Research On Micro-gas Film Of Spiral Groove Dry Gas Seals Based On Boundary Conditions Of The Velocity-slip And Temperature-jump

The spiral groove dry gas seal is widely used in petrochemical industry. The stability and reliability will be the key to petrochemical enterprise security when the seal is running. Along with the deepening of the spiral groove dry gas seal performance research, its application scope is expanded from the low speed and low pressure to the high pressure and high speed. The spiral groove dry gas seal generates a finite amount of heat in high speed and pressure running, which will lead to the thermo-elastic deformation of the sealing ring. Consequently, the unstable operation and leakage increase will appear. The nonlinear dynamical equation of the rarefied gas flow was deduced according to the second order nonlinear sliding boundary conditions of the gas flow in dry gas seal. Furthermore, the energy equation of the gas film was derived with the introduction of boundary conditions of the temperature-jump in the paper. The sealing performance was analyzed based on the thermo-elastic deformation and second order nonlinear sliding boundary conditions. The main contents and conclusions summarized as follow:The gas film pressure and velocity of the spiral groove could be obtained based on the boundary conditions of the slip-flow, and the energy equations were derived considering and without considering the thermal dissipation of the gas film in the paper. The temperature distribution of the gas film could be solved out by using the film pressure, velocity and energy equation under the help of the Maple and Matlab. Based on the thermo-elastic deformation theory, we obtained the deformation of the sealing ring and the gas film thickness. And the theoretical leakage rate could be obtained by using the general Reynolds equation, which would be compared with the experimental leakage rate. The results show that the temperature of the groove is increasing firstly and then decreasing when the gas flows from the external into the interior, the temperature is higher next to the groove root. The changed trends of the thermo-elastic deformation and temperature are consistent, and the trend of gas film thickness is opposite compared with the thermo-elastic deformation. With the increase of deformation, the leakage rate is large, and the leakage rate of the thermo-elastic deformation is nearer to the experimental value. The leakage rate of the thermo-elastic deformation considering the thermal dissipation is the nearest to the experimental value.The gas film pressure and velocity could be obtained based on the boundary conditions of the velocity-slip, and the energy equation of the gas film was derived in the paper with the introduction of boundary conditions of the temperature-jump. The gas film temperature distribution of the three-dimensional coordinates could be solved out by using the film pressure, velocity and energy equation under the numerical calculation of the software Matlab. The results show that the gas film velocity is decreasing firstly and then increasing when the gas flows from the external into the interior, the velocity is smaller next to the groove root. The film temperature is increasing firstly and then decreasing when the gas flows from the external into the interior, the temperature is higher next to the groove root. The temperature in the middle the gas film is higher at the gas film thickness direction. The film temperature distribution has little difference between the temperature considering the temperature-jump and the temperature without considering the temperature-jump. The effect produced by the temperature-jump on the gas film temperature could be ignored.The modified generalized Reynolds equation was derived under the second order nonlinear slip boundary conditions. The nonlinear Reynolds equation was solved to obtain the approximate solution of the film opening force by using the PH linearization method, iterative method. Based on the thermo-elastic deformation theory, we obtained the deformation of the sealing ring and the gas film thickness. Then, the approximately analytical solution of gas film stiffness was obtained. And a trade-off function of the thermal dissipation and rigidity-to-spillage ratio was derived by using multi-objective optimization method. The optimized geometric parameters would be acquired by solving the objective function. The results show that the rigidity-to-spillage ratio is increasing firstly and then decreasing when the gas flows from the external into the interior, the ratio is higher next to the groove root. The best spiral angle will be got when rigidity-to-spillage ratio is the maximum.