international journal of heat and mass...

International Journal of Heat and Mass Transfer 93 (2016) 637–652

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

A numerical study on various pin–fin shaped surface air–oil heatexchangers for an aero gas-turbine engine

http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.10.0350017-9310/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +82 51 510 2598; fax: +82 51 515 4038.E-mail address: [email protected] (J.K. Min).

Minsung Kim a, Man Yeong Ha a, June Kee Min b,⇑a School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Busan 46241, Republic of KoreabRolls-Royce and Pusan National University Technology Centre in Thermal Management, Pusan National University, 2, Busandaehak-ro 63beon-gil, Busan 46241, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 June 2015Received in revised form 22 October 2015Accepted 23 October 2015

Keywords:Surface air–oil heat exchangerAero gas-turbine engineBypass effect

In this study, the performance of a surface air–oil heat exchanger for an aero gas-turbine engine havingplate- and pin–fin shaped geometries was investigated numerically. Basic heat-transfer and pressure-drop characteristics were examined using a simplified channel model. Performance of pin-shaped finsis compared with that of the plate fin as a baseline. Using a parametric study, optimal fin pitches ofthe pin–fin geometries in stream- and span-wise directions were determined. Finally, the high-speedbypass effect of the surface air–oil heat exchanger was calculated using the geometry of a real engine.Aero-thermal performance for such as the heat transfer rate, pressure-drop along the bypass stream ofthe engine, and distorted velocity boundary layer profiles, were evaluated quantitatively. The entropygeneration rate due to the surface air–oil heat exchanger is summarized to assess the irreversibility lossinside the bypass stream and the cooler region.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

The ever-increasing demand for environmentally friendly air-planes has created a demand for aero engines of sharply increasedefficiency. The specific fuel consumption (SFC) of the gas-turbineengine is highly related to the operating pressure ratio (OPR) andthe turbine inlet temperature (TIT). In order to achieve high effi-ciency using an advanced cycle, equipment with an ultra-light heatexchanger is essential. This is because high efficiency aero-enginesrequire minimal weight penalty and high aero-thermal perfor-mance of the heat exchanger. Min et al. [1] reviewed existingand possible candidate heat-exchange technology for the use ofrecuperator, intercooler, and cooling-air cooler applications.

Increasing the bypass ratio (BPR) of the engine is anothermethod by which to increase the efficiency of turbo-fan engines.In this case, the heat from the corresponding oil system, such asthe gear box and generator in the transmission system, should becooled using various oil coolers [2]. The surface air–oil heatexchanger (SAOHE) is located inside the engine fan casing, and dis-sipates the heat from the oil into the air stream in the bypass duct(BPD), as shown in Fig. 1. The main difficulty of SAOHE designs isthe existence of the bypass stream, which affects the pressure drop

inside the bypass duct. Kim et al. [3] studied the effect of coolerinstallation location, in a high-speed aero engine with a plate fin.

There have been a number of studies aimed at enhancing aero-thermal performance by varying the fin-shape of the heat exchan-ger. It was found that a modified fin surface may have a high heattransfer coefficient, but that its pressure drop is sometimes toogreat for wide applications. Yun and Lee [4] compared experimen-tally the performance of plain fins, louvered fins, and three types ofslotted fins. The results showed that the slotted fins with protrud-ing strips have high heat-transfer performance with an acceptablepenalty in pressure drop. Kang et al. [5] compared four kinds ofplate-fin surfaces (plain, corrugated with a triangular-cross-sectional channel, corrugated with a sinusoidal cross-sectionalchannel, and a slotted fin). They found that the slotted-fin surfacecould increase heat transfer rate about 30–40% compared to a plainplate-fin, using identical pumping power.

For pin–fin models, Shaukatullah et al. [6] measured the ther-mal performance of in-line square pin–fins and plate heat-sinksfor different fin thickness, spacing, height, and angle of approachfor velocities under 5 m/s, allowing flow to partially by-pass theexchanger. More recently, Jonsson and Moshfegh [7] experimen-tally studied characteristics of plate and circular, rectangular andstrip pin fins, in both staggered and in-line configurations, for dif-ferent dimensions, while allowing variations on tip and side by-pass. Computational fluid dynamics (CFD) approaches have beenextensively applied to the study of flow and heat transfer in heat

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Nomenclature

Be Bejan numberCp specific heatf Fanning friction factorGv volume goodness factorGa area goodness factorH inlet heighth heat transfer coefficientkf thermal conductivity of airks thermal conductivity of finNu Nusselt numberp static pressureQ heat transfer ratePr Prandtl numberRe Reynolds numberS entropySt Stanton numberT static temperature

U overall heat transfer coefficientu, v, w dimensionless velocity components in x, y and z direc-

tionxi Cartesian coordinate system, xi = (x, y, z)

Greek symbolsa thermal diffusivityl fluid viscositym fluid kinematic viscosityq fluid densitys shear stress

Sub/superscriptsi, j tensor notation

638 M. Kim et al. / International Journal of Heat and Mass Transfer 93 (2016) 637–652

sinks, as can be seen from the works by Jonsson and Moshfegh [8]and Biber and Belady [9].

For the SAOHE application, Outirba and Hendrick [10] con-ducted an experimental study on surface-air-cooled oil coolers(SACOC), describing a new test rig that allowed complete tests ofSACOC breadboards. Ko et al. [11] studied the effect of SAOHEinstallation using a numerical method. In this paper, an efficientnumerical procedure for the study of cooler installation involvingbypass ducts was proposed and successfully demonstrated andimportant design variables were clearly identified. Kim et al. [3]performed a detailed experimental study from which the resultsvalidated this numerical work.

In order to assess the performance of a heat exchanger, anappropriate performance metric should be used. This is becausethe pressure drop and heat-transfer characteristics representedby the friction factor and Colburn j-factor, usually vary in similarpatterns, as can be seen in the Reynolds analogy for flat plate[12]. The concepts of volume and area goodness factors are goodalternatives of such metrics to represent the compactness of agiven geometry of heat exchanger [13]. Adams [14] and Dooet al. [15] used those factors to examine the aero-thermal perfor-mance of variously shaped, primary surface heat exchangers.

Although the loss of energy inside a heat exchanger usuallyarises near solid-wall regions such as the fins, losses due to com-plex flow mixing inside the flow passage are also important. Volu-metric entropy generation [16] is a useful parameter to understand

Fig. 1. Schematic configuration of conventional surface a

the loss mechanism in the heat exchanger. Doo et al. [17] assessedthe pressure-loss mechanism inside a cross-corrugated plate-typeheat exchanger using the volumetric entropy generation rate. Thisarrangement results in a strong mixing layer between the plates.

Although there have been various fundamental studies on pin–fin shaped surfaces for heat exchangers, usually those are doneunder the condition of idealized heat transfer, without consideringthe bypass effect, which makes the problem complex [18,19].Moreover, study of the bypass effect has usually involved anincompressible flow regime, such as heat sink applications forcooling electronic devices [20–22]. It is necessary to carry out stud-ies on the high-speed bypass effect, in relation to the fin-shapes ofvarious heat exchangers, in order to understand the advantages ofenhanced heat-transfer characteristics for application to aeroengines.

In the present study, the influence of various fin shapes of sur-face air–oil heat exchanger on the aero-thermal performance of thecooler, was investigated numerically. To improve the efficiency ofthe calculations, the fundamental pressure drop and heat-transfer characteristics were investigated using an idealized,channel-shaped computational domain without bypass effect. Cor-responding design parameters such as fin pitches in stream- andspan-wise directions were determined by means of a parametricstudy. Finally, the bypass effect due to the installation of the coolerinside an aero engine was calculated using a unitary-fin model, butalso considering the rotational periodicity of the multiple fins. The

ir-to-oil heat exchanger (SAOHE) in an aero-engine.

M. Kim et al. / International Journal of Heat and Mass Transfer 93 (2016) 637–652 639

loss due to irreversibility inside the bypass stream was assessed byconsidering the variation of entropy generation inside the engine.

Fig. 3. Computational domain and boundary conditions for the real engine model.

2. Numerical methodology

2.1. Computational domains and fin geometries

Two types of computational domain were used in this paper, asshown in Figs. 2 and 3. The straight channel model shown in Fig. 2is a simplified model used to examine the aero-thermal perfor-mance of a fin surface having no bypass passage. Using this model,the fundamental heat exchanger performance under ideal condi-tions was examined. The periodic boundary condition wasimposed on the lateral side of the domain so that only one finwould be considered in the computation. No-slip conditions wereapplied for the cooling fin and for the surface of the oil passage.The mass-flow rate was given for the inlet and the static pressurewas set in the outlet boundary regions. The solid region inside thefin was also modeled to calculate the conduction effect of the con-jugate heat-transfer problem. For the oil side, the mean tempera-ture of the oil and the corresponding heat-transfer coefficientwere given (386 K and 2000W/m2 K, respectively). The heightand the length of the computational domain were 24 mm and1600 mm, respectively.

Fig. 3 shows the computational domain of the typical geometryof a real engine, which had a large bypass region. The cooler wasassumed to be located at the downstream end of the outlet guidevane (OGV) of the engine. Similar to the channel model shown inFig. 2, no-slip conditions were applied for the casing, hub, coolingfin, and surface of the oil passage. Considering the swirl velocitycomponent at the inlet of the domain, a rotational periodic condi-tion was used on the lateral surfaces in order to carry out the com-putation for a unitary fin. The total pressure on the inlet boundaryand the static pressure on the outlet were given. The computationwas iterated until the mass flow rate converged to a target value.The height of the inlet was 0.6566 m and the length of the compu-tational domain was 0.8561 m.

Fig. 4(a)–(d) represent the shapes of fins considered in thisstudy: (a) plate fin (baseline), (b) cross-cut pin–fin, (c) laterally-slanted pin–fin and (d) forward-slanted pin–fin. The laterally-and forward-slanted fins had the inclination angle of 60�measuredfrom the bottom. Single-sided fins were considered for the calcula-tion in the channel model, whereas double-sided fins wereconstructed for the engine model. The fin height and length inthe stream-wise direction were 24 mm and 400 mm, respectively,

Fig. 2. Computational domain and boundary co

and the fin pitch in the span-wise direction was 4.1 mm. Forpin–fin models, the fin pitch in the stream-wise direction was2.6 mm and the length of unitary pin fin was 4.3 mm. Here, thespan-wise pitch is defined by the distance between the centers ofeach fin in the lateral direction, whereas the stream-wise pitch isthe distance from the trailing edge of the upstream fin to the lead-ing edge of the next downstream fin. The thickness of all fins was0.8 mm.

Fig. 5(a) shows the grid constructed for the baseline fin used inthe channel model, and Fig. 5(b) is the mesh used for the enginemodel calculation. Based on the grid-dependency test result, a totalof 1.0–2.0 million cells were used for the channel model, and8.5–10 million cells for the engine model calculation.

2.2. Numerical procedures

Assuming the air is an ideal gas, the continuity, momentum, andenergy equations for the steady, compressible, and turbulent floware:

@

@xiðquiÞ ¼ 0 ð1Þ

@

@xjðqui ujÞ ¼ � @p

@xiþ @

@xjl @ui

@xjþ @uj

@xi

� �� qu0

i u0j

� �ð2Þ

@

@xiðqCp uiTÞ ¼ � @

@xi�k

@T@xi

þ qCpu0i T

0� �

ð3Þ

where ui represents the velocity component in i-direction, p the sta-tic pressure and T the temperature. Here, q, l, k, and Cp are the fluid

nditions for the simplified channel model.

Fig. 4. Geometries of fins considered in this study: (a) plate-fin (baseline), (b) cross-cut pin–fin, (c) laterally-slanted pin–fin, and (d) forward-slanted pin–fin.

Fig. 5. Typical grid configuration for (a) idealized channel-model and (b) enginemodel.


density, viscosity, thermal conductivity and specific heat,respectively. All variables are time-averaged mean values andEqs. (1)–(3) are the Reynolds-averaged Navier–Stokes (RANS)equations for compressible flow.

In this study, the commercial computational fluid dynamics(CFD) software FLUENT, was used to solve the above equations.For the turbulent flow, the standard k–emodel with enhanced wallfunction was adopted. The grid was concentrated near the wallregion in order to resolve the high velocity and temperature gradi-ents, and the first grid points away from the walls satisfy approx-imately y+ � 1 as a wall unit. The second order upwind scheme wasused for spatial discretization, and the pressure-based coupledscheme was used for pressure–velocity coupling.

For the channel model calculation, the ground-idle engine con-dition was assumed for the operating condition, which results inthe Reynolds number of 57,000 and Mach number 0.1. The cruiseoperating condition under the International Standard Atmosphere[23] was chosen for the calculation in the engine model, and thecorresponding Reynolds number and Mach numbers were3.9 � 106 and 0.6, respectively. The average temperature of theinlet air was 300 K for the channel model and 271 K for the enginemodel calculations.

The purpose of the channel model calculation is to examine thefundamental aero-thermal performance of tested surfaces. Usually,however, the pin–fin geometry had a very great pressure-droptogether with a high heat-transfer rate; the span- and stream-wise fin pitches were varied by means of a parametric study so thateach pin–fin surface had equivalent performance with the baseline.Finally, selected fin pitches were applied for the real SAOHE fins inthe calculation of real engine conditions, and the effect of thebypass stream was assessed by comparing its computational resultwith that of channel model.

2.3. Performance metrics

In the calculation, the height H at the inlet of the computationaldomain was chosen for the reference length, and the averagevelocity Vavg on the inlet boundary for the reference velocity.The averaged fluid properties were also used for the calculationof dimensionless variables.


Using these variables, the Reynolds number is defined as

Re ¼ VavgHm

ð4Þ

where m is the kinematic viscosity. The Prandtl number is

Pr ¼ ma

ð5Þ

where a is the thermal diffusivity.The Fanning friction factor f, Nusselt number Nu, Stanton num-

ber St, and Colburn j factor are defined as follows:

f ¼ ðDp=DxÞH2qV2

avgð6Þ

Nu ¼ hDh

kð7Þ

St ¼ NuRe Pr

ð8Þ

j ¼ St Pr2=3 ð9ÞIn Eqs. (6)–(9), Dp/Dx is the average pressure gradient in the

stream-wise direction and h the heat transfer coefficient.The volume and area goodness factors [13] are defined by

Gv ¼ St

f 1=3ð10Þ

Ga ¼ jf

ð11Þ

For a given pumping power, a larger volume goodness factoryields a smaller heat-transfer surface area, resulting in a smallerheat-exchanger matrix volume and a larger area goodness factoryields a smaller frontal area for the heat exchanger matrix [15].In the design of a heat exchanger for an aero engine, both goodnessfactors should have equal importance due to the importance of theweight penalty and spatial installation limit.

The volumetric entropy generation in a heat-transfer problemrepresents the loss of energy due to irreversibility and can be cal-culated [16] using

S000 ¼ S000fric þ S000heat ð12Þwhere S000fric and S000heat represent the local entropy generation rates dueto fluid friction and heat transfer, and are defined by:

S000fric ¼leff

T2

@u@x

� �2

þ 2@v@y

� �2

þ 2@w@z

� �2

þ @v@x

þ @u@y

� �2"

þ @w@y

þ @v@z

� �2

þ @u@z

þ @w@x

� �2#

ð13Þ

S000heat ¼keffT2

@T@x

� �2

þ @T@y

� �2

þ @T@z

� �2" #

ð14Þ

In Eqs. (13) and (14), leff and keff are the effective viscosity andthe effective thermal conductivity, respectively, and are defined asthe sum of laminar and turbulent properties. For the standard k–emodel used in this study, these are expressed as:

leff ¼ lþ lt ¼ lþ qClk2

e

!ð15Þ

keff ¼ kþ kt ¼ kþ cplt

Prtð16Þ

where subscript tmeans the turbulent properties and in Eq. (15) k isthe turbulent kinetic energy, e the turbulent dissipation, and Cl theturbulent model constant.

In this study, volume and area goodness factors are adopted forthe evaluation of fundamental aero-thermal performance of eachfin geometry using the channel model calculation. The localentropy generation rate is used to understand the loss mechanism,especially in the bypass region.

3. Results and discussion

3.1. Experiment and CFD validation test

The accuracy of the present calculation methods was validatedusing previous experimental studies. Fig. 6 shows the comparisonof the computational result with the experimental data by Jonssonand Moshfegh [7], which is similar to the present channel-modelcalculation except for the existence of the bypass region in theexperiment. Detailed dimensions of the problem are representedin Fig. 6(a). The agreement between calculation and experimentwas good, showing less than 9.0% difference for pressure dropand 7.5% for thermal resistance at the Reynolds number of12,000. The variation of the pressure drop and thermal resistancewith fin-type is also well captured in the numerical prediction.

Kim et al. [3] conducted an experiment using the engine geom-etry considered in this study. Fig. 7(a) shows the comparison ofstatic pressure distribution along the fin and Fig. 7(b) shows theNusselt number distribution on the SAOHE fin surface under thecruise-flight condition. The accuracy of the calculation was within3.2% for the pressure drop and 4.9% for the Nusselt number. For thedouble-sided SAOHE fin, the heat-transfer coefficient on the lowerfin became high compared to the upper fin due to the high mass-flow in the region. This uneven performance of the fin waspredicted in the calculation as well. It should be noted that allthe reference values were matched to the values used in the exper-imental study, which used the scaled-up model for the test section.

3.2. Performance of pin fins under idealized conditions

3.2.1. Aero-thermal performanceIt is known that the cross-cut pin–fin model has a decreased

weight of heat exchanger and the potential for heat-transferenhancement using re-development of a thermal boundary layerat each fin segment [7,24,25]. Slanted fins, which are consideredin this study, have the additional advantage of increased heat-transfer area under a given limit of vertical height. To examinethese underlying ideas, the fundamental aero-thermal perfor-mance of pin–fins was evaluated using the method described ina previous section.

Table 1 represents the test matrix for the parametric study of finpitch, using eight cases of calculation for each pin–fin model. Thegoal of this calculation is to find the optimal fin pitches that cangenerate aero-thermal performance similar to that of the baselineplate fin, considering the given heat-transfer-rate duty.

The calculated results are summarized in Fig. 8(a)–(d), showingthe normalized pressure drop, heat transfer rate, volume goodnessfactor and area goodness factor. Here, values of pressure drop, heattransfer rate, and goodness factors of the baseline model (plate fin)are used for the normalization. It should be noted that, in thisgraph, the heat-transfer rate per unit width in the span-wisedirection is considered for comparison, because the variation ofspan-wise pitch results in different widths of computationaldomains for each model. Case 01 models, which have the span-and stream-wise pitches of 4.1 mm and 2.6 mm, show drasticincreases in pressure-drop compared to the increase in the

Fig. 6. Comparison of calculation result with experimental data for fins in channel: (a) geometry, (b) pressure drop, and (c) thermal resistance.


heat-transfer rate. The increase in pressure drop for cross-cut finsand laterally-slanted fins is 230% and 325%, respectively, whereasthe increase in the heat transfer rate are 28% and 27%. Theforward-slanted fin of the Case 01 model, however, shows a189% increase in the pressure drop and 33% increase in the heat-transfer rate, which is superior to other pin–fin geometries. Thepressure drop is more sensitive to the span-wise pitch than tothe stream-wise pitch considered in this calculation, while theheat-transfer-rate variation with pitch is not large compared tothe variation of pressure drop, shown in Fig. 8(a) and (b). Thestream-wise pitch affects the heat transfer rate, as shown inFig. 8(b) due to variation in the heat-transfer area.

The volume and area goodness factors (Fig. 8c and d) do notshow great improvement of the compactness. For small span-wise pitch, goodness factors are small due to very large pressuredrops. When the span-wise pitch is increased, goodness factorsbecome large up to 6 mm, but decreases again at 10 mm becauseof the small heat-transfer area.

Among the tested cases, Case 6 (1.5-times larger span-wise finpitch and smaller stream-wise pitch by 0.6 than those of Case 1)shows the best performance of all the pin–fin models. The resultsfor the optimized fin pitches are summarized in Table 2. As shownin this table, the forward-slanted pin–fin shows the best resultshowing a pressure drop decreases by 16%, and a heat-transfer rate

increases by 12%, compared to the baseline plate-fin model. Thevolume goodness factor increased by 6.5%, however the area good-ness factor decreased by 3.6%. Finally, the corresponding reductionof the fin weight is 19.1%.

3.2.2. Characteristics of flow and heat transferFig. 9 shows the distribution of pressure coefficient on the fin

surface of each tested model having optimized pitches (Case 6).Figures are taken at the inlet region (Section-1) and mid-part(Section-2) of the whole fin as shown in the schematic at the topof Fig. 9. Here the pressure coefficient is defined as:

cp ¼ p

1=2qV2avg

ð17Þ

For the baseline plate-fin, cross-cut pin–fin, and laterally-slanted fin, shown in Fig. 9(a)–(c), the overall pressure decreasesmonotonically in the downstream direction, although local varia-tion of pressure on each unitary fin is observed due to the com-bined effect of the stagnation flow and recirculation zonebetween fins. The direction of the pressure gradient for these threefins is almost parallel to the channel direction. For the forward-slanted pin–fin shown in Fig. 9(d), however, it can be seen thatthere is a downward pressure-gradient component due to the

Fig. 7. Comparison of calculation result with experimental data for SAOHE in anengine under cruise-flight condition: (a) normalized static pressure distribution,and (b) Nusselt number distribution on the fin surface.

Table 1Detailed design space for the fin-pitch parametric study for pin–fin geometries.

Cases Span-wise pitch Stream-wise pitch(mm) (mm)

Case 01 4.1 2.6Case 02 4.1 5Case 03 4.1 10Case 04 6 2.6Case 05 8 2.6Case 06 6 1Case 07 8 1Case 08 5 1.5

Fig. 8. Results of the parametric study on the various pin pitches: (a) pressure drop,(b) heat-transfer rate, (c) volume goodness factor, and (d) area goodness factor.


slanted angle of the fin. Because of this effect, the streamline,which is also represented in the figure near the inlet region, tendsto flow in the downward direction as it flows downstream. As aresult, it can be predicted that the flow near the bottom of thefin will be accelerated and the corresponding heat-transfer ratein the bottom region enhanced.

In Fig. 10, the skin friction factor for each optimal fin geometryis depicted. The skin friction factor is

cf ¼ sw1=2qV2

avgð18Þ

and sw represents the wall shear stress on the fin surface. For plate-fin, cross-cut pin–fin, and laterally-slanted pin–fin models

(Fig. 10a–c), the skin friction factor becomes large in the core regionof the channel. Near the upper and lowerwall, the skin friction factoris small because of the effect of channel walls. The forward-slanted

Table 2Results of the optimized pin–fin (Case 6) in the channel-model calculation.

Model DpDp0

ðQ=wÞðQ=wÞ0

GvGv0

GaGa0

Cross-cut pin–fin 0.91 1.13 1.043 0.897Laterally-slanted pin–fin 1.11 1.11 0.963 0.724Forward-slanted pin–fin 0.84 1.12 1.065 0.964


pin–fin shown in Fig. 10(d), however, shows a different pattern ofshear stress. Due to the accelerated flow, shown in Fig. 9(d),the velocity near the bottom of the fin became large compared toother models, and the increased velocity gradient produced greaterskin friction in the region. The region of greater skin friction on thebottom of the fin increases as the flow goes in the downstreamdirection.

Fig. 9. Distribution of the pressure coefficient on the fin surface and streamlines for optim(d) forward-slanted pin–fin.

Fig. 11 shows the distribution of Nusselt number for optimizedfin models. For all cases, the Nusselt number is large at the inletregion and at the bottom of the fin where the temperature differ-ence between the air and the wall is large. For pin–fin models, atthe leading edge of each unitary fin, there is a local increase ofthe Nusselt number because of the re-development of the bound-ary layer. As the flow goes downstream, the average Nusselt num-ber decreases due to the decreasing temperature difference. For thebaseline, cross-cut pin–fin, and laterally-slanted fin models, shownin Fig. 11(a)–(c), the small Nusselt number region near the oil sideincreases due to the growth of the boundary layer from the bottomsurface. As shown in Fig. 11(d), however, the forward-slanted pinfin model shows different variation of the Nusselt number, espe-cially near the bottom region. Due to the accelerated flow on thebottom surface, the Nusselt number in the region remains high,

ized fin pitches: (a) baseline, (b) cross-cut pin–fin, (c) laterally-slanted pin–fin, and

Fig. 10. Distribution of the skin friction coefficient on the fin surface for optimized fin pitches: (a) baseline, (b) cross-cut pin–fin, (c) laterally-slanted pin–fin, and (d) forward-slanted pin–fin.


to the end of the computational domain of the fin considered inthis calculation.

Fig. 12 shows axial velocity profiles on the mid-plane betweenthe fin surface and the periodic boundary surface at the front, mid,and end sections shown in the schematic on the top. Because theoptimized span-wise fin pitch for the pin–fin models is larger thanthat of the baseline, the maximum velocity of each profile is smallcompared to the baseline case. The acceleration of flow on the bot-tom plate of the forward-slanted fin is well captured, as predictedfrom the pressure distribution in Fig. 9. This characteristic isadvantageous for enhancement of heat transfer, because the bot-tom region has the highest temperature in the domain. As a result,it should be possible to construct a light fin heat exchanger having

aero-thermal performance equal to a plate fin, by imposing thispin–fin geometry.

3.3. Application of pin fins to the real engine SAOHE

3.3.1. Aero-thermal characteristics of SAOHE considering the bypasseffect

Because the parametric study of the pin–fin models shows thatthe best results are provided by the span-wise pitch of 6 mm andstream-wise pitch of 1 mm, these pitch dimensions were appliedfor the pin–fins of SAOHE in a real-engine model under cruise-flight condition. Among the slanted-fin models, only the forward-slanted pin–fin is considered in this study because it shows better

Fig. 11. Distribution of the Nusselt numbers on the fin surface for optimized fin pitches: (a) baseline, (b) cross-cut pin–fin, (c) laterally-slanted pin–fin, and (d) forward-slanted pin–fin.

Fig. 12. Axial velocity profiles at (a) the front, (b) mid, and (c) end sections of the finned channel.


performance than that of the laterally-slanted pin–finmodel. Usingthe unitary fin model and rotational periodic boundary conditiondescribed in Section 2, the performance of the SAOHE havingpin–fin geometry was predicted and compared with that of thebaseline plate-fin geometry.

Fig. 13 shows results of the streamline pattern for each finmodel. Because of the double-sided fin configuration, the incomingflow splits into upper and lower fin regions at the leading edge ofthe cooler. The upper flow separates due to the sharp edge of theupper recess gap on the fan casing, and forms a recirculation zonedetrimental to the heat-transfer performance in the region. Thelength of the recirculation bubble becomes longer for the pin–finmodels, and there are two separation bubbles for the forward-slanted pin–fin (shown in Fig. 13c). The length of the bubble isrelated to the difference in the flow resistance, showing that the

flow resistance of the pin–fin model is less than that of plate-finmodel.

Fig. 14 represents the skin-friction-factor distribution on the finsurface. Due to the difference in the flow speed between the upperand lower fins, the shear stress on the lower fin shows large valuescompared to the upper fin in all cases. The level of skin friction onthe fin decreases as the flow goes in the downstream direction,which is different from the result of the channel-model calculation.This is related to the variation of the mass flow rate along the findue to the existence of a bypass region, which will be explainedin a later part of this section. The distribution of the skin frictionon the upper fin is strongly related to the upper wall on the topof the cooler, and to the shape of recirculation zone shown inFig. 13. For pin–fin models, the skin friction at the leading edgeof each fin shows a larger value than that at the trailing edge. For

Fig. 13. Result of streamline patterns for SAOHE models: (a) plate fin, (b) cross-cut pin–fin, and (c) forward-slanted pin–fin.

Fig. 14. Distribution of the skin-friction factor on the surface of SAOHE fins: (a) plate-fin, (b) cross-cut pin–fin, and (c) forward-slanted pin–fin.


Fig. 15. Distribution of the Nusselt number on the surface of SAOHE fins: (a) plate-fin, (b) cross-cut pin–fin and (c) forward-slanted pin–fin.


plate and cross-cut fins, the region of fin connected to the oil-passplate in the middle shows small skin friction due to frictional resis-tance on the middle plate, which can be seen in Figs. 14(a) and (b).The forward-slanted pin–fin, however, shows high skin friction inthe region of the fin stem due to the accelerated flow caused bythe slanting of the fin in the stream-wise direction. These resultsare similar to the results from the channel-model calculation.

Fig. 15 shows the distribution of the local Nusselt number onthe tested fin models of the SAOHE. The local Nusselt numberhas the maximum value at the leading edge of the upper and lowerfins, followed by a gradual decrease as the thermal boundary layerdevelops in the stream-wise direction. The variation pattern of theNusselt number is similar to that of the skin-friction factor,because these values are highly related to the speed of air flow nearthe fin (i.e., the high air speed induces a high heat-transfer coeffi-cient, together with a high velocity gradient near the wall). Theincrease of the local Nusselt number near the plate of the oil pas-sage is also captured, as shown in Fig. 15(c). The average values ofthe Nusselt numbers are also shown in this figure, and the valuesincreased by 24.4% and 25.0% for cross-cut and forward-slantedpin–fin models, respectively.

As shown in Figs. 14 and 15, the decreasing pattern of skin fric-tion and the local Nusslet number along the fin in the downstreamdirection, is related to the variation of the mass flow rate past thefin. Fig. 16 shows the variation of the mass flow rate in each finregion of the cooler in the stream-wise direction. Here, the massflow rate is normalized by the value at the inlet. In the region ofupper gap, shown in Fig. 16(a), the mass flow rate is very small

due to the small gap size, but it increases as it goes to the down-stream, which means the mass flow rate through the upper findecreases along the fin as in Fig. 16(b). The mass flow rate pastthe lower fin is 2–3-times larger than that past the upper fin.The mass flow rate also decreases in the stream-wise direction,and the rate of decrease is also large. The cross-cut and forward-slanted pin–fin models allow more flow in the lower fin regionthan in the upper fin region, which contributed to a large heat-transfer rate on the fin surface.

Additional characteristics of the SAOHE include its effect on thedistortion of the velocity-boundary-layer profile downstream ofthe cooler, as was assessed by Kim et al. [3]. As shown in Fig. 13,the split flows merge as they pass the upper and lower fins afterthe trailing edge of the cooler. This causes a distorted velocity-boundary-layer profile on the upper fan-casing wall. Fig 17 depictsthe boundary-layer profile on the fan-casing wall downstream ofthe cooler (indicated in the top of the figure). For the forward-slanted pin–fin model, the deficit region of the boundary layerbecomes small as the flow past the lower fin becomes large, whencompared to the baseline case. This less distorted velocity profileshould be advantageous for the design of several engine compo-nents, such as the thrust-reversal unit. This is located downstreamof the present computational domain, and is usually designedbased on a non-distorted boundary-layer-velocity profile.

3.3.2. Entropy generation and aero-thermal performanceFigs. 18 and 19 represent distributions of dimensionless volu-

metric entropy-generation rates due to viscous friction and heat

Fig. 16. Mass flow rates along the fin through (a) upper gap region, (b) upper finregion, and (c) lower fin region.

Fig. 17. Velocity profiles downstream for SAOHE models.


transfer, respectively. As in Doo et al. [17], the volumetric entropy-generation rate was made non-dimensional using the followingequation.

S000� ¼ TinH

qV3avg

S000 ð19Þ

The entropy generation due to friction, which is shown inFig. 18, has a large value near the leading edge of the coolerbecause of the sudden increase in the flow resistance. For pin–finmodels with larger span-wise fin pitch, the magnitude becomessmall due to the relatively small resistance, as shown in Fig. 18(b) and (c). Entropy generation in the upper-gap region shows apattern of increase along the flow direction, which is due to theincreasing mass flow rate through the region as shown in Fig. 16(a). The magnitude of entropy generation in the upper gap regionalso becomes smaller for pin–fin models, because increases inthe mass flow rate for pin–finmodels are smaller than for the base-line plate-fin model. Near the tip of the lower fins, high values offrictional entropy generation can be observed. For this region, dif-ferent from the previous region, pin–fin models show highfrictional-entropy-generation rates. This is due to the large massflow rate past the lower pin–fins, compared to the plate-fin.Finally, downstream of the cooler, a long region of high entropygeneration along the stream can be seen. This reflects the wakeregion due to the distorted boundary-layer profile shown inFig. 17. As the level of distortion for the forward-slanted pin finshowed the smallest value, the corresponding entropy-generationregion becomes narrower, as shown in Fig. 18(c).

Fig. 19 shows the distribution of the volumetric entropy-generation due to heat transfer. This entropy generation is promi-nent downstream of the cooler, where the temperature gradientbecomes larger due to transferred heat. It can be also seen thatthe wake region behind the cooler is also important for entropygeneration due to the mixing of the two flows. From theentropy-generation results, it can be seen that the wake regiondownstream of the cooler is important in order to minimize theentropy generation of a SAOHE, and that the use of forward-slanted pin–fins considered in this paper is beneficial for the reduc-tion of the entropy generation in that region.

Table 3 summarizes the predicted aero-thermal performance ofthe SAOHE variants. The first two columns show the comparison ofvolume-averaged entropy generation between the baseline andpin–fin models. For the pin–fin models, the volume-averagedentropy of friction is smaller than that of baseline by 14–15%,and the volume-averaged entropy of heat transfer also decreasedby 17–18%. The third column represents the Bejan number Be,

Fig. 18. Distribution of volumetric entropy generation due to friction: (a) plate fin, (b) cross-cut pin–fin, and (c) forward-slanted pin–fin.


Fig. 19. Distribution of volumetric entropy generation due to heat transfer: (a) plate-fin, (b) cross-cut pin–fin, and (c) forward-slanted pin–fin.


which is the ratio of heat transfer irreversibility to the totalentropy production and defined by

Be ¼ S000�heat;avg

S000�fric;avg þ S000�heat;avgð20Þ

As can be seen in Table 3, entropy generation is dominated bythe flow friction due to the high speed of the airflow consideredin this study.

Finally, the pressure drop in the bypass duct and the heat-transfer rate for each fin model, are also summarizes in Table 3.

Table 3Predicted aero-thermal performance of SAOHE variants.

Model S000�fric;avgS000�fric;avg;0

S000�heat;avgS000�heat;avg;0

Be DpDp0

ðQ=wÞðQ=wÞ0

Plate-fin (baseline) 1.00 1.00 0.46 1.00 1.00Cross-cut pin–fin 0.85 0.82 0.45 0.85 0.89Forward-slanted pin–fin 0.86 0.83 0.45 0.85 0.91


Note that because the span-wise pitch of pin–fin models is 6 mm,which is different from that of the 4-mm baseline pitch, thecomputational result of the heat-transfer rate are divided by itsspan-wise fin pitch and compared with the baseline. Comparedto the baseline plate-fin, the pin–fin models shows 14–15% smallerpressure drops (for the crosscut and forward-slanted pin–fin mod-els). Although the heat-transfer rates for the pin–fin models alsodecreased by 9–11%, its decrements are smaller than those of thepressure drop. Therefore, the desired level of heat transfer ratecould easily be achieved by slightly changing the pitch of thepin–fin models, which will be considered in a future study. Thecorresponding reduction of the fin weight is 23%, which showsthe benefit of pin–fin models for application to SAOHEs.

4. Conclusions

The aero-performance of a surface air–oil heat exchanger for anaero engine with a variety of fin shapes was investigatednumerically. Using a plate-fin as the baseline geometry, the aero-thermal performance of crosscut, laterally slanted, and forward-slanted pin–fin geometries was assessed.

Basic performance, for pressure drop and heat transfer, wasevaluated using an idealized channel computational model with-out the bypass effect. Assuming the same span-wise pitch, all thepin–fin models showed drastic increases in the pressure drop, withan increase in the heat-transfer rate. It was found that the forward-slanted pin–fin showed accelerated airflow near the bottom of thefin, which could enhance heat transfer near the oil side, where thetemperature difference becomes largest. Considering the givenheat-transfer duty of the cooler, optimal fin pitches showing simi-lar performance with the baseline were found by means of a para-metric study. The pitch in the span-wise direction could beincreased 1.5-times to produce a reduced-weight fin for the heatexchanger.

The selected pin–fin models were tested within the geometry ofa real engine using a unitary-fin computational model under acruise-flight condition. The variation of the skin friction and localNusslet number became different due to the existence of thebypass stream. The mass flow rate past the lower fin was higherfor pin–fins than for the plate-fin, which could enhance the heat-transfer rate. A detailed assessment using volumetric entropy gen-eration was conducted, which showed a small loss of irreversibilityfor the pin–fin models, compared to the plate-fin model.

Compared to the baseline plate-fin, the pin–fin models showed14–15% smaller pressure drops, and 9–11% smaller heat-transferrates. This shows a potential margin in the pressure drop thatmight be used to achieve the desired heat-transfer rate. As a result,a lighter SAOHE having a heat-transfer rate similar to existingdesigns, but with a smaller pressure drop, should be possible. Thiswould be advantageous for aero engines as the weight penalty isimportant in this application.

Further studies on the SAOHEs, such as the effect of additionalnovel geometries, and of various operating conditions, would behelpful and important, since the bypass ratio of modern aero

engines must become larger to increase engine efficiency and thiscauses the corresponding oil temperature in the transmission sys-tem to increase rapidly.

Acknowledgments

This work was supported by a National Research Foundation ofKorea (NRF-2013R1A2A2A01067251) grant funded by the Koreagovernment (MSIP).

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