Regeneration-Induced Variances of Aeroelastic Properties of Turbine Blades

Abstract

Regeneration and wear result in geometric deviations between design intent and reality of turbine blades. These deviations influence the aerodynamic flow field and the aeroelastic behaviour of downstream blades. As an example for the effect of such deviations between modules on blade vibration amplitudes, an experiment is set up to determine the influence of cold streaks, which can occur due to widening of cooling air holes. The vibration amplitude for an off-design point is increased by 20% and for the design point as well. We conclude that the forced response caused by cooling air from the turbine blades must be considered during the design process and for life predictions, especially for higher relative cooling air mass flows. Furthermore, different geometric deviations may occur simultaneously, which can magnify the vibration amplitude even further. A probabilistic process presented here investigates these combined effects. It is shown that a maximum amplitude exists within the given geometric boundaries. Using this information, new safety margins can be set for geometric deviations in the repair or manufacturing process.

1 Introduction

High aerodynamic, mechanical and thermal loads in axial turbines lead to extensive wear of turbine blades, especially within the high-pressure turbine module. If such a blade is regenerated to save costs and avoid unnecessary scrapping of the blade, the geometry is different compared to its original design intent. Geometric deviations from the design intent influence the aerodynamics across the blade, e.g., they increase the wake deficit. In such a case of higher wake deficit, there is a high possibility of changes in aeroelastic properties of a downstream vane or blade, which may increases high-cycle fatigue (HCF) and thus reduce the blade’s life. This phenomenon has been investigated in the subproject C4 and is reported below.

A new fifth stage has been designed and manufactured for an existing four-stage axial turbine at the Institute of Turbomachinery and Fluid Dynamics (TFD) within the first funding period. This stage has aeroelastic properties similar to a low-pressure turbine of a real aircraft engine. Furthermore, a computational tool chain is developed for simulating forced response. It is shown experimentally that a stagger angle variation by 1.5° increases the vibration amplitude of the downstream rotor by a factor of 4 for a part-load operating point, and up to a factor of 5 for the design point (Aschenbruck and Seume 2015). An additional stage in between the vane row with geometric deviations and the investigated rotor strongly decreases the influence on the vibration amplitude of the blade. For the design point, the vibration amplitude increases by a factor of 1.2. Lastly, the influence of a change in radial tip gap directly within the investigated rotor stage increases the vibration amplitude slightly (Hauptmann et al. 2018). This is due to an increase of the aerodynamic forcing near the blade tip and at the same time reducing damping.

The early work in funding periods (FP) 1 and 2 shows the importance of considering geometric variances in the decision process of blade regeneration based on aerodynamics and aeroelasticity, as well as component life estimation. The component life is heavily influenced by the aerodynamic force of the blade. However, different geometric variances occur simultaneously in reality, which might enhance the vibration amplitude even further and reduce the blade’s life. An in-detail study of existing blades and their geometric variances is given in Ernst et al. (2016), where worn low-pressure turbine blades are digitized, parametrised, and investigated regarding their sensitivities to geometric variances. The possibly critical vibrations due to simultaneously occurring variances are analysed in a probabilistic study in the last funding period and reported below.

Next to these geometric variances, there are additional effects like burner malfunction or cooling hole degradation that influence the aeroelasticity of a downstream row. These defects can migrate from one module to another, e.g., from high-pressure turbine to low-pressure turbine, thus accurate prediction of these effects is of importance for product life predictions. This cross-module effect is also investigated in the last funding period 3 through a change in cooling air that leads to cold streaks.

2 Test Setup

The test case for both the experimental setup and the probabilistic study is the 5-stage axial turbine of the TFD. Each stage contains 30 blades and 29 vanes. The numerical domain and different application of geometric variances over the three funding periods are shown in Fig. 1. As previously described, the stagger angle is changed by 1.5° relative to the reference cases with the original stagger angle (increase of circumferential velocity at the outlet) for vane stage 5 (V5) in FP1 and for vane stage 4 (V4) in FP2. In this funding period, V4 is selected for applying the cold streak as an example for cross-module effects.

Fig. 1

Overview of different experimental investigations within the three funding periods (FP)

A tip-timing system is applied to measure the vibration amplitude of the rotor blades in stage 5 (B5) for all cases and an aerodynamic measurement plane over 15° circumferential position between V5 and B5 is used for 5-hole probe measurements. At all times, the condition of the inlet is measured with five 5-hole probes equally distributed around the circumference and five rake probes at the outlet. These measurements ensure that the operating point is maintained between different investigations. Four blades are instrumented with eight thermocouples each, to allow further analysis of the cold streak mixing. The thermocouples are placed on the suction side on two blades and on the pressure side of the other two blades.

During the design process of the fifth stage, three different operating points had been selected based on machine loading and resonance crossings in the Campbell diagram. A crossing with the first structural mode of the blade and engine order (EO) 29 or 30 near the low-load operating point. The same EO has a crossing with mode 2 for the part-load operating point. Additionally, blade mode 1 is excited by EO 15 near the part-load operating pointö, which is shown in Fig. 2. The resulting boundary conditions extracted from experimental data during FP 3 and the crossing for the different operating points are shown in Tab. 1.1.

Fig. 2

Campbell diagram

As described earlier, the cold streak is applied in the fourth stage stator vane, V4. There are five cooling holes with a diameter of 2 mm on the pressure side of each vane near mid-span (see Fig. 3), which allow to investigate the radial migration of cold streaks across the stage. Air is provided by an external compressor and every vane is connected independently with the main air source. Therefore, different engine orders can be investigated for the different operating points. Temperature, pressure, and mass flow of the cold streak are measured continuously. The relative mass flow of the cooling air as a fraction of the total mass flow in the axial turbine and the absolute cooling air temperature are shown in Table 1. For both cases, the reduced mass flow and the rotational speed are held constant for each operating point.

Table 1 Operating points

Fig. 3

Close-up of the experimentally investigated stages and cold streak application

For the computational fluid dynamics simulations (CFD), the unsteady Reynolds- averaged Navier–Stokes equations (URANS) are solved in the pseudo-time domain with the implicit solver TRACE Nürnberger et al. (2001), developed by the German Aerospace Centre. A finite-volume scheme is used for spatial discretization. The Reynolds-stress is modelled by the Menter SST model (Menter et al. 2003) assuming fully turbulent flow. A stagnation point fix by Kato and Launder (Kato 1993) is used.

All walls are assumed to be adiabatic; the non-slip condition is implemented at the wall. As convergence criterion, the relative change of mass flow has to be below 10⁻⁴ and the pressure change over one period on different points in the flow field has to be below 10⁻⁵. Solving the unsteady equations is necessary due to the mixing of the cold streaks in the flow panel. Therefore, the vanes are scaled to a vane count of 30 for the numerical investigations. This way, the numerical setup can be reduced to single-passage in comparison with full annulus calculations. The forced response and flutter calculations are conducted within the URANS setup. It is assumed that the vibration amplitudes are relatively small, therefore, the aerodynamics has a linear relationship with the vibrations. Mode-coupling is neglected from the flow on the structure, because the aluminium blade’s mass and stiffness are relatively high in comparison with the influenced surrounding air. However, the impact of structural vibrations on the unsteady flow is taken into account and coupled.

Evaluating the aerodynamic work on the blade, a finite element (FE) simulation with ANSYS Mechanical is used as was done by Pohle et al. (2014). Afterwards, surface displacement is mapped from each FE to a CFD mesh. For this process, the FE mesh is first translated to match the position of the corresponding CFD blade, and then the surface deformations are interpolated to the corresponding CFD cells. This mapping process, described in detail by Voigt et al. (2010), is used to calculate the aerodynamic work W on the blades’ surface S by considering the steady pressure $p^{v}$ and unsteady pressure perturbations p˜ from a CFD by where n is the normal surface and x the surface deformation. Finally, the energy method is used and the vibration amplitude can be calculated when forcing W_f and damping work W_d are in equilibrium. For the aeroelastic calculations, the main convergence criterion is constant aerodynamic work within 0.01% over a span of 100 time-steps.

$$W= -i\pi {\int }_{Z}{\tilde{\bf{x} }}^{H}(\tilde{p }{\bf{n}}^{0}+{p}^{0}\tilde{\bf{n} })dS$$

(1)

3 Aerodynamic and Aeroelastic Results

Applying the cold streak (CS) changes some of the main parameters of the axial turbine. The inlet pressure increases, even if the reduced mass flow and rotational speed are kept constant across both cases, resulting in a higher total pressure ratio between inlet and outlet. Additionally, the thermal power output and isentropic efficiency are increasing for the cold streak case. This is due to two effects:

• 1. Additional mass flow from the cooling air, and

• 2. potential effect upstream to the machine inlet.

Note that this does not mean, that cooling air will increase an axial turbine’s efficiency in all cases, but it is important to investigate the change in the operating point in more detail for further understanding. There are two options: either keeping the reduced mass flow and rotational speed constant or controlling the turbine at constant pressure ratio, thus thermal power output. Due to experimental constraints the first option could be performed only. For aircraft engines the latter would have been closer to reality, where the thrust needs to be constant for the engine to achieve the same aircraft speed with different cooling air mass flows.

This observation in change of axial turbine operating points is confirmed by the pressure profile on V5 at mid-span (see. Fig. 4). For all operating points, a good agreement is achieved between reference and cold streak on the vane’s suction side, but a pressure increase on pressure side is observed over the whole length of the vane for the cold streak case, thus resulting in higher blade loading. This increases the wake deficit for the cold streak case in total pressure and circumferential extent. A closer examination of the wakes confirms the change of the wake width on the pressure side, while the suction side remains constant. For OP1, a separation bubble is detected in the experimental data and accurately predicted by CFD at 0–20% chord length on the suction side. The separation bubble originates from the blade’s high incidence at low-load operating conditions.

Fig. 4

Pressure profile on V5 for all operating points for reference (Ref) and cold streak (CS). 95% confidence interval in scale of marker

The change in total pressure due to the cold streak is confirmed by the circumferential measurement in traverse plane ME2.51 (cf. Fig. 1) as shown for OP2 in Fig. 5, where the normalized total pressure p_norm and temperature T_norm are calculated by

$${p}_{norm}=\frac{{p}_{t}-{p}_{aus}}{{p}_{ein}-{p}_{aus}} \text{ and } {T}_{norm}=\frac{{T}_{t}-{T}_{aus}}{{T}_{ein}-{T}_{aus}}$$

(2)

Fig. 5

Area-averaged measurement in plane ME2.51 for OP2. 95% confidence interval in back-to-back measurements

A reduction by 0.25% of the static temperature drop throughout the axial turbine is measured between the reference and the cold streak case. The Mach number is reduced by 0.08 for the cold streak measurement for OP2. The radial temperature distribution is changed between both cases and the temperature is increased near shroud and hub. A minimal temperature at around 40% relative channel height indicates the cold streak. This is confirmed for OP1 and OP2, while for OP3 the influence is within measurement uncertainties.

Repeatability is attained by conducting all tip-timing measurements four times. The final vibration amplitude analysed is the arithmetic mean of all calculations with a 95% confidence interval. In Fig. 6 the vibration amplitudes of B5 are shown for the three operating points and all investigated cases over the three funding periods. As described earlier, the vibration amplitude in FP1 and FP2 is increased for OP2 and OP3, while the amplitude is reduced for OP1.

Fig. 6

Vibration amplitude of B5 with 95% confidence interval

The vibration amplitude in increased by 20% in OP1 due to the cold streak and decreases for OP2 and OP3 in a small margin within measurement uncertainties. The EO29 for OP1 has the highest relative cooling mass flow and therefore shows the biggest impact. Especially for OP3 and EO15 for OP2 the cooling mass flow is too low to show a measurable impact. Because of the external compressor in order to supply the cooling air without a cooler system, temperature changes were only possible in small margins with external air blower. These small temperature changes of the cooling air did not have any impact on the vibration amplitude outside the measurement uncertainty.

The unsteady pressure perturbations are increased on the pressure side of the blade’s surface as shown in Fig. 7, while the shape between both cases remains the same. On the suction side, the shape is changed. Between 40 and 50% blade length a local reduction occurs of the unsteady pressure for the cold streak case. Outside this area the same behaviour as on the pressure side is observed. These unsteady pressure amplitudes directly impact the force and aerodynamic work on the blade (see Eq. 1).

Fig. 7

Unsteady pressure amplitude from CFD results for OP2 at 90% blade height between leading-edge (LE) and trailing-edge (TE)

The change in vibration amplitude is based on three simultaneously occurring effects. First, changes in overall mass flow in the machine due to the change of operating point directly influence the forcing on the blades. This might change the vibration amplitudes if the additional forces have similar forcing frequency as the blade’s natural frequency. Second, the additional mass flow due to the cold streak increases the flow potential, which increases the excitation forces similar to the first effect. Finally, the local temperature at a constant total pressure changes, which results in a different density and therefore different mass flow.

4 Probabilistic Study

Methodology

Generating a probabilistic data set requires the following steps (see Fig. 8): The first step is creating a parameter model from a given CAD model with 12 characteristic parameters describing a blade section based on the algorithm from Heinze et al. (2014) and Ernst et al. (2016). This parametrisation was conducted on 25 radial blade sections. Using Voronoi diagrams and the Delaunay triangulation Aurenhammer (1991), the camber is approximated, where the smallest distance from the camber to pressure and suction side is determined as profile thickness. The difference between the Delaunay approximation and the true geometry is used as an accuracy criterion and should be below 0.01% thickness deviation for all cases. The leading-edge radius r_LE and trailing-edge thickness t_TE is determined by fitting a circle into the geometry at the respective position with the Levenberg-Marquardt algorithm (Moré 1978). From the thickness distribution, the value t_max and the location x_t,max of maximum thickness are determined. Likewise, using the approximated camber, the value c_max and positioning x_c,max of the maximum camber is calculated. Lastly, the leading-edge angle β_LE, the trailing-edge angle β_TE and the stagger angle γ are calculated relative to the meridional axis. A summary is shown in Table 2 for all necessary airfoil parameters considered in this work.

Table 2 Airfoil parameters symbol description

Fig. 8

Probabilistic work flow

Afterwards, based on the geometrical parameters and the percentage deviations of the geometrical parameters obtained by a Latin-hypercube sampling McKay et al. (2000) within prescribed limits, 25 blade sections are reconstructed. No correlation of the input parameters is assumed to exist, and the limits are set with 10% for each parameter to investigate all possible parameter combinations that could occur during the repair process of a blade. This way a wide geometric range is considered without changing the blade completely. Note that this assumption might impact sensitivity studies, however the final reduced order model can be used for additional sensitivity studies with a correlated input. After applying the reconstruction, the blade sections are transferred to an automatic 3D meshing program. The resulting mesh meets the requirement of a dimensionless distance from the wall y⁺ ≤ 1 for all samples.

The described first step is conducted for the required sample size and is followed by 3D flow simulations. The same solver as described earlier is used, however, only the RANS equations are solved and afterwards flutter and forced response simulations are conducted using the unidirectional time-linearised solver linearTRACE with a frozen gust approach Kersken et al. (2012), saving computational resources in comparison with URANS simulations. A more detailed description of the numerical setup is given in Stania and Seume (2022).

The last stage is isolated for the probabilistic investigation of critical vibration amplitudes. The fifth stator vane V5 is varied and the aerodynamic as well as aeroelastic influence is evaluated for the fifth rotor blade B5. This single stage approach is similar to FP 1. Increasing the simulation domain will increase the required simulation time for each sample, which is not feasible within this project and due to the higher impact of the single stage influence it is not necessary. The inlet boundary condition for the reduced setup is extracted from a 5-stage numerical solution and OP2 is chosen, since the crossing with mode 2 of the blade.

Results

Based on the simulation output, three dimensionless stage parameters and the poly- tropic efficiency are calculated. The work coefficient Ψ, or stage loading coefficient, is calculated with rotational velocity u_i and the tangential velocity component of the flow c_u,i by

$$\Psi =\frac{{u}_{2}{c}_{u,2}-{u}_{1}{C}_{u,1}}{{u}_{2}^{2}}$$

(3)

where 1 denotes the blade inlet and 2 the outlet. It relates the Euler work over the blade in relation to the rotational speed of the blade. A change of this parameter indicates variations of the loading or extracted work of the blade. The flow coefficient Φ is a dimensionless parameter for the axial or tangential potential of the fluid in comparison to the rotational speed. Variations indicate different flow angles at the trailing edge of the blade. If a variation from the design point is high while keeping the rotational velocity constant, the flow on the blade surface might detach. It is calculated with the axial velocity c_ax by

$$\Phi =\frac{{c}_{ax,2}}{{u}_{2}}$$

(4)

The reaction R describes the drop of enthalpy h through the blade in relation to the stage. It is calculated by

$$R=\frac{{h}_{2}-{h}_{1}}{{h}_{2}-{h}_{0}}$$

(5)

where the index 0 notes the vane inlet. Decreasing reaction reduces pressure drop through the blade and shifts the velocity triangles to higher velocities within the vane. Note that the definitions of these parameters may vary between different authors. Finally, the polytropic efficiency is calculated by

$${\eta }_{poly}=\frac{\kappa }{\kappa -1} \frac{\text{log}\frac{{h}_{t2}}{{h}_{t0}}}{\text{log}\frac{{P}_{t2}}{{P}_{t0}}}$$

(6)

for the stage with total enthalpy h_t, pressure P_t and heat capacity ratio κ. Another aeroelastic parameter is obtained by calculating the equilibrium between forcing and damping work which leads to the blades’ vibration amplitude x. Additionally, the characteristic aeroelastic parameter, the reduced frequency k, is calculated by

$$k=2\pi f\frac{l}{c}$$

(7)

where c is the magnitude of flow velocity, l chord length, and f the characteristic frequency of the blade’s mode (eigenfrequency for flutter and vibration frequency for forced response). This parameter is the ratio between the time it takes for the fluid to pass over the blade and the blade’s period of vibration, i.e., the reciprocal of the eigenfrequency. Finally, the vibration amplitude x and aerodynamic damping λ are directly obtained by the simulation.

The variance-based sensitivity indices EASI (Effective Algorithm for Computing Global Sensitivity Indices) Plischke et al. (2013) show negligible influence of most geometric input parameters on the output (see Fig. 9). The aerodynamic and flutter calculations show the most significant sensitivity to exist with respect to stagger angle, maximum thickness, and maximum camber. The forced response output shows the highest sensitivity with respect to maximum camber and trailing-edge angle, with negligible impact of all other parameters. This is due to the direct impact on wake deficit of each parameter, which directly influences forced response. Therefore, for future analysis a reduction of the relevant parameters is possible and reduced-order modelling is possible. Reducing the number of independent input parameters reduces the number of required samples until a regression or artificial intelligence model is able to accurately predict the outcome. This is essential within the overall CRC 871 decision making process. Within the performance assessment of the overall regeneration process, the deep learning model is able to predict mass flow, isentropic efficiency and pressure ratio within 1% accuracy.

Fig. 9

EASI coefficient between geometric variations and CFD output with an error of ± 0.02

However, due to the small sensitivity of the vibration amplitude with respect to a few input parameters, the accurate prediction still requires a large sample size. The EASI between aerodynamic output and aeroelastic output shows a similar behaviour. Flutter shows a high sensitivity with respect to the aerodynamics, while the sensitivity of forced response increases compared to the geometric variances first applied but are only up to 0.37. The additional complexity of forced response calculations is due to the frequency and phase dependency between structural modes and aerodynamic periodic force.

For all geometric variances, the maximum increase in blade vibration amplitude is found to be 20%. Note that the maximum stagger angle considered is smaller than the stagger angle variation considered in funding period 1. With this realization, a safety factor can be derived for calculations of the blade’s product life and high- cycle fatigue. Furthermore, changes of the maximum thickness, maximum camber, and trailing-edge should be avoided in the repair process to avoid influencing the aerodynamic and aeroelastic behaviour of the downstream blades.

5 Conclusions

Initially, within the first two funding periods, it was shown that geometric variances in a stator vane have a significant impact on the vibration amplitude of a downstream rotor blade. Especially the single-stage influence has to be considered in product life estimation during the design and repair process, because the influence on HCF is eminent. Decisions on vane regeneration need to take these deviations into account, to ensure the aircraft engine’s safe operation over many flight cycles. The effect is successfully investigated in an experimental setup and the measurements are used for validating the computational setups, which are able to accurately predict the vibration amplitudes. This approach is applied to a probabilistic study in which a maximum increase of vibration amplitude by 20% is found by simulation for a given parameter range of geometric variances, and important geometrical parameters are identified for changes in the aeroelasticity of the downstream blade. We conclude that reduced order models allow fast estimation of vibration amplitudes by considering only a small amount of parameters. Due to the reduced computational effort in a sensitivity study with less parameters, this is especially important for life predictions, where a data basis has to be created for each blade. The knowledge can be used within the design, repair, and manufacturing process to set new safety margins closer to the calculated worst-case scenario and quickly asses the blades’ influence on the next row. However, this knowledge and approach needs to be transferred to further aircraft engines and operating points for applications in the industry.

Using the same experimental setup in FP3 as was earlier used in FP1 and FP2, the cold streak is successfully applied to an axial turbine as an example for cross-module effects. The experimental investigation shows an increase of vibration amplitude by 20% for the low-load operating point, reaffirming the importance of taking into account the cooling air in the design process. If for the sake of simplification, cooling air is ignored during the design process, the product life prediction will be missing this additional forcing mechanism for blade vibrations. Furthermore, the widening of cooling air holes of high-pressure turbine blades and vanes throughout the blade’s life needs to be investigated as these changes will continuously influence High Cycle Fatigue.