S. Banu YILMAZ, Mehmet SAHIN, M. Fevzi UNAL, Istanbul Technical University, 34469, Maslak/Istanbul, TURKEY 65th Annual Meeting of the APS Division of Fluid Dynamics November 18-20, 2012, San Diego, CA
Contents ITU/FAA 1. The Motivation 2. Governing Equations and Numerical Formulation 3. Validation Cases Case 1, Re = 20000 Case 2, Re = 252 4. Simulation Results Tandem Configurations Biplane Configurations 5. Conclusions and Future Work DFD 2012 2
The Motivation ITU/FAA 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 DFD 2012 3
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. DFD 2012 4
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. DFD 2012 5
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 DFD 2012 6
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 twocycle 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. DFD 2012 7
Computational Domain ITU/FAA 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. DFD 2012 8
Validation- C a s e 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 DFD 2012 9
Validation- C a s e 2 Re=252, k=12.3, h=0.12 (Jones and Platzer, Exp. Fluids, 2009) Current study DFD 2012 10
Grid Convergence Coarse mesh (191606 elements) Fine mesh (747597 elements) DFD 2012 11
Effect of Phase Angle Deflected = 180 o Depending on the location of start-up vortices, the calculations indicate strong hysteresis effects and multiple periodic solutions. Symmetric = 90 o DFD 2012 12
3D Solution NACA0012 Re = 252 = 180 y t = 0.12 sin (12.3t + ) 0 < z < c No strong three-dimensional effects are visible. Mild three-dimensional effects 2,040,568 elements DOF= 20,598,994 DFD 2012 13
Numerical Simulations ITU/FAA Biplane Asynchroneous, closer Detailed look DFD 2012 14
Flow Parameters ITU/FAA The Reynolds number is chosen as 252 The reduced frequency k is 12.3 and plunge amplitude h is 0.12 The equation of motion is, The time between two iterations t is calculated as 1/400 of a period of airfoil motion as, k = 2πfc/U y t = 0.12 sin (12.3t + ) t = 2π/(400f) DFD 2012 15
Flow Parameters (continued ) ITU/FAA y = h sin( t) k = 12.3 h = 0.12 kh = 1.48 (Tuncer and Platzer, AIAA Jou., 1996) DFD 2012 16
Simulation Results DFD 2012 17
Tandem Wing Configurations ITU/FAA Tandem Shifted Tandem, -0.12c Tandem Synchroneous Tandem Asynchroneous DFD 2012 18
Biplane Wing Configurations ITU/FAA Biplane Biplane Synchroneous Biplane Aynchroneous Biplane Asynchroneous-closer DFD 2012 19
Comparison of Tandem Configurations A period of shedding Tandem Shifted Tandem Tandem Synchroneous Tandem Asynchroneous DFD 2012 20
Comparison of Tandem Configurations Streamlines Tandem Shifted Tandem Single Tandem Synchroneous Tandem Asynchroneous DFD 2012 21
Comparison of Biplane Configurations A period of shedding Biplane Biplane Synchroneous later on Biplane Aynchroneous Biplane Asynchroneous-closer DFD 2012 22
Comparison of Biplane Configurations Streamlines Biplane Biplane Synchroneous Single Biplane Aynchroneous Biplane Asynchroneous-closer DFD 2012 23
C T & Power Spectrum - Tandem Configurations Single Tandem Forewing ITU/FAA Hindwing C T mean = 0.9776 C T mean = 0.9843 C T mean = - 0.1002 Shifted Tandem C T mean = 1.0334 C T mean = - 0.0657 DFD 2012 24
C T & Power Spectrum - Tandem Configurations Single Tandem Synchroneous ITU/FAA Forewing Hindwing C T = 0.9776 mean C T = 1.1066 mean C T = 1.3104 mean Tandem Asynchroneous C T mean = 0.8931 C T mean = - 0.0424 DFD 2012 27.11.2012 25 25
C T & Power Spectrum - Biplane Configurations Single Biplane Upper wing ITU/FAA Lower wing C T mean = 0.9776 C T mean = 0.9519 C T mean = - 0.2359 Biplane Synchroneous C T mean = 0.7033 C T mean = 0.6587 26 DFD 2012 26
C T & Power Spectrum - Biplane Configurations Single Biplane Asynchroneous Upper wing ITU/FAA Lower wing C T mean = 0.9776 C T mean = 1.6702 C T mean = 1.6705 Biplane Asynchroneous closer C T mean = 1.7554 C T mean = 1.7556 DFD 2012 27.11.2012 27 27
Mean Lift and Thrust DFD 2012 28
Experimental Setup Large scale water channel Kollmorgen/Danaher Motion AKM33E servo motor and gear system U DFD 2012 29
Conclusions and Future Work ITU/FAA 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. DFD 2012 30
Acknowledgement ITU/FAA The authors gratefully acknowledge the use of the Chimera machine at the 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. DFD 2012 31
Thank you, Any questions? DFD 2012 32
Mesh Refinement 1 st order, coarse mesh (191606 elements) 2 nd order converged solution Although fine mesh and coarse mesh solutions coincide Mesh convergency is not enough for first order time discretization. 1 st order, fine mesh (747597 elements) DFD 2012 33
Time Independency 1 st order, t 2 nd order converged solution 1 st order time discretization converges slowly. So, as t takes smaller values solution is converged. 1 st order, t/4 DFD 2012 34