Machine-learning wall model of large-eddy simulation for low- and high-speed flows over rough surfaces

TL;DR

This work presents BFWM-rough-v2, a wall-model for WMLES that embeds subgrid-scale roughness and compressibility effects across low- to high-speed flows. It relies on a building-block-flow paradigm and dimensionless learning to select four predictive inputs from wall and near-wall data plus roughness descriptors, yielding wall-shear stress and heat-flux predictions with low $L_2$ errors ($\approx$4% and $\approx$3%) and a calibrated uncertainty score via SNGP. The model is trained on a DNS database of 192 incompressible and 180 compressible rough-wall channel cases with Gaussian and Weibull textures, and validated a-posteriori against 162 unseen WMLES cases, a transonic HPT blade, a hypersonic ramp, and blunt bodies, demonstrating robust performance (mostly within 10–15% errors) and reliable confidence near the training manifold. The inclusion of a confidence metric enables explicit identification of extrapolative regions, improving the practical reliability of WMLES in complex rough-wall/high-speed environments. Overall, BFWM-rough-v2 advances high-fidelity predictions of aero-thermal loads in engineering applications where roughness and compressibility interact strongly, such as turbine blades and atmospheric-entry scenarios.

Abstract

We present a wall model for large-eddy simulation that incorporates surface-roughness effects and is applicable across low- and high-speed flows, for both transitional and fully rough conditions. The model, implemented using an artificial neural network, is trained on a direct numerical simulation database of compressible turbulent channel flows over rough walls. The dataset contains 372 cases spanning a wide range of irregular roughness topographies, including Gaussian and Weibull distributions, Mach numbers 0~3.3, and friction Reynolds numbers 180~2000. We employ an information-theoretic, dimensionless learning method to identify the inputs with the highest predictive power for the dimensionless wall friction and wall heat flux. Predictions are accompanied by a confidence score derived from a spectrally normalized neural Gaussian process, which quantifies uncertainty in regions that deviate from the training dataset. The model performance is first evaluated a-priori on 110 turbulent channel flow cases, yielding prediction errors below 4%. The model is assessed a-posteriori in wall-modeled large-eddy simulations across diverse test cases. These include over 160 subsonic and supersonic turbulent channel flows with rough walls, a transonic high-pressure turbine (HPT) blade with Gaussian roughness, a high-speed compression ramp with sandpaper roughness, and three hypersonic blunt bodies with sand-grain roughness. Results show that the proposed wall model typically achieves a-posteriori predictive accuracy within 10% for wall shear stress and within 15% for wall heat flux, with high confidence in the channel flows and HPT blade cases. In the rough-wall compression ramp and hypersonic blunt bodies, the model captures the heating augmentation with errors ranging 0%~20%. In the cases with the highest errors, the reduced performance is correctly detected by a drop in the confidence score.

Figures (21)

• Figure 1: Roughness height $(k)$ contour map of selected rough surface samples: (a) Gaussian roughness GS06; (b) Weibull roughness WB10. The roughness map is applied to turbulent channel walls, where $\delta$ is the channel half-height.
• Figure 2: Scatter plot of pairs of roughness parameters and their correlation for Gaussian (orange) and Weibull (blue) rough surfaces.
• Figure 3: Instantaneous spanwise velocity normalized by the maximum spanwise velocity $w/w_\text{max}$ for DNS of a minimal-span channel flow over a rough wall. The contour legend is from -1 (black) to 1 (white). The case shown is GS1-M1.7-R10000. The zoom-in view shows the grid in the near-wall region. The wetted rough surfaces are colored in dark yellow.
• Figure 4: (a) Streamwise mean velocity profiles of smooth-wall reference cases, with a comparison to the incompressible channel flow DNS data from lee2015direct. (b) Roughness function $\Delta U^+$ as a function of $k_s^+$ for current compressible channel flows with rough walls. The line denotes the Nikuradse's law for incompressible rough-wall turbulent flow nikuradse1933laws.
• Figure 5: Overview of the proposed wall model (BFWM-rough-v2). The flow state at the wall and in the first off-wall control volume, together with statistical roughness parameters, are used to construct dimensionless inputs to the wall model. The model outputs the dimensionless wall-shear stress and wall heat flux, each accompanied by a confidence score. The wall-model mapping is represented with an FNN, while the confidence score in the prediction is quantified using an SNGP.