Potential and Viscous Interactions for a Multi-Blade-Row Compressor

A computationally efficient time-accurate vortex method for unsteady incompressible flows through multiple blade row systems is presented. The method represents the boundary surfaces using vortex systems. A local coordinate system is assigned to each independently moving blade row. Blade shed vorticity is determined from two generating mechanisms and convected using the Euler equation. The first mechanism of vorticity generation is a potential mechanism from a nonlinear unsteady pressure-type Kutta condition applied at the blade trailing edges. The second mechanism is a viscous mechanism from a viscous wake vorticity (VWV) model implemented to simulate the viscous shear layers on the blade pressure and suction sides. Two different two-blade-row compressor systems, a rotor/stator (R/S) system and a stator/rotor (S/R) system, were used to investigate the interaction forces on each blade row. Computational results of the potential and viscous interaction forces are presented and compared to measurements. The comparison suggests that the viscous wake interaction accounts for 25–30% of the peak loading for an axial spacing of 10% chord length between the blade rows. The efficient computational method is particularly attractive for blade indexing study. Therefore a three-blade-row rotor/stator/rotor (R1/S/R2) compressor system is used to demonstrate the indexing calculations between the two rotor positions. Resultant forces on each blade row are presented for ten rotor indexing positions and three axial gap sizes for the gaps between R1 and S and between S and R2. The unsteady peak-to-peak force can reach 10–15% of inflow dynamic head for the gap spacing investigated. The minimum-to-maximum variation of the unsteady force can account for 40–50% of averaged unsteady force.

This two-part paper presents detailed experimental investigations of unsteady aerodynamic blade row interactions in the four-stage Low-Speed Research Compressor of Dresden. In part I of the paper the unsteady profile pressure distributions for the nominal setup of the compressor are discussed. Furthermore the effect of blade row clocking on the unsteady profile pressures is investigated. Part II deals with the unsteady aerodynamic blade forces, which are calculated from the measured profile pressure distributions. The unsteady pressure distributions were analysed in the first, a middle and the last compressor stage both on the rotor and stator blades. The measurements were carried out on pressure side and suction side at midspan. Several operating points were investigated. A complex behaviour of the unsteady profile pressures can be observed, resulting from the superimposed influences of the wakes and the potential effects of several up- and downstream blade rows of the four-stage compressor. The profile pressure changes nearly simultaneously along the blade chord if a disturbance arrives at the leading edge or the trailing edge of the blade. Thus the unsteady profile pressure distribution is nearly independent of the convective wake propagation within the blade passage. A phase shift of the reaction of the blade to the disturbance on the pressure and suction side is observed. In addition clocking investigations were carried out to distinguish between the different periodic influences from the surrounding blade rows. For this reason the unsteady profile pressure distribution on rotor 3 was measured, while stator 1–4 were separately traversed stepwise in the circumferential direction. Thus the wake and potential effects of the up- and downstream blade rows on the unsteady profile pressure could clearly be distinguished and quantified.

This paper investigates the propagation of pressure disturbances due to potential-flow interaction and viscous-wake interaction from upstream blade rows in axial-turbine-blade rotor cascades. Results are obtained by modeling the effects of the stator viscous wake and the stator potential-flow field on the rotor flow field. A computer program is used to calculate the unsteady flow fields. The amplitudes for the two types of interaction are based on a review of available experimental and computational data. We study the propagation of the isolated potential-flow interaction (no viscous-wake interaction), of the isolated viscous wake interaction (no potential-flow interaction), and of the combination of interactions. The discussion uses as example a lightly-loaded cascade for a stator-to-rotor-pitch ratio R = 2. We examine the relative magnitudes of the unsteady forces for two different stator-exit angles. We also explain the expected differences when the stator-to-rotor pitch ratio is decreased (to R = 1) and increased (to R = 4). We offer new and previously unpublished explanations of the mechanisms of generation of unsteady forces on the blades. The potential flow field of the rotor cuts into the potential flow field of the stator. After the potential-flow disturbance from the stator is cut into a rotor cascade, it propagates into the relative flow field of the rotor passage as a potential-flow disturbance. The potential flow field of the rotor near the leading edge and the leading edge itself cut into the wake and generate two counter-rotating vortical patterns flanking the wake centerline in the passage. The vortical pattern upstream of the wake centerline generates an increase in the local pressure (and in the forces acting on the sides of the passage). The vortical pattern downstream of the wake centerline generates a decrease in the local pressure (and in the forces acting on the sides of the passage). The resulting unsteady forces on the blades are generated by the combined (additive) interaction of the two disturbances.

Axial compressors have inherently unsteady flow fields because of relative motion between rotor and stator airfoils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead to progressively more complex wake/wake and wake/airfoil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. In addition, as the Mach number increases the interaction between blade rows can be intensified due to potential effects.It has been shown, both experimentally and computationally, that airfoil clocking can be used to improve the efficiency and reduce the unsteadiness in multiple-stage axial turbomachines with equal blade counts in alternate blade rows. While previous investigations have provided an improved understanding of the physics associated with airfoil clocking, more research is needed to determine if airfoil clocking is viable for use in modern gas-turbine compressors. This paper presents the results of a combined experimental/computational research effort to study the physics of airfoil clocking in a high-speed axial compressor. Computational simulations have been performed for eight different clocking positions of the stator airfoils in a 1-1/2 stage high-speed compressor. To accurately model the experimental compressor, full-annulus simulations were conducted using 34 IGV, 35 rotor and 34 stator airfoils. It is common practice to modify blade counts to reduce the computational work required to perform turbomachinery simulations, and this approximation has been made in all computational clocking studies performed to date. A simulation was also performed in the present study with 1 inlet guide vane, 1 rotor airfoil, and 1 stator airfoil to model blade rows with 34 airfoils each in order to examine the effects of this approximation. Time-averaged and unsteady data (including performance and boundary layer quantities) were examined. The predicted results indicate that simulating the full annulus gives better qualitative agreement with the experimental data, as well as more accurately modeling the interaction between adjacent blade rows.Copyright © 1999 by ASME

Commonly, in the flutter analysis of a turbomachine blade row the blade row studied for stability is treated as isolated from its neighbouring blade rows. This approach neglects the effects caused by the reflection of upstream and downstream propagating waves at the neighbouring blade rows. These reflected waves are the source of additional unsteady forces at the blade surface which may have significant effects on the aeroelastic stability of the blade row. To take this influence in the flutter analysis of a blade row into account a coupled unsteady simulation of all rows considered has to be performed. The usual approach to solve for the unsteady flow with a non-linear time-domain solver is expen-sive in terms of computational resources. Especially if in a multi-row configuration the blade counts of the blade rows considered do not allow restricting the simulation to a few passages in each row. To solve for the unsteady flow field, in this paper an alternative ap-proach based on the nonlinear frequency domain Harmonic Balance method is presented. In the frequency-domain the unsteady flow field can be approximated with a small number of relevant frequencies and the circumferential and temporal periodicity of the problem reduces the computational domain to a single passage per blade row only. The efficiency of this approach for flutter analysis in a multi-row configuration is demonstrated by applying it to an embedded rotor blade row.

A time domain numerical approach is carried out to enhance the understanding of three dimensional blade row aeroelastic characteristics under the parallel computation. The vibration energy of unsteady aerodynamic force on the entire blade row is investigated using numerical solution of 3-D Navier-Stokes equations, coupled with structure finite element models for the blades to identify modal shapes and the structural deformations simultaneously. Interactions between fluid and structure are dealt with in a coupled manner, based on the interface information exchange until convergence in each time step. With this approach good agreement between the numerical results and the experimental data is observed. The flutter mechanism is analyzed according to deformation of the blades. The effect of inter-blade phase angle (IBPA) is included in the analysis by releasing the hypothesis of constant phase angle between adjacent blades in the traveling wave model. The results illustrate fully three dimensional unsteady nonlinear behaviors, such as limit-cycle oscillation. It is shown that all blades flutter at the same mode and frequency, but not at the same amplitude and IBPA. The analysis of the influence of different tip clearance gaps on the flutter characteristics of the blade row is also performed.

With alternative energy becoming more prevalent the acoustic impact of machinery used to generate the energy is of interest. The noise produced from wind turbines is an important factor in the design as it can affect nearby communities. A numerical tool has been developed to predict the unsteady thrust and directly radiated noise from a single or multi-blade row turbomachine, which can easily be applied to a wind turbine. The tool, called TONBROD, can predict blade rate and turbulence ingestion noise, however only the latter is of concern for this work. An asymptotic approach is used to quickly and efficiently predict the unsteady force on each blade from the chopping of incoming turbulence (e.g. turbulence ingestion noise). This force is then used to estimate the radiated noise. A user can prescribe the incoming turbulence intensity (circumferentially and radially varying) and integral length scale (circumferentially uniform but radially varying) that is then modified by the upstream blade row and advected to the downstream blade row through semi-empirical formulations. A prediction of the resulting unsteady force and noise is then made for either blade row. The asymptotic theory is briefly discussed and then the prediction of radiated noise for both homogeneous and inhomogeneous turbulence is compared to experimental data. It is shown that the method provides good results.

Industrial steam turbine applications require a high flexibility in terms of aerodynamically as well as mechanically operating conditions. Mechanical drives run at variable rotor speeds and often face high backpressure levels, which is a particularly challenging aspect for the last-stage moving blade (LSMB) row of a low-pressure (LP) steam turbine. As speed synchronous blade resonances cannot be excluded over the entire operating speed range, the LSMB needs to be designed resonance proof from viewpoint of dynamics and mechanical strength. The subsequent paper describes a new developed LP stage group for variable speed applications, which is available as fully scaled blade family with distinct exhaust area and rotational speed limit reaching from conventional 3000rpm up to high speed utilities for special purposes. It consists of two standard stages, which can be operated at off resonance as well as resonance conditions. For that reason frictional elements were implemented in both moving blade rows. They are loosely assembled into pockets, which are placed on the pressure as well as suction side of each airfoil. Basically, this feature was already introduced for certain Siemens LP blades, see [1], [2], [3] and [4]. However, the recent development on this field utilizes several design changes for the benefit of robustness and reliability. The present paper focuses on the non-linear dynamic behavior of the friction damped, coupled blade rows and outlines the underlying design method as well as calculation process.

Current methods for designing compressor blades in axial turbomachines assume that the flow through each blade row is steady. However, interactions associated with the relative motion of neighbouring blade rows are known to produce a disturbance field with both random and periodic components. Despite a growing amount of research into the influence of these disturbances on the downstream row in a rotor-stator or stator-rotor blade row pair, these effects are still not generally accounted for at the design stage. Recent advances in Low Pressure Turbine blade design have shown that incorporating unsteady effects can lead to increases in blade loading beyond the loading limits inferred from steady flow calculations. The current experimental work investigates the unsteady flow behaviour in the neighbourhood of the outlet stator in a 1.5 stage axial flow compressor using thermal anemometry. The aim is to provide a base for more accurate unsteady modelling, and facilitate the development of compressor blade designs which gain maximum benefit from unsteady effects. High-speed data acquisition with synchronised sampling was used to acquire data ensembles for a specific set of rotor wakes, and estimate the periodic and random components of the stator inflow disturbance field. The stator inflow disturbance flow field was altered by clocking of the inlet guide vane row relative to the stator row, and by changing the rotor-stator axial blade row spacing. The interaction of inlet guide vane and rotor wakes was examined using hot-wire measurements downstream of the rotor row. The interaction process was shown to restrict the relative motion of rotor wake fluid and produce local accumulations of low energy fluid on the suction side of the inlet guide vane wakes. Significant circumferential variations in both time-mean velocity and the periodic disturbance component were observed. Clocking of the downstream stator row relative to the inlet guide vanes altered the mid-span stator blade boundary layer behaviour. Hot-wire measurements performed downstream of the stator were used to evaluate the influence of blade row clocking on the stator mid-span viscous losses. The magnitude of periodic fluctuations in ensemble-average stator wake thickness was significantly influenced by IGV wake-rotor wake interaction effects. The changes in time-mean stator losses were marginal. The periodically unsteady laminar to turbulent transition of the stator blade boundary layer was examined using a hot-film surface array mounted on both the suction and pressure surfaces. Observations were made for stator blade loading or incidence cases near stall, design and maximum flow, and for a range of relative axial and circumferential blade row positions. Ensemble average plots of turbulent intermittency and relaxation factor (extent of calmed flow following the passage of a turbulent spot) are presented for a range of inflow disturbance cases. These show the strength of periodic wake-induced transition phenomena to be significantly influenced by incidence, clocking and blade row spacing effects. The periodic, wake-induced, transition in separation bubbles was also altered by changes in blade row spacing. Significant differences between suction and pressure surface transition behaviour were observed, particularly with regard to the strength and extent of calming. Subsequent collaborative work (not reported within) evaluated the quasi-steady application of conventional transition correlation to predict unsteady transition onset on the blading of an embedded axial compressor stage. The viscous/inviscid interaction code MISES was used to calculate the blade surface pressure distributions and boundary layer development. Predictions of the temporal variation in transition onset based on the measured temporal variation of inflow turbulence were compared with the transition onset observations from the compressor stator. Computations for both natural and bypass transition modes indicated that the natural transition mode predicted by a modified e\\(^n\\) method tended to dominate on the compressor blades. The success of the MISES transition onset predictions provided strong circumstantial evidence for the importance of natural transition mechanisms in strongly decelerating flow and provided the impetus further experimental investigation. Transitional flow data from the surface film gauges were also analysed using wavelet techniques. The primary use of the wavelet analysis was to facilitate identification of transient instability phenomena in the complex periodic transitional flows present in the stator blade boundary layer. Wavelet analysis and high-pass filtering techniques revealed significant wave packet activity in the unstable laminar flow regions. An algorithm was developed to identify instability waves within the Tollmien-Schlichting (T-S) frequency range. This was combined with a turbulent intermittency detection routine to produce space~time diagrams showing the probability of instability wave occurrence prior to regions of turbulent flow. The implications for transition prediction in decelerating flow regions on axial turbomachine blades are discussed.

This paper describes an experimental investigation of rotor–stator interaction in a centrifugal pump with several vaned diffusers. Steady and unsteady diffuser vane pressure measurements were made for a two–dimensional test impeller. Unsteady impeller blade pressure measurements were made for a second two–dimensional impeller with blade number and blade geometry identical to the two–dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted for different flow coefficients and different radial gaps between the impeller blade trailing edge and the diffuser vane leading edge (5% and 8% of the impeller discharge radius). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. The largest pressure fluctuations on the diffuser vanes were observed to occur on the suction side of the vane near the vane leading edge, whereas on the impeller blades the largest fluctuations were observed to occur at the blade trailing edge. However, the dependence of the fluctuations on the flow coefficient was found to be different for the diffuser vanes and the impeller blades; on the vane suction side, the fluctuations were largest for the maximum flow coefficient and decreased with decreasing flow coefficient, whereas at the blade trailing edge, the fluctuations were smallest for the maximum flow coefficient and increased with decreasing flow coefficient. Increasing the number of the diffuser vanes resulted in a significant decrease of the impeller blade pressure fluctuations. The resulting lift on the diffuser vanes was computed from the vane pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

On a blade row in turbomachinery, the unsteady force comes out owing to the following two main sources, i.e. the wake effect and the circulation effect. This paper is planned in order to make clear theoretically the wake effect on the blade. When a cylinder is moving near a stationary blade, the wake sweeps downstream through the blade. The velocity profile in the wake shed by the moving cylinder is approximated by the stationary counterpart. Calculations are done for various values of the velocity of the cylinder and axial spacing, while taking account of wake varying with distance from the cylinder. The cylinder is represented by a doublet traveling in a free-stream in order to predict the unsteady force on the blade due to the theoretical cylinder-thickness effect. The computed unsteady force on the blade due to the wake effect and the cylinder-thickness effect is added and compared with the experimental one. The reason why discrepancies arise is also considered.

Flexible operation at a wide range of operating conditions combined with very high efficiency is a fundamental customer requirement for industrial steam turbines today. The blading of turbines has to be designed with those objectives in mind. Especially for intermediate pressure (IP) blades operating at fixed and variable speed there is high potential for improvement with respect to efficiency. Nonetheless these blades have to satisfy rules of reliability and mechanical integrity, in many cases American Petroleum Institute (API) Standard 612 requirements. In this paper the dynamic behavior of IP blades with an improved and efficient 3D design is investigated numerically and verified by experiments. Shrouded blades are common for IP blade design to ensure a low dynamic stress level. These blades are supposed to form a closed coupling contact between adjacent blades to grant higher stiffness of the blade row and additional contact damping. Natural frequencies and mode shapes mainly remain on stiffness and mass distribution. Contact pressure at assembly state is generated by geometric interferences of the blades. Operational centrifugal forces and untwisting of blades tend to reduce the shroud contact pressure. One focus of this study is the research of different blade shroud contact conditions after the assembly process and the influence on closed shroud conditions during operation. A highly sophisticated numerical 3D model was set up to simulate and predict contact status and dynamic behavior of the blade row. Forced vibrations were imposed on the blade rows in a spin bunker to measure speed dependent frequencies and the effect of reduced shroud forces. Three-dimensional blades as well as cylindrical blades were tested on the same rotor to compare efficiency improved blades with long term industrial proven design. Results of the experiment were in good agreement with results of numerical calculations. A 10 MW steam turbine with one controlled extraction was used for validation. The turbine was operated within and beyond standard operational limits. Amongst others, the predicted contact and dynamic behavior were verified based on centrifugal forces, steam forces and real temperature distributions. Results confirmed that closed shroud contact was maintained at all operating points for properly assembled blade rows.

The film cooling effectiveness on the surface of a high pressure turbine blade is measured using the Pressure Sensitive Paint (PSP). Four rows of fan-shaped, laid-back compound angled cooling holes are distributed on the pressure side while two such rows are provided on the suction side of the blade. The coolant is only injected to either the pressure side or suction side of the blade at five average blowing ratios from 0.4 to 1.5. Presence of wake due to upstream vanes is simulated by placing a periodic set of rods upstream of the test blade. The wake rods can be clocked by changing their stationary positions to simulate a progressing wake. Effect of wake is recorded at four phase locations with equal intervals along the pitch-wise direction. The free stream Reynolds number, based on the axial chord length and the exit velocity, is 750,000 and the inlet and the exit Mach numbers are 0.27 and 0.44, respectively, resulting in a blade pressure ratio of 1.14. Results reveal that the tip leakage vortices and endwall vortices sweep the coolant film on the suction side to the midspan region. The fan-shaped, laid-back compound angled holes produce good coolant film coverage on the suction side except for those regions affected by the secondary vortices. Due to the concave surface, the coolant trace is short and effectiveness level is low on the pressure surface. However, the pressure side acquires relatively uniform film coverage with the design of multiple rows of cooling holes. The presence of stationary upstream wake results in lower film cooling effectiveness on the blade surface. Variation of blowing ratio from 0.4 to 1.5 shows steady increase in effectiveness on the pressure side or the suction side for a given wake rod phases locations. The compound angle shaped holes outperform the compound angle cylindrical holes by the elevated film cooling effectiveness particularly at higher blowing ratios.

In axial turbine, the tip clearance flow occurring in rotor blade rows is responsible for about one-third of the aerodynamic losses in the blade row and in many cases is the limiting factor for the blade lifetime. The tip leakage vortex forms when the leaking fluid crosses the gap between the rotor blade tip and the casing from pressure to suction side and rolls up into a vortex on the blade suction side. The flow through the tip gap is both of high velocity and of high temperature, with the heat transfer to the blade from the hot fluid being very high in the blade tip area. In order to avoid blade tip burnout and a failure of the machine, blade tip cooling is commonly used. This paper presents the physical study and an improved design of a recessed blade tip for a highly loaded axial turbine rotor blade with application in high pressure axial turbines in aero engine or power generation. With use of three-dimensional computational fluid dynamics (CFD), the flow field near the tip of the blade for different shapes of the recess cavities is investigated. Through better understanding and control of cavity vortical structures, an improved design is presented and its differences from the generic flat tip blade are highlighted. It is observed that by an appropriate profiling of the recess shape, the total tip heat transfer Nusselt number was significantly reduced, being 15% lower than the flat tip and 7% lower than the base line recess shape. Experimental results also showed an overall improvement of 0.2% in the one-and-a-half-stage turbine total efficiency with the improved recess design compared to the flat tip case. The CFD analysis conducted on single rotor row configurations predicted a 0.38% total efficiency increase for the rotor equipped with the new recess design compared to the flat tip rotor.

This two-part paper presents experimental investigations of unsteady aerodynamic blade row interactions in the first stage of the four-stage Low-Speed Research Compressor of Dresden. Both the unsteady boundary layer development and the unsteady pressure distribution of the stator blades are investigated for several operating points. The measurements were carried out on pressure side and suction side at midspan. In part I of the paper the investigations of the unsteady boundary layer behaviour are presented. The experiments were carried out using surface-mounted hot-film sensors. Additional information on the time-resolved flow between the blade rows were obtained with a hot-wire probe. The unsteady boundary layer development is strongly influenced by the incoming wakes. Within the predominantly laminar boundary layer in the front part of the blade a clear response of the boundary layer to the velocity and turbulence structure of the incoming wakes can be observed. The time-resolved structure of the boundary layer for several operating points of the compressor is analyzed in detail. The topic “calmed regions”, which can be coupled to the wake passing, is discussed. As a result an improved description of the complex boundary layer structure is given.