# Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Sub-Project A—Periodically Transient Near-Wall Flow within Rotating Compressor Cascades

#### 2.1. Scope of Sub-Project A

#### 2.2. Experimental Setup

#### 2.2.1. Test Facility

_{b}= 2 mm. They are mounted 65.6% C upstream of the R1 leading edge (LE). This approach allows the analysis of the effect of an isolated wake disregarding the complex secondary flow field of a stator row. Furthermore, it enables a more direct comparison to linear cascade investigations where an analog setup was examined, cf. Krug et al. [23]. Due to the discarded IGV, the mass-flow rate is adjusted to ensure the same rotor entry incidences as for the design point (DP) resulting in an adjusted design point at 10% higher mass-flow. All rotor data shown here correspond to this operating point. As this paper gives a short overview of the work done, only the nominal tip clearance cases, s/C = 2.0% for the stator and s/C = 1.36% for the rotor, will be presented here.

#### 2.2.2. Measurement Techniques

_{ax,R1}downstream of the trailing edge (TE) of R1, and at once located 16.3% C

_{ax,S1}upstream of the LE of S1. The second one, MP5, is positioned 21% C

_{ax,S1}downstream of the TE of S1. At both positions the measuring probes can be traversed radially and rotated around their axis. All stator rows are rotated simultaneously around the machine axis to alter the relative position between probe and stator vanes in pitchwise direction. Five-Hole-Probes (FHP) with spherical heads of a diameter of 2 mm are used to capture the steady flow field. Balancing the pressures in the two lateral holes via probe rotation allowed to measure the magnitude and direction of the velocity in absolute frame of reference with an accuracy of $\Delta \mathrm{v}=\pm 0.3\mathrm{m}/\mathrm{s}$ and $\Delta \mathsf{\alpha}=\pm 0.26\xb0$, respectively. The unsteady flow field is acquired using a fast measuring pressure probe (FMP), designed and manufactured at the chair of Turbomachinery and Flight Propulsion in Dresden. This one-hole-probe is equipped with a piezoresistive pressure sensor, see also Lange et al. [24]. Measurements with the FMP are performed at three different angles ($\Delta \mathsf{\alpha}=30\xb0$) virtually creating a three-hole-probe. In the presented results the unsteady flow field data is analyzed by either looking at the time or ensemble average.

#### 2.3. Numerical Setup

^{TM}/Turbo by NUMECA is applied to calculate the three-dimensional RANS equations for the investigated stator cases. Analog to the experiments the combination of IGV and S1 is simulated in a single passage with periodic boundary conditions. The upstream generated wake is passed-through the domain using a perfect connection interface (Full Non Matching Frozen Rotor). The Explicit Algebraic Reynolds Stress Model (EARSM) is exploited to close the system of equations, which was found to deliver the best agreement with experimental results compared with other RANS turbulence models available in the flow solver for the LSRC, see also Lange et al. [24].

^{+}of around 1. In spanwise direction the average density of grid nodes in the tip gap is held constant at a ratio of 22 cells per 1% of gap size normalized by channel height (s/H). The number of cells in the remaining flow channel is adjusted analogously resulting in final meshes with $1.0\cdot {10}^{7}$ up to $1.5\cdot {10}^{7}$ grid points.

#### 2.4. Current Investigations and Results

#### 2.4.1. Influence of the Inlet Boundary Layer Skew

_{t}(in black) and flow angle in absolute frame of reference α (in orange) are shown for MP4. Here lines, solid for un-skewed and dashed for skewed BL, represent results from computational fluid dynamics (CFD) calculations and the symbols, square for un-skewed and delta for skewed BL, denote to the experimental data (EXP).

_{Stator}in pitchwise direction, where θ/P

_{Stator}corresponds to the circumferential distance normalized by S1 pitch. In a compressor cascade a skewed inlet BL reduces the cross passage flow in the vicinity of the hub as its direction of influence directly opposes the pressure gradient from pressure side (PS) to suction side (SS) of two adjacent vanes. This weakens the passage vortex and was observed for a linear compressor cascade by Moore and Richardson [26]. In the current work these findings were confirmed for the axial machine in a non-clearance case for S1, cf. Koppe et al. [27].

#### 2.4.2. Influence of Relative Motion between Vane Tip and Corresponding Endwall

#### 2.4.3. Combined Influence of Boundary Layer Skew and Relative Motion between Vane Tip and Corresponding Endwall

#### 2.4.4. Influence of Incoming Periodic Wakes

_{WG}= 0.00) to two (Δθ/P

_{WG}= 0.25) a reduction in low non-dimensional axial velocity is observed in the tip region where the deterioration progresses as the bar wake approaches the rotor. After passing the rotor wake, the area of low relative axial velocity in the vicinity of the blade tip strengthens again and increases with growing distance of the WG wake, as can be seen in time steps three (Δθ/P

_{WG}= 0.50) and four (Δθ/P

_{WG}= 0.75).

_{WG}= 0.25 and Δθ/P

_{WG}= 0.50 of Figure 5c. This leads to the assumption that the incoming wake influences the transition on the blade profile, which was observed for the linear compressor cascade as well as for the axial turbine configuration, see Section 3.4.5 and Section 5.4.2 respectively. Another explanation could be radially varying pressure profiles on the rotor surface due to the change of the TLV in the tip region. Further investigations are necessary to verify these hypotheses.

#### 2.5. Work in Progress

## 3. Sub-Project B—High Fidelity Numerical Investigations of the Secondary Flow in a Linear Compressor Cascade

#### 3.1. Scope of Sub-Project B

#### 3.2. Geometry

#### 3.3. Numerical Setup and Grid

#### 3.4. Current Investigations and Results

#### 3.4.1. Validation of WRLES with Respect to DNS Data

#### 3.4.2. Validation of WRLES with Respect to Experimental Data

#### 3.4.3. Secondary Flow Effects in Compressor Cascade

#### 3.4.4. Effect of Relative Endwall Motion

#### 3.4.5. Incoming, Periodically Perturbed Flow Field

#### 3.5. Work in Progress

## 4. Sub-Project C – Periodically Transient Near-Wall Flow in the T106 Turbine Row

#### 4.1. Scope of Sub-Project C

_{exit,th}= 0.59, Re

_{exit,th}= 2 × 10

^{5}). The basis of the investigation comprises measurements in the High-Speed Cascade Wind Tunnel (HGK) of the Institute of Jet Propulsion at the Bundeswehr University Munich [40]. URANS simulations provide additional information in areas of limited accessibility and in return, the measurements are utilized to evaluate the computational approach. A major focus is put on the different effects on endwall flow, caused by unsteady inflow conditions, changing inlet endwall boundary layer conditions, and blade loading. In this context, particular attention is given to the components of endwall loss development inside the blade passage and the downstream secondary flow field. Furthermore, an additional goal of sub-project C is investigating the aspect of endwall heat transfer.

#### 4.2. Experimental Setup

_{b}/P = 0.5 and the bar speed is v

_{b}= 20 m/s. The resulting flow conditions are listed in Table 3, including Strouhal number Sr and flow coefficient φ, which describe the number and orientation of wakes present in the blade passage at any given instant.

#### Measurement Techniques

_{2,err}= 0.0043, ζ

_{2,err}= 0.321%, β

_{2,err}= 0.093°, and α

_{2,err}= 0.14°. All integral values of the experimental and CFD data refer to a mass-flow-weighted-average. Inlet boundary layer measurements were conducted using a CTA-probe with a tungsten wire of 1.25 mm length and 5 μm diameter. The sampling time is set to 5 s at a rate of 60 kHz. The velocity calibration was performed in a range of 0.0 ≤ M ≤ 0.5 at constant angles of pitch, yaw, and pressure levels with respect to the ensuing measurements. The overall uncertainty estimate of a velocity sample is Δv ≤ 2.5 m/s. Further details on the experimental setup, measurement techniques, the particular turbine cascade design, which was implemented, and a discussion of the full experimental results can be found in [45].

#### 4.3. Numerical Setup

^{+}≤ 1), resulting in high boundary layer resolution. Sufficient spatial and temporal discretization is ensured by a sensitivity study, which leads to an overall number of nodes of approximately $8\cdot {10}^{6}$ and a number of time steps per moving domain period of 800. Leakage panels are incorporated at the bar gap boundaries to simulate the leakage flow. The imposed static pressure condition is determined based on experimental data. The flow conditions prescribed at the in- and outlet plane match the wind tunnel conditions in the experiment (${\mathrm{M}}_{\mathrm{exit},\mathrm{th}},{\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}=\mathrm{f}\left(\mathrm{T}t1,\mathrm{p}t1,\mathrm{p}3\right)$ and ${\mathrm{TI}}_{1}$). A detailed description of the computational approach can be found in [48].

#### 4.4. Current Investigations and Results

_{x}= 0.95. This discrepancy is attributed to a quicker turbulence decay in the computational domain resulting in a locally lower turbulence intensity, even though ${\mathrm{TI}}_{1,\mathrm{CFD}}$ matches the experimental level. The turbulent dissipation rate could be adjusted by tweaking the inlet level of the turbulent length scale, however, a low level of this quantity is imperative for an accurate prediction of the loss generation. In the case of unsteady inflow conditions, a pitchwise incidence of $\mathrm{i}=-1.5\xb0$ is induced, resulting in decreased blade loading in the front part of the blade suction surface. At the aft section of the suction surface the separation bubble is suppressed due to wake induced transition. Both these effects are predicted well in the numerical simulations [48].

#### 4.5. Work in Progress

## 5. Sub-Project D—Influence of Periodic Wakes on the Transient Near-Wall Flow in an Annular Axial Turbine Cascade

#### 5.1. Scope of Sub-Project D

^{RUB}, was developed within this collaborative project for matching the transition and separation characteristics of the original T106 profile (also applied in sub-project C) at low flow speeds, thus facilitating measurements to be taken in an annular, large-scale test rig (see [51]). The stator flow is periodically perturbed by incoming wakes from a rotating wake generator.

#### 5.2. Experimental Setup

^{RUB}stator row under investigation, presented in Figure 25. The large dimensions of the flow channel allow detailed flow measurements with negligible perturbation by installed probes. Rotatable casing elements with multiple probe accesses facilitate the recording of two-dimensional flow field traverses in various planes. Following, the most important information regarding the setup are given, a more detailed description was provided in [51,52,53].

^{RUB}stator whilst leaving the flow as far as possible unaffected by wakes and secondary flow. With both 60 IGV and T106

^{RUB}profiles, it is ensured that every T106

^{RUB}passage faces identical inflow conditions. The IGV is placed 261% C upstream of the wake generator.

^{RUB}stator was equipped with radially stacked, circular steel bars (bar diameter D

_{b}= 2 mm, bar length L

_{b}= 168 mm). The use of periodically passing circular bars facilitates to isolate both velocity defect and turbulence increase of typical rotor blade wakes without the secondary flow structures emerging in a real rotor passage. Wakes are generated at an axial distance of 33% C upstream in a plane parallel to the stator leading edges, representing a typical axial gap width in a LPT. The investigations were carried out for a bar pitch of P

_{b}= 78 mm, matching the pitch of both the IGV and the T106

^{RUB}.

^{RUB}, is an in-house modification of the well-known T106 LPT blade, with modified distributions of profile thickness and curvature. It was developed to match Reynolds number, blade loading distribution c

_{p}at midspan and thus an equivalent boundary layer development of the original T106 profile at the rig’s low Mach number flow. The principles of the transformation procedure were described by Sinkwitz et al. [51].

#### 5.3. Measurement Techniques

^{RUB}stator and the exit flow field downstream of the T106

^{RUB}stator. Two-dimensional flow field traverses in the exit flow (38 radial and 25 circumferential positions, distributed over two T106

^{RUB}stator passages) have been carried out at 15% C and 35% C downstream of T106

^{RUB}TE. For this, hot-wire anemometry measurements (CTA mode) were conducted using a Dantec Dynamics StreamLine 90N10 CTA anemometer (incorporating three 90C10 CTA modules) and both straight and slanted 1-wire probes in the inflow and Split-Fiber probes (SFP, types 55R56 and 55R57) in the wake-flow, shown in Figure 26a. In the wake regions, characterized by intense flow angle variations, SFP have proven superior usability. Due to this and their increased durability, they have been chosen for most of the measurements. All probes were subjected to a multi-dimensional calibration prior to the measurements, during which the corresponding flow angle and velocity were varied within the anticipated range. Using the two voltage values resulting from the SFP measurement, the respective flow angle as well as the magnitude of the velocity (giving a 2D flow vector) were reconstructed. By combining two consecutive measurements with SFP 55R56 and 55R57, the phase-averaged 3D flow vector was finally reconstructed by analyzing the data sets of both probe measurements simultaneously.

^{RUB}stator passage, several T106

^{RUB}profiles were equipped with surface-mounted hot-film sensor arrays, Kulite-sensors (10 sensors of type LQ-125, sealed gage variant) and static pressure taps. Hot-films (thickness ≈ 0.05 mm, custom-fabricated by Tao of Systems Integration Inc.,) feature 24 sensor elements on the SS layout, 20 elements on the PS layout and a constant spacing of 6 mm between the individual sensor elements. For hot-film sensor operation and data acquisition also the StreamLine 90N10 CTA anemometer along with three 90C10 CTA modules was applied. For data acquisition of hot-wire and hot-film measurements, a National Instruments NI 9215 module was employed. More details regarding the hot-film setup are provided in [54].

^{RUB}profile hot-film, Kulite and static pressure measurements in various radial (direction of blade height) positions, a modular T106

^{RUB}blade was realized. The modular blade is made up of multiple, stackable elements and can be equipped with various instrumented modules at different blade height positions within the modular blade. In Figure 26b the assembled modular blade containing a module with SS hot-film instrumentation at midspan position is shown. Figure 26c gives the Kulite sensor locations.

#### 5.4. Current Investigations and Results

^{RUB}exit Reynolds number ${\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}$ (based on T106

^{RUB}chord length C and the theoretical exit velocity ${\mathrm{v}}_{\mathrm{exit},\mathrm{th}}$ analogous to sub-project C) was applied for the definition and adjustment of the operating point, defined by ${\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}=2\xb7{10}^{5}$ and representing a typical value for LPT operation. To study the effect of periodic flow perturbation, the conditions of unperturbed T106

^{RUB}inflow were compared to two other cases, one with a moderate frequency of perturbation (Sr = 0.43, φ = 2.97) and another one with a high frequency of perturbation (Sr = 1.33, φ = 0.97), whereas Sr was defined with flow quantities at midspan. From the hot-wire traverses, the turbulence intensity at the T106

^{RUB}inlet was estimated to be between TI = 0.5% in the free stream and TI = 2.5% in the IGV wake without bar wake perturbation, whereas the bar wakes induce a periodic TI increase, reaching values of it up to TI = 20%.

#### 5.4.1. Incoming, Periodically Perturbed Flow Field

^{RUB}leading edges with radial traverses.

^{RUB}inflow incidence (Δα ≈ 10°), a velocity defect (Δv > 5 m/s) and a turbulence increase from the unperturbed level of TI ≈ 1.5% up to levels of TI > 15% in the midspan section. Additionally, Figure 28 gives an overview regarding the time-averaged distributions of the discussed flow field quantities for the unperturbed and the two perturbed cases. Despite the additional periodic, bar wake induced perturbations, a certain degree of homogenization for the velocity and the flow angle can be assessed concerning the IGV non-uniformities near the endwalls. In terms of turbulence intensity, the increased rotational speed of the wake generator and thus the higher relative velocities for higher Sr also increases the general level of turbulence from TI < 2% (undisturbed) to TI ≈ 8% for Sr = 1.33 at midspan.

#### 5.4.2. Situation within the T106^{RUB} Blade Row

^{RUB}blade row, the incoming bar wakes evoke both large-scale (blade row kinematics) and micro-scale (profile boundary layer properties) effects, wherefore the following analysis is divided into two parts.

^{RUB}profile at midspan for the already introduced cases (Sr = 0.43, Sr = 1.33) and an intermediate perturbation frequency (Sr = 0.90). In this depiction, $0<\mathrm{S}/{\mathrm{S}}^{*}<1$ describes the suction side flow, whereas $-1<\mathrm{S}/{\mathrm{S}}^{*}<0$ represents the pressure side flow with $\mathrm{S}/{\mathrm{S}}^{*}=0$ marking the LE. For all three cases, the periodic pressure fluctuations (as response on the bar wake convection) can be determined clearly across the profile surface, both on the pressure and the suction side. Near the suction side, the passage flow is compressed and accelerated by the approaching wake structure, so that the wake pushes a regime of accelerated flow in front of it, followed by a region of low velocity fluid, which is vice versa on the pressure side, shaping the typical, negative jet like structure of a wake within a blade passage [59,60].

^{RUB}suction side at midspan for the low and high Sr cases. For means of comparison, on top of the diagrams the QWSS distribution for undisturbed flow is added. The practicable quantity of QWSS is used as a qualitative means for the description of the boundary layer. Following the approach of Hodson [61], the measured voltage values (E) are combined with the sensors’ behavior under zero-flow conditions (E

_{0}) for a semi-quantitative analysis of the wall shear stress τ

_{w}:

- Wake-induced boundary layer instabilities, like locally confined turbulent patches or Klebanoff-Streaks, which are induced in the front part of the profile boundary layer far upstream, propagate slower (0.5 < v/v
_{FS}< 0.88) than the free stream (FS) and the wakes [62]. - Calmed regions exert a damping effect on the boundary layer instabilities, thus counteract transition and separation and spread while propagating downstream [63], while their velocity of convection is also considerably reduced (0.3 < v/v
_{FS}< 0.5).

#### 5.4.3. Impact on the Secondary Flow Structures

^{RUB}blade passage. Thus, especially in the hub region, a distinction between passage vortex (PV) and the pressure side leg of the horse shoe vortex (HSV-PL) is enabled for t/T

_{BP}= 1/3, as the HSV-PL slides beneath the PV and pushes it along the suction side trailing edge radially inward, before it blends again with the PV. As could be shown in detail in [52,53,55,56], this periodic and short-duration event is based on the upstream wake impact on the developing HSV-PL, which is massively diverted in the front part of the blade passage by the impinging wake structure. Also, the unsteadiness of the suction side corner separation, shaping the concentrated shed vortex (CSV) can be realized. Additionally, in the lower half of the figure the temporal evolution of the turbulence intensity (TI) is shown. Different from the vorticity representation, the turbulence intensity not only highlights the secondary flow regions, but also emphasizes the influence of the bar wake with its increased turbulence. This becomes especially evident for t/T

_{BP}= 2/3, when the wake becomes evident in the center of the passage between the two Tes. Even after passing through the passage, the wake still transports significant turbulence. Thus, in multistage environments, the subsequent blade row and the transition processes occurring therein are still inevitably affected.

_{BP}), indicating the wave-like behavior of the vortex-dynamics. Furthermore, this method of data representation clearly illustrates the combination of periodic weakening and the connected displacement, defining the unsteadiness of the secondary flow system. On the one hand, the interaction mechanisms between HSV-PL and PV (periodic displacement and weakening) can be detected. On the other hand, the considerable magnitude of radial CSV-displacement resulting from HSV-PL and PV manipulation is realized. Following the short-duration weakening of PV and HSV-PL, the CSV is shifted towards the endwalls shortly after, as well. Supplementing, Figure 33c shows a three-dimensional depiction of the lower flow channel half between R/H = 0 and R/H = 0.5, thus only the near-hub part of the secondary flow system. This helps to clarify the dynamics of interaction between PV and HSV-PL, illustrating the approaching HSV-PL, its impact on the PV and the following radial PV-displacement.

#### 5.5. Work in Progress

^{RUB}passage flow, the consideration of tip leakage flow, the resulting tip leakage vortices and their impact on the secondary flow system. For this, a radial gap is realized between the T106

^{RUB}-profiles and the hub endwall contour. This increase in complexity means another step from the scientific point of view towards multistage turbomachine flow.

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Roman Symbols | |

ax | Axial Direction (for the annular cascade) |

C | Chord |

c_{f} | Friction Coefficient |

c_{p} | Pressure Coefficient |

D | Diameter |

H | Passage Height, Channel Height |

H_{12} | Shape Factor |

Δh_{t} | Change in Total Enthalpy |

M | Mach Number |

$\dot{\mathrm{m}}$ | Mass Flow |

P | Pitch Distance |

p, p_{dyn}, p_{t} | Static, Dynamic and Total Pressure |

r | Spanwise Direction (for the annular cascade) |

Re | Reynolds Number |

s | Gap Size |

S | Distance along Blade Profile |

Δs | Change in Entropy |

Sr | Strouhal Number |

t | Time |

T_{BP} | Bar Passing Period |

TI | Turbulence Intensity [%] |

u | Circumferential speed |

v | Velocity |

x | Axial Direction |

y | Pitchwise Direction (for the linear cascade) |

y+ | Non-Dimensional Wall Distance |

z | Spanwise Direction (for the linear cascade) |

Greek Symbols | |

α | Yaw Angle, Flow Angle (1 for inflow, 2 for outflow) with respect to pitchwise direction |

β | Flow Angle in Pitchwise Direction with respect to axial direction |

δ | Boundary Layer Thickness |

η | Normal Distance to a Wall |

ζ | Total Pressure Loss Coefficient (Equation (1) for compressor, Equation (6) for turbine) |

θ | Pitch Distance (For the annular cascade) |

λ_{2} | 2nd Eigenvalue of Velocity Tensor |

ρ | Density |

τ_{w} | Wall Shear Stress |

φ | Flow Coefficient |

Abbreviations | |

AVO | Axial Vorticity |

b | Bar (used as a subscript) |

BL | Boundary Layer |

CFD | Computational Fluid Dynamics |

CSV | Concentrated Shed Vortex |

CTA | Constant Temperature Anemometry |

CV | Corner Vortex |

DNS | Direct Numerical Simulation |

DP | Design Point |

EARSM | Explicit Algebraic Reynolds Stress Model |

EXP | Experiment |

FHP | Five Hole Probe |

FMP | Fast Measuring Pressure Probe |

FS | Free Stream |

FTT | Flow Through Time |

HGK | High-Speed Cascade Wind Tunnel (Hochgeschwindigkeits-Gitterwindkanal) |

HS | Half-Span |

HSV | Horse Shoe Vortex |

IGV | Inlet Guide Vane |

LSRC | Low-Speed Research Compressor |

LE | Leading Edge |

LES | Large Eddy Simulation |

LPT | Low Pressure Turbine |

MCV | Million Control Volumes |

MP | Measuring Plane |

MS | Midspan |

NI | National Instruments |

PIV | Particle Image Velocimetry |

PL | Pressure Side Leg |

PS | Pressure Side |

PV | Passage Vortex |

QWSS | Quasi Wall Shear Stress |

R1 | Rotor of Stage 1 |

RANS | Reynolds Averaged Navier Stokes |

Re | Reynolds Number |

ref | Reference Value |

RM | Relative Motion between Blade Tip and Adjacent Wall |

rms | Root Mean Squared |

S1 | Stator of Stage 1 |

SAS | Scale Adaptive Simulation |

sec | Secondary |

SS | Suction Side |

SVO | Streamwise Vorticity |

TE | Trailing Edge |

TKE | Turbulent Kinetic Energy |

th | Theoretical, Thickened |

TLV | Tip Leakage Vortex |

URANS | Unsteady Reynolds Averaged Navier Stokes |

WG | Wake Generator |

WRLES | Wall-resolving LES |

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**Figure 1.**Low Speed Research Compressor (LSRC)—cross section of investigated setups with stator S1 (

**a**) and rotor R1 (

**b**).

**Figure 2.**Pitchwise averaged total pressure p

_{t}(black) and flow angle α (orange) upstream of S1 (MP4) in the hub endwall region, s/C = 2.0%, EXP vs. CFD.

**Figure 3.**Effect of varying hub wall motion on non-dimensional total pressure loss coefficient downstream of S1 (MP5) (

**a**–

**c**) EXP, (

**d**–

**g**) CFD, and on the TLV trajectory (${\mathsf{\lambda}}_{2}(\langle \overrightarrow{\mathrm{v}}\rangle )=-{10}^{6}$) (

**h**–

**k**) CFD, s/C = 2.0%.

**Figure 4.**Effect of varying hub wall motion on pitchwise averaged flow angle in absolute frame of reference downstream of S1 (MP5), s/C = 2.0%, CFD.

**Figure 5.**Effect of incoming periodic transient wakes on (

**a**) time- and pitchwise averaged data up- (MP3) and downstream (MP4) of R1, (

**b**) ensemble- and pitchwise averaged FMP data and (

**c**) ensemble averaged FMP data at discrete relative positions between WG and R1 downstream of R1 (MP4), s/C= 1.36%, EXP.

**Figure 6.**Top down view of the simulated linear cascade profile with zoom of the computational domain (shaded region), repeated in y-direction (grey). Coordinates are scaled using the blade chord. Red dashed line at $\mathrm{x}/\mathrm{C}=0.89$ depicts the stage outlet plane.

**Figure 7.**Linear compressor cascade at ${\mathrm{Re}}_{\mathrm{C}}=1.46\cdot {10}^{4}$. (

**a**) Vortical structure visualized through ${\mathsf{\lambda}}_{2}(\langle \overrightarrow{\mathrm{v}}\rangle )=-2$. (

**b**) Pitchwise averaged total pressure losses downstream of the blade at $\mathrm{x}/\mathrm{C}=0.89$.

**Figure 8.**Comparison of WRLES and DNS results along the blade at different spanwise positions. (

**a**) Friction ${\mathrm{c}}_{\mathrm{f}}$ along the SS and (

**b**) pressure ${\mathrm{c}}_{\mathrm{p}}$ along PS and SS.

**Figure 9.**Time averaged pressure coefficient at the endwall ($\mathrm{z}=0$). Results from (

**a**) WRLES and (

**b**) experiments [23].

**Figure 10.**Pitchwise averaged (

**a**) total pressure losses $\mathsf{\zeta}$ and (

**b**) flow angle deviation ${\Delta \mathsf{\beta}}_{2}$, downstream of the blade (plane at $\mathrm{x}/\mathrm{C}=0.89$). Experimental data from Krug et al. [23].

**Figure 11.**Vortical structure $\left({\mathsf{\lambda}}_{2}\left(\overrightarrow{\mathrm{v}}\right)=-2\right)$ for the linear compressor cascade at ${\mathrm{Re}}_{\mathrm{c}}=3\cdot {10}^{5}$.

**Figure 12.**Pressure (

**a**) and friction (

**b**) coefficients on the blade at two different spanwise positions, near the blade tip ($\mathrm{z}/\mathrm{H}=0.06$) and at midspan ($\mathrm{z}/\mathrm{H}=0.3$).

**Figure 13.**Blade suction side boundary layer state, characterized through the turbulent kinetic energy (TKE) in normal direction to the blade ($\mathsf{\eta}/\mathrm{C}$) and the shape factor (${\mathrm{H}}_{12}$).

**Figure 14.**Cutplanes downstream of the blade (plane at $\mathrm{x}/\mathrm{C}=0.89$) of (

**a**) total pressure losses and (

**b**) TKE. Pitchwise coordinate normalized by cascade pitch P with origin such that the wake is located at the centre, PS on the left.

**Figure 15.**Vortical structure $\left({\mathsf{\lambda}}_{2}(\langle \overrightarrow{\mathrm{v}}\rangle )=-2\right)$ for the linear compressor cascade at ${\mathrm{Re}}_{\mathrm{c}}=3\cdot {10}^{5}$ with relative motion between blade and endwall. Black lines with arrows at the bottom denote the endwall motion.

**Figure 16.**Effect of relative motion downstream of the blade (plane at $\mathrm{x}/\mathrm{C}=0.89$). Cutplane of (

**a**) total pressure and (

**b**) TKE. In these two figures, the pitch is normalized by cascade pitch P and its origin such that the wake appears in the centre. (

**c**) Pitchwise averaged total pressure losses. Experimental data from Krug et al. [23].

**Figure 17.**Effect of incoming wakes on blade performance characteristics at the suction side near the blade tip ($\mathrm{z}/\mathrm{H}=0.06$) and in the midspan region ($\mathrm{z}/\mathrm{H}=0.30$). (

**a**) Time averaged pressure coefficient (Equation 3) with shaded areas denoting the span of transient fluctuations. (

**b**,

**c**) Friction coefficient (${\mathrm{c}}_{\mathrm{f}}$) near the blade tip and in the midspan region, respectively.

**Figure 18.**Effect of the flat plate misalignment on the inlet endwall boundary layer of the T106A cascade.

**Figure 19.**Block topology in the computational domain of the T106A cascade with an integrated two-part flat plate and a moving bar wake generator.

**Figure 20.**Comparison of the predicted and measured isentropic Mach number distributions at midspan of the T106A turbine cascade at ${\mathrm{M}}_{\mathrm{exit},\mathrm{th}}=0.59,{\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}=2\xb7{10}^{5}$.

**Figure 21.**Measured total pressure losses at different endwall boundary layer conditions, (

**a**–

**c**) with and (

**d**–

**f**) without periodically incoming wakes in MP2.

**Figure 22.**Measured spanwise distributions of the pitchwise-averaged secondary pitch angle $\Delta {\mathsf{\beta}}_{2,\mathrm{sec}}$ and secondary total pressure losses ${\mathsf{\zeta}}_{2,\mathrm{sec}}$ under different endwall boundary layer conditions, with and without periodically incoming wakes in MP2.

**Figure 23.**Numerical prediction of the change in (

**a**) integral- and (

**b**,

**c**) local total pressure losses as well as (

**d**,

**e**) streamwise vorticity over time in MP2 with unsteady inflow conditions.

**Figure 24.**Axial entropy development throughout the T106A blade passage with steady and unsteady inflow conditions.

**Figure 26.**Selected devices for the acquisition of time-resolved measurement data: Dantec Dynamics type 55R56 and 55R57 SFP (

**a**), assembly of modular T106

^{RUB}blade with suction side hot-film instrumentation (

**b**), arrangement of Kulite LQ-125 sensors along the profile (

**c**).

**Figure 27.**Time-resolved flow field quantities downstream of the rotating wake generator: velocity v (

**a**), flow angle in circumferential direction α (

**b**) and turbulence intensity TI (

**c**) over channel height R/H for Sr = 1.33, φ = 0.97.

**Figure 28.**Time-averaged distributions of velocity v (

**a**), flow angle in circumferential direction α (

**b**) and turbulence intensity TI (

**c**) over channel height R/H downstream of the rotating wake generator for Sr = 1.33, φ = 0.97 and clean inflow, see [58].

**Figure 29.**c

_{p}distributions for clean and perturbed inflow at T106

^{RUB}midspan, time-averaged results (

**a**), superposition of maximal fluctuation values (

**b**), see [58].

**Figure 30.**Temporal evolution of pressure fluctuations along the T106

^{RUB}profile at midspan for Sr = 0.43 (

**a**), Sr = 0.90 (

**b**) and Sr = 1.33 (

**c**), see [58].

**Figure 31.**Temporal evolution of QWSS along the T106

^{RUB}profile suction side at midspan for Sr = 0.43 (

**a**) and Sr = 1.33 (

**b**), undisturbed condition shown above, see [58].

**Figure 32.**Temporal flow field evolution in the T106

^{RUB}exit flow field (Δx = 0.16 C) at 3 equidistant time steps, Sr = 1.33, φ = 0.97. Axial vorticity (AVO) (

**a**) and turbulence intensity (TI) (

**b**).

**Figure 33.**Temporal AVO flow field evolution (iso-contours) in the T106

^{RUB}exit flow field (Δx = 0.16 C) with the time as the third dimension, Sr = 1.33, φ = 0.97. View of radial-circumferential plane (

**a**), of radial-axial plane (

**b**) and of the lower half of the secondary flow system in a three-dimensional depiction (

**c**), see [58].

Test Rig | Operating Point | ||
---|---|---|---|

Shroud diameter | 1500 mm | Rotational speed at DP | 1000 rpm |

Hub to tip ratio | 0.84 | Mass flow $\dot{\mathrm{m}}$ at DP | 25.35 kg/s |

Rotor R1 | Stator S1 | ||

No. of blades | 63 | No. of vanes | 83 |

Chord length | 110 mm | Chord length | 89 mm |

Solidity, MS | 1.597 | Solidity, MS | 1.709 |

Reynolds number at entry, MS | $6.5\cdot {10}^{5}$ | Reynolds number at entry, MS | $3.7\cdot {10}^{5}$ |

Mach number at entry, MS | 0.25 | Mach number at entry, MS | 0.18 |

Flow coefficient φ, MS ^{1} | 0.651 | Diffusion factor, MS | 0.37 |

Loading coefficient $\left(\frac{\Delta {h}_{t}}{{u}^{2}}\right)$, MS ^{1} | 0.489 |

^{1}: at 10% higher mass flow than DP due to the discarded IGV in test setup (b).

Configuration | Rotor R1 Hub Wall | Stator S1 Hub Wall |
---|---|---|

Un-skewed, w/o RM | Stationary | Stationary |

Skewed, w/o RM | Rotating | Stationary |

Skewed, with RM | Rotating | Rotating |

Geometric Parameters: | |
---|---|

Chord length C | 100 mm |

Pitch-to-chord ratio P/C | 0.799 |

Aspect ratio H/C | 1.31 |

Flow Conditions: | |

Mach number at exit ${\mathrm{M}}_{\mathrm{exit},\mathrm{th}}$ | 0.59 |

Reynolds number at exit ${\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}$ | $2\cdot {10}^{5}$ |

Design inflow pitch angle ${\mathsf{\beta}}_{1}$ | 127.7° |

Design outflow pitch angle | 26.8° |

Turbulence intensity TI | 6.8% |

Unsteady Inflow Conditions: | |

Strouhal number Sr | 0.66 |

Flow coefficient φ | 3.8 |

Test Rig | Turbine Stage | ||
---|---|---|---|

Outer diameter (Casing) | 1660 mm | Chord length IGV | 137 mm |

Inner diameter (Hub) | 1320 mm | Stagger angle IGV | −25.5° |

Chord length T106^{RUB} | 100 mm | ||

Stagger angle T106^{RUB} | 30.7° | ||

Blade count IGV, T106^{RUB} | 60 | ||

Operating Point, Design Point | Design Flow Angles, Midspan | ||

Mass flow $\dot{\mathrm{m}}$ | 12.8 kg/s | IGV inlet ${\mathsf{\alpha}}_{0}$ | 90.0° |

Reynolds number at exit ${\mathrm{Re}}_{\mathrm{exit},\mathrm{th}}$ | $2\cdot {10}^{5}$ | IGV outlet = ${\mathsf{\alpha}}_{1}$ T106 ^{RUB} inlet ${\mathsf{\alpha}}_{2}$ | 52.3° |

Mach number at exit ${\mathrm{M}}_{\mathrm{exit},\mathrm{th}}$ | 0.091 | T106^{RUB} outlet ${\mathsf{\alpha}}_{3}$ | 153.2° |

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**MDPI and ACS Style**

Engelmann, D.; Sinkwitz, M.; di Mare, F.; Koppe, B.; Mailach, R.; Ventosa-Molina, J.; Fröhlich, J.; Schubert, T.; Niehuis, R. Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project. *Int. J. Turbomach. Propuls. Power* **2021**, *6*, 9.
https://doi.org/10.3390/ijtpp6020009

**AMA Style**

Engelmann D, Sinkwitz M, di Mare F, Koppe B, Mailach R, Ventosa-Molina J, Fröhlich J, Schubert T, Niehuis R. Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project. *International Journal of Turbomachinery, Propulsion and Power*. 2021; 6(2):9.
https://doi.org/10.3390/ijtpp6020009

**Chicago/Turabian Style**

Engelmann, David, Martin Sinkwitz, Francesca di Mare, Björn Koppe, Ronald Mailach, Jordi Ventosa-Molina, Jochen Fröhlich, Tobias Schubert, and Reinhard Niehuis. 2021. "Near-Wall Flow in Turbomachinery Cascades—Results of a German Collaborative Project" *International Journal of Turbomachinery, Propulsion and Power* 6, no. 2: 9.
https://doi.org/10.3390/ijtpp6020009