SoftwareApplication Of Evolutive Algorithms and Statistical Analysis in the Numerical Optimisation of an Axial Compressor
Fig.1 - View of the axial compressor
The purpose of this work is to optimise the stator shape of an axial compressor, in order to maximise the global efficiency of the machine, fixing the rotor shape. We have used a 3-D parametric mesh and the CFX Tascflow code for the flow simulation.
To find out the most important variables in this problem, we have run a preliminary DOE series of designs, whose results have been analysed by a statistic tool. This analysis has helped us to choose the most appropriate variables and their ranges in order to implement the optimisation algorithm more efficiently and rapidly.
Fig.2 - View of the mesh
For the simulation of the fluid flow through the machine, a cluster of 12 processors has been used. The rotor and stator blades are realised through the use of NACA 65-(cl0)10 profiles (Naca, 1958). These profiles are the classical low subsonic compressors ones, characterised by an arc of circle as camber and by a maximum thickness of 10% of the chord length. The multi-block structured mesh, completely parametric, is defined by four main blocks. The two central ones contain the rotor and stator blade geometry, both defined properly by four sections. As the machine is symmetric and the lateral surfaces of the two blocks are defined as periodic boundaries, the dimension of these blocks is influenced by the blade number of the rotor and of the stator. We apply a boundary condition of mass flow fixed on the inlet block (3.6 kg/s as defined by the design point conditions) and a static pressure boundary on the outlet, fixed to the atmospheric value.
| Stespan1 | Stespan2 | Stespan3 | |
| Nblade | (16,23) | (16,19) | 18 |
| Thick | (0.5,-1.2) | 1 | 1 |
| Stagg | (-50,50) | (-50,0) | (-60,-25) |
| Ar | (1.5,2,5) | 2 | 2 |
| Cl1 | (-0.4,0.4) | (0,0.5) | (0,0.25) |
| Psi1 | (-5,5) | (0,5) | (2.5,5) |
| Cl2 | (0.1,0.5) | 0.1 | 0.1 |
| Psi2 | (1,3) | (2,3) | (2,2.5) |
| Cl3 | (0.1,0.5) | 0.1 | 0.1 |
| Psi3 | (1,3) | 1 | 1 |
| Cl4 | (0.1,0.5) | 0.1 | 0.1 |
| Psi4 | (1,3) | (2,3) | 2.5 |
| Bezier1 | (0,1) | (0,0.5) | 0.25 |
| Bezier2 | (-0.25,0.25) | (-0.25,0) | (-0.35,-0.1) |
| Bezier3 | (0,1) | (0,0.5) | 0.25 |
| Bezier4 | (-0.25,0.25) | (0,0.25) | (0,0.125) |
Fig.3 - Variable ranges in optimisation steps
An initial number of 16 variables has been chosen for the stator blade shape parameterisation, that are: number of blades, aspect ratio (from which the chord length is derived), 4 Bezier points co-ordinates used to modify the camber curve, the thickness scale factor, the blade angle defined for 4 sections from the hub to the shroud and the curvature of the profile defined by a cl coefficient for each one of the sections, and the stagger or shifting ratio of the barycentre line in tangential direction.
As it is possible to see in fig.3, we have run an initial DOE series of 64 designs (step1), using a reduced factorial Algorithm, and the initial variables range is indicated. Using t-Student statistical post-processing, 6 variables have been found to have a significance percentage of Fig. 3-Variable ranges in optimisation steps less than 50% for the optimisation objective (efficiency), and for this reason they have been kept fixed as constant in a second step (red in fig.3). The range of variation for the other 10 variables has been changed accordingly to the direction of the best efficiency values (i.e. if the variable is in positive correlation with efficiency, the upper boundary for the variable has been raised up). After a second DOE series of other 64 design (step2), a new statistical analysis by t-Student revealed that only 6 variables were still significant (above 50%), and then a BFGS refinement algorithm has been initialized keeping as constant the other 10 variables and requiring only 38 further CFD computations to optimise the efficiency up to 0.948, against 0.85 of the Fig.4 Comparison between original and original configuration.
Fig.4 - Comparison between original and optimised blade sections
References
[1]
R.J. Del Vecchio. Design of Experiments. Hanser Understanding Books, 1997. National Advisory commitee for aeronautics- report 1368, 1958.
[2]
C.Poloni, A.Giurgevich, L.Onesti, V.Pediroda. Hybridization of a multiobjective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics. 403-420. Comput. Methods Appl. Mech.Engrg.186 , 2000.