压缩机工作过程模拟中数值振荡问题的成因分析及改善方法

Analysis and Improvement of Numerical Oscillation in Simulation of Compressor Working Process

为解决数值模拟压缩机工作过程中存在的数值振荡和发散问题,采用四阶后向差分(BDF-4)算法和经典四阶龙格库塔(RK-4)算法分析压缩机基元容积控制方程的稳定性,并对2种算法的计算结果进行对比。结果表明:在吸排气过程中,压力计算的微小偏差会导致质量流量产生较大的误差,从而使基元容积控制方程产生较大的数值刚性,限制了RK-4算法的最大稳定步长;在稳定性上,BDF-4算法的绝对稳定域包含整个负半x轴,可以避免数值刚性引起的振荡和发散,其计算步长不再受数值刚性的限制;对计算效率而言,每步BDF-4算法所消耗时间为同步长RK-4算法的1.7~1.8倍;计算精度上,BDF-4算法与RK-4算法代数精度相同,实际计算时两者的表现也十分接近。BDF-4算法在保证工程精度的前提下提高了压缩机工作过程模拟的稳定性,解决了数值振荡问题,对容积式压缩机的工作过程模拟、新型泄漏通道的研究等有实际意义。

To solve the problems of numerical oscillations and divergence in the simulation of compressor process,4th-order backward difference formula(BDF-4)and classical 4th-order Runge-Kutta(RK-4)method are adopted to analysis the stability of control equations of element volume,and the results of two methods are compared.The analysis results show that a small fluctuation of pressure in the process of suction and exhaust would induce a large fluctuation in the calculation of the mass flow,which would result in a large stiffness of the governing equation and is the key factor to cause numerical oscillations.The results indicate that there is no stability constraint in the calculation using the BDF-4 method,so that the oscillations and divergence due to the numerical stiffness can be avoided.However,the calculation time of the BDF-4 method is 1.7~1.8 times of the RK-4 method at one step,and the simulation accuracy of the BDF-4 method is nearly the same as that of the RK-4 method.The BDF-4 method can greatly improve the simulation stability of the compressor working process without loss of accuracy,and give a reference for simulation of compressor thermal process and the leakage simulation through clearance.