Unsteady Stator-rotor Interaction Research Articles

Numerical Investigation of Unsteady Rotor–Stator Interaction Mechanism and Wake Transportation Characteristics in a Compressor with Non-Uniform Tip Clearance Rotor

This study aims to numerically investigate a transonic compressor by solving the unsteady Reynolds-averaged Navier–Stokes equations. The flow mechanisms related to unsteady flow were carefully examined and compared between rotors with non-uniform tip clearance (D1) and small-value tip clearance (P1). The unsteady flow field near the 50% and 95% blade span characterized by unsteady rotor–stator interaction was analyzed in detail for near-stall (NS) conditions. According to the findings, the perturbation of unsteady aerodynamic force for the stator is much bigger than that of the rotor. At the mid-gap between the rotor and stator, the perturbation of tangential velocity of the D1 scheme in the rotor and stator frame is reduced. At the rotor’s outlet region, the perturbation intensity is divided into three main perturbation regions, which are respectively concentrated in the TLV near the upper endwall, the corner separation at the blade root, and the wake of the whole blade span. Through the analysis of the wake transportation characteristics, it was found that when the wake passes through the stator blade surface, the wake exerts a substantial influence on the flow within the stator passage. It further leads to notable pressure perturbations on the stator’s surface, as well as affecting the development and flow loss of the boundary layer. The negative jet effect induces opposite secondary flow velocity on both sides of the wake near the stator’s surfaces. Therefore, the velocity at a specific point on the stator’s suction surface will decrease and then increase. Conversely, the velocity at a particular point on the pressure surface will increase and then decrease.

A graphics-accelerated deep neural network approach for turbomachinery flows based on large eddy simulation

In turbomachinery, strongly unsteady rotor–stator interaction triggers complex three-dimensional turbulent flow phenomena such as flow separation and vortex dynamics. Large eddy simulation (LES) is an advanced numerical method that has recently been used to resolve large-scale turbulent motions and model subgrid-scale turbulence in turbomachinery. To largely reduce the computing cost of LES for turbomachinery flow, a graphics processing unit (GPU)-accelerated deep neural network-based flow field prediction approach is explored, which combines convolutional neural network autoencoder (CNN-AE) with long short-term memory (LSTM). CNN-AE extracts spatial features of turbomachinery flow by mapping high-dimensional flow fields into low-dimensional space, while LSTM is used to predict the temporal evolution of fluid dynamics. Automatic mixed precision (AMP) is employed to achieve rapid neural network training using Nvidia GTX 1080 Ti GPU, which shows a significant speedup compared with that without AMP. We evaluated the proposed CNN-AE-LSTM (CAL) method against gated recurrent units (GRU) and simple recurrent network (SRN) on two types of turbomachinery, i.e., centrifugal and axial flow pumps. The results show that the proposed CAL shows better capability of capturing the vortex structure details of turbomachinery. When predicting the temporal vorticity field, the mean square error of CAL results is 0.105%–0.124% for centrifugal pumps and 0.071%–0.072% for axial flow pumps. Meanwhile, the structural similarity index measure of the CAL results is 92.51%–92.77% for centrifugal pumps and 93.81%–94.61% for axial flow pumps. The proposed CAL is noticeably better than GRU and SRN in terms of both mean square error and structural similarity index measure.

Investigation of Unsteady Rotor–Stator Interaction and Deterministic Correlation Analysis in a Transonic Compressor Stage

Abstract Unsteady blade row interaction (UBRI) has a large impact on performance in high-speed axial compressors. Thus, the influence of UBRI should be accurately predicted in compressor routine design. In this study, the unsteady rotor–stator interaction in a transonic single-stage compressor, NASA Stage 35, is studied by steady and unsteady Reynolds-Averaged Navier–Stokes methods. First, the UBRI is analyzed. Periodic separation bubbles on the stator suction surface induced by the rotor wake are observed. Comparisons between steady and unsteady results show that the radial distribution of flow angle near the hub and tip region of the stator is strongly influenced by UBRI. Second, deterministic correlations are analyzed based on the average-passage equation system. The distribution of deterministic stress and the relationship between spatial correlations and deterministic correlations are analyzed. Results show that a strong nonlinear interaction caused by the rotor wake and the stator potential field is found in the rotor–stator gap, which is responsible for the generation of spatial–time correlation. Then, the anisotropy of deterministic correlations is analyzed using the Lumley triangle. Results show that the deterministic stress is highly anisotropic in the stator passage, which can be considered in the modeling using a similar strategy of turbulence modeling. At last, the relationships between the harmonics and decay rate of deterministic correlations are analyzed. The decay rate of deterministic correlation is highly related to the corresponding harmonics, and the higher-order harmonic exhibits a higher decay rate. A modified exponential decay model is proposed for deterministic correlation based on harmonics, which provides improved performance.

Influence of Supersonic Nozzle Design Parameters on the Unsteady Stator–Rotor Interaction in Radial-Inflow Turbines for Organic Rankine Cycles

Abstract The use of radial-inflow turbine (RIT) for organic Rankine cycle (ORC) plant sizes below 100 kW is promising, although the application remains challenging. In fact, the single-stage arrangement imposed by economic constraints and hence the large expansion ratio, together with the large molecular weight, which characterizes organic fluids, usually result in highly supersonic flows, so making the use of transonic stators often mandatory. Particularly, the influence of RIT stator design parameters on losses and the level of unsteadiness seen by the subsequent rotor is still scarcely addressed in published literature. The present work investigates the effect of the convergent–divergent stators design parameters and the resulting downstream flow field non-uniformity on the unsteady stator–rotor interaction and loss generation in ORC RIT. To this end, two stator and rotor configurations which differ by the stator design parameters (i.e., discharge metal angle and number of vanes) have been tested by means of three-dimensional (3D) unsteady CFD calculations accounting for real-gas properties. The results show that larger stator–rotor interaction is present for the case featuring higher vane count and lower outlet metal, which also features the largest fluctuations of power output and pressure force on blade, together with a substantially lower average total-to-static efficiency, as a result of a larger stator downstream pitchwise non-uniformity. Ultimately, the results indicate that only aiming for optimal stator efficiency during the stator design phase might lead to highly suboptimal configurations from the whole turbine stage point of view.

How the Approach to Simulating Turbulence Influences the Accuracy of Predicting the Noise Level of a Bypass Turbojet Engine Fan

The study presents the results of how noise level prediction results are influenced by the approach to simulating turbulence when calculating the noise generated by the bypass fan stage. Numerical studies are performed for a model fan stage in the main operating modes, which determine its acoustic properties. Far-field noise level calculations were performed using a finite element method based on the mode composition of the generated noise. We analyze the influence of the turbulence model on the number and amplitudes of acoustic modes excited in the flow at the fundamental harmonics of the fan blade passing frequency. It is shown that simulation of the anisotropic turbulence of a flow when calculating the unsteady rotor–stator interaction makes it possible to obtain noise levels close to experimental ones.

Rotor–Stator Interactions in a 2.5-Stage Axial Compressor—Part I: Experimental Analysis of Tyler–Sofrin Modes

Abstract This two-part paper investigates the influence of rotor–stator interactions on the blade vibrational stresses of the first rotor, excited by the downstream stator. To this end, aeroacoustic and aeroelastic measurements and numerical setup studies for the solver TRACE are conducted in order to improve the predictive accuracy of blade vibrational stresses. Part I compares tip timing data for resonance crossings of three blisk modes to numerical predictions. Due to the single-row analysis within the linearized version of the flow solver TRACE, unsteady rotor–stator interactions are excluded by default. The findings show that leaving out these interactions in the numerical setup can lead to 97% lower vibrational stress predictions with respect to the absolute value measured. To validate the prediction of rotor–stator interactions by the nonlinear frequency domain method of TRACE, unsteady pressure measurements were conducted at the casing in the inter-row section of the first stage. The results were analyzed using an optimized measuring grid and applying a compressed sensing-based azimuthal mode analysis. Predicted azimuthal mode numbers are in accordance with the experiment, whereas amplitudes deviate from the measurements in part. Part II focuses on the prediction of blade vibrational stresses. To this end, a detailed grid study is performed and comparisons to steady and unsteady measurement data are made. In summary, this two-part paper confirms the importance of rotor–stator interactions for blade vibrational stresses excited by downstream vanes at a state-of-the-art high-pressure compressor.

Impact of shape-optimization on the unsteady aerodynamics and performance of a centrifugal turbine for ORC applications

This paper presents the results of the application of a shape-optimization technique to the design of the stator and the rotor of a centrifugal turbine conceived for Organic Rankine Cycle (ORC) applications. Centrifugal turbines have the potential to compete with axial or radial-inflow turbines in a relevant range of applications, and are now receiving scientific as well as industrial recognition. However, the non-conventional character of the centrifugal turbine layout, combined with the typical effects induced by the use of organic fluids, leads to challenging design difficulties. For this reason, the design of optimal blades for centrifugal ORC turbines demands the application of high-fidelity computational tools. In this work, the optimal aerodynamic design is achieved by applying a non-intrusive, gradient-free, CFD-based method implemented in the in-house software FORMA (Fluid-dynamic OptimizeR for turboMachinery Aerofoils), specifically developed for the shape optimization of turbomachinery profiles. FORMA was applied to optimize the shape of the stator and the rotor of a transonic centrifugal turbine stage, which exhibits a significant radial effect, high aerodynamic loading, and severe non-ideal gas effects. The optimization of the single blade rows allows improving considerably the stage performance, with respect to a baseline geometric configuration constructed with classical aerodynamic methods. Furthermore, time-resolved simulations of the coupled stator-rotor configuration shows that the optimization allows to reduce considerably the unsteady stator-rotor interaction and, thus, the aerodynamic forcing acting on the blades.

Investigations of Compressible Turbulent Flow in a High-Head Francis Turbine

Dynamic stability of the high-head Francis turbines is one of the challenging problems. Unsteady rotor–stator interaction (RSI) develops dynamic stresses and leads to crack in the blades. In a high-head turbine, vaneless space is small and the amplitudes of RSI frequencies are very high. Credible estimation of the amplitudes is vital for the runner design. The current study is aimed to investigate the amplitudes of RSI frequencies considering a compressible flow. The hydro-acoustic phenomenon is dominating the turbines, and the compressibility effect should be accounted for accurate estimation of the pressure amplitudes. Unsteady pressure measurements were performed in the turbine during the best efficiency point (BEP) and part load (PL) operations. The pressure data were used to validate the numerical model. The compressible flow simulations showed 0.5–3% improvement in the time-averaged pressure and the amplitudes over incompressible flow. The maximum numerical errors in the vaneless space and runner were 6% and 10%, respectively. Numerical errors in the instantaneous pressure amplitudes at the vaneless space, runner, and draft tube were ±1.6%, ±0.9%, and ±1.8%, respectively. In the draft tube, the incompressible flow study showed the pressure amplitudes up to eight times smaller than those of the compressible. Unexpectedly, the strong effect of RSI was seen in the upper and lower labyrinth seals, which was absent for the incompressible flow.

Optimal Aerodynamic Design of a Transonic Centrifugal Turbine Stage for Organic Rankine Cycle Applications

This paper presents the results of the application of a shape-optimization technique to the design of the stator and the rotor of a centrifugal turbine conceived for Organic Rankine Cycle (ORC) applications. Centrifugal turbines have the potential to compete with axial or radial-inflow turbines in a relevant range of applications, and are now receiving scientific as well as industrial recognition. However, the non-conventional character of the centrifugal turbine layout, combined with the typical effects induced by the use of organic fluids, leads to challenging design difficulties. For this reason, the design of optimal blades for centrifugal ORC turbines demands the application of high-fidelity computational tools. In this work, the optimal aerodynamic design is achieved by applying a non-intrusive, gradient-free, CFD-based method implemented in the in-house software FORMA (Fluid-dynamic Opti-mizeR for turboMachinery Aerofoils), specifically developed for the shape optimization of turbomachinery profiles. FORMA was applied to optimize the shape of the stator and the rotor of a transonic centrifugal turbine stage, which exhibits a significant radial effect, high aerodynamic loading, and severe non-ideal gas effects. The optimization of the single blade rows allows improving considerably the stage performance, with respect to a baseline geometric configuration constructed with classical aerodynamic methods. Furthermore, time-resolved simulations of the coupled stator-rotor configuration shows that the optimization allows to reduce considerably the unsteady stator-rotor interaction and, thus, the aerodynamic forcing acting on the blades.

Investigation of Rotor-Stator Interaction and Flow Unsteadiness in a Low Specific Speed Centrifugal Pump

Instantaneous flow dynamics induced by rotor-stator interaction are detrimental to the stable operation of centrifugal pumps. In this study, unsteady rotor-stator interaction and flow structures within a low specific-speed centrifugal pump are analysed using the Large Eddy Simulation (LES) method. For that purpose, pressure pulsation and the evolution process of a vortical structure are combined to investigate rotor-stator interaction in order to clarify the inherent correlation between pressure amplitude and vorticity distribution. The results show that distinct peaks at blade passing frequency (fBPF) are closely associated with the positions of the monitoring point due to rotor-stator interaction. An unsteady vortical structure at the near tongue region is related to the relative position of the impeller with respect to the tongue, and the upstream effect of the volute tongue significantly affects the vorticity distribution on the blade pressure side. Rotor-stator interaction is dominated by vortex shedding in the wake of the blade trailing edge and their impingement on the volute tongue with subsequent cutting and distortion. Moreover, the high-pressure amplitude is generated with the corresponding high vorticity magnitude observed as well. Therefore, it is confirmed that pressure amplitude is significantly associated with the corresponding vorticity magnitude.

NUMERICAL INVESTIGATIONS OF TWO TYPICAL UNSTEADY FLOWS IN TURBOMACHINERY USING THE MULTI-PASSAGE MODEL

In this paper, the research on two types of unsteady flow problems in turbomachinery including blade flutter and rotor-stator interaction is made by means of numerical simulation. For the former, the energy method is often used to predict the aeroelastic stability by calculating the aerodynamic work per vibration cycle. The inter-blade phase angle (IBPA) is an important parameter in computation and may have significant effects on aeroelastic behavior. For the latter, the numbers of blades in each row are usually not equal and the unsteady rotor-stator interactions could be strong. An effective way to perform multi-row calculations is the domain scaling method (DSM). These two cases share a common point that the computational domain has to be extended to multi passages (MP) considering their respective features. The present work is aimed at modeling these two issues with the developed MP model. Computational fluid dynamics (CFD) technique is applied to resolve the unsteady Reynolds-averaged Navier-Stokes (RANS) equations and simulate the flow fields. With the parallel technique, the additional time cost due to modeling more passages can be largely decreased. Results are presented on two test cases including a vibrating rotor blade and a turbine stage.

Numerical modelling of rotor–stator interaction in rim driven thrusters

An electric rim driven thruster is a relatively new marine propulsion device and the associated fluid dynamics have not been fully investigated. This work develops a robust CFD method and investigates both frozen rotor and unsteady simulations of rotor–stator interaction. Two solvers from OpenFOAM were used. Steady state simulations were performed using MRFSimpleFoam with a frozen rotor treatment of the interface between static and rotational reference frames. The solver for unsteady simulations was pimpleDyMFoam, utilising a sliding mesh interface to handle the dynamic meshing. Both methods are thoroughly verified and validated against experimental data. The k–omega SST turbulence model is found to be robust down to low advance ratios. For the rim driven thruster, analytical models are used to estimate friction forces in the rim gap and their contribution to torque losses. The frozen rotor and unsteady treatments of rotor–stator interaction are compared and found to have similar trends in the variation of thrust produced. However, the frozen rotor method does not predict the same variation of instantaneous torque and does not capture the rotor–stator interaction fully. Analysis of the unsteady rotor–stator interaction shows an oscillating flow over the stators and thus inflow to the blades.

Unsteady effects at the interface between impeller-vaned diffuser in a low pressure centrifugal compressor

In this paper, Proper Orthogonal Decomposition (POD) is applied to the analysis of the unsteady rotor-stator interaction in a low-pressure centrifugal compressor. Numerical simulations are carried out through finite volumes method using the Unsteady Reynolds-Averaged Navier-Stokes Equations (URANS) model. Proper Orthogonal Decomposition allows an accurate reconstruction of flow field using only a small number of modes; therefore, this method is one of the best tools for data storage. The POD results and the data obtained by the Adamczyk decomposition are compared. Both decompositions show the behavior of unsteady rotor-stator interaction, but the POD modes allow quantifying better the numerical errors.

The Whole Annulus Computations of Particulate Flow and Erosion in an Axial Fan

Gas turbine engines operating in a hostile environment, polluted with sand or dust particles, are susceptible to erosion damage, mostly at the front axial fans and compressors. Accurately predicting the erosion pattern and rate due to sand ingestion is one of the major challenges faced by the transportation and power industries. Maintenance costs are scrutinized and intensive research efforts are currently deployed in predictive life assessment tools to minimize the overhaul down time. The conventional prediction methods were usually based on steady-state simulations of gas-phase flows through a single blade passage per blade row to reduce the computational cost. However, the multistage turbomachinery flows are intrinsically subject to unsteadiness, especially due to stator-rotor interactions, which may affect sand particle trajectories even if a one-way coupling method is considered. Furthermore, an unsteady stator-rotor interaction requires a whole-annulus model at great computational cost to avoid simplifications of the geometries or flow physics. To study the effects of the stator-rotor interaction on sand particle trajectories and erosion, an axial fan with inlet guide vanes is investigated, based on the whole annulus computations of both steady and unsteady gas-phase flows, each of which is then followed by a Lagrangian particle tracking step. A numerical algorithm for tracking particles driven by the unsteady gas-phase flow is presented. The comparison of the numerical predictions with the experimental data confirms the validity and necessity of the unsteady computational fluid dynamics (CFD) model in providing adequate predictions of sand erosion in the axial fan.

Experimental Reduction of Transonic Fan Forced Response by Inlet Guide Vane Flow Control

The main contributor to the high cycle fatigue of compressor blades is the response to aerodynamic forcing functions generated by an upstream row of stators or inlet guide vanes. Resonant response to engine order excitation at certain rotor speeds can be especially damaging. Studies have shown that flow control by trailing edge blowing (TEB) can reduce stator wake strength and the amplitude of the downstream rotor blade vibrations generated by the unsteady stator-rotor interaction. In the present study, the effectiveness of TEB to reduce forced fan blade vibrations was evaluated in a modern single-stage transonic fan rig. Data were collected for multiple uniform full-span TEB conditions over a range of rotor speeds including multiple modal resonance crossings. Resonant response sensitivity was generally characterized by a robust region of strong attenuation. The baseline resonant amplitude of the first torsion mode, which exceeded the endurance limit on the critical blade, was reduced by more than 80% with TEB at 1.0% of the total rig flow. The technique was also found to be modally robust; similar reductions were achieved for all tested modal crossings, including more than 90% reduction in the second leading-edge bending response using 0.7% of the rig flow.

Innovative procedure to minimize multi-row compressor blade dynamic loading using rotor-stator interaction optimization

This paper presents a two-dimensional two-objective procedure for minimizing dynamic loading and maximizing efficiency in multi-stage compressors. The procedure arises from the combination of an evolutionary algorithm and a CFD code, in which a sliding mesh technique and a time-dependent approach are implemented, enabling the study of unsteady rotor-stator interaction. The method is then applied to a two-stage compressor cascade (rotor-stator-rotor-stator). The results concerning the optimal set of geometrical parameters considered for optimization (axial distances between successive cascades, circumferential clocking between stators and between rotors) are finally presented and discussed.

An extraction of the dominant rotor-stator interaction modes by the use of Proper Orthogonal Decomposition (POD)

The Proper Orthogonal Decomposition method is applied to the instantaneous velocity field within the rotor-stator inter-row region of a high-speed high-pressure centrifugal compressor. The processed data come from experiments and numerical simulations. In comparison with a Fourier transform, the POD gives the best modal approximation for both initial fields, in terms of the energy expressed on any given number of modes to be taken into account: to reach 98% of the total energy of the velocity field, the required number of POD modes is up to nine times lower than the number of Fourier harmonics. The individual POD modes are given and show that the unsteady rotor-stator interaction is already present in the very first modes.

Three-dimensional unsteady investigation of HP turbine stages

This article deals with a three-dimensional unsteady numerical simulation of the unsteady rotor—stator interaction in a HP turbine stage. The numerical approach consists of a computational fluid dynamics (CFD) parallel code, based on an upwind total variation diminishing finite volume approach. The computation has been carried out using a sliding plane approach with hybrid unstructured meshes and a two-equation turbulent closure. The turbine rig under investigation is representative of the first stage of aeronautic gas turbine engines. A brief description of the cascade, the experimental setup, and the measuring technique is provided. Time accurate CFD computations of pressure fluctuations and Nusselt number are discussed against the experimental data.

Unsteady rotor-stator interaction in high speed compressor and turbine stages

The blade row interaction can alter the time-mean flow and therefore be of interest for aerodynamic design analysis. Whereas results within low subsonic turbomachines are quite numerous in the literature, there have been far fewer works which give results of blade row interaction within high speed cases. Two cases are related in this paper. First, the effects of an incoming wake on the rotor flow field of a transonic compressor are analyzed. The blade row interaction proved to be positive regarding the total pressure ratio, but negative regarding the losses. The second case concerns a transonic turbine. Particular emphasis is placed on the assessment of the deterministic correlations included in the Averaged Passage Equation System.

Numerical Unsteady Flow Analysis of a Turbine Stage With Extremely Large Blade Loads

This paper presents the detailed numerical analysis including parametric studies on the aerodynamic excitation mechanisms in a turbine stage due to the unsteady stator-rotor interaction. The work is part of the predesign study of a high-pressure subsonic turbine for a rocket engine turbopump. The pressure level in such turbines can be remarkably high (in this case 54 MPa inlet total pressure). Hence, large unsteady rotor blade loads can be expected, which impose difficult design requirements. The parameter studies are performed at midspan with the numerical flow solver UNSFLO, a 2-D/Q3-D unsteady hybrid Euler/Navier-Stokes solver. Comparisons to 2-D and steady 3-D results obtained with a fully viscous solver, VOLSOL, are made. The investigated design parameters are the axial gap (∼8–29 percent of rotor axial chord length) and the stator vane size and count (stator-rotor pitch ratio ∼1–2.75). For the nominal case the numerical solution is analyzed regarding the contributions of potential and vortical flow disturbances at the rotor inlet using rotor gust computations. It was found that gust calculations were not capable to capture the complexity of the detected excitation mechanisms, but the possibility to reduce excitations by enforcing cancellation of the vortical and potential effects has been elaborated. The potential excitation mechanism in the present turbine stage is found dominant compared to relatively small and local wake excitation effects. The parameter studies indicate design recommendations for the axial gap and the stator size regarding the unsteady rotor load.