Abstract
Understanding the endwall flow phenomena surrounding low-pressure turbine blades is key to improving performance, as these flow features contribute significantly to loss generation at low Reynolds number cruise. It is well documented that a horseshoe vortex system forms at the junction of the endwall and turbine blade. The vortices develop and gain significant strength in the passage and contribute to total pressure losses. During low Reynolds number conditions, the flow through a low-pressure turbine passage can be greatly impacted by a number of factors, including Reynolds number and incoming turbulence. The focus of this paper is on significant changes to the endwall flow field observed in experimental measurements and an accompanying implicit large-eddy simulation of the flow through a linear cascade of high-lift front-loaded low-pressure turbine blades at low Reynolds number. Results show a significant effect on both the time-averaged endwall flow topology and the unsteady vortical flow characteristics when the Reynolds number based on inlet conditions was decreased to 30,000. Various techniques, such as spectral proper orthogonal decomposition, were used to analyze and compare both high-speed particle image velocimetry measurements and numerical results in order to extract the dominant structures and their unsteady behavior. The total pressure loss development through the passage was assessed in order to better understand how the observed changes in endwall flow structures contribute to the overall losses.
Introduction
In modern high-bypass gas turbine engines, the fan is responsible for producing the majority of the thrust [1]. The fan is powered by the low-pressure turbine (LPT), which is one of the heaviest engine components, constituting up to a third of the total engine weight [2]. Due to the large size, reducing the low-pressure turbine weight has a drastic impact on the engine weight, and thereby the overall thrust-to-weight ratio. One of the most impactful ways to reduce the low-pressure turbine weight is to utilize high-lift blades. By significantly increasing the blade loading, the number of blades per engine stage can be drastically decreased, reducing both the weight and part count of the overall engine. The L2F blade is an example of a highly loaded low-pressure turbine blade. The profile was designed for research purposes by AFRL using an in-house code and has been extensively tested over the past decade [3]. Multiple studies have demonstrated that front-loaded blades have excellent mid-span performance; however, the endwall losses can be exacerbated by the front loading [4–7]. This is largely due to the complex flow field present in the endwall region, which is characterized by several vortical structures.
The flow through gas turbine engines is exceedingly complex in nature, especially within turbomachinery components, such as the low-pressure turbine, where the flow is highly unsteady and intricate [8]. The flow around a low-pressure turbine blade is often broken up into two regions; the mid-span region, where the two-dimensional flow assumption is typically valid, and the endwall region, where the flow is very complex and three-dimensional due to the junction flow phenomena that occur. The major time-averaged flow features in the endwall region of the high-lift front-loaded L2F passage have been described in Refs. [9,10]. A schematic of the significant vortical flow structures is shown in Fig. 1 and is consistent with the experiments and simulations described in Ref. [10]. The incoming boundary layer separates, rolls up, and forms a horseshoe vortex [11–15]. Most of the incoming flow contained in the boundary layer is entrained in the horseshoe vortex [13,15]. Typically, this roll up occurs just upstream of the leading edge of the blade [15,16]. The two legs of the horseshoe vortex are referred to as the pressure-side and suction-side leg, and they rotate in opposite directions [11,13]. The pressure side leg of the horseshoe vortex is strengthened by the secondary flow and becomes a significant vortex in the passage and is referred to as the passage vortex (PV). A strong corner separation exists along the suction surface near the exit of the passage. The vortex in this region is referred to as the suction-side corner separation vortex (SSCSV) and has the same direction of rotation as the passage vortex. These endwall flow features lead to significant loss development. The endwall losses become increasingly important for smaller aspect ratio blades. The large overall impact of the endwall structures on the flow through the passage makes understanding the flow field in the endwall region critically important for the development of design changes aimed at improving the overall blade efficiency.
A complete understanding of the flow field is necessary to accurately predict the losses within the endwall region [17]. Various endwall loss reduction methods have been developed. These techniques range from passive methods, such as endwall contouring and profile contouring, to active methods such as endwall jets [18–22]. In order to effectively control the flow though the passage, it is necessary to have a complete understanding of the overall flow behavior over the full range of flight conditions, which for LPT applications includes very low Reynolds numbers at cruise conditions [23].
Various parameters affect the unsteady endwall flow physics. Researchers have demonstrated that the exact location and temporal behavior of the horseshoe vortex structure at the leading edge junction of symmetric wings depends heavily on the incoming flow characteristics, such as boundary layer state, Reynolds number, and freestream turbulence intensity (FSTI), see for example the review by Gand et al. [24]. Similarly, the endwall flow in LPTs is also strongly dependent on the same parameters [16,25,26]. Wang et al. [25] investigated the flow through a turbine blade passage at a low Reynolds number, Re = 27,000 based on chord length and exit velocity, and a low FSTI of 0.2%. The incoming endwall boundary layer was laminar; however, they reported similar flow characteristics when the boundary layer was turbulent. Wang et al. observed periodically varying patterns of multiple vortices entering the passage near the pressure side and then combining into a single vortex and becoming the passage vortex downstream.
At the leading edge junction, the horseshoe vortex system consists of the horseshoe vortex and a counter rotating secondary vortex upstream of the horseshoe vortex. A weak tertiary vortex is also noted upstream of the secondary vortex, as well as a smaller vortex that is located within the corner region [17,27,24]. This system has an inherent low-frequency instability. Gand et al. noted that the horseshoe vortex behavior and time scales have been associated with the Reynolds number based on momentum thickness [24]. At low values of the horseshoe vortex is steady, while at higher values, the vortex begins to move back and forth between two dominant positions, as described by Devenport and Simpson [28]. Some researchers have related the frequency of the unsteadiness to the boundary layer edge velocity as well as the blade leading edge diameter [26]. Praisner et al. [17] as well as Sabatino et al. [29] hypothesized that the low-frequency unsteadiness was caused by the changing momentum within the turbulent boundary layer. The horseshoe vortex unsteadiness exhibits a quasi-periodic bimodal behavior that is characterized by two dominant modes, the backflow and the zeroflow mode. In the more energetic backflow mode the secondary vortex is ejected from the system [17,30]. The ejection occurs on the same time scales as the bursting events within the turbulent boundary layer, which suggests that the boundary layer turbulence affects the junction flow dynamics [17].
In a previous paper, the effects of FSTI on the endwall flow structures were experimentally investigated at two Reynolds numbers, 30,000 and 50,000 based on incoming velocity and axial chord [31]. At the low FSTI condition, 0.8%, and Reynolds number of 30,000, an endwall flow topology not previously observed in high-lift front-loaded blade passages was documented. However, in that initial study, only a single plane of data was collected making it difficult to infer the flow characteristics throughout the rest of the endwall region. The experimental measurements have been used to validate implicit large-eddy simulations (ILES) at the low FSTI, low Reynolds number flow conditions. The results from the simulation are compared to those seen in the experiment, providing a better understanding of the new flow topology. The experimental results were further processed to determine the time scales associated with the unsteady vortex behavior. Finally, the impacts of the incoming laminar endwall boundary layer and low freestream turbulence intensity on the loss production are discussed.
Methodology
Experimental Setup.
The experiment was completed in a low-speed linear cascade at the Air Force Research Laboratory’s Low Speed Wind Tunnel Facility. The linear cascade consisted of seven L2F blades with six passages, Fig. 2. The L2F is a front-loaded, high-lift research profile, and is part of a family of low-pressure turbine blades designed using an in-house design code [3,32,33]. A passive or active turbulence grid can be installed upstream of the cascade in order to elevate the incoming turbulence level, however, at the Re = 30,000 condition the turbulence grid was removed to investigate the effects of a low FSTI of 0.8%. A splitter plate was installed in the test section in order to generate a clean incoming endwall boundary layer. The splitter plate had an elliptic leading edge, extended upstream 4.97Cx, encompassing the blades, and extending downstream 4.27 Cx. The upstream and downstream splitter plates were connected by small splitter plate sections that covered the area between the blades. The cascade parameters can be found in Table 1. The Reynolds number reported is based on the blade axial chord and approach freestream velocity. The incoming flow velocity was measured by a Pitot-static probe mounted 2 Cx upstream, connected to a 0–0.4 inH2O Druck transducer. High-speed stereoscopic particle image velocimetry (SPIV) data were collected in one of the two center passages. Time was nondimensionalized (T+) by the suction surface length and average passage velocity at mid-span, so that a nondimensional time of one corresponds to the time it takes the core flow to convect through the passage. The SPIV measurement plane was orthogonal to the exit flow direction and spanned entirely from the pressure side to the suction side of the passage, with the location shown by section A-A in Fig. 1. Two Phantom VEO 640L cameras fitted with Scheimpflug adapters were used to collect the SPIV data. The seeding was illuminated by a Photonics Industries DM30 Dual Head 527 nm laser. Fifteen-thousand image pairs were collected at a repetition rate of 2.5 kHz over 90 convective times. The timing was controlled by a LaVision programmable timing unit. The initial processing of the raw images was completed using the DaVis 8 software. Velocity vectors were calculated using two passes of 64 × 64 pixel interogation windows, and a final pass of 32 × 32 pixels. The spatial resolution was 139 vectors per Cx. Additional post processing including, vortex tracking, spectral proper orthogonal decomposition (SPOD), and Q-criterion calculations were completed using in-house codes. The incoming FSTI and boundary layer were measured using a hot-film sensor operated with a TSI IFA 300 constant temperature anemometer. The incoming boundary layer was measured 1.5Cx upstream of the cascade.
General parameters
Axial chord, Cx | 15.24 cm |
Pitch/axial chord, S/Cx | 1.221 |
Suction surface length, SSL | 25.65 cm |
Span/axial chord, H/Cx | 4.17 |
Inlet flow angle (from axial), αin | 35 deg |
Predicted mean profile exit angle, αex | −58.12 deg |
Zweifel coefficient, Zw | 1.59 |
Axial chord, Cx | 15.24 cm |
Pitch/axial chord, S/Cx | 1.221 |
Suction surface length, SSL | 25.65 cm |
Span/axial chord, H/Cx | 4.17 |
Inlet flow angle (from axial), αin | 35 deg |
Predicted mean profile exit angle, αex | −58.12 deg |
Zweifel coefficient, Zw | 1.59 |
Numerical Simulation.
Implicit large-eddy simulations (ILES) were carried out with a research computational fluid dynamics code described in Gross and Fasel [34]. For the ILES, the numerical scheme (as opposed to an explicit subgrid-scale model) removes the proper amount of energy at the smallest grid scales. The code solves the compressible Navier–Stokes equations in curvilinear coordinates. Length scales were made dimensionless by the axial chord and velocities were made dimensionless by the inlet velocity. For robustness, especially on highly distorted grids, a finite volume formulation is employed. The convective terms of the Navier–Stokes equations were discretized with a ninth-order-accurate scheme. The viscous terms were discretized with fourth-order-accuracy and the implicit second-order-accurate trapezoidal rule was employed for time integration. The axial chord length, and inlet velocity, Uin, were selected as reference length and velocity.
The simulations were set up according to the linear cascade experiments. The Reynolds numbers based on axial chord and inlet velocity were Re = 30,000 and 50,000 and the reference Mach number was M = 0.1. This Mach number is small enough to satisfy the incompressible flow assumption without negatively affecting the convergence characteristics of the implicit time-integration scheme. The freestream temperature was 300 K and the Prandtl number was Pr = 0.72. The computational timestep was set to Δt = 0.003 for Re = 30,000 and 0.005 for Re = 50,000.
A two-dimensional grid (Fig. 3) was generated with a Poisson grid generator and served as basis for a three-dimensional grid [35]. The leading edge of the blade was located at x = 0 and the trailing edge was located at x = 1 and y = 0.
The 2-D grid was “extruded” in the spanwise direction to unit depth. Toward that end, a grid line distribution that provides grid line clustering near the endwall and blends toward an equidistant spacing far away from the endwall was employed. The wall-normal grid line spacing at the endwall was Δz = 10−4. The number of cells per block is provided in Table 2. For Re = 50,000, the near-wall grid resolutions in wall units one and a half chord lengths upstream of the junction (x = −1.229) are Δx+ ≈ 16 (axial direction), Δy+ ≈ 0.12 (direction normal to endwall), and Δz+ ≈ 19 (pitchwise direction). This grid resolution was chosen based on earlier simulations for the same LPT cascade at Reynolds numbers of 50,000 and 100,000 [36,37].
Number of cells
Block | |
---|---|
1 | 608 × 80 × 256 |
2 | 256 × 104 × 256 |
3 | 32 × 152 × 256 |
4 | 154 × 152 × 256 |
Total | 20,512,768 |
Block | |
---|---|
1 | 608 × 80 × 256 |
2 | 256 × 104 × 256 |
3 | 32 × 152 × 256 |
4 | 154 × 152 × 256 |
Total | 20,512,768 |
All walls were considered adiabatic. Flow periodicity was imposed in the pitchwise direction. Nonreflecting boundary conditions were applied at the inflow and outflow boundaries. Symmetry conditions were enforced at the spanwise boundary [38]. For the simulation, a Blasius boundary layer profile was prescribed at the inflow for initializing the laminar endwall boundary layer. For the Re = 50,000 simulation, the divergence-free synthetic eddy model (SEM [39,40]) was employed for initiating (or seeding) the turbulent endwall boundary layer. Because this model is driven by a random number generator, it does not favor certain frequencies (or wavelengths). A Reynolds-averaged Navier–Stokes (RANS) boundary layer profile obtained from a calculation with k–ω model served as basis for the SEM and provided the mean boundary layer velocity, v(z), turbulent kinetic energy, k(z), and turbulence dissipation rate ɛ(z), where z is the wall-normal distance.
Results
Incoming Boundary Layer.
The boundary layer profiles, both experimental and computational, for Reynolds numbers of 30,000 and 50,000 at a low turbulence intensity can be found in Fig. 4. The boundary layer characteristics are provided in Table 3. The measured boundary layer shape factor found from the experimental measurements at 30,000 was just below the Blasius value of H = 2.59. The Blasius solution is for a boundary layer on a flat plate with no pressure gradient. The present measurements were collected upstream of the linear cascade where a weak adverse pressure gradient is present. It is well within bounds to draw the conclusion that for a low FSTI at Re = 30,000 the boundary layer was laminar. The boundary layer was transitional to fully turbulent, thicker, and more resistant to separation for the higher Reynolds number case. Since the endwall flow events and structures are strongly tied to the boundary layer state and separation, this is expected to have a drastic impact on the flow field in the endwall region. The Reynolds number based on momentum thickness and incoming flow velocity was very low, around . Based on the literature for these parameters, a bimodal, but not purely periodic behavior of the horseshoe vortex was expected [24]. Finally, since the literature suggests that unsteady flow structures in the turbulent boundary layer drive the temporal behavior of the horseshoe vortex, a completely different endwall flow topology, and unsteady fluid dynamics are expected for the laminar endwall boundary layer [29].
Measured incoming boundary layer characteristics
Reynolds number | 30,000 | 50,000 |
Boundary layer thickness, δ | 6.93 mm | 10.78 mm |
Displacement thickness, δ* | 1.92 mm | 1.54 mm |
Momentum thickness, θ | 0.86 mm | 0.87 mm |
Shape factor, H | 2.23 | 1.76 |
Momentum Reynolds number, Re | 169 | 285 |
Reynolds number | 30,000 | 50,000 |
Boundary layer thickness, δ | 6.93 mm | 10.78 mm |
Displacement thickness, δ* | 1.92 mm | 1.54 mm |
Momentum thickness, θ | 0.86 mm | 0.87 mm |
Shape factor, H | 2.23 | 1.76 |
Momentum Reynolds number, Re | 169 | 285 |
Time-Averaged Flow Description.
The ILES simulation provides insight into the flow field across the entire passage. Visualizations of the time-averaged flow field are presented in Figs. 8 and 9. Shown are skin-friction lines, iso-contours of the u-velocity at the first cell of the wall (which is related to the axial skin-friction coefficient), and iso-surfaces of the Q-criterion flooded by the axial vorticity, ω. Skin-friction lines lie parallel to the local skin-friction, and oil-flow visualizations are often employed to visualize skin-friction lines experimentally. The vortices are colored by their respective sense of rotation, where blue is clockwise and red is counter-clockwise. The simulation results for Re = 50,000 are typical for the flow through LPT passages at higher Reynolds numbers. The horseshoe vortex is positioned close to the leading edge junction. The saddle point (SP) associated with the separation of the endwall boundary layer ahead of the passage is clearly visible. The endwall is red in the approach flow due to the turbulent incoming boundary layer. The horseshoe vortex pressure-side leg gains strength as it extends across the passage. The suction-side leg rotates in the opposite direction and dissipates over a short distance. The boundary layer rolls up along the suction side of the blade, forming the SSCSV which rotates in the same direction as the passage vortex. The passage vortex exits the passage near the suction side of the adjacent blade, and interacts with the SSCSV [9,42].

Time-averaged iso-surfaces of Q = 25 flooded by −25 < ω < 25, skin-friction lines, and iso-contours of −0.1 < u < 0.1 for Re = 50,000

Time-averaged iso-surfaces of Q = 25 flooded by −25 < ω < 25, skin-friction lines, and iso-contours of −0.1 < u < 0.1 for Re = 30,000
The time-averaged simulation results for the lower Reynolds number of 30,000 with a laminar endwall boundary layer are shown in Fig. 9. Compared to Fig. 8, for the Re = 50,000 case the saddle point, SP, and associated separation line, S1, have moved upstream. The incoming boundary layer separates and rolls up into an upstream horseshoe vortex structure ahead of the leading edge of the L2F. The suction-side leg, shown in red, rotates counter-clockwise and is weaker than the pressure-side leg, shown in blue, which rotates clockwise. The suction-side leg of this initial vortex structure remains near the suction side of the blade. The pressure-side leg remains strong and extends across the passage where it eventually merges with other structures in a complex flow region near the adjacent blade suction surface. A second horseshoe vortex structure, located downstream of the first, is present closer to the leading edge, in a similar location as the horseshoe vortex for the higher Reynolds number case. The time-averaged pressure-side leg of the downstream horseshoe vortex structure appears to consist of multiple vortices. This is in agreement with the experimental measurements, Fig. 6. The pressure-side leg does not merge with the suction-side vortices until downstream of the trailing edge. The SSCSV still forms along the suction side, is stronger, and extends out of the passage. However, it originates from a complex flow region where several vortices interact, including the one formed along the first separation line, S1. The interaction means that there is no longer a single coherent vortex in this region. A shed vortex (SV), with opposite sense of rotation than the PV, originates near the trailing edge and extends in the streamwise direction. The dramatic change in the time-averaged flow field compared to Re = 50,000 is believed to be due to the incoming endwall boundary layer being laminar and less resistant to separation for Re = 30,000. However, the change in topology is not consistent with what other researchers have observed for cases with an incoming laminar endwall boundary layer. The flow structures reported in Ref. [25] were generally the same, regardless of whether the incoming boundary layer was laminar or turbulent. A noted decrease in size and downstream shift of the pressure-side leg of the horseshoe vortex was observed when the incoming boundary layer was turbulent in the simulations of Ref. [26], and when the incoming boundary layer was laminar there was a single vortex structure present in the time-averaged results. The complex vortex system is also not present in the time-averaged results of Refs. [17,30].
Figure 10 provides a summary of the time-averaged flow field at Re = 30,000 with a laminar incoming boundary layer. The vortices are colored by their respective sense of rotation, blue being clockwise and red being counter-clockwise. The upstream horseshoe vortex structure is represented by SSHV1 and PSHV1, formed at the first separation line (S1), and the downstream horseshoe vortex structure is represented by SSHV2 and PSHV2. The downstream horseshoe vortex system is fed by vortices shed by the separation associated with the first horseshoe vortex. A suction-side corner separation vortex (SSCV) still forms near the suction side of the passage and a shed vortex (SV) is located downstream of the trailing edge.
Instantaneous Flow Description.
The instantaneous flow fields were investigated in order to obtain a more complete understanding of the flow physics, Fig. 11. The instantaneous flow field is drastically different from the time-averaged flow field. HV1 sheds coherent structures in a periodic manner. The period of the shedding is around T+ = 0.47 or corresponding to a frequency of F+ = 2.1. This was determined based on the instantaneous visualizations of the flow field. Individual structures were tracked and the time for them to travel one wavelength was measured. The coherent vortex structures that are shed by the upstream separation interact with the horseshoe vortex at the leading edge junction. As a result, the PSHV appears to be severed repeatedly. This interaction is illustrated for four different time instances in Fig. 12. In the figure, the three interactions are highlighted as A, B, and C. At the leading edge, an initial interaction, labeled A, takes place and appears to sever the horseshoe vortex. As time progresses, feature A propagates in the axial direction from the pressure side of the passage to the adjacent suction side, and the coherent structures continue to interact, primarily as pairs of co-rotating vortices. For T+ = 0.0423, feature A has traveled far from the leading edge and its location coincides with the previous location of feature B at T+ = 0.0141. Feature C indicates a bursting of the passage vortex. The complex interaction is driven by the velocity gradient that exists across the passage, with the coherent shed vortices convecting faster along the suction side of the passage. The multiple vortex core lines observed in the time-averaged flow field (Fig. 9) indicate that this complex interaction is very time-periodic.

Instantaneous iso-surfaces of Q = 25 flooded by −25 < ω < 25, skin-friction lines, and iso-contours of −0.1 < u < 0.1 for Re = 30,000

Instantaneous iso-surfaces of Q = 25 flooded by vorticity, −25 < ω < 25: (a) T+ = 0, (b) T+ = 0.0141, (c) T+ = 0.0282, and (d) T+ = 0.0423
In Fig. 13, the incoming flow is visualized in a plane extending upstream from the leading edge. The plane is aligned with the incoming flow direction, with the LE located at x/Cx = 0 along the right edge of the image. Four instances of time are shown. The images are flooded by the y-component of vorticity in order to highlight the shedding of coherent structures. The upstream horseshoe vortex, HV1, system consists of shed coherent structures, which extend across the passage and convect in the streamwise direction. The structures that are shed by the upstream separation gain strength as they propagate toward the blade leading edge. Upon reaching the leading edge, the vortices appear to periodically compress and eliminate the second horseshoe vortex only for it to form again. As the vortex reaches the leading edge another one begins to form following the roll up of the upstream boundary layer. These observations also clarify the formation of the downstream horseshoe vortex system. The upstream shedding leads to a periodic reformation of the downstream HV. As the HV reforms, its legs wrap around the blade leading edge.

Instantaneous iso-contours of −25 < ωy < 25 in a plane aligned with the inflow direction and encompassing the leading edge: (a) T+ = 0, (b) T+ = 0.0141, (c) T+ = 0.0282, and (d) T+ = 0.0423
In order to gain a more complete understanding of how the vortex shedding impacts the flow temporal behavior within the passage, the instantaneous SPIV results were further analyzed. The dominant vortex, the PV, in the measurement plane of Section A-A is the vortex adjacent to the suction side. This vortex forms along the upstream separation line. The vortex in the measured velocity field was isolated so that its behavior and movement with time could be identified. The vortex was isolated by restricting the search region in the measurement plane. Space–time plots of iso-surfaces of the Q-criterion were created from the SPIV data and are presented in Fig. 14. There are fluctuations in strength and position of the vortex over time. It is clear from the images that the temporal changes in the vortex occur over many convective times and in a cyclical manner.
The analyses completed in previous studies have demonstrated that by tracking the vortex core pitchwise location and strength, one can isolate relationships between its strength and position, Fig. 15 [18,44]. The vortex core was defined as the location where the maximum Q-criterion value was obtained. Figure 15 highlights the cyclic nature of both the strength and position fluctuations.
In order to clearly isolate the frequencies of the vortex strength change, the power spectral density of the tracked vortex core strength was found, see Fig. 16. A Hanning window was used to calculate the power spectral density [45]. There is clearly a significant peak at a nondimensional frequency near 1.7, which corresponds to around 0.60 convective time scales. The temporal fluctuations on a time scale of a T+ = 0.6 are in the range of the unsteady vortex short period undulations measured at higher Reynolds numbers [43]. This is slightly lower than the upstream shedding frequency of F+ = 2.1; however, at this point the vortex core line is interacting with the suction-side corner separation vortices, so a frequency change is expected. For the ILES, the power spectral density (PSD) of the Q-criterion at the mean vortex core location is shown. The PSD distribution has a peak at F+ = 2.1, which is directly tied to the upstream shedding.
Modal decompositions are one way to gain deeper insight into the underlying physics of a flow field. The SPIV data for Re = 30,000 were analyzed with the SPOD method (see Fig. 17). SPOD can be thought of as a combination between a proper orthogonal decomposition and a discrete Fourier transform. The resulting modes are coherent in both space and time. The modes are extracted at specific frequencies, and then at each frequency the modes are ranked by their respective energy. The exact frequencies extracted cannot be directly controlled, instead they are a result of how the data are blocked during processing, see Towne et al. [46]. A previous modal analysis was completed for endwall flows and has been shown to give insight into the energies and events of the endwall flow [47]. Typically velocity components are used for modal decompositions, however, vorticity or Q-criterion can also be decomposed to better highlight vortical structures. These can be more difficult to interpret since the eigenvalues are then no longer a measure for the kinetic energy content of the modes [48,49]. For the present analysis, the SPOD was carried out for the velocity components and Q-criterion. Velocity vectors and contours of the Q-criterion for two frequencies and the leading two SPOD modes are shown in Fig. 17.

Velocity vectors and Q-criterion contours first mode (top) and second SPOD mode (bottom) of SPIV results
Two frequencies were investigated, 2.1 and 1.7. These are the frequencies associated with the upstream vortex shedding and the cyclical loss of coherence of the dominant suction-side vortex, respectively. The first mode for both frequencies captures unsteadiness of both the pressure and suction-side vortices. In the region associated with the dominant vortex, the velocity vectors are pointing predominantly toward the suction side. For the second mode at both frequencies, the amplitudes in vicinity of the dominant vortex are lower and the velocity vectors are pointing toward the additional pressure-side vortices. The SPOD mode amplitudes in the vicinity of the pressure-side vortices are most pronounced for the first mode at F+ = 1.74 (close to peak in spectrum in Fig. 16) and for the second mode at F+ = 2.1. For the second mode, the amplitudes associated with the pressure-side vortices are larger than for any of the other modes, implying that this mode captures some sort of event or strength change occurring at this frequency. Since this frequency is directly related to the upstream vortex shedding, which is tied to the merging of the shed vortices with the downstream horseshoe vortex, this higher energy region is likely the unsteady behavior captured by this mode.
Total Pressure Loss.
In order to relate the total pressure loss development within the passage to the mean flow structures, the total pressure loss coefficient obtained from the ILES was plotted in several planes, Fig. 18. The planes are normal to the axial direction, x. For the first two planes, located near the middle of the passage, large total pressure losses are noted over the suction side of the blade as a result of the two-dimensional laminar separation and in the region of the strong coherent vortex observed in both experiments and simulations. Closer to the exit of the passage, the loss core associated with the coherent vortex expands in size and moves away from the suction surface and endwall. The strong two-dimensional laminar separation from the suction side and the passage vortex both make a significant contribution to the total pressure losses. This is consistent with previous studies at higher Reynolds number which also found elevated losses associated with the interaction of the suction-side corner separation vortex and the bulk flow along the suction surface [9]. More insight into how the different flow regions contribute to the losses can be found in Refs. [8,50].

Total pressure loss coefficient contours from simulation, Re = 30,000: (a) 60% Cx, (b) 70% Cx, (c) 80% Cx, (d) 85% Cx, (e) 90% Cx, and (f) 100% Cx
Conclusions
The endwall flow through the passage of a low-speed linear cascade of high-lift front loaded turbine blades with a laminar and transitional/turbulent incoming endwall boundary layer was investigated using high-speed SPIV measurements and accompanying implicit large eddy simulations. The Reynolds number based on axial chord and inlet velocity was 30,000 and 50,000 and the freestream turbulence intensity was low enough for the approach endwall boundary layer to remain laminar at the lower Reynolds number. The endwall boundary layer profile measured upstream of the cascade was matched in the simulations. The simulation and experiment for Re = 30,000 showed very good agreement with respect to the vortical structures in the endwall region. A significantly different endwall flow field was observed for the case with a laminar incoming boundary layer compared to prior studies with a fully turbulent endwall boundary layer.
When the incoming boundary layer was laminar, the upstream separation line moved upstream, consistent with observations in the literature and two different horseshoe vortex systems were present in the passage. The laminar separation upstream of the leading edge sheds coherent structures at a frequency of F+ = 2.1. A horseshoe vortex very near the leading edge junction is repeatedly impacted by the shed vortices interacting with the blade leading edge junction. This vortex interaction was observed in both experiments and simulation. The experimental measurement plane was located approximately mid-passage and aligned normal with the secondary flow direction. The dominant vortex in the experimental measurement plane was located near the suction side of the passage. The vortex was observed to cycle through fluctuations in strength and position at a frequency of F+ = 1.7. This behavior is hypothesized to be related to the interaction of the vortex dynamics with the shedding from the upstream vortex. Similar to prior studies at higher Reynolds number, a suction-side corner separation vortex was also observed. Understanding the location of these vortices, as well as how their position relates to their relative strength will provide a basis for the development of flow control methods aimed at a reduction of the endwall losses.
The additional vortices observed near the pressure side of the passage result from the interaction of the vortices shed from the upstream horseshoe vortex and the pressure-side leg of the downstream horseshoe vortex. There is a complex interaction between the shed coherent vortices. All vortical structures contribute to the total pressure losses within the passage. The dominant vortex in the passage located near the suction side and the laminar separation from the suction surface make the most significant contribution to the total pressure losses.
Acknowledgment
Distribution Statement A: Approved for Public Release; Distribution is Unlimited. PA# AFRL-2021-4340. The first author is supported by a SMART Scholarship. This material is based upon work supported by the Air Force Office of Scientific Research under award numbers FA9550-21RQCOR016 and FA9550-19-1-008. Any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
Data provided by a third party listed in Acknowledgment.