GL模型中延迟时间的影响

Study on effect of relaxation time in GL model

为求解同时考虑时空耦合因素和松弛时间因素的高响应速度传热Green and Lindasy（GL）方程，设计了一个半无限长杆的一维GL导热问题，运用Laplace变换获得其解析解．通过比较无限长杆上短时间内的温度、应变、应力分布的解析解与数值仿真结果，得出不考虑松弛时间的温度分布的最大偏差不超过10K，应变和应力分布的最大偏差为5％。依据此结论，在应用GL模型研究高温燃气加热铝质活塞的低周热疲劳问题时，可以忽略松弛时间对仿真结果的影响以简化计算，从而解决了求解极小松弛时间（10^-13～10^-11 s）的多维GL方程的困难．

To solve the super high speed Green and Lindsay （GL） heat transfer model considering relaxation time factors and space-time coupling factors simultaneously, a one-dimensional GL heat transfer process on a half infinite pole was designed. Such an ideal process was solved theoretically through Laplace transformation. Thermal behaviors of the pole such as temperature, strain and stress distribution were compared between analytic results and simulation results. The results showed that the maximum error of temperature was lower than 10 K and 5 % for stress distribution when omitting the impact of relaxation factor in solving GL model. Based on the conclusion, the relaxation factor can be omitted in applying GL model for simulation of high temperature gas heating an aluminum piston.