Heat Transfer Correlations for Smooth and Rough Airfoils
Low-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/8/2/66 |
| _version_ | 1827757425338351616 |
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| author | Sepehr Samadani François Morency |
| author_facet | Sepehr Samadani François Morency |
| author_sort | Sepehr Samadani |
| collection | DOAJ |
| description | Low-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The present study develops correlations for an average heat transfer over smooth and rough airfoil. The correlation coefficients were obtained from a CFD database using RANS equations and the Spalart–Allmaras turbulent model. This work studies the NACA 0009, NACA 0012, and NACA 0015 with and without the leading roughness representative of a small ice accretion. The numerical results are validated against lift and drag coefficients from the literature. The heat transfer at the stagnation point compares well with the experimental results. The database indicates a negligible dependency on airfoil thickness. The work presents two correlations from the database analysis: one for the smooth airfoils and one for the rough airfoils. For the zero lift coefficient, the average Nusselt number is maximum. This increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msup><mi>e</mi><mrow><mn>0.636</mn></mrow></msup></mrow></semantics></math></inline-formula> for the smooth surface and with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msup><mi>e</mi><mrow><mn>0.85</mn></mrow></msup></mrow></semantics></math></inline-formula> for the rough surface. As the lift increases, the average Nusselt is reduced by values proportional to the square of the lift coefficient for the smooth surface, while it is reduced by values proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and the square of the lift coefficient for the rough surface. |
| first_indexed | 2024-03-11T08:50:00Z |
| format | Article |
| id | doaj.art-8d88d163549449a29ebe92fed94de46d |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-11T08:50:00Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-8d88d163549449a29ebe92fed94de46d2023-11-16T20:28:55ZengMDPI AGFluids2311-55212023-02-01826610.3390/fluids8020066Heat Transfer Correlations for Smooth and Rough AirfoilsSepehr Samadani0François Morency1Thermo-Fluids for Transport Laboratory (TFT), Department of Mechanical Engineering, École de Technologie Supérieure (ÉTS), 1100 Notre-Dame St W, Montréal, QC H3C 1K3, CanadaThermo-Fluids for Transport Laboratory (TFT), Department of Mechanical Engineering, École de Technologie Supérieure (ÉTS), 1100 Notre-Dame St W, Montréal, QC H3C 1K3, CanadaLow-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The present study develops correlations for an average heat transfer over smooth and rough airfoil. The correlation coefficients were obtained from a CFD database using RANS equations and the Spalart–Allmaras turbulent model. This work studies the NACA 0009, NACA 0012, and NACA 0015 with and without the leading roughness representative of a small ice accretion. The numerical results are validated against lift and drag coefficients from the literature. The heat transfer at the stagnation point compares well with the experimental results. The database indicates a negligible dependency on airfoil thickness. The work presents two correlations from the database analysis: one for the smooth airfoils and one for the rough airfoils. For the zero lift coefficient, the average Nusselt number is maximum. This increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msup><mi>e</mi><mrow><mn>0.636</mn></mrow></msup></mrow></semantics></math></inline-formula> for the smooth surface and with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msup><mi>e</mi><mrow><mn>0.85</mn></mrow></msup></mrow></semantics></math></inline-formula> for the rough surface. As the lift increases, the average Nusselt is reduced by values proportional to the square of the lift coefficient for the smooth surface, while it is reduced by values proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi></mrow></semantics></math></inline-formula> and the square of the lift coefficient for the rough surface.https://www.mdpi.com/2311-5521/8/2/66heat transferroughnesssymmetric airfoilNusselt numberRANS equationsSpalart–Allmaras turbulence model |
| spellingShingle | Sepehr Samadani François Morency Heat Transfer Correlations for Smooth and Rough Airfoils Fluids heat transfer roughness symmetric airfoil Nusselt number RANS equations Spalart–Allmaras turbulence model |
| title | Heat Transfer Correlations for Smooth and Rough Airfoils |
| title_full | Heat Transfer Correlations for Smooth and Rough Airfoils |
| title_fullStr | Heat Transfer Correlations for Smooth and Rough Airfoils |
| title_full_unstemmed | Heat Transfer Correlations for Smooth and Rough Airfoils |
| title_short | Heat Transfer Correlations for Smooth and Rough Airfoils |
| title_sort | heat transfer correlations for smooth and rough airfoils |
| topic | heat transfer roughness symmetric airfoil Nusselt number RANS equations Spalart–Allmaras turbulence model |
| url | https://www.mdpi.com/2311-5521/8/2/66 |
| work_keys_str_mv | AT sepehrsamadani heattransfercorrelationsforsmoothandroughairfoils AT francoismorency heattransfercorrelationsforsmoothandroughairfoils |