m)f friction factor, see Eq. (1)

f0 friction factor of fully developed turbulent flow in asmooth circular tube

h heat transfer coefficient k @T@n

W/(TWTf), (W/m

2K)k thermal conductivity of air, (W/mK)

kW thermal conductivity of Perspex 0.19 W/(mK),(W/mK)

L ribbed channel length, (m)Nu Nusselt number hDh/k

Nu0 Nusselt number of fully developed turbulent flow in asmooth circular tube

Nu area-averaged Nusselt numberNuF in flow direction averaged Nusselt number

p static pressure, (Pa)P rib pitch, (m)

Dp/Dx regression line gradient of pressure distribution, (Pa/m)Pr Prandtl number of air 0.71Re Reynolds number qDhuAVG/l

t time, (s)T0 initial temperature, (K)Tf fluid temperature, (K)

TW wall temperature, (K)TLC thermochromic liquid crystal

um mean velocity, (m/s)uAVG cross section-averaged mean velocity, (m/s)W/H channel aspect ratio

Wr/H rib section width-to-channel height ratioy dimensionless first cell wall coordinate

l dynamic viscosity of air, (kg/(ms))

q density of air, (kg/m3)qW density of Perspex 1190 kg/m

3, (kg/m3)s discrete time points, (s)

IndicesRRB ribbed wall ribs

TP top wallRW ribbed wallSW sidewall

References[1] Sattelmayer, T., and Polifke, W., 1998, NOx-Abatement Potential of Lean-

Premixed GT-Combustors, ASME J. Eng. Gas Turbines Power, 120, pp.4859.

[2] Maurer, M., von Wolfersdorf, J., and Gritsch, M., 2007, An Experimental andNumerical Study of Heat Transfer and Pressure Loss in a Rectangular ChannelWith V-Shaped Ribs, ASME J. Turbomach, 129, pp. 800808.

[3] Maurer, M., von Wolfersdorf, J., and Gritsch, M., 2007, An Experimental andNumerical Study of Heat Transfer and Pressure Losses of V- and W-ShapedRibs at High Reynolds Numbers ASME Paper No. GT2007-27167.

[4] Maurer, M., Ruedel, U., Gritsch, M., and von Wolfersdorf, J., 2008,Experimental Study of Advanced Convective Cooling Techniques for Com-bustor Liners, ASME Paper No. GT2008-51026.

[5] Bailey, J. C., Intile, J., Topaldi, A., Fric, T., Nirmalan, N. V., and Bunker, R. S.,2000, Experimental and Numerical Study of Heat Transfer in a Gas TurbineCombustor Liner, ASME J. Eng. Gas Turbines Power, 125, pp. 9941002.

[6] Kim, W. K., Arellano, L., Vardakas, M., Moon, H., and Smith, K., 2003,Comparison of Trip-Strip/ Impingement/ Dimple Cooling Concepts at High

Reynolds Numbers, ASME Paper No. GT2003-38935.[7] Park, J. S., Han, J. C., Huang, Y., Ou, S., and Boyle, R. J., 1992, Heat Transfer

Performance Comparisons of Five Different Rectangular Channels With Paral-lel Angled Ribs, Int. J. Heat Mass Transfer, 35(II), pp. 28912903.

[8] Wright, L. M., Fu, W. L., and Han, J. C., 2004, Thermal Performance ofAngled, V-Shaped, and W-Shaped Rib Turbulators in Rotating RectangularCooling Channels (AR 4:1), ASME Paper No. GT2004-54073.

[9] Chandra, P. R., Alexander, C. R., and Han, J. C., 2003, Heat Transfer and Fric-tion Behaviors in Rectangular Channels With Varying Number of RibbedWalls, Int. J. Heat Mass Transfer, 46, pp. 481495.

[10] Cakan, M., 2000, Aero-Thermal Investigation of Fixed Rib-Roughened Cool-ing Passages (Part I II), von Karman Institute for Fluid Dynamics, LectureSeries 2000-03.

[11] Poser, R., von Wolfersdorf, J., and Lutum, E., 2007, Advanced Evaluation ofTransient Heat Transfer Experiments Using Thermochromic Liquid Crystals,

Proc. IMechE Part A: J. Power Energy, 221, pp. 793801.[12] Kays, W. M., Crawford, M. E., and Weigand, B., 2005, Convective Heat and

Mass Transfer, 4th ed., McGraw-Hill, New York.[13] Moffat, R. J., 1988, Describing the Uncertainties in Experimental Results,

Exp. Therm. Fluid Sci., 1(1), pp. 317.

http://dx.doi.org/10.1115/1.2818087http://dx.doi.org/10.1115/1.2720507http://dx.doi.org/10.1115/GT2007-27167http://dx.doi.org10.1115/GT2008-51026http://dx.doi.org/10.1115/1.1615256http://dx.doi.org/10.1115/GT2003-38935http://dx.doi.org/10.1016/0017-9310(92)90309-Ghttp://dx.doi.org/10.1115/GT2004-54073http://dx.doi.org/10.1016/S0017-9310(02)00297-1http://dx.doi.org/10.1243/09576509JPE464http://dx.doi.org/10.1016/0894-1777(88)90043-Xhttp://dx.doi.org/10.1016/0894-1777(88)90043-Xhttp://dx.doi.org/10.1016/0894-1777(88)90043-Xhttp://dx.doi.org/10.1243/09576509JPE464http://dx.doi.org/10.1016/S0017-9310(02)00297-1http://dx.doi.org/10.1115/GT2004-54073http://dx.doi.org/10.1016/0017-9310(92)90309-Ghttp://dx.doi.org/10.1115/GT2003-38935http://dx.doi.org/10.1115/1.1615256http://dx.doi.org10.1115/GT2008-51026http://dx.doi.org/10.1115/GT2007-27167http://dx.doi.org/10.1115/1.2720507http://dx.doi.org/10.1115/1.2818087

Documents

turb_135_3_031004