ITU/FAA Faculty of Aeronautics and Astronautics S. Banu YILMAZ, - - PowerPoint PPT Presentation

ITU/FAA

Faculty of Aeronautics and Astronautics

• S. Banu YILMAZ, Mehmet SAHIN, M. Fevzi UNAL

Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469, Maslak/Istanbul, TURKEY 65th Annual Meeting of the APS Division of Fluid Dynamics November 18-20, 2012, San Diego, CA

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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

Contents

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 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

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The Motivation

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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 .

(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. An unstructured finite volume solver based on Arbitrary Lagrangian-Eulerian formulation is utilized in order to solve the incompressible unsteady Navier-Stokes equations. ITU/FAA

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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 ITU/FAA

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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: ITU/FAA

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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

Governing Equations and Numerical Formulation (continued…)

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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.

Computational Domain

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Re=20000, k=4, h=0.0125

(Young and Lai, Aust. Fluid Mech. Conf., 2001) (Lai and Platzer , AIAA Journal, 1999)

Current study ITU/FAA

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Validation- Case 1

Current study

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Re=252, k=12.3, h=0.12 (Jones and Platzer, Exp. Fluids, 2009) Current study

Validation- Case 2

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Grid Convergence

Fine mesh (747597 elements) Coarse mesh (191606 elements)

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= 180o = 90o

Depending on the location of start-up vortices, the calculations indicate strong hysteresis effects and multiple periodic solutions.

Effect of Phase Angle

Deflected Symmetric

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NACA0012 Re = 252

3D Solution

No strong three-dimensional effects are visible.

2,040,568 elements DOF= 20,598,994 𝑧 𝑢 = 0.12 sin (12.3𝑢 + ∅) ∅ = 180° Mild three-dimensional effects 0 < z < c

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• Biplane Asynchroneous, closer

Detailed look

Numerical Simulations

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• The Reynolds number is chosen as 252
• The equation of motion is,
• The time between two

iterations ∆t is calculated as 1/400 of a period of airfoil motion as,

k = 2𝜌𝑔𝑑/𝑉∞

• The reduced frequency k is 12.3 and

plunge amplitude h is 0.12

Flow Parameters

∆𝑢 = 2𝜌/(400𝑔) 𝑧 𝑢 = 0.12 sin (12.3𝑢 + ∅)

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k = 12.3 h = 0.12 kh = 1.48

(Tuncer and Platzer, AIAA Jou., 1996)

y = h sin(t)

Flow Parameters (continued…)

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Simulation Results

17

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Tandem Shifted Tandem, -0.12c Tandem Synchroneous Tandem Asynchroneous

Tandem Wing Configurations

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Biplane Biplane Synchroneous Biplane Aynchroneous Biplane Asynchroneous-closer

Biplane Wing Configurations

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A period of shedding

Tandem Shifted Tandem Tandem Synchroneous Tandem Asynchroneous

Comparison of Tandem Configurations

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Streamlines

Single Tandem Shifted Tandem Tandem Synchroneous Tandem Asynchroneous

Comparison of Tandem Configurations

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Biplane Biplane Synchroneous Biplane Aynchroneous Biplane Asynchroneous-closer

A period of shedding

Comparison of Biplane Configurations

Biplane Synchroneous later on

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Single Biplane Biplane Synchroneous Biplane Aynchroneous Biplane Asynchroneous-closer

Streamlines

Comparison of Biplane Configurations

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Single Tandem Shifted Tandem

Forewing Hindwing

CT & Power Spectrum - Tandem Configurations

CTmean = 0.9776 CTmean = 0.9843 CTmean = - 0.1002 CTmean = 1.0334 CTmean = - 0.0657 24 Fx

Fx Fx Fx Fx

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Fx

27.11.2012 25

Tandem Synchroneous Tandem Asynchroneous Single

Forewing Hindwing

CT & Power Spectrum - Tandem Configurations

CTmean = 0.9776 CTmean = 1.1066 CTmean = 1.3104 CTmean = 0.8931 CTmean = - 0.0424 25 Fx

Fx Fx Fx

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Biplane Biplane Synchroneous Single

Upper wing Lower wing

CT & Power Spectrum - Biplane Configurations

CTmean = 0.9776 CTmean = 0.9519 CTmean = - 0.2359 CTmean = 0.7033 CTmean = 0.6587 26 Fx

Fx Fx Fx Fx

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Fx

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Biplane Asynchroneous Biplane Asynchroneous closer Single

Upper wing Lower wing

CT & Power Spectrum - Biplane Configurations

CTmean = 0.9776 CTmean = 1.6702 CTmean = 1.6705 CTmean = 1.7554 CTmean = 1.7556 27 Fx

Fx Fx Fx

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Mean Lift and Thrust

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U∞

Experimental Setup

Kollmorgen/Danaher Motion AKM33E servo motor and gear system

Large scale water channel

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 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.

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Conclusions and Future Work

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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

Acknowledgement

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Thank you, Any questions?

32

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1st order, coarse mesh (191606 elements) 1st order, fine mesh (747597 elements)

Mesh convergency is not enough for first order time discretization.

Mesh Refinement

2nd order converged solution Although fine mesh and coarse mesh solutions coincide

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1st order, ∆t 1st order, ∆t/4

So, as ∆t takes smaller values solution is converged. 2nd order converged solution 1st order time discretization converges slowly.

Time Independency