轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟

李凡; 李志辉; 李中华; 罗万清; 陈爱国

doi:10.7638/kqdlxxb-2023.0064

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轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟

研究论文 | 更新时间：2026-05-28

- 轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟
- Unified algorithm for axisymmetric Boltzmann model equation and simulation of nozzle flow in aerospace flight environment
- 空气动力学学报 2024年42卷第2期页码：47-55
- 作者机构：
  
  1. 北京流体动力科学研究中心,北京,100011
  2. 国家计算流体力学实验室,北京,100191
  3. 中国空气动力研究与发展中心超高速空气动力研究所,绵阳,621000
- 作者简介：
  
  李凡（1995—），男，湖北黄冈人，博士研究生，研究方向：稀薄气体动力学. E-mail：748867007@qq.com
  李志辉*，研究员，研究方向：稀薄气体动力学、计算流体力学. E-mail：zhli0097@x263.net
- 基金信息：
  
  国家自然科学基金（11902339，11325212）;基础加强计划重点项目（2019JCJQZD17701）
- DOI：10.7638/kqdlxxb-2023.0064
  中图分类号： O356;V211.3
- 纸质出版：2024
- 稿件说明：
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李凡, 李志辉, 李中华, 等. 轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟[J]. 空气动力学学报, 2024, 42(2): 47−55.

LI Fan, LI Zhihui, LI Zhonghua, et al. Unified algorithm for axisymmetric Boltzmann model equation and simulation of nozzle flow in aerospace flight environment[J]. 2024, 42(2): 47-55.
李凡, 李志辉, 李中华, 等. 轴对称Boltzmann模型方程统一算法与空天飞行环境喷管流动模拟[J]. 空气动力学学报, 2024, 42(2): 47−55. DOI： 10.7638/kqdlxxb-2023.0064

LI Fan, LI Zhihui, LI Zhonghua, et al. Unified algorithm for axisymmetric Boltzmann model equation and simulation of nozzle flow in aerospace flight environment[J]. 2024, 42(2): 47-55. DOI： 10.7638/kqdlxxb-2023.0064.

摘要

拦截机动飞行器周围大范围区域存在主喷/侧喷流/羽流影响，而传统的纳维-斯托克斯（Navier-Stokes

N-S）方程不能很好模拟发动机喷管扩张段出口附近流动情况，需要一种新的方法来处理这种全流域流动问题。为解决该问题，针对特定轴对称喷管内流动，本文通过数学推导确立描述不同克努森数稀薄环境条件下的轴对称喷管内流动Boltzmann模型方程，初步建立适于该模型方程的数值格式与气体动理论统一算法。通过开展同轴圆筒间的定常/非定常旋转流动以及轴对称喷管内流动数值计算研究，发现统一算法计算流场与其他途径得到的结果吻合较好，验证了统一算法在全局克努森数喷管流动模拟的适应性和可靠性。通过与低密度风洞实验对比，喷管出口核心区羽流结构一致，羽流轴线压力分布一致，表明统一算法可以有效解决喷管入口压缩段到扩张段多流域混合，尤其是出口附近稀薄气体真空低压环境流动问题。

Abstract

The influence of main/side jet and plume exists in a wide area around the intercepting maneuvering aircraft

and the traditional Navier-Stokes (N-S) equation cannot simulate the flow near the outlet of the engine nozzle expansion well

so a new method is needed to deal with the whole flow regime flow problem. In order to solve this problem

the Boltzmann model equation governing the flow in an axisymmetric nozzle under the rarefied environment of different Knudsen numbers is mathematically derived

and the numerical scheme and gas kinetic unified algorithm for the model equation are established. Numerical results for steady/unsteady rotating flow between two coaxial cylinders

as well as flow in an axisymmetric nozzle

both agree with existing studies

which verifies the reliability of the present algorithm in the whole flow regime. By comparing with the low-density wind tunnel experiment

the plume structure in the core area of the nozzle outlet and the pressure profile along the plume axis from the simulation show good agreement with the experiment

which suggests that the proposed algorithm can effectively solve the problem of mixing in the multi-flow regime from the nozzle compression section to the expansion section

especially in the low-pressure vacuum environment near the outlet.

关键词

Keywords

references

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