Hello everyone, my name is Niklas Marvold, I'm from the Institute of Turbo machinery and fluid dynamics and today I'm going to be talking about subproject C6, which is about the aeroelasticity of multistage axial compressors. The project was done together with the Institute of Dynamics and Vibration Research.

Subproject C6 is a consolidation of subproject C3 and C6 from the second funding period. While subproject C6 was focusing on the aeroelasticity of compressor bliss, in particular blend repairs and its influence on aerodynamics and aerodynamic damping. Subproject C3 was focusing on regeneration-induced mistuning, in particular reduce order models for single-stage structures.

The presentation today will be about the subproject C6. C3 will be presented tomorrow at 11 am and will be focusing on these results and will also contain some parts of subproject C6 in the third funding period containing reduced order modeling of mistuned single-stage structures.

As explained before, in the second funding period the influence of blend repairs was investigated. To do so, a new 1.5 stage axial compressor was designed and manufactured.

The compressor features two bliss variants. One bliss variant has three blades, which have typical blend repairs, which are shown on this picture, at different radial heights. Those blades are distributed uniformly around the circumference. Using an acoustic excitation system, the aerodynamic damping could be determined during operation.

Also, an unmodified bliss variant is available to compare those results and see which impact the blend repairs have on the aerodynamic damping. On this slide you can see the experimental results of the first bending mode family.

The aerodynamic damping is plotted against the nodal diameter. In green the reference results are shown, the unmodified bliss. As you can see, the flutter curve has the typical ash shape. Additionally, the blend repairs are shown in dark blue. No measurable influence of the blend repairs can be seen, as the results are pretty similar.

Additionally, our numerical results are shown in lighter blue. You can see that we are pretty well capable of capturing the aerodynamic damping in our numerics as well. Furthermore, we investigated the force response of the 1.5 stage axial compressor.

In the compressor we are able to rotate the IGV around an angle of 0 to 20°. In this way we are able to change the excitation forces done on the rotor. We investigated mode 3, which is torsional mode, at the resonance crossing with engine order 23, which is the number of vanes of the IGV.

This resonance crossing is occurring at around 6600 RPM. The results are shown in this graph. As you can see, the vibration amplitude is measured with increasing stagger angle.

Additionally, you can see that we are pretty well capable of capturing these effects and reproducing the experimental results with the CFD. However, there are some differences at 20° stagger angle. This is due to the vast typical deficits while predicting flow separations at the IGV under large flow turning.

Now we look on the third funding period. The motivation of the third funding period is a contribution to the particular prediction of the overall engine. This means that it is necessary to include inter-stage interactions within a turbo machinery, for example a compressor.

The objectives are to quantify the influence, especially under the influence of additional geometric variances on the vibration amplitudes during operation.

Therefore, we want to contribute to the calculation of the remaining lifetime. The approach is based on a multi-stage numerical model, based on a reduced order model, which is used to calculate those effects.

We include multi-harmonic excitation and also validate those models using experiments. As said before, we have a look on the geometric mistuning. The simulation chain is shown on the slide. It consists of three steps, which are done to calculate the vibrational response of a multi-stage turbo machinery.

First, the model reduction is performed in the self-developed tool Rambo. As output, we get the displacement of the degrees of freedom, which are then input for the aero-elastic simulations, which are done in trace using a harmonic balance approach.

Flutter and force response calculations are performed in trace. These lead to the aero-elastic coefficients, which are aerodynamic damping and also aerodynamic stiffness and also the excitation forces for the degrees of freedom.

Those outputs are then fed back into Rambo to calculate the system modes and the frequency response of the structure. The calculations were performed for an example, which is shown here.

This is a 2.5 stage axial compressor, which is an extension of the 1.5 stage axial compressor, which was shown before. For the setup, we chose there were 922 dUFS, which had to be considered in the calculations. Therefore, a large simulation time or computational effort was needed for the trace calculations.

First, we will have a look on the model reduction, the reduced-order model. When considering multi-stage structures, there are some differences compared to single-stage structures.

Usually in single-stage structures, the harmonic indices are not directly coupled. Therefore, each harmonic index can be considered as a substructure. However, in multi-stage configurations, those harmonic indices can be coupled indirectly through another stage.

As you for example can see here, harmonic index 1 of the first stage is coupled with harmonic index 3 of the second stage. And harmonic index 3 is then coupled with harmonic index 2 of the first stage. Therefore, an indirect coupling occurs and the substructuring approach is not valid or efficient anymore.

Therefore, usually an interface is introduced to the structure. This interface is shown here. It is added between stage 1 and stage 2. And it couples the harmonic indices between the stages. Now, a certain amount of harmonic indices can be chosen.

Those are usually Fourier harmonics in circumferential directions. This is a state-of-the-art approach, which is already known in literature. This way it is possible to reduce the number of harmonic indices, which are used to couple those stages.

As you can see here, reducing the structure and creating a very efficient model with less harmonic indices to consider. Additionally, to the Fourier series used in circumferential direction, we added a new approach, which has not been known in literature before.

This approach is based on a polynomial in radial direction to decrease the computational effort anymore and also drop some requirements regarding the mesh. As you can see here, we have the node diameter increasing the harmonic index

and therefore the number of waves around the circumference. Now we also added a polynomial, which is increasing in this direction from constant to linear and quadratic. This increases the efficiency of the model even more.

Based on this interface reduction approach, we now get three different types of DOFs, which we use for the model and also for the aeroelastic calculations. First we have the interface DOFs, which we have shown before, using the circumferential and the radial basis functions.

We also now have two other types, those are fixed interface DOFs or modes, which are obtained by fixing the interface and doing a modal analysis of stage 1 and stage 2.

Those DOFs are then combined to create the reduced order model. Now every DOF is always assigned to only one harmonic index, so that we are able to do the calculations in harmonic balance for flutter and force response later on.

Now we look at the relative eigenfrequency error when changing the basis function used at the interface. We now use a more simplified test case to illustrate this. When looking at the degree of polynomial zero, you see that the error stays quite high.

When the number of degrees of freedom is increased, this means that harmonic indices are added to the calculation. Thus the number of degrees of freedom increases. After a short time you can see that the addition of more DOFs does not significantly increase the calculation accuracy.

At this point it is more suitable to add another degree of the polynomial, the polynomial degree 1. Thus you see that the accuracy drops and that you can get even less errors in the calculation.

Thus you have a tradeoff between the accuracy and the computational effort you want to make for the calculation. Now we have a look on the error elastic harmonic balance calculations.

The calculations were done using the flowsolver trace harmonic balance by DLR. For the calculations we mapped the degrees of freedom on rotor 1 and rotor 2. We have again the fixed interface modes and the interface DOFs which are mapped on both rotors at the same time.

We then conducted force response and flutter calculations. For the force response calculations we transported the engine order 23 of the IGV again throughout the compressor but we also included some mode scattering. For example in rotor 1 the aerodynamic mode 23 is scattered into the circumferential mode 1

which is also the natural response of rotor 1 to engine order 23 with nodal diameter 1. This circumferential mode is acoustically transported through the compressor and also reaches rotor 2 and excites rotor 2 with

nodal diameter 1 which is not the natural response of engine order 23 which would be nodal diameter 8. This is also excited by the aerodynamic disturbance which is as I said before transported through the compressor and also circumferential mode 8 is then transported back to rotor 1 and can excite rotor 1 with circumferential mode 8.

Additionally we conducted the flutter simulations using only the circumferential mode of the DOF considered in the calculation. We set one DOF to active thus it vibrates in the calculation which could be at rotor 1 or rotor 2 or both at the same time.

We then calculated the aerodynamic work for all DOFs not only the active but also the inactive DOFs thus it is possible to create an unsteady pressure distribution on rotor 2 by a DOF which is said to vibrate in rotor 1 only.

Now we have a look on the results of the flutter calculations. We exemplary look on nodal diameter minus 6 and minus 8 and we again look at the active degrees of freedom which was said to vibrate but also the inactive degrees.

Each row represents one flutter calculation which was performed and for example if we look at the third row we see the third DOF and this is the aerodynamic damping calculated for the third DOF.

Now we get also the impact of the vibration of the third DOF on other DOFs for example the first one which is negative meaning that it is actually excited by the third DOF. We also get the interaction with the interface DOFs and also with the DOFs of

the second stage therefore we are able to get coupling interstage coupling effects into the calculation. This also works the other way around if we look at the second rotor we can see that we have coupling effects with the first stage as well. When looking at nodal diameter minus 8 we can see that those interstage coupling effects are highly

decreased. This is due to the fact that nodal diameter minus 8 is an acoustic cutoff mode and therefore is not able to propagate and therefore the interactions are highly damped within the compressor.

Now we use those calculated excitation forces and the aeroelastic coefficients to feed them back into the reduced order model and to calculate the system modes and the frequency response. Now we look on these frequency responses which were calculated for the test case.

First we have to consider two different cases again nodal diameter 1 and nodal diameter 8. If we look at the excitation of stage 1 with nodal diameter 1 which is again the natural response of the first rotor then we can see that there are many peaks.

For example here we can see one peak which is mainly located in stage 1 but there are also some modes for example here which are coupled modes of both stages where both stages have a significant amplitude. And those modes would not be occurring when doing one stage calculations.

The excitation of stage 2 occurs due to mode scattering at rotor 1 which is then transported to rotor 2 acoustically and there are still amplitudes visible which are significant although they are still lower than when exciting the first stage.

And again those coupled modes are excited and mainly modes which are located in stage 2 as those are excited when exciting the rotor 2 with unsteady pressure.

When we look at nodal diameter 8 let's first look at the excitation of stage 2. We can see there is only one significant peak which is the second stage at 130 Hz approximately and it seems like there are no coupling modes occurring with such high nodal diameter.

When looking at the excitation of stage 1 it is visible that the vibration amplitudes are quite low. This is due to the fact that in the mode 23 the aerodynamic disturbance needs to be transported to rotor 2 then needs to be scattered and transported back to rotor 1.

There is a lot of scattering occurring in two different circumferential modes and therefore there are only very low amplitudes visible in this case.

All these responses can be combined into a total response which is shown here. As I said before this is mainly influenced by engine order 23 and nodal diameter 1. What you now can also see is that there are differences between those lines which

are the individual blade amplitudes and thus those multistage effects act as a mistuning effect. Therefore this can lead to an amplitude amplification and therefore it is necessary to investigate those effects.

We then did calculations with actual mistuning. For this we performed Monte Carlo simulations using random mistuning adding this to the structure and we compared two cases. First a full aerodynamic coupling calculation which you have seen before and

then a single stage calculation where we only considered the single stage effects. Therefore the interstage coupling effects for aerodynamic damping and stiffness were omitted. As you can see here there are some large differences between the full and the single stage case.

When omitting the interstage coupling going from full to single stage the amplitude magnification actually increase in this case. Therefore it seems necessary to add those interstage coupling effects into the calculations to accurately predict the vibrational behavior.

To conclude my presentation we have seen that blend repairs have no significant influence on aerodynamic damping at least for the investigated compressor and the investigated mode family. We then validated our used numerical models and extended them towards aerodynamically coupled multistage machinery.

For this we used a new approach using polynomial interface functions to reduce the computational effort. We found that multistage coupling must be taken into account for accurate predictions of blade vibrations in multistage trouble machinery.

Thus to make a statement regarding the fatigue life and the impact of also blade repairs it is really necessary to take those effects into account. However we have seen it is very computationally costly to do those calculations.

Thank you for your attention. Please feel free to ask questions in the chat or contact me or my co-workers via email. Thank you.