On Numerical Simulations of Turbulent Flows over a Bluff Body with Aerodynamic Flow Control Based on Trapped Vortex Cells: Viscous Effects
Abstract
:1. Introduction
- To perform numerical simulations based on LES on a simplified bluff body with AFC at Re = 130,000 and zero angle of attack. To investigate its aerodynamic characteristics and energy losses and to verify that the flow is practically unseparated, except for small-scale turbulence.
- Based on the classical RANS approach, to numerically investigate the effect of viscosity on the design efficiency and to show that this concept is practically invariant with respect to the Reynolds number, i.e., the lift-to-drag ratio is approximately constant over a wide range of Reynolds numbers (50,000 ≤ Re ≤ 1,000,000) and converges to an asymptotic value. The limiting case when the Reynolds number tends to infinity, , is estimated based on both analytical considerations and a numerical experiment in which the Euler equations are solved. As a general result, it was found that the lift force of the developed concept is approximately of its limiting analytical value ().
2. Problem Statement and Theoretical Considerations
2.1. Overview of the Aerodynamic Flow Control Concept Based on the Trapped Vortex Cells
2.2. Overview of the Large Eddy Simulation Technique
2.3. Ultimate Analytical Lift Properties of Airfoils in Potential Flows
- —flow around a flat-plate airfoil installed at a given angle of attack (see Figure 3a): . The max theoretical value of the lift force of a thin plate is achieved at the angle of attack, ,
- —flow around a curved plate in the form of a half-circle (see Figure 3b). In this case, the following values of can be obtained:One can see clearly that the maximum lift coefficient can be achieved for . Of course, the value of depends on the length used as a reference. Here, it is assumed that the conventional chord is applied. For a circle, under the imposed assumptions, it is possible to recover as a limit. In the same spirit, the half-circle limit of can be considered. That is the limiting value for any single-element airfoil [30].
3. Brief Aspects of the Numerical Simulations
3.1. Overview of the Numerical Methodology
3.2. Computational Grids
3.3. Boundary and Initial Conditions
4. Results
4.1. LES Results
4.2. Analysis of the Viscous Effects Based on the RANS Approach
- The results obtained in 2D deviate by approximately 7% from the 3D results for Reynolds numbers of 75,000 and 130,000. As the Reynolds number increases, this discrepancy diminishes.
- There is almost perfect agreement between the baseline simulations using the realizable k- turbulence model on the A0 and A1 grids, indicating grid independence.
- The influence of turbulence models is limited; both RKE and SA models show the same trend but have a systematic shift of around .
- For the limiting case of inviscid fluid, the lift coefficient value is about 5% lower than the values obtained using RKE for a Reynolds number of 1,000,000. This is explained by vortex breakups or the coexistence of small coherent vortex structures in the trapped vortex cells and additional vortices in the system channels, as demonstrated in Figure 8d. The limiting case confirms the general trend.
- From the perspective of numerical modeling, satisfactory agreement is achieved between the aerodynamic coefficients, with a minimum difference of 5% for LES and RANS for a Reynolds number of 130,000. It is important to emphasize that for both approaches, grid dependence of the solution is practically non-existent. The agreement between the results can be attributed to the consistency of both methodologies and the use of a differential, algebraic equation for the kinetic energy to close the Navier–Stokes equations.
5. Discussion
5.1. Critical Remark on the Grid Independence Study
5.2. Comparison of Results Obtained by the LES and RANS Approaches
5.3. Effects of Compressibility
6. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AF | Ansys Fluent |
AFC | Aerodynamic Flow Control |
AMG | Algebraic Multigrid Method |
BB | Bluff Body |
BDF | Backward Differencing Formula |
CC | Circular Cylinder |
CDS | Central Differencing Scheme |
CFD | Computational Fluid Dynamics |
CRANE | Control of Revolutionary Aircraft with Novel Effectors |
FVM | Finite Volume Method |
GAMG | Geometric Multigrid Method |
HC | Semi-Circular Cylinder |
LES | Large Eddy Simulation |
LIC | Line Integral Convolution |
Probability Density Distribution | |
RANS | Reynolds-Averaged Navier–Stokes |
SOU | Second-Order Upwind Scheme |
TVC | Trapped Vortex Cell |
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Run | Re/1000 | |||
---|---|---|---|---|
LES-AFC-A0 | 0.870 | 5.094 | 5.855 | 130 |
LES-AFC-A1 | 0.875 | 5.092 | 5.819 | 130 |
LES-HC-H0 | 0.387 | −0.883 | −2.152 | 130 |
Previous results | ||||
LES-AFC02 [13] | 0.525 | 0.760 | 1.448 | 50 |
LES-HC2-dTKE [21] | 0.469 | −1.035 | −2.207 | 50 |
TM | Mesh | Re/1000 | Case ID | |||
---|---|---|---|---|---|---|
SA | A1 | 0.84 | 3.88 | 4.62 | 75 | |
SA | A1 | 0.84 | 4.3 | 5.12 | 130 | |
SA | A1 | 0.85 | 4.72 | 5.55 | 500 | |
SA | A1 | 0.87 | 4.88 | 5.61 | 1000 | |
RKE | A0 | 0.82 | 4.4 | 5.37 | 75 | |
RKE | A0 | 0.81 | 4.86 | 6.00 | 130 | AFC-RANS-A0 |
RKE | A0 | 0.82 | 5.37 | 6.55 | 500 | |
RKE | A0 | 0.83 | 5.43 | 6.54 | 1000 | |
RKE | A1 | 0.83 | 4.4 | 5.30 | 75 | |
RKE | A1 | 0.82 | 4.86 | 5.93 | 130 | AFC-RANS-A1 |
RKE | A1 | 0.83 | 5.35 | 6.45 | 500 | |
RKE | A1 | 0.83 | 5.41 | 6.52 | 1000 | |
RKE | 2D | 0.84 | 4.83 | 5.75 | 75 | |
RKE | 2D | 0.85 | 5.15 | 6.06 | 130 | |
RKE | 2D | 0.86 | 5.24 | 6.09 | 500 | |
RKE | 2D | 0.87 | 5.28 | 6.07 | 1000 | |
Inviscid | 2D | 0.85 | 5.1 | 6.00 | ∞ | |
Incompressible RKE | A0 | 0.82 | 4.82 | 5.88 | 130 |
Mesh | ||
---|---|---|
A0 | 0.81 | 4.86 |
A1 | 0.82 | 4.86 |
A11 | 0.83 | 4.83 |
A12 | 0.83 | 4.83 |
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Lysenko, D.A. On Numerical Simulations of Turbulent Flows over a Bluff Body with Aerodynamic Flow Control Based on Trapped Vortex Cells: Viscous Effects. Fluids 2025, 10, 120. https://doi.org/10.3390/fluids10050120
Lysenko DA. On Numerical Simulations of Turbulent Flows over a Bluff Body with Aerodynamic Flow Control Based on Trapped Vortex Cells: Viscous Effects. Fluids. 2025; 10(5):120. https://doi.org/10.3390/fluids10050120
Chicago/Turabian StyleLysenko, Dmitry A. 2025. "On Numerical Simulations of Turbulent Flows over a Bluff Body with Aerodynamic Flow Control Based on Trapped Vortex Cells: Viscous Effects" Fluids 10, no. 5: 120. https://doi.org/10.3390/fluids10050120
APA StyleLysenko, D. A. (2025). On Numerical Simulations of Turbulent Flows over a Bluff Body with Aerodynamic Flow Control Based on Trapped Vortex Cells: Viscous Effects. Fluids, 10(5), 120. https://doi.org/10.3390/fluids10050120