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IGTI/ASME TURBO EXPO 2002June 2002 Amsterdam The Netherlands

AERODYNAMIC CHARACTER OF PARTIAL SQUEALER TIPARRANGEMENTS

IN AN AXIAL FLOW TURBINE

Part : 2 Detailed Aerodynamic Field Modifications via Three Dimensional Viscous Flow SimulationsAround the Baseline Tip

Levent Kavurmacioglu1, Debashis Dey2 and Cengiz Camci3

Turbomachinery Heat Transfer LaboratoryDepartment of Aerospace Engineering

The Pennsylvania State University

223 Hammond Building, University Park, PA 16802

ABSTRACT

This paper deals with the viscous flow simulations of thecomplex tip leakage flow-field existing in the Axial FlowTurbine Facility (AFTRF). Special attention in this part is paidto the 3D structure of the tip leakage flow mechanisms in abaseline tip configuration with no desensitization. Thebaseline tip flow mechanisms that are already explained froma set of aerodynamic measurements in Part-1 of this paper arevisualized in a detailed manner. Although the experimentalstudy presented in Part-1 provides much insight into thephysical understanding of the tip region aerodynamics, thereare still many areas of the flow-field in which experiments areextremely difficult to perform. Fine details of the entranceflow near the pressure side where the tip leakage jet starts toform, the leakage jet formation between the pressure side andthe suction side, the re-circulatory flow zone very near thepressure side corner in the tip gap zone, the interaction area ofthe tip vortex with the conventional passage vortex system, theinfluence of the relative motion of the outer casing andleakage flow reversal can all be visualized in great detail byusing computational tools solving the three-dimensionalReynolds Averaged Navier-Stokes Equations. The currentstudy uses a two-equation method for the representation of theturbulent flow field. After a brief grid independencydiscussion, baseline tip predictions are discussed in detail. Thecurrent computational results are interpreted with the help ofexperimental aerodynamic measurements that are presented inPart-1 of this paper. This part of the paper dealing withdetailed baseline predictions forms a useful basis for thevisualizations that are presented for partial squealer tipconfigurations in Part-3.

NOMENCLATURE

c Rotor axial chord length at tip = 0.129 mBS100 Baseline tip configuration with no tip treatment,

full cover , t/h=1.03 % and s=0 mm.

BS33 Baseline tip configuration with no tip treatment,

full cover , t/h=0.33 % and s=0 mm.Cp Static pressure coefficient

C p p Wp ref inlet= −( ) / .0 5 2ρε Turbulent dissipation rateh Rotor blade height = 0.123 mk Turbulent kinetic energy k u ui i= / 2κ Von Karman constantpo Total pressurepatm Ambient pressure (also pref)pin Inlet total pressurep Static pressurePS, SS Pressure side, suction sideRe Reynolds numberρ Densityr/h Non-dimensional radial position measured from hub surface (also y/h in contour plots)t Rotor tip clearance height

on the part without a squealer rim (baseline)TE Trailing edgeUi Mean velocity componentsUm Mean wheel speed at rotor mid-spanτmax blade maximum thicknessν Absolute velocityW Relative velocity with respect to turbine rotorx,y,z Coordinate system for the numerical analysis (axial, tangential, radial direction in the linear cascade arrangement for computations)X,Y,Z,T Flow visualization planes used for numerical laser

sheet visualizations (see Figure 7)z/t distance between the plane of visualization and the

tip platform (see Figures 6)

INTRODUCTION

Tip Clearance Flow: The spacing required between thetips of blades and the stationary casing of an axial flow turbineis a significant source of inefficiency. The leakage flowinduced by the pressure differential between the pressure sideand suction side of a rotor tip section usually rolls into a

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1 Visiting Professor2 Research Assistant3 Professor of Aerospace Engineering , c-camci@psu.edu1

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streamwise vortical structure. Total pressure losses of thispassage flow structure measured at the exit of a turbine stageare directly proportional with the tip gap distance. Theleakage flow mixing with the rotor passage flow causes totalpressure loss and significantly reduces turbine stageefficiency. Tip leakage related losses might account for as much as athird of the total losses in a stage. Because of the extremelysmall length scales involved and highly complex 3D, viscous,unsteady, turbulent flow structures, tip gap flows have alwaysbeen challenging to turbomachinery researchers. Turbine tipgap leakage fluid passes through tip gap region withoutexperiencing a significant expansion and cooling that istypical in the core section of the turbine passage. The leakagefluid with relatively high total temperature flowing throughturbine tip gaps can create important turbine durability andendurance problems. Although there are many past experimental studies aimedat understanding the physical reasons governing the tip vortexflow and heat transfer problem, there is still a need forreasonably accurate three dimensional viscous flowsimulations in this region. A computational visualizationsystem used in the tip vortex problem is attractive because ofits ability to visualize local flow details that are extremelydifficult to measure in inherently tight and 3D tip gap region. Flow Visualizations via Computations: A numericalsimulation of compressible flow near a turbine tip gap regionin a linear cascade arrangement was presented by Liu andBozzola [1]. A significant reduction of gap exit leakage massflux rate for the case of a moving outer casing was presentedwhen compared to a stationery outer wall. Basson andLakshminarayana [2] implemented an embedded gridgeneration method into a three dimensional pressure basedsemi-implicit scheme for the prediction of tip clearance flows.Sell, Treiber, Casciaro and Gyarmathy [3] presentedcomputational tip aerodynamics results from a linear turbinecascade with an exit Mach number of 0.5. They reported thatthe computational simulations agree well with theirmeasurements. The effect of tip clearance height and outercasing relative motion in axial flow turbines were investigatedby Tallman and Lakshminarayana [4,5] . They reported thatthe structure of aerothermal losses in the turbine passagechange dramatically when the outer casing motion wasincorporated into the analysis. Ameri et al. [6]computationally investigated the effect of tip recess on tip heattransfer and efficiency. They found that the numericalprediction of the effect of the casing recess on blade and tipheat transfer and efficiency was reliable. Bunker, Bailey and Ameri [7] obtained tip heat transfer andpressure measurements in a three bladed linear cascadesimulating the first stage blade geometry on a large powergenerating turbine with flat and smooth tip surfaces. Theynoticed a central “sweet spot” of low heat transfer extendinginto the mid chord region and toward the suction side.Measured surface heat transfer coefficients increased 10-20 %when free stream turbulence intensity level was increasedfrom 5 to 9 %. When the sharp tip edge was rounded, the tipheat transfer increased by about 10 %, presumably due tohigher allowed tip leakage flow. Bunker and Ameri [8] alsopublished the results of a study dealing with the numericalprediction of the tip gap heat transfer problem defined in [7].The casing upstream of the blade was recessed. The numericalresults with a radiused-edge blade agreed better with theexperimental data. They attributed this feature to the absenceof a separation bubble in the gap region. Lin, Shih, Chyu andBunker [9] studied the effects of gap leakage on fluid flow in acontoured turbine nozzle guide vane in a computational study.A numerical analysis of tip vortex flow in an annular turbine

cascade configuration was performed by Han, Han, Jin andGoldstein [10] Current objectives: The present investigation deals withthe aerodynamic visualization of tip leakage flow existing inthe baseline tip configuration of the (AFTRF) Thecomputational visualizations obtained from three dimensionalturbulent flow simulations using a general purpose RANSsolver are interpreted using recent aerodynamic fieldmeasurements presented in Part-1. The details of the turbinefacility and the recent measurements in a naseline tipconfiguration are presented in Lakshminarayana, Camci,Halliwell & Zaccaria [11] and Dey, Kavurmacioglu & Camci[12], respectively. The comparisons of the numericallyvisualized tip gap flow field to measured aerodynamic field inthe turbine suggest that RANS simulations can be extremelyeffective in explaining local three dimensional flow fielddetails in turbine flow zones in which aerodynamicmeasurements are extremely difficult to perform. Numericallygenerated “surface oil flow visualizations” on the tip surfaceand numerically generated “vortical flow details” on user

Figure 1, 3D computational grid for the AFTRF turbinerotor flow simulations

Figure 2, Grid structure near the baseline tiptip configuration

BASELINE TIPIN AFTRF

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(4)

(5)

defined planes can be effectively used to discuss local tip flowphysics. The “vortical flow details” in user-defined planes arenumerical equivalent of “laser sheet visualizations” frequentlyused in wind tunnel studies. The study clearly shows that theturbine tip gap region includes many different leakage flowregimes depending upon the effective tip clearance, localloading conditions and the rotational speed of the rotor.

NUMERICAL ANALYSIS

Governing Equations: The numerical simulations of thesteady-state 3D flow field inside the turbine rotor passage withtip clearance are obtained by solving the three dimensionaland incompressible Reynolds Averaged Navier-Stokesequations. A 3D linear cascade equivalent of the annularturbine blade passage is used as shown in Figure 1. Thecontinuity equation and momentum equations in this modelare :

Ui i, = 0 , (1)

and ρ µUU

x

p

x

U

x x

R

xj

i

j i

i

j j

i j

j

∂∂

= − ∂∂

+ ∂∂ ∂

+∂∂

2 (2)

where jiij uuR ρ−= are the Reynolds Stresses. The Reynoldsstresses are modeled by using the Boussinesq hypothesis.

R u u k

Ux

U

xij i j ij ti

j

j

i

= − = − + ∂∂

+∂∂

ρ ρ δ µ2

3 (3)

For two-equation models, the turbulent viscosity is related toturbulent kinetic energy k u ui i= / 2 and the dissipation rate εas

µ ρ εµt C k= 2/ . The turbulent kinetic energy equation is asfollows,

ρ µ µ µ σ ρεUkx

U

xUx

U

x xkxi

it

j

i

i

j

j

i it k

i

∂∂

=∂∂

+ ∂∂

∂∂

+ ∂∂

+ ∂∂

−( ) .

The dissipation rate equation is,

ρ ε ε µ ε

µ µ σ ε

ε ε

ε

Ux

Ck

U

xUx

U

xC

k

x x

ii

tj

i

i

j

j

i

it

i

∂∂

=∂∂

+ ∂∂

∂∂

− + ↵

+ ∂∂

+ ∂∂

1 2

2

a ( )

where

σ σε ε εk C C, , . , . , .= = = =1 1 3 1 44 1 921 2

are empirical constants. Near Wall Modeling: The most widely utilized wallfunctions based on Launder and Spalding [13] are used for thenear wall treatment. The law-of-the-wall for mean velocity is,

U C kLn Eyp p

wp

µ

τ ρ κ

1 4 1 21

/ /

/= ( )* (6)

where y C k yp p p

* = ρ µµ1 4 1 2/ / / and (yp, kp) are the normal

distance from wall to cell center and turbulent kinetic energyat wall-adjacent cell, respectively. The law-of-the-wall formean velocity is based on wall unit y* instead of y+ = ρuτy/µsince these are approximately equal to each other inequilibrium turbulent boundary layers.

Method of Solution: The numerical solutions of equations1 through 5 with proper boundary conditions were carried outby using a finite volume technique based on Fluent 5.5.QUICK discretization scheme was preferred for improvedaccuracy. SIMPLEC algorithm was selected for the pressure-velocity coupling in order to improve convergence for such acomplicated turbulent flow. A multi-grid scheme was used tosolve the discretized equations in order to accelerate theconvergence of the solver. Boundary Conditions: All of the computations areperformed for Re=291,000 that are based on axial chordlength at the tip diameter and mass averaged relative inletvelocity to the rotor passage in the turbine facility. Thespecific relative velocities from the velocity triangles of theAFTRF rotor described in Part-1 of this paper are used. Figure4 shows the measured and design values of the axial,tangential and radial velocity components measured justupstream of the turbine rotor in AFTRF. The velocitymagnitude and boundary layer profiles at the “inlet section”

Figure 3 Tip leakage visualization planes(cross-stream direction & blade height)

-0.50 0.00 0.50 1.00 1.50 2.00Velocity (Normalized by Um)

0.0

0.2

0.4

0.6

0.8

1.0

r/h

o

Figure 4, Turbine rotor inlet flow conditions(measured and design values for AFTRF)

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of the three-dimensional computational domain shown inFigure 1 are specified in such a way that the calculated flowdirection and magnitude “ just upstream of the turbine rotorreasonably represents the tip velocity triangles of the rotor inAFTRF. The values of k and ε that are imposed at the inletboundary are based on measured turbulence intensity

Tu k U∞ ∞= 2 3/ / and length scale defined as L C k p= µ ε3 2/ / .

The measured values of Tu∞ and L from the AFTRF are used. Velocities, turbulent kinetic energy and the dissipation rateare all set to zero on solid boundaries except outer casing. Thetangential velocity of outer casing that is used for thesimulation of casing relative motion is set to a constant. Therelative velocity of the outer casing in tangential direction iscomputed from the turbine rotational speed (N=1320 rpm) atthe outer casing diameter (D=0.914 m). The outlet boundary is set at a sufficient distance from thetrailing edge to ensure that there is no influence of the outletboundary on the flow structure inside the domain. Thestreamwise gradients of all variables are set to zero for outletboundary conditions. The steady mean flow through an axialturbomachinery blade row can be modeled as periodic in thecircumferential direction. Figure 1 shows the periodicboundaries of the domain in circumferential direction in threedimensional space. Grid Structure: The grid structure shown in Figures 1 and2 was generated using a grid-generating program known asGAMBIT. Two different block structured grids that have130x65x88 points (fine mesh) and 105x51x74 points (mediummesh) in axial, pitchwise and spanwise directions weregenerated after initial experiments with a relatively coarsergrid. The grid was clustered near the leading, trailing edgesand near the tip region when squealer rims were utilized (Part-3). Grid spacing along the spanwise direction was set to obtainan adequate y+ value near the hub, blade tip surface andcasing. The flow field results obtained from the medium meshand fine mesh were almost identical at the blade mid spanlocation. Figure 2 shows a typical grid structure used for thetip region without a partial squealer rim. 75x65x26 and50x51x26 grid points were used for the fine mesh and medium

mesh inside the tip region respectively. The numerical resultswere displayed on planes that are almost normal to the turbineblade. The plane definitions in the computational domain aredefined in Figure 3.

RESULTS FROM THEBASELINE TIP CONFIGURATION

Static Pressure Field on the Baseline Tip Platform:Figure 5 shows the static pressure distribution on the baselinetip platforms BS100 and BS33 without any squealer rims. Thenon-dimensional tip gap for BS100 is t/h=1.03 %. The tip gapfor BS33 is one third of that of BS100. BS 100 forms thelargest tip gap studied in this investigation. BS33 is theminimum tip gap used for a comparative study. The Cpdistribution for BS100 shows a (red-yellow) “high pressurezone” in the first 20 % chord distance measured from theleading edge. Between 20 and 35 % chord distance, a greenintermediate pressure zone appears just before the portion ofthe blade where there is a significant amount of leakage flowfrom the pressure side to the suction side of the blade. Thedark blue Cp zone marks the “dominant leakage zone” inwhich most of the fluid leaking from the pressure side tosuction side is contained (blue zone). The last 20 % chord ofthe blade is dominated by a “relatively low leakage zone” asmarked by the green zone in BS100. The insets in Figure 5show the Cp line distribution on the suction side and pressureside of the tip platform. The free stream velocities on both thepressure side and suction side of the blade reach to almostidentical levels resulting in very similar chordwise Cpdistributions on both sides of the blade in the last 20 % chord. BS33 presented in Figure 5 shows the spread of the red-yellow “high pressure” zone up to the first 40 % chordwisedistance from the leading edge. Since the tip gap is one thirdof that of BS100, the low momentum fluid contained in thisarea is not expected to generate a significant leakage flow intothe suction side. Relatively low fluid velocities are expected inthis zone. The static pressure level indicated by green after thefirst 40 % chord is not as low as the case BS100. A reduced

Figure 5, Static pressure distribution on the tip surface of the blade (BASELINE TIP-full cover)

BS100t/h=1.03%

BS33t/h=0.33%Cp

0.0 0.2 0.4 0.6 0.8 1.0x/Ca

-12

-10-8

-6

-4-2

02

Cp

0.0 0.2 0.4 0.6 0.8 1.0x/Ca

-12

-10-8

-6

-4-2

02

Cp

high pressurezone up to20 % c

intermediatepressurezone (green)

significantleakage

PS and SSpressuresreaches thesame level

high pressure zonespreads into higherchordwise positions

reducedleakage

PS and SSpressuresreaches thesame level

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qqq

Figure 6, Velocity vectors at various planes in the tip gap (BASELINE TIP - full cover)

BS100 t/h=1.03 % z/t=1/3 lower plane

Tip vortexboundary

BS100 t/h=1.03 % z/t=5/6 higher plane

Near PS corner, velocitymagnitudes are reducedwhen compared to z/t=1/3

Flow is slightlyturned towardspressure side inthe higher plane

BS33 t/h=0.33 % z/t=1/3 lower plane

Leakage flow isreversed back intoPS

An extremelyweakened tipvortex neartheSS corner

Start of aweak tip vortex

I

J

BS33 t/h=0.33 % z/t=5/6 higher plane

Leakage flow isreversed back intoPS

leakageflow is notclearly visible

78 m/s

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leakage consistent with this elevated pressure region (green) isexpected in BS33. The narrow baseline gap also shows agradual increase in Cp in the last 20 % chord distance near thetrailing edge. The insets in Figure 5 clearly show that thepressure differential between the suction side and pressureside is minimal in this zone. Velocity Field in Planes Parallel to Baseline TipSurface: Figure 6 shows the velocity vectors in two selectedplanes parallel to the blade tip platform. z/t=1/3 “lower plane”plane contains the velocity vectors near the tip platformmainly dominated by the pressure driven flow. z/t=5/6 “higherplane” shows the velocity vectors in a plane very close to theouter casing that is inducing a significant shear effect on theleakage flow in the gap. For the baseline case BS100 thegeneral trends in terms of the velocity magnitude and directionare similar in the lower plane and higher plane. Near the bladetip platform, most of the flow originating near the pressureside corner tends to pass to the suction side. The strongestleakage velocities are observed as orange-red vectors near thepressure side corner, after 40 % chord distance from theleading edge. The fluid particles from the passage accelerateinto the tip gap. The leakage flow vectors in the last 20 %chord are not significant in the trailing edge wedge zone.Although the velocity magnitudes are not small in this zone,the velocity direction is in blade camber-line direction and thisflow does not actively participate in the formation of the lossgenerating vortical system termed as tip vortex in the passage.When one moves to higher plane near the outer casing, aqualitatively similar flow picture is evident This outer casinginfluence in general works against the leakage flow in the tipgap. The upper right figure in Figure 6 clearly shows the slightturning of the velocity vectors towards the pressure side. Thisturning is less severe in locations where the pressuredifference between the pressure side and the suction side isstrong. The turning of the vectors because of the outer casinginfluence is more significant in regions where the drivingpressure difference is minimal between the PS and SS. Theleading edge and the last 20 % chord of the blade significantturning of the flow in the upper plane is apparent. The lower left and right frames in Figure 6 show thevelocity vectors when the tip gap is small (t/h=0.33%). Themost apparent observation is the dramatic influence of theouter casing motion that is felt equally in both lowervisualization plane and upper plane because of the tightclearance. When compared to BS100, the velocity vectors inthe planes of the narrow gap termed BS33, there is at least 20 o

to 30 o directional change towards the pressure side (a counterclockwise turn). When the leakage flows form in the narrowgap, the outer casing has a tremendous ability to pull the fluidlayers in a direction opposite to the typical leakage direction.It is interesting to note that the high pressure zone indicated bya red-yellow color in Figure 5 contains an extremely lowmomentum fluid in the first 20 % of the chord length. Theleakage flow in this region is from the suction side to pressureside at a very low velocity. The suction side of the blade doesnot contribute to a strong tip vortex formation. The boundaryIJ for the lower plane in BS33 marks the location where theleakage to the suction side is initiated. Some of the fluidentering from the suction side may travel inside the tip gap fora while before it joins the weak tip vortex formation at about25 % chord distance just before point J. Near the trailing edge, the leakage direction is clearlyreversed. Because of the extremely narrow tip gap, in thetrailing edge region where there is almost no leakage potentialfor leakage, the tip gap flow is severely turned back into thepressure side of the channel via turbulent shear action. Acomparison of BS100 and BS 33 shows a dramatic weakeningof the tip vortex by just designing the tip gap in an extremely

tight manner. Although not practical for daily turbineoperation, BS33 forms a baseline case for comparativepurposes in this study. It is expected that when the tightclearance of BS33 is used only in a very narrow region on topof a partial squealer rim, similar flow physics (outer casingshear effect) should contribute to the de-sensitization process. Recirculatory Tip Flow Patterns in Cross-stream Planes:Figure 7 shows numerically generated flow visualizationsinside planes (X,Y,Z and T) defined by the cross streamdirection and radial direction. The visualization weregenerated by drawing pathlines using the velocity componentsinside the visualization planes. This type of numericalvisualization is equivalent to smoke flow visualizationsperformed in laser sheets of visible light in wind tunnels. Aclear leakage flow from the pressure side to suction side isapparent for the baseline gap BS100 at plane X (0.27 % c).The outer casing effect in this zone is not detectable. Most ofthe fluid leaking in this zone approaches the pressure sidecorner in a radially outward direction.. An extremely smallseparation bubble is expected near the pressure side corner. Inplane Y (0.59 % c), Leakage flow character is the same as X,however, the tip vortex on the suction side starts growing at afaster rate. Plane Z (0.77 % c) is interesting because of thestart of a major directional change of the velocity vectorstrying to turn into the pressure side. The leakage flowsuddenly looses its driving pressure differential in the last 20-25 % of the trailing edge as shown in the Cp distributions ofFigure 5. The turbulent shear action in this region startspulling some of the tip gap fluid back to the pressure side inregion M. A counter clockwise vorticity is induced near thepressure side of the gap. In addition to some weak leakage tothe suction side, a highly circulatory bubble (M) forms in thegap. In plane T that is located in the last 10 % of the chord,this flow reversal process is complete. A full reversal of theleakage flow from the suction side to pressure side isobserved. Some of the fluid trapped inside the tip vortexstructure near the suction side (N) can go back to the tip gapregion, eventually crossing to the pressure side of the passage. The right hand side column in Figure 7 shows thepathlines inside the visualization planes for the small tip gaptermed as BS33, t/h=0.33 %. In plane X, although the gap isextremely tight, a weak leakage originates from the pressureside to suction side. The tip vortex keeps growing extremelyslowly compared to BS100 as one moves to the trailing edge.The cross section of the leakage vortex near the suction sideis much smaller than the case for BS100. The leakage flow iscompletely reversed in plane Z showing the strongviscous/turbulent shear effect imposed by the outer casing in azone where the pressure differential between the pressure sideand suction side starts to diminish. If the visualization plane Zfor BS100 is examined, it is noticed that only a partial reversalto pressure side is apparent. The viscous/turbulent shearingeffect of the outer casing starts dominating at a much fasterrate when the clearance is tight. There is a remnant of the original counter clockwise rotating“weak” tip vortex (formed previously), near the suction sidecorner in plane Z . In plane T, the tip gap flow is completelyreversed from the suction side to pressure side. At thislocation very near the trailing edge, the original “weak” tipvortex is not visible anymore. A slight curvature of thepathlines near the suction side corner is all that is visible.Figure 7 clearly demonstrates the de-sensitization of a large tipvortex area that may contain a tremendous momentum deficitand energy loss in the turbine passage by just reducing the tipgap space. Leakage Flow Patterns in Planes Parallel to TipSurface: Figure 8 shows the pathlines for tip gap flows in twodifferent planes (z/t=1/3 and 5/6) for the baseline cases of

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Figure 7, Leakage flow patterns in the tip gap spaceinside cross stream planes(BASELINE TIP, full cover)

BS100t/h=1.03 %

BS33t/h=0.33 %

PLANE T = 0.91.cComplete leakage flow reversal

STRONG tip vortexforming

NSome of the fluidtrapped inside thetip vortex may goback to the tipgap (eventually tocross to PS

PLANE Y = 0.59.c

PLANE X = 0.27.c

PLANE Z = 0.77.c

leakage flow starts forming

CCWRe-circulation

A small tip vortex fromUpstream leakage paths

WEAK tip vortexforming

M

Viscous/turbulent shear from the outer casing motionstarts pulling the tip gap fluid back to PS

A WEAK leakage flow starts forming

PLANE T = 0.91.c

leakage reversal topressure side

leakage reversal topressure side

leakage reversal topressure side

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BS100 t/h=1.03 % z/t=1/3 gap lower plane

BS33 t/h=0.33 % z/t=1/3 gap lower plane

Figure 8, Leakage flow patterns in planes parallel to the tip surface, (BASELINE TIP, full cover)

BS100 t/h=1.03 % z/t=5/6 higher plane

P

S

boundaryof tip vortex

R

BS33 t/h=0.33 % z/t=5/6 higher plane

U

TT

U1

U2

boundaryof theweaktip vortex

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BS100 and BS33. The fluid particles entering the tip gap spaceon the suction side near the leading edge follow a path eithervery close to the blade boundary near the suction side (P) orin the middle section (R) of the leading edge before thelocation X=0.27.c. The leakage paths for the particlesoriginating from the pressure side corner are well defined. Theparticles tend to form a clear boundary for the tip vortex in thepassage (S). The pathlines are only slightly different in thehigher plane at z/t=5/6 (upper-left frame) because of the outercasing pulling effect via viscous/turbulent shear in a directionopposite to a typical leakage direction. The pathlines in thefirst 1/3 of the blade slightly turn towards the pressure side inthe higher plane. When the tip gap is small, a leading edge and trailing edgemodification of leakage flows occur due to the outer casemotion in regions where driving pressure differentials aresmall. In both the lower and higher visualization plane inFigure 8, the fluid from the suction side crosses the gap in adirection towards the pressure side near the leading edge(T) and trailing edge (U). Some of the fluid particles near thesuction side corner enters the tip gap space only to leave itafter turning back to suction side. They usually mix with theweak tip vortex forming near the suction side corner. Figure

8 shows that the outer boundaries of the tip leakage vortexfor BS 33 is much smaller than that of BS100 that has threetimes the tip gap height. The weak tip vortex for this casesuddenly turns into pressure side of the channel (U1). Theleakage flow reversal shown in the vertical visualizationplanes Z and T in Figure 7 may form a secondary reversedleakage vortex (U2) discharging into the pressure side of theblade near the trailing edge. Because of the extremely narrow tip gap in BS33, in thetrailing edge region where there is almost no potential forleakage; the tip gap flow is turned back into the pressure sideof the channel via viscous/turbulent shear action. Acomparison of BS100 and BS 33 shows the effectiveweakening of the tip vortex by just designing the tip gap in anextremely tight manner. Although not practical for actualturbine operation, BS33 forms a baseline case for comparativepurposes in this study. It is expected that when the tightclearance of BS33 is used only in a very narrow region ontop of a partial squealer rim, similar flow physics shouldcontribute to the success of the de-sensitization process.Partial squealer tip visualizations are provided in Part-3 of thispaper.

CONCLUSIONS

3D viscous flow simulations of the complex tip leakageflow-field existing in the Axial Flow Turbine Facility(AFTRF) are presented for the baseline tip configuration.Although the experimental study presented in Part-1 providesmuch insight into the physical understanding of the tip regionaerodynamics, there are still many areas of the flow-field inwhich experiments are extremely difficult to perform. The leakage flow patterns visualized on the baseline tipresult in a stage exit total pressure field that is highlycomparable to the measurements presented in Part-1. Moredetails on this comparison is provided in Part-3. Fine details of the entrance flow near the pressure sidecorner where the tip leakage jet starts to form, the leakage jetformation between the pressure side and the suction side, there-circulatory flow zone near the pressure side corner in the tipgap zone, the interaction area of the tip vortex with theconventional passage vortex system, the influence of therelative motion of the outer casing and leakage flow reversalcan all be visualized in great detail by using computationaltools solving the three-dimensional Reynolds Averaged

Navier-Stokes Equations. This part of the paper dealing withdetailed baseline predictions forms a useful basis for thepartial squealer tip visualizations that are presented in Part-3. The general attributes of the physical aspects of the leakageflows on the baseline tip configuration are successfullysimulated in a numerical visualization effort.

The static pressure distributions obtained on the tipplatform surface for two different clearance values revealmany important flow features such as low momentum/highstatic pressure zone near the leading edge, a dominant leakagearea near blade mid-chord location and a minimum pressuredifference zone between the PS and SS near the trailing edgewedge area.

A strong static pressure modification is apparent when theclearance is reduced to t/h=0.33 % (BS33) from the baselinecase of t/h=1.03 % (BS100). The high-pressure zone near theleading edge spread into the mid-chord region of the bladewhen the clearance is reduced. The velocity vectors in thiszone have small magnitude compared to the dominant leakagezone. This high-pressure zone coincides with the centralsweet spot observed in cascade heat transfer measurementson similar blades by a number of researchers. Leakage flowpaths in this region can be from the pressure side to suctionside area as observed from the leakage flow patterns.

Velocity field visualized in planes parallel to the tipplatform provides insight in terms of the direction and themagnitude of the leakage flow patterns in the tip gap zone.The viscous/turbulent shearing effect of the outer casing isclearly visible in velocity vector maps especially in the higherplane located very close to the outer casing. When theclearance is tight (BS33), the outer casing viscous/turbulentshear effect is felt even in the lower plane located very nearthe tip platform of the blade. A clear visualization of the tip vortex structure for thebaseline clearance (BS100) and tight clearance (BS33) ispresented in vertical planes (X,Y,Z and T). Vortical flowdetails in these vertical planes show that a large tip vortexstructure rolling near the suction side corner may occupy alarge area with significant momentum deficit and energy lossfor (BS100). When the clearance is reduced to one third ofthat of (BS100), an extremely weakened tip vortex structure isvisible. The leakage flow direction, amount and momentum iscontrolled by the delicate balance between the pressure forces,the shear forces imposed by the outer casing and inertialforces resulting from convective accelerations. It is likely thatthe shear influence of the outer casing is dominant in bladezones where the driving pressure differentials are minimizedby the tip loading conditions. The numerical visualizations clearly show that the smallzone near the leading edge of the blade and the trailing edgewedge zone may have flow leakage from the suction side topressure side. Leakage flow reversals in the last 20 % chord of the bladeis common. The reversal of the leakage flow occurs in theareas where the driving pressure differential along a leakageflow path between the pressure side and suction side isminimized. The pressure differential is minimal in mostturbine blade trailing edge zones because of the highlyaccelerated passage flows on both sides of the blade arebrought into similar Mach number values by design. The viscous/turbulent shearing effect of the outer casingstarts dominating at a much faster rate (earlier chordwisepositions) when the clearance is tight.

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Strong driving pressure differential in fluid layers near thetip platform and a strong shear force imposed by the outercasing near the outer wall may create sizeable re-circulatoryflow patterns in the gap especially in the second half of theblade. The re-circulatory flow zones numerically visualized invertical planes form as angular deviations of leakage flowfrom the mean camber line direction. Flow velocities are suchthat a typical leakage is sustained from the pressure side tosuction side after the mid-chord location. However, in the last20 % chord of the blade, leakage flow reversal occurs. Theleakage flow tends to turn back to the pressure side. Althoughclearly visible even for the baseline clearance (BS100) case ,the reversal of the leakage flow is much stronger for the tightclearance case (BS33). When tip leakage reversal occurs, some of the fluid trappedinside the conventional tip vortex (located near the suctionside corner) may go back into the tip gap zone. This fluid mayeventually finds its way to the pressure side. Heat transferimplications of this feature need to be studied since the fluidtrapped inside the tip vortex is likely to have higher totaltemperature than the core flow.

REFERENCES

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