# FSI Application in the Parametric Analysis of Blade-Disk Connection of Turbojet Engine Compressor
## 2 Object of Research  
For the numerical research, a virtual model of the axial compressor rotor stage was developed. For this purpose, curves were used to map the scanned object, which was the blade of the high-pressure compressor of the turbine jet engine. First, the blade was modeled, and then the root was modeled. Because of the small angle of twisting within the blade, its model was limited to a few of its cross-sections, which, in this case, was sufficient to reproduce the correct geometry of the blade (Figure 4). It should be noted that in the case of modeling planes, the appropriate number of curves should be selected to obtain a non-distorted modeled surface. The high-pressure compressor support element with a disk-drum design was mapped using the available engine technical documentation. The developed geometric model of the compressor blade was also the starting point for the preparation of a virtual model for numerical flow simulation. Considering the repeatability of elements in the rotor stage (Figure 5a) and the fact that the Fluent program allows the use of periodic boundary conditions, in the case of rotating machines, the model was limited to the construction of a small, repeating fragment of the rotor palisade (Figure 5b). These boundary conditions allow interference between successive elements of  
Figure 3: Parametric analysis algorithm with FSI. the model to be considered. In the model under consideration, the compressor stage had 68 rotor blades, so the angle of the modeled design area was 5.29\({}^{\circ}\). The discretization of the rotor stage structure was limited to generating a finite element grid of the slice (Figure 6a) including one blade (Figure 6b) because of the possibility of using a condition of cyclic symmetry. In addition, in sensitive areas of the structure, such as the connection area, appropriate mesh compaction was introduced (Figure 6c). The discrete model is shown in Figure 6.  
The condition of cyclic symmetry [21; 22] used in FEM calculations of rotating disks and blades allows us to shorten the calculation time. This is because the cyclically symmetrical structure contains sectors of repetitive shapes arranged circumferentially around the axis of symmetry. The FEM model of such a construction is one basic sector divided into finite elements. The remaining sectors are calculated based on the performance of the basic sector using the combined Fourier series [21]. In the analysis of rotor stages, additional difficulties are introduced by the need to consider contact on the mating surfaces of bodies. This is particularly difficult when the contact zone is not precisely known or when the contacting surfaces of the bodies may come into contact or lose contact in a way that is difficult to predict. In this type of construction, a model with nonlinear frictional contact is mainly considered. This model requires defining  
Figure 4: Geometric model of the rotor blade and its main dimensions in millimeters. Figure 5: Geometric model of the rotor stage with the repeating slice (marked in green) (**a**) and model of the calculation domain of a single rotor blade (**b**). the value of the friction coefficient and considering the influence of the set value on the distribution of stresses and displacements. The boundary conditions for the CFD task were given during the creation of the design area geometry and mesh generation (Figure 7). It consisted of indicating suitable surfaces in the calculation area, representing selected boundary conditions [23]: inlet (in the inlet to the compressor stage) in the boundary condition of Pressure Inlet; outlet (in the outlet from the compressor stage) in the boundary condition of Pressure Outlet; hub (disk/load-bearing structure) in boundary condition of Wall; shroud (outer cover) in boundary condition of Wall. In addition, because in the analyzed case, only the repeating element of the rotor stage was considered, periodic boundary conditions were imposed. They allowed us to consider the interference between subsequent elements of the model.