15 October 2005

Vermelding onderdeel organisatie

Numerical simulation of amoving mesh problem

Application: insect aerodynamics

Workshop: Computational Life Sciences

Frank Bos

2/23

Overview Presentation

1. Problem description• Insect aerodynamics• Objectives• Material and methods

2. Numerical modelling3. Validation and verification4. Kinematic modelling5. Results and discussions

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

3/23

Background of insect flight (1/2)

Insect flight still not fully understood:

•Quasi-steady aerodynamics could not predict unsteady forces

•Experiments showed highly vortical flow

•Vortex generation enhanced lift

Leading Edge Vortex

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

4/23

Background of insect flight (2/2)

•Flow dominated by low Reynolds number:

•Highly viscous and unsteady flow

•At low Reynolds numbers flapping leads to efficient lift generation

Insects interesting to develop Micro Air Vehicles

(intelligence, investigate hazardous environments)

ReUL

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

5/23

Problem Statement

•Performance in insect flight is strongly influenced by wing kinematics.•Literature shows a wide range of different kinematic models.

Main question

What is the effect of different kinematic models on the performance in insect flight?

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

6/23

Objectives

1. Numerical modelling using general tools to solve Navier-Stokes equations.

2. Validation of the numerical model using static and moving cylinders.3. Investigate influence of different wing kinematics on performance in

hovering fruit-fly flight.

Procedure

1. To develop an accurate numerical model for this challenging application.

2. Unravel unsteady aerodynamics of flapping insect aerodynamics.

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

7/23

Configuration set-up

•Hovering fruit-fly (Drosophila Melanogaster)•Low Reynolds number = 110•Low Mach number = 0.03 incompressible flow•2-dimensional laminar flow Direct Numerical Simulation (DNS)•Airfoil = 2% thick ellipse•Different wing kinematics, derived from literature

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

8/23

Material and methods

•Finite volume based general purpose CFD solvers: Fluent (and HexStream)•Solve the Navier-Stokes equations:

•Moving mesh using Arbitrary Lagrangian Eulerian (ALE) formulation:

upuut

u

21)(

meshuuu

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

9/23

Numerical modelling

object

Mesh generation:•Body conform in inner domain•Re-meshing in outer domain at 25 diameters•Body moves arbitrarily•Motion restricting time step

Quarter of entire domain: Cells near the boundary:

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

10/23

Time step restrictions

2

N

refr R

yN

y

y

reft

2

N = number of cells on the surface = relative angular displacementy = relative linear displacementR = radius of cylinderref = angular length of smallest cellyref = linear length of smallest cell

Rotation: Translation:

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

11/23

Validation using moving cylinders

Summarising:

•All cells are optimal and moving

•Mesh size = 50k and considered sufficient

•Re-meshing occurs at 25 diameters

•Validated for moving (rotating and translating) cylinders with literature

•Timestep restriction due to interpolation in time

Extend this method to moving wings !!!

When relative cell displacement < 10% then the corresponding time step leads results within 5% of literature.

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

12/23

Verification using moving wing

)cosh( iiyx

cosh( )x iy i

T/t Error (%)

200 15.61

2000 1.34

20000 Ref.

Numerical model:

•Conformal mapping:

•2% thick ellipse

Close-up at the Leading Edge:

Grid size Error (%)

25k 12.48

50k 0.87

100k Ref.

Time step dependence:

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

Grid size dependence:

fine

13/23

Definition of motion parameters

3D parameters:

•Amplitude:

•Angle of Attack:

•Deviation: 2D parameters:

•Amplitude: x = Rg / c

•Angle of Attack:

•Deviation: y = Rg / cy

x

Rg = radius of gyration; c = averaged chordIntroduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

14/23

4 different kinematic models

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

Experiment:

Model 1: Harmonic• : cosine• : sine• : no ‘figure of eight’

Model 2: Robofly• : ‘Sawtooth’• : ‘Trapezoidal’• : no ‘figure of eight’

Model 3: Fruit-fly• : cosine• : Extra ‘bump’ • : ‘Figure of Eight’

Model 4: Simplified Fruit-fly• : symmetrised• : symmetrised• : symmetrisedAll Fruit-fly characteristics preserved

15/23

Matching kinematic models

A reference is needed to make comparison of results between different models meaningfull

Matching the quasi-steady lift of the cases to be compared

0.225 1.58sin(2.13 7.20)

1.920 1.55cos(2.04 9.82)

L eff

D eff

C

C

Derived using

3D robofly

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

16/23

Performance influence strategy

1. Compare complete Robofly with the fruit-fly models

2. Compare Robofly characteristics with harmonic model

3. Compare fruit-fly characteristics with harmonic model

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

Performance:•Investigate influence on lift, drag and performance•Glide ratio CL/CD is used as a first indication of performance•Look at vorticity!

17/23

Comparison robofly and fruit-fly model

•Robofly: mean lift 8% less than fruit-fly•Robofly: mean drag 80% more than fruit-fly•The symmetry less influence•Mean lift is well predicted, succesfull matching

Take a closer look at the force diagrams and vorticity

Model CL CD CL/CD

Robofly -8.0% 80.6% -48.8%

Sym. Fruit-fly -5.6% -3.7% 7.1%

Robofly and real Fruit-fly compared:

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

18/23

Comparison different shapesInfluence of different kinematic shapes w.r.t. harmonic model:

1. Comparable mean lift coefficients2. Mean drag is strongly affected !3. Robofly decreases performance, -25% to -30%4. ‘bump’ in angle of attack increases performance considerably,

25%!5. Deviation slightly decreases drag but strongly influences force

variation!

Model CL CD CL/CD

`Sawtooth’ amplitude influence

-7.9% 21.8% -24.3%

`Trapezoidal’ influence -8.9% 36.6% -31.3%

Extra `bumb’ in 0.0% -13.4% 25.4%

Deviation -10.8% -2.8% -8.4%

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

Closer look at fruit-fly kinematics: ‘bump’ and deviation

Robofly

Fruit-fly

19/23

- ‘bump’ increases performance

Harmonic

Harmonic+ ‘bump’ AOA

1. ‘bump’ decreases early angle of attack

2. Wing orientation high lift, low drag

3. ‘bump’ responsible for higher performanceIntroduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

20/23

Deviation levels the forces

1. Deviation leads to changes in the effective angle of attack

2. Deviation is levelling forces3. Early low peak is increased4. Late high peak is decreased

Deviation causes more balanced force distributions

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

21/23

Conclusions

1. Altough first order in time, accurate results were obtained with the model

2. The mean lift is comparable for all kinematic models. The mean lift deviates less than the mean drag.

3. Extra `bumb’ in angle of attack reduces drag considerably, thus increases performance

4. Deviation in fruit-fly levels the forces stability and control or more comfortable flight

Evidence was found that a fruit-fly uses the ‘bump’ to increase performance and the deviation to manipulate stability and control

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

22/23

Recommendations

1. Use or develop higher order time discretisation methods2. Investigate 3D effects3. Varying broader parameter spectrum4. Use other performance parameters, like work, required

energy5. Not only hovering, but also forward flapping flight may be

interesting

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

23/23

Questions ?

24/23

Extra slides ?

25/23

Cells in vortices, Re=150

Extra slides

26/23

Drag robofly 80% higher than fruit-fly

1. Large in Roboflyleads to high drag and strong vortices

2. Orientation wing leads to higher drag

3. Possibly large influence of the large acceleration in amplitude and angle of attack (sawtooth and trapezoidal shapes)

Fruit-fly Robofly

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

27/23

‘sawtooth’ increases drag

Harmonic+ `sawtooth’ amp.

Harmonic

1. Sawtooth responsible for high dragat the beginning ! High accel.

2. Stronger vortices

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions

28/23

- ‘trapezoidal’ increases drag

Harmonic+ `trapezoidal’ angle of attack.

Harmonic

1. High drag: 48% increase Wake capture of its LEV at t=0.6T2. LEV longer attached due to constant

angle of attack in Trapezoidal model

Vortex shedding

Introduction – Problem – Numerical modelling – Validation – Kinematic Modelling – Results – Conclusions