Abstract
In the present study, numerical assessment of the \(\gamma - {\text{Re}}_{\theta t} - {\text{CF}}^{ + }\) transition model was carried out using a Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) flow solver based on unstructured meshes. A three-dimensional bump-in-channel verification case was first tested in a fully turbulent manner to verify the implementation of the \(k - {\upomega }\) shear stress transport turbulence model, which was coupled with the laminar-turbulent transition model. In addition, to validate the \(\gamma - {\text{Re}}_{\theta t} - {\text{CF}}^{ + }\) transition model, transition onset locations were compared with the experimental results for three angles-of-attack with a 6:1 prolate spheroid configuration. Then, the \(\gamma - {\text{Re}}_{\theta t} - {\text{CF}}^{ + }\) transition model was utilized to predict the skin friction distributions, surface pressure distributions, and transition onset locations of the natural-laminar-flow version of the common research model (CRM-NLF). For this purpose, a grid-resolution study was carried out for a fixed angle-of-attack on coarse, medium, and fine meshes. The aerodynamic performance of the CRM-NFL was compared with the experimental for four angles of attack.
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Abbreviations
- \(\gamma\) :
-
Intermittency
- \({\text{Re}}_{\theta t}\) :
-
Momentum thickness Reynolds number at transition onset, streamwise
- \({\text{CF}}^{ + }\) :
-
Cross-flow plus
- \({\text{RANS}}\) :
-
Reynolds-averaged Navier–Stokes
- \({\text{CFD}}\) :
-
Computational fluid dynamics
- \(k\) :
-
Turbulence kinetic energy
- \(\omega\) :
-
Specific turbulence dissipation rate
- \({\text{CRM}}\) :
-
Common research model
- \({\text{NLF}}\) :
-
Natural-laminar flow
- \({\text{MPI}}\) :
-
Massage passing interface
- \({\text{SST}}\) :
-
Shear stress transport
- \(P_{\gamma }\) :
-
Production term in transport equation for the intermittency
- \(D_{\gamma }\) :
-
Destruction term in transport equation for the intermittency
- \(S\) :
-
Strain rate magnitude
- \(\Omega\) :
-
Vorticity magnitude
- \(F_{{{\text{onset1\_3D}}}}\) :
-
Transition length function
- \({\text{Re}}_{\delta 2c}\) :
-
Displacement thickness Reynolds number at transition onset, crosswise (transition criterion)
- \(\theta\) :
-
Momentum thickness, streamwise
- \(\mu\) :
-
Molecular viscosity
- \(\mu_{{\text{t}}}\) :
-
Eddy viscosity
- \(\rho\) :
-
Density
- \(\phi\) :
-
Local sweep angle
- \(y^{ + }\) :
-
Non-dimensional distance from the wall to the first mesh node
- \(P_{{\text{t}}}\) :
-
Total pressure
- \(P_{{{\text{ref}}}}\) :
-
Pressure at reference point
- \(T_{{\text{t}}}\) :
-
Total temperature
- \(T_{{{\text{ref}}}}\) :
-
Temperature at reference point
- \(P\) :
-
Pressure
- \(k_{\infty }\) :
-
Freestream turbulence kinetic energy
- \(\omega_{\infty }\) :
-
Freestream specific rate of dissipation
- \(a_{\infty }\) :
-
Freestream speed of sound
- \(\mu_{\infty }\) :
-
Viscosity of the freestream
- \(\rho_{\infty }\) :
-
Freestream density
- \({\text{TI}}\) :
-
Turbulence intensity
- \(M_{\infty }\) :
-
Freestream Mach number
- \(L^{*}\) :
-
Non-dimensional length from the object to the far-field
- \(\eta\) :
-
Spanwise location
- \(d\) :
-
Wall distance vector
- \(\widetilde{r}\) :
-
Reynolds number ratio, crosswise
- \(\lambda_{\theta }\) :
-
Pressure gradient parameter
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Acknowledgements
This work was conducted at High-Speed Compound Unmanned Rotorcraft (HCUR) research laboratory with the support of Agency for Defense Development (ADD).
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Park, S.H., Han, J. & Kwon, O.J. Prediction and Analysis of Transitional Crossflows Using \(\gamma - {\text{Re}}_{\theta t} - {\text{CF}}^{ + }\) Model. Int. J. Aeronaut. Space Sci. 23, 461–470 (2022). https://doi.org/10.1007/s42405-022-00457-4
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DOI: https://doi.org/10.1007/s42405-022-00457-4