Application of γ-Reθ transition model for high-speed flow based on high-order WCNS platform

XIE Chunhui; WANG Dongfang; ZHENG Shichao

doi:10.7638/kqdlxxb-2024.0040

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Application of γ-Re_θ transition model for high-speed flow based on high-order WCNS platform

更新时间：2026-05-28

- Application of γ-Re_θ transition model for high-speed flow based on high-order WCNS platform
- Vol. 42, Issue 12, Pages: 25-34(2024)
- 作者机构：
  
  1. 国防科技大学空天科学学院,长沙,410073
  2. 中国空气动力研究与发展中心,绵阳,621000
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0040
  CLC： V211.3
- Published：2024
- 稿件说明：
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谢春晖, 王东方, 郑世超. 基于WCNS高精度软件平台的γ-Re_θ转捩模型超高速流动应用研究[J]. 空气动力学学报, 2024, 42(12): 25−34. DOI: 10.7638/kqdlxxb-2024.0040

XIE Chunhui, WANG Dongfang, ZHENG Shichao. Application of γ-Re_θ transition model for high-speed flow based on high-order WCNS platform[J]. 2024, 42(12): 25-34. DOI: 10.7638/kqdlxxb-2024.0040.
谢春晖, 王东方, 郑世超. 基于WCNS高精度软件平台的γ-Re_θ转捩模型超高速流动应用研究[J]. 空气动力学学报, 2024, 42(12): 25−34. DOI: 10.7638/kqdlxxb-2024.0040 DOI：

XIE Chunhui, WANG Dongfang, ZHENG Shichao. Application of γ-Re_θ transition model for high-speed flow based on high-order WCNS platform[J]. 2024, 42(12): 25-34. DOI: 10.7638/kqdlxxb-2024.0040. DOI：

摘要

为研究

γ-Re

转捩模型在超高速流动中的适用性问题，本文基于WCNS高精度软件平台开展

γ-Re

转捩模型的修正在超高速流动中的应用研究。首先，针对超高速湍流平板开展了二阶和五阶格式的对比研究，结果表明：高阶算法对网格分辨率要求更低，计算花费更小，对摩擦阻力系数等关注量模拟得更加精准；相比RANS方程，湍流模型方程对格式精度更敏感，更需要高精度离散。其次，在WCNS高精度软件平台上分别针对SST湍流模型和

γ、Re

输运方程以及

进行超高速修正，通过不同马赫数的平板、尖锥算例进行了数值验证，尖锥算例考虑了等温壁和绝热壁两种壁面条件，数值结果与实验值吻合较好。最后，相比于传统的

γ-Re

转捩模型，SST湍流模型修正有效改善超高速湍流区域摩擦阻力计算结果，且预测的转捩位置比其他修正方法要提前一些；

γ、Re

输运方程的

修正大大改善了对于超高速流动转捩位置的预测；

修正有效改善超高速流动转捩区域和湍流区域绝热壁温的预测准度，对于等温壁的热流预测也稍有改进。

Abstract

The prediction of boundary-layer transition is crucial for designing high-speed aircraft

yet high-fidelity high-speed transition prediction models with broad application prospects ar

e still not available. While extensive efforts have been directed towards modifying the

γ-Re

transition model

which has proven effective in low-speed flows

for its application in high-speed scenarios

these refined

γ-Re

models continue to encounter challenges in attaining widespread application. To develop a more practical engineering transition model

we have implemented a high-speed correction to the

γ-Re

transition model

leveraging the high-order WCNS platform. Firstly

we compared the performance of second and fifth-order schemes in simulating a high-speed flat-plate turbulent boundary layer. The results reveal that the higher-order scheme delivers more accurate results

even with a coarse grid

evidenced by its precise prediction of the skin friction coefficient. This underscores the importance of employing high-order schemes for discretizing the turbulence model. Then we refined the SST turbulence model

the transport equations of

and

as well as the turbulent Prandtl number (

)

yielding results in line with experimental data in a wide range of Mach numbers

geometries

and wall thermal conditions. The obtained transition model exhibits not only high accuracy in predicting the transition position but also the aerodynamic force/heat downstream of the transition front. Finally

compared to the original

γ-Re

transition model

the modified SST turbulence model can effectively improve the skin friction prediction accuracy in the turbulent area

and limited improvement on the transition location. Notably

the

-modified

and

transport equations have significantly improved the prediction accuracy of the transition location. Furthermo

the modified

effectively improves the adiabatic wall temperature in transitional and turbulent regions but slightly improves the heat flux on isothermal walls.

关键词

Keywords

references

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