Numerical Investigation on the Transition Flow around NLF Airfoil
Abstract
:1. Introduction
2. Numerical Method
2.1. Transition Model
2.2. Physical Model and Computational Domain
2.3. Numerical Settings
2.4. Independence Test of Mesh
2.5. Verification of Numerical Methods
3. Result and Discussion
3.1. Influence of Turbulent Intensity
3.2. Influence of Surface Temperature
3.3. Influence of Angle of Attack
3.4. Influence of Mach Number
3.5. Correlation
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
γ | intermittency |
k | turbulent kinetic energy |
ω | turbulent frequency |
kL | laminar kinetic energy |
Reθ | momentum thickness Reynolds number |
ρ | density |
ui | velocity |
μ | dynamic viscosity |
μt | turbulent eddy viscosity |
σk | constant in governing equation of k |
γeff | effective intermittency |
S | strain rate |
β | model coefficient |
σω | constant in governing equation of ω |
αω | model coefficient in governing equation of ω |
F1 | function in k-ω turbulence model |
σω,2 | constant in governing equation of ω |
Ce1 | constant in governing equation of γ |
Ca1 | constant in governing equation of γ |
Flength | empirical correlation that controls the length of the transition region |
Fonset | empirical correlation that controls the transition onset location |
Ce2 | constant in governing equation of γ |
Ca2 | constant in governing equation of γ |
Ω | vorticity magnitude |
Fturb | model coefficient in governing equation of γ |
cθ | constant in governing equation of Reθ |
Reθt | transition Reynolds number |
Fθ | blending function to turn off the source term in the boundary layer |
σθ | constant in governing equation of Reθ |
C | chord length |
ε | turbulent intensity |
α | angle of attack |
Tw | surface temperature |
xtol,s | transition onset location on suction side |
xtol,p | transition onset location on pressure side |
θ | normalized angle of attack |
τ | normalized surface temperature |
Appendix A
ε/% | Tw/K | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
0.1 | 293 | 0.5903 | 0.5931 |
0.5 | 293 | 0.5180 | 0.5694 |
1 | 293 | 0.3731 | 0.4182 |
0.1 | 313 | 0.5903 | 0.5931 |
0.5 | 313 | 0.5180 | 0.5694 |
1 | 313 | 0.3731 | 0.4262 |
Tw/K | α/° | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
293 | −6 | 0.1447 | 0.6391 |
313 | −6 | 0.1447 | 0.6391 |
293 | −3 | 0.4409 | 0.6169 |
313 | −3 | 0.4409 | 0.6169 |
293 | 0 | 0.5180 | 0.5694 |
313 | 0 | 0.5180 | 0.5694 |
293 | 3 | 0.6374 | 0.1344 |
313 | 3 | 0.6374 | 0.1344 |
293 | 6 | 0.6815 | 0.0969 |
313 | 6 | 0.6815 | 0.0969 |
Tw/K | α/° | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
293 | −6 | 0.1447 | 0.5869 |
313 | −6 | 0.1447 | 0.5869 |
293 | −3 | 0.1519 | 0.5697 |
313 | −3 | 0.1519 | 0.5776 |
293 | 0 | 0.3892 | 0.4819 |
313 | 0 | 0.3892 | 0.4819 |
293 | 3 | 0.5732 | 0.1344 |
313 | 3 | 0.5732 | 0.1344 |
293 | 6 | 0.6092 | 0.1048 |
313 | 6 | 0.5931 | 0.0969 |
Tw/K | α/° | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
293 | −6 | 0.1523 | 0.5869 |
313 | −6 | 0.1447 | 0.5869 |
293 | −3 | 0.1278 | 0.5539 |
313 | −3 | 0.1278 | 0.5618 |
293 | 0 | 0.3086 | 0.4023 |
313 | 0 | 0.3166 | 0.3863 |
293 | 3 | 0.5009 | 0.1344 |
313 | 3 | 0.4768 | 0.1344 |
293 | 6 | 0.5851 | 0.1048 |
313 | 6 | 0.6012 | 0.1048 |
Tw/K | α/° | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
293 | −6 | 0.1904 | 0.7436 |
313 | −6 | 0.1827 | 0.7511 |
293 | −3 | 0.1519 | 0.5303 |
313 | −3 | 0.1439 | 0.5933 |
293 | 0 | 0.3166 | 0.4262 |
313 | 0 | 0.3489 | 0.5614 |
293 | 3 | 0.5572 | 0.1344 |
313 | 3 | 0.5331 | 0.1344 |
293 | 6 | 0.5851 | 0.1048 |
313 | 6 | 0.6012 | 0.1048 |
α/° | Ma | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
−6 | 0.4 | 0.1447 | 0.6391 |
−3 | 0.4 | 0.4409 | 0.6169 |
0 | 0.4 | 0.5180 | 0.5694 |
3 | 0.4 | 0.6374 | 0.1344 |
6 | 0.4 | 0.6815 | 0.0969 |
−6 | 0.6 | 0.1447 | 0.5869 |
−3 | 0.6 | 0.1519 | 0.5697 |
0 | 0.6 | 0.3892 | 0.4819 |
3 | 0.6 | 0.5732 | 0.1344 |
6 | 0.6 | 0.6092 | 0.1048 |
−6 | 0.7 | 0.1523 | 0.5869 |
−3 | 0.7 | 0.1278 | 0.5539 |
0 | 0.7 | 0.3086 | 0.4023 |
3 | 0.7 | 0.5009 | 0.1344 |
6 | 0.7 | 0.5851 | 0.1048 |
−6 | 0.75 | 0.1904 | 0.7436 |
−3 | 0.75 | 0.1519 | 0.5303 |
0 | 0.75 | 0.3166 | 0.4262 |
3 | 0.75 | 0.5572 | 0.1344 |
6 | 0.75 | 0.5851 | 0.1048 |
α/° | Ma | Transition Onset Location | |
---|---|---|---|
Suction Side | Pressure Side | ||
−6 | 0.4 | 0.1447 | 0.6391 |
−6 | 0.6 | 0.1447 | 0.5869 |
−6 | 0.7 | 0.1523 | 0.5869 |
−6 | 0.75 | 0.1904 | 0.7436 |
−3 | 0.4 | 0.4409 | 0.6169 |
−3 | 0.6 | 0.1519 | 0.5697 |
−3 | 0.7 | 0.1278 | 0.5539 |
−3 | 0.75 | 0.1519 | 0.5303 |
0 | 0.4 | 0.5180 | 0.5694 |
0 | 0.6 | 0.3892 | 0.4819 |
0 | 0.7 | 0.3086 | 0.4023 |
0 | 0.75 | 0.3166 | 0.4262 |
3 | 0.4 | 0.6374 | 0.1344 |
3 | 0.6 | 0.5732 | 0.1344 |
3 | 0.7 | 0.5009 | 0.1344 |
3 | 0.75 | 0.5572 | 0.1344 |
6 | 0.4 | 0.6815 | 0.0969 |
6 | 0.6 | 0.6092 | 0.1048 |
6 | 0.7 | 0.5851 | 0.1048 |
6 | 0.75 | 0.5851 | 0.1048 |
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No. | Mesh Quantity | Streamwise Grids | Lift Coefficient | Drag Coefficient |
---|---|---|---|---|
1 | 2.39 × 106 | 282 | 0.2672 | 0.0053 |
2 | 3.07 × 106 | 376 | 0.2781 | 0.0051 |
3 | 3.75 × 106 | 470 | 0.2797 | 0.0051 |
4 | 4.43 × 106 | 564 | 0.2800 | 0.0050 |
Turbulent Intensity ε/% | Surface Temperature Tw/K | Angle of Attack α/° | Mach Number Ma |
---|---|---|---|
0.1, 0.5, 1 | 293, 313 | −6, −3, 0, 3, 6 | 0.4, 0.6, 0.7, 0.75 |
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Wang, H.; Tan, L.; Liu, M.; Liu, X.; Zhu, B. Numerical Investigation on the Transition Flow around NLF Airfoil. Energies 2023, 16, 1826. https://doi.org/10.3390/en16041826
Wang H, Tan L, Liu M, Liu X, Zhu B. Numerical Investigation on the Transition Flow around NLF Airfoil. Energies. 2023; 16(4):1826. https://doi.org/10.3390/en16041826
Chicago/Turabian StyleWang, Hongbiao, Lei Tan, Ming Liu, Xiang Liu, and Baoshan Zhu. 2023. "Numerical Investigation on the Transition Flow around NLF Airfoil" Energies 16, no. 4: 1826. https://doi.org/10.3390/en16041826
APA StyleWang, H., Tan, L., Liu, M., Liu, X., & Zhu, B. (2023). Numerical Investigation on the Transition Flow around NLF Airfoil. Energies, 16(4), 1826. https://doi.org/10.3390/en16041826