Groove Casing Research Articles

Stability enhancement using a new combined casing treatment strategy in an ultra-highly loaded transonic compressor rotor

Low-reaction compressors are promising for achieving high loads but face severe flow instability challenges. This study investigates a low-reaction transonic compressor rotor using casing treatment technologies to control unstable flow dynamics precisely. First, a design integrating self-recirculating and circumferential groove casing treatments near the leading edge is implemented. This design enhances flow capacity at the tip passage inlet. However, it causes a “stall transposition” phenomenon. The unstable flow structures shift from shock-tip leakage vortex interactions at the front to corner separation at the rear. Consequently, the stall mechanism transitions from an end-wall stall to a blade stall. To address this issue, a new casing treatment layout is proposed. Grooves are added after the mid-chord of the initial front casing configuration. This adaptation suppresses emerging unstable flow structures and extends the stall margin by approximately 12.07 %. Detailed flow field analysis shows that the rear grooves effectively reduced the trailing edge separation vortex. They also limit downstream corner separation and mitigate disturbances from tip leakage flows in the rear of the passage.

Effects of the circumferential casing groove configuration on aerothermal performance of a transonic turbine stage

In order to control tip leakage flow and improve the tip aerothermal performance, a circumferential casing groove (CG) configuration is proposed. Taking the typical transonic turbine stage TTM (Thermal Turbomachinery and Machine Dynamics) as the research object, the effects of CG with different heights (b), initial locations (IL) and widths (w) on the aerodynamic loss of the turbine stage and heat transfer characteristics of the tip region are investigated numerically. Results indicate that due to the introduction of CG, the vortex system topology in the tip region changes remarkably. Tip leakage vortex (TLV) is separated into two parts, with TLV-1 being entrained and dissipated by upper passage vortex (UPV) and TLV-2 rebuilding behind the groove and extending to the trailing edge. The interaction between TLV and UPV changes with the development of both. Also, complicated flow-thermal interplays lead to the change of thermal load in the tip region, which attributes to the difference of local turbulence mixing intensity. More quantitatively, a CG with the groove of b = 3.0 g, IL = 0.20 Cax and w = 0.05 Cax can increase ηTS by 0.38%, and reduce the area-averaged heat transfer coefficient (HTC) by 5.28% and 1.49% for the tip and casing surface, respectively, with a slight increase of area-averaged HTC on the blade by 0.29%. Overall, CG with appropriate geometrical parameters can improve aerothermal performance of the turbine tip significantly, without any serious increase of thermal load on the blade.

Numerical Investigation of the Interaction of a Circumferential Groove Casing Treatment and Near-Tip Modifications for a Highly Loaded Low-Speed Rotor Under the Influence of Double Leakage

Abstract Eckel et al. (2023, “Numerical Investigation of Near-Tip Modifications for a Highly Loaded Low-Speed Rotor Under the Influence of Double Leakage,” ASME J. Turbomach., 145(4), p. 041003) proposed using a convex-profiled pressure side region close to the tip, known as belly, as an effective method of extending the operating range of low-speed axial compressor rotors. In the literature, circumferential grooves are another well-described technique for improving the stable working range of a compressor rotor. No research has been conducted to date to determine which modification is more effective and how they interact when used together. This paper numerically investigates the influence of circumferential casing grooves and near-tip modifications on the flow field in the tip region of a highly loaded, low-speed axial compressor rotor. The simulated rotor consists of a hybrid blade configuration with a tandem profile in the mid-span region and single blade profiles near the endwalls. The single blade profile close to the tip features three different convex-profiled elements, which differ in their respective thicknesses. The aim of the numerical analysis is to explain the interaction of the secondary flow phenomena when applying the circumferential grooves and the belly geometries. For this purpose, eight different axial positions of the circumferential groove are investigated for each of the three belly configurations. These are arranged in 10% increments from −7% to 63% along the axial rotor tip chord. The potential of the concept is evaluated by a numerical investigation in the 1.5-stage setup with an inlet guide vane and tandem stator. It is shown that a circumferential groove can further increase the operating range for all belly configurations when positioned axially correctly. In this respect, equalization of the near-casing deceleration in the circumferential direction leads to an extension of the stall margin with both modifications. Concentrated regions of low-momentum fluid with a large extent in the radial direction should be avoided consequently. A tip vortex stability factor is introduced to quantitatively evaluate this effect. The operating range can thus already be estimated in a first approximation at the design point. In general, the groove and belly should be positioned where the tip leakage vortex meets the pressure side of the adjacent blade. If the groove is used together with the belly, the leading edge of the former should be situated at the location of maximum thickness of the near-tip modification. The effects of the circumferential groove and the belly are then superimposed. If using only one modification, the belly appears better suited for ensuring an extension of the operating range while maintaining high efficiencies.

Design optimization of a hybrid casing treatment based on axial momentum budget analysis in the tip flow region

In this paper, a novel slot–groove hybrid casing treatment is designed and optimized to improve the stall margin of a low-speed axial compressor. A combination of the axial slot and circumferential groove casing treatments is utilized to increase the stall margin without incurring efficiency loss. The slot meridional profile is described with 2 B-spline curves. Circumferential grooves are parametrically described with groove height and width. An in-house optimization design platform is constructed based on the nondominated sorting genetic algorithm II and Kriging surrogate model. The optimization objectives are the stall margin and the peak efficiency of the compressor at the design rotating speed. To avoid the large number of unsteady simulations that are required to predict the stall margin, a stall margin improvement indicator is proposed based on the axial momentum budget analysis at the rotor tip region. The performance of the optimal slot–groove hybrid casing treatment design is tested and simulated. The experimental data show that the optimal slot–groove hybrid casing treatment improves the stall margin by 8.42% without generating efficiency loss. The flow details are captured by unsteady simulations and analyzed in depth. The application of the optimal casing treatment enhances the blade tip axial momentum and the interface between tip leakage flow and incoming main flow is pushed downstream. Consequently, the stability of the compressor is improved.

Study of Circumferential Grooved Casing Treatment on Cascade Aerodynamic Performance

To explore the influence of circumferential grooved casing treatment on subsonic cascade performance, a numerical simulation of subsonic cascade was conducted. In contrast to traditional research on variable single parameters for casing treatment, this paper used the Latin hypercube sampling method to randomly sample multiple geometric parameters of casing treatment and compared many sample data with the total pressure loss of the cascade as a measurement standard. After selecting several typical cases of high and low total pressure loss cases for in-depth flow field analysis, it was found that casing treatment affects the strength and structure of the leakage vortex, thereby reducing the blockage of fluid in the passage of the cascade. Changes in the total pressure loss and in the margin of the cascade meant that casing treatment affected cascade performance. This prompted analysis of the correlation between the casing treatment parameters and total pressure loss of the cascade. The clearance height and groove depth had the greatest influence on the total pressure loss of the cascade.

Numerical study of two types of rough groove in suppressing the tip clearance cavitation

Tip clearance cavitation (TCC) which is consisted of tip leakage vortex (TLV) cavitation and gap cavitation (occurs inside the gap region) is a common phenomenon in the gap flow filed in axial turbomachinery, and can trigger a series of negative effects. Based on the suppression mechanism of a type of prototypical horizontal casing groove, two types of rough groove structures are proposed in this paper aiming at enhancing the suppression effect on the TCC by utilizing the Coanda effect of the gap leakage jet. The gap flow field is generated via a NACA0009 hydrofoil and a solid wall. The gap size is fixed as 2 mm. The numerical simulation method is adopted. The results show that combining the detached-eddy simulation (DES) approach, SchnerrSauer cavitation model and a type of varRhoTurbVOF method on the OpenFOAM platform, accurate numerical results of cavitating gap flow fields under the small gap conditions can be obtained. The gap flow field analysis reveals that the control ability of the grooves on the leakage flow is enhanced via divergent–convergent flow passage in the roughness groove cases. The leakage rate is reduced while the local turbulence intensity is increased, which weakens the TLV and the tip separation vortex (TSV) dramatically. The rough casing grooves show a superior suppression effect on the TCC. The present work can inspire new casing treatment method for improving the anti-cavitation performance in the axial-flow hydraulic machinery.

Influence of Casing Groove on Rotating Instabilities in a Low-Speed Axial Compressor

AbstractRotating instability (RI) can be regarded as a pre-stall signal because such phenomena are usually detected when a compressor operates at a near-stall point. Since RI is closely relevant to aerodynamic, acoustic, and structural issues, its mechanism has attracted industrial concerns and in-depth analysis. In this paper, a low-speed axial single compressor rotor row is selected as the baseline research object. A circumferential casing groove is mounted over the shroud. The solid casing and the casing treated configurations were simulated using the zonal large eddy simulation model, and the simulations present remarkable predictions in capturing the averaged and dynamic characteristics of the investigated compressor. By implementing a data-driven method called dynamic mode decomposition, the mode with the highest amplitude is proved to be correlated to the dominant RI frequency. The spatial and temporal property of the RI is visualized. The results show that the casing groove has limited influence on the averaged flow field but manipulates the dynamic features. The groove allows the RIs to shift from around 0.5 blade passing frequency to higher frequencies in the upstream region and effectively suppresses the unsteadiness in the zones under and downstream of the groove. The RIs are triggered by the flow interaction of the tip leakage flow at the front part of the blade. It can be depicted as pressure waves staggering with the rotor blade and propagating over the blade tip region at around half of the blade speed. With the existence of the casing groove, the dominant wavelength changes, and the fluctuation is damped under the groove, which finally modifies the properties of RIs.

Impact of Operating Conditions and Axial Casing Grooves on the Evolution of Flow Structure Across Blade Rows in an Axial Compressor

Abstract Stereo particle image velocimetry (SPIV) measurements in a series of axial planes investigate the impact of operating conditions and semicircular axial casing grooves (ACGs) on the evolution of flow structure across multiple blade rows in an axial compressor. The field of view extends radially from the hub to the tip and circumferentially over entire blade passages. Previous studies in this machine have shown that the ACGs improve the stall margin significantly but reduce the peak efficiency. At pre-stall flowrate and without ACGs, intermittent reverse axial flow near the casing is induced by backflow vortices, tip leakage vortex (TLV), and the leakage flow extend upstream of the rotor leading edge. Inside the rotor, the tip region blockage, characterized by low axial and high circumferential momentum, expands radially inward as the flow evolves axially. This extreme non-uniformity diminishes rapidly within the stator. In addition to previously shown ACGs effects, the current data reveal that the flow jetting out from the groove upstream of the rotor generates axially aligned vortices on both sides of each jet. These vortices substantially reduce the flow non-uniformity over the entire passage by entraining the faster mid-span flow into the tip region. Near the best efficiency point, the jets become weaker, the blockage is confined to the tip region, and differences between the global flow structure with and without ACGs become subtle. However, interactions of the TLV with secondary flows entrained from the grooves into the passage expand the TLV signature, which has adverse effects on the compressor performance.

Effect of Inclination Grooves on Axial Flow Compressor Stability: An Experimental and Numerical Simulation Study

In the present study, various groove casing treatments were evaluated under a high-speed subsonic axial flow compressor using experimental and numerical simulation methods. The aim of this study was to explore the effect of inclination of grooves on compressor stability and performance. The potential flow mechanisms were also evaluated. Three different inclination grooves were designed in this study: grooves with no inclination, grooves with 30 degrees upstream inclination and grooves with 30 degrees downstream inclination. Similar effect of the grooves on the compressor stability and efficiency was observed under experimental and numerical analyses. The grooves with no inclination, 30 degrees upstream inclination and 30 degrees downstream inclination enhanced stall margin by 6.08%, 8.74% and 3.03%, respectively. The peak efficiency losses of the three types of grooves were 1.62%, 0.94% and 2.33%, respectively. Tip flow field analyses demonstrated that the radial transport effect caused by grooves effectively reduced tip loads and alleviated tip blockage. This explains why the grooves enhanced the compressor stability. The radial transport effect was enhanced, and a larger stall margin improvement was obtained when grooves inclined upstream were applied. The tip flow loss was the dominant loss observed after grooves were applied on the compressor. The grooves with upstream inclination markedly reduced the tip flow loss, indicating that they exhibited the lowest effect on reducing compressor efficiency compared with the other types of grooves.

Stall Margin Improvement in a Transonic Compressor With a Casing Treatment: Flow Mechanism

Abstract A compressor casing treatment with circumferential casing grooves (CCGs) is studied in detail. The primary objective of the current paper is to unearth the main driving fluid mechanism that changes the stall margin in a transonic compressor with CCGs. Large eddy simulation (LES) is applied to calculate the transonic compressor flow fields with and without CCGs. The present investigation shows that CCGs reduce the mass flow through the tip gap by about 16% near the stall condition. Calculated flow fields show that most of this reduction of tip leakage flow occurs near the CCGs. Reinjected flow from the CCGs pushes the tip leakage flow radially inward below the casing and changes how the tip leakage flow collides with the incoming main passage flow. However, a detailed examination of the calculated flow in the tip region shows that the reinjected flow does not contribute to the reduction of the overall blockage generation. The primary driver for reducing blockage generation with CCGs is the reduction of overall mass flowrate through the tip gap. In the present investigation, measurements show a very small decrease in efficiency with CCGs at the design flow condition, although the difference in efficiency is within the measurement uncertainty. Results from the LES simulation at the design condition with CCGs show that the tip leakage vortex (TLV) is pulled toward the blade suction side and double leakage flow is eliminated. The result is that the simulated efficiencies with and without CCGs are almost the same.

Evolution of Turbulence and Its Modification by Axial Casing Grooves in a Multi-Stage Axial Compressor

Abstract This experimental study examines the evolution of turbulence across an axial compressor and its modification by semicircular axial casing grooves (ACGs) at the pre-stall and near the best efficiency (BEP) flowrates. The turbulence is highly anisotropic and spatially inhomogeneous, with each normal Reynolds stress component evolving differently. Most of the observed trends can be explained by examining the dominant production rate terms. At the pre-stall flowrate, the turbulence increases significantly upon entering the rotor with peak RMS values of axial velocity fluctuations reaching as high as 71% of the mean axial velocity. The region with elevated turbulent kinetic energy (TKE) covers 30% of the outer span near the rotor leading edge, expanding to 50% near the trailing edge. While the TKE in the outer span decays rapidly in the stator, the local turbulence production persists in the stator blade boundary layer. By stabilizing and homogenizing the flow, the ACGs reduce the turbulence production, hence the TKE, in the rotor and the stator. The only exception is an increase in turbulence in the region dominated by groove–passage flow interactions. Near BEP, the TKE is much lower everywhere, except for the region influenced by the outflow from grooves. Downstream of the rotor and the stator, the turbulence level with or without ACGs are similar. The large variations in the magnitude and even the sign of the measured eddy viscosity highlight the extreme non-equilibrium conditions over the entire machine, questioning the fundamental assumptions of local equilibrium in eddy viscosity-based Reynolds stress models.

Performance assessment of a modified wells turbine using an integrated casing groove and Gurney flap design for wave energy conversion

The present study investigates the effect of a triangular casing groove depth and width on Wells turbine performance. Furthermore, it presents an integrated method to boost the power produced by the Wells turbine and delay the stall. This integrated method is implemented by combining the effect of the triangular casing groove with a rectangular Gurney flap (GF). The Gurney flap (GF) increases the lift coefficient by modifying the Kutta condition at the trailing edge. At the same time, the triangular casing groove improves the flow near the blade tip, leading to a delay in the stall inception. The Wells turbine performance is evaluated by solving numerically 3D incompressible Reynolds-Averaged Navier-Stokes equations. To solve the flow characteristics through the turbine, an SST k-ω turbulence model is used, which is validated and verified using previous experimental and numerical works. The results proved that the Wells turbine average torque coefficient increased by 81.11% when using a triangular casing groove and a rectangular Gurney flap. Moreover, the stall inception is delayed from a flow coefficient of 0.225–0.350, which increases the operating range by 55.50% and reduces the maximum efficiency compared with the conventional Wells turbine.

Performance Evaluation of Transonic Axial Flow Compressor under Distorted Conditions by Groove Casing Technique with Tip Injection and Surface Roughness Effects

The aerodynamic performance and pressure ratio of modern aircraft engine compressor are degrading due to unsteady flow distorted aerodynamic loads and complex phenomena in the blade tip. This paper attempts to improve the performance of modern axial flow transonic compressor stage under distorted flow conditions by incorporating the combination of groove casing, tip injection technique with surface roughness effects. This is performed for the Mach number ranging between 0.8 and 1.3. The obtained numerical results are compared with experimental studies and found to be in good agreement. Through the numerical analysis, the compressor stage flow interaction with the shock waves as well as vortex formation and boundary layer separation is studied in detail. While evaluating the performance of the axial flow compressor, more emphasis is given to the flow properties like pressure, density, temperature, velocity, etc. The performance improvement is observed at a particular Mach number for a specified aerodynamic flow property.

AERODYNAMIC PERFORMANCES OF A SINGLE-STAGE TRANSONIC AXIAL COMPRESSOR USING AN INCLINED CASING GROOVE

ABSTRACT This paper presents the effect of an inclined casing groove on the aerodynamic performance of a single-stage transonic axial compressor, NASA Stage 38, using three-dimensional Reynold-averaged-Navier-Stokes equations with the k-ε turbulence model. The research was carried out to examine the effects of four casing groove parameters: angle, width, depth, and location. Validation of a numerical model for a single-stage transonic axial compressor was conducted to evaluate the computational fluid dynamics method. Most of the simulations showed positive results with an increase in stall margin, adiabatic efficiency, and total pressure ratio, in which the maximum stall margin, adiabatic efficiency, and total pressure ratio can be raised by 87.09%, 0.13%, and 1.57%, respectively, as compared to the smooth casing case.

Effect of blade skew, endplate and casing groove on the aerodynamic performance of Wells turbine for OWC: a review

Abstract The geometry modification of a bidirectional flow Wells turbine used in a wave energy converter can assist in overcoming the mammoth stall triggered by tip leakage, secondary flow on the blade surface, corner vortex, passage vortex, tip scrubbing, tip trailing edge vortex, boundary layer formation on hub and casing, and combination of all the listed making it a complex 3D flow. As the flow varies almost sinusoidally in each wave cycle in the ocean, it is inevitable to get a turbine having a higher operating range and average power output. Skewing a blade reduces the radial flow on the blade suction surface. A casing groove and endplate reduce tip leakage flow. These modifications give a significant improvement in the turbine performance. There are several design alternatives reported in the articles, and they have shown different results. In this article, the modifications and their effects are discussed in detail and concluded for future recommendations.

Multi-Objective Optimization of Circumferential Groove Casing Treatment in an Ultra-Highly Loaded Low-Reaction Transonic Compressor Rotor

This study concerns a multi-objective optimization of circumferential single grooved casing treatment for a low-reaction transonic rotor with ultra-high loading. The axial location, width and depth of the groove are investigated as design variables. The optimization problem seeks to fully extend the operation range of the rotor while minimizing efficiency degradation. Artificial neural network of radial basis function is applied to construct the surrogate model. The optimal groove configuration was determined using non-dominated sorting genetic algorithm II (NSGA II) in conjunction with technique for order preference by similarity to ideal solution (TOPSIS). Detailed analysis of flow field reveals that two flow features involving stability enhancement for the low-reaction rotor are the inhibition of shock/vortex interaction in the rotor tip region and the reduction or elimination of double-leakage tip gap flow. The blocking region located right downstream of the interface between the tip leakage flow and the main flow is decreased due to the tip unloading effect and recirculation flow induced by the groove. Additionally, the efficiency improvement can be observed as the intensity of tip leakage vortex decreases. Based on the single groove optimization, the prospect of a particular multiple groove casing configuration consisting of component grooves with varied geometrical dimensions is also discussed in the paper. The simulation results indicate that the new-type multiple groove configuration is more advantageous to the rotor’s performance.

Effect of the Axial Casing Groove Geometry on the Production and Distribution of Reynolds Stresses in the Tip Region of an Axial Compressor Rotor

AbstractStereo-PIV data are used for investigating the effect of axial casing groove (ACG) geometry on the distribution, evolution, and production rates of turbulent kinetic energy (TKE) and Reynolds stresses near a rotor tip. The ACGs delay the onset of stall by entraining the tip leakage vortex (TLV) and cause periodic changes to incidence angle. These effects are decoupled using semicircular, U-shaped, and S-shaped grooves that have similar inlets, but different outflow directions. Most TKE distribution trends can be explained by the local turbulence production rates, elucidating the different mechanisms involved and providing a unique database for turbulence modeling. Interaction of the tip flow with the ACGs modifies the highly anisotropic and inhomogeneous passage turbulence. In all cases, the TKE is high in the TLV center and shear layer connecting the TLV to the rotor tip. At prestall flowrate, TLV entrainment reduces the passage turbulence level, but introduces elevated turbulence in the corner vortex formed at the downstream corner of grooves, and in shear layers developing at the exit from grooves. The location of peaks and the dominant components vary among grooves. Near the best efficiency point, interactions of the TLV with the circumferentially negative outflow from the U and semicircular ACGs generate high turbulence levels, which extend deep into the passage. In contrast, interactions with S grooves are limited, resulting in a substantially lower turbulence level. Accordingly, the S groove maintains the untreated endwall efficiency, while the U and semicircular grooves reduce the peak efficiency.

Optimization of a circumferential groove in a centrifugal compressor

Abstract In this work, a circumferential groove on the shroud was applied to a centrifugal compressor and optimized to improve the stability of the compressor. To reduce the number of design variables before optimization, the position of the casing groove that maximizes the stall margin of the compressor was firstly selected. The width and height of the casing groove were optimized using the RSM (Response Surface Method) and the full factorial design of experiments to increase the stall margin further. It was observed that the optimized case with the casing groove can increase the stall margin by 7.0% but the adiabatic efficiency at the design condition decreases by 0.99%, in comparison to the reference case without the groove. Finally, the flow field of both cases with and without the optimized casing groove was compared to each other to analyze effects of the casing groove on the stall margin and design efficiency. The casing groove decreases the leakage flow across the impeller tip and weakens the tip leakage vortex, consequently decreasing the blockage near the shroud and improving the stall margin. However, it was found that the spillage of the flow from the casing groove increases the mixing loss near the shroud.

Effects of Axial Casing Grooves on the Structure of Turbulence in the Tip Region of an Axial Turbomachine Rotor

Abstract Challenges in turbulence modeling in the tip region of turbomachines include anisotropy, inhomogeneity, and non-equilibrium conditions, resulting in poor correlations between Reynolds stresses and the corresponding mean strain-rate components. The geometric complexity introduced by casing grooves exacerbates this problem. Taking advantage of a large database collected in the refractive index-matched liquid facility at Johns Hopkins University (JHU), this paper examines the effect of axial casing grooves on the distributions of turbulent kinetic energy (TKE), Reynolds stresses, anisotropy tensor, and TKE production rate in the tip region of an axial turbomachine. The comparisons are performed at flowrates corresponding to prestall and best efficiency points of the untreated machine. Common features include high TKE near the tip leakage vortex center and in the shear layer connecting it to the blade suction side tip corner. The turbulence is highly anisotropic and inhomogeneous, with the anisotropy tensor shifting from one-dimensional (1D) to 2D and 3D structures over small distances. With the grooves, the flow structure, hence the distribution of Reynolds stresses, becomes more complex. Additional sites with elevated turbulence include the corner vortex that develops at the entrance to the grooves, and in the flow jetting out of the grooves into the passage. Consistent with trends of the production rates of normal Reynolds stress components, the grooves increase the axial but reduce the radial velocity fluctuations as the inflow and outflow from the groove interact with the passage flow. These findings might assist the development of Reynolds stress models suitable for tip flows.

Effect of Axial Casing Groove Geometry on Rotor-Groove Interactions in the Tip Region of a Compressor

Abstract This experimental study characterizes the interactions of axial casing grooves (ACGs) with the flow in the tip region of an axial turbomachine. The tests involve grooves with the same inlet overlapping with the rotor blade leading edge, but with different exit directions located upstream. Among them, U grooves, whose circumferential outflow opposes the blade motion, achieve a 60% reduction in stall flowrate, but degrade the efficiency around the best efficiency point (BEP) by 2%. The S grooves, whose outlets are parallel to the blade rotation, improve the stall flowrate by only 36%, but do not degrade the BEP performance. To elucidate the mechanisms involved, stereo-PIV measurements covering the tip region and interior of grooves are performed in a refractive index-matched facility. At low flowrates, the inflow into both grooves, which peaks when they are aligned with the blade pressure side (PS), rolls up into a large vortex that lingers within the groove. By design, the outflow from S grooves is circumferentially positive. For the U grooves, fast circumferentially negative outflow peaks at the base of each groove, causing substantial periodic variations in the flow angle near the blade leading edge. At BEP, interactions with both grooves become milder, and most of the tip leakage vortex (TLV) remains in the passage. Interactions with the S grooves are limited; hence, they do not degrade the efficiency. In contrast, the inflow into and outflow from the U grooves reverses direction, causing entrainment of secondary flows, which likely contribute to the reduced BEP efficiency.