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DDES Study of Confined and Unconfined NACA Wing Sections Using Spectral Elements

Vishal Kumar, Ananias Tomboulides, Paul Fischer, Misun Min

Abstract

We develop hybrid RANS-LES strategies within the spectral element code Nek5000 based on the $k-τ$ class of turbulence models. We chose airfoil sections at small flight configurations as our target problem to comprehensively test the solver accuracy and performance. We present verification and validation results of an unconfined NACA0012 wing section in a pure RANS and in a hybrid RANS-LES setup for an angle of attack ranging from 0 to 90 degrees. The RANS results shows good corroboration with existing experimental and numerical datasets for low incoming flow angles. A small discrepancy appears at higher angle in comparison with the experiments, which is in line with our expectations from a RANS formulation. On the other hand, DDES captures both the attached and separated flow dynamics well when compared with available numerical datasets. We demonstrate that for the hybrid turbulence modeling approach a high-order spectral element discretization converges faster (i.e., with less resolution) and captures the flow dynamics more accurately than representative low-order finite-volume and finite-difference approaches. We also revise some of the guidelines on sample size requirements for statistics convergence. Furthermore, we analyze some of the observed discrepancies of our unconfined DDES at higher angles with the experiments by evaluating the side wall "blocking" effect. We carry out additional simulations in a confined 'numerical wind tunnel' and assess the observed differences as a function of Reynolds number.

DDES Study of Confined and Unconfined NACA Wing Sections Using Spectral Elements

Abstract

We develop hybrid RANS-LES strategies within the spectral element code Nek5000 based on the class of turbulence models. We chose airfoil sections at small flight configurations as our target problem to comprehensively test the solver accuracy and performance. We present verification and validation results of an unconfined NACA0012 wing section in a pure RANS and in a hybrid RANS-LES setup for an angle of attack ranging from 0 to 90 degrees. The RANS results shows good corroboration with existing experimental and numerical datasets for low incoming flow angles. A small discrepancy appears at higher angle in comparison with the experiments, which is in line with our expectations from a RANS formulation. On the other hand, DDES captures both the attached and separated flow dynamics well when compared with available numerical datasets. We demonstrate that for the hybrid turbulence modeling approach a high-order spectral element discretization converges faster (i.e., with less resolution) and captures the flow dynamics more accurately than representative low-order finite-volume and finite-difference approaches. We also revise some of the guidelines on sample size requirements for statistics convergence. Furthermore, we analyze some of the observed discrepancies of our unconfined DDES at higher angles with the experiments by evaluating the side wall "blocking" effect. We carry out additional simulations in a confined 'numerical wind tunnel' and assess the observed differences as a function of Reynolds number.
Paper Structure (21 sections, 33 equations, 10 figures, 5 tables)

This paper contains 21 sections, 33 equations, 10 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Numerical framework
  3. RANS and Hybrid RANS-LES formulations
  4. Standard $k-\tau$ model and its SST formulation
  5. $k-\tau$ SST DDES formulation
  6. Simulation Results
  7. Grid generation and boundary conditions
  8. RANS model validation
  9. Assessment of DDES statistical sample requirements
  10. Assessment of DDES accuracy
  11. Instantaneous flow
  12. Averaged flow and aerodynamic forces
  13. Assessment of confinement effect
  14. Conclusions
  15. Numerical framework
  16. ...and 6 more sections

Figures (10)

  • Figure 1: (a) (not to scale) O-domain used for carrying out wing simulations; blue and red (based on incoming angle) represent inflow and outflow conditions, respectively; (b) cross section of spectral element mesh used; (c) sample grid with all GLL points; (d) close-up of airfoil region; (e) close-up of leading-edge region; and (f) close-up of trailing-edge regions.
  • Figure 2: (a) Cross-section view of mesh used for "wind tunnel" wing simulations; (b) close-up on airfoil. For resolution details refer to Table \ref{['table:ddes_re2m']}.
  • Figure 3: (a) Pressure coefficient $(C_p)$ and (b) friction coefficient, $(C_f)$ for flow over NACA0012 at $Re=6\times 10^6$ as predicted by the $k-\tau$ SST model. "Data" in the legend refers to data obtained with NASA's CFL3D code.
  • Figure 4: (a) Time evolution of spanwise-averaged lift coefficient for NACA0021 at $Re=2.7\times10^5$ and $AoA=60^o$; green and blue dashed lines depict $\pm \sigma(C_l)$ and $\pm 2 \sigma(C_l)$, respectively; (b) running average of span-averaged $C_l$; dashed-black line shows the sample mean; (c)$C_l$ power spectral density; red line: Nek5000, black line: DES data of Garbaruk2009; grey line: exp. data of Swalwell2003; (d) histogram (percent occurrence) of $C_l$; (e) histogram (percent occurrence) of $C_d$.
  • Figure 5: Visualization of vortical structures using contours of the Q-criterion ($Qc^2/U_o^2=1$) for the DDES cases at $AoA=45^o$; (a) coarse grid; (b) Fine grid; contours are colored by velocity magnitude.
  • ...and 5 more figures