Errors and uncertainties in CFD validation for non-equilibrium turbulent boundary layer flows at high Reynolds numbers

Figures & data

Figure 1. Left: Virginia Tech 2D smooth wall flow (2D VT) (from [11]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.). Right: DLR/UniBw 2D smooth wall flow (reprinted with permission from [16]).

Figure 2. Left: 3D BeVERLI Hill flow (from [17]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.). Right: Body-of-Revolution in turbulent flow.

Figure 3. Left: Grid metrics using arithmetic average and root-mean-square cell areas for the grid levels for the 2D VT flow. Right: Grid levels 1, 3, 5 showing hierarchical refinement (zoom of the mesh for the 2D VT flow)(Figures from [11]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.).

Figure 4. Convergence study for 2D VT flow. Left: Mesh convergence for $C_f$ using the SST model using the CFD solver Kestrel. Middle and right: Code to code comparison for $C_f$ and mean velocity profiles $u^{+}$ vs. $y^{+}$ on grid level 3(Figures from [11]; reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.).

Figure 5. Illustration of the impact of an adjusted computational set-up compared to the original set-up for the 2D DLR/UniBw flow for the displacement thickness ${\delta }^{\ast }$ along the contour (left) and for the mean velocity profile in the region of strong adverse pressure gradient at $x=9.944\mathrm{m}$ (right).

Figure 6. $C_p$ and $C_f$ along the centerline in the streamwise $x_1$-direction (left) and the centerspan in the spanwise $x_3$-direction (right) from the ${45}^{\circ }$ yaw case BeVERLI Hill at $R{e}_H\approx \mathrm{650,000}$ on grid levels GL1 to GL4 (from [13]; reprinted by permission of the American Society of Mechanical Engineers ASME). Note that $x_1\equiv x$ and $x_3\equiv z$ in Figure 2 (left). The dotted line shows the hill geometry.

Figure 7. Uncertainty due to the discretisation error (DE) in $C_f$ along the centerline in $x_1$-direction (top) and the centerspan in $x_3$-direction (bottom) of the ${45}^{\circ }$ yaw case BeVERLI Hill at $R{e}_H\approx \mathrm{650,000}$ for SA-model (left) and SST-model (right) (from [13]; reprinted by permission of the American Society of Mechanical Engineers ASME). Note that $x_1\equiv x$ and $x_3\equiv z$ in Figure 2 (left). The dotted line shows the hill geometry.

Figure 8. Left: Uncertainty bars of the discretisation error for $C_f$ for the SST model for two different families of meshes (baseline meshes by VT and meshes with refinement around the airfoil by MARIN/IST (MI)). Right: Estimate of the error of the turbulence model ${\delta }_{\mathrm{tm}}$ for $C_f$ with reference model SST 2003 for model-scale $\mathrm{Re}=2\times {10}^6$ and for full-scale $\mathrm{Re}={10}^9$(Figures reprinted from [34]).

Figure 9. Mean velocity profiles in viscous units for the 2D VT flow at model-scale $\mathrm{Re}=2\times {10}^6$ and at full scale $\mathrm{Re}={10}^9$ at $x=3.5\mathrm{m}$ for the airfoil incidence angles $\alpha =-{10}^{\circ }$ (left), $\alpha =0^{\circ }$ (middle), and $\alpha ={12}^{\circ }$ (right)(Figures reprinted from [34]).

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