An optimization design method is developed, which is motivated by the optimal design of a cryogenic liquid turbine (including an asymmetric volute, variable stager vane nozzles, shroud impeller and diffuser) for replacement of the Joule-Thompson throttling valve in the internal compression air-separation unit. The method involves mainly three elements: geometric parameterization, prediction of objective function, and mathematical optimization algorithm. Traditional parameterization approach is used for the geometry representation, while some novel work in the latter two aspects (i.e. objective function evaluation and optimization algorithm) is done to reduce the computing time and improve the optimization solution. A modified Cooperative Coevolution Genetic Algorithms (CCGA) is developed by incorporating a modified variable classification algorithm and some new self-adapted GA operators, which help to enhance the global search ability with an excessive number of optimization variables. Design of Experiment (DOE) is carried out to initialize the kriging approximation model, which is used to approximate the time-costly objective function. Then the CCGA is started, and once a potential superior individual is found, a decision will be made by the in-house code on whether or not it needs a updating. If required, the true objective function prediction based on the real model will be conducted and the obtained value of objective function will be used to update the kriging model. In such a way, the CCGA can complete its optimal searching with a limited number of real evaluations for objective function. All the above features are integrated into the optimization framework and encoded for the optimal turbine design. In addition, CFD software ANSYS CFX is used for the real objective function evaluations, and a well-organized batch code is developed by the authors for calling the CFD simulation which helps to promote this automation of the optimization process. For validation, the optimization method is used to solve some classical mathematical optimization problems and its effectiveness is demonstrated. The method is then used in the optimal design of the cryogenic liquid turbine stage, it is demonstrated that the optimal design method can help to reduce significantly the searching time for the optimal design and improve the design solution to the liquid turbine.

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