Forced Response Excitation due to Stagger Angle Variation in a Multi-Stage Axial Turbine

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1 International Journal of Gas Turbine, Propulsion and Power Systems October 217, Volume 9, Number 3 Forced Response Excitation due to Stagger Angle Variation in a Multi-Stage Axial Turbine Thomas Hauptmann 1, Jens Aschenbruck 2 and Joerg R. Seume 1 1 Institute of Turbomachinery and Fluid Dynamics, Leibniz Universität Hannover Appelstr. 9, 3167 Hannover, GERMANY 2 Formerly at the Institute of Turbomachinery and Fluid Dynamics, Leibniz Universität Hannover Appelstr. 9, 3167 Hannover, GERMANY ABSTRACT Blade repair is often economically more attractive than the replacement of damaged blades by spare parts. Such regenerated turbine blades, however, can introduce non-uniform flow conditions which lead to additional forced response excitation of blades. A forced response excitation due to a typical geometric variation, introduced through current repair methods applied in an upstream stage, is investigated using a fluid-structure interaction (FSI) model previously experimentally validated in a five-stage axial turbine. In this study, geometrical variations are applied to the stator vane of the fourth stage of the five-stage axial turbine. The reference configuration, without variations, is compared with experimental data. The focus of the analysis is the determination of the aerodynamic excitation in a multi-stage setup. For both configurations, with and without variations, the stage loading coefficient of the last turbine stage remains constant. In contrast, the aerodynamic work acting on the last rotor blade increases by a factor of 4 dependent on the operating point. The vibration amplitude of the downstream blade is determined using a unidirectional fluid-structure interaction approach. The impact of the variations on the vibration amplitude decreases by a factor of 1 with increasing number of blade rows between the modified vane row and the analyzed blade row. However, the geometric variations induce vibration amplitudes 4 times higher than the reference case. Based on the methodology used, a linear correlation between the excitation of the blade by the aerodynamic work and the vibration amplitude is shown to exist. NOMENCLATURE c absolute velocity c p pressure coefficient D damping ratio f frequency F force h enthalpy i inner ṁ mass flow rate n normal vector to blade surface o outer p pressure p pressure fluctuation P power r radius rpm rotor speed T temperature T period of time u circumferential velocity u W aero α γ λ ψ mode displacement aerodynamic work yaw angle pitch angle stagger angle stage loading coefficient Indices dyn dynamic in turbine inlet local local max maximum out turbine outlet stat static tot total u circumferential 1 stage inlet 2 stage outlet Abbreviations BPF blade passing frequency CFD computational fluid dynamics CRC collaborative research center EO engine order FSI fluid-structure interaction LE leading edge MP measuring plane OP operating point PS pressure side SS suction side T E trailing edge INTRODUCTION The overhaul process of jet engines, also referred to as regeneration, represents 8% of the operating costs of an airplane [1] and is therefore of great interest. The main cost factor at the overhaul is caused by the blades, which are responsible for approximately 5% of the cost. This cost is mainly incurred by the replacement of worn blades from the high-pressure turbine, because they are one of the most highly loaded parts and therefore subject to substantial wear. For this reason the collaborative research center (CRC) 871 Regeneration of Complex Capital Good aims to develop the scientific basis for the overhaul of jet engines. The main objective is to save as many of the worn components as possible [2]. Manuscript Received on January 3, 217 Review Completed on August 9, 217 Copyright 217 Gas Turbine Society of Japan 1

2 One approach in the CRC 871 is to investigate and reduce the aerodynamic excitation which occurs due to regeneration-induced variances. This excitation can be introduced by geometrical variations in the upstream blade rows. Hence, the main objective of the present study is to determine the effect of regeneration-induced variances in the blading on the excitation of the blade row one stage further downstream. Additionally, the focus is set on estimating the vibration amplitude due to geometric variations using a forced response method. Several numerical studies exist in the literature [3 8] investigating the influence of geometric variations on the aerodynamic force in a single stage turbine. All these studies have shown that the influence of several kinds of geometric variation in an upstream stator vane row is significant. These results were verified by experimental investigations in [7, 9]. The aerodynamic excitation mechanisms occuring in a high pressure turbine stage were numerically investigated in [1]. It was shown that the potential excitation mechanism in the investigated turbine stage was dominant in comparison with the wake excitation effect. In [11] geometrical variations on the stator vanes one stage further upstream of the excited blade row was investigated. It was shown that a stagger angle variation has the highest impact in the vibration analysis by modifying the vane geometry of the fourth stage of a five-stage axial turbine even though it is one stage further downstream. To determine the aerodynamic excitation in turbomachinery, a unidirectional fluid-structure interaction (FSI) is used because the required computational effort is lower compared to bidirectional FSI. Additionally, the unidirectional FSI assumes that the vibrations are small, and therefore the reaction on the fluid is negligible. This is only valid for a forced response analysis. For using this approach unsteady CFD calculations are conducted in order to determine the unsteady aerodynamic loads acting on the structure. Subsequently, the aerodynamic loads are applied to a structural model in a finite element analysis. This analysis is conducted using damping values determined from tip-timing measurements. OUTLINE The first part of this paper presents the five-stage axial air turbine and the geometric variation implemented into the turbine blading. The geometric variation is typical for those introduced through current repair methods [12]. The influence of this variation on the aerodynamics downstream of the varied vane is numerically analyzed using CFD. The reference configuration is also compared with experimental data. The focus is on the impact of the variation one stage downstream, in order to determine the influence of the variation on the wake behavior, as the wake excitation is one of the main excitation sources [1]. Finally, forced response analyses are conducted with the varied stator vanes. The analyzed blade row is not adjacent to the varied vane row. The vibration amplitude is numerically predicted using a unidirectional fluid-structure approach validated experimentally in [9]. The results are compared with the reference case, and additionally with a variation in the vane row adjacent to the excited blade. TEST FACILITY A multi-stage axial turbine test facility in the Institute of Turbomachinery and Fluid-Dynamics is used for the numerical and experimental investigations in this study. The modular casing of the turbine enable the use of several turbine configurations using various inner casing contours and blade designs. In this study, a five-stage axial turbine configuration is used to investigate the influence of the regeneration-induced variances on the aerodynamic and aeroelastic performance (see Fig.1). The single solid rotor consists of 3 axial fir tree grooves, in which the rotor blades are mounted. Therefore, the rotor blade count of the fifth stage is identical to stages one to four. Additionally, all five vane rows have the same vane count of 29. The stator vanes are mounted in the inner casing of the turbine. The fifth stage of MP2_1 MP2_1 Modified vane row St. 1 3 MP2_51 MP2_41 St. 4 MP2_41 Tip-Timing MP2_52 St. 5 MP2_51 Tip-Timing Fig.1: Five-stage axial turbine MP3_2 MP2_52 Diffuser MP3_2 Table 1: Operating points of the five-stage axial turbine Operating Points OP1 OP2 OP3 Mass flow rate ṁ in kg/s Rotor speed in n rpm Pressure ratio p in /p out Inlet temperature T in in K Outlet temperature T out in K the axial turbine was specially designed for the investigation of the aeroelastic behavior. Further information, including the design process are presented in [8]. In contrast to the investigations in [3], [5], and [9] geometric variances were applied on the stator vanes one stage upstream of the excited blade row. Therefore, the stator vanes of the fourth stage were modified with a regeneration-specific geometric variation. This variation was implemented in the fourth stage of the turbine on every second stator vane, with reference vanes in between. In the present study a stagger angle variation of λ = 1.5 deg is implemented in the fourth stage and compared with the reference case where all vanes are identical. The alternating distribution of the geometric variation is typical after the regeneration of turbine blades because the mistuning results in a positive effect of the flutter stability ([13] and [14]). This study is performed for two part-loaded operating points (OP1 and OP2) and the design point (OP3) listed in Tab.1. At these operating points only one crossing exist with the eigenfrequencies and the blade passing frequency at OP1. At OP2 and OP3, no resonance case exists with the BPF. The first and the second eigenfrequencies can only be excited by the 8 th and the 15 th engine order as depicted in the Campbell Diagram (Fig. 2). These engine orders normally do not occur. However, the 15 th engine order can appear as a result of an alternating vane pattern of reference and varied blades. Such a distribution can lead to an excitation of the second eigenfrequency by the 15 th engine order. 2

3 JGPP Vol. 9, No. 3 OP1. m=3.3 kg/s π= 1.33 OP3. m=8.5 kg/s π= 2.74 OP2. m=4.3 kg/s π= 1.58 Frequency in Hz mm EO 3 EO th: 3954 Hz 3rd: 2952 Hz nd: 1841 Hz EO st: 967 Hz EO 8 5 EO Rotational speed in rpm 1st Mode 2nd Mode 3rd Mode Fig.3: Pneumatic 5-hole probe with probe-head diameter of 3 mm are of particular interest because they can be excited by the blade passing frequency and lower engine orders at the relevant operating points. The tip-timing probes are therefore placed at this axial position to determine the highest blade deflection and to get accurate data for the eigenfrequency. The circumferential probe positions are equal to the positions in [9]. In this case, eight probes are circumferentially distributed using an algorithm by AGILIS to ensure that the eigenfrequencies and engine orders can be captured accurately. This probe location algorithm is based on the Campbell-Diagram, and is optimized for the measurement of synchronous blade vibrations. In this study, the focus is on the investigation of synchronous vibrations. Therefore, a least-square model fitting (LSMF) analysis is used which is recommended for these kind of vibrations. This method is briefly described in [18]. The LSMF analysis determines vibration frequency, phase, and deflection of each rotor blade. 4th Mode Fig.2: Campbell-Diagram and eigenmodes of rotor blade 5 [9] EXPERIMENATL SETUP For the investigation of the excitation and the vibration behavior of the fifth rotor blade row, detailed instrumentation is selected to collect detailed flow data. In Figure 1, the main measurement planes used for the aerodynamic measurements are indicated. In MP2 1, radial probe traverses using 5-hole vector-probes are conducted to capture the inlet boundary conditions. The outlet boundary conditions are captured by rotatable total pressure and total temperature rake-probes in MP3 2. Five rake-probes are equally spaced in circumferential direction and implemented with combined kielhead and 5-hole-probe rakes. In addition to these measurements, radial and circumferential 5-hole-probe traverses were conducted in MP2 51 and MP2 52 in front and behind the rotor blade row 5, in order to capture the aerodynamic flow field exciting the rotor blade row. The mass flow rate is determined by a Venturi nozzle located 9 m upstream of the turbine inlet. The probe traverses are conducted with pneumatic 5-hole-probes with a probe head diameter of 3 mm (see Fig. 3). The 5-hole probes are calibrated for a range yaw ( 24 < α < 24 ) and pitch ( 3 < γ < 3 ) angles and for Mach numbers between.1 < Ma <.9. The thermocouple is located in a kiel-head above the probe head for measuring the temperature. From measuring pressure and temperature with the 5-hole-probe, velocity, the Mach number, and flow angles can be calculated. These values are then used to determine the excitation of the rotor blade row. As described in [15], [16], and [17], the total pressure, static pressure, and flow angles can be calculated from the measured pressures and the calibration coefficients of the probe. For the detection of the blade vibration, a commercial optical tiptiming system by AGILIS is used. The vibration amplitudes and the eigenfrequencies are determined by eight optical probes circumferentially distributed at the same axial position at the trailing edge of the fifth rotor blade row. All probes measure the time of arrival (TOA) of all blades on each revolution. The arrival times are then converted to deflections, as the rotational velocity and the radius at the measurement location is known. A detailed description is given in [9]. The first and second eigenmode of the fifth rotor blade have their highest mode displacement at the trailing edge. These eigenmodes AERODYNAMIC ANALYSIS In this section, the impact of the stagger angle variation on the aerodynamic behavior is investigated. These results are necessary to show the influence on the aerodynamic excitation of a geometric vane variation on the adjacent blade row and on the blade row one stage downstream. The results one stage downstream are of particular interest, because they indicate the impact of the flow on the vibration behavior of the fifth rotor blade row. A dependence on such typical variations on the aerodynamic behavior is shown and compared to the reference case. Numerical Setup The numerical investigations of the aerodynamic behavior were conducted in detail for the reference case and the stagger angle variation in the fourth stator vane row. The numerical model used in this study is depicted in Fig. 4. The inlet conditions for the CFD simulations were determined by steady CFD simulations of the complete five stage air turbine. The velocity direction and the temperature were derived from the preceding simulations according to the investigated operating points. Afterwards, they were used as inlet boundary condition for stage four with a specified mass flow rate. The outlet boundary condition was set with a specified static pressure at diffuser outlet. A medium turbulence intensity of 5% was used at the inlet of stage 4. The numerical model consists of two passages of the fourth and the fifth stage and one pitch of the diffuser. Instead of 29 stator vanes and 3 rotor blades, the simulations were conducted with 3 vanes and 3 blades. This ensures an equal pitch of the domains for the unsteady simulations. The vane size was not modified. The scaling of 29 vanes to 3 vanes has a negligible effect on the aerodynamics 3

4 St. 4 vane St. 4 blade sliding mesh St. 5 vane sliding mesh St. 5 blade flow direction sliding mesh Fig.4: Numerical model Span height Exp Reference OP2 CFD Reference OP stage loading coefficient ψ 1.6 and turbine performance, as shown in [19]. For the current investigation, the reference and modified stator vanes of the fourth stage were modeled as an alternating distribution. Rotational periodicity was specified at the circumferential boundaries of the 24 degree segment. In the steady simulations, the rotor-stator interfaces were defined as a frozen rotor interface. This interface is selected to ensure that the wake behavior is propagated through the stages. The interface between the rotor blade row 5 and the diffuser was set to a mixing plane interface in order to reduce computational effort. For the unsteady simulations, the frozen rotor interfaces were replaced by a transient rotor-stator interface (sliding mesh). The numerical model was discretized with million nodes in total. All domains were meshed solely with hexahedral elements. In particular, the stator and rotor domains have a high mesh resolution to minimize discretization errors and to ensure the propagation of the wake through all stages. This high resolution was necessary to obtain the accurate excitation on the blade surface for the forced response analysis. It is important that the numerical error caused by the mesh resolution is negligible. A mesh study of the numerical domain has been performed already in previous studies of this project to confirm this (see [12] and [11]). All simulations were performed with the CFD software ANSYS CFX 15. using the SST turbulence model. In the unsteady computations, one half rotation of the rotor was simulated for stabilization with 32 time steps per pitch. Subsequently, another half rotation with 64 time steps per pitch was conducted. These time steps were used for the determination of the unsteady surface pressures. Steady Aerodynamic Results This section presents the conducted measurements of the reference configuration and the comparison with the predicted flow field by the numerical model. Additionally, the simulated case of the stagger angle variation in the fourth stage is analyzed for comparison. The experimental measurements depicted in the following sections are indicated with error bars. All error bars are indicated with a 95% confidence interval of the measured values. These error bars include the error propagation due to accuracy of the measurement instrumentation, repeatability and calibration. In a first step the aerodynamic performance of the fifth stage is evaluated with the stage loading coefficient ψ Fig.5: Radial distribution of the stage loading at OP2 h tot = Ṗ 2 m = u dc u = u (c u2 c u1 ) (1) 1 ψ = h tot u 2 (2) The index 1 denotes the measuring plane between stator 5 and rotor 5 (MP2 51) and the index 2 the plane behind the rotor (MP2 52). By determining the velocity in circumferential direction of the probe measurements, the stage loading coefficient of the fifth rotor blade can be calculated. Figure 5 shows the absolute value of the stage loading from hub to shroud for the reference configuration at OP2. It shows a good agreement between the simulations and the experiments over the complete channel height. The stage loading coefficient decreases from hub to shroud and reaches its maximum at 1% channel height. The averaged values of the stage loading coefficient at all operating points are presented in Fig. 6. The stage loading coefficient ψ at the investigated operating points is almost identical for both configurations. Therefore, the angular momentum of the flow in the circumferential direction, averaged over the span height, upstream and downstream of the fifth rotor blade row is almost identical for the configurations with and without modifications. For the aeroelastic investigation of the fifth rotor blade row, the inflow conditions must be determined in order to extract the wake excitation source. For this purpose, the aerodynamic flow field is analyzed at different axial positions. The influence of the stagger angle variation on the aerodynamics downstream of the varied vane is compared to the reference case, in order to estimate the influence of the wake. Beside the potential effect, the wakes of the vanes are the main excitation mechanism of the rotor blades. Accordingly, the wake behavior is of main interest in the analysis of the aerodynamic behavior of the flow. In MP2 51, the simulated data of the reference configuration are compared with experimental data by circumferential probe traverses at OP2. First, the pressure distribution of vane row 5 has to be determined 4

5 stage loading coefficient ψ CFD Reference CFD Multi Stage Alternating Vanes OP1 OP2 OP3 Operating Points Fig.6: Averaged stage loading coefficient for all operating points p tot /p tot,in.56,56.555,555.55,55.545,545.54,54 6.5%.535, ,2 1,1.4,4 1,2.6,6 1,3.8,8 1,4 1. 1, ,2 1, ,4 1, ,6 1, ,8 1, Pitch CFD Reference.44% CFD Multi-Stage Alternating Vanes Fig.8: Circumferential total pressure distribution for operating point 3 (OP3) in MP2 41 at 8% span height % span heigth OP2 CFD Experiment.754, ,752.75,75 normalized Pressure p tot /p tot,in.748, ,746.7%.744,744 6%.742,742., 1.2,2 1,1.4,4 1,2.6,6 1,3.8,8 1,4 1. 1, 1, ,2 1, ,4 1, ,6 1, ,8 1,9 2. 2,2 Pitch.93 CFD Reference CFD Multi-Stage Alternating Vanes normalized chord length Fig.9: Circumferential total pressure distribution for operating point 2 (OP2) in MP2 41 at 8% span height Fig.7: Pressure distribution at midspan of vane 5 to make sure that the predicted inflow conditions are in accordance with the experimental data. Figure 7 shows the comparison of the pressure distribution throughout the chord length between the experimental data and CFD simulations at 5% span height for OP2. The experimental and simulated data are in a good agreement around the chord length. Thus, the inflow condition to the fifth rotor blade are predicted well by CFD. To analyze the wake behavior, the total pressure distribution is investigated behind stator vane row 4 and behind stator vane row 5 at 8% span. The investigation in these planes also indicates the propagation of the vane wake through the blade rows. The simulated total pressure distribution is calculated from the time-averaged data of the unsteady CFD simulations. The relative total pressure p tot /p tot,in downstream of the stator vane row 4 and 5 is shown as a function of the normalized pitch in Fig. 8 to Fig. 11. The stagger angle variation causes a shift by 6.5% of the wake position in the circumferential direction directly behind the modified vane row in MP2 41 at OP3 (see Fig.8). Additionally, the alternating stagger angle variation causes a.44% higher deficit in relative total pressure. The large difference in total pressure in the mid-passage between both configurations is caused by the change of the stagger angle of every second vane. As already shown in [12], a stagger angle variation causes a shift of the wake in circumferential direction, and also causes a reduction of total pressure. Because of the stagger angle variation more losses are generated in the vane passage due to an earlier separation. Compared to OP3, the stagger angle variation causes a change of the wake deficit in relative total pressure of.7% in MP2 41 as shown in Fig. 9. However, the stagger angle variation also results in a shift of the wake position in the circumferential direction by 6%. Therefore, a significant disturbance of the flow field, especially in the wake region is detected downstream of the stagger angle variation at both operating points. Figure 1 illustrates the impact of the stagger angle variation on the flow field one stage downstream of the implemented variation in MP2 51 at OP3. One stage downstream, no remarkable shift of the wake position is detected. Apart from that, the alternating stagger angle variation in vane row 4 causes a reduction in the wake deficit by.2%. Total pressure in the passage area is reduced by.1% due to the influence of the stagger angle variation. Beside these differences, the total pressure distribution is similar to the reference case. In comparison with OP3 it can be seen in Fig. 11 that the stagger 5

6 p tot /p tot,in,47.47, ,46.46, , ,445.44,44..2,2,4.4.6,6.8, , , , , Pitch CFD Reference CFD Multi-Stage Alternating Vanes.2% Fig.1: Circumferential total pressure distribution for operating point 3 (OP3) in MP2 51 at 8% span height p tot p /p tot tot,in /p tot,in,79.79,78.78,77.77,77,76,76.76,75,74,75.75,73, %,72, %,71.72,72,2,4,6,8 1 1,2 1,4 1,6 1,8 2.71,71 Pitch..2,2,4.4.6,6.8, , , , , Pitch Exp Reference CFD Reference CFD Multi-Stage Alternating Vanes Exp Reference CFD Reference CFD Multi-Stage Alternating Vanes Fig.11: Circumferential total pressure distribution for operating point 2 (OP2) in MP2 51 at 8% span height angle variation also causes a negligible shift of the wake position in the circumferential direction one stage further downstream in MP2 51 at OP2. The variation causes a reduction of the wake deficit by.8%. However, at the same time.1% higher total pressure is detected in the passage area. This is the same difference as determined at OP3 in the passage area. In conclusion, a disturbance of the flow field compared to the reference case is detected for both operating points one stage further downstream as it was detected immediately downstream of the modified stator vane row 4. These changes in the flow field between reference case and the investigated geometric variation lead to small pressure perturbations on the rotor blade surface. The influence on the excitation of the rotor blade in blade row 5 is shown in the next section. In Fig. 11 experimental data of the measurements of the reference case is included and indicated with error bars. All error bars indicate a 95% confidence interval of the measured values. In the passage area, the predicted total pressure distribution is in accordance to the experimental data. The wake region is overestimated by the numerical prediction and shows a difference of.4% in the wake deficit. The reason for errors for an accurate prediction of the measured flow field, is the influence of the potential effect Pressure Coefficient c c p,16.16,14.14,12.12,1.1,8.8,6.6,4.4,2.2 Ref Var,. 18 TE PS LE SS TE Fig.12: 12Unsteady pressure amplitudes along the chord length for the blade passing frequency (3EO) at OP3-8% span 6height Phase in -6 by the pneumatic five-hole probe. In [15] the authors showed, by simulating -12 the flow field including the five-hole probe, that the wake -18 region is predicted accurately. TE LE TE PS SS Unsteady Aerodynamic Results The vibration of the rotor blades are caused by pressure fluctuations on the blade surface. These pressure fluctuations are influenced by the change of the flow field, which can be modified by geometric variations as described before. For this purpose, the unsteady pressure on the rotor blade is analyzed by the pressure coefficient cp = p p tot,mp51 p stat,mp51 = p p dyn,mp51 (3) In this equation p denotes the pressure fluctuation on the blade surface and p dyn,mp51 the dynamic pressure in MP2 51. The rotor blades are not instrumented with unsteady pressure sensors. Therefore, the analysis is conducted with simulated data. In Figure 12, the unsteady surface pressure amplitude occurring at the blade passing frequency (3EO) at OP3 is shown at 8% span height. The pressure fluctuation distribution close to the leading edge of the rotor blade differs only slightly on the pressure and suction side. Further downstream on the rotor blade, the pressure fluctuations in the reference case increases compared to the alternating stagger angle variation. In contrast to that, the pressure fluctuations for the case with stagger angle variation occurring at the half blade passing frequency (15EO) are significantly higher around the chord length compared to the reference (see Fig. 13). In the reference case only the 3EO (BPF) occurs. Thus, the pressure fluctuations of the reference case are negligible for the 15EO, as shown in Fig. 13. The stagger angle variation with the alternating vane pattern causes this additional frequency of the 15EO. This results in a higher excitation of the rotor blade in most of the chord length at 8% span height. AERODYNAMIC WORK In order to examine the excitation of the unsteady surface pressures on the eigenmodes of the rotor blade, the aerodynamic work W aero has to be determined. The calculation of the aerodynamic work in Eq.(4) and Eq.(5) is based on the method of [2] and [21]. The integral value of the aerodynamic work can be examined by W aero = T ( ro r i S p n u ds dr) dt max( u ) with the unsteady surface pressures p on the rotor blade, the normal blade surface vector n, and the local deflection u of the blade for a specific eigenmode as described in [1]. As the pahse shift between aerodynamic excitation and vibration behavior of the blade is (4) 6

7 Pressure Coefficient c c p,16.16,14.14,12.12,1.1,8.8,6.6,4.4,2.2 Ref Var,. 18 TE PS LE SS TE Fig.13: 12Unsteady pressure amplitudes along the chord length for one half of the blade passing frequency (15EO) at OP3-68% span height Phase in -6 unknown, the most critical case is assumed. This is the case when the -12 aerodynamic work is maximal. The maximum aerodynamic work is calculated with -18 TE LE TE PS T ( ro SS r W aero,max = i S p n u ds dr) dt max( u ). (5) In Figure 14 the maximum aerodynamic work on the blade is shown for the reference case and the alternating stagger angle variation implemented in stage 4 at all operating points. The aerodynamic work is normalized to the aerodynamic work of the reference case in OP1. At OP1, there is a crossing of the blade passing frequency at the first eigenfrequency. Thus, the maximum aerodynamic work is examined with the first eigenmode caused by the unsteady surface pressure at the BPF. At OP2 the aerodynamic work is also examined for the first eigenmode but with the unsteady surface pressure at the 15EO. At this operating point, a resonance case with the half blade passing frequency (15EO) exists. As shown in the Campbell-diagram (see Fig. 2), a crossing between the 15EO and the second eigenmode exists at OP3. Therefore, the aerodynamic work is determined with these conditions and compared to the other operating points. Figure 14 shows that the alternating stagger angle variation reduces the excitation of the blade passing frequency at OP1. The maximum aerodynamic work is 22% lower compared to the reference case. At the other operating points an increase of the maximum aerodynamic work for the alternating vanes is detected. The implemented variation in an alternating pattern in vane row 4 causes an increase by a factor of 3.5 at OP2, and by a factor of 4. at OP3 compared to the reference case. This is due to the increase in the unsteady surface pressures around the chord length shown in Fig. 13. The implemented stagger angle variation causes an additional excitation frequency. These results show a remarkable increase of the excitation of the first eigenfrequency at OP2 and of the second eigenfrequency at OP3. In addition, it also causes a reduction of the excitation of the first eigenfrequency at OP1. At OP1, the first eigenmode is close to resonance with the blade passing frequency. The excitation caused by vane row 4 is then superimposed with the excitation by vane row 5 and the intensity at the blade passing frequency weakened by vane row 5. This causes the reduction of the maximum aerodynamic work at OP1. The aerodynamic work can also be determined as local value on rotor blade with T p n u dt W aero,local = max( u ) This local aerodynamic work is determined for each element of the (6) normalized aerodynamic work W aero Reference Multi Stage Alternating Vanes OP1 OP2 OP3 Operating Points Fig.14: Maximum aerodynamic work on rotor blade 5 for all operating points, normalized with the aerodynamic work of the reference configuration at OP1 rotor blade with the respective unsteady surface pressure and displacement of the eigenmode at the specific surface element. In Figure 15 the local aerodynamic work on the rotor blade surface is shown. The trend of aerodynamic work as a function of the operating point is the same as for the maximum aerodynamic work in Fig. 14. At OP1, the excitation of the first eigenfrequency with its bending mode shape is clearly visible. The highest aerodynamic work is located at these positions as the eigenmode has its highest displacements. The nodal line of the bending mode is indicated with the white areas on the pressure side of the rotor blade. Compared to OP1, the aerodynamic work acting on the rotor blade is much lower at the other operating points. For the reference configuration, almost no work is acting on the blade with the first eigenfrequency excited by the 15EO at OP2. This is in accordance with Fig. 13 and Fig. 14. In contrast to this, the 15EO excites the first eigenfrequency in the case of the stagger angle variation. The highest aerodynamic work acting on the rotor blade is located at the tip trailing edge where the highest mode displacement occurs. Similar results are shown at OP3. The second eigenfrequency has a low excitation at the 15EO in the reference case. The reference configuration has a negligible 15EO content due to the numerical model, which used two passages with periodic boundary condition. For the stagger angle variation, a significant increase of the local aerodynamic work is determined. In this case, the nodal line of the torsion mode is indicated by the white areas from hub to tip. The highest excitation is again located at the tip trailing edge. To conclude the aerodynamic analysis, the relative total pressure shows remarkable change of the wake position and wake deficit directly behind the implemented stagger variation. One stage further downstream, the total pressure shows a negligible effect on the wake position and minor effect on the wake deficit. Nevertheless, the results in the flow passage and the unsteady pressure fluctuations on the rotor blade in particular reveal that the alternating vane pattern still has an effect one stage downstream of the implemented variation. The high difference in pressure fluctuations at one half of the blade passing frequency shows that the alternating vane pattern still has an effect on the excitation of the rotor blade even if the variation is not implemented in the upstream vane row immediately adjacent. This confirms the results of the analysis of aerodynamic work. The stagger angle variation in an alternating pattern causes a higher excitation compared to the reference case due to the ad- 7

8 Pressure Side nodal line Suction Side Pressure Side nodal line Suction Side Steady CFD Initial CFD Solution Unsteady CFD OP1 Pressure Time Domain OP2 Averaging Fast Fourier Transform nodal line nodal line Mean Pressure Pressure Frequency Domain OP3 Static Structual Analysis Pre- Stress Harmonic Response Analysis low high low high Aerodynamic Work in J/m Aerodynamic Work in J/m Reference Alternating Vanes (Multi-Stage) Fig.15: Local aerodynamic work on the blade surface of rotor 5 Responses Superimpose Responses Time Series of Deflection Fig.16: Flow chart of the unidirectional FSI approach using the harmonic analysis [9] ditional frequency at the 15EO. The next step is to investigate the aeroelastic behavior caused by the excitation sources. FORCED RESPONSE ANALYSIS In this section the focus is on the influence of the alternating variation of stator vane on the vibration amplitude of the rotor blade one stage downstream. For this purpose, a forced response analysis was conducted. A unidirectional fluid-structure interaction (FSI) approach was used to calculate the vibration amplitudes. This method was previously used and described in [8, 9], and is summarized below. Forced Response Method The vibration amplitude of the rotor blades resulting from the aerodynamic excitation is predicted numerically by performing a forced response analysis. A unidirectional FSI approach is used which is shown in Fig. 16. In this approach unsteady CFD calculations have to be performed in order to extract the unsteady blade surface pressures. Subsequently the unsteady surface-pressures are mapped from the CFD mesh onto the FEM mesh and transformed into the frequency domain using a FFT. Afterwards, harmonic analyses are conducted seperately for the main occurring excitation frequencies. The responses for each excitation frequency are then superimposed. For this analysis, the values of the aerodynamic and structural damping must be estimated. In this study, the values of the damping ratio are determined from the tip-timing measurements with the half power bandwidth method. A detailed description of the calculation of the damping ratio is described in [9, 22]. As the damping ratio is estimated from tip-timing measurements, this ratio includes the aerodynamic and structural damping of the blade. The analysis is performed with a damping ratio of D =.12 for OP1, D =.16 for OP2 and D =.175 for the design point OP3. This approach of the forced response analysis is described in detail in [8] and was developed to reduce the computational effort in comparison to a bidirectional fluid-structure analysis. Forced Response Results In this section, the results of the unidirectional FSI simulations are presented. This approach was conducted for the reference case with identical vanes, and for the case with stagger angle variation in stator vane row 4 in an alternating pattern. The following blade displacements are evaluated at the tip trailing edge of rotor blade 5, which is equal to the axial position of the tip-timing probes. Beside the amplitudes determined by the FSI, the vibration amplitudes of the tip-timing measurements for the reference configuration are included for comparison. At OP1 high amplitudes occur because of the resonance between the BPF and the first eigenfrequency for the reference configuration. The vibration amplitudes of the numerical and experimental results are normalized to their respective amplitude of the reference configuration at OP1. Although the absolute value of the damping ratio cannot be determined precisely in simulations, the relative magnitude of vibration amplitudes can be compared between simulations and experiments using this normalization. In the following sections, the vibration amplitudes determined by the tip-timing measurements are a data average of all 3 blades. A scatter of the vibration amplitude for the reference configuration is shown in [9]. In addition, the vibration amplitudes were determined only with specific mode content for better comparison with the stagger angle variation, which has a dominant 15EO content. The alternating vane pattern in the fourth vane row decreases the vibration amplitude to.94 (see Fig. 17). This is in accordance with the reduction of the aerodynamic work at OP1. The decreased aerodynamic work, which includes the unsteady pressure amplitudes and modal displacement, causes a lower excitation of the rotor blade. At OP2, the normalized vibration amplitudes increases from less than.2 for the reference configuration to.62 for the alternating vane configurations because the alternating stagger angle variation causes an excitation of the first eigenfrequency by the 15EO. Thus, the aerodynamic work on the rotor blade is also higher by a factor of 3 compared to the reference. Similar results are shown in Fig. 17 at OP3. The aerodynamic work increases 8

9 normalized Vibration Amplitude Reference Num. Reference Exp. Multi Stage Alternating Vanes Num. OP1 OP2 OP3 Operating Points Fig.17: Vibration amplitude of rotor blade 5 at different operating points normalized with the vibration amplitude of the reference configuration at OP1 - error bars indicate a 95% confidence interval of the measurements from the reference case to the case of stagger angle variation by a factor of 4. The alternating pattern induces the additional excitation frequency of the 15EO, which in turn causes a greater excitation of the second eigenfrequency as shown in Fig. 15. This leads to the increased vibration amplitude (.16) at OP3. As already described in [9], some uncertainties exist which can cause differences between measurements and simulations. One uncertainty may be the variable contact of the blade in the fir tree at partly loaded operating conditions due to the lower rotational speed. Additionally, excitation mechanisms in the turbine can occur, which cannot be captured accurately by the numerical simulations (e.g. imbalance in the rotor, excitations caused by the drive train, excitations caused by supporting rib, clearances, etc.). As the vibration amplitudes are higher in the experiments which is not caputured by the numerics it does not result from the aerodynamics. Additionally, [23] and [24] show that the mistuning of the blades has a large impact on the amplitude of the blades. The experimental validation in these studies examined that the vibration amplitude can be significantly higher in the experiments compared to the numerical amplitudes of a tuned model. These differences may cause the differences at OP2. Comparison to a single stage In this section, the stagger angle variation of 1.5 deg applied to vane row 4 is compared with a stagger angle variation of 1.5 deg in vane row 5, in order to determine the influence on the vibration amplitude of the blade row 5. The geometric variation in vane row 5 has already been investigated in [9]. This comparison is performed in order to investigate the influence of the variations at different locations. In Figure 18, the unsteady pressure amplitudes at 8% span height for the 15EO at OP3 is shown for the stagger angle variation in the adjacent vane row. The stagger angle variation in vane row 5 (green) generates higher unsteady pressure amplitudes on the rotor blade. On the pressure side, the maximum c p is at.6. On the suction side the pressure amplitudes have their maximum (.25) at the leading edge and a second maximum (.5) at 7% chord length, both of which are higher compared to the pressure amplitudes caused by the variation in vane row 4. The comparison of the experimental and simulated normalized vi- Pressure Coefficient c c p,4.4,35.35,3.3,25.25,2.2,15.15,1.1,5.5 Ref Alternate Alternate Multi-Stage,. TE PS LE SS TE 18 Fig.18: Comparison of the unsteady pressure amplitudes along the 12 chord length for one half of the blade passing frequency 6(15EO) at OP3 with the variation in stage 5-8% span height Phase in normalized Vibration Amplitude Reference Num. Reference Exp TE Alternating Vanes Num. LE TE Alternating PS Vanes Exp. SS 1.75 Multi Stage Alternating Vanes Num OP1 OP2 OP3 Operating Points Fig.19: Comparison of the vibration amplitudes with the variation in stage 5 - error bars indicate a 95% confidence interval of the measurements (see [9]) bration amplitudes for the alternating vane configuration of vane row 5 was published in [9]. Here, the focus is on the impact of the stagger angle variation in vane row and the difference caused by the one stage in between. In Figure 19, the normalized vibration amplitude is presented for all operating points, including the comparison of the single stage variation. It shows that the impact of a geometrical variation in the adjacent blade row is higher by a factor of 1 compared to a defect one stage upstream for OP2 and OP3. In the adjacent blade row, the excitation sources, the potential effect, and the wake excitation, are not extenuated. As the wakes are mixed out in the flow passage and the potential effect is a localized effect, the influence of the variation is much lower after one stage downstream. Nevertheless, this geometric variation causes higher vibration amplitude at OP2 and OP3. At OP1 the excitation of the blade passing frequency is reduced by the stagger angle variation in vane row 5. Thus, a geometric variation one stage between the excited blade row and the geometric variation induces a higher vibration amplitude. This is still lower (.94) than the reference case. These results are in accordance with the results shown in Fig. 2. This diagram shows a correlation between the normalized vibration amplitude and the normalized aerodynamic work. As above, the 9

10 normalized vibration amplitude OP1 Reference OP1 Alternating Vanes OP1 Multi-Stage Alternating Vanes OP2 Reference OP2 Alternating Vanes OP2 Multi-Stage Alternating Vanes OP3 Reference OP3 Alternating Vanes OP3 Multi-Stage Alternating Vanes Mode 1 Mode normalized aerodynamic work Fig.2: Correlation between normalized vibration amplitude and normalized aerodynamic work amplitudes are normalized to that of mode 1 in the reference case at OP1. The three cases are presented for all operating points. An almost linear correlation exists which shows that higher aerodynamic work causes higher vibration amplitudes. As the first and second eigenmode have different mode shapes, the linear correlation is also different. The response to aerodynamic work is different for both mode shapes. Consequently, the influence of variations one stage downstream on the vibration amplitude is non-negligible. As the potential effect is a localized effect between stator vane row 5 and rotor blade row 5, the remaining main excitation mechanism due to the variances in stator vane row 4 is the wake excitation. The potential effect on the excitation at half of the blade passing frequency is of minor importance, because the vanes in row 5 have no variation. As a consequence of the mixing process, the wake excitation due to variances in an upstream stage has a lower influence compared to the adjacent vane row. If the variation was applied to the adjacent vane row both, the wake excitation, as well as excitation by the potential effect, could have a significant impact on the vibration amplitude. CONCLUSIONS AND OUTLOOK The effect on the aerodynamic excitation caused by an upstream blade row, which is not adjacent to the excited blade row is investigated using a FSI method. This method was previously validated against experimental data. For this purpose, a typical regeneration-induced variance is applied to the fourth stage of the five-stage axial turbine in an alternating distribution, which was previously shown in [11]. It was shown that a variation in stagger angle has the highest impact on the aeroelastic behavior of the downstream turbine blades. The influence of a stagger angle variation on the aerodynamic excitation and the vibration amplitude of the last rotor blade row is analyzed in detail. The prediction of the forced response amplitude using the unidirectional FSI approach shows an increase of the amplitudes due to the geometric variation. These variations lead to an additional excitation frequency. Dependent of the operating points, this can cause up to a fourfold increase in aerodynamic work acting on the analyzed blade row, the additional excitation induces fourfold greater vibration amplitudes compared to the reference case. If a geometric variation is applied to the adjacent vane row upstream of the analyzed blade, the impact on the vibration amplitude is greater by a factor of 1 compared to the case where the variation is applied one stage further upstream. At other operating points the geometric variation can have a positive effect on the vibration amplitude. The additional excitation frequency causes a reduction of the excitation by the blade passing frequency, which can in turn reduce the vibration amplitude up to a factor of.25 depending on in which vane row the geometric variation is present. Additionally, a linear correlation between the aerodynamic work and the vibration amplitude was found. A future step will be the experimental validation of the geometric variation vane row 4 in the axial air-turbine for experimental verification. ACKNOWLEDGMENTS The authors kindly thank the German Research Foundation (DFG) for the financial support to accomplish the research project C4 Regeneration-induced Variances of Aeroelastic Properties of Turbine Blades within the Collaborative Research Center (CRC) 871. Furthermore, the authors thank ANSYS for providing CFX in an academic license and the Leibniz Universität Hannover IT Services (LUIS) for the computational resources provided. Finally, we acknowledge the valuable suggestions of the anonymous reviewers. References [1] Rupp, O., 21, Instandhaltungskosten bei zivilen Strahltriebwerken, Deutscher Luft- und Raumfahrtkongress 21, Hamburg DGLR [2] Aschenbruck, J., Adamczuk, R., and Seume, J., 214, Recent Progress in Turbine Blade and Compressor Blisk Regeneration, Proceedings of 3rd International Conference on Through-life Engineering Services, November , Cranfield, England. [3] Vahdati, M., Sayma, A., and Imegrun, M., 2, An Integrated Nonlinear Approach for Turbomachinery Forced Response Prediction. Part II: Case Studies, Journal of Fluids and Structures, Vol. Vol. 14(1), pp [4] Bréard, C., Green, J., and Imregun, M., 23, Low-Engine- Order Excitation Mechanisms in Axial-Flow Turbomachinery, Journal of Propulsion and Power, Vol. Vol. 23(19), pp [5] Di Mare, L., Imregun, M., Smith, A., and Elliott, R., 27, A Numerical Study of High Pressure Turbine Forced Response in the Presence of Damaged Nozzle Guide Vanes, Aeronautical Journal, Vol. Vol. 111 / 3177, pp [6] Meyer, M., Parchem, R., and Davison, P., 211, Prediction of Turbine Rotor Blade Forcing due to in-service Stator Vane Trailing Edge Damage, Proceedings of ASME Turbo Expo, June , Vancouver, British Columbia, Canada, GT [7] Petrov, E., Di Mare, L., Hennings, H., and Elliott, R., 21, Forced Response of Mistuned Bladed Disks in Gas Flow: A Comparative Study of Predictions and Full-Scale Experimental Results, Journal of Engineering for Gas Turbines and Power, Vol. Vol. 132(5) / [8] Aschenbruck, J., Meinzer, C., Pohle, L., Panning-von Scheidt, L., and Seume, J., 213, Regeneration-induced Forced Response in Axial Turbines, Proceedings of ASME Turbo Expo, June , San Antonio, Texas, USA, GT [9] Aschenbruck, J., and Seume, J., 215, Experimentally Verified Study of Regeneration-Induced Forced Response in Axial Turbines, ASME Journal of Turbomachinery, Vol. Vol. 137(3) / 316. 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