ITU/FAA Faculty of Aeronautics and Astronautics S. Banu YILMAZ, Mehmet SAHIN, M. Fevzi UNAL 65th Annual Meeting of the APS Division of Fluid Dynamics November 18-20, 2012, San Diego, CA Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469, Maslak/Istanbul, TURKEY
ITU/FAA Faculty of Aeronautics and Astronautics Contents The Motivation 1. 2. Governing Equations and Numerical Formulation Validation Cases 3. Case 1, Re = 20000 Case 2, Re = 252 Simulation Results 4. Tandem Configurations Biplane Configurations Conclusions and Future Work 5. 2 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics The Motivation Understanding the Nature • 3D, combined pitch plunge sweep motions of birds, insects and fishes Imitating Nature • MAVs; potential civil and military applications such as terrestrial and indoor monitoring • Alternative propulsion systems • Power generators, energy harvesting 3 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Governing Equations and Numerical Formulation (continued …) The governing equations of an incompressible unsteady Newtonian fluid can be written in dimensionless form as follows: Integrating the differential equations over an arbitrary moving irregular control volume . 4 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Governing Equations and Numerical Formulation (continued …) An unstructured finite volume solver based on Arbitrary Lagrangian-Eulerian formulation is utilized in order to solve the incompressible unsteady Navier-Stokes equations. (a) Two-dimensional dual volume (b) Three-dimensional dual volume The side centered finite volume method used by Hwang (1995) and Rida et al. (1997). The present arrangement of the primitive variables leads to a stable numerical scheme and it does not require any ad-hoc modifications in order to enhance pressure-velocity coupling. The most appealing feature of this primitive variable arrangement is the availability of very efficient multigrid solvers. 5 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Governing Equations and Numerical Formulation (continued …) The discrete contribution from the right cell is given for the momentum equation along the x-axis. The time derivation: The convective term The pressure term The viscous term 6 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Governing Equations and Numerical Formulation (continued …) The continuity equation is integrated within each quadrilateral elements and evaluated using the mid-point rule on each of the element faces. The discretization of above equations leads to a saddle point problem of the form: The preconditioner matrix is Where . For the inverse of the scaled Laplacian S, we use two- cycle AMG solver provided by the HYPRE library, a high performance preconditioning package developed at Lawrence Livermore National Laboratory, which we access through the PETSC library. 7 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Computational Domain The computational mesh consists of 747,597 quadrilateral elements and 748,508 nodes (DOF = 3,739,807) including a fine boundary layer region around airfoil. The boundary layer grid is created using Gambit2.1.6 software and the rest of the grid is generated via Cubit9.1 software using mapping and paving algorithms. 8 DFD 2012
ITU/FAA ITU/FAA Faculty of Aeronautics and Astronautics Faculty of Aeronautics and Astronautics Validation- Case 1 Re=20000, k=4, h=0.0125 (Lai and Platzer , AIAA Journal , 1999) (Young and Lai, Aust. Fluid Mech. Conf., 2001) Current study Current study 9 DFD 2012 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Validation- Case 2 Re=252, k=12.3, h=0.12 (Jones and Platzer, Exp. Fluids , 2009) Current study 10 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Grid Convergence Coarse mesh (191606 elements) Fine mesh (747597 elements) 11 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Effect of Phase Angle = 180 o Deflected Depending on the location of start-up vortices, the calculations indicate strong hysteresis effects and multiple periodic solutions. = 90 o Symmetric 12 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics 3D Solution NACA0012 Re = 252 ∅ = 180° 𝑧 𝑢 = 0.12 sin (12.3𝑢 + ∅) 0 < z < c No strong three-dimensional effects are visible. Mild three-dimensional effects 2,040,568 elements DOF= 20,598,994 13 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Numerical Simulations Detailed look Biplane Asynchroneous, closer 14 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Flow Parameters • The Reynolds number is chosen as 252 • The reduced frequency k is 12.3 and k = 2𝜌𝑔𝑑/𝑉 ∞ plunge amplitude h is 0.12 • The equation of motion is, 𝑧 𝑢 = 0.12 sin (12.3𝑢 + ∅) • The time between two iterations ∆ t is calculated as ∆𝑢 = 2𝜌/(400𝑔) 1/400 of a period of airfoil motion as, 15 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Flow Parameters (continued … ) y = h sin( t) k = 12.3 h = 0.12 kh = 1.48 (Tuncer and Platzer, AIAA Jou., 1996) 16 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Simulation Results 17 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Tandem Wing Configurations Tandem Shifted Tandem, -0.12c Tandem Asynchroneous Tandem Synchroneous 18 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Biplane Wing Configurations Biplane Biplane Synchroneous Biplane Aynchroneous Biplane Asynchroneous-closer 19 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Comparison of Tandem Configurations A period of shedding Tandem Shifted Tandem Tandem Synchroneous Tandem Asynchroneous 20 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Comparison of Tandem Configurations Streamlines Tandem Shifted Tandem Single Tandem Synchroneous Tandem Asynchroneous 21 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Comparison of Biplane Configurations A period of shedding Biplane Biplane Synchroneous Biplane Synchroneous later on Biplane Aynchroneous Biplane Asynchroneous-closer 22 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Comparison of Biplane Configurations Streamlines Biplane Biplane Synchroneous Single Biplane Aynchroneous Biplane Asynchroneous-closer 23 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics C T & Power Spectrum - Tandem Configurations Forewing Hindwing C Tmean = 0.9776 C Tmean = 0.9843 C Tmean = - 0.1002 Single Tandem F x F x F x C Tmean = - 0.0657 C Tmean = 1.0334 Shifted Tandem F x F x 24 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics C T & Power Spectrum - Tandem Configurations Forewing Hindwing C Tmean = 1.1066 C Tmean = 1.3104 C Tmean = 0.9776 Single Tandem Synchroneous F x F x F x C Tmean = 0.8931 C Tmean = - 0.0424 Tandem Asynchroneous F x F x 25 27.11.2012 25 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics C T & Power Spectrum - Biplane Configurations Upper wing Lower wing C Tmean = 0.9776 C Tmean = 0.9519 C Tmean = - 0.2359 Single Biplane F x F x F x C Tmean = 0.6587 C Tmean = 0.7033 Biplane Synchroneous F x F x 26 26 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics C T & Power Spectrum - Biplane Configurations Upper wing Lower wing C Tmean = 0.9776 C Tmean = 1.6702 C Tmean = 1.6705 Single Biplane Asynchroneous F x F x F x C Tmean = 1.7556 C Tmean = 1.7554 Biplane Asynchroneous closer F x F x 27 27.11.2012 27 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Mean Lift and Thrust 28 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Experimental Setup Large scale water channel Kollmorgen/Danaher Motion AKM33E servo motor and gear system U ∞ 29 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Conclusions and Future Work The numerical method has been validated for the numerical and the experimental results available in the literature. The temporal and spatial resolution scales have been investigated. The single plunging airfoil case at Re=252 reveals a very strong hysteresis effects and multiple periodic solutions even though the Reynolds number is relatively low. Several wing combinations are investigated, by means of flow field characteristics and force statistics, The most interesting vortex fields appeared at biplane synchroneous and asynchroneous cases, In tandem synchroneus , biplane asynchroneous and asynchroneous-closer cases, the thrust force is increased considerably. Frequency, Reynolds number effects will be studied both experimentally and numerically. Experiments will be conducted using PIV (Particle Image Velocimetry) for further validation of the results. 30 DFD 2012
ITU/FAA Faculty of Aeronautics and Astronautics Acknowledgement The authors gratefully acknowledge the use of the Chimera machine at the Faculty of Aeronautics and Astronautics at ITU, the computing resources provided by the National Center for High Performance Computing of Turkey (UYBHM) under grant number 10752009 and the computing facilities at TUBITAK ULAKBIM, High Performance and Grid Computing Center. 31 DFD 2012
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