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

王炳棋; 畅云峰

doi:10.7652/xjtuxb202006021

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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

更新时间：2025-07-09

- 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
- 西安交通大学学报 2020年54卷第6期页码：161-167
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202006021
  中图分类号： TB652
- 网络首发：2020-06-10，
  
  纸质出版：2020
- 稿件说明：
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王炳棋, 畅云峰. 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[J]. 西安交通大学学报, 2020,54(6):161-167.

Analysis and Improvement of Numerical Oscillation in Simulation of Compressor Working Process
[J]. 2020, 54(6): 161-167. DOI: 10.7652/xjtuxb202006021.
王炳棋, 畅云峰. 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[J]. 西安交通大学学报, 2020,54(6):161-167. DOI： 10.7652/xjtuxb202006021.

Analysis and Improvement of Numerical Oscillation in Simulation of Compressor Working Process
[J]. 2020, 54(6): 161-167. DOI: 10.7652/xjtuxb202006021. DOI：

摘要

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。

Abstract

To solve the problems of numerical oscillations and divergence in the simulation of compressor process

-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 me

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