[Paper Review] Quantifying Model Form Uncertainty in RANS Simulation of Wing-Body Junction Flow

Jinlong Wu, Jianxun Wang+1 more|arXiv (Cornell University)|May 19, 2016

Model Reduction and Neural Networks10 references3 citations

TL;DR

This paper extends a physics-informed Bayesian framework to quantify model-form uncertainty in RANS simulations of wing-body junction flow with wall functions. By injecting uncertainty into Reynolds stress anisotropy—particularly the orientation of principal stress axes—it improves posterior mean velocity and Reynolds stress anisotropy agreement with experiments at the corner region, though performance remains limited near the leading edge due to unaccounted orientation misalignment in rapidly varying strain fields.

ABSTRACT

Wing-body junction flows occur when a boundary layer encounters an airfoil mounted on the surface. The corner flow near the trailing edge is challenging for the linear eddy viscosity Reynolds Averaged Navier-Stokes (RANS) models, due to the interaction of two perpendicular boundary layers which leads to highly anisotropic Reynolds stress at the near wall region. Recently, Xiao et al. proposed a physics-informed Bayesian framework to quantify and reduce the model-form uncertainties in RANS simulations by utilizing sparse observation data. In this work, we extend this framework to incorporate the use of wall function in RANS simulations, and apply the extended framework to the RANS simulation of wing-body junction flow. Standard RANS simulations are performed on a 3:2 elliptic nose and NACA0020 tail cylinder joined at their maximum thickness location. Current results show that both the posterior mean velocity and the Reynolds stress anisotropy show better agreement with the experimental data at the corner region near the trailing edge. On the other hand, the prior velocity profiles at the leading edge indicate the restriction of uncertainty space and the performance of the framework at this region is less effective. By perturbing the orientation of Reynolds stress, the uncertainty range of prior velocity profiles at the leading edge covers the experimental data. It indicates that the uncertainty of RANS predicted velocity field is more related to the uncertainty in the orientation of Reynolds stress at the region with rapid change of mean strain rate. The present work not only demonstrates the capability of Bayesian framework in improving the RANS simulation of wing-body junction flow, but also reveals the major source of model-form uncertainty for this flow, which can be useful in assisting RANS modeling.

Motivation & Objective

• To address the challenge of model-form uncertainty in RANS simulations of complex wing-body junction flows, particularly near the trailing edge corner where linear eddy viscosity models fail.
• To extend a physics-informed Bayesian framework to incorporate wall functions, reducing computational cost while maintaining accuracy in uncertainty quantification.
• To identify the dominant source of uncertainty in RANS predictions by analyzing the role of Reynolds stress anisotropy and orientation misalignment.
• To evaluate whether perturbing the orientation of Reynolds stress eigenvectors improves inference performance in regions with high strain rate gradients, such as near the leading edge stagnation point.

Proposed method

• A Bayesian inference framework is applied to RANS simulations with wall functions, using sparse experimental data to update prior distributions of model-form uncertainty.
• Uncertainty is injected directly into the RANS-predicted Reynolds stresses under the constraint of turbulence realizability to ensure physical consistency.
• The iterative ensemble Kalman method is used to assimilate experimental data and compute posterior distributions of velocity and Reynolds stress fields.
• The framework perturbs the orientation of the principal stress axes (v₁, v₂, v₃) to explore uncertainty space, especially in regions with strong strain rate gradients.
• Reynolds stress anisotropy is visualized in Barycentric triangles to compare baseline RANS, prior uncertainty, and posterior predictions against experimental data.
• The approach evaluates the impact of uncertainty in stress orientation on mean velocity prediction, particularly in regions with rapid changes in mean strain rate.

Experimental results

Research questions

• RQ1 Can a Bayesian framework incorporating wall functions effectively reduce model-form uncertainty in RANS simulations of wing-body junction flows?
• RQ2 How does uncertainty in the orientation of Reynolds stress eigenvectors affect the accuracy of mean velocity predictions in regions with high strain rate gradients?
• RQ3 Why does the Bayesian framework show limited improvement in velocity predictions near the leading edge despite uncertainty injection?
• RQ4 To what extent does Reynolds stress anisotropy, rather than individual stress components, govern secondary flow development in the corner region?
• RQ5 Can perturbing the principal stress directions expand the uncertainty space sufficiently to cover experimental data in complex flow regions?

Key findings

• At the corner region near the trailing edge, the posterior mean velocity and Reynolds stress anisotropy show significantly improved agreement with experimental data, demonstrating the framework’s effectiveness in complex flow zones.
• The posterior Reynolds stress components do not show noticeable improvement, but the anisotropy is better captured, indicating that anisotropy is the key driver of secondary flow prediction.
• Near the leading edge, the prior velocity profiles remain close to baseline RANS predictions, and the posterior mean velocity shows little improvement due to insufficient uncertainty space coverage.
• The misalignment of principal stress axes (v₁, v₂) between RANS predictions and experimental data at the leading edge is identified as the primary source of model-form uncertainty.
• Perturbing the orientation of the stress eigenvectors allows the uncertainty space to cover experimental data, suggesting that orientation uncertainty is critical for accurate inference in high-strain regions.
• Extending the framework to include orientation perturbations is necessary to improve performance in regions with rapidly varying strain rates, though it increases numerical complexity and instability risk.