Semnan University Press Journal of Modeling in Engineering 2008-4854 Articles in Press 2026 05 17 Numerical Analysis of Stable Tellurium Isotope Separation in the Square Cascade Numerical Analysis of Stable Tellurium Isotope Separation in the Square Cascade 10623 10.22075/jme.2025.37136.2826 FA Fatemeh Mansourzadeh Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran Mohammad Mahdi Shadman Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran Journal Article 2025 03 12 In this article, the modeling of a square cascade with a gas centrifuge for the separation of multicomponent isotopes has been discussed. In this regard, a calculation code has been developed in MATLAB software. Maximizing the value of the product recovery coefficient during one year of using the cascade by considering the maximum concentration of the desired isotope in the product stream (99.9%) as the objective function has been evaluated and studied. In this code, cascade feed flow rate, machine feed flow rate, cascade cut, feed point, and cut of stage are defined as optimization variables for several simultaneous steps. The results show that the D function will be a suitable tool to determine the number of stages in the cascade, and in this way, the computational cost and the time spent to determine the structure of the square cascade will be greatly reduced. Assuming that a centrifuge machine with a separation factor α0=2.506×f-0.229 is used in a square chain to separate the third isotope of tellurium from among 8 isotopes of natural feed, it is suggested to use the D function of the cascade with 50 stages. Based on the optimization calculations, the recovery rate for the chain with 50 stages will be 86.5%, which is 85.3% for the cascade with 40 stages, and this is a confirmation for choosing the right method and using the D function. In this article, the modeling of a square cascade with a gas centrifuge for the separation of multicomponent isotopes has been discussed. In this regard, a calculation code has been developed in MATLAB software. Maximizing the value of the product recovery coefficient during one year of using the cascade by considering the maximum concentration of the desired isotope in the product stream (99.9%) as the objective function has been evaluated and studied. In this code, cascade feed flow rate, machine feed flow rate, cascade cut, feed point, and cut of stage are defined as optimization variables for several simultaneous steps. The results show that the D function will be a suitable tool to determine the number of stages in the cascade, and in this way, the computational cost and the time spent to determine the structure of the square cascade will be greatly reduced. Assuming that a centrifuge machine with a separation factor α0=2.506×f-0.229 is used in a square chain to separate the third isotope of tellurium from among 8 isotopes of natural feed, it is suggested to use the D function of the cascade with 50 stages. Based on the optimization calculations, the recovery rate for the chain with 50 stages will be 86.5%, which is 85.3% for the cascade with 40 stages, and this is a confirmation for choosing the right method and using the D function.