General-purpose Data-driven Wall Model for Low-speed Flows Part I: Baseline Model

Abstract

We present a general-purpose wall model for large-eddy simulation. The model builds on the building-block flow principle, leveraging essential physics from simple flows to train a generalizable model applicable across complex geometries and flow conditions. The model addresses key limitations of traditional equilibrium wall models (EQWM) and improves upon shortcomings of earlier building-block-based approaches. The model comprises four components: (i) a baseline wall model, (ii) an error model, (iii) a classifier, and (iv) a confidence score. The baseline model predicts the wall-shear stress, while the error model estimates epistemic errors and aleatoric errors, both used for uncertainty quantification. In Part I of this work, we present the baseline model, while the remaining three components are introduced in Part II. The baseline model is designed to capture a broad range of flow phenomena, including turbulence over curved walls and zero, adverse, and favorable mean pressure gradients, as well as flow separation and laminar flow. The problem is formulated as a regression task to predict wall shear stress using a neural network. Model inputs are localized in space and dimensionless, with their selection guided by information-theoretic criteria. Training data include, among other cases, a newly generated direct numerical simulation dataset of turbulent boundary layers under favorable and adverse PG conditions. Validation is carried out through both a priori and a posteriori tests. The a priori evaluation spans 140 diverse high-fidelity numerical datasets and experiments (67 training cases included), covering turbulent boundary layers, airfoils, Gaussian bumps, and full aircraft geometries, among others. We demonstrate that the baseline wall model outperforms the EQWM in 90% of test scenarios, while maintaining errors below 20% for 98% of the cases.

Figures (44)

• Figure 1: Overview of the building-block flow wall model version 2 (BFM-WM-v2). The model comprises four components: (i) a baseline wall model, (ii) an error model, (iii) a classifier, and (iv) a confidence score. Each panel contains the question the module is aiming to answer. When appropriate, the error model corrects the baseline prediction. The model inputs and output are formulated in dimensionless form. In Part I of this work, we present the baseline model. The other three components are presented in Part II.
• Figure 2: Workflow of the training data, dimensionless input/output design, training process, and testing of the baseline model.
• Figure 3: (a) Wall-model mesh (dashed red) defined in the local $(n,s)$ coordinates over a curved wall; the surrounding unstructured LES mesh is shown in black. (b) Dimensional inputs investigated to construct the wall model, in addition to fluid properties such as density and viscosity. Subscripts $1$–$4$ denote the $i$-th off-wall grid point, and the subscript $w$ indicates wall values.
• Figure 4: Schematics of representative training cases. (a) APG and FPG turbulent boundary layers; (b) turbulent channel flows; (c) FPG Falkner--Skan laminar flow; (d) APG Falkner--Skan laminar flow; (e) spanwise-periodic Gaussian bumps; (f) pressure-induced turbulent separation bubbles. Regions enclosed by grey lines indicate separated flow.
• Figure 5: The sampling region for the training data covering the range 0.005-0.25 $\delta(x)$, where $\delta(x)$ is boundary layer thickness.