Abstract
A Differential Evolution (DE) algorithm is used to optimize the backface geometry of a centrifugal impeller, with respect to the calculated maximum stress, in order to extend its overspeed limits. A detailed fully parametric 3D model of the impeller was initially constructed using CATIA V5; the backface geometry is defined using a Bezier curve with its parameters used as design variables for the present optimization procedure. The stress analysis is performed using the Generative Structural Analysis workbench of CATIA. Two different versions of the same DE algorithm are utilized in this work. The first one was developed in order to cooperate with different analysis software, in the form of executables or batch files, which are automatically called to evaluate each candidate solution; for the problem at hand, CATIA software is used to analyze each solution in a batch optimization procedure. The values of the independent design variables of each solution are provided to CATIA by using specific macro commands in batch mode, thus automatically updating the geometry, along with the corresponding mesh and the following stress calculation, in an automated manner. As an alternative approach to the same optimization problem, a DE plug-in, fully compatible with CATIA has been developed, utilizing exposed objects of CATIA (open CAA V5 automation architecture), which provide all the necessary properties and methods to interact directly with a part or analysis document through the VBA programming language. This plug-in also features a friendly and ‘easy to use’ graphical interface, which enables the user to manipulate the part’s design and analysis parameters, as well as the objective function, in order to specify the problem as suited. Optimization results are presented and compared with the results provided by the Simulated Annealing (SA) optimizer embedded in CATIA. The advantages of the proposed procedures are discussed with respect to the alternative approach.
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Abbreviations
- A,B,C:
-
Three members of the current population different to each other (DE optimization procedure).
- Cr :
-
DE’s second control parameter (crossover parameter).
- d:
-
Density.
- E:
-
Young’s modulus.
- F:
-
DE’s first control parameter (mutation parameter).
- f:
-
The objective function in the optimization procedure.
- G:
-
Generation.
- i:
-
Index referring to the member of the population in the optimization procedure.
- j:
-
Index referring to the design variable in the optimization procedure.
- k:
-
A random integer within [1,n param ].
- N:
-
Impeller’s rotational speed.
- nparam :
-
Number of design variables in the optimization procedure.
- r:
-
A uniformly distributed random value within [0, 1].
- X = (x1,x2,…,x{fx186-01}):
-
The vector of design variables in the optimization procedure.
- X ′(G+1)i :
-
The temporary vector of design variables of thei th member of the population during the(G+1) th generation.
- x (L)j , x (U)j :
-
Lower and upper boundaries of thej th design variable.
- x (G)i,j :
-
The value of thej th design variable of thei th member of the population during theG th generation.
- v:
-
Poisson’s ratio.
- σvm :
-
Von Mises equivalent stress.
- σ maxvm :
-
Maximum value of von Mises stress.
- σs :
-
Yield strength.
References
Aungier R.H. (2000). Centrifugal compressors — A Strategy for aerodynamic design and analysis. ASME Press: New York.
Cameron D.W., Geise P.R., Abbott J.S. (2002). Establishing overspeed limits for centrifugal compressor impellers. DRESSER-RAND Technical Papers, Turbo Products (TP006), New York.
Dornberger R., Stoll P., Buche D., Neu A. (2000). Multidisciplinary turbomachinery blade design optimization. Paper: AIAA-2000-0838.
Gerteisen E.A., Bobach E.A., Nawotki A.C. (2004). Issues of the CAD-CAE interface in optimization. CD Proceedings of the ERCOFTAC Conference in Design Optimization: Methods and Applications. Athens, Greece.
Japikse D. (2000). Decisive factors in advanced centrifugal compressor design and development. Proceedings of the International Mechanical Engineering Congress & Exposition (IMechE).
Japikse D., Baines N., Platt M.J. (2000). Design study of a low-cost LOX turbopump. Proceedings of the 1st Joint Army-Navy-NASA-Air Force (JANNAF) Modeling and Simulation Subcommittee Meeting, Monterey, CA.
Japikse D. (2001). Progress and potential in agile engineering for turbomachinery. Plenary presentation at the ASME 2001 Fluids Engineering Division, New Orleans, LA.
Japikse D., Platt M.J. (2004). Optimization in component design and redesign. Proceedings of the 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii.
Japikse D., Oliphant K.N. (2005). Turbomachinery modeling: explicit and implicit knowledge capturing. Proceedings of GT2005, ASME Turbo Expo 2005: Power for Land, Sea, and Air, Reno-Tahoe, Nevada, USA.
Nikolos I.K. (2004). Inverse design of aerodynamic shapes using differential evolution coupled with artificial neural network. CD Proceedings of the ERCOFTAC Conference in Design Optimization: Methods and Applications, Athens, Greece.
Oi M., Suzuki M., Matsuura N. (2000). Structural analysis and shape optimization in turbocharger development. Proceedings of the 2nd MSC Worldwide Automotive User’s Conference.
Osborne C., Platt M.J., Weitzman P.S., Denus K. (2003). Multidisciplinary optimization applied to a turbocharger compressor impeller. Proceedings of the 9th International Conference of Rotary Fluid-Flow Machines, Rzeszow, Poland.
Platt M.J., Yu M.M., Marsh M. (2003). Multidisciplinary optimization of a LH2 turbopump design in agile engineering environment. Proceedings of the AIAA Joint Propulsion Conference and Exhibit, Huntsville, Alabama. Paper: AIAA-2003–4765.
Price K.V., Storn R.M., Lampinen J.A. (2005). Differential evolution, a practical approach to global optimization. Springer: Berlin/Heidelberg.
Samareh J.A. (1999). A novel shape parameterization approach. Report No. NASA-TM-1999-209116.
Samareh J.A. (2001). Survey of shape parameterization techniques for high-fidelity multidisciplinary shape optimization. AIAA Journal, 39(5), pp. 877–884.
Shahpar S. (2004). A review of automatic optimization Applications in aerodynamic design of turbomachinery components. CD Proceedings of the ERCOFTAC Conference in Design Optimization: Methods and Applications, Athens, Greece.
Storn R., Price K. (1995). DE — a simple and efficient adaptive scheme for global optimization over continuous space. Technical Report TR-95-012, ICSI.
Vaidyanathan R., Santhanam S., Ramamurti V. (2003). Static and dynamic analysis of an aerofoil bladed disc using the concept of cyclic symmetry. Communications in Numerical Methods in Engineering, 19, pp. 313–324.
Watanabe H., Okamoto H., Guo S., Goto A., Zangeneh M. (2004). Optimization of microturbine aerodynamics using CFD, inverse design and FEM structural analysis (2nd Report: Turbine Design). Proceedings of ASME Turbo Expo 2004, Vienna, Austria.
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Valakos, I.M., Ntipteni, M.S. & Nikolos, I.K. Structural optimization of a centrifugal impeller using differential evolution in CATIA™ environment. Oper Res Int J 7, 185–211 (2007). https://doi.org/10.1007/BF02942387
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DOI: https://doi.org/10.1007/BF02942387