International Journal of Heat and Fluid Flow 42 (2013) 151–163

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International Journal of Heat and Fluid Flow

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Flow and performance characteristics of an Allison 250 gas turbineS-shaped diffuser: Effects of geometry variations

0142-727X/$ - see front matter � 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.ijheatfluidflow.2013.02.004

⇑ Corresponding author.E-mail address: Goni.Boulama@rmc.ca (K. Goni Boulama).

Gavin G. Lee, William D.E. Allan, Kiari Goni Boulama ⇑Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario, Canada K7K7B4

a r t i c l e i n f o

Article history:Received 27 March 2012Received in revised form 31 January 2013Accepted 12 February 2013Available online 7 March 2013

Keywords:S-shaped diffuserAircraft inlet duct

a b s t r a c t

The S-shaped diffuser which connects the exit of the compressor to the inlet of the combustion chamberof the Allison 250 gas turbine has been investigated using the Shear-Stress Transport turbulence model(SST) and the commercial code ANSYS-CFX. The diffuser geometry includes an initial conical diffuserwhich smoothly transitions into a constant cross-section S-duct. The numerical model and setup werevalidated using both in-house processed experimental data and experimental data from the literatureon a similar geometry. The stream-wise velocity profile was observed to flatten in the initial divergentsection, and then the region of the flow with the highest velocity is pushed toward the outer surfaceof the first bend, with a secondary-flow in the plane of the cross-section. This distortion of the stream-wise velocity intensified when the inlet turbulence intensity was decreased or when the Reynolds num-ber was increased. An increase of the Reynolds number also translated into higher static pressure recov-ery potential and lower wall friction coefficients. Six variations of the diffuser geometry were considered,all having the same total cross-sectional area ratio and centreline offset. The qualitative results were thesame as those of the Allison 250 diffuser, but unlike the base geometry, all the considered variantsshowed separated-flow regions (and reversed-flow regions in some cases) of different sizes and at differ-ent locations. The performance indicators for the Allison 250 S-shaped diffuser were the highest overall.Most interestingly, the current duct geometry outperformed its variant with a cross-sectional area expan-sion extending over its entire length, which is the most common inlet duct configuration.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction

Turbulent flows in passages with gradually varying cross-sec-tional area and bends are present in a large variety of applica-tions and have long been the subject of interest from thescientific community. 2D and 3D planar diffusers and curvedrectangular ducts have thus been investigated using both theexperimental and numerical approaches, evidencing occurrencesof separated-flow regions, the extents of which depend on thepassage area ratio and the severity of the duct curvature whenapplicable, and the Reynolds number (Gullman-Strand et al.,2004; Cherry et al., 2008; Schneider et al., 2010; Jakirlic et al.,2010; Gopaliya et al., 2011). As far as axisymmetric geometriesare concerned, Azad (1996) authored a review of three-decadesof experimental research on an 8� conical diffuser at the Univer-sity of Manitoba. According to the author, diffusers can beviewed as devices that convert kinetic energy into potential en-ergy, and the efficiency of such conversion is the highest fordivergence angles between 6� and 8� for a conical diffuser, adivergence angle of 11� for a rectangular 2D diffuser, and a

divergence angle of 6� for a square cross-section diffuser. Thisefficiency is on the other hand dependent upon the nature ofthe boundary layer at the inlet of the diffuser. Among other con-clusions, the existence of an internal layer was conjectured, andlater verified numerically (Wu et al., 2006). Sparrow et al. (2009)also conducted research on conical diffusers and noted an incon-sistency in the literature, with some sources stating that theflow does not separate for divergence angles less than 7�, whileother sources state that divergence angles greater than 15� causeflow separation. Furthermore, the authors noted that the Rey-nolds number effect on the flow separation vs. divergence anglecorrelation is often overlooked. Based on these observations,they numerically investigated a wide range of divergence anglesand Reynolds numbers, and observed flow separation at diver-gence angles as small as 5� in the laminar regime, while simula-tions with 10–30� divergence angles all predicted flowseparations for Reynolds numbers varying between 500 and33,000, the extent of the separated-flow region being the great-est at lower Reynolds numbers. The latter conclusion contrastswith that of Herbst et al. (2007), who observed that the sepa-rated-flow region in planar diffusers becomes larger withincreasing Reynolds number, while Yang and Hou (1999) con-cluded that the Reynolds number effect was ambiguous.

Nomenclature

a, A, B, C see grid nomenclature in Fig. 3 and Table 1Cf friction coefficient ð2sw=ðqu2

0ÞÞCL coefficient of total pressure loss ð¼ 2ðPT;0 � PTÞ=ðqu2

0ÞÞCp pressure coefficient ð¼ 2ðPs � Ps;0Þ=ðqu2

0ÞÞD local duct diameter, mKE turbulence kinetic energy, m2/s2

NUI non-uniformity index ð¼P ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

v2 þw2p

=P ffiffiffiffiffiffi

u2pÞ

Ps, PT static pressure, total pressure, N/m2

Re Reynolds number (=qu0D0/l)r, z, x space coordinates, m, see Figs. 1 and 3R�, Z�, X� non-dimensional space coordinates. Radial coordinates

r and z are non-dimensionalized by the local duct diam-eter, while the axial coordinate x is non-dimensional-ized by the total diffuser length

Tu turbulence intensity (=(1.5KE)0.5/u0)u, v, w velocity vector components, m/sU� stream-wise velocity non-dimensionalized by the local

mean velocityus friction velocity ð¼

ffiffiffiffiffiffiffiffiffiffiffiffisw=q

pÞ, m/s

Y+ non-dimensionalized wall distance (=ypus/m)yp initial wall spacing, msw wall shear-stress (=l(@u/@r)|r=±0.5D), N/m2

l dynamic viscosity, N s/m2

q fluid density, kg/m3

m kinematic viscosity (=l/q), m2/s

152 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

Most important early advances in the study of flows in curvedpipes are due to WR Dean and his discovery that the primary mo-tion along the line of the conduit was accompanied by a secondarymotion in the plane of the cross-section, an outward shift of the re-gion where the primary flow velocity is the greatest, and a de-creased mass flow-rate for a given pressure gradient (Dean andHurst, 1959). Following suit, several other researchers investigatedthe flows in curved ducts and ducts with a series of bends (Talbotand Wong, 1982; Patankar et al., 1975; Towne, 1984; Rudolf andDesova, 2007). The study by Talbot and Wong (1982)) specificallyexamined the nature of the secondary-flow boundary-layer colli-sion, corresponding to the point where the wall shear stress van-ishes without changing sign. Patankar et al. (1975) and Towne(1984) are examples of early applications of computational ap-proaches for complex turbulent flow investigations.

The interest in the 1980s for turbo-prop powered airplanescame along with the requirement of specific inlet configurationsfor the double purpose of ensuring the most uniformly distributedflow possible and the highest possible pressure recovery at the in-let of the engines (McDill, 1989). Furthermore, Anderson (1991)noted that the inlet geometry should minimize vortex, wake andboundary layer ingestion, and minimize flow field interferencefrom weapon carriage and firing, landing gear deployment, etc.According to the author, engine face spatial and temporal flow dis-tortion was one of the least understood problems that early ver-sions of the B70, F-111, F-14, MIG-25, Tornado, Airbus A300, andother aircraft encountered. The shape optimization study by McDill(1989) started with an arbitrary superellipse at the diffuser throatand resulted in a circular cross-section at the compressor face, fol-lowing a specific area expansion which is, for example, the shapeadopted for the F/A-18 inlet duct (Anderson, 1991). In anothershape optimization study, Saha et al. (2007) compared elliptic,semi-circular, oval, rectangular and square duct inlet geometries,while maintaining the same outlet diameter, duct turning angle,area ratio and Reynolds number. They concluded that the ductwith the semi-circular inlet has the highest pressure recoveryand the lowest pressure loss coefficient, while the elliptic inlet ducthas the least total pressure distortion at the exit plane. The squaredinlet duct performed the poorest overall. Anand et al. (2003) exper-imentally investigated the effect of the turning angle on the flow inan S-shaped diffuser with an area ratio of 1.9, at a Reynolds num-ber of 100,000. They observed that the velocity distribution wasmore uniform and the pressure recovery was lower for the higherof the two turning angles tested (i.e. the smaller radius of curva-ture, or greater centreline offset). A numerical study on anS-shaped diffuser with a rectangular inlet and a semi-circular out-let reproduced the same trends for the pressure recovery, but not

for the flow uniformity (Gopaliya et al., 2007). The latter study alsopredicted that an increase in the Reynolds number does not have asignificant effect on the pressure recovery. Abdellatif et al. (2008)adopted the numerical approach in their investigation of the effectof the area ratio on the performance of S-shaped diffusers. Consider-ing an S-shaped diffuser of a constant turning angle and centrelinelength, they changed the area ratio from 1 to 1.51, which resultedin a static pressure recovery variation from �0.19 to 0.40. A furtherincrease of the area ratio to 1.9 did not significantly improve thepressure recovery, but the flow distortion increased. The authorstherefore concluded that for the given constraints, the area ratio of1.51 constitutes an optimum. Whitelaw and Yu (1993) experimen-tally studied an S-shaped diffuser tube: the Royal Aerospace Estab-lishment (RAE) series 2129, which has an area ratio of 1.4 and a non-dimensionalized offset of 0.3. They used a Reynolds number of400,000 and two different thicknesses of the boundary layer at theinlet of the diffuser. In both cases, a region of separation was ob-served at the inside surface of the first bend, just upstream of thejunction between the first and second bends, and it was larger forthe thinner inlet boundary layer. A pair of counter-rotating vorticeswas also observed at the exit plane, which increased the non-unifor-mity of the stream-wise velocity. No significant pressure recoverychanges were observed for the two inlet boundary layer thicknessesconsidered in the study. The RAE2129 was later reexamined by Leeand Yu (1994) using a Reynolds Averaged Navier–Stokes (RANS)method. Despite the simplicity of the method, the calculated meanflow features reproduced the experimental data in Whitelaw andYu (1993) with sufficient accuracy.

This literature survey confirms that the research on turbulentflows in curved and/or diffusing ducts is topical, and several ofits aspects have been studied using both the experimental andnumerical approaches. RANS models have been used in the litera-ture with a wide variety of prediction accuracy and implementa-tion cost (Gullman-Strand et al., 2004; Schneider et al., 2010;Gopaliya et al., 2007, 2011; Sparrow et al., 2009; Yang and Hou,1999; Patankar et al., 1975; Rudolf and Desova, 2007; Saha et al.,2007; Lee and Yu, 1994; El-Behery and Hamed, 2011). Herbstet al. (2007) mentioned that a suitable RANS model could resultin a reasonable agreement with experimental data, but cautionedthat the prediction capability is highly model-dependent. Theirown Large Eddy Simulation (LES) study predicted a slightly smallerseparated-flow region than the one measured, as well as delayedseparation and reattachment. Abe and Ohtsuka (2010) also usedthe LES approach and observed a significantly under-predictedwall friction, resulting in an overly early separation. Muchimproved prediction capability was obtained when a hybridLES/RANS method was used. On the other hand, Ohlsson et al.

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 153

(2010) adopted the Direct Numerical Simulation (DNS) approachand demonstrated its capability to provide accurate and detailedinformation about the physics of the flow in a 3D straight diffuser.However, the cost of the DNS approach is currently prohibitive forhigh Reynolds number flows in complex geometries includingcross-sectional area variations and curvatures.

In collaboration with a manufacturer partner, our lab is conduct-ing a comprehensive study of the Allison 250 gas turbine model(A250). The present study focuses on the turbulent flow in the ductconnecting the exit of the compressor to the inlet of the combustionchamber of the A250. This duct has an initial conical diffuser shapethat smoothly transitions into a constant cross-sectional area, S-shaped duct. With the exception of preliminary results recently pre-sented at a conference by the present authors (Lee et al., 2012), noprevious work has been reported on this particular geometry inthe literature, most inlet ducts having a continuously expandingcross-sectional area (McDill, 1989; Anderson, 1991; Saha et al.,2007; Anand et al., 2003; Gopaliya et al., 2007; Abdellatif et al.,2008; Whitelaw and Yu, 1993; Lee and Yu, 1994). The RANS Shear-Stress Transport (SST) turbulence model is adopted as the investiga-tion tool. An experimental rig is constructed and used to collect datathat are used for validation. Further validation is performed againstexperimental data on the RAE2129 from the literature (Whitelawand Yu, 1993). After the main flow features of the A250 S-shaped dif-fuser duct are calculated, the discussion is continued with a sensitiv-ity analysis on the inlet turbulence intensity and Reynolds number,and the flow in the A250 S-Diffuser is compared to that in a numberof slightly different geometrical configurations.

2. Experimental setup

The geometry of the Allison 250 model diffuser duct (hereafterreferred to as A250 S-Diffuser) is shown in Fig. 1a. It has a totallength of 426 mm, which includes a 155.2 mm conical section fol-lowed by a 270.8 mm constant diameter S-shaped duct. The inletand outlet diameters are 46.83 mm and 65.11 mm, respectively,giving an area ratio of 1.933. The offset between the inlet andthe outlet is 48.2 mm. The top edge of the duct in the view inFig. 1a is adjoining the combustion chamber and turbine, and willherein be referred to as the inner surface of the first bend, or thewall at R� = 0.5. Accordingly, the bottom edge will be referred toas the outer surface of the first bend, or the wall at R� = �0.5.

A service-worn sample of the A250 S-Diffuser was obtained as atest article. A flexible traverse system with a 0.8 mm pitch,equipped with a Pitot-static tube is designed to be placed at threestream-wise locations (1: entrance; 2: end of conical section; 4:exit plane of diffuser). Furthermore, pressure measurements couldbe taken in the four directions indicated in Fig. 1b. An OmegaPX139 pressure transducer rated for ±0.3 psi with an output volt-age between 0.25 and 4.25 V is used, in conjunction with a Na-tional Instruments Analog/Digital converter (NI cRIO9201). Ateach position, measurements are taken over a period of 10 s at

Fig. 1. (a) Geometry of the A250 S-Diffu

100 Hz, which allows for the calculation of a mean value alongwith its standard deviation. A Westinghouse 1.5 hp, 3450 rpm mo-tor, mated to a Canadian Blower & Forge Co. centrifugal blower, isused to generate the desired flow. A 2 m long steel, drawn-over-mandrel, tube of inside diameter equal to that of the inlet of theA250 S-Diffuser is configured to the blower of outlet diameter4.5 in via a plain reducer and a contraction cone. Honeycomb flowstraighteners are placed at the entrance of this initial tube in orderto minimize instabilities before the flow enters the test-section. Inaddition, a 1 m steel extension tube, with an inside diameter equalto that of the exit of the A250 S-Diffuser, is placed at the exit of thediffuser in order to prevent outlet conditions from affecting theflow in the region of interest. This practice is common in bothexperimental and numerical approaches (Gullman-Strand et al.,2004; Cherry et al., 2008; Schneider et al., 2010; Jakirlic et al.,2010; Sparrow et al., 2009; Saha et al., 2007; Anand et al., 2003;Gopaliya et al., 2007; Abdellatif et al., 2008; Whitelaw and Yu,1993; Lee and Yu, 1994; El-Behery and Hamed, 2011; Ohlssonet al., 2010). Under the considered conditions, a mass flow-rateof 0.055 kg/s and a Reynolds number of 80,000 are obtained. Thearea averaged turbulence intensity at the inlet plane of the compo-nent (Station 1) is estimated to be 1.6%. Note that the experimentalrig is, in the long-term, meant to be used in order to study thepropagation of flow instabilities from the compressor to the com-bustion chamber.

In the following, the radial coordinates z (AA direction) and r(CC direction) are non-dimensionalized by the local duct diameter,the axial coordinate x is non-dimensionalized by the total diffuserlength, and the velocity components u, v and w are non-dimension-alized by the local bulk velocity.

In this study, the sensitivity of the flow features and performancecharacteristics of the A250 S-Diffuser are discussed by consideringseveral geometrical variations, see Fig. 2. All geometries in Fig. 2have the same inlet and outlet diameters and centreline offset asthe A250 S-Diffuser. For the S-Diffuser 1/3 (Fig. 2a), the cross-sec-tional area expansion occurs between Sections 1 and 3. For the S-Dif-fuser 1/4 (Fig. 2b), the area expansion extends over the entire ductlength, as it is for the RAE2129 and most inlet ducts. For the S-Dif-fuser 2/3 (Fig. 2c), the area expansion occurs between Sections 2and 3. The same nomenclature convention is adopted for the S-Dif-fuser 2/4 (Fig. 2d), S-Diffuser 3/4 (Fig. 2e) and S-Diffuser 1/2–3/4 (notshown). Consistently, the A250 S-Diffuser (Fig. 1a) could be referredto as S-Diffuser 1/2. Finally, an S-shaped duct (not shown) with aconstant cross-sectional area, a diameter equal to that of the inletof the A250 S-Diffuser, and the same centreline offset as the A250S-Diffuser will also be considered for comparison purposes.

3. Numerical approach

The commercial CFD software ANSYS-CFX is adopted for thisstudy to solve the steady-state Cartesian coordinates Navier–Stokes equations using a fully conservative, control-volume-based,

ser and (b) pressure traverse paths.

Fig. 2. (a) S-Diffuser 1/3, (b) S-Diffuser 1/4, (c) S-Diffuser 2/3, (d) S-Diffuser 2/4 and (e) S-Diffuser 3/4.

154 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

finite-element method. To ensure robustness, the discretization isperformed with a combination of the upwind and central differ-encing schemes. The resulting hybrid scheme is first- and sec-ond-order accurate, switching from the latter to the former inregions of steep gradients, based on the boundedness principle ofBarth and Jespersen (1989). The resolution scheme is second-orderaccurate. Pressure–velocity coupling is enforced with a non-stag-gered grid and the fourth-order-accurate algorithm of Rhie andChow (1983).

The Shear-Stress Transport model (SST) is based on the two fol-lowing transport equations:

@ðqUjkÞ@xj

¼ fPk � b�qkxþ @

@xjðlþ rkltÞ

@k@xj

� �ð1Þ

ð@UjxÞ@xj

¼ aqS2 � bqx2 þ @

@xjðlþ rxltÞ

@x@xj

� �

þ 2ð1� F1Þqrx21x

@k@xj

@x@xj

ð2Þ

where F1 is equal to zero away from the surface (j–e model) andequal to one inside the boundary layer (j–x model). The model alsoincludes a slight amendment to the definition of the eddy viscosityfor a better prediction of the turbulent shear stress. The calculationof the distance from the wall is achieved by the solution of a Poissonequation. More details on the SST model could be found in Sparrowet al. (2009), and Menter (1994), and are not reproduced here forconciseness. The suitability of the SST turbulence model is dis-cussed in the next section. For each simulation, the convergence

Table 1Characteristics of some of the tested grid resolutions.

Grid resolution Wall spacing (Y+) A a B C Total

G1 45.4 10 15 100 180 288,108G2 6.98 25 55 100 180 2,770,893G3 1.12 20 70 100 180 2,692,188G4 1.12 20 70 50 90 1,789,148G5 1.12 20 70 150 270 3,905,648G6 0.68 30 100 100 180 5,907,168

X*

Cf

0 0.25 0.5 0.75 10

0.002

0.004

0.006

G1G2G3G4G5G6

(a) R* = 0.5

0.002

0.004

0.006

G1G2G3G4G5G6

Cf

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 155

is judged based on the variations of the scaled residuals of the gov-erning equations (values in the order of or below 10�6 are desired)and verified using an integral mass balance.

The wall boundary conditions are the standard no-slip andimpermeability conditions. At the inlet of the computational do-main, a uniform velocity profile corresponding to the desired Rey-nolds number is prescribed. This results in fully-developed flowconditions at the inlet of the component under study. At the otherend of the computational domain, stream-wise second derivativesof velocities are assigned a zero value to represent fully-developedflow conditions. Finally, all simulations are performed with stan-dard air at the constant temperature of 25 �C.

3.1. Grid sensitivity

The A250 S-Diffuser used in the physical experiment has beendigitized and imported into ICEM, a grid generator compatible withthe ANSYS-CFX CFD solver. Consistently with the experimental set-up, a 1.5 m entrance length (upstream the diffuser) and a 1 m longextension (downstream the diffuser) are used in the numericalmodel. An illustration of the grid topology is shown in Fig. 3. Thegrid is uniformly distributed along the component (not shown);while in the plane of the cross-section the adopted O-grid meshis relatively coarse in the central region with a geometric refine-ment as the wall region is approached. This meshing technique al-lows for an even wall size distribution, and is superior to a purelyhexagonal mesh (Lee and Yu, 1994).

Different grids have been tested, with different stream-wise andcross-flow resolutions. The most important features of some ofthese grids are summarized in Table 1. ‘‘A’’ represents the numberof nodes along the side of the square central box of Fig. 3, ‘‘a’’ rep-resents the number of nodes along the line from the corner of thecentral square box to the wall, while ‘‘B’’ and ‘‘C’’ represent thestream-wise grid distribution in the conical and S-shaped sectionsof the duct, respectively. The calculated friction coefficients forgrids G1–G6 are shown in Fig. 4. Refining the cross-sectional planeresolution from G1 to G2, while maintaining the longitudinal reso-lution unchanged, results in a very significant change of the frictioncoefficient values (as much as 16% in average at the outer surfaceof the first bend). A further refinement of the cross-sectional planeresolution particularly in the wall region (G2–G3) results in anaverage variation of the friction coefficient values of 8.4% at theR� = �0.5 wall, and this variation falls to 0.90% only when G3 iscompared to the finest grid G6. On the other hand, the variationsin the friction coefficient values are small (about 0.20% in average

Fig. 3. Cross-sectional plane grid topology.

X*0 0.25 0.5 0.75 10

(b) R* = -0.5

Fig. 4. Effects of the grid resolution on the calculated the friction coefficients.

at R� = �0.5) when the longitudinal resolution is refined from G4 toG3 and from G3 to G5, while maintaining the cross-sectional planeresolution unchanged. In view of these results, and in order to pre-serve both accuracy and cost, G3 is considered as sufficiently well-resolved to be adopted for all subsequent simulations. Notwith-standing, a wall resolution Y+ � 1.0 was recommended in a similardiffuser flow with separation in the literature (Rudolf and Desova,2007; El-Behery and Hamed, 2011; Abe and Ohtsuka, 2010).

3.2. Validation

The calculated velocity profiles using the grid resolution G3, aReynolds number of 80,000, a turbulence intensity of 5% at the in-let of the computational domain, and the ANSYS-CFX SST turbu-lence model are compared with the experimental data in Fig. 5. A

U*

Z*

0 0.5 1 1.5 2

-0.4

-0.2

0

0.2

0.4

Station 1Station 2Station 4

(a) AA line

U*

R*

0 0.5 1 1.5 2

-0.4

-0.2

0

0.2

0.4

Station 1Station 2Station 4

(b) CC line

Fig. 5. Development of the stream-wise velocity profile in the A250 S-Diffuser.

U*

Z*

0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4κ−εκ−ωSST

(a) AA line

U*

R*

0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4

κ−εκ−ωSST

(b) CC line

Fig. 6. Comparison of the prediction capability by different turbulence models.

156 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

very good qualitative and quantitative agreement is observed at allthree measurement stations (see Fig. 1a), and along the two cross-flow directions AA and CC (see definition in Fig. 1b).

In order to further assess the suitability of the adopted turbu-lence model, the results shown in Fig. 5 are re-calculated usingthe two turbulence models it builds upon: the standard j–e andj–x models. As discussed in the introduction, several variants ofthese models have been used in the literature with different levelsof success (Gullman-Strand et al., 2004; Schneider et al., 2010;Gopaliya et al., 2007, 2011; Sparrow et al., 2009; Yang and Hou,1999; Patankar et al., 1975; Rudolf and Desova, 2007; Saha et al.,2007; Lee and Yu, 1994; El-Behery and Hamed, 2011; Menter,1994). Fig. 6a shows that the stream-wise velocity distributionalong the AA direction at the exit plane of the A250 S-Diffuser(see Station 4 results in Fig. 5) is not well predicted by either thej–e and j–x models, with the latter model qualitatively predictingthe existence of the two overshoot regions next to the wall, and theformer model completely failing to do so. Fig. 6b also shows thatboth the j–e and j–x models fail to predict the magnitude ofthe velocity profile distortion. Of particular importance is thevelocity gradient predicted by the j–e model at R� = 0.5 on theone hand, and the one predicted by the SST model at aboutR� = 0.3 on the other hand. According to El-Behery and Hamed(2011), the better performance of the SST and j–x models com-pared to the j–e model (which also requires more computational

time) may be explained by the fact that the former two models ac-count for some near-wall turbulence anisotropy, which is not thecase for the j–e model. Menter (1994) also noted the very littlesensitivity of the j–e model to the pressure gradient, and attrib-uted the better performance of the SST model compared to thej–x model to the presence of an additional cross-diffusion termin the dissipation rate transport equation (last term on the righthand side of Eq. (2)).

In the absence of published data on the A250 S-Diffuser, thenumerical code has finally also been tested against available exper-imental data on the RAE2129 diffuser from the literature (White-law and Yu, 1993). The RAE2129 S-shaped inlet duct differs fromthe A250 S-Diffuser in that it has a smaller area ratio (1.4), a largeroffset (0.3), and its cross-sectional area expands over its entirelength. The test is conducted for the fully-developed flow inlet con-dition of Whitelaw and Yu (1993) at a Reynolds number of400,000. Fig. 7 shows that the development of the stream-wisevelocity profile is well predicted by the model (present calculatedresults are shown in the form of velocity vectors), while Fig. 8 alsoshows a reasonably good agreement between the experimentaland numerical data; this agreement is by all means at least as goodas the one obtained by the same authors when they adopted thenumerical approach (Lee and Yu, 1994).

In view of the grid resolution sensitivity analysis (Fig. 4), theexperimental validation cases (Figs. 5, 7 and 8) and the turbulence

Fig. 7. Development of the stream-wise velocity profile in the RAE2129.

X

Cp

-0.1 0 0.1 0.2 0.3-0.4

-0.2

0

0.2

0.4

R* = 0.5R* = 0.0R* = -0.5

Present Study Exp

Fig. 8. Development of the pressure coefficient in the RAE2129 (Experimental dataare from Whitelaw and Yu, 1993).

(a) AA line

(b) CC line

Fig. 9. Development of the stream-wise velocity in the A250 S-Diffuser.

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 157

model discussion (Fig. 6), the numerical model (the SST turbulencemodel as imbedded in ANSYS-CFX) and the implementationadopted in this study are considered validated and appropriatefor the investigation of the problem at hand.

4. Results

4.1. Development of the stream-wise velocity profile in the A250 S-Diffuser

Fig. 9 shows the variations of the stream-wise velocity profilealong the A250 S-Diffuser at a Re = 80,000. In the AA direction(Fig. 9a), the velocity profile is symmetrical and gradually flattensdownstream, until the centreline velocity becomes smaller thanthe velocity in the wall region, with the emergence of an increas-ingly pronounced overshoot. Along the CC line (Fig. 9b), the sym-metrical profile at the inlet gets increasingly distorted towardsthe wall at R� = �0.5, while the flow near the wall at R� = 0.5 isdecelerated. This is an indication of the presence of a secondary-flow in the plane of the cross-section as it will be discussed laterin this report.

4.2. Effects of the turbulence intensity at the inlet on the flow andperformance of the A250 S-Diffuser

While rarely investigated in the literature, different operatingconditions could result in significantly different inlet turbulence

levels, considerably affecting the flow and performance of the dif-fuser (Sullerey et al., 1983). Three turbulence intensity values aretherefore tested here: Tu = 1%, Tu = 5% and Tu = 10%. The Reynoldsnumber has been kept constant at 80,000 for all three simulations,and Figs. 10–12 present calculated data at the exit plane of the dif-fuser (Station 4). The qualitative trends are similar, but increasingthe inlet turbulence intensity (equivalent to enhancing the mixing)results in a markedly less pronounced overshoot of the velocityprofile in the AA direction (Fig. 10a), and also a less pronounceddistortion of the velocity profile along the CC direction (Fig. 10b).Fig. 11a shows an initial rapid decrease of the friction coefficientsat the wall at R� = 0.5 in the conical section of the A250 S-Diffuser,followed by a brief increase at the convex bend, and then a gradualdecrease until about X� = 0.8 where the boundary layer seems todetach from the surface though a flow reversal does not actuallyoccur, corresponding to what is referred to as a boundary layer col-lision in Talbot and Wong (1982). At the second bend, the frictioncoefficient starts increasing again. Near the outer surface of thefirst bend (R� = �0.5), the friction coefficients for all three inlet tur-bulent intensities decrease as the flow passage enlarges, closelyapproaching zero, then sharply increase after the concave bendas a consequence of the flow acceleration in that region of the pas-sage (see also Fig. 9b). This increase is sustained until the convexbend, at which the friction coefficients drop sharply. The effect ofthe inlet turbulence intensity on the quantitative Cf variations islimited overall, except along the R� = �0.5 wall far downstreamwhere the highest turbulence level correlates with the least fric-tion losses (Fig. 11b). Finally, Fig. 12 shows that the pressure coef-ficient variations for the three inlet turbulence intensity valuesconsidered are qualitatively similar, indicating a gradual pressure

U*

Z*

0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4 Tu=1%Tu=5%Tu=10%

(a) AA line

U*

R*

0 0.5 1 1.5

-0.4

-0.2

0

0.2

0.4 Tu=1%Tu=5%Tu=10%

(b) CC line

Fig. 10. Effects of the inlet turbulence intensity on the stream-wise velocity profileat the exit plane of the A250 S-Diffuser.

X*

Cf

0 0.25 0.5 0.75 10

0.002

0.004

0.006

Tu = 1%Tu = 5%Tu = 10%

(a) R* = 0.5

X*0 0.25 0.5 0.75 10

0.002

0.004

0.006

Tu = 1%Tu = 5%Tu = 10%

(b) R* = -0.5

Cf

Fig. 11. Effects of the inlet turbulence intensity on the calculated frictioncoefficients along the wall of the A250 S-Diffuser.

158 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

recovery, one of the most important diffuser performance parame-ters. Quantitatively however, the highest inlet turbulence intensityreturns slightly higher pressure coefficients, while the lowest tur-bulence intensity value consistently results in lower pressure coef-ficient values. These results may be explained by the fact that highturbulence intensity is synonymous to more important mixing, andare consistent with published experimental observations from theliterature (Sullerey et al., 1983).

4.3. Effects of the Reynolds number on the flow and performance of theA250 S-Diffuser

Fig. 13 shows the effects of the Reynolds number on the distri-bution of the stream-wise velocity at the exit plane of the A250 S-Diffuser. Four Reynolds number values are considered in thisstudy: 25,000, 80,000, 116,000 and 209,000 (the latter value beingclose to the actual operation condition of the A250 S-Diffuser). Theinlet turbulence intensity is 5% in all cases. At the inlet of the duct,the profiles are identical for all Reynolds numbers, and the differ-ence is also small at the end of the conical section. These profiles,not given here for conciseness, indicate a flattening tendency as theReynolds number is increased, which is expected. At the exit plane,

the profiles along the AA line (Fig. 13a) reveal an increasingly pro-nounced overshoot in the near wall region, and monotonicallydecreasing stream-wise velocities in the centreline when the Rey-nolds number is increased. Along the CC line (Fig. 13b), the distor-tion of the velocity profile toward the R� = �0.5 wall is alsoobserved to intensify as the Reynolds number is increased. It isworth noting that the slope of the velocity profile at aboutR� = 0.3 suggests that a second overshoot may appear next to theinner surface of the first bend should the Reynolds number be fur-ther increased. The effect of the Reynolds number on the frictioncoefficient variations is illustrated in Fig. 14. The qualitative trendsare again similar for all four Reynolds numbers tested, and the dif-ferences in the calculated Cf values are small along the inner sur-face of the first bend (slight decrease of the friction coefficientsas the Reynolds number is increased). Along the R� = �0.5 wallhowever, the friction coefficient variations are extremely sensitiveto the Reynolds number, the simulation at the lowest Reynoldsnumber returning the highest Cf values over most of the lengthof the duct, and most importantly downstream its conical section.The effect of the Reynolds number on the variations of the pressurecoefficients is shown in Fig. 15, which displays qualitativelysimilar results in all cases; however the highest Reynolds number

X*

Cp

0 0.25 0.5 0.75 10

0.2

0.4

0.6

0.8

Tu = 1%Tu = 5%Tu = 10%

(a) R* = 0.5

X*0 0.25 0.5 0.75 10

0.2

0.4

0.6

0.8

Tu = 1%Tu = 5%Tu = 10%

(b) R* = -0.5

Cp

Fig. 12. Effects of the inlet turbulence intensity on the calculated pressurecoefficients along the wall of the A250 S-Diffuser.

U*

Z*

0 0.5 1 1.5 2

-0.4

-0.2

0

0.2

0.4

25K80K116K209K

(a) AA line

R*

0 0.5 1 1.5 2

-0.4

-0.2

0

0.2

0.425K80K116K209K

(b) CC line U*

Fig. 13. Effects of the Reynolds number on the stream-wise velocity profile at theexit plane of the A250 S-Diffuser.

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 159

consistently returned the highest pressure coefficient values onboth walls.

4.4. Sensitivity of the flow and performance parameters to thegeometry of S-shaped diffuser ducts

The seven S-shaped diffuser geometries defined in Figs. 1 and 2,and an S-shaped duct with a constant cross-sectional diameter andthe same centreline offset as the A250 S-Diffuser are considered inthis paragraph in order to investigate the sensitivity of the hydro-dynamic fields and performance indicators to the duct geometry.Fig. 16 shows the axial variation of the stream-wise velocity distri-bution in the cross-sectional plane, as well as the variation of thecross-flow velocity for four of the considered configurations. Atthe inlet of the ducts, the stream-wise velocity is symmetricallydistributed, with the highest velocity magnitudes in the centrelineregion. The A250 S-Diffuser and the S-Diffuser 1/4 show somesmall outward velocity vectors, which is consistent with the factthat the expansion of their cross-sectional area starts at the inletof the ducts. At X� = 0.35, both the stream-wise velocity contoursand the cross-flow velocity vectors show a slight movement to-ward the convex surface of the first bend. The direction of the sec-ondary-flow vectors however, swiftly reverses direction thereafter,

and the region of the flow where the stream-wise velocity is max-imum gradually shifts toward the concave surface under the dou-ble effect of centrifugal forces and radial pressure gradients. For theS-Diffuser 1/4, a separated-flow region is visible at X� = 0.81. A sep-arated-flow region is also observed for the S-Diffuser 2/3 atX� = 0.51; it is bigger at X� = 0.66, smaller at X� = 0.81, and seemsto have disappeared by the exit of the duct. As for the S-Diffuser3/4, the separated-flow region is first observed at X� = 0.81, and itis bigger at the exit plane. One single pair of recirculation vorticesis predicted in most cases. Most of these observations are in veryclose agreement with those by previous authors on similar geom-etries (Dean and Hurst, 1959; Patankar et al., 1975; Lee and Yu,1994). In order to quantify the intensity of the secondary-flow, Ta-ble 2 gives the calculated non-uniformity index (NUI) at the exitplane for the eight geometries considered in this study. The non-diffusing duct (S-Duct) is seen to correspond to the lowest NUI,agreeing with conclusions in a previous LES study (Abdellatifet al., 2008). The NUI for the A250 S-Diffuser is relatively high,but it is the S-Diffuser 2/3 geometry that corresponds to the high-est NUI. It is also interesting to note that the normalized maximumsecondary-flow velocity at the exit plane is smaller for all thegeometries in this study than for the RAE2129 in Whitelaw andYu (1993). While the most uniform flow possible is desired atthe exit plane of inlet ducts (NUI < 10% qualifies as uniform flow)

X*

Cf

0 0.25 0.5 0.75 10

0.002

0.004

0.006

25K80K116K209K

(a) R* = 0.5

X*

Cf

0 0.25 0.5 0.75 10

0.002

0.004

0.006

25K80K116K209K

(b) R* = -0.5

Fig. 14. Effects of the Reynolds number on the development of the frictioncoefficients along the wall of the A250 S-Diffuser.

X*

C p

0 0.25 0.5 0.75 10

0.2

0.4

0.6

0.8

25K80K116K209K

(a) R* = 0.5

X*0 0.25 0.5 0.75 10

0.2

0.4

0.6

0.8

25K80K116K209K

(b) R* = -0.5

C p

Fig. 15. Effects of the Reynolds number on the development of the pressurecoefficients along the wall of the A250 S-Diffuser.

160 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

(Gopaliya et al., 2011; McDill, 1989; Anderson, 1991), the practicalsignificance of the non-uniformity index for a transition duct lo-cated between the compressor and the combustion chamber is un-known to us.

Fig. 17 compares the calculated friction coefficients along thewalls of the different variants of the S-shaped diffuser geometriesin this study. Initial friction coefficient curve slopes allow for aclear differentiation between geometries presenting cross-sec-tional area expansions starting at the inlet, which show a gradualdecrease of the Cf graphs, and those geometries for which the areaexpansion starts farther downstream. The S-shaped duct withoutany cross-sectional area expansion is the one that produces thelargest friction losses, which validates the preference for diffusingducts in turbomachinery applications. The friction coefficientgraphs also allow for a better appraisal of separated-flow regionfeatures, including nature, location and size. The separated-flowon the inner surface of the first bend of the S-Diffuser 1/3(Fig. 17a) for example qualifies as an ‘‘incipient separation’’ (Leeand Yu, 1994), that is the friction coefficients decrease down tozero, without ever changing sign, while the finite negative frictioncoefficient values for four of the considered geometries indicate re-versed-flow occurrences. The summary in Table 3 shows that theseparated-flow region for the S-Diffuser 2/3 geometry initiates

the earliest, is the biggest, and extends over more than half thelength of the duct, while the flow separates but does not reattach(within the component) for three other geometrical configurations.Overall, Fig. 17 and Table 3 suggest that the A250 S-Diffuser is themost efficient geometry, as it produces the least friction losses, andit resists flow separation.

The static pressure recovery potentials for each of the geome-tries considered are shown in Fig. 18. It is seen that the geometriesthat present cross-sectional area expansions starting at the inlet ofthe duct are the ones that allow for the highest performances.These geometries also correspond to the shortest lengths of sepa-rated-flow region, if any. It is also worth noting that the superiorperformance of the A250 S-Diffuser compared to the S-Diffuser1/4 suggests that the current most common inlet duct design (i.e.cross-sectional area variation over the entire length of the duct)is not optimal, at least as far as the static pressure recovery poten-tial is concerned. The S-Diffuser 2/3 and the S-Diffuser 2/4 alsopossess decent static pressure recovery potentials, but they arepenalized by the pressure loss between Sections 1 and 2. Limitingthe cross-sectional area expansion to the last section of the duct isobviously counterproductive. It is also noted that the value of thestatic pressure recovery coefficient for the constant cross-sectionalarea S-shaped duct is exactly equal to that predicted by the LES

A250 S-Diffuser S-Diffuser 1/4 S-Diffuser 2/3 S-Diffuser 3/4

X* = 0

X* = 0.35

X* = 0.51

X* = 0.66

X* = 0.81

X* = 1

Fig. 16. Sensitivity of the stream-wise and cross-flow velocity to the geometry of the duct.

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 161

investigation in Abdellatif et al. (2008), which constitutes both anadditional validation and a confirmation that this geometry is notappropriate for the considered application. Finally, the total pres-

sure loss coefficients are compared in Fig. 19, confirming the betterperformance of geometries with cross-sectional area expansionsstarting at the inlet. At the other end of the spectrum, the

Table 2Sensitivity of the non-uniformity index (NUI) to the geometry of the duct.

Duct geometry Non-uniformity index

A250 S-Diffuser (S-Diffuser 1/2) 0.085S-Diffuser 1/2–3/4 0.065S-Diffuser 1/3 0.073S-Diffuser 1/4 0.064S-Diffuser 2/3 0.112S-Diffuser 2/4 0.071S-Diffuser 3/4 0.059S-Duct 0.027

X*

C f

0 0.25 0.5 0.75 1

0

0.002

0.004

0.006

0.008

0.01A250 S-DiffuserS-DuctS-Diffuser 1/2-3/4S-Diffuser 1/3S-Diffuser 1/4S-Diffuser 2/3S-Diffuser 2/4S-Diffuser 3/4

(a) R* = 0.5

X*

C f

0 0.25 0.5 0.75 10

0.002

0.004

0.006

0.008

A250 S-DiffuserS-DuctS-Diffuser 1/2-3/4S-Diffuser 1/3S-Diffuser 1/4S-Diffuser 2/3S-Diffuser 2/4S-Diffuser 3/4

(b) R* = -0.5

Fig. 17. Sensitivity of the friction coefficients to the geometry of the duct.

Table 3Separated flow regions for the S-shaped diffuser geometries investigated.

Separationpoint

Reattachmentpoint

Separatedflowlength

A250 S-Diffuser (S-Diffuser 1/2) n/a n/a n/aS-Diffuser 1/2–3/4 0.765 n/a n/aS-Diffuser 1/3 0.569 0.744 0.175S-Diffuser 1/4 0.747 0.989 0.242S-Diffuser 2/3 0.443 0.969 0.526S-Diffuser 2/4 0.618 n/a n/aS-Diffuser 3/4 0.716 n/a n/aS-Duct n/a n/a n/a

X*

Pres

sure

Rec

over

y

0 0.25 0.5 0.75 1-0.2

0

0.2

0.4

0.6

Fig. 18. Sensitivity of the static pressure recovery to the geometry of the duct (samelegend as in Figs. 17 and 19).

X*

CL

0 0.25 0.5 0.75 10

0.05

0.1

0.15

0.2A250 S-DiffuserS-DuctS-Diffuser 1/2-3/4S-Diffuser 1/3S-Diffuser 1/4S-Diffuser 2/3S-Diffuser 2/4S-Diffuser 3/4

Fig. 19. Sensitivity of the total pressure loss coefficient to the geometry of the duct.

162 G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163

S-Diffuser 2/3 and the S-Diffuser 3/4 produce total pressure lossesequivalent to those of the constant cross-sectional area, S-shapedduct.

5. Conclusions

An investigation has been conducted on the Allison 250 gas tur-bine S-shaped diffuser which connects the exit of the compressorto the inlet of the combustion chamber using the standard j–eand j–x models, as well as the Shear-Stress Transport (SST) modelimplemented in the commercial code ANSYS-CFX. Data measuredusing an in-house purpose-designed test rig and other experimen-tal data taken from the literature were used for validation. Thestandard j–x model was shown to qualitatively reproduce thegeneral trends, but the quantitative agreement with the experi-mental data was poor. The standard j–e model performed evenworse. Conversely, the SST model successfully passed the valida-tion tests and was therefore adopted for the remainder of the anal-ysis. Among other calculated results, the stream-wise velocityprofile was observed to flatten in the initial divergent section,experience a slight shift toward the inner surface at the first bend,before a gradually intensifying secondary-flow is initiated, pushingthe region of the flow with the highest velocity toward the concavesurface of the first bend. This was accompanied by an increase of

G.G. Lee et al. / International Journal of Heat and Fluid Flow 42 (2013) 151–163 163

the friction coefficient in that region. In the direction normal to theoffset, the velocity distribution remained symmetrical, with twoovershoot regions close to the wall. The distortion of the stream-wise velocity intensified when the inlet turbulence intensity wasdecreased, with a small effect on the friction and pressure coeffi-cients. On the other hand, the severity of the distortion of thestream-wise velocity profile was shown to increase with the Rey-nolds number. The static pressure recovery potential also increasedwith the Reynolds number, while higher Reynolds numbers consis-tently translated into lower wall friction coefficients. Six variationsof the diffuser geometry have been considered in this study, allhaving the same total cross-sectional area ratio and centreline off-set, but differing on the location and length of the area expansionsection. The general variation trends were the same as those of theAllison 250 diffuser, but the decrease of the friction coefficientsnear the inner surface of the first bend continued beyond the zeroline, and separated-flow regions (and reversed-flow regions insome cases) of different sizes and at different locations were ob-served for all of these geometries. The friction coefficients werethe lowest overall, the static pressure recovery was the highest,and the total pressure loss coefficient was among the lowest forthe base geometry. Particularly worth noting is that the Allison250 S-shaped diffuser duct has overall better performance charac-teristics than its variant presenting a cross-sectional area expan-sion extending over its entire length. This is interesting becausemost common inlet ducts actually have cross-sectional area expan-sion over their entire length.

Acknowledgements

The financial support of Standard Aero Ltd. (SAL), the NationalSciences and Engineering Research Council of Canada (NSERC)and the Royal Military College Academic Research Program (ARP)is acknowledged.

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