Martin Sinkwitz
email: martin.sinkwitz@rub.de

Benjamin Winhart

David Engelmann

Francesca Di Mare

Ronald Mailach

Francesca Di Mare

S Y Mpo

O Tatin

Experimental and Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact

Keywords:

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Blade count reduction in the low pressure part of the aero engine can provide a substantial contribution to the reduction of the overall weight of an engine. However, this must be compensated through the design of high-li , heavy-loaded blades which in turn are exposed to increased pressure gradients, affecting in particular blade profile and end wall flow which is already prone to separation. Intensified boundary layer separation at end walls and on the profile suction side results in pronounced secondary flow systems. ese in turn induce high loss, a loss of li and main flow perturbation [ , ]. Different secondary flow models have been proposed, extended and modified, resulting in a basic, broadly accepted, secondary flow model representation (e.g. [ ]). is concept mainly consists of passage vortices (PV), horse shoe vortices (HSV), tip leakage vortex, corner vortices (CV) and a vortex street that is shed from the blade trailing edge (TEWV). A few of the models incorporate yet another vortex structure originating from the separated suction side boundary layer, labeled as the concentrated shed vortex (CSV) [ ], resulting from end wall boundary layer fluid (PV) impinging on the blade suction side and leading to a separation of the suction side boundary layer itself close to the end wall. Analysis and potential reduction of these vortical structures are complicated by the multistage environment in turbomachines, where rotor stator interaction affects the transport and shedding of blade wakes and vortices, resulting in an extremely non-uniform, distorted and time-dependent flow field. us, it is difficult to separate the distinct interacting flow structures from each other and to determine their degree of influence on aerodynamic loss generation mechanisms. Numerous tests have been conducted under simplified conditions in linear cascades. To include the influence of periodically unsteady rotor blade wakes in linear setups, linear wake generators have been employed, using cylindrical bars to simulate wakes [ , , , , , , , ]. An important common finding of these investigations is that unsteady wake inflow can stabilize boundary layer flow. us, periodic rea achment of a boundary layer, which would separate under unperturbed inflow conditions, is promoted [ , , ]. However, the investigation of secondary flow within linear cascades neglects several essential effects present in real turbomachinery flow.

In this study an experimental setup for the time-resolved analysis of wake-stator flow interaction, using an annular geometry instead of a linear cascade, is applied. is way, the influence of curvilinear end walls, non-uniform, radially increasing pitch and radial flow migration is incorporated. Incoming wakes are generated by a variable-speed driven rotor disk equipped with cylindrical bars. Special emphasis is put on wake-induced, time-dependent weakening and dis- placement of particular vortices of the secondary flow system. Furthermore, wake-boundary layer flow interaction and flow separation along the blade suction surface is studied. e distinction between time-averaged and time-resolved analysis of secondary flow phenomena and the importance of time-resolved measurement is emphasized and the temporal evolution of characteristic flow field quantities is utilized to analyze the periodic impact on the vortices. By relating measurement data of two-dimensional flow field traverses and time-accurate blade profile pressure signals to each other, a deeper understanding of the complex interaction between bar wake, boundary layer and secondary flow can be obtained.

. EXPERIMENTAL TEST FACILITY

For this study an existing large scale axial flow turbine test rig installed at the Chair of ermal Turbomachines of Ruhr-Universität Bochum was retrofi ed to allow highly resolved measurements of unsteady wake-stator flow interaction. Pivotmounted casing elements with multiple probe accesses have been constructed which are placed between the IGV and the stator row as well as downstream of the stator. Stepwise rotation of these elements and radial translation of the probes enable the automated recording of two-dimensional flow traverses. e test facility is operated continuously in an open circuit, with ambient air. Flow is induced by a kW variable speed engine coupled to a radial blower with a ṁ = kg/s mass flow capacity. e blower is placed downstream of the test section, so that the rig is operated in suction mode.

e large dimensions of the flow channel allow detailed flow measurements with negligible blockage and perturbation by installed probes.

e a -loaded blade profile under investigation, labeled as T RUB , is an in-house modification of the well-known T LPT blade. It was developed for matching the characteristics of the T profile at the rig's low Mach number flow. e development and underlying principles of the transformation procedure are described in [ ]. e profile is characterized by a cylindrical geometry with a chord length of C = . m and an aspect ratio of H/C = . . is aspect ratio ensures that near end wall vortices do not merge and as a consequence quasi two-dimensional flow conditions at mid-span. e stator row consists of blades with a stagger angle of λ T = . °and a pitch-to-chord ratio at mid-span of g/C = . . An inlet guide vane (IGV) row ensures proper inflow angles to the stator. It is made up of vanes (NACA profile) and was developed for correct flow turning whilst leaving the T RUB inflow as far as possible unaffected by wakes and secondary flow structures. e choice of NACA profiles is the result of an elaborate numerical study, comparing different profile geometries and several blade counts. e IGV is placed . C upstream of the bar plane utilizing the maximal possible distance the axial test rig dimensions allowed.

To simulate blade wakes, the rotor disk was equipped with radially stacked steel bars (bar diameter D B = .

m, bar length L B = .

m, bar pitch g B = . / . / . m). us, it is possible to isolate both velocity defect and turbulence increase of rotor blade wakes without the additional secondary flow system, associated with flow turning in a blade passage. Wakes are generated in a plane parallel to the stator leading edges (LE), located at an axial distance of . C upstream of the LE, which represents a typical axial gap width in a LPT. e investigations were carried out for three different values of bar pitch. e same stator and IGV blade counts ( ) as well as the number of wake generator bars ( / / ) allow time-efficient numerical studies.

A kW AC engine controlled by a frequency converter drives the rotor sha . e setup of IGV, wake generator and T RUB stator is shown in Figure .   .

MEASUREMENT TECHNIQUES

Adjustment and monitoring of the operating point was realized with help of multiple Prandtl-probes (p t , p s and hence c) at different characteristic planes, a stationary five hole probe ( HP) (p t , p s , c, flow angles α and γ) in the stator exit and a combined temperature and relative humidity sensor at the test rig inlet. e ambient pressure (reference pressure, abso-lute) was measured by a Rosemount absolute pressure transducer (accuracy ± . % of calibrated transducer measuring range). All remaining pressures (relative to ambient) were recorded by a -channel Scanivalve ZOC / Px miniature pressure scanner module (accuracy ± . % of transducer fullscale range) controlled by a Scanivalve ERAD unit. e individual high-sensitivity low-range ( mbar) pressure sensors enable simultaneous data acquisition of all incorporated pneumatic pressure probes. By recording pressures practically without temporal offset between one and another, the systematic measurement uncertainty -e.g. of HP, wall or profile pressure measurements -is reduced considerably. For this study, two-dimensional ( D) (in radial and circumferential direction) flow field traverses have been carried out downstream of stator TE (Figure , plane . ) to quantify the bar wake impact on the downstream secondary flow system. For time-averaged traverses, miniature HP (head diameter of mm, bore diameter of . mm) were employed. Hot wire anemometry measurements (CTA mode) provided time-resolved traverse data. For acquisition of the time-resolved D flow vector these were conducted with two different types of Split Fiber Probes (SFP), fabricated by Dantec Dynamics. SFP probes of type R were used for measuring axial and radial velocity components (for computing flow angle δ) and probes of type R for measuring axial and circumferential components (for computing flow angle α). Hot wire signals have been recorded at a rate of kHz ( times higher than the maximum bar passing frequency) for at least samples, triggered by a one/revolution signal from an inductive encoder on the rotor sha . e minimum of samples was defined as the best trade-off between time consumption (of D traverses) and validity of the phase-averaged results. For the discussed investigations, where unsteady fluctuations in the wake flow exceed the angular range of ± °and where recording rates of kHz are sufficient, SFP have shown superior performance over conventional X-array probes. As D SFP are not available and conventional triple-sensor wireprobes are too large in diameter for the test rig probe accesses, acquisition of all three velocity components requires the combined use of the two different types of SFP. Measurement data of both probes were correlated and post-processed to obtain D flow vectors. For SFP data acquisition a StreamLine N CTA anemometer by Dantec Dynamics (incorporating three C CTA modules) in combination with a National Instruments NI A/D converter was employed. High spatial traverse resolution was achieved by D measurement grids of up to radial and circumferential positions. e circumferential positions were evenly distributed over two stator pitches, whereas the radial increments were refined close to the end walls. In the case of time-consuming SFPmeasurements the spatial resolution was decreased slightly. At the start of every measurement, probes were aligned to the main flow direction at mid-span. HP measurements were carried out with fully calibrated probes in a non-nulling mode. For additional data acquisition within the T RUB stator passage, blade profile pressures were measured on various T RUB stator blades.

pressure taps, evenly distributed to positions of constant span (near hub at R/H = %, at mid-span at R/H = %, near casing at R/H = %) enabled time-averaged, pneumatic pressure measurement. Furthermore, time-resolved, piezo-electric pressure measurements were conducted at mid-span, using flush-mounted Kulite type LQ-sensors (see Figure ). An IMC CRONOSflex system was incorporated for recording Kulite signals with an acquisition rate of kHz. At every measurement position samples were collected, also triggered once per revolution. A phase-locked ensemble averaging technique was applied to the recorded time-resolved data samples to obtain reliable quantities from SFP and Kulite sensor measurements.

is facilitates the separation of periodically unsteady signals originating from wake impact from stochastic turbulent fluctuations without losing the time-dependent character. All shown time-resolved results have been averaged with this method.

.

EXPERIMENTAL RESULTS AND DISCUS-SION

For all investigations discussed in this paper, the theoretical exit Reynolds number was kept constant at Re exit, th = , (based on T RUB chord length C, with the fluid's dynamic viscosity µ, the theoretical exit velocity c exit, th and the corresponding density ρ exit, th ):

Re exit, th = c exit, th • ρ exit, th • C µ ( )
is is a typical value for LPT operation at high altitude where suction side boundary layer separation can occur.

e theoretical exit state (using upstream total pressure and downstream static pressure) is a common way to account for altered losses when bar velocity or bar count are modified while maintaining comparability. As the main dimensionless quantities for characterizing unsteady flow disturbances, the Strouhal number Sr and flow coefficient φ have been identified [ , ]:

Sr = f BP • C c ax = c B g B • C c ax ( ) φ = c ax c B ( )
To study the effect of different periodically unsteady inflow conditions (disturbance by incoming wakes), these have been varied in wide ranges including values for typical LPT operation. As for all discussed measurements the axial velocity c ax is approximately held constant, bar wake frequency f AVO distribution for steady undisturbed case (le ) and for a case with significant wake disturbed inflow (Sr = . , φ = . ) (right).

e AVO can be derived from those components of the velocity vector, tangential to the axial direction (c y and c z ) and the geometry of the measurement grid:

AVO = ∂c z ∂ y - ∂c y ∂z ( )
e flow field is given for the undisturbed (le ) and a perturbed (right) case, whereas the direction of view is upstream. Relevant vortices of the stator secondary flow system, the estimated stator wake position as well as the position of suction and pressure side of the stator wake have been labeled to aid interpretation.

e particular vortices have been identified by their direction of rotation and their location in the vicinity of characteristic flow regions, such as the suction side or the end walls. us, the passage vortex (PV) pair could be detected near the end walls on the suction side of the stator wake. e PV pair is a result of low momentum end wall boundary layer fluid, following the cross passage pressure gradient from the pressure side to the suction side of the neighboring blade. Impinging at the profile suction side, this crossflow is diverted across the blade towards mid-span, consequently shaping the PV. Furthermore, near the profile LE the horse shoe vortex (HSV) system is formed, when the end wall boundary layer from upstream hits the LE and splits due to the local adverse pressure gradient. e suction side legs (HSV-SL) propagate close to the suction side as they are pushed against the blade by the cross passage pressure gradient. As the suction side legs are concentrated within the corner between end wall and blade suction side, they do not contain much material, stay small and potentially merge with the respective nearby corner vortex (CV). e pressure side legs (HSV-PL), instead, are diverted from the blade pressure side to the suction side of the adjacent blade, also following the cross passage pressure gradient. For the steady, unperturbed case the HSV-PL can clearly be identified among the PV and the respective end wall. Despite the same direction of rotation, these have not merged entirely with the PV, as reported for other setups e.g. in [ , ]. Instead they push the PV towards mid-span. In close proximity, a spacious system can be detected, rotating in opposite direction. is system is supposed to contain the concentrated shed vortex (CSV), the described combination of CV and HSV-SL, as well as the trailing edge wake vortex street (TEWV). e origin of the CSV is a direct consequence of the low momentum PV flow impinging at the blade suction side. It induces separation of the suction side boundary layer, which then rolls up into a counter rotating vortex next to the PV [ ]. At TE the adverse directions of radial blade flow migration on pressure and suction side form a shear layer (TEWV) that unites with the CSV.

In the right part of Figure , with Sr = . , φ = . a case with significant periodical inflow perturbation is displayed. In direct comparison with the unperturbed case an apparent impact on several vortical structures can be observed. Near the casing both a decrease in size and a displacement of the PV + HSV-PL system towards the end wall can be seen. Furthermore, a significant weakening of the CSV + TEWV takes place.

is can be justified by the impact of the bar wakes, which interact with boundary layer flow on the blade and on end walls. e wakes, acting as negative jets, promote boundary layer transition and leave the wall flow in a temporarily unperturbed condition a er the wake has passed [ , , ]. In this state the boundary layer is not as prone to separation and deflection as in the undisturbed case. Intermi ently, cross passage transport of end wall flow is reduced and less low momentum fluid is provided to the PV, reducing its dimensions. Further on, separation of boundary layer flow at the profile suction side is periodically reduced, as well. As a consequence, particularly the CSV is weakened, as it results from boundary layer material both from the end wall and from the profile suction side. Near the hub, impact on the secondary flow system seems slightly different. e PV appears even larger, but also more diluted. A weakening of the CSV+TEWV system is observable, but not as pronounced as near the casing.

us inspection of the time-averaged exit flow field already indicates the spatial imbalance (hub/casing) of bar wake impact in an annular cascade contrary to the uniform flow in linear cascades.

. . Time-resolved measurement data

For a more detailed insight into the intermi ent flow phenomena downstream of the T RUB stator passage, time-accurate data were recorded with SFP. e probes were traversed similarly to HP measurements in the same plane .

∆c (R, θ, t) = c (R, θ, t) -c (R, θ) steady ( )
For the AVO, absolute values are shown. Approximate locations of the stator wakes have been marked with do ed vertical lines, also suction side (SS) and pressure side (PS) flow.

e velocity field is perturbed periodically with the bar (wake) passing frequency (t BP = / f BP correlates to the duration of one bar passing). However, the situation that can be observed downstream of the stator is not just a periodical perturbation by the passing bar wake, but a superposition of several effects, which can be traced back to wake kinematics and the displacement of vortices. While propagating through the stator passage, the incoming bar wakes are cut, stretched, bowed, undergo mixing and interact with the passage flow as well as with the near wall flow at the blade suction and pressure side and at the end walls. e bar wakes, acting as local regions of low pressure, momentum and velocity can be described as negative jets [ , ], pointing in the opposite direction than the main flow. When impinging on the profile pressure side and passing over it, the bar wake induces two counter rotating, vortical-like structures (radial rotational direction) (compare e.g. [ ] or [ ]). is results in a flow deceleration in front of the wake and a flow acceleration immediately a er the wake has passed. On the suction side the impact on flow is reversed. Here, the wake pushes a region of accelerated squeezed passage flow in front of it and is followed by a low-speed region. is interaction between bar wake and profile flow will be discussed in more detail in section . and in [ ]. e described local flow acceleration and deceleration within the stator passage finally result in four characteristic, periodically passing parcels of altered velocity that can still be observed in the stator exit flow field.

For the flow at mid-span (R/H = %) these four parcels close to the bar wake have been labelled with A-D in Figure (top center). e distorted bar wakes have been highlighted, as well. Immediately before the wake arrives, decelerated volume A and accelerated volume C are present. When the bar wake has passed the observed plane, parcels B and D follow. Based on their origin, these four volumes are located near the blade suction and pressure side respectively and thus close to the stator profile wakes. Consequently, especially close to the profile wake a pulsating flow field is induced, whereas the free passage flow is li le disturbed. Downstream of the passage, the accelerated parcels B and C from previously separated, adjacent passages merge. Interestingly, there is nearly no change at all regarding the AVO (bo om center), remaining fairly constant over time, indicating that no additional vortices with axial sense of rotation are generated. is corresponds to the observation that the vortical structures, induced by the negative jet like propagation of the bar wake, generate vortices with primary radial rotational direction.

Near the end walls, the situation is far more complex than at mid-span. Beyond the pulsating bar wake impact, the flow field here is affected by the stator secondary flow structures. Both at R/H = % and R/H = % the velocity distributions undergo a similar periodical perturbation as already described for the flow at mid-span. But although the characteristic parcels can be found again, an apparent difference is noticed regarding structures C and D, as they are broken up and displaced from the suction side into the passage. is can be traced back to the periodical interaction between bar wake and the nearby secondary flow system. It has to be noted that the altered velocity is a result both of the passing bar wake velocity field and of displaced vortical structures carrying low velocity fluid. By including the evolution of the AVO into the analysis, this interaction can be observed more clearly. In the range of -. °≤ θ ≤ . °a periodical weakening of the PV (within the regarded plane) becomes visible. is weakening can be linked to the approaching bar wake carrying the accelerated flow regime C. When the wake has passed, the decelerated structure D is split, as is wraps around the PV. At the same time, the nearby CSV (θ ≈ . °) is periodically weakened as well. As the comparison with adjacent spanwise slices (below and above, not shown here) has revealed, additionally to the intermi ent weakening and strengthening of PV and CSV, they are also displaced radially. Both weakening as well as radial displacement out of the observed plane reduce the local magnitude of the AVO. As the CSV is far more displaced (in radial direction) than the PV, its core is intermi ently located within the observed plane, above or below. is wavelike in-and-out of plane movement must not be misinterpreted as a pa ern occurring at a doubled frequency. e influence on the secondary flow structures in turn can be traced back to a combination of a direct and an indirect bar wake impact. When the bar wake passes, its local velocity field (parcels A-D) has a direct impact on the exit flow field including the secondary flow system. Additionally, the vortex development has already been affected upstream by the bar wake passing through the stator passage, but back in time. As only the temporal offset consequences of this effect can be observed in the exit flow, the authors term this the indirect impact. Based on the interaction between the bar wake (periodical altered velocity field and injection of momentum and turbulence) and the flow through the passage near the end walls, the cross passage transport is decreased and vortex formation and propagation are seriously influenced. e authors assume, that initially the propagation of the HSV-PL is massively perturbed by the passing wakes. Its impingement position at the adjacent blade suction side is shi ed downstream, reducing impact on suction side flow and thus on PV and CSV. Under unperturbed inflow both PV and CSV are pushed towards mid-span by the intense HSV-PL. Under wake impact, they are periodically shi ed back towards the end wall. Due to slower propagation of the vortical secondary flow structures than the main flow, the effects of passing bar wake (direct) and affected secondary flow structures (indirect) arrive at different instants of time in the observed plane in the stator exit flow. Furthermore, the different propagation velocities at mid-span, hub and casing also induce a temporal shi between the impact of the bar wakes at different spanwise positions.

. Profile pressure distribution

Evaluation of the stator exit flow field allows an analysis of bar wake-secondary flow interaction. To examine the immediate impact of periodically unsteady bar wakes on stator blade profile flow, experimental data from within the passage is necessary.

us, multiple positions on various T RUB stator blades were equipped with pressure taps. At first, time-averaged, pneumatic pressure readings will be discussed, followed by time-accurate measurement data from piezoelectric sensors, embedded in the blade surfaces.

. . Time-averaged measurement data

c p = p (x) -p p t, -p ( )
For reasons of clarity, error bars have been omi ed, see part [ ] for those values including error bars. e undisturbed steady situation is given by the black curve, the green curve (Sr = . , φ = . ) shows a lightly disturbed case, whereas the red curve (Sr = . , φ = . ) represents the already introduced case with heavy disturbance. e disturbed operating points exhibit constant bar pitch (g B = .

m) but differing bar speed and thus wake frequency. At first sight the distributions are very similar and do not feature any striking differences. On closer examination, variations confined to the regions close to LE (details A and B for ≤ x/C ax ≤ . ) and close to TE (detail C for . ≤ x/C ax ≤ )) become visible. Due to the wake generator rotation closely upstream of LE, for the perturbed operating points the T RUB stator profiles experience inflow with considerable periodical incidence. As shown in prior work by the authors [ ] this results in maximal deviation angles from design inflow of ∆α = -°. e negative incidence inflow shi s the stagnation point at LE towards the suction side. is decreases the velocity on the suction side (detail B) and increases it on the pressure side (detail A) close to LE. Although this is a time-accurate effect, its time-averaged impact can be observed in Figure . Near TE only suction side flow is influenced by the unsteady inflow (detail C). is different behavior of suction side flow near TE can possibly be traced back to the interaction between the passing bar wake and a separation bubble in the rear part of the suction side.

From comparison of these three operating points it becomes obvious that the impact of unsteady inflow on the time-averaged blade pressure distribution is very small. As a consequence, the use of pneumatic pressure taps alone giving time-averaged blade pressure distributions is not suitable for detailed analysis of the discussed unsteady phenomena.

. . Time-resolved measurement data For deeper insight into the unsteady interaction between bar wakes and stator passage flow, time-accurate measurement data of T RUB blade pressures have been conducted. In For all operating points, periodical pressure fluctuations at the blade surface caused by impinging bar wakes can be observed. By analyzing the fluctuations (deviation from the undisturbed condition), the propagation of the wake disturbance from LE across suction and pressure side towards TE can be tracked. Wake kinematics, derived in the context of Figure , can be applied to the profile flow, as well. However, it must be noted that, as bar wake flow around one single profile is now considered in relation to the flow of multiple bar wakes through a passage of adjacent profiles (chapter . . ), bar wake paths and the configuration of the induced flow structures look different. Furthermore, as static blade pressures are considered, the color scale is inverted. Parcels of high velocity correspond to decreased static pressure and vice versa. Before the bar wake impinges at LE, it wraps around it and is cut by the LE. Volume C of squeezed passage flow (high velocity and low static pressure) becomes visible at the suction side and is transported downstream towards TE. Immediately a er the wake has passed, volume D (low velocity, high static pressure) follows. is corresponds to the observations from the stator exit flow field (chapter . . ).

Under low disturbance frequency (Sr = . , φ = . ), the period of time between individual wake events is sufficient for blade flow to switch back to the unperturbed condition. With raising disturbance frequency and thus Sr, the amplitude of time-resolved pressure fluctuations increases significantly, reaching maximum oscillations of ±10 % (relative to cascade outlet dynamic pressure) during one bar wake passing. is results in a highly periodically unsteady blade loading under wake impact. Furthermore, for the lightly disturbed case an additional periodical oscillation can be observed close to TE ( . ≤ x/C ax ≤ ), pointing toward the periodical suppression of a laminar separation bubble. Under steady inflow, the suction side boundary layer is assumed to separate towards TE, forming a separation bubble. With an increasing disturbance frequency the oscillations connected to this phenomenon are reduced. is is indicative of the bubble not switching back to its undisturbed condition for sufficiently high bar wake frequencies.

Figure .

T RUB profile pressure fluctuations at mid-span (Sr = . , φ = . ). Temporal evolution for one bar passing, divided into time instants. e impact of the passing bar wake on the profile flow can furthermore be investigated using Figure , showing the blade pressure fluctuations for four representative time instants of one bar wake passing, again for Sr = . , φ = . . One sensor position on the suction side (x/C ax = . ) is highlighted with a red circle. For t/t BP = this position is already facing the approaching bar wake (parcel C) with decreasing pressure, which further decreases at time instant t/t BP = / . At t/t BP = / the wake has passed and parcel D with maximum local pressure is following. For t/t BP = / the wake has nearly le the profile. On the pressure side similar behavior can be recognized with lower fluctuation amplitudes.

. CONCLUSIONS Within the present work experimental investigations have been performed, focusing on periodically unsteady flow phenomena in a LPT stator passage of a . stage annular cascade. Conventional time-averaged measurement data is completed and combined with phase-averaged, highly time-resolved data, thus simplifying analysis within the time-domain. rough combination of flow field data in the stator exit flow and blade pressure data a link could be established between secondary flow structures downstream of the passage and underlying effects directly at the blade. e well-known secondary flow model could be applied to the stator exit flow field. Analyzthe temporal velocity and vorticity evolution in three characteristic slices of constant span, vortex displacement and weakening could be described. Furthermore, periodically unsteady structures could be identified downstream of the passage.

ese represent the remaining portion of the bar wakes, carrying a velocity field of four characteristic volumes of decreased and increased velocity. Finally the immediate interaction between the bar wakes and T RUB stator profile flow was presented. Similarly to observations made in the passage exit flow, on the blade suction side pressure fluctuations are enhanced considerably for the high Sr case. e interaction of bar wake and profile boundary layer flow could be characterized by the passing negative jet and its alternating sharp decrease and increase of local pressure, respectively velocity.

e negative jet effect, not only describes a fluctuating velocity field, but also an injection of turbulence at various scales into the near wall flow.

ACKNOWLEDGMENTS

e investigations reported in this paper were conducted within the framework of the joint research project "Unsteady Flow and Secondary Flow in Compressor and Turbine Cascades" (PAK-). e authors wish to gratefully acknowledge funding and support by the Deutsche Forschungsgemeinscha (DFG). e experimental investigations would not have been possible without the efforts of our technical staff. e responsibility for the contents of this publication lies entirely by the authors.

NOMENCLATURE

Figure .

 . Figure . Experimental Test Facility. Sectional view (a), D illustration (b).

Figure

  Figure . T RUB blade, instrumented with Kulite LQsensors for time-resolved profile pressure measurements. Pressure side view (le ) and arrangement of sensors (right).

  BP and thus Sr and φ were modified by altering bar speed c B and/or bar pitch g B . e results presented in this article are based on findings from previous work by the authors [ ] where detailed analysis of D flow field traverses were conducted for different combinations of Sr and φ. By including time-resolved blade pressure data for the present work, a causality relationship between the blade passage and downstream flow can be established. . Stator exit flow D flow field traverses have been conducted in multiple planes downstream of the T RUB stator row. Measurement data from these planes permit an evaluation of the secondary flow system emerging upstream within the stator passage. By comparing flow fields of different stator exit flow planes, the processes based on the mixing of stator wakes and vortices with the free passage flow can be described. By considering different operating points -defined by combinations of Sr and φ -and comparing them with the unperturbed case, the effect of bar wakes and the temporal evolution of secondary flow structures can be derived (for detailed underlying analysis see [ ]). . . Time-averaged measurement data Figure shows time-averaged (obtained with HP) distributions of axial vorticity (AVO) in plane . (Figure a), . C downstream of stator TE in the range of two stator pitches.

Figure .

 . Figure . Time-averaged results . C downstream of TE.AVO distribution for steady undisturbed case (le ) and for a case with significant wake disturbed inflow (Sr = . , φ = . ) (right).

  C downstream of stator TE. ree observation stations have been selected at various spanwise positions (R/H = %, %, %) and the corresponding flow field temporal evolution over three bar passing periods of c and AVO are represented in Figure . e stations capture the secondary flow systems near the hub and the shroud and the flow at mid-span. e operating point (Sr = . , φ = . ) matches the one chosen in Figure (right). us, Figure (right) represents the timeaveraged picture of the time-resolved phenomena depicted in Figure .

Figure .

 . Figure . Time-resolved results . C downstream of TE. Time-space evolution of ∆c (top) and AVO (bo om) for three slices at constant span, Sr = . , φ = . . In the upper part of Figure the temporal evolution of velocity c is given, in the lower the same can be seen for the AVO. For the velocity evolution, the respective local values at undisturbed condition have been subtracted from the timeresolved, phase-averaged velocity values:

Figure .

 . Figure . Time-averaged c p distributions at T RUB mid-span for three different operating points.

Figure

  Figure shows time-averaged, non-dimensionalized static blade pressure distributions (c p ) at mid-span (R/H = %) for different operating points, whereas c p was defined as follows:

  Figure the temporal evolution of local blade pressure fluctuations over two bar passing periods are given for profile flow at mid-span. Pressures on suction side ( ≤ x/C ax ≤ ) and on pressure side (-≤ x/C ax ≤ ) are shown for the two already introduced unsteady operating points with light and heavy disturbance and a third one with intermediate perturbation (Sr = . , φ = . ). Similarly to equation ( ), the respective values at undisturbed condition have been subtracted from the time-resolved, phase-averaged pressures.

Figure .

 . Figure . Time-space evolution of T RUB profile pressure fluctuations at mid-span for three periodically disturbed operating points.

Table .

 . Main geometric test rig properties and turbine stage parameters

	Test rig
	Outer diameter (Casing)	D C	.	m
	Inner diameter (Hub)	D H	.	m
	Mid-span diameter	D m	.	m
	Turbine stage
	Blade height IGV, T RUB	H	.	m
	Chord length IGV	C IGV	.	m
	Stagger angle IGV length T RUB Stagger angle T RUB count IGV, T RUB	λ IGV C T =C λ T n IGV,T	-. . .	°Chord m °Blade
	Design flow angles, mid-span:
	IGV inlet	α	.	°IGV
	outlet = T RUB inlet	α =α	. °T
	RUB outlet	α	.	°Axial
	distances:
	IGV TE -bar plane bar plane -T RUB LE	x/C T x/C T	. .
	Bar diameter	D B	.	m
	Bar length	L B	.	m
	Bar pitch at mid-span	g B	.	m,
			.	m,
			.	m
	Operating point, Design point
	Mass flow	ṁ	. kg/s
	Reynolds number (exit, th.)	Re exit, th	,
	Mach number (exit, th.)	Ma exit, th	.
	Strouhal number range	Sr	. -.
	Flow coefficient range	φ	. -.


Benjamin Winhart
email: benjamin.winhart@rub.de

Martin Sinkwitz

Andreas Schramm

David Engelmann

Francesca Di Mare

Ronald Mailach

Francesca Di Mare

S Y Mpo

O Tatin

Experimental and Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact

Keywords:

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Experimental and Numerical Investigation of Secondary Flow Structures in an Annular LPT Cascade under Periodical Wake Impact -Part : Numerical Results

INTRODUCTION

e numerical prediction of interaction effects between incoming wakes and secondary flow structures is challenging as the participating flow phenomena are highly unsteady and three dimensional. is paper discusses the capability of URANS simulations in predicting interaction mechanisms between periodically incoming wakes and the secondary flow system inside a modified, low speed, annular T turbine stator test facility located at the Chair of ermal Turbomachines at Ruhr-Universität Bochum.

Over the years a wide range of experimental and numerical studies about the T secondary flow system interacting with periodically incoming wakes has been carried out. Schulte and Hodson [ ] investigated the impact on loss generation and found that the wake-boundary layer interaction can reduce profile losses by suppressing suction side boundary layer separation. Michelassi et al. investigated the impact of incoming wakes on losses of a linear T A cascade using direct numerical simulations (DNS) and large eddy simulations (LES) [ , , , ]. ey found that the incoming wake dilation can account for % of the overall -dimensional passage losses. ey also highlighted the effect of varying reduced frequency F red and flow coefficient φ on the wake flow path and thus on the overall losses. In an experimen-tal and numerical investigation of the flow through a linear T low-pressure turbine cascade Koschichow et al. focused on the complex flow phenomena near the end wall region of the cascade with and without the influence of incoming wakes [ , ]. ey found that the incoming wakes periodically reduce secondary flow and suppress the propagation of the horseshoe vortex and the passing wakes induce additional vortex structures which interact with the crossflow.

e majority of the aforementioned works focus on linear cascades. However, some important flow features present in real turbomachines flow can not be considered in such configurations.

In a two part research work we present the investigations of an annular low-speed LPT which provides excellent access possibilities and where spatially and temporally highly resolved measurements could be obtained. In part of this study the capability of -dimensional URANS simulations to predict the complex interaction mechanisms involved in the flow inside the investigated stator row is assessed. e turbine is equipped with a modified T RUB stator blading to match the characteristics of the well known and frequently investigated T profile under low Mach-number flow. Based on the numerical results an analysis of the -dimensional flow field is conducted in order to gain insight in the secondary flow structures. e interaction mechanisms between the periodically incoming wakes and the secondary flow structures are further analyzed through an investigation of the kinematics of the incoming wakes based on of flow coefficient φ and Strouhal number Sr in one configuration. Finally a link between wake impacted secondary flow structures and total pressure loss distributions is proposed.

. NUMERICAL SETUP

In this chapter the test case as well as the numerical model, boundary conditions and the numerical setup are briefly described. Finally the solution method is summarized.

. Test Case Description e test case chosen for this study is a large scale low speed axial turbine test rig, located at the chair of ermal Turbomachines of Ruhr-Universität Bochum. e annular test rig consists of an inlet guide vane (IGV) row, a rotating wake generator row and the investigated stator row equipped with a newly designed T RUB LPT blading to match the characteristics of the T profile at low speed conditions. An isometric view of the above mentioned relevant parts is shown in figure with the rotating parts highlighted in red. e main test rig parameters are summarized in table . A more detailed description of the test case is given in [ ] and in [ ]. conditions (BCs) were measured downstream the IGV and imposed at the domain inlet (Fig. ). ese encompass total pressure, velocity direction and turbulence intensity. At the outlet the mass flow rate is adjusted to match the measured axial flow velocity. As the number of wake generators as well as the blade count of the stator is , simple periodic BCs can be set in circumferential direction. is leads to increased demands on the numerical mesh in all spatial directions. e mesh for the wake generator domains has been created using ANSYS ICEM, while the T RUB has been meshed with ANSYS Tur-boGrid. e objective was to create as cubical cell volumes as possible in the area of the vortex generators and the T RUB stator row.

e final mesh consists of approximately . million cells. e main mesh parameters are summarized in table , where d w represents the first cell offset at all wall surfaces, n p and n r stand for the number of cells along the blade profile and along the radial direction and n for the total cell count.

Time step and mesh size sensitivity studies revealed that time steps per wake generator bar passing are sufficient to resolve all relevant frequencies. is leads to a minimum time step of ∆t = 2.1701 • 10 -5 s and a maximum time step of ∆t = 1.3021 • 10 -4 s depending on Sr and φ. .

Solution Method

e calculations presented in this paper have been performed using ANSYS CFX release . . In ANSYS CFX the RANS equations are solved using a pressure-based, coupled, unstructured finite-volume algorithm [ ]. e solver is implicit in time using a second order backward Euler discretization. For convergence acceleration a coupled algebraic multi-grid method is used to solve the discrete system of flow equations

. RESULTS AND DISCUSSION

In this section the numerical predictions are compared with experimental data and discussed.

. Static Pressure Distribution e development of secondary flow structures is strongly affected by the blade loading. To verify that the same blade loading as in the experimental test rig is also reproduced in the calculations, the distribution of pressure coefficient .

c p = p(x)-p 1 p t,1 -p 1 ( ) at %

Integral Flow Values

Integral flow values are compared in this section to verify the correspondence of the operating conditions in the numerical calculations. e inflow axial velocity c x,1 , outflow absolute velocity c 2 and outflow absolute velocity flow angle α 2 are shown in e extension of the lower loss region is a li le more extended in radial direction in the experiment and thus shows a slighlty higher core velocity.

. -Dimensional Field Traverse Data

e topology of the upper secondary loss region is consistent with the measurement data. Both cores with high velocity drops are captured by the CFD although the numerical data show a slightly higher drop in velocity. e connection between the upper core and shroud is a li le less distinct in the numerical data.

Total pressure loss coefficient ζ p : e distribution of time averaged total pressure loss coefficient

ζ p = p t,1 -p t (r, θ) p t,1 -p(r, θ) ( )
shows a consistent structure between experiment and CFD, similar to the velocity field. e loss levels in the areas of profile losses and secondary flow are described very well while the the lower loss region shows a larger radial extension in the experimental data. e freestream loss is also in good agreement.

Vorticity ω x : Vorticity is a quantity which describes the local spinning motion of a continuum. It can be invoked to get a basic idea of the secondary vortex systems in turbomachines, although this method can not distinguish between swirling motions and shearing motions. In Cartesian coordinates the axial vorticity is given by:

ω x = ∂c z ∂ y - ∂c y ∂z .
( ) e comparison between experimental and numerical data shows that the main vorticity distribution is captured well by CFD, although it reveals slight deviations in the upper counter clockwise rotating area.

. IDENTIFICATION OF SECONDARY FLOW STRUCTURES . General Description

To gain a be er understanding of the different vortices which constitute the secondary flow system, an analysis of the D flow field is conducted. A valuable quantity to visualize vortex structures is provided by the Q-criterion which is defined as the second invariant of the velocity gradient tensor ∂u i /∂ x j :

Q = 1 2 Ω i j Ω i j -S i j S i j ( )
with

Ω i j = 1 2 ∂u i ∂ x j - ∂u j ∂ x i and S i j = 1 2 ∂u i ∂ x j + ∂u j ∂ x i , ( )
where Ω i j is the vorticity tensor and S i j is the rate-of-straintensor. us, in contrast to the aforementioned vorticity, the Q-criterion represents the local balance between shear strain rate and vorticity magnitude, defining vortices as areas where the vorticity magnitude is greater than the magnitude of strain rate [ ].

e main vortex structures participating in the secondary flow system of the investigated T RUB stator are visualized in figure at two different angles of view via a -dimensional iso surface of time averaged Q-criterion. is helps tracing the origins and trajectories of individual vortices.

e iso surface is colored with the axial vorticity ω x to provide an impression of the direction of rotation of each vortex.

Utilizing the information obtained by the -dimensional field analysis, an overview of the vortex structures on the evaluation plane . downstream the T RUB stator is presented in figure . is provides a be er indication of the vortex structure expansion and relative positions inside the annulus. In addition, the findings of this analysis build a basis for the interpretation of the experimentally achieved vorticity distributions presented in [ ]. Corner vortex: e corner vortex acts as a balancing vortex between the PV, blade and endwalls, thus it has an opposite sense of rotation as the PV. As mentioned above the CV and the suction side leg of the HSV connect and are not distinguishable downstream of the blade. e resulting vortex is very small compared to the other vortices but is still notice- Trailing edge wake vortices (TEWV): e trailing edge wake vortices originate from the shear layer, starting at the blade trailing edge. Fluid from from suction side and pressure side have different momentum and radial velocity components which results in wake vortices being shed along the blade trailing edge.

. WAKE KINEMATICS

In this chapter the kinematics of the incoming wakes are discussed. Figure shows a temporal evolution of the distribution of velocity fluctuation

c = c(x, θ, t) -c(x, θ) ( )
caused by the incoming wakes at four equally distributed time steps per bar passing on a surface at % span. e projected velocity fluctuation vectors are superimposed as black arrows in order to indicate the direction of the induced wake influence.

t/T = 0: At this point of time the incoming wakes impinge on the pressure side of the T RUB stator right behind the leading edge (A). Inside the wake an adverse velocity fluctuation is induced due to the prevalent total pressure drop, which causes a negative jet. Due to the blockage caused by the incoming wake an area of accelerated flow appears above the upper boundary of the wake (B).

t/T = 1/4: e incoming wake has propagated further into the passage within this snapshot. At the pressure side of the blade the wake front is pushing a region of decreased velocity (C) due to the fluid transport caused by the negative jet effect (highlighted by curved arrows), whilst behind the wake the near wall velocity is increased (D). e wake shape is slightly bowed (highlighted by a black curve) because of the low momentum fluid near the blade surface and higher passage flow velocity.

t/T = 2/4: e wake moves closer to the upper blade suction side which causes the fluid in this area to accelerate further (E). In the presence of the upper blade potential field the wake gets deflected and a aches to its suction side, which additionally increases the wake bow. In front of the wake a clearly distinguishable, clockwise rotating vortex structure is observable (F) which balances the crossflow fluctuations induced by the negative jet.

is vortex causes a velocity reduction at the blade pressure side while it increases the velocity at the neighboring blade suction side. Behind the wake a counter clockwise rotating vortex (G) has the opposite influence on the near wall flow.

t/T = 3/4: Due to the contraction of the passage and the consequently rising convection velocity the wake gets further dilated. Additionally the vortices upstream (H) and downstream (K) of the wake get intensified resulting in higher induced velocity fluctuations.

e front part of the upper blade suction side is covered with low momentum fluid as the wake further bends over its surface.

t/T = 4/4 ∨ 0: is point refers to the le -most picture at t/T = 0 again, but to the wake further downstream (L) of the one described above. Compared to the previous snapshot the wake bow has further increased as well as the intensity of the counter rotating vortices (M,N). e area influenced by the wake is marked by dashed black lines and stretches almost throughout half the passage due to the increasing wake dilation. e area of negative velocity fluctuation (blue) in front of the wake is about to be convected through the first evaluation plane ( . ), which is located at the right boundary of the figure .   t/T = 5/4 ∨ 1/4: e blue area of negative velocity fluctuation in front of the wake now propagates through the evaluation plane whilst the red area at the neighboring blade suction side is directly in front of it. As the four wake affected cells have already passed the lower blade surface, they are now bounded by the stator's wake. e development of the individual vortices is discussed subsequently for eight equally distributed time steps within one bar passing t/T. As the underlying interaction mechanisms are highly complex and coupled, it is not always possible to reduce the explanation of these mechanisms to one fundamental process. erefore, it is important to understand that the observable fluctuations of the participating vortex systems inside the evaluation plane are not only triggered by the wake as it crosses this evaluation plane, but also by the impact of these wakes on the boundary layers at blade and endwalls, as well as on the vortices inside the passage. ese indirect effects occur further upstream and, consequently, it is not always possible to a ribute them to the direct effect of the wake inside the evaluation plane.

As boundary layer investigations are not part of this paper the subsequent analysis focuses on the aforementioned direct effects of incoming wakes on the secondary flow sys-tem. e wake affected flow propagates through the passage and carries cells of lower and higher momentum fluid (figure ), which correlates to lower and higher total pressure. As a consequence also the static pressure distribution gets distorted which directly influences the vortex structures due to the prevalent pressure gradient. In addition cells of high total pressure temporarily decrease the local total pressure loss as they pass the evaluation plane, whereas cells of low total pressure increase it.

To help further the interpretation, the bar passing period is divided into three phases. Within the first phase the vortex in front of the incoming wake passes the evaluation plane. In the present case the first phase spreads from 1/8 ≤ t/T ≤ 3/8, which is deducible from the distribution of total pressure loss coefficient ζ p (right side of each plot) as well as from the distribution of velocity fluctuations shown in figure , which coincide directly with regions of higher and lower total pressure. Within the second phase (4/8 ≤ t/T ≤ 6/8) the vortex behind the incoming wake is convected through the evaluation plane. Inside the third phase almost no wake affected fluid passes the evaluation plane (0 ≤ t/T ≤ 7/8).

Phase (1/8 ≤ t/T ≤ 3/8): Within this section the two cells of wake influenced fluid in front of the wake start to propagate through the evaluation plane. At first the pressure sided cell of low total pressure propagates through the evaluation plane (cf. figure ). is is clearly visible in the total pressure loss distribution shown in figure at time step t/T = 1/8, indicated by high values of ζ p at the pressure side boundary of the stator's wake (A). is cell is intensified until time step t/T = 2/8 where it reaches its maximum extension (B) before the pressure loss is decreased in this area while the cell of low pressure fluid leaves the evaluation plane (C). At the suction side boundary of the stator's wake the wake influence is shi ed in time as the cell of high pressure fluid passes the evaluation plane later within the bar passing period. is process starts at t/T = 2/8 and is indicated by an area of lower total pressure loss coefficient (D) until it reaches its minimum values at t/T = 3/8 where larger areas of negative ζ p are indicated via blanked values (E).

e vortex structures, the TEWV at first are strengthened and subsequently weakened, indicated by the shown contour isolines of Q-criterion (F). As described above, this phenomenon is caused by the positive and negative fluctuations of momentum transferred to the blade's boundary layer via the periodically incoming wakes. e evolution of the lower vortex system shows a continuous weakening of the HSV inside the evaluation plane (G). An analysis of the temporal evolution of the -dimensional vortex structures is presented in figure . For the sake of brevity only two time steps are shown. On the le side the HSV has its maximum extension (t/T = 0), whilst on the right side the HSV has its smallest extension (t/T = 4/8).

e analysis revealed that further upstream (A) the pressure side HSV is deflected by the cells of high and low pressure inside the wake. is deflection causes the HSV to periodically impinge on the suction side near the area where the PV is affected by the corner separationn. (B). Due to this impingement the system consisting of PV and CSV is deflected towards midspan direction. Another effect is that the HSV loses momentum, which is observable inside the evaluation plane shortly therea er. As a consequence of the weakened HSV a shi of PV and CSV back towards the endwalls is observable inside the evaluation plane at (H). is results in a fluctuating migration of the participating vortices in radial direction which is additionally influenced by the wake induced crossflow pressure gradient.

Phase (4/8 ≤ t/T ≤ 6/8): Within this part the vortex structure located upstream of the incoming wake is passing the evaluation plane. At the suction side boundary of the stator's wake this passing is indicated by an emerging area of high total pressure loss (K) which is induced by the low pressure cell passing the evaluation plane. is area of high total pressure loss has its maximum extension around t/T = 5/8 (L) before it is weakened again (M) as the low pressure cell leaves the evaluation plane. At the pressure side boundary the high pressure cell causes a loss reduction with an area of negative ζ p marked by blanked values (N). In the following time steps the total pressure loss in this area rises again (O).

e main vortex systems are further shi ed towards the endwalls, weakened and reach their minimum extension around 5/8 ≤ t/T ≤ 6/8 (P). is process is the continuation of the process described above in Phase . While both HSV are continuously weakened until t/T = 5/8 (Q), they get intensified at t/T = 6/8 until they reach their maximum ex- Phase (0 ≤ t/T ≤ 7/8): During the third phase only fluid which is not affected by the wake passes the evaluation plane. In comparison to the time-averaged distribution in figure the topology in this phase shows almost the same distribution of vortex structures and all vortex structures are clearly distinguishable. e HSVs are very pronounced, especially at the hub-side. e vortex systems consisting of PV & CSV are shi ed towards midspan. is creates enough room for the HSV to spread and is a direct consequence of a strong corner separation which is caused by strong secondary flow. is TEWV system gets periodically suppressed by the incoming wakes which is in accordance to the findings of the experimental investigations by Sinkwitz et al. [ , ] and can be explained by the transport of energy to the boundary layer described above.

. SUMMARY AND CONCLUSION

In the present study URANS simulations of a large scale, low Mach number, annular turbine equipped with a newly designed T RUB LPT blading were conducted. e blading was modified to match the characteristics of the well known and frequently investigated T profile at low speed conditions. e results achieved by this simulations were compared with against stationary measurement data by means of static pressure distribution around the blade profile, integral flow values and -dimensional field traverse data and showed excellent agreement. e validation ensured that a detailed flow field analysis based on the CFD data is admissible. Well resolved CFD results were then used to identify the different vortex structures which interact in the secondary flow system of the investigated stator profile via an analysis of the -dimensional distribution of vortex structures visualized by the time averaged Q-criterion.

e information of this analysis were utilized to deduce the distribution of vortex structures inside the evaluation plane. Based on these findings a link between vortices and the distribution of axial vorticity was established supporting the interpretation of the experimental data. An analysis of the wake kinematics revealed that the negative jet effect, caused by the periodically incoming wakes, induces two counter rotating vortices in front and behind the wake which extend in radial direction. As the wake affected fluid propagates through the passage these vortices create cells of low and high momentum fluid which affect boundary layers at blades and end walls.

A study of the temporal evolution of participating secondary flow structures revealed a strong interaction between the incoming wakes and the vortices, which are periodically weakened and intensified. It was found that the wake affected fluid causes a fluctuation of the pressure side legs of the horse shoe vortices, which interact with the passage vortices.

is results in a radial shi of the passage vortices and concentrated shed vortices. In addition the horse shoe vortices get weakened due to the transfer of momentum into the passage vortices.

Regarding the distribution of total pressure loss on the evaluation plane, the temporal analysis revealed that the main impact on total pressure loss is caused by the cells of high and low pressure fluid inside the wake affected flow which causes a periodical reduction and rise of total pressure loss compared to the undisturbed flow.

It can be concluded that URANS simulations are capable of predicting the secondary flow structures for the underlying test case to a good degree of detail. Some minor deviations between CFD predictions and measurement are observed but the main vortex system is depicted very well.

ACKNOWLEDGMENTS

e investigations reported in this paper were conducted within the framework of the joint research project Unsteady Flow and Secondary Flow in Compressor and Turbine Cascades (PAK-). e authors wish to gratefully acknowledge its funding and support by the Deutsche Forschungsgemeinscha (DFG). e responsibility for the contents of this publication is entirely with the authors.

NOMENCLATURE

Figure .

 . Figure . Isometric view of the test rig's relevant parts including IGV, rotating wake generator (red) and investigated T RUB stator row

Figure .

 . Figure . Numerical domain with visualized total pressure inlet BC

  [ ]. All steady and unsteady simulations were performed using the shear stress transport (SST) Menter two equation turbulence model [ ]. To capture transitional effects, the γtransition model is used [ ], which is a further development of the widely used γ-Re θ -transition model.

  span is compared to experimental data. e results are shown in Figure and are in a good overall agreement with slight deviations in the a pressure side distribution.

Figure .

 . Figure . Comparison of experimentally and numerically achieved pressure coefficient c p at % span (Sr = 1.35, φ = 0.97); experimental data are shown with error bars of % confidence interval

  Figure . Schematic meridional view of numerical domain and measurement planes downstream T RUB stator trailing edge

Figure .

 . Figure . Secondary flow structures for Sr = 1.35, φ = 0.97 visualized using time averaged Q-criterion iso surface at Q = 2 • 10 5 1/s colored with vorticity ω x

Figure .

 . Figure . Contour plot of time averaged vorticity ω x with isolines of time averaged Q-criterion Q = 2 • 10 5 1/s at measurement plane . (Sr = 1.35, φ = 0.97)

Figure .

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

Figure .

 . Figure . Temporal evolution of secondary flow structures visualized via isolines of Q-criterion Q = 2 • 10 5 1/s and contours of axial vorticity ω x (le ) and contours of total pressure loss coefficient ζ p at Sr = 1.35 and φ = 0.97 at measurement plane . (0.15 • C downstream T RUB TE)

Figure .

 . Figure . Distribution of secondary flow structures at two instants of time for Sr = 1.35, φ = 0.97 visualized using Q-criterion iso surface at Q(t) = 2 • 10 5 1/s colored with vorticity ω x

Table .

 . Main test rig parameters

	Test rig
	Outer diameter (Casing)	D C	. m
	Inner diameter (Hub)	D H	. m
	Mass flow	m	. kg/s
	Operating point, Design point
	Reynolds number (exit. theor.)	Re exit,th	,
	Mach number (exit. theor.)	Ma exit,th	.
	Strouhal number range	Sr	. -.
	Flow coefficient range	φ	. -.

Table .

 . Summary of important mesh parameters

		d w [m] n p	n r	n
	WG	5 • 10 -6		. m.
	T	5 • 10 -6		. m.
	total			. m.

Table .

 . Comparison of integral flow values

		c x,1 [m/s] c 2 [m/s] α 2 [°]
	EXP	.	.	.
	CFD	.	.	.
	∆ [%]	.	.	.

  Stokes the turbulent flow through a low-pressure turbine cascade in the endwall region. Number , pages -. Proceedings in Applied Mathematics and Mechanics. [ ] D. Koschichow, J. Fröhlich, I. Kirik, and R. Niehuis. DNS of the flow near the endwall in a linear low pressure turbine cascade with periodically passing wakes. Number GT -. Proceedings of ASME Turbo Expo . [ ] M. Sinkwitz, B. Winhart, D. Engelmann, F. di Mare, and R. Mailach. Experimental and numerical investigation of secondary flow structures in an annular LPT cascade under periodical wake impact -part : Experimental results. Proceedings of ISROMAC, Maui, Hawaii, December -. [ ] M. Sinkwitz, D. Engelmann, and R. Mailach. Experimental investigation of periodically unsteady wake impact on secondary flow in a . stage full annular LPT cascade with modified T blading. Number GT -. Proceedings of ASME Turbo Expo, Charlo e, NC, USA, June -. [ ] G. Schneider and M. Raw. Control volume finite-element method for heat transfer and fluid flow using collocated variables -. computational procedure. Numerical Heat Transfer, ( ): -, . [ ] B. Winhart, D. Micallef, and D. Engelmann. Application of the time transformation method for a detailed analysis of multistage blade row interactions in a shrouded turbine. Number ETC -. Proceedings of th ETC, F. Menter, P.E. Smirnov, T. Liu, and R. Avancha. A oneequation local correlation-based transition model. Flow, Turbulence and Combustion, July . [ ] V. Kolář. Vortex identification: New requirements and limitations. International Journal of Heat and Fluid flow, pages -, .

				r	[m]	radial coordinate
				r ′	[m]	transformed radial coordinate
				Re	[-]	Reynolds number
				S i j	[1/s]	rate-of-strain tensor
				Sr	[-]	Strouhal number
				t	[s]	time
				T	[s]	bar passing time
				c x	[m/s]	axial velocity
				x	[m]	axial coordinate
				x ′	[m]	transformed axial coordinate
				Greek Symbols
				α	[°]	absolute velocity flow angle
				ζ p	[-]	pressure loss coefficient
				θ	[°]	circumferential coordinate
				ρ	[kg/m 3 ] mass density
				φ	[-]	flow coefficient
				ω x	[1/s]	axial vorticity
				Ω i j	[1/s]	vorticity tensor
				Abbreviations BC	boundary condition
				CFD	computational fluid dynamics
				CSV	concentrated shed vortex
				CV	corner vortex
				IGV	inlet guide vane
				HSV	horseshoe vortex
				PV	passage vortex
				TEWV	trailing edge wake vortex
	URANS Navier-April -, Unsteady Reynolds Averaged ; Stockholm, Sweden. [ ] F. Menter. Two-equation eddyviscosity turbulence
	models for engineering applications. AIAA Journal,
	( ):	-	,	.
	[ ]
	Latin Symbols
	arc SS	[m]		suction side arc length
	c	[m/s]		absolute velocity
	C	[m]		chord length
	c p	[-]		pressure coefficient
	g	[-]		pitch
	H	[m]		blade height
	p	[Pa]		pressure
	p t	[Pa]		total pressure
	Q	[1/s 2 ]		velocity invariant Q