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Numerical Modelling and Entropy Analysis of Pitching Aerofoil Under the Dynamic Stall

  • Research Article-Mechanical Engineering
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Abstract

In this research, the improvement of wind turbine blade undergoing pitching motion by means of identifying optimized aerofoil profile has been studied as a crucial part of enhancing effectiveness of wind energy turbine system. Here, the projected air is considered as unidirectional with flow speed range of Re 5*105 to 106. The effect of different pitching aerofoil blade profiles ranging from NACA 0012, S-809, and SD 7062 has been investigated in addition to the aerodynamic characteristics, entropy generation in the flow and exergy which are also proposed as a criterion for selecting optimum design for the oscillating aerofoil blade. Finally, increment in Re shows increase in the entropy generation rate and decrease in exergy efficiency. Consequently, aerofoil profile shows prominent variations in exergy with SD 7062 experiencing least entropy generation rate and exergy efficiency of around 93% due to its streamlined profile as compared to other profiles in this study. Meanwhile, NACA 0012 experiences minimum exergy efficiency of around 39% for Re 106.

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Abbreviations

C:

Chord length [m]

\({C}_{\mathrm{D}}\) :

Coefficient of drag

\({C}_{\mathrm{L}}\) :

Coefficient of lift

\(\dot{E}\) :

Exergy [W]

\(I\) :

Irreversibility [W/m3]

\({I}_{\mathrm{l}}\) :

Local entropy generation

\(K\) :

Reduced frequency

\(k\) :

Turbulence kinetic energy [m2/s2]

\(P\) :

Pressure [Pa]

\(\mathrm{Re}\) :

Reynolds number

\({S}_{\mathrm{G}}\) :

Total entropy generation rate [W/K]

\({S}_{\mathrm{gen}}\) :

Local entropy generation rate [W/(m3K)]

\({S}_{x}\) :

Source term for body force-x

\({S}_{y}\) :

Source term for body force-y

\(t\) :

Flow time [s]

\({T}_{0}\) :

Reference temperature [K]

\(u\) :

Stream-wise velocity [m/s]

\({u}_{\infty }\) :

Free-stream velocity [m/s]

\(v\) :

Cross-stream velocity [m/s]

\(x\) :

Stream-wise dimension of coordinates [m]

\(y\) :

Cross-stream dimension of coordinates [m]

y + :

Non-dimensional wall distance

\(\alpha\) :

Angle of attack [deg]

\({\alpha }_{\mathrm{mean}}\) :

Mean \(\alpha\) [deg]

\({\alpha }_{\mathrm{amp}}\) :

Amplitude \(\alpha\) [deg]

ϵ:

Turbulence dissipation rate [m2/s2]

\(\rho\) :

Density of fluid [kgm−3]

\({\tau }_{ij}\) :

Shear stress tensor

\(\mu\) :

Viscosity of fluid [Pa s]

\({\mu }_{t}\) :

Turbulent viscosity [Pa s]

\(\omega\) :

Angular frequency [rad/s

NACA:

National Advisory Committee for Aeronautics

NREL:

National renewable energy laboratory

SIMPLE:

Semi-implicit method for pressure-linked equations

SST:

Shear stress transport

NACA:

National Advisory Committee for Aeronautics

NREL:

National renewable energy laboratory

SIMPLE:

Semi-implicit method for pressure-linked equations

SST:

Shear stress transport

References

  1. Zhao, Y.; Cheng, Z.; Sandvik, P.C.; Gao, Z.; Moan, T.: An integrated dynamic analysis method for simulating installation of single blades for wind turbines. Ocean. Eng. 152, 72–88 (2018)

    Google Scholar 

  2. Castellani, F.; Astolf, D.; Garinei, A.; Proietti, S.; Sdringola, P.; Terzi, L.; Desideri, U.: How wind turbines alignment to wind direction affects effciency? A case study through SCADA data mining. Energy Procedia 75, 697–703 (2015)

    Google Scholar 

  3. Li, X.; Zhang, L.; Song, J.; Bian, F.; Yang, K.: Aerofoil design for large horizontal axis wind turbines in low wind speed regions. Renew. Energy 145, 2345–2357 (2020)

    Google Scholar 

  4. Liu, P.; Yu, G.; Zhu, X.; Du, Z.: Unsteady aerodynamic prediction for dynamic stall of wind turbine aerofoils with the reduced order modeling. Renew. Energy 69, 402–409 (2014)

    Google Scholar 

  5. Yan, C.; Archer, C.Y.: Assessing compressibility effects on the performance of large horizontal-axis wind turbines. Appl. Energy 212, 33–45 (2018)

    Google Scholar 

  6. Chan, C.H.; Bai, H.L.; He, D.Q.: Blade shape optimization of the Savonius wind turbine using a genetic algorithm. Appl. Energy 213, 148–157 (2018)

    Google Scholar 

  7. Wernert, P.; Geissler, W.; Raffel, M.; Kompenhans, J.: Experimental and numerical investigations of dynamic stall on a pitching aerofoil. AIAA J. 34(5), 982–989 (1996)

    Google Scholar 

  8. Soltani, M.R.; Mahmoudi, M.: Measurements of velocity field in the wake of an oscillating wind turbine blade. Aeronaut. J. 114(1158), 493–504 (2010)

    Google Scholar 

  9. Akbari, M.H.; Price, S.J.: Simulation of dynamic stall for a NACA 0012 aerofoil using a vortex method. J. Fluids Struct. 17, 855–874 (2003)

    Google Scholar 

  10. Rezaeiha, A.; Kalkman, I.; Blocken, B.: Effect of pitch angle on power performance and aerodynamics of a vertical axis wind turbine. Appl. Energy. 197, 132–150 (2017)

    Google Scholar 

  11. Cui, A.; Knight, D.D.: Parallel computation of the 2-d navier-stokes flowfield of a pitching aerofoil. Int. J. Comput. Fluid Dyn. 4(1–2), 111–135 (2007)

    Google Scholar 

  12. Gharali, K.; Johnson, D.A.: Dynamic stall simulation of a pitching aerofoil under unsteady freestream velocity. J. Fluids Struct. 42, 228–244 (2013)

    Google Scholar 

  13. Gharali, K.; Johnson, D.A.: Effects of nonuniform incident velocity on a dynamic wind turbine aerofoil. Wind Energy 18(2), 237–251 (2014)

    Google Scholar 

  14. Gharali, K.; Johnson, D.A.; Lam, V.; Gu, M.: A 2D blade element study of a wind turbine rotor under yaw loads. Wind Eng. 39(5), 557–567 (2015)

    Google Scholar 

  15. Gharali, K.; Gharaei, E.; Soltani, M.; Raahemifar, K.: Reduced frequency effects on combined oscillations, angle of attack and free stream oscillations, for a wind turbine blade element. Renew. Energy 115, 252–259 (2018)

    Google Scholar 

  16. Gharali, K.; Johnson, D.A.: Numerical modeling of an S809 aerofoil under dynamic stall, erosion and high reduced frequencies. Appl. Energy 93, 45–52 (2012)

    Google Scholar 

  17. Wilcox, D.C.: Turbulence Modeling for CFD. DCW Industries Inc, La Canada, California (1998)

    Google Scholar 

  18. Menter, F.R.: Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994)

    Google Scholar 

  19. Xu, H.Y.; Qiao, C.L.; Ye, Z.Y.: Dynamic stall control on the wind turbine aerofoil via a Co-flow jet. Energies 9, 429–454 (2016)

    Google Scholar 

  20. Liu, X.; Lu, C.; Liang, S.; Godbole, A.; Chen, Y.: Vibration-induced aerodynamic loads on large horizontal axis wind turbine blades. Appl. Energy. 185, 1109–1119 (2016)

    Google Scholar 

  21. Bejan, A.: A study of entropy generation in fundamental convective heat transfer. J. Heat Transf. 101(4), 718 (1979)

    Google Scholar 

  22. Bejan, A.: Second law analysis in heat transfer. Energy 5(8–9), 720–732 (1980)

    Google Scholar 

  23. Wenterodt, T.; Redecker, C.; Herwig, H.: Second law analysis for sustainable heat and energy transfer: The entropic potential concept. Appl. Energy. 139, 376–383 (2015)

    Google Scholar 

  24. Vatanmakan, M.; Lakzian, E.; Mahpeykar, M.R.: Investigating the entropy generation in condensing steam flow in turbine blades with volumetric heating. Energy 147, 701–714 (2018)

    Google Scholar 

  25. Walsh, E.J.; McEligot, D.: Relation of entropy generation to wall ‘laws’ for turbulent flows. Int. J. Comput. Fluid Dyn. 22(10), 649–657 (2008)

    MATH  Google Scholar 

  26. Foroozesh, F.; Khoshnevis, A.B.; Lakzian, E.: Improvement of the wet steam ejector performance in a refrigeration cycle via changing the ejector geometry by a novel EEC (Entropy generation, Entrainment ratio, and Coefficient of performance) method. Int. J. Refrig 110, 248–261 (2020)

    Google Scholar 

  27. Shehata, A.S.; Xiao, Q.; Saqr, K.M.; Alexander, D.: Wells turbine for wave energy conversion: a review. Int. J. Energy Res. 41(1), 6–38 (2016)

    Google Scholar 

  28. Wen, C.; Zhang, J.; Wang, C.; Dong, X.; Peng, H.; Gao, H.; Wang, J.: An analysis method for exergy efficiency of wind turbines based on experiment and simulation. Energy Sources Part A Recov. Util. Environ. Effects 42(9), 1072–1084 (2020)

    Google Scholar 

  29. Mortazavi, M.; Sobhgahi, S.: Numerical investigation on the exergetic performance of NREL aerofoil families for wind turbine application. Int. J. Exergy 18, 387 (2015)

    Google Scholar 

  30. Mamouri, A.R.; Khoshnevis, A.B.; Lakzian, E.: Entropy generation analysis of S825, S822, SD7062 offshore wind turbine aerofoil geometries. Ocean. Eng. 173, 700–715 (2019)

    Google Scholar 

  31. Mamouri, A.R.; Lakzian, E.; Khoshnevis, A.B.: Entropy analysis of pitching aerofoil for offshore wind turbines in the dynamic stall condition. Ocean Eng. 187, 106229 (2019)

    Google Scholar 

  32. Mamouri, A.R.; Khoshnevis, A.B.; Lakzian, E.: Experimental study of the effective parameters on the offshore wind turbine’s aerofoil in pitching case. Ocean. Eng. 198, 106955 (2020)

    Google Scholar 

  33. Karthikeyan, N.; Kalidas Murugavel, K.; Arun Kumar, S.; Rajakumar, S.: Review of aerodynamic developments on small horizontal axis wind turbine blade. Renew. Sustain. Energy Rev. 42, 801–822 (2015)

    Google Scholar 

  34. Gross, A.; Fasel, H.F.: Flow control for NREL S822 wind turbine aerofoil. AIAA J. 50(12), 2779–2789 (2012)

    Google Scholar 

  35. Gupta, S.; Leishman, J.G.: Dynamic stall modeling of the S809 aerofoil and comparison with experiments. Wind Energy 9(6), 521–547 (2006)

    Google Scholar 

  36. Guillaud, N.; Balarac, G.; Goncalves, E.: Large Eddy Simulations on a pitching aerofoil: analysis of the reduced frequency influence. Comput. Fluids 161, 1–13 (2018)

    MathSciNet  MATH  Google Scholar 

  37. Hand, B.; Kelly, G.; Cashman, A.: Numerical simulation of a vertical axis wind turbine aerofoil experiencing dynamic stall at high Reynolds numbers. Comput. Fluid 149, 12–30 (2017)

    MATH  Google Scholar 

  38. Zhong, J.; Li, J.; Guo, P.; Wang, Y.: Dynamic stall control on a vertical axis wind turbine aerofoil using leading-edge rod. Energy 174, 246–260 (2019)

    Google Scholar 

  39. Versteeg, H.K.; Malalasekera, W.: An Introduction to Computational Fluid Dynamics. Pearson Education Limited, London (2007)

    Google Scholar 

  40. Sayed, M.A.; Kandil, H.A.; Shaltot, A.: Aerodynamic analysis of different wind turbine-blade profles using fnite-volume method. Energy Convers. Manag. 64, 541–550 (2012)

    Google Scholar 

  41. Kock, F.; Herwig, H.: Local entropy production in turbulent shear flows: a high-Reynolds number model with wall functions. Int. J. Heat Mass Transf. 47(10–11), 2205–2215 (2004)

    MATH  Google Scholar 

  42. Herwig, H.; Kock, F.: Direct and indirect methods of calculating entropy generation rates in turbulent convective heat transfer problems. Heat Mass Transf. 43(3), 207–215 (2006)

    Google Scholar 

  43. ANSYS Inc. ANSYS FLUENT 12.0 (Theory Guide); (2009)

  44. Ramsay, R.; Homan, M.; Gregorek, G.: Effects of grit roughness and pitch oscillation on the S809 aerofoil. Tech. Rep., NREL. NREL/TP-442–7817 (1995)

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Acknowledgements

This research is supported by the Product Development Laboratory and the Computational Fluid Dynamics Laboratory of the SRM Institute of Science and Technology. These supports are gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mechanical Engineering, SRM Institute of Science and Technology, Kattankulathur, 603 203, India

    Amit Varakhedkar & Rajendran Senthil Kumar

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  1. Amit Varakhedkar
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Correspondence to Rajendran Senthil Kumar.

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Varakhedkar, A., Kumar, R.S. Numerical Modelling and Entropy Analysis of Pitching Aerofoil Under the Dynamic Stall. Arab J Sci Eng 48, 11333–11350 (2023). https://doi.org/10.1007/s13369-022-07424-x

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