Cryogenic turboexpander is an essential component to produce the refrigeration effect in various helium liquefaction system. The convergent nozzle and small-scale radial inflow turbine (turboexpander) are important components that are responsible for increasing the performance of the cycle. In this paper, an optimum preliminary design approach of the turbine and nozzle is explained using real gas properties. Initially, the Sobol method is used to determine the sensitivity indices and optimized range of ten important non-dimensional variables for better performance of the radial turbine. Three turboexpanders of a modified Collins cycle-based helium liquefaction system have been designed considering the optimized ranges. The proposed method improves the isentropic efficiency and power output of the turbine up to 3.86 % and 5.14 % respectively as compared to the initial design. Hereafter, a comparative three-dimensional numerical analysis is conducted to characterize the flow physics and thermal properties of three turboexpander systems (16 bar and 40 K, 6 bar and 20 K, and 16 bar and 10 K). The thermal and fluid flow properties such as temperature, Prandtl number, static enthalpy, entropy, velocity vectors, Reynolds number, turbulence kinetic energy, etc. are determined at different spans and streamwise locations. Moreover, the present numerical results are also verified with the experimental and numerical results obtained from the existing literature. The study highlights the optimal range of design variables for helium turbine, methodology for helium liquefaction system, and numerical analysis to understand the flow physics and thermal properties of helium near its boiling point.