3. Finite element-based displacement simulation

#### 3.1 Thermal boundary conditions and mechanical loads

As shown in Figure 1 and described in Section 2, the displacements of the heated parts depend on thermal boundary conditions and mechanical loads applied. Shown in Figure 3, the design scheme of the disk, which is the most complex HP, illustrates these conditions and loads.

The boundary conditions are set by an external air and gas temperature T and heat transfer coefficient α at the disk surface. Since these conditions considerably vary at different parts of the surface, it is broken down into 24 sections with constant temperatures Ti and coefficients αi. At one engine steady state called a

Figure 3. Design scheme of disk thermal boundary conditions and mechanical loads.

reference mode, the values T<sup>0</sup> <sup>i</sup> and α<sup>0</sup> <sup>i</sup> of these parameters are known on the basis of the experimental information. In a peripheral disk part, in addition to hot gases, heat is transmitted from the blades. This additional heat transfer is taken into account by elevated values T1 and α<sup>1</sup> in Section 1 of the disk surface.

As to the mechanical loads, the centrifugal force acting on the disk is a body force that is applied to each elemental volume of the disk. The centrifugal force from the rotating blades is given as a surface force by a uniform distribution σ<sup>B</sup> in Section 1. The design schemes of the blade and the casing are similar.
