叶轮机械通道内压力的修正方程和数值模拟

陈浩 1; 李开泰 2; 王尚锦 1

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叶轮机械通道内压力的修正方程和数值模拟

更新时间：2025-07-09

- 叶轮机械通道内压力的修正方程和数值模拟
- Pressure Correction Equation in Channel of Turbomachine and Numerical Simulation
- 西安交通大学学报 2010年44卷第11期页码：98-102
- 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：
  
  : 2010-03-19. 作者简介: 陈浩(1983-),男,博士生;王尚锦(联系人),男,教授,博士生导师. 基金项目: 国家自然科学基金资助项目(10971165)
- DOI：
  中图分类号： O343
- 网络首发：2010-11-10，
  
  纸质出版：2010
- 稿件说明：
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陈浩 1, 李开泰 2, 王尚锦 1. 叶轮机械通道内压力的修正方程和数值模拟[J]. 西安交通大学学报, 2010,44(11):98-102.

Pressure Correction Equation in Channel of Turbomachine and Numerical Simulation[J]. 2010, 44(11): 98-102.
陈浩 1, 李开泰 2, 王尚锦 1. 叶轮机械通道内压力的修正方程和数值模拟[J]. 西安交通大学学报, 2010,44(11):98-102. DOI：

Pressure Correction Equation in Channel of Turbomachine and Numerical Simulation[J]. 2010, 44(11): 98-102. DOI：

摘要

为了解决有限元法直接求解不可压流动存在离散Babuska-Brezzi条件限制而使得压力求解精度相对较低的问题

根据维数分裂法思想提出了叶轮机械通道内二维流形上压力Laplace-Beltrami方程(LB-2D).该椭圆型压力修正方程不受离散Babuska-Brezzi条件的限制

因而可采用任意高阶有限元空间进行逼近.另外

由于维数分裂算法只需在二维流形上进行求解

所以自然避免了三维窄边单元的问题.以NASA低速大尺度离心叶轮(LSCC)作为算例

在3个典型二维流形上定性、定量比较了LB-2D与FLUENT商业软件的计算结果

结果表明:相比来自FLUENT的相邻二维流形上的流场数据

LB-2D能够给出与FLUENT基本一致的计算结果

证实了压力LB-2D方程是可靠的.

Abstract

A Laplace-Beltrami equation(LB-2D)of the 2D-manifolds was proposed on the basis of the dimensional split method to enhance pressure solution precision of the simulation on incompressible flow using the finite element method directly. The elliptic equation proposed for pressure correction can be approximated by the higher order element because it is not restricted by the B-B condition. The 3D strip cell can be avoided since pressure correction is only carried out on the 2D-manifolds according to the dimensional split method. In addition

the solution of LB-2D was qualitatively and quantitatively compared with that of FLUENT on three 2D-manifolds of the channel in a low speed centrifugal compressor(LSCC)from NASA. The results show that the flow field data by LB-2D are in reasonable consistency with those by FLUENT on the neighboring 2D-manifolds. It is likely that the pressure correction equation(LB-2D)is reliable.

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references

LI Kaitai, HUANG Aixiang. Mathematical aspect of the stream-function equations of compressible turbomachinery flow and their finite element approximation using optimal control [J]. Comp Mech Appl Mech and Eng, 1983,41(2):175-194.

LI Kaitai, HUANG Aixiang, ZHANG Wenling. A dimension split method for the 3-D compressible Navier-Stokes equations in turbomachine [J]. Communications in Numerical Methods in Engineering, 2002,18(1):1-14.

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李开泰, 刘德民. 透平机械内部三维可压缩Navier-Stokes方程的流面方法和维数分裂算法 [J]. 应用数学学报, 2008,31(3):397-418.

LI Kaitai, LIU Demin. The stream surface method and dimension split method for 3D viscous compressible flow in turbomachinery[J]. Acta Mathematicae Applicatae Sinica, 2008,31(3):397-418.

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LI Kaitai, SU Jian, GAO Limin. Optimal shape design for blade's surface of an impeller via the Navier-Stokes equations [J]. Communications in Numerical Methods in Engineering, 2006,22(6):657-676.

李开泰, 黄艾香. 张量分析及其应用[M]. 北京: 科学出版社, 2004.

HATHAWAY M D, CHRISS R M, WOOD J R, et al. Experimental and computational investigation of the NASA low speed centrifugal compressor flow field[J]. ASME Journal of Turbomachinery, 1993,115(3):527-542.

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