Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations

Luo Jingwei; Yuan Zhenyu; Li Chengrui; Yang Guang

doi:10.7638/kqdlxxb-2026.0146

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Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations

更新时间：2026-10-14

- Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations
- Vol. 44, Issue 8, Pages: 140-152(2026)
- 作者机构：
  
  1. 南京理工大学能源与动力工程学院,南京,210094
  2. 临近空间物理重点实验室,北京,100076
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2026.0146
  CLC： V211.3;O356
- Published：2026
- 稿件说明：
移动端阅览
罗经纬, 袁震宇, 李城锐, 等. 基于非线性耦合本构关系的高速升力体流动计算与分析[J]. 空气动力学学报, 2026, 44(8): 140−152.

Luo Jingwei, Yuan Zhenyu, Li Chengrui, et al. Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations[J]. 2026, 44(8): 140-152.
罗经纬, 袁震宇, 李城锐, 等. 基于非线性耦合本构关系的高速升力体流动计算与分析[J]. 空气动力学学报, 2026, 44(8): 140−152. DOI： 10.7638/kqdlxxb-2026.0146

Luo Jingwei, Yuan Zhenyu, Li Chengrui, et al. Computation and analysis of high-speed lifting-body flows based on nonlinear coupled constitutive relations[J]. 2026, 44(8): 140-152. DOI： 10.7638/kqdlxxb-2026.0146.

摘要

临近空间高速流动包含连续流与稀薄流的跨尺度效应。传统基于牛顿黏性定律和傅里叶热传导定律的线性本构关系，难以准确描述非平衡条件下应力与热流之间的非线性耦合特性。本文采用结合不动点迭代法与牛顿迭代法优势的混合迭代方法来求解非线性耦合本构关系（nonlinear coupled constitutive relations

NCCR）。控制方程在结构网格上采用有限体积法离散，并采用LU-SGS隐式推进加速收敛。针对HyTRV升力体在不同高度（30、60、90 km）、马赫数（5～20）和攻角（0°～20°）条件下，开展NCCR与Navier-Stokes（N-S）方程的对比计算与分析。研究结果表明：在30 km和60 km工况下，两种模型预测的主要流场结构和壁面压力系数曲线基本一致；在90 km、

= 20工况下，NCCR预测的压力峰值与热流峰值明显低于N-S方程结果，且随攻角增大差异进一步扩大，稀薄效应与非平衡耦合修正的重要性逐渐显现。该模型在近连续流区可自然退化为N-S线性本构结果，在非平衡效应显著的区域则通过非线性耦合本构提供更合理的预测。本文研究结果可为高速升力体在宽流域和大速域范围内的气动力及气动热特性分析提供参考。

Abstract

Near-space high-speed flows involve cross-scale effects spanning from continuum regimes to rarefied regimes. Conventional linear constitutive relations based on Newton's law of viscosity and Fourier's law of heat conduction are inadequate for accurately describing the stress-heat flux nonlinear coupling effect under nonequilibrium conditions. In this paper

the nonlinear coupled constitutive relations (NCCR) were solved using a hybrid iterative method which combines the advantages of fixed-point iteration and Newton iteration. The governing equations were discretized by a finite-volume method on structured grids

and the LU-SGS implicit scheme was employed to accelerate convergence. Comparative computations and analyses between the NCCR model and the Navier-Stokes(N-S) equations were performed for the HyTRV lifting-body vehicle over a range of altitudes (30

90 km)

Mach numbers (5–20)

and angles of attack (0°–20°). The results indicate that at altitudes of 30 km and 60 km

the primary flowfield structures and surface pressure coefficient distributions predicted by the two models are in good agreement

suggesting that the flow remains in the near-continuum regime and the nonlinear correction of NCCR is weak. At 90 km and Mach 20

the pressure and heat-flux peaks predicted by NCCR are notably lower than those of the N-S solutions

and the discrepancies further increase with angle of attack

highlighting the growing importance of rarefaction effects and nonlinear coupled constitutive modifications. The NCCR model naturally reduces to the N-S linear constitutive results in the near-continuum regime

while providing more reasonable predictions through nonlinear coupled constitutive relations in regions with significant nonequilibrium effects. The findings of this study can serve as a reference for the aerodynamic and aerothermodynamic evaluation of high-speed lifting-body vehicles across a broad range of altitudes and Mach numbers.

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