Multi-Objective Optimization of Aerodynamic Performance for a Small Single-Stage Turbine

Document Type : Regular Article


School of Power and Energy, Northwestern Polytechnical University, Xi’an, Shanxi, 710129, China



In order to improve the performance of single-stage turbines, blade profiling optimization was conducted for the guide vane and rotor under design condition. Support vector regression (SVR) and non-dominated sorting genetic algorithm-II (NSGA-II) were used to execute the optimization, with the objective of maximizing the efficiency and total pressure ratio of single-stage turbines. The gas turbine chosen for the initial study was the KJ66, which is one of the most robust and primitive small gas turbine designs available. The influence mechanism of the stator and rotor profiling on flow field and performance was discussed. The results revealed that compared with the prototype, the adiabatic efficiency increased by 5.95% and the total pressure ratio increased by 0.9%. Furthermore, the matching of flows between the stator blade and rotor blade obviously improved. The optimized guide vane suppressed the flow separation by increasing the leading edge and improving the distribution of the inlet angle of attack. The load distribution of rotors with a 50% spanwise position changed from the original "C" loaded to post-loaded. The leading load obviously decreased, and the angle of attack was smaller than that of the prototype, which effectively weakened the flow separation at the leading edge of the rotor. Compared with the original rotor, the higher lean angle and pressure ratio of the turbine stage also improved. However, the leakage loss near the shroud of the rotor increased, which led to decreased efficiency.


Ainley, D. and G. Mathieson (1951). An examination of the flow and pressure losses in blade rows of axial-flow turbines. Technical report 1-35, HMSO.##
Arora, J. (2004). Introduction to optimum design (Elsevier).##
Balje, O. (1968). Axial turbine performance evaluation. Part A—Loss-Geometry relationships. Journal of Engineering for Gas Turbines and Power 90, 341–348.##
Basson, J. (2014). Design methodology of an axial-flow turbine for a micro jet engine. Ph. D. thesis, University of Stellenbosch, South Africa.##
Benner, M. W., S. A. Sjolander and S. H. Moustapha (2006a). An empirical prediction method for secondary losses in turbines-part I: A new loss breakdown scheme and penetration depth correlation. Journal of Turbomachinery 128(2), 273-280.##
Benner, M. W., S. A. Sjolander and S. H. Moustapha (2006b). An empirical prediction method for secondary losses in turbines-part II: A new secondary loss correlation. Journal of Turbomachinery 128(2), 281-291.##
Benner, M. W., S. A. Sjolander and S. H. Moustapha (2004). Measurements of secondary flows downstream of a turbine cascade at off-design incidence. In Proceeding of ASME TURBO EXPO 2004, Vienna, Austria, GT2004-53786.##
Chen, L. H. (2007). Aerodynamic optimization design of compressor blade based on neural network and genetic algorithm. Ph. D. thesis, Northwestern Polytechnical University, Xi an, China.##
Craig, H. and H. Cox (1970). Performance estimation of axial flow turbines. Proceedings of the Institution of Mechanical Engineers 185, 407–424.##
Davis, L. (1991). Handbook of genetic algorithms. Handbook of Genetic Algorithms.##
Deb, K., S. Agrawal, A. Pratap and T. Meyarivan (2000). A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization: NSGA-II. Lecture Notes in Computerence 1917, 849-858.##
Dunham, J. and P. M. Came (1970). Improvements to the ainley-mathieson method of turbine performance prediction. Journal of Engineering for Gas Turbines and Power 92, 252–256.##
Ennil, A., R. K. Al-Dadaha, S. Mahmouda and A. M. Al-Jubori (2018, January). Optimization of small scale axial air turbine using ansys cfx. In Proceedings of 22 nd the IIER international conference, London, United Kingdom.##
Ferrari, V. (2008). Libsvm : A library for support vector machines. ACM Transactions on Intelligent Systems and Technology.##
Horn, J. (1994, July). A niched Pareto genetic algorithm for multiobjective optimization. In Proceedings of the first IEEE conference on evolutionary computation, IEEE.##
Huang, M. X. (2019). Research on Blade Optimization Design of Analysis Code Using Artificial Neural Network and Genetic Algorithm. Master's thesis, Nanjing University of Aeronautics and Astronautics, Nanjing, China.##
Kacker, S. C. and U. Okapuu (1982). A mean line prediction method for axial flow turbine efficiency. Journal of Engineering for Power 104,1 (1).##
Li, T. Y. (2019). Three-dimensional Numerical Simulation of An Entire Micro Turbojet Engine. Ph. D. thesis, Dalian University of Technology, China.##
Massardo, A., A. Satta and M. Ma (1990). e axial flow compressor design optimization. part ii: through-flow analysis. Journal of Turbomachinery 112(3), 405-410.##
Mckay, Beckman and Conover (2000). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics  42(1), 55-61.##
Mohamed, M. H. and S. Shaaban (2013). Optimization of blade pitch angle of an axial turbine used for wave energy conversion. Energy 56, 229–239.##
Moroz, L., Y. Govoruschenko, L. Romanenko and P. Pagur (2004, June). Methods and tools for multidisciplinary optimization of axial turbine stages with relatively long blades. In Asme turbo expo: Power for land, sea, and air, Vienna, Austria, GT2004-53379.##
Moustapha, H., A. Cooling, M. F. Zelesky and D. Japikse (2003). Axial and radial turbines. Concepts NREC.##
Moustapha, S. H., S. C. Kacker and B. Tremblay (1990). An improved incidence losses prediction   method for turbine airfoils. Journal of Turbomachinery 112, 267–276.##
Mohamad, S. K., R. Mehrdad, S. Saeed, H. Patrick and N. Ahmad (2021). Robust optimization of the NASA C3X gas turbine vane under uncertain operational conditions. International Journal of Heat and Mass Transfer 164.##
Müller, K. R., A.J. Smola, G. Ratsch, B. Schlkopf, J. Kohlmorgen and V. Vapnik (1997, October). Predicting time series with support vector machines. In ICANN ’97: Proceedings of the 7th international conference on artificial neural networks, Springer, Berlin, Heidelberg.##
Murray, P. W. (2009). Microturbine for micro-cogeneration application. Ph. D. thesis, Queen's University, Canada.##
Park, J. S. (1994). Optimal Latin-hypercube designs for computer experiments. Journal of Statistical Planning & Inference 39, 95–111.##
Picus, D. (1983). Computed tomography in the staging of esophageal carcinoma. Radiology 146, 433–438.##
Tian, B. L. (2003). A Survey of the Development of Engines for the Unmanned Aircraft and the Cruise Missile in the World. Aeroengine 29(4), 51-54.##
Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization. Ph. D. thesis, Cambridge, England.##
Smith, S. F. (1965). A simple correlation of turbine efficiency. Aeronautical Journal 69, 467–470.##
Sobol, I. (1990). On sensitivity estimation for nonlinear mathematical models. Keldysh Applied Mathematics Institute: 112–118.##
Sobol, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation 55, 271–280.##
Sudret, B. (2008). Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety 93, 964–979.##
Vapnik, V., S. E. Golowich and A. Smola (2008). Support vector method for function approximation, regression estimation, and signal processing. Advances in Neural Information Processing Systems 9, 281–287.##
Wakeley, J. and J. Hey (1997). Estimating ancestral population parameters. Genetics 145, 847–855.##
Yang, W. and R. Xiao (2014). Multiobjective optimization design of a Pump–Turbine impeller based on an inverse design using a combination optimization strategy. Journal of Fluids Engineering 136, 249–256.##
Zhao, W. and X. N. Wen (2003). Applied Statistics Course. Xidian University, Xian, China.##
Zhou, L., F. Xiang and Z. Wang (2018). CFD investigation on the application of optimum non-axisymmetric endwall profiling for a vaned diffuse. Journal of Applied Fluid Mechanics 11, 1703–1715.##
Zhu, J. and S. A. Sjolander (2005, June). Improved profile loss and deviation correlations for axial-turbine blade rows. In Asme turbo expo: Power for land, sea, and air, Reno-Tahoe, Nevada, USA, GT2005-69077.##
Zitzler, E., K. Deb and L. Thiele (1999). Comparison of multiobjective evolutionary algorithms on test functions of different difficulty.##