A regularization method for the inverse design of solidification processes with natural convection |
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| Affiliation: | 1. Mechanical Engineering Department, The University of Alabama, 35487, United States;2. Department of Mechanical Engineering, Michigan State University, United States;1. School of Energy and Power Engineering, Chongqing University, Chongqing 400044, PR China;2. Key Laboratory of Low-grade Energy Utilization Technologies and Systems, Chongqing University, Ministry of Education, Chongqing 400044, PR China;1. State Key Laboratory of Frozen Soils Engineering, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China;2. University of Chinese Academy of Sciences, Beijing, 100049, China;3. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, 730050, China;1. School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, PR China;2. Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, PR China;1. School of Power Engineering, Chongqing University, Chongqing 400044, PR China;2. Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400044, PR China |
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| Abstract: | An inverse algorithm is developed for the design of the solidification processing systems. The algorithm entails the use of the Tikhonov regularization method, along with the L-curve method to select an optimal regularization parameter. Both the direct solution of moving boundary problems and the inverse design formulation are presented. The design algorithm is applied to determine the optimal boundary heat flux distribution to obtain a unidirectional solid–liquid interface in a 2-D cavity. The inverse calculation is also performed with a prescribed sinuous solid–liquid interface. To this end, a whole time-domain method and a sequential method are used and evaluated. The L-curve based regularization method is found to be reasonably accurate for the purpose of designing solidification processing systems. We also found that the sequential method with appropriately selected time domains is comparative to the whole time-domain method. |
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