Adjoint Optimization Design of Nozzle Considering Uncertainty Quantification of Turbulence Model

LI Anna; SUN Zhongguo; HUANG Zhu; XI Guang

doi:10.7652/xjtuxb202503001

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Adjoint Optimization Design of Nozzle Considering Uncertainty Quantification of Turbulence Model

更新时间：2026-01-06

- Adjoint Optimization Design of Nozzle Considering Uncertainty Quantification of Turbulence Model
- Journal of Xi’an Jiaotong University Vol. 59, Issue 3, Pages: 1-8(2025)
- 作者机构：
  
  西安交通大学能源与动力工程学院， 710049，西安
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb202503001
  CLC： V211.3
- Received：30 June 2024，
  
  Online First：24 October 2024，
  
  Published：10 March 2025
- 稿件说明：
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LI Anna, SUN Zhongguo, HUANG Zhu, et al. Adjoint Optimization Design of Nozzle Considering Uncertainty Quantification of Turbulence Model[J]. Journal of Xi’an Jiaotong University, 2025, 59(3): 1-8.
DOI：

LI Anna, SUN Zhongguo, HUANG Zhu, et al. Adjoint Optimization Design of Nozzle Considering Uncertainty Quantification of Turbulence Model[J]. Journal of Xi’an Jiaotong University, 2025, 59(3): 1-8. DOI： 10.7652/xjtuxb202503001.

摘要

为提高工程中广泛采用的基于雷诺平均Navier-Stokes（RANS）模型设计优化的可靠性和稳健性，针对RANS模型存在的结构不确定性，通过质心图和雷诺应力的可实现性对其进行合理量化，采用自适应非均匀扰动方法对湍流各向异性张量的特征值和特征空间施加扰动，并对模型预测的不确定区间进行数值估计。提出了一种RANS模型不确定性量化框架下的伴随设计优化方法，探索了该方法在拉瓦尔喷管优化设计中的应用，通过6次模拟获得了不同扰动下的优化几何型线，不同型线所围成的区域（置信区间）反映了模型结构不确定性引起的几何优化差异。研究结果表明：在不同扰动下，优化后的喷管总压损失降低了6.7%~19.2%，实现了喷管性能的稳健提升，获得的置信区间降低了对制造公差的敏感性，从而在一定程度上降低了精度要求和制造成本。研究结果展示了考虑RANS模型不确定性量化的优化设计在航空航天工程应用中的潜在价值和指导作用。

Abstract

In order to improve the reliability and robustness of design optimization based on the Reynolds-averaged Navier-Stokes (RANS) models

which are widely used in engineering

this paper addresses the structural uncertainties present in RANS models. By using centroidal diagrams and the feasibility of Reynolds stresses

these uncertainties are reasonably quantified. An adaptive non-uniform perturbation method is employed to apply disturbances to the eigenvalues and eigenspaces of the turbulence anisotropy tensor

and a numerical estimation of the uncertainty interval predicted by the model is conducted. This paper proposes a method for adjoint design optimization under the uncertainty quantification framework of the RANS model and explores its application in the optimization design of a Laval nozzle. Through six simulations

optimized geometric shapes under different perturbations are obtained

and the areas enclosed by different shapes (confidence intervals) reflect the geometric optimization differences caused by structural uncertainties in the model. The results indicate that after optimization under different perturbations

the total pressure loss of the nozzle is reduced by 6.7% to 19.2%

achieving a robust improvement in nozzle performance. The resulting confidence intervals reduce sensitivity to manufacturing tolerances

thus lowering precision requirements and manufacturing costs to some extent. The findings demonstrate the potential value and guiding role of optimization design considering the uncertainty quantification of the RANS model in aerospace engineering applications.

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references

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