Analysis and Experimental Verification of Similitude Modeling Method for Helium Turbo-expander

Because the test platform and supporting facilities for cryogenic performance testing of helium turbo-expanders under design conditions are difficult to meet, and the design conditions are difficult to achieve, the expander is usually tested in air to test its performance, and then the performance of the expander at cryogenic temperature is obtained by similarity modeling method. By analyzing the flow and energy conversion process of the working fluid in the turbo-expander, it is found that the characteristic ratio U₁/C_S, expansion ratio P₁/P₂, Mach number Ma, and Reynolds number Re are the key parameters that affect the performance of the expander. Based on similar theories and the calculation results of the turbo-expander performance prediction program under variable conditions, four groups of similarity criteria were selected with U₁/C_S as the first similarity criterion and Ma, k⁻¹ Ma⁻², Ma·k⁻¹, k·Ma² as the second similarity criterion. Based on the calculation results of computational fluid dynamics, the similarity criterion with the smallest modeling error is selected from the four sets of similarity criteria, namely the combination of U₁/C_S and Ma·k⁻¹. Theoretical calculation results show that the maximum error of isentropic efficiency between helium and air turbo-expanders before and after similar modeling is within ±1.4%, and it also has a good model in terms of internal flow field prediction （Mach number, velocity distribution）, etc. Finally, experimental data of isentropic efficiency of helium turbo-expander under set working conditions and air turbo-expander under similar modeling conditions show that the variation trend is consistent, and the error is less than 1%.