1 Introduction

The use of renewable energies has been the subject of many research works [1, 2]. Nowadays, the centrifugal compressors are used when looking for a high pressure ratio with a low volume flow. The limitation of the pressure ratio now comes from mechanical stresses, thermal stresses and materials rather than the flow. These causes play a significant role in the problem of increasing the efficiency of centrifugal compressors which has become a major issue for designers. Centrifugal compressors must always be more efficient. In such problems the consideration of thermo mechanical coupling is essential for the understanding of the failure mechanisms of the compressor blades. The behavior of the centrifugal compressor is significantly affected by the physical or construction angle β₂ at the outlet of the blades. The interest of this thermo mechanical study on the blade consists in discovering the distribution of the stress fields and displacements as well as the flows of heat while varying the blade outlet angle β₂. A simulation of three-dimensional thermo mechanical behavior of a centrifugal compressor blade is carried out by means of calculation codes based on the finite element method ”Abaqus”. The research works that had been undertaken and which have a direct or indirect relation and impact on the purpose of the present work can be summarized as follows:

A numerical analysis of a centrifugal compressor blade subjected to loading under multiple operating conditions with the CFX code [3] was mentioned by Xie et al. Jiao et al. [4] performed a numerical simulation of the flow in a centrifugal compressor blade based on ANSYS Work-bench. Zheng et al. [5] tried to analyze the effect of temperature and pressure on the stresses in an axial and centrifugal compressor combined with CFX. Gurlovleen et al. [6] worked on modeling and stress simulation in a centrifugal compressor. Setiya et al. [7] performed in their work a structural analysis in a blade under the load of an aircraft compressor using the ANSYS code while changing the material. An experimental investigation was carried out in the framework of the cracking of the wheel of a centrifugal compressor by Li et al. [8] in 2013. The study of the blade rupture was evoked by Xiaolong Zhang et al. [9] in 2015. In general, most of the works done were focused on the flow studies and the performance of centrifugal compressors. The originality of this work is an analysis of the thermo mechanical behavior with the Abaqus code of a centrifugal compressor blade with shape change by means of the outlet angle β₂. Finally, it is understood that the prediction of the stress fields have a crucial role in the dimensioning as well as the manufacture and the choice of constituent material in order that the blade retains the required mechanical qualities from the point of view of resistance contributing to a better performance of centrifugal compressor.

2 The theory of compressor

2.1 Velocity triangles

At the compressor inlet and from Figure 1 (a and b),we can define the following parameters:

Figure 1

Velocity triangles (input-output) in a centrifugal compressor

• The absolute velocity V₁ such that: V1=qvs=qmρ1s1

• The training velocity U₁ such that: U₁ = R₁ω

• The triangle then closes by the relative velocity W₁ which is the speed that would see an observer placed on the wheel with, in general: v→1=u→1+w→1

• For the centrifugal compressor Figure (a):

s1=2πR11

The velocityv₁ is radial.

At the exit of the wheel Figure 1 (a and b),we also have:

1. The absolute velocity V₂ decomposing in velocity V_2m (projection of V₂ on the radius) and in tangential velocity V_2u (projection of V₂ on the tangent to the wheel);

2. The drive velocity U₂ such that:

   U2=R2ω;

3. The relative velocity W₂ with:

v→2=u→2+w→2

2.2 Various blade shapes of a mobile compressor wheel

They are represented as follows according to the outlet angle β₂ as shown in the Figure 2:

Figure 2

Various blade shapes of a mobile compressor wheel

3 Creation of a 3D blade shape in Abaqus

The geometric shape of the centrifugal compressor wheel created in the Abaqus Software Part Module. It is represented by Figure 3 as follows:

Figure 3

Centrifugal compressor wheel: (a) open; (b) closed

Figure 4 shows the location and position of the blades on the lower part of the wheel.

Figure 4

The location and position of the blades on the lower part of the wheel

The geometric shape of the 3D blade of the centrifugal compressor that will be studied is represented by the following configuration:

4 Property of the material

The definition of material properties has been introduced in the ”Property” module. The following Table 1 includes the mechanical characteristics of the material of the blade (Aluminum):

5 Boundary conditions and loading

1. The fixing (embedding) was performed at the trailing edge section (Figure 6).

   

   Figure 5

   Geometry of the blade of the centrifugal compressor under study

   

   Figure 6

   Loading and boundary conditions

2. The load is a combination of both the centrifugal load and the aerodynamic load that has been applied to the blades of the centrifugal compressor wheel as a static pressure load.

   A pressure of 2500 MPa was applied to the intrados of the blade.

3. With an inlet temperature equal to: Te = 30^∘C and an outlet temperature equal to: Ts = 20^∘C. The blade thickness is equal to 8mm.

6 Model mesh

This module contains all the necessary tools to generate a finite elements mesh on an assembly. The mesh using 4-node volume linear tetrahedral elements has been adopted for the model under study. In this volume element, no simplification hypotheses were assumed on the deformations and the constraints.

Figure 7

Mesh of blade

7 Results and discussions

An attempt has been made to simulate the thermo mechanical behavior of a centrifugal compressor blade. At the blade an inlet temperature and an outlet temperature were imposed which were coupled with a static pressure estimated to be equal to the resultant of the centrifugal and aerodynamic loads. In this simulation the geometry of the blade has been changed by varying its outlet angle β₂.We have worked with the angles of the following blade: blade lying backward β₂ = 75^∘, radial blade β₂ = 90^∘ and blade lying forward β₂ = 120^∘. Through this simulation we try to find the impact of the change of the outlet angle β₂ on the response of the blade in this case of behavior. The visualization of the displacements, the stresses and the flux distributions for outlet angle β₂ = 75^∘, β₂ = 90^∘ and β₂ = 120^∘ are shown respectively in (Figures 8 to 10) which allow us to deduce the following results:

Figure 8

Displacement fields for: (a) β₂ = 75^∘; (b) β₂ = 90^∘; (c) β₂ = 120^∘

Figure 9

Von Mises stress fields for: (a) β₂ = 75^∘; (b) β₂ = 90^∘; (c) β₂ = 120^∘

Figure 10

Heat flux fields for: (a) β₂ = 75^∘; (b) β₂ = 90^∘; (c) β₂ = 120^∘

8 Conclusion

In this study the problem has been presented in thermo mechanical coupled form since the geometry is a function of the temperature field which is itself influenced by the pressure forces. The impact of the change of the outlet angle β₂ on the holding of the blade (constraint of Von Mises, displacement) and on the flow of heat was discussed. A comparison with respect to the obtained thermo mechanical results for the three outlet angles, we can conclude that:

1. The angle β₂ = 120^∘ (the forward lying blade) gives a better result vis-à-vis the thermo mechanical resistance of the blade. Also the displacements are lower compared to the two other cases. This is in good agreement with the result found which deals with the influence of the angle β₂ on the performance of the compressor on the compression ratio. On the other hand, high power consumption with a less flow rate was observed for this same angle. Moreover, the outlet angle β₂ = 75^∘ is the most favorable for better performances and at the same time the concentrations of stresses and maximum displacements are acceptable according to the results found. The outlet angle β₂ = 90^∘ of the blade gives good performance but there can be a risk of breaking the fact that the Von Mises maximum stresses can exceed the limit of resistance of the material easily.