Effect of Mesh Shape and Turbulence Model on Aerodynamic Performance at NACA 4415

Document Type : Regular Article


Department of Mechanical Engineering, Universitas Pembangunan Nasional Veteran Jakarta, 12450, Indonesia



This study uses three turbulence model variations, i.e., S - A, k - ε, and k – ω turbulence models. In addition, there are two variations of cell shape and three variations of cell number. The number of cells is 500, 5000, 50000, and 100000. Verification is carried out in the mesh refinement study and validated by aerodynamic performances. Based on the mesh refinement study, quadrilateral cells with the k - ε are in the asymptotic convergence range. Based on the Cl, it can be concluded that the quadrilateral mesh with 50000 and 100000 cells simulated using the k-ε turbulence model shows very low errors, namely 4.1151% and 3.8643%, respectively. It shows consistency based on the quadrilaterals Cd mesh data with the k-ε and k-ω turbulence models. However, k-ε shows the lowest error with the number of cells 50000 and 100000, i.e., 127.7682% and 110.4175%, respectively. However, choosing mesh 50000 cells are advisable because it only takes 23 minutes 48 seconds in computation, while mesh 100000 cells take 1 hour 17 minutes 21 seconds. Only Cm from quadrilateral mesh with the turbulence model k-ω shows consistency. An error of mesh 50000 cells is 22.0717%, and the error value for 100000 cells is 18.1630%. By considering computation time, mesh 50000 cells are preferable because it only takes 27 minutes 16 seconds, which is faster 43 minutes 14 seconds than 100000 cells.


Aftab, S. M. A., Mohd Rafie, A. S., Razak, N. A., & Ahmad, K. A. (2016). Turbulence model selection for low Reynolds number flows. PloS One, 11(4), e0153755. https://doi.org/10.1371/journal.pone.0153755
Ahadi, A., Sullivan, P. E., & Saghir, Z. (2018). Comparison of Numerical and Experimental Results over a NACA0025 Airfoil Undergoing Separation. https://doi.org/10.15406/fmrij.2018.02.00017
Ali, Z., Tucker, P. G., & Shahpar, S. (2017). Optimal mesh topology generation for CFD. Computer Methods in Applied Mechanics and Engineering, 317, 431-457. https://doi.org/10.1016/j.cma.2016.12.001
Anzalotta, C., Joshi, K., Fernandez, E., & Bhattacharya, S. (2020). Effect of forcing the tip-gap of a NACA0065 airfoil using plasma actuators: A proof-of-concept study. Aerospace Science and Technology, 107. https://doi.org/10.1016/j.ast.2020.106268
Bhattacharya, S., & Ahmed, A. (2020). Effect of aspect ratio on the flow over a wall-mounted hemispherical turret. International Journal of Heat and Fluid Flow, 84. https://doi.org/10.1016/j.ijheatfluidflow.2020.108600
Bhattacharya, S., & Gregory, J. W. (2013). The optimum wavelength of spanwise segmented plasma actuator forcing of a circular cylinder wake. 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 2013. https://doi.org/10.2514/6.2013-1011
Bouaziz, S., Deuss, M., Schwartzburg, Y., Weise, T., & Pauly, M. (2012). Shape‐up: Shaping discrete geometry with projections. Computer Graphics Forum, 31(5), 1657–1667. https://doi.org/10.1111/j.1467-8659.2012.03171.x
Hills, J. L., Šafařík, P., & Sládek, A. (2005). Numerical modelling of turbulent flow past an airfoil. Czech Technical University in Prague, Prague.
Hoffmann, M. J., Reuss Ramsay, R., & Gregorek, G. M. (1996). Effects of grit roughness and pitch oscillations on the NACA 4415 airfoil. National Renewable Energy Lab.(NREL), Golden, CO (United States). https://doi.org/10.2172/266691
Hornshøj-Møller, S. D., Nielsen, P. D., Forooghi, P., & Abkar, M. (2021). Quantifying structural uncertainties in Reynolds-averaged Navier–Stokes simulations of wind turbine wakes. Renewable Energy, 164, 1550–1558. https://doi.org/10.1016/j.renene.2020.10.148
Iskandar, W., Julian, J., Wahyuni, F., Ferdyanto, F., Prabu, H. K., & Yulia, F. (2022). Study of airfoil characteristics on NACA 4415 with reynolds number variations. International Review on Modelling and Simulations (IREMOS), 15(3), 162. https://doi.org/10.15866/iremos.v15i3.21684
Islam, M., Fürst, J., Wood, D., & Ani, F. N. (2016). Analysis of an airfoil using a transition and turbulence model. Applied Mechanics and Materials, 819, 356–360. https://doi.org/10.4028/www.scientific.net/AMM.819.356
Jacobs, E. N., & Sherman, A. (1937). Airfoil section characteristics as affected by variations of the Reynolds number. NACA Technical Report, 586, 227–267.
Jia, K., Scofield, T., Wei, M., & Bhattacharya, S. (2021). Vorticity transfer in a leading-edge vortex due to controlled spanwise bending. Physical Review Fluids, 6(2). https://doi.org/10.1103/PhysRevFluids.6.024703
Joshi, K., & Bhattacharya, S. (2019). Large-eddy simulation of the effect of distributed plasma forcing on the wake of a circular cylinder. Computers and Fluids, 193. https://doi.org/10.1016/j.compfluid.2019.104295
Julian, J., Iskandar, W., & Wahyuni, F. (2022a). Aerodynamics improvement of NACA 0015 by using Co-Flow jet. International Journal of Marine Engineering Innovation and Research, 7(4). https://doi.org/10.12962/j25481479.v7i4.14898
Julian, J., Iskandar, W., Wahyuni, F., & Ferdyanto, F. (2022b). Computational fluid dynamics analysis based on the fluid flow separation point on the upper side of the naca 0015 airfoil with the coefficient of friction. Media Mesin: Majalah Teknik Mesin, 23(2), 70–82. https://doi.org/10.23917/mesin.v23i2.18217
Julian, J., Iskandar, W., & Wahyuni, F. (2022c). Effect of single slat and double slat on aerodynamic performance of NACA 4415. International Journal of Marine Engineering Innovation and Research http://dx.doi.org/10.12962/j25481479.v7i2.12875
Julian, J., Iskandar, W., Wahyuni, F., & Bunga, N. T. (2022d). Characterization of the Co-Flow jet effect as one of the flow control devices. Jurnal Asiimetrik: Jurnal Ilmiah Rekayasa & Inovasi, 185–192. https://doi.org/10.35814/asiimetrik.v4i1.3437
Julian, J., Wahyuni, F., Iskandar, W., & Ramadhani, R. (2023a). The effect of curvature ratio towards the fluid flow characteristics in bend pipe based on numerical methods. Turbo: Jurnal Program Studi Teknik Mesin, 12(1). http://dx.doi.org/10.24127/trb.v12i1.2564
Julian, J., Iskandar, W., Wahyuni, F., & Nely Toding Bunga, dan. (2023b). Aerodynamic Performance Improvement on NACA 4415 Airfoil by Using Cavity. Jurnal Asiimetrik: Jurnal Ilmiah Rekayasa Dan Inovasi, 5, 135–142. https://doi.org/10.35814/asiimetrik.v5i1.4259
Julian, J., Iskandar, W., & Wahyuni, F. (2023c). Leading edge modification of NACA 0015 and NACA 4415 inspired by beluga whale. International Journal of Marine Engineering Innovation and Research, 8(2). http://dx.doi.org/10.12962/j25481479.v8i2.16432
Kekina, P., & Suvanjumrat, C. (2017). A comparative study on turbulence models for simulation of flow past NACA 0015 airfoil using OpenFOAM. https://doi.org/10.1051/matecconf/20179512005
Khan, S. A., Bashir, M., Baig, M. A. A., & Ali, F. A. G. M. (2020). Comparing the effect of different turbulence models on the CFD predictions of NACA0018 airfoil aerodynamics. CFD Letters, 12(3), 1–10. https://doi.org/10.37934/cfdl.12.3.110OpenAccess
Kumar, B. R. (2019). Enhancing aerodynamic performance of NACA 4412 aircraft wing using leading edge modification. Wind and Structures, 29(4), 271–277. https://doi.org/10.12989/was.2019.29.4.271
Launder, B. E., & Spalding, D. B. (1983). The numerical computation of turbulent flows. Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion, 96–116. Elsevier. https://doi.org/10.1016/0045-7825(74)90029-2
Loftin Jr, L. K., & Poteat, M. I. (1948). Aerodynamic characteristics of several NACA airfoil sections at seven Reynolds numbers from 0.7 x 10 (exp 6) to 9.0 x 10 (exp 6).
Panagiotou, C. F., Kassinos, S. C., & Aupoix, B. (2015). The ASBM-SA turbulence closure: Taking advantage of structure-based modeling in current engineering CFD codes. International Journal of Heat and Fluid Flow, 52, 111–128. https://doi.org/10.1016/j.ijheatfluidflow.2014.12.002
Reggio, M., Villalpando, F., & Ilinca, A. (2011). Assessment of turbulence models for flow simulation around a wind turbine airfoil. Modelling and Simulation in Engineering, 2011. https://doi.org/10.1155/2011/714146
Sadikin, A., Yunus, N. A. M., Abd Hamid, S. A., Salleh, S. M., Rahman, M. N. A., Mahzan, S., & Ayop, S. S. (2018). A comparative study of turbulence models on aerodynamics characteristics of a NACA0012 airfoil. International Journal of Integrated Engineering, 10(1). https://doi.org/10.30880/ijie.2018.10.01.019 
Siddiqi, Z., & Lee, J. W. (2019). A computational fluid dynamics investigation of subsonic wing designs for unmanned aerial vehicle application. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 233(15), 5543–5552. https://doi.org/10.1177/0954410019852553
Sirignano, J., MacArt, J. F., & Freund, J. B. (2020). DPM: A deep learning PDE augmentation method with application to large-eddy simulation. Journal of Computational Physics, 423. https://doi.org/10.1016/j.jcp.2020.109811
Suvanjumrat, C. (2017). Comparison of turbulence models for flow past NACA0015 airfoil using OpenFOAM. Engineering Journal, 21(3), 207–221. https://doi.org/10.4186/ej.2017.21.3.207
Villalpando, F., Reggio, M., & Ilinca, A. (2011). Assessment of turbulence models for flow simulation around a wind turbine airfoil. Modelling and Simulation in Engineering, 2011, 1–8. https://doi.org/10.1155/2011/714146
Wilcox, D. C. (1998). Turbulence modeling for CFD (Vol. 2). DCW industries La Canada, CA.
Zhang, L., Gong, S., Lu, Z., Cheng, P., & Wang, E. N. (2022). Boiling crisis due to bubble interactions. International Journal of Heat and Mass Transfer, 182. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121904