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 应用科技  2020, Vol. 47 Issue (3): 51-57  DOI: 10.11991/yykj.201908020 0

### 引用本文

ZHANG Zhilian, WANG Lingyu, XU Kang, et al. Systematic numerical simulation of micro helium turbine expander[J]. Applied Science and Technology, 2020, 47(3): 51-57. DOI: 10.11991/yykj.201908020.

### 文章历史

Systematic numerical simulation of micro helium turbine expander
ZHANG Zhilian, WANG Lingyu, XU Kang, WU Bo, LYU Tao
School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102617, China
Abstract: For the design of helium turbine expander at present, there is neither complete, accurate design process, nor design system being formed, except the design method and step for each part. A smart digital design flow based on CAD/CAE/CFD is proposed to ensure safety, reliability and high efficiency in the operation of the micro helium turbine expander in the environment control system. Through the one-dimensional thermal calculation, two-dimensional aerodynamics design, three-dimensional aerodynamics analysis and strength check, three-dimensional modeling and rotor dynamics analysis, numerical simulation is carried out to design the micro helium turbine expander, and the design process is simulated systematically, to ensure that the design scheme can meet the design requirements of helium refrigeration system and provide the integrated technology for the design and manufacture of micro helium turbine expander.
Keywords: helium    turbine expander    micro    numerical simulation    system    aerodynamics    strength    rotor dynamics

1 微型氦透平膨胀机设计

 $\rho {\rm{ = }}\frac{{1 - {{\left( {{u_1}\varphi/\cos {\alpha _1}^\prime } \right)}^2}}}{{2{h_s}^\prime }}$

PR能量方程为

 $P = \frac{{RT}}{{{V_m} - b}} - \frac{{\alpha a}}{{V_m^2 + 2b{V_m} - {b^2}}}$ (1)

2 微型氦透平膨胀机的性能分析

2.1 运行效率

 $\frac{{\partial U}}{{\partial t}} + \nabla {F_1} + \nabla {F_V} = Q$

 ${v_t} = \frac{{{u_t}}}{\rho } = v \times 100\% \times{f_{v_1}}$

 $\begin{array}{c} \dfrac{{\partial v \times 100\% }}{{\partial t}} + W \cdot v \times 100\% = \\ \dfrac{1}{\sigma }\left\{ {\nabla \cdot \left[ {{v} + \left( {1 + {c_{b_2}}} \right)v \times 100\% \cdot \nabla v} \right] - {c_{b_2}}v \times } \right.\\ \left. {100\% \nabla v} \right\} + Q \end{array}$

 $\eta =\frac{1-{T}_{2}/{T}_{1}}{1-{\mathrm{\pi }}^{\left(k-1/k\right)}}$

B2B截面为相邻叶片间流体流动区域，图7分别给出5%、50%、95%叶高处B2B截面的相对马赫数、压力、流线分布云图。

2.2 运行安全性

 $U = 6\;350\left( {{W_1} + {W_2}} \right)/N$

 ${\rm{SM}} = 17\left( {1 - \frac{1}{{{\rm{AF}} - 1.5}}} \right)$

2.3 运行可靠性