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Near-the-Wall Analysis of the NASA Wall-Mounted Hump

A​uthors: Pedro Munoz
(Barcelona Supercomputing Center, Spain; Delft University of Technology, The Netherlands)

Bernat Font
(Delft University of Technology, The Netherlands)

Matteo Rosellini, Maria Vittoria Salvetti
(University of Pisa, Italy)

Oriol Lehmkuhl
(Barcelona Supercomputing Center, Spain)

The video starts with an overview of the NASA Wall-Mounted Hump geometry, followed by a transition towards a two-dimensional visualization of the velocity field magnitude at its leading edge. From here, the camera moves with the free-stream velocity towards the leading edge of the hump, portraying the relaminarization, separation, and reattachment of the boundary layer. After the boundary layer reattaches, the camera transitions back to an overview of the geometry, this time displaying the coherent structures identified using the Q-criterion, colored with the magnitude of the velocity field. The video is composed of a total of 1800 frames at a resolution of 3840 x 2160 pixels, visualizing the flow over the hump in 4K resolution at 60 FPS.

Scientific Abstract

First proposed as a validation case for turbulence models during the workshop on CFD Validation of Synthetic Jets and Turbulent Separation Control held by NASA in 2004, the NASA Wall-Mounted Hump (WMH) constitutes one of the most widely used benchmark cases in the literature for turbulence modelling applications. The WMH features an essentially two-dimensional high-Reynolds number flow, Rec ≈ 936000, over a Glauert- Goldschmied body in which an incoming fully developed turbulent boundary layer (TBL) relaminarizes and retransitions over the foremost part of the hump to later on separate and reattach in the vicinity of its trailing edge. This wide variety of boundary layer phenomena induced by such a relatively simple geometry is precisely what makes this case so appealing for turbulence modelling from a numerical perspective.

Despite its popularity, most of the literature on the case concentrates either on Reynolds-Averaged Navier- Stokes (RANS) or wall-modelling Large Eddy Simulation (WMLES), comparing their solutions against wellestablished experimental measurements. As a result, there exist only a handful of studies that have tackled the case via high-fidelity approaches, either with wall-resolved Large Eddy Simulation (WRLES) or Direct Numerical Simulation (DNS). In this context, the present work tackles the WMH using a WRLES approach, and rather than focusing solely on a comparison against experimental measurements, as has been done typically in the literature, it focuses on the analysis of the near-wall flow mechanisms governing the relaminarization, separation, and reattachment of the boundary layer.

The computational domain considered in this study extends 2.15c and 5c in the streamwise direction before and after the leading edge of the hump, respectively, and 0.3c in the spanwise direction, c denoting the chord of the hump. The classical top-wall contour, which aims to mimic the blockage effects of the end-plates featured in the experiments, is also used in this work. This computational domain is meshed using 4th-order hexahedral elements and 2.17 · 109 nodes, resulting in a resolution of the incoming TBL of 20, 0.7, and 12 wall units in the streamwise (x+), wall-normal (y+), and spanwise (z+) directions. To deal with the remarkably high computational requirements of such a high-fidelity approach, the simulations conducted throughout this study have been executed on the accelerated partition of the MareNostrum V supercomputer at the Barcelona Supercomputing Center using the numerical solver SOD2D. Introduced by Gasparino et al. [1], this high-order code features a continuous Galerkin spectral-finite element method for both incompressible and compressible formulations of the Navier-Stokes equations, specifically tailored to run efficiently on modern GPU architectures.

The comparison of the present WRLES solution against those available in the literature shows an overall better agreement with well-established experimental measurements, particularly in the separated region located at the after part of the hump. The near-the-wall analysis performed by considering the wall-normal distributions of the budgets of the boundary layer equations provides insights into the dynamics of the inner layer that are of interest to the turbulence modelling community, particularly for wall modelling applications. Examples of these insights include the uniformity of the pressure-gradient effects across the viscous wall region and how the existence of a balancing mechanism between mean-flow convection and pressure gradient effects above it introduces consistency requirements for non-equilibrium wall models.

The next steps of this research are focused on the generation of an open-access dataset of results that complements those of experimental measurements available in the literature, aiming to provide a numerical means with which to validate exhaustively current turbulence modelling approaches.

References:

[1] Gasparino, L., Spiga, F., Lehmkuhl, O. : SOD2D: A GPU-enabled Spectral Finite Elements Method for compressible scale-resolving simulations. Computer Physics Communications, 297(1), 109067 (2024).
[2] Radhakrishnan, S., Calafell, J., Miro, A., Font, B., Lehmkuhl, O. : Data-driven wall modeling for LES involving non-equilibrium boundary layer effects. International Journal of Numerical Methods for Heat and Fluid Flow, 34(8), 3166–3202 (2024).
[3] Munoz, P., Font, B., Rosellini, M., Salvetti, M.V., Lehmkuhl, O. : Near-the-wall analysis of the NASA Wall-Mounted Hump. Division of Fluid Dynamics Annual Meeting 2025, (2025).
[4] Greenblatt, D., Paschal, K., Yao, C., Harris, J., Schaeffler, N., Washburn, A. : A Separation Control CFD Validation Test Case. Part 1: Baseline & Steady Suction. AIAA Flow Control Conference, 2004-2220 (2004).

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