The simulation of the loads' effect upon the geometry of a turbine rotor.

Cuciumita, Cleopatra Florentina ; Vilag, Valeriu ; Petcu, Romulus 等

1. INTRODUCTION

It is well known that turbines are the most solicited parts of a gas turbine, due to high speeds and temperatures which induce very high stresses. In order to fully design a turbine, one must take into account these stresses and their effects (Pimsner, 1984). The content of this paper is the first step of a larger project which aims to determine the influence of the working regime upon the efficiency of a turbine. For now, this work is limited to theoretical and numerical determination of stresses and deformations. The stress calculus has two important benefits: the establishment of the physical capability of withstanding the required loads and the determination of shape changing due to dilatation caused by these loads. These deformations can seriously affect the functioning of a turbine rotor which requires a certain shape of the fluid passing canal in order to ensure a certain power output. The calculus requires the knowledge of the geometrical parameters as well as the loading. In this case, for the stress analysis of a turbine rotor, it had to be previously designed by means of gas dynamic methods. The response of the rotor to these loads is calculated in two ways, theoretically and numerically, using the dedicated software Ansys 11. The theoretical calculus is conducted in two major steps. First, the blades are calculated separately and then, using these results as an input, the disc. For this type of calculus some hypotheses were made. The results are then compared with the ones obtained with Ansys for error detection.

2. THEORETICAL CALCULUS

2.1 Airfoil calculus

[FIGURE 1 OMITTED]

As specified before, in order to conduct a structural analysis of an element its geometry must be known. The airfoil is divided into 10 sections and the calculus is made step by step in these sections (Manole, 1978a). The geometrical parameters are defined as shown in figure 1.

These parameters represent, for each section considered (Carafoli & Constantinescu, 1984):

--R, the radius measured from the centre of the rotor

--A, the area

--b, the chord

--[c.sub.max], maximum thickness

--[h.sub.max], maximum bend

--CDG, gravity centre

--[xi], [eta], the main inertia system

The hypotheses made for this calculus, in order to facilitate the results are:

--the airfoil is embedded at one end and free at the other one;

--the airfoil is a stiff body;

--it is elastic deformation domain, where Poisson coefficient is 0.3;

--is divided into 9 sectors using 10 sections; for each sector the parameters are constant and equal with the average between the values at the two sections which margin it;

--the airfoil is rotating with 22000 rpm and also is loaded with the gas pressure determined in the preliminary design.

The airfoil is solicited, due to the pressure and centrifugal loads, but also due to the fact that being a turbine blade it is significantly bended, to tension, flexure and torsion. After calculating all these stresses in each section, it was determined the equivalent stress and the safety factors in the characteristic points along the airfoil: A, leading edge; B, on the back of the blade, according to the maximum thickness; C, trailing edge.

Regarding the airfoil, some conclusions can be withdrawn. The safety factors are within reasonable limits all along the airfoil, which means that it has no problem withstanding the loads imposed. The minimum, as expected, is at the bottom of the airfoil, at trailing edge and has a value of 1.42, which is a between the recommended values in aviation. These stresses represent loads in the disc's calculus.

The vibration calculus was conducted with the energetic method. The frequency diagram was obtained and, according to it, the resonance regimes which can be determined at the intersection of dynamic frequencies with the driving ones. The most dangerous regime from this point of view, and which is recommended to be avoided, is at approximately 13% before the maximum regime of 22000 rpm (367 rotations per second).

[FIGURE 2 OMITTED]

2.2 The disc calculus

The disc calculus is similar to the one conducted for the airfoil, with the difference that it was taken into account the supplementary stress given by the 61 rotor blades which it sustains (Manole, 1984b). This time, the disc was divided only in 5 sections, where its thickness varies.

In table 1 are given the results for the equivalent stress obtained along the disc, starting with the maximum radius, with the mention that at the work temperature, the material's allowable stress is of 640 MPa.

The problem of resistance is, for the disc as well, within the admissible limits, with a minimum safety factor of 1.36. As it can be seen from table one, the maximum stress is not at the end of the disc or at its centre, but near the place where the disc is fixed and where its thickness is smaller.

A similar vibration calculus to the one made for the airfoil shows that the most dangerous resonance regime is, as well, approximately with 13% below the maximum rotational speed, meaning 19150 rpm (approximately 320 rotations per second).

3. NUMERICAL ANALYSIS

The numerical analysis was conducted using the 3D model and the Ansys 11 soft (Raghavan, 2008). As a first step, the mesh of the model was obtained for the entire rotor.

After this step being completed, the model is assigned a material, NCK18TDA, by defining all its properties which were given by Turbomeca in the material's fiche.

The selected analyse type is static structural. The rotor was constrained according to its connections with the shaft and the bearing, which is placed in front of the turbine.

Next step is the appliance of the loads, the centrifugal force and the pressure of the gases. This pressure was imported from a CFX result.

When all these steps are completed, and after the solver converges to a solution, the results can be visualised. Two of the results are the most important with respect to the topic of this paper.

One very important conclusion can be already withdrawn based on figure 3, that the maximum equivalent stress has a value extremely close to the one obtained in the theoretical calculus. That means the results obtained can be trusted, being validated through the comparison of two different methods.

Another very important result is the deformation of the rotor, especially at the tip of the blade. This dilatation is null at the centre of the rotor, growing towards its tips, where it reaches a maximum value of 82 [micro]m.

For a turbine rotor, this deformation can be consistent taking into account that the clearance at the tip of the blades should be as small as possible to decrease the fluid pressure losses. Once this maximum deformation was calculated, the clearance between the blades and the casing could be established.

Also the total deformation distribution gives the real geometry of the rotor while functioning at a certain speed. Therefore, it is recommended for further studies to make an analysis of the performances obtained for the rotor using its deformed geometry compared to the initial ones.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

4. CONCLUSION

This paper conducted the calculus of the equivalent stress and total deformation for a turbine rotor using two methods, a theoretical and a numerical one, simulating the loads and the restrains using dedicated software. The results were validated by comparison of the two methods. Regarding the equivalent stress, the maximum stress obtained on the airfoil was at its base at the trailing edge and on the disc near the bearing where the thickness is minim. In both cases, the maximum equivalent stress was below the allowable stress for the material considered. Another very important result was the total deformation on the rotor, maximum at the tip of the blade. Future work requires these results, especially the deformed geometry of the turbine, to compare its performances with the ones obtained for the original geometry. The next steps of this research project assume CFD analysis and experimentation on the original and deformed turbine and the determination of loss in efficiency due to loading. Therefore, this calculus is vital for a turbine rotor in terms of resistance and performances of the rotor.

5. REFERENCES

Carafoli, E. & Constantinescu, V. N. (1984). Dynamics of compressible fluids, Editura Academiei R.S.R., Bucharest

Manole, I. (1978a). Stress and vibration analysis of the aviation jet engine blades, Editura Academia Militara, Bucharest

Manole, I. (1978b). Stress and vibration analysis of the aviation jet engine discs, Editura Academia Militara, Bucharest

Raghavan, K. S. (2008). ANSYS Simulation of Flexible machine Elements and Practical Applications, Available from: 2008, Accesed on: 2008-04-25

Pimsner, V. (1984). Teoria si constructia sistemelor de propulsie (The theory and construction of propulsion systems), Institutul Politehnic Bucuresti, Bucharest

CUCIUMITA, C[leopatra] F[lorentina]; VILAG, V[aleriu]; PETCU, R[omulus]; BOGOI, A[lina] & STANCIU, V[irgil] *

* Supervisor, Mentor Tab. 1. Equivalent stress along the disc Equivalent stress [MPa] 367 346 470 357 77