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Semiu A. Gbadebo

Tom P. Hynes

Whittle Laboratory,University of Cambridge,

Cambridge, United Kingdom

Nicholas A. CumpstyRolls-Royce Plc,

Derby, United Kingdom

Influence of Surface Roughnesson Three-Dimensional Separationin Axial CompressorsSurface roughness on a stator blade was found to have a major effect on thedimensional (3D) separation at the hub of a single-stage low-speed axial compressochange in the separation with roughness worsened performance of the stage. A prnary study was carried out to ascertain which part of the stator suction surface anwhat operating condition the flow is most sensitive to roughness. The results showstage performance is extremely sensitive to surface roughness around the leadingand peak-suction regions, particularly for flow rates corresponding to design and lovalues. Surface flow visualization and exit loss measurements show that the sizeseparation, in terms of spanwise and chordwise extent, is increased with rougpresent. Roughness produced the large 3D separation at design flow coefficient tfound for smooth blades nearer to stall. A simple model to simulate the effect of rougwas developed and, when included in a 3D Navier–Stokes calculation method, was showto give good qualitative agreement with measurements.@DOI: 10.1115/1.1791281#

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IntroductionAlmost all treatments of boundary layer effects, including t

effect of surface roughness, have been two-dimensional in tapproach. This is most obvious in the use of linear cascades balso applies to consideration of losses around mid-span, afrom the ‘‘complicating’’ effects of the endwalls. The emphasisthis paper is on 3D effects, including 3D separation, found whthe suction surface meets the hub of a shrouded stator. Worported by Gbadebo, Cumpsty, and Hynes@1# shows how wide-spread 3D separation is, and how much it affects performaThe surprising aspect of the present paper is the importancsurface roughness to the size of these 3D effects.

Most of the work carried out on the effect of rotor surfaroughness on performance has been concerned with profilean essentially two-dimensional view. An example is the workSuder et al.@2#, who carried out a detailed study on the effectadding roughness and thickness to a transonic compressorThey used different rough and smooth coating configuratiowhich were tested for a range of chordwise coating extents. Msurements were performed both at part and full speed. Theisults showed that a rough coating over the front 10% of blchord resulted in about 70% of the performance degradacaused by full-chord roughness coverage. About 9% loss in psure ratio across the rotor near design mass flow was also repfor the rough coatings. Bammert and Woelk@3# also carried outmeasurements on a 3-stage axial compressor with smoothemery-grain roughened blades. They observed that the overaficiency reduced between 6% and 13% over the range of differoughness grades considered and there was a maximum reduof 30% in the overall pressure ratio.

From a numerical approach, Boyle@4# used a quasi-3D Navier–Stokes analysis to predict the change in turbine efficiency duchange in blade surface roughness and incidence. The efferoughness was determined using a mixing length turbulemodel of Cebeci and Chang@5#, in which the original mixinglength ~for a smooth blade! was augmented to account for th

Contributed by the International Gas Turbine Institute~IGTI! of THE AMERICANSOCIETY OF MECHANICAL ENGINEERSfor publication in the ASME JOURNAL OFTURBOMACHINERY. Paper presented at the International Gas TurbineAeroengine Congress and Exhibition, Vienna, Austria, June 13–17, 2004, Pape2004-GT-53619. Manuscript received by IGTI, October 1, 2003; final revisiMarch 1, 2004. IGTI Review Chair: A. J. Strazisar.

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aded 12 Nov 2009 to 138.250.83.153. Redistribution subject to ASME l

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roughness height. A similar method was employed by Suder e@2#. Although the numerical results yielded the correct trendperformance deterioration, the impact of surface roughness onperformance was underpredicted.

The issue of whether or not distributed surface roughness athree-dimensional~3D! separations, which contribute to perfomance deterioration, has not previously been investigated.conventional two-dimensional view that surface roughness tgers transition and promotes turbulence, which will suppress flreversal and hence two-dimensional separation, may not be acable to three-dimensional flows. Three-dimensional separadoes not need flow reversal as a condition for its occurre~Chang@6#!. However, boundary layer thickening, characterisof rough surfaces due to an increased skin-friction coefficiemay also increase the size of separations in three-dimensiflows under adverse pressure gradients. In this light, the influeof surface roughness on 3D separation in a compressor statothe consequent effect on stage performance, have been stuboth experimentally and numerically. These were carried outsingle-stage low-speed axial compressor. Tests performed incoil-flow visualization to examine the pattern of 3D separationthe suction surface and a 3-hole probe area traverse downstof the stator to measure losses and deviation. The effect of rouness on loading redistribution~shown using measurements maof surface static pressures! and on the measured stage charactistic is also presented. A simple model to simulate the effectroughness was incorporated into a 3D Navier–Stokes calculaand the results are compared with the experiments.

Experimental Faciltiy and ProcedureThe experiments were performed on a large-scale single-s

low-speed facility, the Deverson compressor, in the Whittle laratory of the University of Cambridge. A detailed descriptionthe rig arrangement can be found in Place@7# as well as in Bolger@8#. The stage tested consists of radially stacked modcontrolled-diffusion airfoils~CDA! with a rotor tip clearance ofabout 1.15% chord and a sealed stator hub. Preceding the staa row of inlet guide vanes~IGV! which produce the requiredamount of swirl into the rotor. Also incorporated are turbulengenerators in the freestream, upstream of the IGV, and devicethe hub and casing to create endwall boundary layers similar tembedded stage in a multistage compressor. The rig is equipwith an auxiliary fan that allows the mass flow rate to be var

ndr No.n,

004 by ASME OCTOBER 2004, Vol. 126 Õ 455

icense or copyright; see http://www.asme.org/terms/Terms_Use.cfm

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independently of the rotor speed. A brief summary of the stgeometric and design parameters at mid-height is given in Tab

The roughness height for the stators of the low-speed compsor rig was chosen by scaling roughness measurements obtfrom Rolls-Royce on a modern turbofan engine after a long peof airline operation. The center-line average roughness (kCLA) istypically about 60–80 micro-inches~1.53–2.03mm!. A roughnessscaling factor for the rig was obtained by matching the engReynolds number at take-off, based on the relative velocityroughness height, to that of the research rig. The corresponroughness value for the rig was calculated to be about 25mm,which from the Koch and Smith’s@9# correlation corresponds toan equivalent sand roughness of approximately 160mm. Artificialroughness in the form of distributed patches of sand roughnwas achieved using strips of ASTM150 emery paper. The rouness strip was cut into lengths covering 50% and 100% spanof width about 20% chord. Although in real engines the surfaroughness is usually not uniform, it was thought that simple tewith uniform roughness will be useful in exploring the signicance of surface roughness itself@10#.

A strip of emery paper secured on the stator blade using dosided tape increased the blade thickness by 0.3 mm, whicabout 3.5% increase in blade thickness at the hub and 2.2% acasing. This also resulted in a step at the edges of the striporder to separate any effect due to thickness from the effect duroughness, tests were performed by covering the leading epeak-suction region with smooth strips of thin cardboard of silar thickness to that of the emery paper. This configurationreferred to as a ‘‘stepped’’ blade row.

An area traverse was performed downstream of the statora pneumatic probe to assess the influence of roughness on pmance. The uncertainty in the yaw angle measurement wasmated to be60.6 deg. The uncertainty of total pressure w61.0% of dynamic head and the measurement of the dynahead was correct within65 Pa. The area traverses were carriout at four operating flow coefficients~f50.45, 0.51, 0.55, and0.57!. The performance was evaluated by calculating the maveraged exit total pressure rise coefficient, made nondimensby dynamic pressure based on the mid-height blade sp(1/2rUm

2 ).

Numerical ProcedureA numerical simulation of patch and full roughness on the bla

surfaces, similar to the experiment, is implemented with rouness modeled mainly in terms of its effect on skin-friction as was on turbulent mixing. Rough surfaces are known to deveconsiderably larger skin friction coefficients under turbulent flowhen compared to smooth surfaces. In addition, roughness uscauses the velocity gradient near the wall to be less steep anboundary layer thicker compared with hydraulically smooth sfaces~Schlichting @10# and White@11#!. The roughness effect istherefore modeled as a shift in the wall functions (u1 and y1).With average roughness height denoted ask, the velocity distribu-tion taking account of roughness can be written as

Table 1 Deverson compressor stage parameters

f DH0 /U2 Re(chord)0.51 0.45 2.73105

Rotor Stator

Profile CDA CDAChord ~m! 0.1215 0.1215s/c 0.6954 0.7192h/c 1.25 1.25Camber~deg.! 31.0 31.0Stagger~deg.! 35.4 34.4No. of blades 51 49Hub radius~m! 0.6096 0.6096Casing radius~m! 0.762 0.762

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DBsandgrain5A ln~110.3k1! (2)

and substituting for constantsA andB, (A50.4 andB55.24), Eq.~1! can be expressed in terms of the wall skin frictiotw /(1/2ru2) and the average roughness heightk as

u15S tw

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22.5 lnF110.3 ReS k

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ru2D 1/2G (3)

In Eq. ~3!, k15ku* /n has been replaced by Re(k/y)(tw /ru2)1/2

and Re5yu/n is the Reynolds number based on the perpendicudistancey from the wall.

The average roughness height is assumed to be uniformalso to cover both transitional and fully rough regimes. Equat~3! is solved iteratively to obtain the wall skin friction explicitly interms of Re for various values of (k/y), similar to the approach ofDenton@12# for a smooth wall. The model was incorporated inthe original code, which is a fully three-dimensional multi-staturbomachinery Reynolds-averaged Navier–Stokes solver of Dton @13#. The calculations are performed using a control volumformulation on an ‘‘H’’ type mesh. Shear stress is modeled usa thin shear approximation to the Navier–Stokes equation aneddy viscosity mixing length is used for turbulence modeling. Tturbulence model therefore enables the contribution of surfroughness to turbulent mixing to be taken care of by augmenthe originally specified mixing length for the smooth surfacethe average roughness height. Further detail of the modelingcedure can be found in Gbadebo@14#. The stage calculations wercarried out using a grid distribution of 413226363 in the pitch-wise, streamwise and spanwise directions respectively with a tof nine spanwise mesh points used in the rotor tip clearance sp

Results and Discussion

Performance of a Single Roughened Stator. Initial testswere carried out on asingle roughened stator with the roughnestrip located at 3 different parts of the blade; leading edgepeak-suction, around mid-chord and towards the trailing edThis was to establish on which part of the stator suction surfaand under which operating condition, is the flow most sensitiveroughness. A diagram showing the stator blade with the roughnstrip at different locations tested is presented in Fig. 1. It wfound that the performance at flow coefficients near the despoint ~f50.51!, is particularly sensitive to roughness over thleading edge to peak-suction region. This corresponds to confirationsa and c in Fig. 1, where the roughness strip covers bofull span and the first half of the blade from the hub.

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This effect can be seen in the contours of stage total presrise coefficients, measured by traversing behind the smooth band single roughened blade with full-span strip plotted in Fig~The traverse result for the half strip of roughness near leadedge is qualitatively the same as that of the full strip and ispresented.! As can be seen from Fig. 2, the roughness resultssignificant loss of total pressure rise notably in the hub corregion with a marked increase in the size of the separated regThe experiments with roughness patches near the mid-chordsition and rearward~near the trailing edge! ~configurationsb anddin Fig. 1! indicated conclusively that roughness in these regihad negligible effect and, for brevity, the results are not shoThe overall mass-averaged exit pressure rise coefficient was fo

Fig. 1 Schematic diagram of stator blade with roughness „a…full strip „leading edge to peak-suction …; „b… full strip „mid-chord …; „c… 50% span from hub „leading edge to peak-suction …;„d… full strip „near trailing edge …

Fig. 2 Contours of total pressure rise coefficient at the exit ofa smooth and single stator roughened around leading edge Õpeak-suction at design point, fÄ0.51 „contour interval Ä0.03…

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to drop by about 5% when the blade was operated at the deflow rate, with the roughness element element located aroundleading edge/peak-suction.

The radial profile of the exit flow angles at design point fdifferent locations of the roughness element is shown in Fig. 3is apparent from the figure that the deviation towards the hincreases considerably when the blade is roughened around psuction and is virtually insensitive to roughness at other locatioSurface and hubwall flow visualization at the design operatpoint of this test blade show separation on the suction surfacecorner for the smooth blade and for the roughened blade, FigWith roughness over the leading edge to peak-suction regiolarger 3D separation on the suction surface and hubwall is ap

Fig. 3 Influence of location of roughness strip on stator exitflow angles at design point, fÄ0.51

Fig. 4 Suction surface flow visualization on smooth androughened stator around leading edge Õpeak-suction at designpoint, fÄ0.51

OCTOBER 2004, Vol. 126 Õ 457

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ent and the increased size of the separated region is clearlycause of the extra loss and deviation when compared witsmooth blade.

The roughness element near the leading edge is at thesensitive location in the blade passage because the boundaryin this region is very thin. The ratio of average roughness heighthe boundary layer thickness~k/d! may be significant enough toinduce earlier transition, while at the same time introducing csiderable frictional drag into the flow. In the presence of the psage adverse pressure gradient this can lead to premature thiing of the boundary layer. The compressor stage is of 5reaction at mid-height and the requirement of the stator to remmuch of the swirl out of the upstream rotor implies that the stapressure rise across the stator is highest at the hub~Cumpsty@15#!.The combination of these factors is believed to provoke the la3D separation observed and consequent loss of performance.roughness downstream of the suction peak it is presumed tharoughness~chosen to model that measured on blades whichbeen in airline service! is too small to penetrate beyond the vicous sublayer, so the surface appears to be hydraulically sm

The single roughened blade gave a quick means to assesfects but the additional blockage caused by separations increin size by surface roughness was able to influence the behavineighboring passages, as presented in Gbadebo@14#. The in-creased blockage caused by increased separation on the susurface of the roughened blade causes the upstream flow tdiverted away from this blocked passage. This increases thedence onto the blades on one side and decreases it for those oother side. As a result, four or five succeeding passages onside of the single roughened blade also exhibited increased sration due to these incidence changes.

Smooth, Stepped, and Roughened Blade-Row PerformancFollowing the above observations, tests were carried out atdesign flow coefficient with all the stator blades in the row rougened with full-span strip around the leading edge~covering fromabout 5% chord on the pressure surface over to the peak-sucwhich is about 20% chord from the leading edge on the suctsurface!. The emery strip was carried around onto the presssurface to avoid blade-to-blade irregularities in the most sensregion of the flow. The pattern of flow visualization on the suctisurface of roughened and stepped~thickness but no roughness!blade-rows showed a larger separation region for the roughecase. The suction surface separation line for the roughened brow started at a distance of about 20% chord from the leadedge, extended diagonally from the hub towards the mid-spawind into a focus near the trailing edge like that on the sinroughened blade. A discussion of this type of pattern can be foin Gbadebo, Cumpsty, and Hynes@1#. The separation line for thestepped stator started at a distance of about 35% chord fromleading edge at the hub and terminated at the trailing edge at a25% span from the endwall, which closely resembles the paton the smooth blade.

Figure 5 compares contours of stage total pressure rise cocient for smooth and roughened blade rows at different operaflow coefficients. Similar to the observation for a single rougened stator, it is evident from the figure that the performancvery sensitive to roughness around the design point,f50.51, andvirtually insensitive to roughness at much higher flow coefficienThis may be because of the reduced overall static pressure rihigh flow coefficients. In addition, at high flow coefficient thflow approaches the blade at negative incidence so the stagnpoint is moved to the suction side of the leading edge and themay be less affected by the roughness because of the redsuction-peak. For the smooth blade-row, the wake around mspan at design point and at higher flow coefficients can be seebe comparatively thin and nearly two dimensional. The mheight wake momentum thickness for the roughened blade-rowthe design point, is about 40% higher than that of the smoblade-row.

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The roughness has a marked effect for all flow coefficients wsmall or positive incidence. However the biggest differencetween smooth and rough was close to the design incidencecause for this the roughness was sufficient to alter the flow patto have the large 3D separation that only occurred for the smoblade at lower flow rates.

Figure 6 shows the contours of stage pressure rise coefficfor the stepped blade-row at design point~f50.51!. By compar-ing this figure with the corresponding ones for smooth and rouened blade-rows, Fig. 5, it is clear that the thickness/step hnegligible contribution to wake thickening and virtually no effeon three-dimensional hub corner blockage. Consequently theof performance within the blade-row can be attributed to the sface roughness itself.

The radial distribution of pitchwise mass-averaged stagetotal pressure rise coefficient, axial velocity and swirl angleplotted for the smooth, stepped and roughened blade rows in F7, 8, and 9. Also presented in each case is the profile forpreliminary single-roughened blade, which can be seen to bedicative of the trend but not quite correct in magnitude. Againthickness/step formation seems to have negligible influence ondistributions of loss and axial velocity. From the pitchwisaveraged exit axial velocities, it is apparent that surface roughnover the leading edge and peak-suction significantly increasesloss, reduces the axial velocity and increases deviation fromhub to about 30% span.

Figure 10 compares the surface static pressure distributionsthe blades roughened between the leading edge/peak-suctionthat of the smooth blades.~The stepped blades showed the sadistribution as smooth blades almost within experimental scat!The comparison is at design operating point at 20%, 50%,80% span, respectively, for which stator incidence was aboutdeg,22.0 deg, and22.5 deg, respectively. There is evidenceloading redistribution caused by surface roughness in these dbutions; at all three spanwise locations, the influence of the rouness causes an overall lowering of static pressure on the preand suction surfaces of the entire blade-row with a net reducin the average static pressure rise. This is mainly because oextra blockage at the hub, which increases the axial velocity inmid-span and the upper half of the passage, as depicted in FiNear the hub~20% span! of the roughened blade row, the pressudistribution around the leading edge suggests an increase ineffective incidence onto the airfoil and an increased loading~i.e.,larger difference between the suction and pressure surfaces!. Al-though at 20% span the flow is separated, there is still static psure rise over the rear of the blade.

The total-to-total and total-to-static stage characteristics ploin Fig. 11 clearly show the degradation of stage performacaused by surface roughness, which is most apparent betweedesign operating point,f50.51, and stall. The characteristic fothe stepped blade-row are virtually identical to that of the smostage at all operating points except very close to the design pand are omitted for clarity. At high flow coefficients, corresponing to a negative incidence and reduced loading, the effecroughness seems to be insignificant, and the curves collapse

Numerical Results. The numerical ‘‘roughness’’ is applied tocover the leading edge to the peak suction of the airfoil, as forexperiments. Figure 12 shows the predicted streamlines onsuction surface for the smooth and roughened blades at deflow coefficient,f50.51. The smooth blade displays a small seprated region with a pattern very similar to the oil-flow patteobserved experimentally. However, a closer look at the compustreamlines in the trailing edge/casing region shows thatstreamlines turn more perpendicular to the casing but not inoil-flow pattern in Fig. 4. It is not clear which aspect of the flophysics, not captured by the CFD, is responsible for this.

For the roughened airfoil, the comparatively large separaregion agrees reasonably well with experiment. The separaline can be seen to emanate from a saddle point on the suc

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Fig. 5 Contours of stage total pressure rise coefficients for smooth and roughened blade-rows atdifferent flow coefficients. „Roughness from LE to peak-suction. …

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surface/endwall corner at a similar location to that in the oil flovisualization and winds into a focus near the trailing edge.

The predicted stator exit contours of total pressure riseshown in Fig. 13 for smooth and rough blades at design fl

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coefficient, f50.51. This shows a large increase in hub lossassociated with growth in the 3D separations induced by surroughness. The calculation also shows a significant wake thicking due to roughness when compared with the smooth bla

OCTOBER 2004, Vol. 126 Õ 459

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a

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However the predicted change in loss is not as high as measthe measured overall mass-averaged total pressure rise coeffireduced by about 5.4% with roughness while the calculated vreduced by about 2.4%. Table 2 compares the measured andculated values of the overall mass-averaged total pressurecoefficient at the design point.

Fig. 6 Contours of stage exit total pressure rise coefficient forstepped blade-row at design point, fÄ0.51. „Roughness fromLE to peak-suction. …

Fig. 7 Radial profiles of pitchwise mass-averaged stage totalpressure rise coefficients for smooth, stepped and roughenedblade-rows and single roughened blade at design point,fÄ0.51. „Roughness from LE to peak-suction. …

Fig. 8 Radial profiles of pitchwise area-averaged axial veloci-ties for smooth, stepped and roughened blade-rows togetherwith single roughened blade at design point, fÄ0.51. „Rough-ness from LE to peak-suction. …

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red:cientluecal-rise

Fig. 9 Radial profiles of pitchwise mass-averaged exit flowangles for smooth, stepped and roughened blade-rows andsingle roughened blade at design point, fÄ0.51. „Roughnessfrom LE to peak-suction. …

Fig. 10 Comparison of surface static pressure distribution atdifferent spanwise locations of smooth and roughened blade-rows at design point, fÄ0.51. „Roughness from LE to peak-suction. …

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The measured and predicted variation of the mass-averagetal pressure rise coefficient as a function of flow coefficientplotted in Fig. 14 for smooth and roughened blades. The measments are for single roughened blade as well as for the enroughened blade-row. The calculation with roughness can beto capture the trend of measurements although the effect is un

Fig. 11 Comparison of total-to-total and total-to-static stagepressure rise characteristics for smooth and roughened blade-rows. „Roughness from LE to peak-suction. …

Fig. 12 Numerical suction surface streamlines for smooth androughened stator at design point, fÄ0.51

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estimated, especially below the design point~f50.51!. As can beseen in Fig. 14, the experimental value of the average total psure rise coefficient for the single roughened blade atf50.45, ishigher than that of the smooth blade. At this flow coefficient, tflow for the smooth blade has a large separated region androughness in the single passage may have other effects on thein this near-stall condition such that it is possible it makes tseparation smaller. The discrepancy between calculated and msured pressure rise as stall is approached is perhaps to be expbecause of the increased difficulty of modeling the flow in thregime.

Table 2 Comparison of measured and calculated overallmass-averaged total pressure rise coefficient for smooth androughened blade-rows at design point, fÄ0.51

Smooth Rough

Measured 0.842 0.796Calculated 0.841 0.821

Fig. 13 Predicted contours of exit total pressure rise coeffi-cients for smooth and roughened stator blade at design point,fÄ0.51. „Roughness from LE to peak suction. …

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ConclusionsThe following conclusions can be drawn from this study:

~1! The experiments described in this paper have shown thatface roughness, typical of that which is likely to form durinengine operating lifetime, can lead to a significant reductin performance due to its effect on 3D separation.

~2! For the stator used in these experiments, roughness induclarge hub corner separation at the design flow coefficient, ging high loss, increased blockage and deviation. The portof the blade affected extended from the hub to about 3span.

~3! When tested as part of a stage, the 3D separation induceroughness caused a significant loss in stage stagnation psure rise over a wide range of flow.

~4! The blockage induced by the separation is responsible fosignificant radial movement of flow, with a consequent radredistribution of loading and change of effective incidence

~5! In contrast to the strong effect on performance when appbetween the leading edge and suction peak, roughness apdownstream of suction peak had negligible effect.

~6! A simple model for the effect of roughness on wall shestress has been developed, suitable for use with RANS calation methods. Calculations performed with this roughnemodel show that the effects of patch roughness on bladefaces are reasonably well modelled.

~7! The predicted streamline pattern on the suction surface anthe hub wall show that the increase in the size of theseparation induced by roughness is reasonably well captuas are the overall results for pressure rise. The extra lossesthe increase in thickness of the boundary layer and separregion are underpredicted.

~8! Although only the stator blades were roughened in this stuit is also appropriate to carry out experiments on roughenrotor blades as well as on both stators and endwalls. Tperhaps can be considered as a future work.

AcknowledgmentsThis work was supported by Rolls-Royce Plc, the Applied R

search Program of the Ministry of Defense, the DepartmentTrade and Industry Aeronautic Research Program and QineLtd. The authors are very grateful for this and for their permissto publish. In particular, the many fruitful discussions with DJohn Bolger of Rolls-Royce Plc have been appreciated. The

Fig. 14 Comparison of measured and calculated mass-averaged stage exit total pressure rise coefficients at differentoperating points for smooth and roughened stator blade.„Roughness from LE to peak suction. …

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thors would also like to thank Professor J. D. Denton of tWhittle Laboratory, University of Cambridge for the use of hCFD code, into which the roughness model was incorporated.opinions expressed here are those of the authors and not neceily those of Rolls-Royce plc or any other organization.

Nomenclature

c 5 chordCp 5 pressure coefficient (P2P% 02)/(1/2rV2

2)h 5 blade height~span!, height from surfacek 5 roughness heighti 5 incidence

LE 5 leading edgeP 5 pressure

PS 5 pressure surface/sider 5 radius

Re 5 Reynolds numbers 5 blade pitch

SS 5 suction surface/sidet 5 blade thicknessu 5 local velocityU 5 blade speedV 5 absolute velocityx 5 axial distancey 5 perpendicular distance

Greek Symbols

a 5 absolute flow angleb 5 blade~metal! angled 5 boundary layer thicknessD 5 change across the stagef 5 flow coefficient (Vx/U)n 5 kinematic viscosityr 5 density

tw 5 wall shear stress

Subscripts

0 5 stagnation1 5 rotor inlet2 5 stator inlet3 5 stator exit

abs 5 absolutecalc 5 calculated values

CLA 5 center-line averageexp 5 experiment

mid,m 5 mid-heighth 5 hubs 5 staticx 5 axial

Superscript

% 5 passage averaged

References@1# Gbadebo, S. A., Cumpsty, N. A., and Hynes, T. P., 2004, Three-dimensi

Separations in Axial Compressors, ASME Paper GT-2004-53617.@2# Suder, K. L., Chima, R. V., Strazisar, A. J., and Roberts, W. B., 1994, Effec

Adding Roughness and Thickness to a Transonic Axial Compressor RASME Paper 94-GT-339.

@3# Bammert, K., and Woelk, G. U., 1980, ‘‘Influence of the Blading SurfaRoughness on the Aerodynamic Behavior and Characteristic of an Axial Cpressor,’’ ASME J. Eng. Gas Turbines Power,102, pp. 579–583.

@4# Boyle, R. J., 1994, ‘‘Prediction of Surface Roughness and Incidence EffectTurbine Performance,’’ ASME J. Turbomach.,116, pp. 745–751.

@5# Cebeci, T., and Chang, K. C., 1978, ‘‘Calculation of Incompressible RouWall Boundary-Layer Flows,’’ AIAA J.,16, pp. 730–735.

@6# Chang, P. K., 1970,Separation of Flow, Interdisciplinary and Advanced Topicin Science and Engineering, Vol. 3, Pergamon Press.

@7# Place, J. M. M., 1997, ‘‘Three-Dimensional Flow in Axial CompressorsPh.D. thesis, University of Cambridge, United Kingdom.

Transactions of the ASME

icense or copyright; see http://www.asme.org/terms/Terms_Use.cfm

w

m-

rs,’’

Downlo

@8# Bolger, J. J., 1999, ‘‘Three-Dimensional Design of Compressor Blades,’’ Phthesis, University of Cambridge, United Kingdom.

@9# Koch, C. C., and Smith, L. H., 1976, ‘‘Loss Sources and Magnitudes in AxFlow Compressors,’’ ASME J. Eng. Gas Turbines Power,98, pp. 411–424.

@10# Schlichting, H., 1979,Boundary Layer Theory, McGraw–Hill, New York.@11# White, F. M., 1991,Viscous Fluid Flow, McGraw–Hill, New York.@12# Denton, J. D., 1992, ‘‘Calculation of Three-Dimensional Viscous Flo

Journal of Turbomachinery

aded 12 Nov 2009 to 138.250.83.153. Redistribution subject to ASME l

.D.

ial

s

Through Multistage Turbomachines,’’ ASME J. Turbomach.,114, pp. 18–26.@13# Denton, J. D., 1999, ‘‘Multistage Turbomachinery Flow Calculation Progra

MULTIP,’’ Whittle Laboratory, University of Cambridge, United Kingdom.@14# Gbadebo, S. A., 2003, ‘‘Three-Dimensional Separations in Compresso

Ph.D. thesis, University of Cambridge, United Kingdom.@15# Cumpsty, N. A., 1989,Compressor Aerodynamics, Longman Scientific and

Technical.

OCTOBER 2004, Vol. 126 Õ 463

icense or copyright; see http://www.asme.org/terms/Terms_Use.cfm