Numerical simulation of a moving mesh problem

1
Numerical simulation of amoving mesh problem

• Application insect aerodynamics

Workshop Computational Life Sciences
Frank Bos
2
Overview Presentation

• Problem description
• Insect aerodynamics
• Objectives
• Material and methods
• Numerical modelling
• Validation and verification
• Kinematic modelling
• Results and discussions

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
3
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
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)

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
5
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
Objectives

• To develop an accurate numerical model for this
  challenging application.
• Unravel unsteady aerodynamics of flapping insect
  aerodynamics.

Procedure

• Numerical modelling using general tools to solve
  Navier-Stokes equations.
• Validation of the numerical model using static
  and moving cylinders.
• Investigate influence of different wing
  kinematics on performance in hovering fruit-fly
  flight.

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
7
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
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

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
9
Numerical modelling
Quarter of entire domain
Cells near the boundary
object

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

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
10
Time step restrictions
Rotation
Translation
N number of cells on the surface ??
relative angular displacement ?y relative
linear displacement R radius of
cylinder ?ref angular length of smallest
cell yref linear length of smallest cell
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
11
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

When relative cell displacement lt 10 then the
corresponding time step leads results within 5
of literature.
? Extend this method to moving wings !!!
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
12
Verification using moving wing
Close-up at the Leading Edge

• Numerical model
• Conformal mapping
• 2 thick ellipse

Time step dependence
Grid size dependence
fine
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
13
Definition of motion parameters

• 3D parameters
• Amplitude ?
• Angle of Attack ?
• Deviation ?

• 2D parameters
• Amplitude x Rg f / c
• Angle of Attack ?
• Deviation y Rg q / c

y
x
Rg radius of gyration c averaged chord
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
14
4 different kinematic models

• 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
• ? symmetrised
• All Fruit-fly characteristics
• preserved

Experiment
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
15
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
Derived using 3D robofly
Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
16
Performance influence strategy

• Compare complete Robofly with the fruit-fly
  models
• Compare Robofly characteristics with harmonic
  model
• Compare fruit-fly characteristics with harmonic
  model

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

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
17
Comparison robofly and fruit-fly model
Robofly and real Fruit-fly compared

• 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

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
18
Comparison different shapes
Influence of different kinematic shapes w.r.t.
harmonic model
Robofly
Fruit-fly

• Comparable mean lift coefficients
• Mean drag is strongly affected !
• Robofly decreases performance, -25 to -30
• bump in angle of attack increases performance
  considerably, 25!
• Deviation slightly decreases drag but strongly
  influences force variation!

• Closer look at fruit-fly kinematics bump and
  deviation

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
19
? - bump increases performance
Harmonic
Harmonic bump AOA

• bump decreases early angle of attack
• Wing orientation ? high lift, low drag
• bump responsible for higher performance

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
20
Deviation levels the forces

• Deviation leads to changes in the effective angle
  of attack
• Deviation is levelling forces
• Early low peak is increased
• Late high peak is decreased
• ? Deviation causes more balanced force
  distributions

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
21
Conclusions

• Altough first order in time, accurate results
  were obtained with the model
• The mean lift is comparable for all kinematic
  models. The mean lift deviates less than the mean
  drag.
• Extra bumb in angle of attack reduces drag
  considerably, thus increases performance
• 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
Recommendations

• Use or develop higher order time discretisation
  methods
• Investigate 3D effects
• Varying broader parameter spectrum
• Use other performance parameters, like work,
  required energy
• Not only hovering, but also forward flapping
  flight may be interesting

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
23
Questions ?
24
Extra slides ?
25
Cells in vortices, Re150
Extra slides
26
Drag robofly 80 higher than fruit-fly
Fruit-fly
Robofly

• Large a in Robofly leads to high drag and strong
  vortices
• Orientation wing leads to higher drag
• Possibly large influence of the large
  acceleration in amplitude and angle of attack
  (sawtooth and trapezoidal shapes)

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
27
sawtooth increases drag
Harmonic
Harmonic sawtooth amp.

• Sawtooth responsible for high drag
• at the beginning ! High accel.
• 2. Stronger vortices

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions
28
? - trapezoidal increases drag
Harmonic
Vortex shedding
Harmonic trapezoidal angle of attack.

• High drag 48 increase
• ? Wake capture of its LEV at t0.6T
• 2. LEV longer attached due to constant
• angle of attack in Trapezoidal model

Introduction Problem Numerical modelling
Validation Kinematic Modelling Results
Conclusions