基于二阶滑移边界的螺旋槽干气密封泄漏量计算与分析

Leakage calculation and analysis for the spiral groove dry gas seal based on the second-order slip boundary

为解决螺旋槽干气密封流场计算中一阶线性滑移边界条件下得到的泄漏量与实验结果之间存在较大误差的问题,在一阶线性滑移边界条件的基础上,推导出二阶非线性滑移边界条件下的修正的广义雷诺方程,应用迭代法、PH线性化方法等求解非线性雷诺方程,获得了气膜压力、流速、泄漏量的近似解。利用Maple程序计算了工程实例中不同转速和不同压力情况下的泄漏量,并与一阶线性滑移边界条件下的泄漏量和实验数值进行比较。结果表明:在工程实例中,压力相同时,泄漏量随转速的增大而增大,一、二阶最大相对误差分别为14.4%、5.4%;转速相同时,泄漏量随压力的增大而增大,一、二阶最大相对误差分别为33.3%、13.3%。本文未考虑干气密封内部的振动情况,因此一、二阶理论计算值小于实际测试值。二阶非线性滑移边界条件下的泄漏量值比一阶线性滑移边界条件下的泄漏量值更加接近实验数值,特别是在工程实例中转速、压力较低的工况下更加明显。

Practice shows that the errors of the leakage under the first-order linear slip boundary condition are larger than experimental values in the spiral groove dry gas seal flow fields.So the modified generalized Reynolds equation can be deduced by the second-order nonlinear slip boundary condition from the first-order linear slip boundary condition.The nonlinear Reynolds equation is solved by iterative method and PH linearization method.The approximation of gas film pressure,flowing speed rate and leakage are obtained.Under different revolving speeds and pressure,the leakage values are calculated by Maple program in the engineering examples,and comparing with the leakages under the first-order linear slip boundary condition or experiments.The results show that the leakage increases with the revolving speeds under the same pressure in the numerical examples.The maximum relative errors of the first-order linear and the second-order nonlinear slip boundary conditions are 14.4% and 5.4% respectively.The leakages are increasing with the pressures under the same revolving speed.The maximum relative errors of them are 33.3% and 13.3% respectively.Because the vibration is not considered in the dry gas seal,the theoretical values are smaller than experimental values.Compared with the leakages under the first-order linear slip boundary condition,the leakages which are obtained from the second-order nonlinear slip boundary condition are much closer to experimental values in the engineering examples,especially in the condition of the low revolving speeds and low pressures.