High Reynolds Viscous Flow Simulation Past the Elliptical Airfoil by Random Vortex Blob

Authors

1 Department of Mechanical Engineering, Institute of Energy & Hydro Technology (IEHT), Mashhad, Iran

2 Department of Mechanical Engineering, Islamic Azad University of Mashhad, Mashhad, Iran

Abstract

In this paper, numerical simulation for a two-dimensional viscous and incompressible flow past the elliptical airfoil is presented by Random Vortex Blob (RVB). RVB is a numerical technique to solve the incompressible, two-dimensional and unsteady Navier-Stocks equations by converting them to rotational non-primitive formulations. In this method, the velocity vector at a certain point can be calculated without considering any grid around it, so the RVB method can be treated as a meshless method. Accordingly, the turbulent flow past a cylinder as well as an elliptical airfoil is investigated. In both cases, the obtained mean time velocities are compared with available numerical and experimental results where an acceptable agreement is observed. Having known the velocity field, by employing momentum balance, the drag and lift coefficients caused by flow past the elliptical airfoil with different diameter ratios and Re=105 are calculated and compared with experimental data where a good consistency is achieved.

Keywords


1.     Assel, T.W., "Computational study of flow over elliptic airfoils for rotor/wing unmanned aerial vehicle applications",  Master of Science thesis. Missouri University of Science and Technology, (2007).

2.     Zahm, A., Smith, R. and Louden, F., "Forces on elliptic cylinders in uniform air stream", NACA report No. 289, NACA TR-315, (1929).

3.     W., H. and H., W., "The compressible potential flow past elliptic cylinder at zero angle of attack and with no circulation", Luftfahrtforschung,  Vol. 18, (1942), 311-316.

4.     Johnson S.A., M.C., T. and K., H., "Flow past the elliptical cylinder at low reynolds number", in 14th Australasian Fluid Mechanics Conference, Australia. (2001 of Conference).

5.     Kim, M.-S. and Sengupta, A., "Unsteady viscous flow over elliptic cylinders at various thickness with different reynolds numbers", Journal of Mechanical Science and Technology,  Vol. 19, No. 3, (2005), 877-886.

6.     Kwon, K. and Park, S.O., "Aerodynamic characteristics of an elliptic airfoil at low reynolds number", Journal of Aircraft,  Vol. 42, No. 6, (2005), 1642-1644.

7.     Razaghi, R., Amanifard, N. and Nariman-Zadeh, N., "Modeling and multi-objective optimization of stall control on naca 0015 airfoil with a synthetic jet using gmdh type neural networks and genetic algorithms", International Journal of Engineering Transactions A: Basics,  Vol. 22, No. 1, (2009), 69-88.

8.     Askari, S. and Shojaeefard, M., "Mathematical modeling of potential flow over a rotating cylinder",  International Journal of Engineering Transactions A: Basics, Vol. 24, (2011), 55-63.

9.     Mehmooda, N., Lianga, Z. and Khanb, J., "Study of naca 0015 for diffuser design in tidal current turbine applications", International Journal of Engineering Transactions C: Aspects,  Vol. 25, No. 4, (2012), 373-380.

10.   Chen, C., Seele, R. and Wygnanski, I., "Separation and circulation control on an elliptical airfoil by steady blowing", AIAA Journal,  Vol. 50, No. 10, (2012), 2235-2247.

11.   Lysak, P.D., Capone, D.E. and Jonson, M.L., "Measurement of the unsteady lift of thick airfoils in incompressible turbulent flow", Journal of Fluids and Structures,  Vol. 66, (2016), 315-330.

12.   Mirzaee, B., Khoshravan, E. and Razavi, S., "Finite-volume solution of a cylinder in cross flow with heat transfer", Algorithms,  Vol. 3, (2002), 303-314.

13.   Sabetghadam, F., Soltani, E. and Ghassemi, H., "A fast immersed boundary fourier pseudo-spectral method for simulation of the incompressible flows", International Journal of Engineering-Transactions C: Aspects,  Vol. 27, No. 9, (2014), 1457-1466.

14.   Chorin, A.J., "Numerical study of slightly viscous flow", Journal of Fluid Mechanics,  Vol. 57, No. 4, (1973), 785-796.

15.   Chorin, A.J., "Vortex sheet approximation of boundary layers", Journal of Computational Physics,  Vol. 27, No. 3, (1978), 428-442.

16.   Beale, J.T. and Majda, A., "Rates of convergence for viscous

splitting of the navier-stokes equations", Mathematics of Computation,  Vol. 37, No. 156, (1981), 243-259.

17.   Benfatto, G. and Pulvirenti, M., "Generation of vorticity near the boundary in planar navier-stokes flows", Communications in Mathematical Physics,  Vol. 96, No. 1, (1984), 59-95.

18.   Cheer, A., "Unsteady separated wake behind an impulsively started cylinder in slightly viscous fluid", Journal of Fluid Mechanics,  Vol. 201, (1989), 485-505.

19.   Cottet, G.-H. and Koumoutsakos, P.D., "Vortex methods: Theory and practice, Cambridge university press,  (2000).

20.   Yokota, R. and Obi, S., "Vortex methods for the simulation of turbulent flows", Journal of Fluid Science and Technology,  Vol. 6, No. 1, (2011), 14-29.

21.   Sohn, S.-I., "Two vortex-blob regularization models for vortex sheet motion", Physics of Fluids,  Vol. 26, No. 4, (2014), 044105- 1-20.

22.   Ramesh, K., Gopalarathnam, A., Granlund, K., Ol, M.V. and Edwards, J.R., "Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding", Journal of Fluid Mechanics,  Vol. 751, (2014), 500-538.

23.   Duan, Y. and Liu, J.-G., "Convergence analysis of the vortex blob method for the b-equation", Discrete Contin. Dyn. Syst,  Vol. 34, (2014), 1995-2011.

24.   B., Z., M., S. and A., H.N., "Analysis of the characteristics, physical concepts and entropy generation in a turbulent channel flow using vortex blob method", International Journal of Engineering Transactions A: Basics,  Vol. 29, No. 7, (2016), 985-994.

25.   Cantwell, B. and Coles, D., "A flying hot wire study of the turbulent near wake of a circular cylinder at re= 140000", Ph. D. Thesis, California lnstitute of Technology,  (1976),

26.   Blevins, R.D., "Applied fluid dynamics handbook", New York, Van Nostrand Reinhold Co., (1984).