Turbomachine assemblies and the challenges of designing them – What’s New
Turbomachines are made of assemblies of different bladed disks
In our previous blogs, we introduced how to model large turbomachines made of assemblies of many bladed-disks. An interesting exploitation of the periodicity of the structure is to consider cyclic symmetry sectors, instead of the whole 3D structure. When the industrial application requires the machine to be made of different stages, each with a different number of sectors, special care is required when connecting those sectors to ensure a smooth junction between the two stages.
When the periodic structure deviates from its regular axisymmetry shape like at the propellers with few blades, a simulation in a rotating frame can no longer be avoided, as we described in a previous blog, ‘Advances in response and cyclic symmetry of bladed rotor assemblies.’ We also explained that limitations on the non-rotating parts apply for such calculations: indeed, the non-rotating parts (stator and bearings) must be isotropic, which can be a rough assumption for industrial applications.
For such cases, the Simcenter nastran solver for Rotor Dynamics proposes a method of avoiding model limitations with the use of Coleman transformation. Indeed, with this method, bladed rotors assembled to an anisotropic stator and bearings can be computed! While this is a challenge to complete, it allows you to model the complexities and explore more possibilities when simulating and modeling rotating structures.
For industrial applications like turbochargers, steam turbines, or jet engines, the assembly is made of multiple stages of bladed disks, and the assumption that the rotor has axisymmetry is not always true. Therefore, Simcenter 3D 2506 for Rotor Dynamics has expanded the use of the Coleman transformation to assemblies of multiple stages of cyclic symmetry rotors.
Coleman transformation for multiple stages of cyclic symmetry rotors
In our previous blog, ‘Advances in resonance and cyclic symmetry of bladed rotor assemblies,’ we presented the Coleman transformation, as the solution to produce time invariant matrices in the fixed frame for cyclic symmetrical rotors as outlined by Kirchgassner 2016. We then used Campbell diagrams and stability analysis for the calculation of the critical speeds at which resonance occurs. This method is equivalent to the Floquet method when the structure is strictly cyclic symmetrical outlined by Skjoldan 2009.
Simcenter 3D advanced capabilities for bladed rotors
Simcenter 3D has taken a step further in the simulation of advanced bladed rotors applications, allowing an assembly to be computed satisfying the hypothesis of rotor dynamics calculations based on the axisymmetry or unsymmetry of the different parts of the system. It allows easy postprocessing including the production of Campbell diagrams and presents modes as output in a fixed reference frame for easy interpretation
Complex modal analysis in 5 steps
Step one
In Simcenter 3D, prepare an associative model, where the different stages can be linked to the geometry. It will allow any changes in the geometry to be communicated to the finite element model and adapted in such a way that only the simulation has to be computed again, to account for the changes. This method is called the master model concept, a video explaining this concept can be found here.
What else can cyclic symmetry do?
For all these applications that show a periodic structure, cyclic symmetry is an interesting alternative to full 3D models, since it enables the use of model reduction and makes the simulation time more reasonable.
But what else? let’s review what Simcenter 3D Rotor Dynamics can do with cyclic symmetry models:
If we consider hybrid models, that is, a model that consists of sections that are 1D, 2D, and/or 3D, it is now possible to model a rotor made of a cyclic symmetry sector, in one or multiple stages, with a connection to a 2D Fourier portion of the rotor, a 1D shaft, as well as a 3D portion of the structure. Bearings, springs, dampers, etc can be used to connect the rotor to the ground with stiffness and damping properties or to a casing.
If you want to go further in the model reduction, you can create a super-element of the cyclic symmetry sectors, for one or multiple stages, using Component Mode Synthesis methods. This super-element can then be used in an assembly with bearings, in rotor dynamics solutions. The postprocessing enables you to recover the results for the original cyclic symmetry sectors and for the whole recombined structure.
For bladed rotors that can have large deformations due to centrifugal loads or other types of solicitations, which might occur when the blades are long and thin, it is possible to compute a modal basis of the structure with a preliminary nonlinear prestress. The nonlinear prestress of the structure computes the equilibrium state due to large deformations, and the modal basis is computed around this equilibrium state. Afterwards, you can use that tangent modal basis in a modal frequency response to compute the vibrations of the system due to external loading.
For the Campbell diagram, stability study and complex modes computations, we have shown in this blog that Simcenter 3D Rotor Dynamics can now be used to solve multiple stages rotors modeled in cyclic symmetry, with anisotropic bearings, and output results in fixed reference frame.
Related blogs on rotor dynamics
Did you enjoy reading this blog and want to know more? You may also like the following blog posts:
Rotating systems – tune your intuition
Efficient rotor dynamics for multi-stage turbo machinery
Containing aircraft engine failure
Combine solution speed and accuracy for axisymmetric rotor dynamics
Bearing modeling makes or breaks rotor dynamics simulation
Multi stage cyclic symmetry in rotor dynamics
Advances in resonance and cyclic symmetry of bladed rotor assemblies
Identify the peaks of harmonic response during operation of nonlinear rotor dynamics
Smooth vibrations in rotating systems – How to monitor clearance consumption
