Thermodynamics model updating of cryogenic wind tunnel diffuser based on response surface method
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摘要: 低温风洞运行过程消耗大量液氮和电力，洞体结构产生附加热应力和热变形，建立可靠的低温风洞热力学模型对研究风洞运行安全性和经济性是必不可少的。以低温风洞扩散段为方法研究对象，建立有限元热力学模型，为提高热力学模型和实际模型的相关性，使用响应面法对有限元热力学模型多个参数进行修正。通过对比分析温度、应力监测点试验数据和仿真数据的差别，确定驻室锥形体内表面对流换热系数为待修正参数；使用中心复合试验设计生成有限元热分析样本空间，以温度、应力监测点试验数据和仿真数据的残差均方和为考核指标，在样本空间内对残差均方和进行非线性回归分析，建立残差均方和的响应面模型；以所有监测点残差均方和总和为目标函数，在样本空间内进行多目标非线性优化分析，得到最优解；验证修正后的热力学模型，结果表明：（1）基于响应面法的热力学模型修正是可行的；（2）修正后的热力学模型分析数据与试验数据吻合性提高，并且适用于其它降温试验。Abstract: A great amount of liquid nitrogen and power is consumed to run the cryogenic wind tunnel. The temperature variation of the wind tunnel may cause excessive thermal deformation and stress, which can have a significant influence on the wind tunnel safety. Thus, it is indispensable to develop the reliable thermodynamic model of the cryogenic wind tunnel for evaluating the safety, performance and economy efficiency. In this paper the cryogenic wind tunnel diffuser is studied and its thermodynamic model is established based on the finite elements method. Moreover, the response surface method is adopted to correct some model parameters for purposes of improving the consistency between the finite elements model and the actual model. Firstly, according to the differences between the test data and simulation results the internal surface convective heat transfer coefficients of the plenum tapered shell are chosen as the parameters that need to be corrected. Secondly, the sample space of the finite elements thermal analysis is generated by using the central composite experiment design. Thirdly, the nonlinear regress analysis of the residual mean square is carried out in the sample space to establish the response surface model. Finally, the residual mean square sum of all monitor results is taken as the objective function and then the thermodynamic model is analyzed and optimized by means of the nonlinear multi-object optimization algorithm. The model verification results show that the updated thermodynamic model is highly consistent with the actual model and it is feasible to correct the thermodynamic model with the response surface method.
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表 1 修正目标水平表(单位：W/(m2·K))
Table 1 Modal updating parameters and level
Level -2 -1 0 1 2 h 2 7.75 13.5 19.25 25 
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表 2 参数修正结果(单位：W/(m2·K))
Table 2 Model updating result
Parameter h1 h2 h3 h4 h5 Updated level 1.88 -1.95 -1.55 -1.66 0.35 Updated h 24.34 2.32 4.59 3.95 15.48
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表 3 试验应力值和修正应力值误差分析
Table 3 Stress error analysis of test and updated model
Time/s Update value/MPa Test value/MPa Error/% 1000 1.90 15.35 107.8 2000 47.74 37.07 28.8 3000 53.88 43.16 24.8 4000 59.20 48.27 22.7 5000 73.83 68.44 7.9 6000 90.79 88.56 2.5
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