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Prediction and Analysis of Transitional Crossflows Using \(\gamma - {\text{Re}}_{\theta t} - {\text{CF}}^{ + }\) Model

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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

References

  1. Medida S, Baeder J (2013) A new crossflow transition onset criterion for RANS turbulence models. In: Paper presented at the 21st AIAA computational fluid dynamics conference, 24–27 June, San Diego. https://doi.org/10.2514/6.2013-3081

  2. Jain R (2017) CFD performance and turbulence transition predictions on an installed model-scale rotor in hover. In: Paper presented at the 55th AIAA Aerospace Sciences Meetings, 9–13 January, Grapevine. https://doi.org/10.2514/6.2017-1871

  3. Langtry RB, Menter FR (2009) Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA J 47(12):2894–2906. https://doi.org/10.2514/1.42362

    Article  Google Scholar 

  4. Watanabe Y, Misaka T, Obayashi S, Arima T, Yamaguchi Y (2009) Application of crossflow transition criteria to local correlation-based transition model. In: Paper presented at the 47th AIAA aerospace science meetings, 5–8 January, Orlando. https://doi.org/10.2514/6.2009-1145

  5. Grabe C, Krumbein A (2013) Correlation-based transition transport modeling for three-dimensional aerodynamic configurations. J Aircr 50(5):1533–1539. https://doi.org/10.2514/1.C032063

    Article  Google Scholar 

  6. Choi JH, Kwon OJ (2017) Recent improvement of a correlation-based transition model for simulating three-dimensional boundary layers. AIAA J 55(6):2013–2018. https://doi.org/10.2514/1.J055182

    Article  Google Scholar 

  7. Meier HU, Kreplin HP (1980) Experimental investigation of the boundary layer transition and separation on a body of revolution. Z für Flugwiss und Weltraumforsch 4:65–71

    Google Scholar 

  8. Boris D, Thomas JL, Pandya MJ, Rumsey CL (2016) Reference solutions for benchmark three dimensional turbulent flows. In: Proceedings of the AIAA Scitech 2016 Forum, 4–8 January, San Diego. https://doi.org/10.2514/6.2016-0858

  9. Kreplin HP, Meier HU, Maier A (1978) Wind tunnel model and measuring techniques for the investigation of three-dimensional turbulent boundary layers. In: Proceedings of the 10th AIAA aerodynamic testing conference, San Diego. https://doi.org/10.2514/6.1978-781

  10. Kreplin HP, Vollmers H, Meier HU (1985) Wall shear stress measurements on an inclined prolate spheroid in the DFVLR 3 m × 3 m low speed wind tunnel, Göttingen. Deutsche Forschungs and Versuchsanstalt für Luft und Raumfahrt Rept 33:222–284

    Google Scholar 

  11. Lynde MN, Campbell RL, Rivers MB, Viken SA, Chan DT, Watkins AN (2019) Preliminary results from an experimental assessment of a natural laminar flow design method. In: Proceedings of the AIAA Scitech 2019 Forum, 7–11 January, San Diego. https://doi.org/10.2514/6.1978-781

  12. Lynde MN, Campbell RL, Viken SA (2019) Additional findings from the common research model natural laminar flow wind tunnel test. In: Proceedings of the AIAA aviation 2019 forum, 17–21 June 2019, Dallas. https://doi.org/10.2514/6.2019-3292

  13. Jung MS, Kwon OJ, Kang HJ (2007) Assessment of rotor hover performance using a node-based flow solver. Int J Aeronaut Space Sci 8(2):44–45

    Article  Google Scholar 

  14. Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference. J Comput Phys 43(2):357–372. https://doi.org/10.1016/0021-9991(81)90128-5

    Article  MathSciNet  MATH  Google Scholar 

  15. Mathur SR, Murthy JY (1997) A pressure-based method for unstructured meshes. Numer Heat Transf 31(2):195–215. https://doi.org/10.1080/10407799708915105

    Article  Google Scholar 

  16. Venkatakrishnan V (1995) Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J Comput Phys 118(1):120–130. https://doi.org/10.1006/jcph.1995.1084

    Article  MATH  Google Scholar 

  17. Karypis G, Kumar V (1998) Multilevel k-way partitioning schemes for irregular graphs. J Parallel Distrib Comput 48(1):96–129

    Article  Google Scholar 

  18. Cooke JC (1950) The boundary layer of a class of infinite yawed cylinders. Math Proc Camb Philos Soc 46(4):645–648. https://doi.org/10.1017/S0305004100026220

    Article  MathSciNet  MATH  Google Scholar 

  19. Coder JG (2018) Standard test cases for transition model verification and validation in computational fluid dynamics. In: Proceedings of the AIAA Scitech 2018 Forum, 8–12 January, Kissimmee. https://doi.org/10.2514/6.2018-0029

  20. Menter FR, Smirnov PE, Liu T, Avancah R (2015) A one-equation local correlation-based transition model. Flow Turbul Combust 95:583–619. https://doi.org/10.1007/s10494-015-9622-4

    Article  Google Scholar 

  21. Park SH, Kwon OJ (2021) Numerical study of effects of fuselage and facility wall on PSP rotor performance in hover. Int J Aeronaut Space Sci. https://doi.org/10.1007/s42405-021-00420-9

    Article  Google Scholar 

  22. Park SH, Han J, Kwon OJ (2021) Numerical study of HVAB rotor using a mixed mesh flow solver. In: Proceedings of the AIAA Scitech 2021 Forum, 11–15 & 19–21 January 2021, Online event. https://doi.org/10.2514/6.2021-0619

  23. Jung YS, Lee B, Baeder J (2021) Validation of SA- turbulence/transition models. In: Proceedings of the 1st AIAA transition modeling and prediction workshop, 21–22 January, Online event

  24. Zore K, Shah S, Matyushenko A (NTS), Menter F, Stokes J (2021) Ansys submission to 1st AIAA transition modeling prediction workshop. In: Proceedings of the 1st AIAA transition modeling and prediction workshop, 21–22 January, Online event.

  25. Denison M (2021) Lantry–Menter model based simulation in OVERFLOW. In: Proceedings of the 1st AIAA transition modeling and prediction workshop, 21–22 January, Online event.

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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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Correspondence to Oh Joon Kwon.

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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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