Abstract. Airfoil aerodynamics at high Reynolds numbers (on the order of 106) are of significant interest due to the increasing dimensions of wind turbine rotors. Recent studies indicate that the stall mechanisms at high Reynolds numbers differ from those at lower values, raising questions regarding the validity of conventional low-order prediction tools for simulating aerodynamic performance under these conditions. In this study, static and dynamic stall simulations employing Unsteady Reynolds-Averaged Navier–Stokes (URANS) and Delayed Detached Eddy Simulation (DDES) methods are validated against experimental data for a NACA 0021 airfoil at Re=5.5 x 106. Firstly, two spanwise extensions of a Q3D model are simulated using URANS. Results demonstrate that an aspect ratio (AR) of 0.25 is insufficient for accurately capturing large-scale stall cells, resulting in overpredicted lift values. Subsequent simulations with AR=2.5 confirm that the assumption of fully turbulent boundary layers is valid at such high Reynolds numbers. The DDES method—a hybrid approach combining RANS and LES—shows promise in predicting both the abrupt onset of stall and turbulent flow separation with minimal additional computational cost. Further simulations using DDES with varying inflow turbulence intensities reveal a stall-delay effect as freestream turbulence increases. While the sensitivity of freestream turbulence on dynamic stall during airfoil pitching is negligible, it significantly influences post-stall behaviour. Spectral analysis indicates that the post-stall regime is dominated by the shedding of dynamic stall vortices at a Strouhal number of 0.5.

Maintenance, repair, and overhaul (MRO) of jet engines rely on geometric inspection and aerothermodynamic performance analysis of compressor and turbine blades. In order to analyze the variability of airfoil parameters due to manufacturing tolerances and deterioration effects and to investigate the impact of the geometric variability on jet engine efficiency, previous studies have developed various airfoil parameterization and reconstruction methods. However, these methods were adapted for blades and vanes of specific compressor or turbine stages, while general-purpose methods have not been developed yet for stator vanes and rotor blades. Therefore, this study compiled nominal and measurement data for several compressor and turbine stages of four different commercial turbofan engines. These data were subsequently used to develop general-purpose parameterization and reconstruction methods based on new approaches for (i) the determination of the camber line, (ii) the mathematical description of airfoil profiles at leading and trailing edges, and (iii) the reconstruction of airfoil shapes. The parameterization and reconstruction of both nominal and measurement data show that the methods are robust and reliable and provide accurate results. The methods can be utilized for the geometry analysis of non-nominal (especially deteriorated) blades and for the geometry alteration of nominal blades to investigate deterioration effects. Furthermore, the analysis demonstrates that robust methods should have fewer underlying assumptions and more complex software routines compared to tailored approaches for specific compressor or turbine stages. Such routines are, in particular, recommended for nominal blades of high-pressure turbines (HPT) and deteriorated blades.

In turbomachinery, mixing in the blade tip region between tip leakage and mainstream flow leads to irreversible entropy production, which is detrimental to efficiency. Despite extensive efforts to reduce leakage flows, the mixing process remains a significant source of performance loss, even at small massflow rates. Introducing Vane Bleed Holes (VBH) into existing machines offers a promising solution to reduce these losses. Vane Bleed Holes operate by extracting the leakage flow from the rear section of the outer air seal cavity of the rotor blade and reintroducing it into the main gas path in the shroud region of the subsequent vane. This process significantly reduces mixing losses between leakage and mainstream flows and improves inflow conditions at the vane's near-endwall region. The aim of this paper is to present the numerical design and optimization of a Vane Bleed Hole that will be experimentally integrated and tested in a 1.5-stage low-pressure turbine. Within the framework of this study, a VBH geometry is generated, parameterized, and optimized using a genetic algorithm to maximize isentropic efficiency. The study particularly focuses on the quantitative assessment of the loss-generating mechanisms using an entropy production-based decomposition of the losses, which is crucial for the development of future VBH improvement strategies.

Corner separations are a complex physical phenomenon that significantly affects the off-design operation of axial compressors, contributing to instability and limiting their operating range. At the same time, most Reynolds-averaged Navier–Stokes (RANS) models struggle to capture the interaction of endwall and airfoil boundary layers accurately, leading to incorrect predictions of aerodynamic performance, local blade loading, and instability mechanisms. This article evaluates the predictive capabilities of state-of-the-art, steady-state RANS modeling approaches for the aerodynamics of the linear compressor cascade of the École Centrale de Lyon. The evaluation is based on comprehensive studies of the computational fluid dynamics setup, focusing on the tripping process of the blade boundary layers, endwall treatment, and inflow boundary conditions. An optimized RANS setup is presented, featuring a meshed trip for the blade boundary layers, fully-turbulent endwalls, and a corrected inflow angle. This setup yields accurate predictions of static pressure distributions at various spanwise positions, including in direct proximity to the endwall, and a precise representation of the total-pressure losses induced by corner separations downstream of the cascade. Boosting the momentum of the fluid in endwall boundary layers, either by prescribing fully-turbulent endwall boundary layers or neglecting endwalls in the inflow conditions, improves the prediction of loaded operating points, enhances the blade loading, and makes the suction-sided boundary layer more resistant toward diffusion. A comparison with other RANS- and large eddy simulations-based results of this test case from the literature highlights the improved prediction capabilities of the proposed strategies. This study identifies the limitations of the RANS simulations concerning corner separation-induced vortex trajectories and the pitchwise spread of loss distributions downstream of the blade, providing a foundation for future improvements in the RANS modeling.

In this study, the modeling of rough surfaces by eddy-viscosity-based roughness models is investigated, specifically focusing on surfaces representative of deterioration in aero-engines. In order to test these models, experimental measurements from a rough T106C blade section at a Reynolds number of 400 K are adopted. The modeling framework is based on the k-ω-SST with Dassler’s roughness transition model. The roughness model is recalibrated for the k-ω-SST model. As a complement to the available experimental data, a high-fidelity test rig designed for scale-resolving simulations is built. This allows us to examine the local flow phenomenon in detail, enabling the identification and rectification of shortcomings in the current RANS models. The scale-resolving simulations feature a high-order flux-reconstruction scheme, which enables the use of curved element faces to match the roughness geometry. The wake-loss predictions, as well as blade pressure profiles, show good agreement, especially between LES and the model-based RANS. The slight deviation from the experimental measurements can be attributed to the inherent uncertainties in the experiment, such as the end-wall effects. The outcomes of this study lend credibility to the roughness models proposed. In fact, these models have the potential to quantify the influence of roughness on the aerodynamics and the aero-acoustics of aero-engines, an area that remains an open question in the maintenance, repair, and overhaul (MRO) of aero-engines.

The aerodynamic performance of a wind turbine rotor blade depends on the geometry of the airfoils used. The airfoil shape can be affected by elastic deformations of the blade during operation due to structural loads. This paper provides an initial estimation of the extent to which cross-sectional deformations influence the aerodynamic loads on the rotor. The IEA 15 MW reference wind turbine model is used for this study. A constant wind field at rated wind speed is applied as an operational load test case. The resulting loads are calculated by an aero-servo-elastic simulation of the turbine. The loads are applied to a three-dimensional (3D) finite shell element model of the rotor blade, which serves to calculate the cross-sectional deformations. For the individual cross-sections in the deformed configuration, the new lift and drag coefficients are calculated. These are then included in the aero-servo-elastic simulation, and the obtained results are compared with those of the initial simulation that is based on the undeformed cross-sections. The cross-sectional deformations consist of a change in the chord length and the geometry of the trailing edge panels and depend on the azimuth position of the blade. The change in the airfoil geometries results in altered aerodynamic characteristics and therefore a deviation of the blade root bending moments, the maximum change of which is -1.4 % in the in-plane direction and +0.71 % in the out-of-plane direction. These results show that cross-sectional deformations have a minor influence on the internal loads of rotor blades in normal operation.

This study shows an extensive analysis of dynamic stall on wind turbine airfoils, preparing for the development of a reduced-order model applicable to thick airfoils (t/c>0.21) in the future. Utilizing unsteady Reynolds-averaged Navier–Stokes (URANS) simulations of a pitching FFA-W3-211 airfoil with a Reynolds number of 15 × 106, our analysis identifies the distinct phases in the course of the evolution of dynamic stall. While the dynamic stall is conventionally categorized into the primary-instability transitioning to the vortex formation stage, we suggest two sub-categories for the first phase and an intermediate stage featuring a plateau in lift prior to entering the full stall region. This delays the inception of deep stall, approximately 3° for a simulation case. This is not predictable with existing dynamic-stall models, which are optimized for applications with a low Reynolds number. These features are attributed to the enhanced flow attachment near the leading edge, restricting the stall region downstream of the position of maximum thickness. The analysis of the frequency spectra of unsteady pressure confirms the distinct characteristics of the leading-edge vortex street and its interaction with large-scale mid-chord vortices in forming the dynamic-stall vortices (DSVs). Examination of the leading-edge suction parameter (LESP) proposed by Ramesh et al. (2014) for thin airfoils with low Reynolds numbers reveals that the LESP is a valid criterion in predicting the onset of the stall for thick airfoils with high Reynolds numbers. Based on the localized separation behavior during a dynamic-stall cycle, we suggest a mid-chord suction parameter (MCSP) and trailing-edge suction parameter (TESP) as supplementary criteria for the identification of each stage. The MCSP exhibits a breakdown in magnitude at the onset of the dynamic-stall formation stage and full stall, while the TESP supports indicating the emergence of a full stall by detecting the trailing-edge vortex.

At Leibniz University of Hannover, Germany, a new turbomachinery test facility has been built over the last few years. A major part of this facility is a new 6 MW compressor station, which is connected to a large piping system, both designed and built by AERZEN. This system provides air supply to several wind tunnel and turbomachinery test rigs, e.g., axial turbines and axial compressors. These test rigs are designed to conduct high-quality aerodynamic, aeroelastic, and aeroacoustic measurements to increase physical understanding of steady and unsteady effects in turbomachines. One primary purpose of these investigations is the validation of aerodynamic and aeroacoustic numerical methods. To provide precise boundary conditions for the validation process, extremely high homogeneity of the inflow to the investigated experimental setup is imminent. Thus, customized settling chambers have been developed using analytical and numerical design methods. The authors have chosen to follow basic aerodynamic design steps, using analytical assumptions for the inlet section, the “mixing” area of a settling chamber, and the outlet nozzle in combination with state-of-the-art numerical investigations. In early 2020, the first settling chamber was brought into operation for the acceptance tests. In order to collect high-resolution flow field data during the tests, Leibniz University and AERZEN have designed a unique measurement device for robust and fast in-line flow field measurements. For this measurement device, total pressure and total-temperature rake probes, as well as traversing multi-hole probes, have been used in combination to receive high-resolution flow field data at the outlet section of the settling chamber. The paper provides information about the design process of the settling chamber, the developed measurement device, and measurement data gained from the acceptance tests.

Abstract. This study shows an extensive analysis of dynamic stall on wind turbine airfoils preparing the development of a reduced-order model applicable to thick airfoils (t / c > 0.21) in the future. Utilizing URANS simulations of a pitching FFA-W3-211 airfoil at the Reynolds number of 15 million, our analysis identifies the distinct phases in the course of the evolution of dynamic stall. When the dynamic stall is conventionally categorized into the primary instability transitioning to the vortex formation stage, we suggest two sub-categories in the first phase, and an intermediate stage featuring a plateau in lift prior to entering the full stall region. This delays the inception of deep stall, approximately 3° for a simulation case. This is not predictable with existing dynamic stall models, optimized for low Reynolds number applications. These features are attributed to the enhanced flow attachment near the leading-edge, restricting the stall region downstream of the position of maximum thickness. The analysis on the frequency spectra of unsteady pressure confirms the distinct characteristics of the leading-edge vortex street and its interaction with large-scale mid-chord vortices to form the dynamic stall vortices (DSVs). Examination of the leading-edge suction parameter (LESP) proposed by Ramesh et al. (2014) for thin airfoils under low Reynolds numbers reveals that LESP is a valid criterion in predicting the onset of the static stall for thick airfoils under high Reynolds numbers. Based on the localized separation behavior during a dynamic stall cycle, we suggest a mid-chord suction parameter (MCSP) and trailing-edge suction parameter (TESP) as supplementary criteria for the identification of each stage. The MCSP exhibits a breakdown in magnitude at the onset of the dynamic stall formation stage and full stall, while TESP supports indicating the emergence of a deep stall by detecting the trailing-edge vortex.

In order to improve the efficiency of modern turbomachinery, the simulation setups in design processes become increasingly detailed, and thus computationally more expensive. This paper aims to quantify the numerical influence of squealer tips on the performance of a 4½-stage axial compressor. For this purpose, the performance map, obtained by steady-state calculations using the k-w SST turbulence model and the TRACE flow solver, is simulated for two setups: the reference setup and a setup with squealer tips added. The inclusion of squealer tips enhances the stage-wise compressor performance by reducing secondary flow and flow separation at the casing. This improvement results from the change in blade-tip geometry. The stage total-pressure ratio is thus improved by up to 0:28%. However, a deterioration of the fourth-stage flow as a result of the squealer tips prevents these improvements from enhancing the overall compressor performance. NOMENCLATUR

The exact prediction of clocking angle effects is important for the aerodynamic and aeroelastic design of turbomachinery. Predicting accurately the wake propagation, wake-boundary-layer interaction, and potential field effect remains a challenge for eddy-viscosity-based turbulence-models and transition-models, even with (U)RANS. Therefore, this paper investigates the sensitivities of the prediction towards boundary conditions. The test case is the T106A low-pressure turbine cascade with upstream and downstream moving bars. This includes different inlet turbulence intensities and clocking angles. The influence of simplifications such as modeling the fully 3D (F3D) flow as a quasi 3D flow (Q3D) combined with a linear distribution of an axial velocity density ratio (AVDR) in axial direction will be demonstrated. The k-wSST turbulence model combined with the g - Req transition model is used. Special emphasis will be put on the analysis of the suction side boundary-layer, its separation, and transitional behavior. The numerical results are compared to the experimental data of the cascade test-case. Current results indicate that Q3D models with linear approximations of AVDR effects struggle to predict the influence of the clocking angle variation on the flow. While the potential field effect from the downstream bars is well predicted with Q3D simulations, the authors show that Q3D simulations combined with the choice of AVDR influence the dynamics of the boundary-layer. Furthermore, it will be shown that the interaction between wake and boundary-layer, as well as the development of the boundary-layer are not predicted well by the current (U)RANS model for both F3D and Q3D. This requires more attention in future work.

Steady-state simulations of turbomachinery often require the use of mixing planes in between blade rows to remove unsteady rotor-stator interactions. In multistage configurations with many mixing planes, the errors caused by this removal of information accumulate and make accurate predictions very challenging, especially at off-design operating conditions. In a recent publication, the effect of mixing planes on the production of turbulent kinetic energy is addressed with an additional differential equation. In this study, this modification is applied to steady-state simulations of a 4.5-stage and an 8.5-stage axial compressor. The boundary conditions are varied to assess the potential of this modification near the choke and surge limits of the compressors. Results are shown from simulations of both setups. The turbulent kinetic energy and eddy viscosity, as well as global performance parameters like efficiency and mass flow rate are evaluated. Based on these quantities, it is shown that the use of the modification leads to more accurate predictions compared to URANS simulations and allows for simulations closer to the surge limit. Furthermore, it is demonstrated that the modification underestimates the production of turbulent kinetic energy when a shock interacts with an upstream mixing plane.

In recent years, the research on roughness has focused on various roughness features, rather than the roughness height only, in order to improve the understanding of roughness effects on wall bounded flows. A special focus is placed on the skewness of the roughness height profile. The skewness measures whether the height profile is dominated by negative or positive roughness elements. Surfaces with both features can be found on worn blades: On the leading edge, roughness is caused by the impact of particles resulting in a negative skewness. Rough surfaces around the trailing edge, however, develop due to depositions leading to a positive skewness. In this paper, rough surfaces taken from a compressor blade of an aero engine are systematically varied to investigate the isolated effect of skewness on aerodynamic losses. By direct numerical simulations of a periodic flow channel. The results show that the skewness has a major influence on loss generation. Based on these results, an existing model which essentially uses the shape-and-density parameter, is extended by a skewness factor. The modified correlation predicts the influence of the rough surfaces investigated well.

The successful design of highly efficient and operationally flexible axial-flow compressors requires reliable CFD predictions. The selection of a suitable turbulence model, including turbulence and transition model extensions, is crucial for an accurate prediction of the integral compressor performance. Often, however, the impact of different models and extensions, such as stagnation-point anomaly fixes and streamline-curvature models depends on the flow field investigated and cannot be determined a priori. Rather, suitable model combinations are selected on a case-to-case basis after extensive sensitivity studies. In order to provide a foundation for a systematic selection of turbulence models, this paper aims to quantify the sensitivities of performance-map predictions with respect to the choice of mesh, turbulent boundary conditions, and various modeling approaches for turbulence and transition. For this purpose, steady-state simulations based on the k- and k--SST turbulence models combined with different transition and turbulence extensions are conducted for a four-stage axial compressor. It is shown that the prediction sensitivity increases for aerodynamically highly loaded operating points.

Abstract. This study addresses the challenge of predicting dynamic stall on wind turbine airfoils, focusing on the development of a reduced-order model applicable to thick airfoils (t/c > 0.21). Utilizing a Delayed Detached-Eddy simulation of a pitching FFA-W3-211 airfoil at Re = 15 M, our analysis identifies the transition from the primary instability phase to the vortex formation stage as a critical aspect of dynamic stall. By examining the dynamic time scales, we observed a ten-fold increase in the growth rate of the shear layer height during the transition of these stages. The stall delays attributed to these stages are substantially dependent on the airfoil's camber distribution and the location of the maximum thickness. We discovered that the Leading-Edge Suction-Parameter (LESP) proposed by Ramesh et al. (2014) for thin airfoils is also helpful in predicting the onset of the vortex formation stage for thick airfoils. Based on this finding, we propose a Mid-Chord Suction-Parameter (MCSP), that is more effective for wind turbine airfoils. The MCSP exhibits a breakdown in magnitude at the onset of the vortex formation stage and deep stall.

Labyrinth seals are an essential and widely used component of modern turbomachines and can contribute significantly to their efficiency. Their often complex geometry is intended to generate pressure losses to reduce leakage flow. Acoustic resonances can occur within the cavities used for this purpose, which, when combined with a matched source of excitation, can result in high noise emissions and vibration excitation of the mechanical components of the labyrinth seal. In this work, an analytical model is developed and validated with numerical data to predict the resonant frequencies of axial standing waves within the cavities for propagating acoustic modes. The model is based on a RANS simulation of the cavity flow and determines the axial characteristics of the acoustic modes propagating upstream and downstream at several axial positions. Two acoustic wave equations commonly used in turbomachinery applications are used to analytically estimate the sound propagation within the seal’s cavity. An overall axial wavelength across the cavity is estimated based on the wavenumbers determined at each axial position and a resonance condition is formulated to iterate the modal resonance frequency. This modeling approach is used to estimate the resonant frequency of an axial standing wave for different acoustic mode orders. Comparison of the models with numerical results in a generic labyrinth seal for three aerodynamic operating points shows a deviation between the analytically and numerically determined resonant frequency of approximately 0.68% on average with resonant frequencies occurring at Helmholtz numbers between 58.69 and 64.20 at Mach numbers of up to 0.4. Numerical setup studies regarding the influence of turbulence models, turbulent production limiters, and modeling of rotational effects on the turbulence in RANS simulations yielded in a deviation smaller than 1% of the numerically predicted resonance frequencies.

The flow around wind turbine blades dynamically stalls when the local angle of attack temporarily rises above the angle of static separation. This introduces increased loads, which can lead to the destruction of the blade. The research reported here provides a computational fluid dynamics setup in OpenFOAM that solves the unsteady Reynolds-averaged NavierStokes equations to investigate dynamic stall on WT blades. The rotating and pitching motion of the blades is implemented via a novel combination of a dynamic and a sliding mesh approach. Simulations are carried out with different mesh resolutions and the results are compared with experimental data. It is shown that the usage of wall functions in the boundary layer is not suitable for investigating dynamic stall. When resolving the boundary layer instead, the results correctly predict the characteristics of a dynamic stall hysteresis with a maximum deviation of 8%. With the help of the developed setup, the computational effort of investigating dynamic stall on a large wind turbine (rated capacity 20 MW) can be reduced by 10% to approx. ≈ 2.8 · 106 CPUh when compared to similar setups in the literature.

In the present study, the curved element capabilities of a high-order solver are scrutinized. The devised approach not only suggests a plausible way to adopt a body-fitted grid approach as an alternative to immersed boundary method (IBM), but also enables performing LES instead of DNS without under-resolving the roughness. The method is first tested using various polynomial degrees. Then, it is validated against reference DNS-IBM results from a rough channel flow setup having various Reyn-olds numbers corresponding to the entire roughness range. The results confirm the validity of the new approach.

Roughness generally consists of structures that are either oriented anisotropic in directions tangential to the surface or isotropic, or a superposition of both components. Interactions between the roughness elements exert a significant influence on the fluid mechanical losses. Costeffective maintenance of the functionality of the surfaces of aerodynamically relevant components such as blades requires the quantitative prediction of the flow influence, which can be achieved through ReynoldsAveragedNavierStokes Simulations (RANS). An established roughness parameter used to model the influence on the flow is the equivalent sand grain roughness ks. By contrast, the research presented here employs Direct Numerical Simulations (DNS) with Immersed Boundary Method (IBM) of channel flows over anisotropic, isotropic, and superimposed surfaces in order to investigate the aerodynamic losses, for example, due to turbulent production and dissipation. The simulation results show that the equivalent sand grain roughness does not correctly predict flow losses from anisotropic and superimposed surfaces, because in reality, the ”angle of attack” with respect to the anisotropic structures changes the turbulence due to altered turbulent production and dissipation. A nonlinear relationship between the flow resistance and this angle of attack is a result of local changes in pressure gradients.