Experimental and Numerical Investigation ofSecondary Flow Structures in an Annular LPT Cascadeunder Periodical Wake Impact – Part 2: NumericalResultsBenjamin Winhart1*, Martin Sinkwitz1, Andreas Schramm1, David Engelmann1, Francesca di Mare1,Ronald Mailach2

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

AbstractIn this work we present the results of the numerical investigations of periodic wake-sekondaryow interaction carried out on a low pressure turbine (LPT) equipped with modied T106-proleblades. e numerical predictions obtained by means of unsteady Reynolds-Averaged Navier-Stokes(URANS) simulations using a k-ω-model have been compared with measurements conducted in thesame conguration and discussed in part 1 of this 2-part work. e Q-criterion has been employedto characterize the secondary ow structures and accurately identify their origin. Based on theseinformation a correlation between the time-dependent interactions of the incoming wakes and thevortex structures is proposed and discussed.Keywordssecondary ow structures — low pressure turbine — wake interaction

1Chair of Thermal Turbomachines, Ruhr-Universitat Bochum, Bochum, Germany2Chair of Turbomachinery and Flight Propulsion, Technische Universitat Dresden, Dresden, Germany*Corresponding author: Benjamin.Winhart@rub.de

INTRODUCTIONe numerical prediction of interaction eects between in-coming wakes and secondary ow structures is challengingas the participating ow phenomena are highly unsteadyand three dimensional. is paper discusses the capability ofURANS simulations in predicting interaction mechanisms be-tween periodically incoming wakes and the secondary owsystem inside a modied, low speed, annular T106 turbinestator test facility located at the Chair of ermal Turboma-chines at Ruhr-Universitat Bochum.

Over the years a wide range of experimental and numeri-cal studies about the T106 secondary ow system interact-ing with periodically incoming wakes has been carried out.Schulte and Hodson [1] investigated the impact on loss gen-eration and found that the wake-boundary layer interactioncan reduce prole losses by suppressing suction side bound-ary layer separation. Michelassi et al. investigated the impactof incoming wakes on losses of a linear T106A cascade usingdirect numerical simulations (DNS) and large eddy simula-tions (LES) [2, 3, 4, 5]. ey found that the incoming wakedilation can account for 25% of the overall 2-dimensionalpassage losses. ey also highlighted the eect of varyingreduced frequency Fred and ow coecient φ on the wakeow path and thus on the overall losses. In an experimen-

tal and numerical investigation of the ow through a linearT106 low-pressure turbine cascade Koschichow et al. focusedon the complex ow phenomena near the end wall regionof the cascade with and without the inuence of incomingwakes [6, 7]. ey found that the incoming wakes periodi-cally reduce secondary ow and suppress the propagationof the horseshoe vortex and the passing wakes induce addi-tional vortex structures which interact with the crossow.e majority of the aforementioned works focus on linearcascades. However, some important ow features presentin real turbomachines ow can not be considered in suchcongurations.

In a two part research work we present the investigationsof an annular low-speed LPT which provides excellent ac-cess possibilities and where spatially and temporally highlyresolved measurements could be obtained. In part 2 of thisstudy the capability of 3-dimensional URANS simulationsto predict the complex interaction mechanisms involved inthe ow inside the investigated stator row is assessed. eturbine is equipped with a modied T106RUB stator blading tomatch the characteristics of the well known and frequently in-vestigated T106 prole under low Mach-number ow. Basedon the numerical results an analysis of the 3-dimensional oweld is conducted in order to gain insight in the secondary

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 2/10

ow structures. e interaction mechanisms between the pe-riodically incoming wakes and the secondary ow structuresare further analyzed through an investigation of the kine-matics of the incoming wakes based on of ow coecient φand Strouhal number Sr in one conguration. Finally a linkbetween wake impacted secondary ow structures and totalpressure loss distributions is proposed.

1. NUMERICAL SETUPIn this chapter the test case as well as the numerical model,boundary conditions and the numerical setup are brieydescribed. Finally the solution method is summarized.

1.1 Test Case Descriptione test case chosen for this study is a large scale low speedaxial turbine test rig, located at the chair of ermal Turbo-machines of Ruhr-Universitat Bochum. e annular test rigconsists of an inlet guide vane (IGV) row, a rotating wakegenerator row and the investigated stator row equipped witha newly designed T106RUB LPT blading to match the charac-teristics of the T106 prole at low speed conditions. An iso-metric view of the above mentioned relevant parts is shownin gure 1 with the rotating parts highlighted in red. emain test rig parameters are summarized in table 1. A moredetailed description of the test case is given in [8] and in [9].

Figure 1. Isometric view of the test rig‘s relevant partsincluding IGV, rotating wake generator (red) andinvestigated T106RUB stator row

1.2 NumericalModel&BoundaryConditionse numerical domain is shown in Figure 2 for the congura-tion with 60 wake generator bars. In order to save computa-tional cost and reduce modeling inaccuracies the IGV row isnot included in the numerical domain. However, as it is veryimportant to take the eects of the wakes generated by theIGV into account, highly resolved 2-dimensional boundary

Table 1. Main test rig parameters

Test rig

Outer diameter (Casing) DC 1.66 mInner diameter (Hub) DH 1.32 mMass ow Ûm 12.8 kg/sOperating point, Design point

Reynolds number (exit. theor.) Reexit,th 200,000Mach number (exit. theor.) Maexit,th 0.091Strouhal number range Sr 0.60 - 3.15Flow coecient range φ 0.81 - 2.84

conditions (BCs) were measured downstream the IGV andimposed at the domain inlet (Fig. 2). ese encompass totalpressure, velocity direction and turbulence intensity. At theoutlet the mass ow rate is adjusted to match the measuredaxial ow velocity. As the number of wake generators aswell as the blade count of the stator is 60, simple periodicBCs can be set in circumferential direction.

Figure 2. Numerical domain with visualized total pressureinlet BC

1.3 Numerical Mesh & Time Stepe vortex-structures resulting from the inuence of incom-ing wakes on secondary ow are inherently three dimen-sional and unsteady. is leads to increased demands onthe numerical mesh in all spatial directions. e mesh forthe wake generator domains has been created using ANSYSICEM, while the T106RUB has been meshed with ANSYS Tur-boGrid. e objective was to create as cubical cell volumes aspossible in the area of the vortex generators and the T106RUB

stator row. e nal mesh consists of approximately 7.21million cells. e main mesh parameters are summarized intable 2, where dw represents the rst cell oset at all wallsurfaces, np and nr stand for the number of cells along theblade prole and along the radial direction and n for the totalcell count.

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 3/10

Time step and mesh size sensitivity studies revealed that128 time steps per wake generator bar passing are sucientto resolve all relevant frequencies. is leads to a minimumtime step of ∆t = 2.1701 · 10−5 s and a maximum time stepof ∆t = 1.3021 · 10−4 s depending on Sr and φ.

Table 2. Summary of important mesh parameters

dw [m] np nr nWG 5 · 10−6 60 170 2.10 m.T106 5 · 10−6 415 160 5.11 m.total 7.21 m.

1.4 Solution Methode calculations presented in this paper have been performedusing ANSYS CFX release 18.2. In ANSYS CFX the RANSequations are solved using a pressure-based, coupled, un-structured nite-volume algorithm [10]. e solver is implicitin time using a second order backward Euler discretization.For convergence acceleration a coupled algebraic multi-gridmethod is used to solve the discrete system of ow equations[11]. All steady and unsteady simulations were performedusing the shear stress transport (SST) Menter two equationturbulence model [12]. To capture transitional eects, the γ-transition model is used [13], which is a further developmentof the widely used γ-Reθ -transition model.

2. RESULTS AND DISCUSSIONIn this section the numerical predictions are compared withexperimental data and discussed.

2.1 Static Pressure Distributione development of secondary ow structures is stronglyaected by the blade loading. To verify that the same bladeloading as in the experimental test rig is also reproduced inthe calculations, the distribution of pressure coecient

cp =p(x) − p1pt,1 − p1

(1)

at 50% span is compared to experimental data. e resultsare shown in Figure 3 and are in a good overall agreementwith slight deviations in the a pressure side distribution.

2.2 Integral Flow ValuesIntegral ow values are compared in this section to verify thecorrespondence of the operating conditions in the numericalcalculations. e inow axial velocity cx,1, outow absolutevelocity c2 and outow absolute velocity ow angle α2 areshown in Table 3 for one operating point and show also avery good agreement between simulations and experiments.Both velocities are related to the stationary frame as well asα2.

Figure 3. Comparison of experimentally and numericallyachieved pressure coecient cp at 50% span (Sr = 1.35,φ = 0.97); experimental data are shown with error bars of95% condence interval

Table 3. Comparison of integral ow values

cx,1 [m/s] c2 [m/s] α2 [°]EXP 13.6 30.6 153.6CFD 13.7 30.6 153.6∆ [%] 0.3 0.0 0.0

2.3 2-Dimensional Field Traverse DataIn this section the computational time averaged eld dataof velocity ratio c/cax, total pressure loss coecient ζ p andvorticity ωx are compared with results obtained by means of5 hole probe (5HP) traverse measurements at 0.34 · C down-stream of the T106RUB stator trailing edge (plane 3.2 shownin gure 4), where C represents the chord length of the in-vestigated stator blade. e distributions are shown in gure5 in comparison with the experimental data. e viewingdirection is in upstream direction.Velocity c: e distribution of time averaged absolute ve-locity c is predicted very well by the CFD. e free streamvelocity eld reveals the same topologies of high velocity uid(0 ≤ r/H ≤ 0.2), medium velocity uid (0.2 ≤ r/H ≤ 0.8)and low velocity uid (0.8 ≤ r/H ≤ 1) compared to the

Figure 4. Schematic meridional view of numerical domainand measurement planes downstream T106RUB statortrailing edge

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 4/10

Figure 5. Distribution of velocity eld data c, total pressure loss coecient ζ p and vorticity ωx at Sr = 1.35, φ = 0.97 inmeasurement plane 3.2 at 0.34 · C downstream of T106RUB stator’s trailing edge (view in upstream direction)

experimental data. e velocity drop caused by the prolelosses in the areas of the stator wakes is also depicted verywell by the numerical prediction. In the areas of secondaryow structures the decit of velocity is captured well by CFD.e extension of the lower loss region is a lile more ex-tended in radial direction in the experiment and thus showsa slighlty higher core velocity. e topology of the uppersecondary loss region is consistent with the measurementdata. Both cores with high velocity drops are captured bythe CFD although the numerical data show a slightly higherdrop in velocity. e connection between the upper core andshroud is a lile less distinct in the numerical data.Total pressure loss coecient ζp: e distribution of timeaveraged total pressure loss coecient

ζ p =pt,1 − pt (r, θ)pt,1 − p(r, θ)

(2)

shows a consistent structure between experiment and CFD,similar to the velocity eld. e loss levels in the areas ofprole losses and secondary ow are described very wellwhile the the lower loss region shows a larger radial extensionin the experimental data. e freestream loss is also in goodagreement.Vorticityωx : Vorticity is a quantity which describes the localspinning motion of a continuum. It can be invoked to get abasic idea of the secondary vortex systems in turbomachines,although this method can not distinguish between swirlingmotions and shearing motions. In Cartesian coordinates theaxial vorticity is given by:

ωx =

(∂cz∂y−∂cy∂z

). (3)

e comparison between experimental and numerical datashows that the main vorticity distribution is captured wellby CFD, although it reveals slight deviations in the uppercounter clockwise rotating area.

3. IDENTIFICATIONOF SECONDARY FLOWSTRUCTURES3.1 General DescriptionTo gain a beer understanding of the dierent vortices whichconstitute the secondary ow system, an analysis of the 3Dow eld is conducted. A valuable quantity to visualizevortex structures is provided by the Q-criterion which isdened as the second invariant of the velocity gradient tensor∂ui/∂xj :

Q =12

(Ωi jΩi j − Si jSi j

)(4)

with

Ωi j =12

(∂ui∂xj−∂u j

∂xi

)and Si j =

12

(∂ui∂xj+∂u j

∂xi

), (5)

where Ωi j is the vorticity tensor and Si j is the rate-of-strain-tensor. us, in contrast to the aforementioned vorticity,the Q-criterion represents the local balance between shearstrain rate and vorticity magnitude, dening vortices as areaswhere the vorticity magnitude is greater than the magnitudeof strain rate [14].

e main vortex structures participating in the secondaryow system of the investigated T106RUB stator are visualizedin gure 6 at two dierent angles of view via a 3-dimensionaliso surface of time averaged Q-criterion. is helps tracingthe origins and trajectories of individual vortices. e isosurface is colored with the axial vorticity ωx to provide animpression of the direction of rotation of each vortex.

Utilizing the information obtained by the 3-dimensionaleld analysis, an overview of the vortex structures on theevaluation plane 3.1 downstream the T106RUB stator is pre-sented in gure 7. is provides a beer indication of thevortex structure expansion and relative positions inside theannulus. In addition, the ndings of this analysis build abasis for the interpretation of the experimentally achievedvorticity distributions presented in [8].

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Figure 6. Secondary ow structures for Sr = 1.35, φ = 0.97visualized using time averaged Q-criterion iso surface atQ = 2 · 105 1/s colored with vorticity ωx

3.2 InterpretationPassage Vortex (PV): e passage vortex is a main compo-nent of the secondary ow system in turbomachines. ePV is the direct consequence of secondary ow caused bythe blade ow turning and forms in the hub region as wellas in the shroud region. Concerning the 3-dimensional oweld the PV originates inside the passage and propagates to-wards mid-span direction due to a strong corner separationwhich induces a radial crossow (gure 8). e 2-dimensionalanalysis of the PV dimensions in the investigated test casereveals that the PV on the hub side has a bigger expansionthan the PV on the shroud side. is can be addressed tothe lower velocity magnitude near the shroud caused by theradial equilibrium resulting in a less developed secondaryow compared to the hub region.Concentrated shed vortex (CSV): e concentrated shedvortex is an indirect consequence of the secondary owwhich peels o the boundary layer uid as it impinges theblade suction side. is separated ow region results in cor-ner separations (gure 8) which lead to the concentratedshed vortex. Analysis of the 3-dimensional ow eld revealsthat in contrast to the PV the CSV originates along the bladeedge separation line and has an opposite rotational direction.Horseshoe vortex (HSV): e horseshoe vortex originatesat the blade leading edge. Due to the low impulse of boundarylayer uid, two counter rotating vortices are generated nearthe blades stagnation point and are convected through thepassage. Due to the prevailing pressure gradient the pressureside leg of the HSV is convected towards the neighboringblade’s suction side (cf. gure 6) and interact with the PV,

Figure 7. Contour plot of time averaged vorticity ωx withisolines of time averaged Q-criterion Q = 2 · 105 1/s atmeasurement plane 3.1 (Sr = 1.35, φ = 0.97)

Figure 8. Streamlines of time averaged velocity v along theblade suction side transformed into the x ′-r ′-plane atSr = 1.35, φ = 0.97; contour showing velocity componentvr′

which has the same direction of rotation. e suction sideleg propagates along the blade surface and connects with thecorner vortex (CV). In the present test case the pressure sideHSV interacts with the PV but remains visible in the struc-ture of the resulting vortex system which can be explainedby the momentum of the HSV uid which is strong enoughto withstand the momentum of the uid transported insidethe PV. Due to the stronger corner separation near the bladehub and the subsequent radial deection of the PV, the HSVhas more room to spread between PV and hub, which resultsin a more expanded HSV (cf. gure 7).Corner vortex: e corner vortex acts as a balancing vortexbetween the PV, blade and endwalls, thus it has an oppositesense of rotation as the PV. As mentioned above the CV andthe suction side leg of the HSV connect and are not distin-guishable downstream of the blade. e resulting vortex isvery small compared to the other vortices but is still notice-

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 6/10

Figure 9. Temporal evolution of wake kinematics at 50% constant span visualized via contours of velocity uctuation c atSr = 1.35, φ = 0.97; black arrows represent the projected velocity uctuation vectors

able in the vorticity distribution while it creates a shear layerbetween the counter rotating vortex structures consisting ofPV & HSV and CV/HSV & CSV. e advantage of utilizingthe Q-criterion becomes clear at this point as it is not possibleto distinguish between the individual vortex structures bysolely analyzing the vorticity distribution.Trailing edge wake vortices (TEWV): e trailing edgewake vortices originate from the shear layer, starting at theblade trailing edge. Fluid from from suction side and pressureside have dierent momentum and radial velocity compo-nents which results in wake vortices being shed along theblade trailing edge.

4. WAKE KINEMATICSIn this chapter the kinematics of the incoming wakes arediscussed. Figure 9 shows a temporal evolution of the distri-bution of velocity uctuation

c = c(x, θ, t) − c(x, θ) (6)

caused by the incoming wakes at four equally distributedtime steps per bar passing on a surface at 50% span. eprojected velocity uctuation vectors are superimposed asblack arrows in order to indicate the direction of the inducedwake inuence.t/T = 0: At this point of time the incoming wakes impingeon the pressure side of the T106RUB stator right behind theleading edge (A). Inside the wake an adverse velocity uc-tuation is induced due to the prevalent total pressure drop,which causes a negative jet. Due to the blockage caused bythe incoming wake an area of accelerated ow appears abovethe upper boundary of the wake (B).t/T = 1/4: e incoming wake has propagated further intothe passage within this snapshot. At the pressure side ofthe blade the wake front is pushing a region of decreasedvelocity (C) due to the uid transport caused by the negativejet eect (highlighted by curved arrows), whilst behind thewake the near wall velocity is increased (D). e wake shapeis slightly bowed (highlighted by a black curve) because ofthe low momentum uid near the blade surface and higher

passage ow velocity.t/T = 2/4: e wake moves closer to the upper blade suctionside which causes the uid in this area to accelerate further(E). In the presence of the upper blade potential eld thewake gets deected and aaches to its suction side, whichadditionally increases the wake bow. In front of the wake aclearly distinguishable, clockwise rotating vortex structureis observable (F) which balances the crossow uctuationsinduced by the negative jet. is vortex causes a velocityreduction at the blade pressure side while it increases thevelocity at the neighboring blade suction side. Behind thewake a counter clockwise rotating vortex (G) has the oppo-site inuence on the near wall ow.t/T = 3/4: Due to the contraction of the passage and the con-sequently rising convection velocity the wake gets furtherdilated. Additionally the vortices upstream (H) and down-stream (K) of the wake get intensied resulting in higherinduced velocity uctuations. e front part of the upperblade suction side is covered with low momentum uid asthe wake further bends over its surface.t/T = 4/4 ∨ 0: is point refers to the le-most picture att/T = 0 again, but to the wake further downstream (L) ofthe one described above. Compared to the previous snapshotthe wake bow has further increased as well as the intensityof the counter rotating vortices (M,N). e area inuencedby the wake is marked by dashed black lines and stretchesalmost throughout half the passage due to the increasingwake dilation. e area of negative velocity uctuation (blue)in front of the wake is about to be convected through the rstevaluation plane (3.1), which is located at the right boundaryof the gure.t/T = 5/4 ∨ 1/4: e blue area of negative velocity uctua-tion in front of the wake now propagates through the eval-uation plane whilst the red area at the neighboring bladesuction side is directly in front of it. As the four wake af-fected cells have already passed the lower blade surface, theyare now bounded by the stator’s wake.

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Figure 10. Temporal evolution of secondary ow structures visualized via isolines of Q-criterion Q = 2 · 105 1/s andcontours of axial vorticity ωx (le) and contours of total pressure loss coecient ζp at Sr = 1.35 and φ = 0.97 atmeasurement plane 3.1 (0.15 · C downstream T106RUB TE)

5. TEMPORALEVOLUTIONOFSECONDARYFLOW STRUCTURES & LOSS REGIONSIn this section the temporal evolution of secondary owstructures and loss regions under the inuence of periodicallyincoming wakes is discussed for one combination of Strouhalnumber Sr and ow coecient φ. Figure 10 shows contoursof axial vorticity ωx and isolines of Q-criterion at Q = 2 ·105 1/s on the le side of each plot. On the right side thecorresponding distribution of pressure loss coecient ζp isshown. e direction of view is in upstream direction.

e development of the individual vortices is discussedsubsequently for eight equally distributed time steps withinone bar passing t/T . As the underlying interaction mech-anisms are highly complex and coupled, it is not alwayspossible to reduce the explanation of these mechanisms toone fundamental process. erefore, it is important to un-derstand that the observable uctuations of the participatingvortex systems inside the evaluation plane are not only trig-gered by the wake as it crosses this evaluation plane, butalso by the impact of these wakes on the boundary layersat blade and endwalls, as well as on the vortices inside thepassage. ese indirect eects occur further upstream and,consequently, it is not always possible to aribute them tothe direct eect of the wake inside the evaluation plane.

As boundary layer investigations are not part of this pa-per the subsequent analysis focuses on the aforementioneddirect eects of incoming wakes on the secondary ow sys-

tem. e wake aected ow propagates through the passageand carries cells of lower and higher momentum uid (g-ure 9), which correlates to lower and higher total pressure.As a consequence also the static pressure distribution getsdistorted which directly inuences the vortex structures dueto the prevalent pressure gradient. In addition cells of hightotal pressure temporarily decrease the local total pressureloss as they pass the evaluation plane, whereas cells of lowtotal pressure increase it.

To help further the interpretation, the bar passing periodis divided into three phases. Within the rst phase the vortexin front of the incoming wake passes the evaluation plane. Inthe present case the rst phase spreads from 1/8 ≤ t/T ≤ 3/8,which is deducible from the distribution of total pressure losscoecient ζp (right side of each plot) as well as from thedistribution of velocity uctuations shown in gure 9, whichcoincide directly with regions of higher and lower total pres-sure. Within the second phase (4/8 ≤ t/T ≤ 6/8) the vortexbehind the incoming wake is convected through the evalua-tion plane. Inside the third phase almost no wake aecteduid passes the evaluation plane (0 ≤ t/T ≤ 7/8).Phase 1 (1/8 ≤ t/T ≤ 3/8): Within this section the two cellsof wake inuenced uid in front of the wake start to propa-gate through the evaluation plane. At rst the pressure sidedcell of low total pressure propagates through the evaluationplane (cf. gure 9). is is clearly visible in the total pressureloss distribution shown in gure 10 at time step t/T = 1/8,

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 8/10

indicated by high values of ζp at the pressure side boundaryof the stator’s wake (A). is cell is intensied until time stept/T = 2/8 where it reaches its maximum extension (B) beforethe pressure loss is decreased in this area while the cell oflow pressure uid leaves the evaluation plane (C). At the suc-tion side boundary of the stator’s wake the wake inuenceis shied in time as the cell of high pressure uid passes theevaluation plane later within the bar passing period. isprocess starts at t/T = 2/8 and is indicated by an area oflower total pressure loss coecient (D) until it reaches itsminimum values at t/T = 3/8 where larger areas of negativeζp are indicated via blanked values (E).

e vortex structures, the TEWV at rst are strength-ened and subsequently weakened, indicated by the showncontour isolines of Q-criterion (F). As described above, thisphenomenon is caused by the positive and negative uctu-ations of momentum transferred to the blade’s boundarylayer via the periodically incoming wakes. e evolution ofthe lower vortex system shows a continuous weakening ofthe HSV inside the evaluation plane (G). An analysis of thetemporal evolution of the 3-dimensional vortex structures ispresented in gure 11. For the sake of brevity only two timesteps are shown. On the le side the HSV has its maximumextension (t/T = 0), whilst on the right side the HSV hasits smallest extension (t/T = 4/8). e analysis revealedthat further upstream (A) the pressure side HSV is deectedby the cells of high and low pressure inside the wake. isdeection causes the HSV to periodically impinge on thesuction side near the area where the PV is aected by thecorner separationn. (B). Due to this impingement the systemconsisting of PV and CSV is deected towards midspan direc-tion. Another eect is that the HSV loses momentum, whichis observable inside the evaluation plane shortly thereaer.As a consequence of the weakened HSV a shi of PV and CSVback towards the endwalls is observable inside the evaluationplane at (H). is results in a uctuating migration of theparticipating vortices in radial direction which is additionallyinuenced by the wake induced crossow pressure gradient.Phase 2 (4/8 ≤ t/T ≤ 6/8): Within this part the vortex

structure located upstream of the incoming wake is passingthe evaluation plane. At the suction side boundary of thestator’s wake this passing is indicated by an emerging area ofhigh total pressure loss (K) which is induced by the low pres-sure cell passing the evaluation plane. is area of high totalpressure loss has its maximum extension around t/T = 5/8(L) before it is weakened again (M) as the low pressure cellleaves the evaluation plane. At the pressure side boundarythe high pressure cell causes a loss reduction with an area ofnegative ζp marked by blanked values (N). In the followingtime steps the total pressure loss in this area rises again (O).

e main vortex systems are further shied towards theendwalls, weakened and reach their minimum extensionaround 5/8 ≤ t/T ≤ 6/8 (P). is process is the continuationof the process described above in Phase 1. While both HSVare continuously weakened until t/T = 5/8 (Q), they getintensied at t/T = 6/8 until they reach their maximum ex-

Figure 11. Distribution of secondary ow structures at twoinstants of time for Sr = 1.35, φ = 0.97 visualized usingQ-criterion iso surface at Q(t) = 2 · 105 1/s colored withvorticity ωx

tension around 0 ≤ t/T ≤ 7/8 (R). e prominent uctuationof the HSV can be explained by the above mentioned directinteraction of wake aected uid and the HSV.Phase 3 (0 ≤ t/T ≤ 7/8): During the third phase only uidwhich is not aected by the wake passes the evaluation plane.In comparison to the time-averaged distribution in gure 7the topology in this phase shows almost the same distribu-tion of vortex structures and all vortex structures are clearlydistinguishable. e HSVs are very pronounced, especially atthe hub-side. e vortex systems consisting of PV & CSV areshied towards midspan. is creates enough room for theHSV to spread and is a direct consequence of a strong cornerseparation which is caused by strong secondary ow. isTEWV system gets periodically suppressed by the incomingwakes which is in accordance to the ndings of the exper-imental investigations by Sinkwitz et al. [8, 9] and can beexplained by the transport of energy to the boundary layerdescribed above.

6. SUMMARY AND CONCLUSIONIn the present study URANS simulations of a large scale, lowMach number, annular turbine equipped with a newly de-signed T106RUB LPT blading were conducted. e bladingwas modied to match the characteristics of the well knownand frequently investigated T106 prole at low speed con-ditions. e results achieved by this simulations were com-pared with against stationary measurement data by meansof static pressure distribution around the blade prole, inte-gral ow values and 2-dimensional eld traverse data andshowed excellent agreement. e validation ensured that adetailed ow eld analysis based on the CFD data is admissi-ble. Well resolved CFD results were then used to identify thedierent vortex structures which interact in the secondaryow system of the investigated stator prole via an analysisof the 3-dimensional distribution of vortex structures visu-alized by the time averaged Q-criterion. e information

Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact — 9/10

of this analysis were utilized to deduce the distribution ofvortex structures inside the evaluation plane. Based on thesendings a link between vortices and the distribution of axialvorticity was established supporting the interpretation of theexperimental data.

An analysis of the wake kinematics revealed that the neg-ative jet eect, caused by the periodically incoming wakes,induces two counter rotating vortices in front and behind thewake which extend in radial direction. As the wake aecteduid propagates through the passage these vortices createcells of low and high momentum uid which aect boundarylayers at blades and end walls.

A study of the temporal evolution of participating sec-ondary ow structures revealed a strong interaction betweenthe incoming wakes and the vortices, which are periodicallyweakened and intensied. It was found that the wake af-fected uid causes a uctuation of the pressure side legs ofthe horse shoe vortices, which interact with the passage vor-tices. is results in a radial shi of the passage vorticesand concentrated shed vortices. In addition the horse shoevortices get weakened due to the transfer of momentum intothe passage vortices.

Regarding the distribution of total pressure loss on theevaluation plane, the temporal analysis revealed that themain impact on total pressure loss is caused by the cells ofhigh and low pressure uid inside the wake aected owwhich causes a periodical reduction and rise of total pressureloss compared to the undisturbed ow.

It can be concluded that URANS simulations are capableof predicting the secondary ow structures for the underlyingtest case to a good degree of detail. Some minor deviationsbetween CFD predictions and measurement are observed butthe main vortex system is depicted very well.

ACKNOWLEDGMENTSe investigations reported in this paper were conductedwithin the framework of the joint research project UnsteadyFlow and Secondary Flow in Compressor and Turbine Cas-cades (PAK-530). e authors wish to gratefully acknowledgeits funding and support by the Deutsche Forschungsgemein-scha (DFG). e responsibility for the contents of this pub-lication is entirely with the authors.

NOMENCLATURE

Latin SymbolsarcSS [m] suction side arc lengthc [m/s] absolute velocityC [m] chord lengthcp [-] pressure coecientg [-] pitchH [m] blade heightp [Pa] pressurept [Pa] total pressureQ [1/s2] velocity invariant Q

r [m] radial coordinater ′ [m] transformed radial coordinateRe [-] Reynolds numberSi j [1/s] rate-of-strain tensorSr [-] Strouhal numbert [s] timeT [s] bar passing timecx [m/s] axial velocityx [m] axial coordinatex ′ [m] transformed axial coordinate

Greek Symbolsα [°] absolute velocity ow angleζp [-] pressure loss coecientθ [°] circumferential coordinateρ [kg/m3] mass densityφ [-] ow coecientωx [1/s] axial vorticityΩi j [1/s] vorticity tensor

AbbreviationsBC boundary conditionCFD computational uid dynamicsCSV concentrated shed vortexCV corner vortexIGV inlet guide vaneHSV horseshoe vortexPV passage vortexTEWV trailing edge wake vortexURANS Unsteady Reynolds Averaged

Navier-Stokes

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